Nonlinear Objects in Rotor Balancing: Causes, Symptoms, and Practical Approach<\/title>\n <meta name=\"title\" content=\"Nonlinear Objects in Rotor Balancing: Causes, Symptoms, and Practical Approach\" \/>\n \n <meta name=\"keywords\" content=\"rotor balancing, nonlinear object, linear object, influence coefficient, trial weight, resonance, vibration instability, Balanset-1A, vibration diagnostics, field balancing, bearing clearance, looseness, dry friction\" \/>\n <meta name=\"author\" content=\"Vibromera\" \/>\n <meta name=\"robots\" content=\"index, follow, max-image-preview:large, max-snippet:-1, max-video-preview:-1\" \/>\n <meta name=\"language\" content=\"English\" \/>\n\n \n \n \n \n \n\n \n \n \n \n\n \n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\" \/>\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin \/>\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Onest:wght@300;400;500;600;700;800&display=swap\" rel=\"stylesheet\" \/>\n\n <style>\n \/* ========================================\n VIBROMERA ARTICLE STYLES (ISOLATED)\n Prefix: vma-\n All styles scoped to .vma-wrapper\n ======================================== *\/\n .vma-wrapper{\n --vma-primary:#0052cc;\n --vma-primary-dark:#003d99;\n --vma-primary-50:#e6f0ff;\n --vma-gray-50:#f8fafc;\n --vma-gray-100:#f1f5f9;\n --vma-gray-200:#e2e8f0;\n --vma-gray-500:#64748b;\n --vma-gray-700:#334155;\n --vma-gray-800:#1e293b;\n --vma-gray-900:#0f172a;\n --vma-white:#ffffff;\n max-width:1600px;\n margin:0 auto;\n font-family:'Onest',system-ui,-apple-system,sans-serif;\n font-size:18px;\n line-height:1.75;\n color:var(--vma-gray-700);\n -webkit-font-smoothing:antialiased;\n -moz-osx-font-smoothing:grayscale;\n }\n .vma-hero{\n background:linear-gradient(135deg,var(--vma-primary) 0%,var(--vma-primary-dark) 100%);\n color:var(--vma-white);\n padding:56px 20px;\n text-align:center;\n position:relative;\n overflow:hidden;\n }\n .vma-hero::before{\n content:'';\n position:absolute;\n inset:0;\n opacity:.14;\n background-image:\n radial-gradient(circle at 18% 82%, rgba(255,255,255,.35) 0%, transparent 55%),\n radial-gradient(circle at 82% 18%, rgba(255,255,255,.28) 0%, transparent 45%);\n pointer-events:none;\n }\n .vma-hero > *{ position:relative; 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text-align:left; }\n .vma-kbd{\n font-weight:800;\n color:var(--vma-gray-900);\n }\n .vma-formula{\n background:linear-gradient(135deg,var(--vma-gray-50) 0%, var(--vma-primary-50) 100%);\n border:1px solid rgba(0,82,204,.18);\n border-radius:14px;\n padding:14px 16px;\n margin:14px 0;\n font-size:16px;\n color:var(--vma-gray-900);\n overflow:auto;\n white-space:nowrap;\n }\n .vma-qa{\n background:var(--vma-gray-50);\n border:1px solid var(--vma-gray-200);\n border-radius:16px;\n padding:18px 18px;\n margin:18px 0;\n }\n .vma-q{\n margin:0 0 8px 0;\n font-weight:800;\n color:var(--vma-gray-900);\n font-size:18px;\n }\n .vma-a{\n margin:0;\n }\n .vma-anchor{ scroll-margin-top: 16px; }\n @media (max-width: 820px){\n .vma-title{ font-size:30px; }\n }\n <\/style>\n\n \n \n\n \n<\/head>\n<body>\n <div class=\"vma-wrapper\">\n <header class=\"vma-hero\">\n <h1 class=\"vma-title\">Nonlinear Objects in Rotor Balancing<\/h1>\n <p class=\"vma-subtitle\">Why balancing \u201cdoes not work\u201d, why influence coefficients change, and how to proceed in real field conditions<\/p>\n <\/header>\n\n <main class=\"vma-content\">\n <div class=\"vma-inner\">\n <nav class=\"vma-toc\" aria-label=\"Table of contents\">\n <div class=\"vma-toc-title\">\u76ee\u9304<\/div>\n <ol>\n <li><a href=\"#intro\">\u6982\u8ff0<\/a><\/li>\n <li><a href=\"#linear-nonlinear-vibrations\">Linear & nonlinear vibrations<\/a><\/li>\n <li><a href=\"#linear-vs-nonlinear\">Linear vs nonlinear objects<\/a><\/li>\n <li><a href=\"#what-are-linear-objects\">What are linear objects?<\/a><\/li>\n <li><a href=\"#linearity-graph\">Graph of linearity<\/a><\/li>\n <li><a href=\"#influence-coefficient\">Influence coefficient (IC)<\/a><\/li>\n <li><a href=\"#linear-phase\">Vibration phase in linear objects<\/a><\/li>\n <li><a href=\"#linear-balancing-steps\">Steps for balancing a linear object<\/a><\/li>\n <li><a href=\"#serial\">Serial balancing and stored coefficients<\/a><\/li>\n <li><a href=\"#nonlinear-definition\">What is a nonlinear object?<\/a><\/li>\n <li><a href=\"#nonlinear-signs\">Signs of nonlinearity<\/a><\/li>\n <li><a href=\"#nonlinear-graph\">Graph of nonlinearity<\/a><\/li>\n <li><a href=\"#nonlinear-examples\">Examples of nonlinear objects<\/a><\/li>\n <li><a href=\"#nonlinear-types\">Types of nonlinearity<\/a><\/li>\n <li><a href=\"#causes\">Common causes of nonlinearity<\/a><\/li>\n <li><a href=\"#instability\">Vibration instability<\/a><\/li>\n <li><a href=\"#resonance\">Balancing near resonance<\/a><\/li>\n <li><a href=\"#high-after\">High vibration after \u201csuccessful\u201d balancing<\/a><\/li>\n <li><a href=\"#nonlinear-methods\">Balancing methods for nonlinear objects<\/a><\/li>\n <li><a href=\"#nonlinear-howto-linear-tool\">How to balance with a linear tool<\/a><\/li>\n <li><a href=\"#art-science\">The art & science of balancing<\/a><\/li>\n <li><a href=\"#measurement\">Measurement repeatability<\/a><\/li>\n <li><a href=\"#approach\">Practical approach for nonlinear objects<\/a><\/li>\n <li><a href=\"#reduced-correction\">Reduced correction weight technique<\/a><\/li>\n <li><a href=\"#conclusion\">Final principle<\/a><\/li>\n <li><a href=\"#faq\">Questions & answers<\/a><\/li>\n <\/ol>\n <\/nav>\n\n <section id=\"intro\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u6982\u8ff0<\/h2>\n <p>In practice, rotor balancing is almost never reduced to simply calculating and installing a correction weight. Formally, the algorithm is well known and the instrument performs all calculations automatically, but the final result depends far more on the behavior of the object itself than on the balancing device. This is why, in real work, situations constantly arise where balancing \u201cdoes not work\u201d, influence coefficients change, vibration becomes unstable, and the result is not repeatable from one run to another.<\/p>\n <\/section>\n\n <section id=\"linear-nonlinear-vibrations\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u7dda\u6027\u8207\u975e\u7dda\u6027\u632f\u52d5\u3001\u5176\u7279\u5fb5\u53ca\u52d5\u5e73\u8861\u6821\u6b63\u65b9\u6cd5<\/h2>\n <p>\u6210\u529f\u7684\u52d5\u5e73\u8861\u6821\u6b63\u9700\u8981\u7406\u89e3\u7269\u4ef6\u5c0d\u8cea\u91cf\u589e\u52a0\u6216\u79fb\u9664\u7684\u53cd\u61c9\u3002\u5728\u6b64\u80cc\u666f\u4e0b\uff0c\u7dda\u6027\u8207\u975e\u7dda\u6027\u7269\u4ef6\u7684\u6982\u5ff5\u626e\u6f14\u8457\u95dc\u9375\u89d2\u8272\u3002\u4e86\u89e3\u7269\u4ef6\u662f\u7dda\u6027\u9084\u662f\u975e\u7dda\u6027\uff0c\u6709\u52a9\u65bc\u9078\u64c7\u6b63\u78ba\u7684\u52d5\u5e73\u8861\u6821\u6b63\u7b56\u7565\uff0c\u4e26\u5e6b\u52a9\u9054\u5230\u9810\u671f\u7d50\u679c\u3002<\/p>\n <p>\u7dda\u6027\u7269\u4ef6\u56e0\u5176\u53ef\u9810\u6e2c\u6027\u548c\u7a69\u5b9a\u6027\u800c\u5728\u8a72\u9818\u57df\u4f54\u6709\u7279\u6b8a\u5730\u4f4d\u3002\u5b83\u5011\u5141\u8a31\u4f7f\u7528\u7c21\u55ae\u4e14\u53ef\u9760\u7684\u8a3a\u65b7\u548c\u52d5\u5e73\u8861\u6821\u6b63\u65b9\u6cd5\uff0c\u4f7f\u5176\u7814\u7a76\u6210\u70ba\u632f\u52d5\u8a3a\u65b7\u4e2d\u7684\u91cd\u8981\u4e00\u6b65\u3002<\/p>\n <\/section>\n\n <section id=\"linear-vs-nonlinear\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Linear vs nonlinear objects<\/h2>\n <p>Most of these problems are rooted in a fundamental but often underestimated distinction between linear and nonlinear objects. A linear object, from the balancing point of view, is a system in which, at a constant rotational speed, the vibration amplitude is proportional to the amount of unbalance, and the vibration phase follows the angular position of the unbalanced mass in a strictly predictable way. Under these conditions, the influence coefficient is a constant value. All standard dynamic balancing algorithms, including those implemented in the Balanset-1A, are designed precisely for such objects.<\/p>\n <p>For a linear object, the balancing process is predictable and stable. Installing a trial weight produces a proportional change in vibration amplitude and phase. Repeated starts give the same vibration vector, and the calculated correction weight remains valid. Such objects are well suited both for one-time balancing and for serial balancing using stored influence coefficients.<\/p>\n <p>A nonlinear object behaves in a fundamentally different way. The very basis of the balancing calculation is violated. Vibration amplitude is no longer proportional to unbalance, the phase becomes unstable, and the influence coefficient changes depending on the trial weight mass, operating mode, or even time. In practice, this appears as chaotic behavior of the vibration vector: after installing a trial weight, the vibration change may be too small, excessive, or simply non-repeatable.<\/p>\n <\/section>\n\n <section id=\"what-are-linear-objects\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u4ec0\u9ebc\u662f\u7dda\u6027\u7269\u4ef6\uff1f<\/h2>\n <p>\u7dda\u6027\u7269\u4ef6\u662f\u4e00\u7a2e\u632f\u52d5\u8207\u4e0d\u5e73\u8861\u91cf\u5927\u5c0f\u6210\u6b63\u6bd4\u7684\u7cfb\u7d71\u3002<\/p>\n <p>A linear object, in the context of balancing, is an idealized model characterized by a direct proportional relationship between the magnitude of the imbalance (unbalanced mass) and the vibration amplitude. This means that if the imbalance is doubled, the vibration amplitude will also double, provided the rotor's rotational speed remains constant. Conversely, reducing the imbalance will proportionally decrease the vibrations.<\/p>\n <p>\u8207\u975e\u7dda\u6027\u7cfb\u7d71\u4e0d\u540c\uff0c\u5f8c\u8005\u4e2d\u7269\u4ef6\u7684\u884c\u70ba\u53ef\u80fd\u6703\u56e0\u591a\u7a2e\u56e0\u7d20\u800c\u8b8a\u5316\uff0c\u7dda\u6027\u7269\u4ef6\u5247\u80fd\u4ee5\u6700\u5c0f\u7684\u52aa\u529b\u5be6\u73fe\u9ad8\u7cbe\u5ea6\u3002<\/p>\n <p>\u6b64\u5916\uff0c\u5b83\u5011\u9084\u4f5c\u70ba\u52d5\u5e73\u8861\u6821\u6b63\u4eba\u54e1\u57f9\u8a13\u548c\u5be6\u8e10\u7684\u57fa\u790e\u3002\u7406\u89e3\u7dda\u6027\u7269\u4ef6\u7684\u539f\u7406\u6709\u52a9\u65bc\u57f9\u990a\u6280\u80fd\uff0c\u9019\u4e9b\u6280\u80fd\u96a8\u5f8c\u53ef\u61c9\u7528\u65bc\u66f4\u8907\u96dc\u7684\u7cfb\u7d71\u3002<\/p>\n <\/section>\n\n <section id=\"linearity-graph\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u7dda\u6027\u7684\u5716\u5f62\u8868\u793a<\/h2>\n <p>Imagine a graph where the horizontal axis represents the magnitude of the unbalanced mass (imbalance), and the vertical axis represents the vibration amplitude. For a linear object, this graph will be a straight line passing through the origin (the point where both the imbalance magnitude and the vibration amplitude are zero). The slope of this line characterizes the object's sensitivity to imbalance: the steeper the slope, the greater the vibrations for the same imbalance.<\/p>\n\n <div class=\"vma-image\">\n <a href=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2024\/11\/output-1.png\" class=\"vma-img-link\">\n <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2024\/11\/output-1-1024x804.png\" alt=\"\u5716 1\uff1a\u632f\u52d5\u5e45\u5ea6\uff08\u00b5m\uff09\u8207\u4e0d\u5e73\u8861\u8cea\u91cf\uff08g\uff09\u4e4b\u9593\u7684\u95dc\u4fc2\" width=\"750\" height=\"589\" \/>\n <\/a>\n <p class=\"vma-caption\"><strong>\u5716 1\uff1a\u632f\u52d5\u5e45\u5ea6\uff08\u00b5m\uff09\u8207\u4e0d\u5e73\u8861\u8cea\u91cf\uff08g\uff09\u4e4b\u9593\u7684\u95dc\u4fc2<\/strong><\/p>\n <\/div>\n\n <p>\u5716 1 \u8aaa\u660e\u4e86\u7dda\u6027\u52d5\u5e73\u8861\u6821\u6b63\u7269\u4ef6\u7684\u632f\u52d5\u5e45\u5ea6\uff08\u00b5m\uff09\u8207\u8f49\u5b50\u4e0d\u5e73\u8861\u8cea\u91cf\uff08g\uff09\u4e4b\u9593\u7684\u95dc\u4fc2\u3002\u6bd4\u4f8b\u4fc2\u6578\u70ba 0.5 \u00b5m\/g\u3002\u53ea\u9700\u5c07 300 \u9664\u4ee5 600 \u5373\u53ef\u5f97\u5230 0.5 \u00b5m\/g\u3002\u5c0d\u65bc 800 g \u7684\u4e0d\u5e73\u8861\u8cea\u91cf\uff08UM=800 g\uff09\uff0c\u632f\u52d5\u5c07\u70ba 800 g * 0.5 \u00b5m\/g = 400 \u00b5m\u3002\u8acb\u6ce8\u610f\uff0c\u9019\u9069\u7528\u65bc\u8f49\u901f\u6046\u5b9a\u7684\u60c5\u6cc1\u3002\u5728\u4e0d\u540c\u7684\u8f49\u901f\u4e0b\uff0c\u4fc2\u6578\u5c07\u4e0d\u540c\u3002<\/p>\n <p>\u6b64\u6bd4\u4f8b\u4fc2\u6578\u7a31\u70ba\u5f71\u97ff\u4fc2\u6578\uff08\u654f\u611f\u5ea6\u4fc2\u6578\uff09\uff0c\u5176\u91cf\u7db1\u70ba \u00b5m\/g\uff0c\u6216\u5728\u6d89\u53ca\u4e0d\u5e73\u8861\u91cf\u7684\u60c5\u6cc1\u4e0b\u70ba \u00b5m\/(g*mm)\uff0c\u5176\u4e2d (g*mm) \u662f\u4e0d\u5e73\u8861\u91cf\u7684\u55ae\u4f4d\u3002\u77e5\u9053\u5f71\u97ff\u4fc2\u6578\uff08IC\uff09\u5f8c\uff0c\u4e5f\u53ef\u4ee5\u89e3\u6c7a\u9006\u554f\u984c\uff0c\u5373\u6839\u64da\u632f\u52d5\u5e45\u5ea6\u78ba\u5b9a\u4e0d\u5e73\u8861\u8cea\u91cf\uff08UM\uff09\u3002\u70ba\u6b64\uff0c\u5c07\u632f\u52d5\u5e45\u5ea6\u9664\u4ee5 IC\u3002<\/p>\n <p>\u4f8b\u5982\uff0c\u5982\u679c\u6e2c\u5f97\u7684\u632f\u52d5\u70ba 300 \u00b5m\uff0c\u4e14\u5df2\u77e5\u4fc2\u6578\u70ba IC=0.5 \u00b5m\/g\uff0c\u5c07 300 \u9664\u4ee5 0.5 \u5373\u53ef\u5f97\u5230 600 g\uff08UM=600 g\uff09\u3002<\/p>\n <\/section>\n\n <section id=\"influence-coefficient\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u5f71\u97ff\u4fc2\u6578\uff08IC\uff09\uff1a\u7dda\u6027\u7269\u4ef6\u7684\u95dc\u9375\u53c3\u6578<\/h2>\n <p>A critical characteristic of a linear object is the influence coefficient (IC). It is numerically equal to the tangent of the slope angle of the line on the graph of vibration versus imbalance and indicates how much the vibration amplitude (in microns, \u00b5m) changes when a unit of mass (in grams, g) is added in a specific correction plane at a specific rotor speed. In other words, IC is a measure of the object's sensitivity to imbalance. Its unit of measurement is \u00b5m\/g, or, when imbalance is expressed as the product of mass and radius, \u00b5m\/(g*mm).<\/p>\n <p>IC is essentially the \"passport\" characteristic of a linear object, enabling predictions of its behavior when mass is added or removed. Knowing the IC allows solving both the direct problem \u2013 determining vibration magnitude for a given imbalance \u2013 and the inverse problem \u2013 calculating imbalance magnitude from measured vibration.<\/p>\n\n <h3 class=\"vma-h3\">\u76f4\u63a5\u554f\u984c\uff1a<\/h3>\n <div class=\"vma-formula\">Vibration Amplitude (\u00b5m) = IC (\u00b5m\/g) * Unbalanced Mass (g)<\/div>\n\n <h3 class=\"vma-h3\">\u9006\u554f\u984c\uff1a<\/h3>\n <div class=\"vma-formula\">Unbalanced Mass (g) = Vibration Amplitude (\u00b5m) \/ IC (\u00b5m\/g)<\/div>\n <\/section>\n\n <section id=\"linear-phase\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u7dda\u6027\u7269\u4ef6\u4e2d\u7684\u632f\u52d5\u76f8\u4f4d<\/h2>\n <p>In addition to amplitude, vibration is also characterized by its phase, which indicates the rotor's position at the moment of maximum deviation from its equilibrium position. For a linear object, the vibration phase is also predictable. It is the sum of two angles:<\/p>\n <ol>\n <li>The angle that determines the position of the rotor's overall unbalanced mass. This angle indicates the direction in which the primary imbalance is concentrated.<\/li>\n <li>The argument of the influence coefficient. This is a constant angle that characterizes the object's dynamic properties and does not depend on the magnitude or angle of the unbalanced mass installation.<\/li>\n <\/ol>\n <p>\u56e0\u6b64\uff0c\u901a\u904e\u77e5\u9053 IC \u7684\u5e45\u89d2\u4e26\u6e2c\u91cf\u632f\u52d5\u76f8\u4f4d\uff0c\u53ef\u4ee5\u78ba\u5b9a\u4e0d\u5e73\u8861\u8cea\u91cf\u5b89\u88dd\u7684\u89d2\u5ea6\u3002\u9019\u4e0d\u50c5\u5141\u8a31\u8a08\u7b97\u6821\u6b63\u8cea\u91cf\u7684\u5927\u5c0f\uff0c\u9084\u5141\u8a31\u5176\u5728\u8f49\u5b50\u4e0a\u7cbe\u78ba\u653e\u7f6e\u4ee5\u9054\u5230\u6700\u4f73\u5e73\u8861\u3002<\/p>\n <\/section>\n\n <section id=\"linear-balancing-steps\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u7dda\u6027\u7269\u4ef6\u7684\u52d5\u5e73\u8861\u6821\u6b63<\/h2>\n <p>\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u5c0d\u65bc\u7dda\u6027\u7269\u4ef6\uff0c\u4ee5\u9019\u7a2e\u65b9\u5f0f\u78ba\u5b9a\u7684\u5f71\u97ff\u4fc2\u6578\uff08IC\uff09\u4e0d\u53d6\u6c7a\u65bc\u8a66\u91cd\u5b89\u88dd\u7684\u5927\u5c0f\u6216\u89d2\u5ea6\uff0c\u4e5f\u4e0d\u53d6\u6c7a\u65bc\u521d\u59cb\u632f\u52d5\u3002\u9019\u662f\u7dda\u6027\u7684\u4e00\u500b\u95dc\u9375\u7279\u5fb5\u3002\u5982\u679c\u7576\u8a66\u91cd\u53c3\u6578\u6216\u521d\u59cb\u632f\u52d5\u6539\u8b8a\u6642 IC \u4fdd\u6301\u4e0d\u8b8a\uff0c\u5247\u53ef\u4ee5\u81ea\u4fe1\u5730\u65b7\u8a00\u8a72\u7269\u4ef6\u5728\u6240\u8003\u616e\u7684\u4e0d\u5e73\u8861\u91cf\u7bc4\u570d\u5167\u8868\u73fe\u70ba\u7dda\u6027\u3002<\/p>\n\n <h3 class=\"vma-h3\">\u7dda\u6027\u7269\u4ef6\u52d5\u5e73\u8861\u6821\u6b63\u7684\u6b65\u9a5f<\/h3>\n <ol>\n <li><strong>\u6e2c\u91cf\u521d\u59cb\u632f\u52d5\uff1a<\/strong> \u7b2c\u4e00\u6b65\u662f\u6e2c\u91cf\u5176\u521d\u59cb\u72c0\u614b\u4e0b\u7684\u632f\u52d5\u3002\u78ba\u5b9a\u6307\u793a\u4e0d\u5e73\u8861\u65b9\u5411\u7684\u5e45\u5ea6\u548c\u632f\u52d5\u89d2\u5ea6\u3002<\/li>\n <li><strong>\u5b89\u88dd\u8a66\u91cd\uff1a<\/strong> \u5728\u8f49\u5b50\u4e0a\u5b89\u88dd\u5df2\u77e5\u91cd\u91cf\u7684\u8cea\u91cf\u3002\u9019\u6709\u52a9\u65bc\u4e86\u89e3\u7269\u4ef6\u5c0d\u984d\u5916\u8ca0\u8f09\u7684\u53cd\u61c9\uff0c\u4e26\u5141\u8a31\u8a08\u7b97\u632f\u52d5\u53c3\u6578\u3002<\/li>\n <li><strong>\u91cd\u65b0\u6e2c\u91cf\u632f\u52d5\uff1a<\/strong> \u5b89\u88dd\u8a66\u91cd\u5f8c\uff0c\u6e2c\u91cf\u65b0\u7684\u632f\u52d5\u53c3\u6578\u3002\u901a\u904e\u5c07\u5b83\u5011\u8207\u521d\u59cb\u503c\u9032\u884c\u6bd4\u8f03\uff0c\u53ef\u4ee5\u78ba\u5b9a\u8cea\u91cf\u5982\u4f55\u5f71\u97ff\u7cfb\u7d71\u3002<\/li>\n <li><strong>\u8a08\u7b97\u6821\u6b63\u8cea\u91cf\uff1a<\/strong> \u6839\u64da\u6e2c\u91cf\u8cc7\u6599\uff0c\u78ba\u5b9a\u6821\u6b63\u914d\u91cd\u7684\u8cea\u91cf\u548c\u5b89\u88dd\u89d2\u5ea6\u3002\u5c07\u6b64\u914d\u91cd\u653e\u7f6e\u5728\u8f49\u5b50\u4e0a\u4ee5\u6d88\u9664\u4e0d\u5e73\u8861\u3002<\/li>\n <li><strong>\u6700\u7d42\u9a57\u8b49\uff1a<\/strong> \u5b89\u88dd\u6821\u6b63\u914d\u91cd\u5f8c\uff0c\u632f\u52d5\u61c9\u986f\u8457\u964d\u4f4e\u3002\u5982\u679c\u6b98\u9918\u632f\u52d5\u4ecd\u8d85\u904e\u53ef\u63a5\u53d7\u6c34\u5e73\uff0c\u5247\u53ef\u4ee5\u91cd\u8907\u8a72\u7a0b\u5e8f\u3002<\/li>\n <\/ol>\n\n <div class=\"vma-note\">\n <p><span class=\"vma-kbd\">\u6ce8\u610f\uff1a<\/span> \u7dda\u6027\u7269\u4ef6\u662f\u7814\u7a76\u548c\u5be6\u969b\u61c9\u7528\u52d5\u5e73\u8861\u6821\u6b63\u65b9\u6cd5\u7684\u7406\u60f3\u6a21\u578b\u3002\u5b83\u5011\u7684\u7279\u6027\u5141\u8a31\u5de5\u7a0b\u5e2b\u548c\u8a3a\u65b7\u4eba\u54e1\u5c08\u6ce8\u65bc\u57f9\u990a\u57fa\u672c\u6280\u80fd\u4e26\u7406\u89e3\u8207\u8f49\u5b50\u7cfb\u7d71\u5de5\u4f5c\u7684\u57fa\u672c\u539f\u7406\u3002\u5118\u7ba1\u5b83\u5011\u5728\u5be6\u969b\u61c9\u7528\u4e2d\u7684\u61c9\u7528\u6709\u9650\uff0c\u4f46\u5c0d\u7dda\u6027\u7269\u4ef6\u7684\u7814\u7a76\u4ecd\u7136\u662f\u63a8\u9032\u632f\u52d5\u8a3a\u65b7\u548c\u52d5\u5e73\u8861\u6821\u6b63\u7684\u91cd\u8981\u4e00\u6b65\u3002<\/p>\n <\/div>\n\n <div class=\"vma-note\">\n <p><span class=\"vma-kbd\">Placeholder shortcode:<\/span> \t\t<section class=\"woocommerce hestia-shop products is-shortcode\" id=\"products\" data-sorder=\"hestia_shop\" >\n\t\t\t\t\t\t<div class=\"\">\n\t\t\t\t\t\t<div class=\"hestia-shop-content\">\n\t\t\t<div class=\"row\" 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https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-272x182.webp 272w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/devices\/\" rel=\"tag\">\u8a2d\u5099<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/balanset-1\/\" title=\"Portable balancer & Vibration analyzer Balanset-1A\">\u4fbf\u651c\u5f0f\u5e73\u8861\u5100 & \u632f\u52d5\u5206\u6790\u5100 Balanset-1A<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div 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data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1820\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/optical-sensor-for-balanset-and-arbalance\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"\u5149\u5b78\u611f\u6e2c\u5668\uff08\u96f7\u5c04\u6e2c\u901f\u5100\uff09\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"\u5149\u5b78\u611f\u6e2c\u5668\uff08\u96f7\u5c04\u6e2c\u901f\u5100\uff09\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-1536x1023.webp 1536w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU.webp 1600w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/parts\/\" rel=\"tag\">\u96f6\u4ef6<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"\u5149\u5b78\u611f\u6e2c\u5668\uff08\u96f7\u5c04\u6e2c\u901f\u5100\uff09\">\u5149\u5b78\u611f\u6e2c\u5668\uff08\u96f7\u5c04\u6e2c\u901f\u5100\uff09<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>124.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1832\" data-quantity=\"1\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1832\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1832\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" aria-label=\"Add to cart: \u201cOptical Sensor (Laser Tachometer)\u201d\" rel=\"nofollow\" data-success_message=\"\u201cOptical Sensor (Laser Tachometer)\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1832\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/balanset-4\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/balanset-4\/\" title=\"Balanset-4\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Vibromera rotor balancing kit: carry case, multi-channel signal conditioner, handheld analyzer, magnetic base, vibration sensors, and coiled cables.\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4.webp 640w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/devices\/\" rel=\"tag\">\u8a2d\u5099<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/balanset-4\/\" title=\"Balanset-4\">Balanset-4<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>6,803.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1833\" data-quantity=\"1\" data-product_id=\"1833\" data-product_sku=\"BS-4\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1833\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1833\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1833\" data-product_sku=\"BS-4\" aria-label=\"Add to cart: \u201cBalanset-4\u201d\" rel=\"nofollow\" data-success_message=\"\u201cBalanset-4\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1833\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div><div class=\"row\">\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/magnet-stand\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/magnet-stand\/\" title=\"Insize-60-kgf \u78c1\u6027\u652f\u67b6\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Magnet base.\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36.webp 1280w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/parts\/\" rel=\"tag\">\u96f6\u4ef6<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/magnet-stand\/\" title=\"Insize-60-kgf \u78c1\u6027\u652f\u67b6\">Insize-60-kgf \u78c1\u6027\u652f\u67b6<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>46.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1852\" data-quantity=\"1\" data-product_id=\"1852\" data-product_sku=\"MS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1852\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1852\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1852\" data-product_sku=\"MS-1\" aria-label=\"Add to cart: \u201cMagnetic Stand Insize-60-kgf\u201d\" rel=\"nofollow\" data-success_message=\"\u201cMagnetic Stand Insize-60-kgf\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1852\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/reflective-tape\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/reflective-tape\/\" title=\"\u53cd\u5149\u8cbc\u7d19\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"\u53cd\u5149\u8cbc\u7d19\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-16x12.webp 16w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-272x182.webp 272w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/parts\/\" rel=\"tag\">\u96f6\u4ef6<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/reflective-tape\/\" title=\"\u53cd\u5149\u8cbc\u7d19\">\u53cd\u5149\u8cbc\u7d19<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>10.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=2329\" data-quantity=\"1\" data-product_id=\"2329\" data-product_sku=\"rt-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=2329\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_2329\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"2329\" data-product_sku=\"rt-1\" aria-label=\"Add to cart: \u201cReflective tape\u201d\" rel=\"nofollow\" data-success_message=\"\u201cReflective tape\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_2329\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/dynamic-balancer-balanset-1a\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/dynamic-balancer-balanset-1a\/\" title=\"\u52d5\u614b\u5e73\u8861\u5100\u300cBalanset-1A\u300dOEM\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A kit contents with interface unit, sensors, tachometer and accessories\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-1024x683.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-1536x1024.webp 1536w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-2048x1366.webp 2048w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-e1732998877834.webp 708w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/devices\/\" rel=\"tag\">\u8a2d\u5099<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/dynamic-balancer-balanset-1a\/\" title=\"\u52d5\u614b\u5e73\u8861\u5100\u300cBalanset-1A\u300dOEM\">\u52d5\u614b\u5e73\u8861\u5100\u300cBalanset-1A\u300dOEM<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>1,735.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=4193\" data-quantity=\"1\" data-product_id=\"4193\" data-product_sku=\"BS-1OEM\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=4193\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_4193\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"4193\" data-product_sku=\"BS-1OEM\" aria-label=\"Add to cart: \u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d\" rel=\"nofollow\" data-success_message=\"\u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_4193\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/section>\n\t\t<\/p>\n <\/div>\n <\/section>\n\n <section id=\"serial\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Serial balancing and stored coefficients<\/h2>\n <p>Serial balancing deserves special attention. It can significantly increase productivity, but only when applied to linear, vibration-stable objects. In such cases, influence coefficients obtained on the first rotor can be reused for subsequent identical rotors. However, as soon as support stiffness, rotational speed, or bearing condition changes, repeatability is lost and the serial approach stops working.<\/p>\n <\/section>\n\n <section id=\"nonlinear-definition\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7269\u4ef6\uff1a\u7576\u7406\u8ad6\u8207\u5be6\u8e10\u80cc\u9053\u800c\u99b3\u6642<\/h2>\n <h3 class=\"vma-h3\">\u4ec0\u9ebc\u662f\u975e\u7dda\u6027\u7269\u4ef6\uff1f<\/h3>\n <p>\u975e\u7dda\u6027\u7269\u4ef6\u662f\u4e00\u7a2e\u632f\u52d5\u5e45\u5ea6\u8207\u4e0d\u5e73\u8861\u91cf\u5927\u5c0f\u4e0d\u6210\u6bd4\u4f8b\u7684\u7cfb\u7d71\u3002\u8207\u7dda\u6027\u7269\u4ef6\u4e0d\u540c\uff0c\u5f8c\u8005\u4e2d\u632f\u52d5\u8207\u4e0d\u5e73\u8861\u8cea\u91cf\u4e4b\u9593\u7684\u95dc\u4fc2\u7531\u76f4\u7dda\u8868\u793a\uff0c\u800c\u5728\u975e\u7dda\u6027\u7cfb\u7d71\u4e2d\uff0c\u9019\u7a2e\u95dc\u4fc2\u53ef\u80fd\u9075\u5faa\u8907\u96dc\u7684\u8ecc\u8de1\u3002<\/p>\n <p>\u5728\u73fe\u5be6\u4e16\u754c\u4e2d\uff0c\u4e26\u975e\u6240\u6709\u7269\u4ef6\u90fd\u8868\u73fe\u70ba\u7dda\u6027\u3002\u975e\u7dda\u6027\u7269\u4ef6\u8868\u73fe\u51fa\u975e\u76f4\u63a5\u6b63\u6bd4\u7684\u4e0d\u5e73\u8861\u8207\u632f\u52d5\u95dc\u4fc2\u3002\u9019\u610f\u5473\u8457\u5f71\u97ff\u4fc2\u6578\u4e0d\u662f\u6046\u5b9a\u7684\uff0c\u53ef\u80fd\u6703\u6839\u64da\u591a\u7a2e\u56e0\u7d20\u800c\u8b8a\u5316\uff0c\u4f8b\u5982\uff1a<\/p>\n <ul>\n <li><strong>\u4e0d\u5e73\u8861\u91cf\u5927\u5c0f\uff1a<\/strong> Increasing the imbalance can change the stiffness of the rotor's supports, leading to nonlinear changes in vibration.<\/li>\n <li><strong>\u8f49\u901f\uff1a<\/strong> \u5728\u4e0d\u540c\u7684\u8f49\u901f\u4e0b\u53ef\u80fd\u6703\u6fc0\u767c\u4e0d\u540c\u7684\u5171\u632f\u73fe\u8c61\uff0c\u5f9e\u800c\u5c0e\u81f4\u975e\u7dda\u6027\u884c\u70ba\u3002<\/li>\n <li><strong>\u6e38\u9699\u548c\u9593\u9699\u7684\u5b58\u5728\uff1a<\/strong> \u8ef8\u627f\u53ca\u5176\u4ed6\u9023\u63a5\u8655\u7684\u6e38\u9699\u8207\u9593\u9699\uff0c\u5728\u7279\u5b9a\u689d\u4ef6\u4e0b\u53ef\u80fd\u5c0e\u81f4\u632f\u52d5\u767c\u751f\u7a81\u8b8a\u3002<\/li>\n <li><strong>\u6eab\u5ea6\uff1a<\/strong> \u6eab\u5ea6\u8b8a\u5316\u6703\u5f71\u97ff\u6750\u6599\u7279\u6027\uff0c\u9032\u800c\u5f71\u97ff\u8a72\u7269\u4ef6\u7684\u632f\u52d5\u7279\u6027\u3002<\/li>\n <li><strong>\u5916\u90e8\u8ca0\u8377\uff1a<\/strong> \u4f5c\u7528\u65bc\u8f49\u5b50\u4e0a\u7684\u5916\u90e8\u8ca0\u8377\u53ef\u80fd\u6539\u8b8a\u5176\u52d5\u614b\u7279\u6027\uff0c\u4e26\u5c0e\u81f4\u975e\u7dda\u6027\u884c\u70ba\u3002<\/li>\n <\/ul>\n\n <h3 class=\"vma-h3\">\u70ba\u4f55\u975e\u7dda\u6027\u7269\u4ef6\u5177\u6311\u6230\u6027\uff1f<\/h3>\n <p>\u975e\u7dda\u6027\u6703\u70ba\u52d5\u5e73\u8861\u6821\u6b63\u904e\u7a0b\u5f15\u5165\u8a31\u591a\u8b8a\u6578\u3002\u6210\u529f\u8655\u7406\u975e\u7dda\u6027\u7269\u4ef6\u9700\u8981\u66f4\u591a\u7684\u6e2c\u91cf\u8207\u66f4\u8907\u96dc\u7684\u5206\u6790\u3002\u4f8b\u5982\uff0c\u9069\u7528\u65bc\u7dda\u6027\u7269\u4ef6\u7684\u6a19\u6e96\u65b9\u6cd5\uff0c\u5c0d\u975e\u7dda\u6027\u7cfb\u7d71\u4e26\u4e0d\u4e00\u5b9a\u80fd\u7522\u751f\u6e96\u78ba\u7684\u7d50\u679c\u3002\u9019\u9700\u8981\u66f4\u6df1\u5165\u5730\u4e86\u89e3\u904e\u7a0b\u7684\u7269\u7406\u539f\u7406\uff0c\u4e26\u4f7f\u7528\u5c08\u9580\u7684\u8a3a\u65b7\u65b9\u6cd5\u3002<\/p>\n <\/section>\n\n <section id=\"nonlinear-signs\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7684\u5fb5\u5146<\/h2>\n <p>\u975e\u7dda\u6027\u7269\u4ef6\u53ef\u900f\u904e\u4ee5\u4e0b\u5fb5\u5146\u4f86\u8b58\u5225\uff1a<\/p>\n <ul>\n <li><strong>\u975e\u6bd4\u4f8b\u632f\u52d5\u8b8a\u5316\uff1a<\/strong> \u96a8\u8457\u4e0d\u5e73\u8861\u91cf\u7684\u589e\u52a0\uff0c\u632f\u52d5\u53ef\u80fd\u6bd4\u7dda\u6027\u7269\u4ef6\u9810\u671f\u7684\u589e\u9577\u66f4\u5feb\u6216\u66f4\u6162\u3002<\/li>\n <li><strong>\u632f\u52d5\u76f8\u4f4d\u504f\u79fb\uff1a<\/strong> \u632f\u52d5\u76f8\u4f4d\u53ef\u80fd\u96a8\u8457\u4e0d\u5e73\u8861\u91cf\u6216\u8f49\u901f\u7684\u8b8a\u5316\u800c\u4e0d\u53ef\u9810\u6e2c\u5730\u6539\u8b8a\u3002<\/li>\n <li><strong>\u8ae7\u6ce2\u8207\u6b21\u8ae7\u6ce2\u7684\u5b58\u5728\uff1a<\/strong> \u632f\u52d5\u983b\u8b5c\u53ef\u80fd\u986f\u793a\u51fa\u9ad8\u6b21\u8ae7\u6ce2\uff08\u8f49\u983b\u7684\u500d\u6578\uff09\u8207\u6b21\u8ae7\u6ce2\uff08\u8f49\u983b\u7684\u5206\u6578\uff09\uff0c\u9019\u8868\u660e\u5b58\u5728\u975e\u7dda\u6027\u6548\u61c9\u3002<\/li>\n <li><strong>\u6eef\u5f8c\u73fe\u8c61\uff1a<\/strong> \u632f\u52d5\u5e45\u503c\u4e0d\u50c5\u53d6\u6c7a\u65bc\u7576\u524d\u7684\u4e0d\u5e73\u8861\u91cf\uff0c\u9084\u53ef\u80fd\u53d6\u6c7a\u65bc\u5176\u6b77\u53f2\u8b8a\u5316\u3002\u4f8b\u5982\uff0c\u7576\u4e0d\u5e73\u8861\u91cf\u589e\u52a0\u5f8c\u518d\u6e1b\u5c11\u56de\u521d\u59cb\u503c\u6642\uff0c\u632f\u52d5\u5e45\u503c\u53ef\u80fd\u4e0d\u6703\u56de\u5230\u539f\u59cb\u6c34\u5e73\u3002<\/li>\n <\/ul>\n <p>\u975e\u7dda\u6027\u6703\u70ba\u52d5\u5e73\u8861\u6821\u6b63\u904e\u7a0b\u5f15\u5165\u8a31\u591a\u8b8a\u6578\u3002\u6210\u529f\u64cd\u4f5c\u9700\u8981\u66f4\u591a\u7684\u6e2c\u91cf\u8207\u8907\u96dc\u7684\u5206\u6790\u3002\u4f8b\u5982\uff0c\u9069\u7528\u65bc\u7dda\u6027\u7269\u4ef6\u7684\u6a19\u6e96\u65b9\u6cd5\uff0c\u5c0d\u975e\u7dda\u6027\u7cfb\u7d71\u4e26\u4e0d\u4e00\u5b9a\u80fd\u7522\u751f\u6e96\u78ba\u7684\u7d50\u679c\u3002\u9019\u9700\u8981\u66f4\u6df1\u5165\u5730\u4e86\u89e3\u904e\u7a0b\u7269\u7406\u539f\u7406\uff0c\u4e26\u4f7f\u7528\u5c08\u9580\u7684\u8a3a\u65b7\u65b9\u6cd5\u3002<\/p>\n <\/section>\n\n <section id=\"nonlinear-graph\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7684\u5716\u5f62\u8868\u793a<\/h2>\n <p>\u5728\u632f\u52d5\u5c0d\u4e0d\u5e73\u8861\u91cf\u7684\u5716\u8868\u4e2d\uff0c\u975e\u7dda\u6027\u8868\u73fe\u70ba\u504f\u96e2\u76f4\u7dda\u3002\u5716\u8868\u53ef\u80fd\u5177\u6709\u5f4e\u6298\u3001\u66f2\u7387\u3001\u6eef\u5f8c\u8ff4\u5708\u53ca\u5176\u4ed6\u7279\u5fb5\uff0c\u8868\u660e\u4e0d\u5e73\u8861\u91cf\u8207\u632f\u52d5\u4e4b\u9593\u5b58\u5728\u8907\u96dc\u7684\u95dc\u4fc2\u3002<\/p>\n\n <div class=\"vma-image\">\n <a href=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2024\/11\/output-3.png\" class=\"vma-img-link\">\n <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2024\/11\/output-3-1024x816.png\" alt=\"\u5716 2. \u975e\u7dda\u6027\u7269\u4ef6\" width=\"750\" height=\"598\" \/>\n <\/a>\n <p class=\"vma-caption\"><strong>\u5716 2. \u975e\u7dda\u6027\u7269\u4ef6<\/strong><\/p>\n <p class=\"vma-caption\"><strong>50g; 40\u03bcm (yellow), 100g; 54.7\u03bcm (blue).<\/strong><\/p>\n <\/div>\n\n <p>\u6b64\u7269\u4ef6\u5448\u73fe\u5169\u500b\u7dda\u6bb5\uff0c\u5373\u5169\u689d\u76f4\u7dda\u3002\u5c0d\u65bc\u5c0f\u65bc 50 \u516c\u514b\u7684\u4e0d\u5e73\u8861\u91cf\uff0c\u5716\u8868\u53cd\u6620\u7dda\u6027\u7269\u4ef6\u7684\u7279\u6027\uff0c\u4fdd\u6301\u516c\u514b\u70ba\u55ae\u4f4d\u7684\u4e0d\u5e73\u8861\u91cf\u8207\u5fae\u7c73\u70ba\u55ae\u4f4d\u7684\u632f\u52d5\u5e45\u503c\u4e4b\u9593\u7684\u6bd4\u4f8b\u95dc\u4fc2\u3002\u5c0d\u65bc\u5927\u65bc 50 \u516c\u514b\u7684\u4e0d\u5e73\u8861\u91cf\uff0c\u632f\u52d5\u5e45\u503c\u7684\u589e\u9577\u6703\u6e1b\u7de9\u3002<\/p>\n <\/section>\n\n <section id=\"nonlinear-examples\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7269\u4ef6\u7684\u7bc4\u4f8b<\/h2>\n <p>\u5728\u52d5\u5e73\u8861\u6821\u6b63\u80cc\u666f\u4e0b\uff0c\u975e\u7dda\u6027\u7269\u4ef6\u7684\u7bc4\u4f8b\u5305\u62ec\uff1a<\/p>\n <ul>\n <li><strong>\u5e36\u6709\u88c2\u7d0b\u7684\u8f49\u5b50\uff1a<\/strong> \u8f49\u5b50\u4e0a\u7684\u88c2\u7d0b\u53ef\u80fd\u5c0e\u81f4\u525b\u6027\u767c\u751f\u975e\u7dda\u6027\u8b8a\u5316\uff0c\u9032\u800c\u5c0e\u81f4\u632f\u52d5\u8207\u4e0d\u5e73\u8861\u91cf\u4e4b\u9593\u5448\u73fe\u975e\u7dda\u6027\u95dc\u4fc2\u3002<\/li>\n <li><strong>\u5e36\u6709\u8ef8\u627f\u6e38\u9699\u7684\u8f49\u5b50\uff1a<\/strong> \u8ef8\u627f\u6e38\u9699\u5728\u7279\u5b9a\u689d\u4ef6\u4e0b\u53ef\u80fd\u5c0e\u81f4\u632f\u52d5\u767c\u751f\u7a81\u8b8a\u3002<\/li>\n <li><strong>\u5e36\u6709\u975e\u7dda\u6027\u5f48\u6027\u5143\u4ef6\u7684\u8f49\u5b50\uff1a<\/strong> Some elastic elements, such as rubber dampers, may exhibit nonlinear characteristics, affecting the rotor's dynamics.<\/li>\n <\/ul>\n <\/section>\n\n <section id=\"nonlinear-types\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7684\u985e\u578b<\/h2>\n <h3 class=\"vma-h3\">1. \u8edf\u786c\u975e\u7dda\u6027<\/h3>\n <p>\u5728\u6b64\u985e\u7cfb\u7d71\u4e2d\uff0c\u53ef\u89c0\u5bdf\u5230\u5169\u500b\u7dda\u6bb5\uff1a\u8edf\u6bb5\u8207\u786c\u6bb5\u3002\u5728\u8edf\u6bb5\u4e2d\uff0c\u884c\u70ba\u985e\u4f3c\u7dda\u6027\uff0c\u5373\u632f\u52d5\u5e45\u503c\u8207\u4e0d\u5e73\u8861\u8cea\u91cf\u6210\u6bd4\u4f8b\u589e\u52a0\u3002\u7136\u800c\uff0c\u5728\u9054\u5230\u67d0\u500b\u95be\u503c\uff08\u65b7\u9ede\uff09\u5f8c\uff0c\u7cfb\u7d71\u6703\u8f49\u63db\u70ba\u786c\u6bb5\u6a21\u5f0f\uff0c\u6b64\u6642\u5e45\u503c\u589e\u9577\u6703\u6e1b\u7de9\u3002<\/p>\n <h3 class=\"vma-h3\">2. \u5f48\u6027\u975e\u7dda\u6027<\/h3>\n <p>\u7cfb\u7d71\u5167\u652f\u6490\u6216\u63a5\u89f8\u9ede\u7684\u525b\u6027\u8b8a\u5316\uff0c\u4f7f\u632f\u52d5\u8207\u4e0d\u5e73\u8861\u91cf\u7684\u95dc\u4fc2\u8b8a\u5f97\u8907\u96dc\u3002\u4f8b\u5982\uff0c\u7576\u8de8\u8d8a\u7279\u5b9a\u8ca0\u8377\u95be\u503c\u6642\uff0c\u632f\u52d5\u53ef\u80fd\u6703\u7a81\u7136\u589e\u52a0\u6216\u6e1b\u5c11\u3002<\/p>\n <h3 class=\"vma-h3\">3. \u6469\u64e6\u8a98\u767c\u975e\u7dda\u6027<\/h3>\n <p>\u5728\u5177\u6709\u986f\u8457\u6469\u64e6\u7684\u7cfb\u7d71\u4e2d\uff08\u4f8b\u5982\u8ef8\u627f\u5167\uff09\uff0c\u632f\u52d5\u5e45\u503c\u53ef\u80fd\u96e3\u4ee5\u9810\u6e2c\u3002\u6469\u64e6\u53ef\u80fd\u5728\u67d0\u4e00\u8f49\u901f\u7bc4\u570d\u5167\u964d\u4f4e\u632f\u52d5\uff0c\u800c\u5728\u53e6\u4e00\u7bc4\u570d\u5167\u653e\u5927\u632f\u52d5\u3002<\/p>\n <\/section>\n\n <section id=\"causes\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Common causes of nonlinearity<\/h2>\n <p>The most common causes of nonlinearity are increased bearing clearances, bearing wear, dry friction, loosened supports, cracks in the structure, and operation near resonance frequencies. Often, the object exhibits so-called soft\u2013hard nonlinearity. At small unbalance levels the system behaves almost linearly, but as vibration increases, stiffer elements of the supports or casing become involved. In such cases, balancing is possible only within a narrow operating range and does not provide stable long-term results.<\/p>\n <\/section>\n\n <section id=\"instability\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Vibration instability<\/h2>\n <p>Another serious issue is vibration instability. Even a formally linear object may show changes in amplitude and phase over time. This is caused by thermal effects, changes in lubricant viscosity, thermal expansion, and unstable friction in the supports. As a result, measurements taken only minutes apart can produce different vibration vectors. Under these conditions, meaningful comparison of measurements becomes impossible, and the balancing calculation loses reliability.<\/p>\n <\/section>\n\n <section id=\"resonance\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Balancing near resonance<\/h2>\n <p>Balancing near resonance is especially problematic. When the rotational frequency coincides with, or is close to, a natural frequency of the system, even a small unbalance causes a sharp increase in vibration. The vibration phase becomes extremely sensitive to small speed variations. The object effectively enters a nonlinear regime, and balancing in this zone loses physical meaning. In such cases, the operating speed or the mechanical structure must be changed before balancing can be considered.<\/p>\n <\/section>\n\n <section id=\"high-after\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">High vibration after \u201csuccessful\u201d balancing<\/h2>\n <p>In practice, it is common to encounter situations where, after a formally successful balancing procedure, the overall vibration level remains high. This does not indicate an error of the instrument or the operator. Balancing eliminates mass unbalance only. If vibration is caused by foundation defects, loosened fasteners, misalignment, or resonance, correction weights will not solve the problem. In these cases, analyzing the spatial distribution of vibration across the machine and its foundation helps to identify the true cause.<\/p>\n <\/section>\n\n <section id=\"nonlinear-methods\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7269\u4ef6\u7684\u52d5\u5e73\u8861\u6821\u6b63\uff1a\u4e00\u9805\u9700\u8981\u975e\u50b3\u7d71\u89e3\u6c7a\u65b9\u6848\u4e4b\u8907\u96dc\u4efb\u52d9<\/h2>\n <p>\u975e\u7dda\u6027\u7269\u4ef6\u7684\u52d5\u5e73\u8861\u6821\u6b63\u662f\u4e00\u9805\u5177\u6311\u6230\u6027\u7684\u4efb\u52d9\uff0c\u9700\u8981\u5c08\u9580\u7684\u65b9\u6cd5\u8207\u9014\u5f91\u3002\u70ba\u7dda\u6027\u7269\u4ef6\u958b\u767c\u7684\u6a19\u6e96\u8a66\u91cd\u6cd5\uff0c\u53ef\u80fd\u7522\u751f\u932f\u8aa4\u7684\u7d50\u679c\u6216\u5b8c\u5168\u7121\u6cd5\u9069\u7528\u3002<\/p>\n\n <h3 class=\"vma-h3\">\u975e\u7dda\u6027\u7269\u4ef6\u7684\u52d5\u5e73\u8861\u6821\u6b63\u65b9\u6cd5<\/h3>\n <ul>\n <li><strong>\u9010\u6b65\u52d5\u5e73\u8861\u6821\u6b63\uff1a<\/strong> This method involves gradually reducing imbalance by installing corrective weights at each stage. After each stage, vibration measurements are taken, and a new corrective weight is determined based on the object's current state. This approach accounts for changes in the influence coefficient during the balancing process.<\/li>\n <li><strong>\u591a\u8f49\u901f\u52d5\u5e73\u8861\u6821\u6b63\uff1a<\/strong> \u6b64\u65b9\u6cd5\u89e3\u6c7a\u4e86\u4e0d\u540c\u8f49\u901f\u4e0b\u5171\u632f\u73fe\u8c61\u7684\u5f71\u97ff\u3002\u5728\u63a5\u8fd1\u5171\u632f\u7684\u6578\u500b\u8f49\u901f\u4e0b\u9032\u884c\u52d5\u5e73\u8861\u6821\u6b63\uff0c\u4f7f\u6574\u500b\u904b\u8f49\u8f49\u901f\u7bc4\u570d\u5167\u7684\u632f\u52d5\u964d\u4f4e\u66f4\u70ba\u5747\u52fb\u3002<\/li>\n <li><strong>\u4f7f\u7528\u6578\u5b78\u6a21\u578b\uff1a<\/strong> \u5c0d\u65bc\u8907\u96dc\u7684\u975e\u7dda\u6027\u7269\u4ef6\uff0c\u53ef\u63a1\u7528\u63cf\u8ff0\u8f49\u5b50\u52d5\u614b\u4e26\u8003\u616e\u975e\u7dda\u6027\u6548\u61c9\u7684\u6578\u5b78\u6a21\u578b\u3002\u9019\u4e9b\u6a21\u578b\u6709\u52a9\u65bc\u9810\u6e2c\u7269\u4ef6\u5728\u5404\u7a2e\u689d\u4ef6\u4e0b\u7684\u884c\u70ba\uff0c\u4e26\u78ba\u5b9a\u6700\u4f73\u7684\u52d5\u5e73\u8861\u6821\u6b63\u53c3\u6578\u3002<\/li>\n <\/ul>\n\n <p>The experience and intuition of a specialist play a crucial role in balancing nonlinear objects. An experienced balancer can recognize signs of nonlinearity, select an appropriate method, and adapt it to the specific situation. Analyzing vibration spectra, observing vibration changes as the object's operating parameters vary, and considering the rotor's design features all assist in making the right decisions and achieving the desired results.<\/p>\n <\/section>\n\n <section id=\"nonlinear-howto-linear-tool\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u5982\u4f55\u4f7f\u7528\u70ba\u7dda\u6027\u7269\u4ef6\u8a2d\u8a08\u7684\u5de5\u5177\u4f86\u6821\u6b63\u975e\u7dda\u6027\u7269\u4ef6<\/h2>\n <p>\u9019\u662f\u500b\u597d\u554f\u984c\u3002\u6211\u500b\u4eba\u6821\u6b63\u6b64\u985e\u7269\u4ef6\u7684\u65b9\u6cd5\u59cb\u65bc\u4fee\u5fa9\u6a5f\u4ef6\uff1a\u66f4\u63db\u8ef8\u627f\u3001\u710a\u63a5\u88c2\u7d0b\u3001\u9396\u7dca\u87ba\u6813\u3001\u6aa2\u67e5\u9328\u56fa\u6216\u6e1b\u9707\u5668\uff0c\u4e26\u78ba\u8a8d\u8f49\u5b50\u672a\u8207\u975c\u6b62\u7d50\u69cb\u5143\u4ef6\u767c\u751f\u6469\u64e6\u3002<\/p>\n <p>\u63a5\u8457\uff0c\u6211\u6703\u8b58\u5225\u5171\u632f\u983b\u7387\uff0c\u56e0\u70ba\u5728\u63a5\u8fd1\u5171\u632f\u7684\u8f49\u901f\u4e0b\u7121\u6cd5\u5c0d\u8f49\u5b50\u9032\u884c\u52d5\u5e73\u8861\u6821\u6b63\u3002\u70ba\u6b64\uff0c\u6211\u4f7f\u7528\u885d\u64ca\u6cd5\u4f86\u78ba\u5b9a\u5171\u632f\u983b\u7387\uff0c\u6216\u4f7f\u7528\u8f49\u5b50\u60f0\u8f49\u964d\u901f\u5716\u3002<\/p>\n <p>Then, I determine the sensor's position on the mechanism: vertical, horizontal, or at an angle.<\/p>\n <p>\u8a66\u904b\u8f49\u5f8c\uff0c\u8a2d\u5099\u6703\u6307\u793a\u6821\u6b63\u8ca0\u8f09\u7684\u89d2\u5ea6\u8207\u91cd\u91cf\u3002\u6211\u6703\u5c07\u6821\u6b63\u8ca0\u8f09\u7684\u91cd\u91cf\u6e1b\u534a\uff0c\u4f46\u4f7f\u7528\u8a2d\u5099\u5efa\u8b70\u7684\u89d2\u5ea6\u4f86\u5b89\u88dd\u8f49\u5b50\u3002\u5982\u679c\u6821\u6b63\u5f8c\u7684\u6b98\u9918\u632f\u52d5\u4ecd\u8d85\u904e\u53ef\u63a5\u53d7\u7bc4\u570d\uff0c\u6211\u6703\u518d\u6b21\u904b\u8f49\u8f49\u5b50\u3002\u7576\u7136\uff0c\u9019\u9700\u8981\u66f4\u591a\u6642\u9593\uff0c\u4f46\u6709\u6642\u7d50\u679c\u4ee4\u4eba\u9f13\u821e\u3002<\/p>\n <\/section>\n\n <section id=\"art-science\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u65cb\u8f49\u8a2d\u5099\u52d5\u5e73\u8861\u6821\u6b63\u7684\u85dd\u8853\u8207\u79d1\u5b78<\/h2>\n <p>\u65cb\u8f49\u8a2d\u5099\u7684\u52d5\u5e73\u8861\u6821\u6b63\u662f\u4e00\u500b\u8907\u96dc\u7684\u904e\u7a0b\uff0c\u7d50\u5408\u4e86\u79d1\u5b78\u8207\u85dd\u8853\u7684\u5143\u7d20\u3002\u5c0d\u65bc\u7dda\u6027\u7269\u4ef6\uff0c\u52d5\u5e73\u8861\u6821\u6b63\u6d89\u53ca\u76f8\u5c0d\u7c21\u55ae\u7684\u8a08\u7b97\u8207\u6a19\u6e96\u65b9\u6cd5\u3002\u7136\u800c\uff0c\u8655\u7406\u975e\u7dda\u6027\u7269\u4ef6\u9700\u8981\u6df1\u5165\u7406\u89e3\u8f49\u5b50\u52d5\u529b\u5b78\u3001\u5206\u6790\u632f\u52d5\u4fe1\u865f\u7684\u80fd\u529b\uff0c\u4ee5\u53ca\u9078\u64c7\u6700\u6709\u6548\u52d5\u5e73\u8861\u6821\u6b63\u7b56\u7565\u7684\u6280\u5de7\u3002<\/p>\n <p>\u7d93\u9a57\u3001\u76f4\u89ba\u8207\u6301\u7e8c\u7684\u6280\u80fd\u63d0\u5347\uff0c\u662f\u8b93\u52d5\u5e73\u8861\u6821\u6b63\u4eba\u54e1\u6210\u70ba\u771f\u6b63\u5927\u5e2b\u7684\u95dc\u9375\u3002\u7562\u7adf\uff0c\u52d5\u5e73\u8861\u6821\u6b63\u7684\u54c1\u8cea\u4e0d\u50c5\u6c7a\u5b9a\u4e86\u8a2d\u5099\u904b\u8f49\u7684\u6548\u7387\u8207\u53ef\u9760\u6027\uff0c\u4e5f\u78ba\u4fdd\u4e86\u4eba\u54e1\u7684\u5b89\u5168\u3002<\/p>\n <p> <\/p>\n <\/section>\n\n <section id=\"measurement\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Measurement repeatability<\/h2>\n <p>Measurement issues also play a major role. Incorrect installation of vibration sensors, changes in measurement points, or improper sensor orientation directly affect both amplitude and phase. For balancing, it is not enough to measure vibration; repeatability and stability of measurements are critical. This is why, in practical work, sensor mounting locations and orientations must be strictly controlled.<\/p>\n <\/section>\n\n <section id=\"approach\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Practical approach for nonlinear objects<\/h2>\n <p>Balancing a nonlinear object always begins not with installing a trial weight, but with evaluating vibration behavior. If amplitude and phase clearly drift over time, change from one start to another, or react sharply to small speed variations, the first task is to achieve the most stable operating mode possible. Without this, any calculations will be random.<\/p>\n <p>The first practical step is choosing the correct speed. Nonlinear objects are extremely sensitive to resonance, so balancing must be performed at a speed as far as possible from natural frequencies. This often means moving below or above the usual operating range. Even if vibration at this speed is higher, but stable, it is preferable to balancing in a resonant zone.<\/p>\n <p>Next, it is important to minimize all sources of additional nonlinearity. Before balancing, all fasteners should be checked and tightened, clearances eliminated as much as possible, and supports and bearing units inspected for looseness. Balancing does not compensate for clearances or friction, but it may be possible if these factors are brought to a stable condition.<\/p>\n <p>When working with a nonlinear object, small trial weights should not be used out of habit. Too small a trial weight often fails to move the system into a repeatable region, and the vibration change becomes comparable to instability noise. The trial weight must be large enough to cause a clear and reproducible change in the vibration vector, but not so large that it drives the object into a different operating regime.<\/p>\n <p>Measurements should be performed quickly and under identical conditions. The less time passes between measurements, the higher the chance that the dynamic parameters of the system remain unchanged. It is advisable to perform several control runs without changing the configuration to confirm that the object behaves consistently.<\/p>\n <p>It is very important to fix vibration sensor mounting points and their orientation. For nonlinear objects, even a small sensor displacement can cause noticeable changes in phase and amplitude, which may be mistakenly interpreted as the effect of the trial weight.<\/p>\n <p>In calculations, attention should be paid not to exact numerical agreement, but to trends. If vibration consistently decreases with successive corrections, this indicates that balancing is moving in the right direction, even if influence coefficients do not formally converge.<\/p>\n <p>It is not recommended to store and reuse influence coefficients for nonlinear objects. Even if one balancing cycle is successful, during the next start the object may enter a different regime and the previous coefficients will no longer be valid.<\/p>\n <p>It should be remembered that balancing a nonlinear object is often a compromise. The goal is not to achieve the lowest possible vibration, but to bring the machine into a stable and repeatable condition with an acceptable vibration level. In many cases, this is a temporary solution until bearings are repaired, supports are restored, or the structure is modified.<\/p>\n <p>The main practical principle is to stabilize the object first, then balance it, and only after that evaluate the result. If stabilization cannot be achieved, balancing should be considered an auxiliary measure rather than a final solution.<\/p>\n <\/section>\n\n <section id=\"reduced-correction\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Reduced correction weight technique<\/h2>\n <p>In practice, when balancing nonlinear objects, another important technique often proves effective. If the instrument calculates a correction weight using a standard algorithm, installing the full calculated weight frequently makes the situation worse: vibration may increase, the phase may jump, and the object may shift into a different operating mode.<\/p>\n <p>In such cases, installing a reduced correction weight works well \u2014 two or sometimes even three times smaller than the value calculated by the instrument. This helps avoid \u201cthrowing\u201d the system out of the conditionally linear region into another nonlinear regime. In effect, the correction is applied gently, with a small step, without causing a sharp change in the dynamic parameters of the object.<\/p>\n <p>After installing the reduced weight, a control run must be performed and the vibration trend evaluated. If the amplitude steadily decreases and the phase remains relatively stable, the correction can be repeated using the same approach, gradually approaching the minimum achievable vibration level. This step-by-step method is often more reliable than installing the full calculated correction weight at once.<\/p>\n <p>This technique is especially effective for objects with clearances, dry friction, and soft\u2013hard supports, where full calculated correction immediately drives the system out of the conditionally linear zone. Using reduced correction masses allows the object to remain in the most stable operating regime and makes it possible to achieve a practical result even where balancing is formally considered impossible.<\/p>\n <p>It is important to understand that this is not an \u201cinstrument error\u201d, but a consequence of the physics of nonlinear systems. The instrument correctly calculates for a linear model, while the engineer adapts the result in practice to the real behavior of the mechanical system.<\/p>\n <\/section>\n\n <section id=\"conclusion\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Final principle<\/h2>\n <p>Ultimately, successful balancing is not merely about calculating a weight and an angle. It requires understanding the dynamic behavior of the object, its linearity, vibration stability, and distance from resonance conditions. The Balanset-1A provides all necessary tools for measurement, analysis, and calculation, but the final result is always determined by the mechanical condition of the system itself. This is what distinguishes a formal approach from real engineering practice in vibration diagnostics and rotor balancing.<\/p>\n <\/section>\n\n <section id=\"faq\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Questions & answers<\/h2>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why do vibration amplitude and phase change unpredictably after installing a trial weight, and why does the correction weight calculation give a poor result?<\/div>\n <p class=\"vma-a\">This is a sign of a nonlinear object. In a linear object, vibration amplitude is proportional to the amount of unbalance, and the phase changes by the same angle as the angular position of the weight. When these conditions are violated, the influence coefficient is no longer constant and the standard balancing algorithm starts to produce errors. Typical causes are bearing clearances, loosened supports, friction, and operation near resonance.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is a linear object from the balancing point of view?<\/div>\n <p class=\"vma-a\">A linear object is a rotor system in which, at the same rotational speed, vibration amplitude is directly proportional to the magnitude of unbalance, and the vibration phase strictly follows the angular position of the unbalanced mass. For such objects, the influence coefficient is constant and does not depend on the mass of the trial weight.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is considered a nonlinear object in balancing?<\/div>\n <p class=\"vma-a\">A nonlinear object is a system in which the proportionality between vibration and unbalance and\/or the constancy of the phase relationship is violated. Vibration amplitude and phase begin to depend on the mass of the trial weight. Most often this is associated with bearing clearances, wear, dry friction, soft\u2013hard supports, or the engagement of stiffer structural elements.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Is it possible to balance a nonlinear object using an instrument designed for linear systems?<\/div>\n <p class=\"vma-a\">Yes, but the result is unstable and depends on the operating mode. Balancing is possible only within a limited range where the object behaves conditionally linearly. Outside this range, influence coefficients change and result repeatability is lost.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is the influence coefficient in simple terms?<\/div>\n <p class=\"vma-a\">The influence coefficient is a measure of vibration sensitivity to changes in unbalance. It shows how much the vibration vector will change when a known trial weight is installed in a given plane at a given speed.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does the influence coefficient change from one measurement to another?<\/div>\n <p class=\"vma-a\">The influence coefficient is unstable if the object is nonlinear, if vibration is unstable over time, or if resonance, thermal warm-up, loosened fasteners, or changing friction conditions are present. In such cases, repeated starts produce different amplitude and phase values.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">When can stored influence coefficients be used?<\/div>\n <p class=\"vma-a\">Stored influence coefficients may be used only for identical rotors operating at the same speed, under the same installation conditions and support stiffness. The object must be linear and vibration-stable. Even a slight change in conditions makes the old coefficients unreliable.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does vibration change during warm-up even without a change in unbalance?<\/div>\n <p class=\"vma-a\">During warm-up, bearing clearances, support stiffness, lubricant viscosity, and friction level change. This alters the dynamic parameters of the system and, as a result, changes vibration amplitude and phase.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is vibration instability and why does it interfere with balancing?<\/div>\n <p class=\"vma-a\">Vibration instability is a change in amplitude and\/or phase over time at a constant rotational speed. Balancing relies on comparing vibration vectors, so when vibration is unstable, the comparison loses meaning and the calculation becomes unreliable.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What types of vibration instability exist?<\/div>\n <p class=\"vma-a\">There are inherent structural instability, slow \u201ccreeping\u201d instability, variation from start to start, warm-up-related instability, and resonance-related instability when operating near natural frequencies.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why is it impossible to balance a rotor in the resonance zone?<\/div>\n <p class=\"vma-a\">In the resonance zone, even a small unbalance causes a sharp increase in vibration, and the phase becomes extremely sensitive to small changes. Under these conditions, the object becomes nonlinear and the balancing results lose physical meaning.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">How can one tell that the balancing speed is close to a resonant speed?<\/div>\n <p class=\"vma-a\">Typical signs are a sharp increase in vibration with small speed changes, unstable phase, broad humps in the spectrum, and high sensitivity of vibration to minor RPM variations. A vibration maximum is often observed during run-up or coast-down.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does high vibration not always mean large unbalance?<\/div>\n <p class=\"vma-a\">High vibration can be caused by resonance, loosened structures, foundation defects, or bearing problems. In such cases, balancing will not eliminate the cause of vibration.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is the difference between vibration displacement, vibration velocity, and vibration acceleration?<\/div>\n <p class=\"vma-a\">Vibration displacement characterizes the motion amplitude, vibration velocity characterizes the speed of this motion, and vibration acceleration characterizes the acceleration. These quantities are related, but each is better suited to detecting certain types of defects and frequency ranges.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why are vibration limits usually specified in terms of vibration velocity?<\/div>\n <p class=\"vma-a\">Vibration velocity reflects the energy level of vibration over a wide frequency range and is convenient for assessing the overall condition of machines according to ISO standards.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Is it possible to directly convert vibration displacement to vibration velocity and vice versa?<\/div>\n <p class=\"vma-a\">Correct conversion is possible only for single-frequency harmonic vibration. For complex vibration spectra, such conversions provide only approximate results.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does vibration remain high after balancing?<\/div>\n <p class=\"vma-a\">Possible reasons include resonance, foundation defects, loosened fasteners, bearing wear, misalignment, or object nonlinearity. Balancing removes unbalance only, not other defects.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">How can one tell that the problem is not in the rotor but in the foundation?<\/div>\n <p class=\"vma-a\">If mechanical defects are not detected and vibration does not decrease after balancing, it is necessary to analyze the vibration distribution over the machine and the foundation. Typical signs are high vibration of the casing and base, and phase shifts between measurement points.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why is correct installation of vibration sensors important?<\/div>\n <p class=\"vma-a\">Incorrect sensor installation distorts amplitude and phase, reduces measurement repeatability, and can lead to incorrect diagnostic conclusions and erroneous balancing results.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why do different measurement points show different vibration levels?<\/div>\n <p class=\"vma-a\">Vibration is distributed unevenly throughout the structure. Stiffness, masses, and mode shapes differ, so amplitude and phase can vary significantly from point to point.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Is it possible to balance a rotor with worn bearings?<\/div>\n <p class=\"vma-a\">As a rule, no. Wear and increased clearances make the object nonlinear. Balancing becomes unstable and does not provide a long-term result. Exceptions are possible only with design clearances and stable conditions.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does the balancing result differ after each start?<\/div>\n <p class=\"vma-a\">Starting creates high dynamic loads. If the structure is loosened, the relative positions of elements change after each start, leading to changes in vibration parameters.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">When is serial balancing using influence coefficients acceptable?<\/div>\n <p class=\"vma-a\">Serial balancing is possible for identical rotors installed under identical conditions, with vibration stability and absence of resonance. In this case, influence coefficients from the first rotor can be applied to subsequent ones.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does the result suddenly stop being repeatable during serial balancing?<\/div>\n <p class=\"vma-a\">This is usually due to changes in support stiffness, assembly differences, changes in rotational speed, or transition of the object into a nonlinear operating regime.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is the main criterion for successful balancing?<\/div>\n <p class=\"vma-a\">Reduction of vibration to a stable level while maintaining repeatability of amplitude and phase from start to start, and the absence of signs of resonance or nonlinearity.<\/p>\n <\/div>\n <\/section>\n <\/div>\n <\/main>\n <\/div>\n<\/body>\n<\/html>\n\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Nonlinear Objects in Rotor Balancing: Causes, Symptoms, and Practical Approach Nonlinear Objects in Rotor Balancing Why balancing \u201cdoes not work\u201d, why influence coefficients change, and how to proceed in real field conditions Contents Overview Linear & nonlinear vibrations Linear vs nonlinear objects What are linear objects? Graph of linearity Influence […]<\/p>\n","protected":false},"author":2,"featured_media":5200,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ai_generated_summary":"","footnotes":""},"categories":[4,113,9,5,110],"tags":[],"class_list":["post-5199","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-example","category-measurement","category-rotors","category-solutions","category-vibration-diagnostics"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/posts\/5199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/comments?post=5199"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/posts\/5199\/revisions"}],"predecessor-version":[{"id":20911,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/posts\/5199\/revisions\/20911"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/media\/5200"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/media?parent=5199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/categories?post=5199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/tags?post=5199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

\n\n\n \n \n\n \n Nonlinear Objects in Rotor Balancing: Causes, Symptoms, and Practical Approach<\/title>\n <meta name=\"title\" content=\"Nonlinear Objects in Rotor Balancing: Causes, Symptoms, and Practical Approach\" \/>\n \n <meta name=\"keywords\" content=\"rotor balancing, nonlinear object, linear object, influence coefficient, trial weight, resonance, vibration instability, Balanset-1A, vibration diagnostics, field balancing, bearing clearance, looseness, dry friction\" \/>\n <meta name=\"author\" content=\"Vibromera\" \/>\n <meta name=\"robots\" content=\"index, follow, max-image-preview:large, max-snippet:-1, max-video-preview:-1\" \/>\n <meta name=\"language\" content=\"English\" \/>\n\n \n \n \n \n \n\n \n \n \n \n\n \n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\" \/>\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin \/>\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Onest:wght@300;400;500;600;700;800&display=swap\" rel=\"stylesheet\" \/>\n\n <style>\n \/* ========================================\n VIBROMERA ARTICLE STYLES (ISOLATED)\n Prefix: vma-\n All styles scoped to .vma-wrapper\n ======================================== *\/\n .vma-wrapper{\n --vma-primary:#0052cc;\n --vma-primary-dark:#003d99;\n --vma-primary-50:#e6f0ff;\n --vma-gray-50:#f8fafc;\n --vma-gray-100:#f1f5f9;\n --vma-gray-200:#e2e8f0;\n --vma-gray-500:#64748b;\n --vma-gray-700:#334155;\n --vma-gray-800:#1e293b;\n --vma-gray-900:#0f172a;\n --vma-white:#ffffff;\n max-width:1600px;\n margin:0 auto;\n font-family:'Onest',system-ui,-apple-system,sans-serif;\n font-size:18px;\n line-height:1.75;\n color:var(--vma-gray-700);\n -webkit-font-smoothing:antialiased;\n -moz-osx-font-smoothing:grayscale;\n }\n .vma-hero{\n background:linear-gradient(135deg,var(--vma-primary) 0%,var(--vma-primary-dark) 100%);\n color:var(--vma-white);\n padding:56px 20px;\n text-align:center;\n position:relative;\n overflow:hidden;\n }\n .vma-hero::before{\n content:'';\n position:absolute;\n inset:0;\n opacity:.14;\n background-image:\n radial-gradient(circle at 18% 82%, rgba(255,255,255,.35) 0%, transparent 55%),\n radial-gradient(circle at 82% 18%, rgba(255,255,255,.28) 0%, transparent 45%);\n pointer-events:none;\n }\n .vma-hero > *{ position:relative; 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text-align:left; }\n .vma-kbd{\n font-weight:800;\n color:var(--vma-gray-900);\n }\n .vma-formula{\n background:linear-gradient(135deg,var(--vma-gray-50) 0%, var(--vma-primary-50) 100%);\n border:1px solid rgba(0,82,204,.18);\n border-radius:14px;\n padding:14px 16px;\n margin:14px 0;\n font-size:16px;\n color:var(--vma-gray-900);\n overflow:auto;\n white-space:nowrap;\n }\n .vma-qa{\n background:var(--vma-gray-50);\n border:1px solid var(--vma-gray-200);\n border-radius:16px;\n padding:18px 18px;\n margin:18px 0;\n }\n .vma-q{\n margin:0 0 8px 0;\n font-weight:800;\n color:var(--vma-gray-900);\n font-size:18px;\n }\n .vma-a{\n margin:0;\n }\n .vma-anchor{ scroll-margin-top: 16px; }\n @media (max-width: 820px){\n .vma-title{ font-size:30px; }\n }\n <\/style>\n\n \n \n\n \n<\/head>\n<body>\n <div class=\"vma-wrapper\">\n <header class=\"vma-hero\">\n <h1 class=\"vma-title\">Nonlinear Objects in Rotor Balancing<\/h1>\n <p class=\"vma-subtitle\">Why balancing \u201cdoes not work\u201d, why influence coefficients change, and how to proceed in real field conditions<\/p>\n <\/header>\n\n <main class=\"vma-content\">\n <div class=\"vma-inner\">\n <nav class=\"vma-toc\" aria-label=\"Table of contents\">\n <div class=\"vma-toc-title\">\u76ee\u9304<\/div>\n <ol>\n <li><a href=\"#intro\">\u6982\u8ff0<\/a><\/li>\n <li><a href=\"#linear-nonlinear-vibrations\">Linear & nonlinear vibrations<\/a><\/li>\n <li><a href=\"#linear-vs-nonlinear\">Linear vs nonlinear objects<\/a><\/li>\n <li><a href=\"#what-are-linear-objects\">What are linear objects?<\/a><\/li>\n <li><a href=\"#linearity-graph\">Graph of linearity<\/a><\/li>\n <li><a href=\"#influence-coefficient\">Influence coefficient (IC)<\/a><\/li>\n <li><a href=\"#linear-phase\">Vibration phase in linear objects<\/a><\/li>\n <li><a href=\"#linear-balancing-steps\">Steps for balancing a linear object<\/a><\/li>\n <li><a href=\"#serial\">Serial balancing and stored coefficients<\/a><\/li>\n <li><a href=\"#nonlinear-definition\">What is a nonlinear object?<\/a><\/li>\n <li><a href=\"#nonlinear-signs\">Signs of nonlinearity<\/a><\/li>\n <li><a href=\"#nonlinear-graph\">Graph of nonlinearity<\/a><\/li>\n <li><a href=\"#nonlinear-examples\">Examples of nonlinear objects<\/a><\/li>\n <li><a href=\"#nonlinear-types\">Types of nonlinearity<\/a><\/li>\n <li><a href=\"#causes\">Common causes of nonlinearity<\/a><\/li>\n <li><a href=\"#instability\">Vibration instability<\/a><\/li>\n <li><a href=\"#resonance\">Balancing near resonance<\/a><\/li>\n <li><a href=\"#high-after\">High vibration after \u201csuccessful\u201d balancing<\/a><\/li>\n <li><a href=\"#nonlinear-methods\">Balancing methods for nonlinear objects<\/a><\/li>\n <li><a href=\"#nonlinear-howto-linear-tool\">How to balance with a linear tool<\/a><\/li>\n <li><a href=\"#art-science\">The art & science of balancing<\/a><\/li>\n <li><a href=\"#measurement\">Measurement repeatability<\/a><\/li>\n <li><a href=\"#approach\">Practical approach for nonlinear objects<\/a><\/li>\n <li><a href=\"#reduced-correction\">Reduced correction weight technique<\/a><\/li>\n <li><a href=\"#conclusion\">Final principle<\/a><\/li>\n <li><a href=\"#faq\">Questions & answers<\/a><\/li>\n <\/ol>\n <\/nav>\n\n <section id=\"intro\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u6982\u8ff0<\/h2>\n <p>In practice, rotor balancing is almost never reduced to simply calculating and installing a correction weight. Formally, the algorithm is well known and the instrument performs all calculations automatically, but the final result depends far more on the behavior of the object itself than on the balancing device. This is why, in real work, situations constantly arise where balancing \u201cdoes not work\u201d, influence coefficients change, vibration becomes unstable, and the result is not repeatable from one run to another.<\/p>\n <\/section>\n\n <section id=\"linear-nonlinear-vibrations\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u7dda\u6027\u8207\u975e\u7dda\u6027\u632f\u52d5\u3001\u5176\u7279\u5fb5\u53ca\u52d5\u5e73\u8861\u6821\u6b63\u65b9\u6cd5<\/h2>\n <p>\u6210\u529f\u7684\u52d5\u5e73\u8861\u6821\u6b63\u9700\u8981\u7406\u89e3\u7269\u4ef6\u5c0d\u8cea\u91cf\u589e\u52a0\u6216\u79fb\u9664\u7684\u53cd\u61c9\u3002\u5728\u6b64\u80cc\u666f\u4e0b\uff0c\u7dda\u6027\u8207\u975e\u7dda\u6027\u7269\u4ef6\u7684\u6982\u5ff5\u626e\u6f14\u8457\u95dc\u9375\u89d2\u8272\u3002\u4e86\u89e3\u7269\u4ef6\u662f\u7dda\u6027\u9084\u662f\u975e\u7dda\u6027\uff0c\u6709\u52a9\u65bc\u9078\u64c7\u6b63\u78ba\u7684\u52d5\u5e73\u8861\u6821\u6b63\u7b56\u7565\uff0c\u4e26\u5e6b\u52a9\u9054\u5230\u9810\u671f\u7d50\u679c\u3002<\/p>\n <p>\u7dda\u6027\u7269\u4ef6\u56e0\u5176\u53ef\u9810\u6e2c\u6027\u548c\u7a69\u5b9a\u6027\u800c\u5728\u8a72\u9818\u57df\u4f54\u6709\u7279\u6b8a\u5730\u4f4d\u3002\u5b83\u5011\u5141\u8a31\u4f7f\u7528\u7c21\u55ae\u4e14\u53ef\u9760\u7684\u8a3a\u65b7\u548c\u52d5\u5e73\u8861\u6821\u6b63\u65b9\u6cd5\uff0c\u4f7f\u5176\u7814\u7a76\u6210\u70ba\u632f\u52d5\u8a3a\u65b7\u4e2d\u7684\u91cd\u8981\u4e00\u6b65\u3002<\/p>\n <\/section>\n\n <section id=\"linear-vs-nonlinear\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Linear vs nonlinear objects<\/h2>\n <p>Most of these problems are rooted in a fundamental but often underestimated distinction between linear and nonlinear objects. A linear object, from the balancing point of view, is a system in which, at a constant rotational speed, the vibration amplitude is proportional to the amount of unbalance, and the vibration phase follows the angular position of the unbalanced mass in a strictly predictable way. Under these conditions, the influence coefficient is a constant value. All standard dynamic balancing algorithms, including those implemented in the Balanset-1A, are designed precisely for such objects.<\/p>\n <p>For a linear object, the balancing process is predictable and stable. Installing a trial weight produces a proportional change in vibration amplitude and phase. Repeated starts give the same vibration vector, and the calculated correction weight remains valid. Such objects are well suited both for one-time balancing and for serial balancing using stored influence coefficients.<\/p>\n <p>A nonlinear object behaves in a fundamentally different way. The very basis of the balancing calculation is violated. Vibration amplitude is no longer proportional to unbalance, the phase becomes unstable, and the influence coefficient changes depending on the trial weight mass, operating mode, or even time. In practice, this appears as chaotic behavior of the vibration vector: after installing a trial weight, the vibration change may be too small, excessive, or simply non-repeatable.<\/p>\n <\/section>\n\n <section id=\"what-are-linear-objects\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u4ec0\u9ebc\u662f\u7dda\u6027\u7269\u4ef6\uff1f<\/h2>\n <p>\u7dda\u6027\u7269\u4ef6\u662f\u4e00\u7a2e\u632f\u52d5\u8207\u4e0d\u5e73\u8861\u91cf\u5927\u5c0f\u6210\u6b63\u6bd4\u7684\u7cfb\u7d71\u3002<\/p>\n <p>A linear object, in the context of balancing, is an idealized model characterized by a direct proportional relationship between the magnitude of the imbalance (unbalanced mass) and the vibration amplitude. This means that if the imbalance is doubled, the vibration amplitude will also double, provided the rotor's rotational speed remains constant. Conversely, reducing the imbalance will proportionally decrease the vibrations.<\/p>\n <p>\u8207\u975e\u7dda\u6027\u7cfb\u7d71\u4e0d\u540c\uff0c\u5f8c\u8005\u4e2d\u7269\u4ef6\u7684\u884c\u70ba\u53ef\u80fd\u6703\u56e0\u591a\u7a2e\u56e0\u7d20\u800c\u8b8a\u5316\uff0c\u7dda\u6027\u7269\u4ef6\u5247\u80fd\u4ee5\u6700\u5c0f\u7684\u52aa\u529b\u5be6\u73fe\u9ad8\u7cbe\u5ea6\u3002<\/p>\n <p>\u6b64\u5916\uff0c\u5b83\u5011\u9084\u4f5c\u70ba\u52d5\u5e73\u8861\u6821\u6b63\u4eba\u54e1\u57f9\u8a13\u548c\u5be6\u8e10\u7684\u57fa\u790e\u3002\u7406\u89e3\u7dda\u6027\u7269\u4ef6\u7684\u539f\u7406\u6709\u52a9\u65bc\u57f9\u990a\u6280\u80fd\uff0c\u9019\u4e9b\u6280\u80fd\u96a8\u5f8c\u53ef\u61c9\u7528\u65bc\u66f4\u8907\u96dc\u7684\u7cfb\u7d71\u3002<\/p>\n <\/section>\n\n <section id=\"linearity-graph\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u7dda\u6027\u7684\u5716\u5f62\u8868\u793a<\/h2>\n <p>Imagine a graph where the horizontal axis represents the magnitude of the unbalanced mass (imbalance), and the vertical axis represents the vibration amplitude. For a linear object, this graph will be a straight line passing through the origin (the point where both the imbalance magnitude and the vibration amplitude are zero). The slope of this line characterizes the object's sensitivity to imbalance: the steeper the slope, the greater the vibrations for the same imbalance.<\/p>\n\n <div class=\"vma-image\">\n <a href=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2024\/11\/output-1.png\" class=\"vma-img-link\">\n <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2024\/11\/output-1-1024x804.png\" alt=\"\u5716 1\uff1a\u632f\u52d5\u5e45\u5ea6\uff08\u00b5m\uff09\u8207\u4e0d\u5e73\u8861\u8cea\u91cf\uff08g\uff09\u4e4b\u9593\u7684\u95dc\u4fc2\" width=\"750\" height=\"589\" \/>\n <\/a>\n <p class=\"vma-caption\"><strong>\u5716 1\uff1a\u632f\u52d5\u5e45\u5ea6\uff08\u00b5m\uff09\u8207\u4e0d\u5e73\u8861\u8cea\u91cf\uff08g\uff09\u4e4b\u9593\u7684\u95dc\u4fc2<\/strong><\/p>\n <\/div>\n\n <p>\u5716 1 \u8aaa\u660e\u4e86\u7dda\u6027\u52d5\u5e73\u8861\u6821\u6b63\u7269\u4ef6\u7684\u632f\u52d5\u5e45\u5ea6\uff08\u00b5m\uff09\u8207\u8f49\u5b50\u4e0d\u5e73\u8861\u8cea\u91cf\uff08g\uff09\u4e4b\u9593\u7684\u95dc\u4fc2\u3002\u6bd4\u4f8b\u4fc2\u6578\u70ba 0.5 \u00b5m\/g\u3002\u53ea\u9700\u5c07 300 \u9664\u4ee5 600 \u5373\u53ef\u5f97\u5230 0.5 \u00b5m\/g\u3002\u5c0d\u65bc 800 g \u7684\u4e0d\u5e73\u8861\u8cea\u91cf\uff08UM=800 g\uff09\uff0c\u632f\u52d5\u5c07\u70ba 800 g * 0.5 \u00b5m\/g = 400 \u00b5m\u3002\u8acb\u6ce8\u610f\uff0c\u9019\u9069\u7528\u65bc\u8f49\u901f\u6046\u5b9a\u7684\u60c5\u6cc1\u3002\u5728\u4e0d\u540c\u7684\u8f49\u901f\u4e0b\uff0c\u4fc2\u6578\u5c07\u4e0d\u540c\u3002<\/p>\n <p>\u6b64\u6bd4\u4f8b\u4fc2\u6578\u7a31\u70ba\u5f71\u97ff\u4fc2\u6578\uff08\u654f\u611f\u5ea6\u4fc2\u6578\uff09\uff0c\u5176\u91cf\u7db1\u70ba \u00b5m\/g\uff0c\u6216\u5728\u6d89\u53ca\u4e0d\u5e73\u8861\u91cf\u7684\u60c5\u6cc1\u4e0b\u70ba \u00b5m\/(g*mm)\uff0c\u5176\u4e2d (g*mm) \u662f\u4e0d\u5e73\u8861\u91cf\u7684\u55ae\u4f4d\u3002\u77e5\u9053\u5f71\u97ff\u4fc2\u6578\uff08IC\uff09\u5f8c\uff0c\u4e5f\u53ef\u4ee5\u89e3\u6c7a\u9006\u554f\u984c\uff0c\u5373\u6839\u64da\u632f\u52d5\u5e45\u5ea6\u78ba\u5b9a\u4e0d\u5e73\u8861\u8cea\u91cf\uff08UM\uff09\u3002\u70ba\u6b64\uff0c\u5c07\u632f\u52d5\u5e45\u5ea6\u9664\u4ee5 IC\u3002<\/p>\n <p>\u4f8b\u5982\uff0c\u5982\u679c\u6e2c\u5f97\u7684\u632f\u52d5\u70ba 300 \u00b5m\uff0c\u4e14\u5df2\u77e5\u4fc2\u6578\u70ba IC=0.5 \u00b5m\/g\uff0c\u5c07 300 \u9664\u4ee5 0.5 \u5373\u53ef\u5f97\u5230 600 g\uff08UM=600 g\uff09\u3002<\/p>\n <\/section>\n\n <section id=\"influence-coefficient\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u5f71\u97ff\u4fc2\u6578\uff08IC\uff09\uff1a\u7dda\u6027\u7269\u4ef6\u7684\u95dc\u9375\u53c3\u6578<\/h2>\n <p>A critical characteristic of a linear object is the influence coefficient (IC). It is numerically equal to the tangent of the slope angle of the line on the graph of vibration versus imbalance and indicates how much the vibration amplitude (in microns, \u00b5m) changes when a unit of mass (in grams, g) is added in a specific correction plane at a specific rotor speed. In other words, IC is a measure of the object's sensitivity to imbalance. Its unit of measurement is \u00b5m\/g, or, when imbalance is expressed as the product of mass and radius, \u00b5m\/(g*mm).<\/p>\n <p>IC is essentially the \"passport\" characteristic of a linear object, enabling predictions of its behavior when mass is added or removed. Knowing the IC allows solving both the direct problem \u2013 determining vibration magnitude for a given imbalance \u2013 and the inverse problem \u2013 calculating imbalance magnitude from measured vibration.<\/p>\n\n <h3 class=\"vma-h3\">\u76f4\u63a5\u554f\u984c\uff1a<\/h3>\n <div class=\"vma-formula\">Vibration Amplitude (\u00b5m) = IC (\u00b5m\/g) * Unbalanced Mass (g)<\/div>\n\n <h3 class=\"vma-h3\">\u9006\u554f\u984c\uff1a<\/h3>\n <div class=\"vma-formula\">Unbalanced Mass (g) = Vibration Amplitude (\u00b5m) \/ IC (\u00b5m\/g)<\/div>\n <\/section>\n\n <section id=\"linear-phase\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u7dda\u6027\u7269\u4ef6\u4e2d\u7684\u632f\u52d5\u76f8\u4f4d<\/h2>\n <p>In addition to amplitude, vibration is also characterized by its phase, which indicates the rotor's position at the moment of maximum deviation from its equilibrium position. For a linear object, the vibration phase is also predictable. It is the sum of two angles:<\/p>\n <ol>\n <li>The angle that determines the position of the rotor's overall unbalanced mass. This angle indicates the direction in which the primary imbalance is concentrated.<\/li>\n <li>The argument of the influence coefficient. This is a constant angle that characterizes the object's dynamic properties and does not depend on the magnitude or angle of the unbalanced mass installation.<\/li>\n <\/ol>\n <p>\u56e0\u6b64\uff0c\u901a\u904e\u77e5\u9053 IC \u7684\u5e45\u89d2\u4e26\u6e2c\u91cf\u632f\u52d5\u76f8\u4f4d\uff0c\u53ef\u4ee5\u78ba\u5b9a\u4e0d\u5e73\u8861\u8cea\u91cf\u5b89\u88dd\u7684\u89d2\u5ea6\u3002\u9019\u4e0d\u50c5\u5141\u8a31\u8a08\u7b97\u6821\u6b63\u8cea\u91cf\u7684\u5927\u5c0f\uff0c\u9084\u5141\u8a31\u5176\u5728\u8f49\u5b50\u4e0a\u7cbe\u78ba\u653e\u7f6e\u4ee5\u9054\u5230\u6700\u4f73\u5e73\u8861\u3002<\/p>\n <\/section>\n\n <section id=\"linear-balancing-steps\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u7dda\u6027\u7269\u4ef6\u7684\u52d5\u5e73\u8861\u6821\u6b63<\/h2>\n <p>\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u5c0d\u65bc\u7dda\u6027\u7269\u4ef6\uff0c\u4ee5\u9019\u7a2e\u65b9\u5f0f\u78ba\u5b9a\u7684\u5f71\u97ff\u4fc2\u6578\uff08IC\uff09\u4e0d\u53d6\u6c7a\u65bc\u8a66\u91cd\u5b89\u88dd\u7684\u5927\u5c0f\u6216\u89d2\u5ea6\uff0c\u4e5f\u4e0d\u53d6\u6c7a\u65bc\u521d\u59cb\u632f\u52d5\u3002\u9019\u662f\u7dda\u6027\u7684\u4e00\u500b\u95dc\u9375\u7279\u5fb5\u3002\u5982\u679c\u7576\u8a66\u91cd\u53c3\u6578\u6216\u521d\u59cb\u632f\u52d5\u6539\u8b8a\u6642 IC \u4fdd\u6301\u4e0d\u8b8a\uff0c\u5247\u53ef\u4ee5\u81ea\u4fe1\u5730\u65b7\u8a00\u8a72\u7269\u4ef6\u5728\u6240\u8003\u616e\u7684\u4e0d\u5e73\u8861\u91cf\u7bc4\u570d\u5167\u8868\u73fe\u70ba\u7dda\u6027\u3002<\/p>\n\n <h3 class=\"vma-h3\">\u7dda\u6027\u7269\u4ef6\u52d5\u5e73\u8861\u6821\u6b63\u7684\u6b65\u9a5f<\/h3>\n <ol>\n <li><strong>\u6e2c\u91cf\u521d\u59cb\u632f\u52d5\uff1a<\/strong> \u7b2c\u4e00\u6b65\u662f\u6e2c\u91cf\u5176\u521d\u59cb\u72c0\u614b\u4e0b\u7684\u632f\u52d5\u3002\u78ba\u5b9a\u6307\u793a\u4e0d\u5e73\u8861\u65b9\u5411\u7684\u5e45\u5ea6\u548c\u632f\u52d5\u89d2\u5ea6\u3002<\/li>\n <li><strong>\u5b89\u88dd\u8a66\u91cd\uff1a<\/strong> \u5728\u8f49\u5b50\u4e0a\u5b89\u88dd\u5df2\u77e5\u91cd\u91cf\u7684\u8cea\u91cf\u3002\u9019\u6709\u52a9\u65bc\u4e86\u89e3\u7269\u4ef6\u5c0d\u984d\u5916\u8ca0\u8f09\u7684\u53cd\u61c9\uff0c\u4e26\u5141\u8a31\u8a08\u7b97\u632f\u52d5\u53c3\u6578\u3002<\/li>\n <li><strong>\u91cd\u65b0\u6e2c\u91cf\u632f\u52d5\uff1a<\/strong> \u5b89\u88dd\u8a66\u91cd\u5f8c\uff0c\u6e2c\u91cf\u65b0\u7684\u632f\u52d5\u53c3\u6578\u3002\u901a\u904e\u5c07\u5b83\u5011\u8207\u521d\u59cb\u503c\u9032\u884c\u6bd4\u8f03\uff0c\u53ef\u4ee5\u78ba\u5b9a\u8cea\u91cf\u5982\u4f55\u5f71\u97ff\u7cfb\u7d71\u3002<\/li>\n <li><strong>\u8a08\u7b97\u6821\u6b63\u8cea\u91cf\uff1a<\/strong> \u6839\u64da\u6e2c\u91cf\u8cc7\u6599\uff0c\u78ba\u5b9a\u6821\u6b63\u914d\u91cd\u7684\u8cea\u91cf\u548c\u5b89\u88dd\u89d2\u5ea6\u3002\u5c07\u6b64\u914d\u91cd\u653e\u7f6e\u5728\u8f49\u5b50\u4e0a\u4ee5\u6d88\u9664\u4e0d\u5e73\u8861\u3002<\/li>\n <li><strong>\u6700\u7d42\u9a57\u8b49\uff1a<\/strong> \u5b89\u88dd\u6821\u6b63\u914d\u91cd\u5f8c\uff0c\u632f\u52d5\u61c9\u986f\u8457\u964d\u4f4e\u3002\u5982\u679c\u6b98\u9918\u632f\u52d5\u4ecd\u8d85\u904e\u53ef\u63a5\u53d7\u6c34\u5e73\uff0c\u5247\u53ef\u4ee5\u91cd\u8907\u8a72\u7a0b\u5e8f\u3002<\/li>\n <\/ol>\n\n <div class=\"vma-note\">\n <p><span class=\"vma-kbd\">\u6ce8\u610f\uff1a<\/span> \u7dda\u6027\u7269\u4ef6\u662f\u7814\u7a76\u548c\u5be6\u969b\u61c9\u7528\u52d5\u5e73\u8861\u6821\u6b63\u65b9\u6cd5\u7684\u7406\u60f3\u6a21\u578b\u3002\u5b83\u5011\u7684\u7279\u6027\u5141\u8a31\u5de5\u7a0b\u5e2b\u548c\u8a3a\u65b7\u4eba\u54e1\u5c08\u6ce8\u65bc\u57f9\u990a\u57fa\u672c\u6280\u80fd\u4e26\u7406\u89e3\u8207\u8f49\u5b50\u7cfb\u7d71\u5de5\u4f5c\u7684\u57fa\u672c\u539f\u7406\u3002\u5118\u7ba1\u5b83\u5011\u5728\u5be6\u969b\u61c9\u7528\u4e2d\u7684\u61c9\u7528\u6709\u9650\uff0c\u4f46\u5c0d\u7dda\u6027\u7269\u4ef6\u7684\u7814\u7a76\u4ecd\u7136\u662f\u63a8\u9032\u632f\u52d5\u8a3a\u65b7\u548c\u52d5\u5e73\u8861\u6821\u6b63\u7684\u91cd\u8981\u4e00\u6b65\u3002<\/p>\n <\/div>\n\n <div class=\"vma-note\">\n <p><span class=\"vma-kbd\">Placeholder shortcode:<\/span> \t\t<section class=\"woocommerce hestia-shop products is-shortcode\" id=\"products\" data-sorder=\"hestia_shop\" >\n\t\t\t\t\t\t<div class=\"\">\n\t\t\t\t\t\t<div class=\"hestia-shop-content\">\n\t\t\t<div class=\"row\" 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class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>1,975.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=986\" data-quantity=\"1\" data-product_id=\"986\" data-product_sku=\"BS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=986\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_986\" data-quantity=\"1\" class=\"button 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title=\"\u632f\u52d5\u611f\u6e2c\u5668\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A vibration sensor close-up\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-3.webp 1280w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/parts\/\" rel=\"tag\">\u96f6\u4ef6<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/vibration-sensor\/\" title=\"\u632f\u52d5\u611f\u6e2c\u5668\">\u632f\u52d5\u611f\u6e2c\u5668<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>90.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1820\" data-quantity=\"1\" data-product_id=\"1820\" data-product_sku=\"VS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1820\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1820\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1820\" data-product_sku=\"VS-1\" aria-label=\"Add to cart: \u201cVibration sensor\u201d\" rel=\"nofollow\" data-success_message=\"\u201cVibration sensor\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1820\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/optical-sensor-for-balanset-and-arbalance\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"\u5149\u5b78\u611f\u6e2c\u5668\uff08\u96f7\u5c04\u6e2c\u901f\u5100\uff09\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"\u5149\u5b78\u611f\u6e2c\u5668\uff08\u96f7\u5c04\u6e2c\u901f\u5100\uff09\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-1536x1023.webp 1536w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/ZKqzGXSCCBU.webp 1600w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/parts\/\" rel=\"tag\">\u96f6\u4ef6<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"\u5149\u5b78\u611f\u6e2c\u5668\uff08\u96f7\u5c04\u6e2c\u901f\u5100\uff09\">\u5149\u5b78\u611f\u6e2c\u5668\uff08\u96f7\u5c04\u6e2c\u901f\u5100\uff09<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>124.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1832\" data-quantity=\"1\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1832\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1832\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" aria-label=\"Add to cart: \u201cOptical Sensor (Laser Tachometer)\u201d\" rel=\"nofollow\" data-success_message=\"\u201cOptical Sensor (Laser Tachometer)\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1832\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/balanset-4\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/balanset-4\/\" title=\"Balanset-4\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Vibromera rotor balancing kit: carry case, multi-channel signal conditioner, handheld analyzer, magnetic base, vibration sensors, and coiled cables.\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-18x12.webp 18w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2022\/12\/balkom4.webp 640w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/devices\/\" rel=\"tag\">\u8a2d\u5099<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/balanset-4\/\" title=\"Balanset-4\">Balanset-4<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>6,803.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1833\" data-quantity=\"1\" data-product_id=\"1833\" data-product_sku=\"BS-4\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1833\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1833\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1833\" data-product_sku=\"BS-4\" aria-label=\"Add to cart: \u201cBalanset-4\u201d\" rel=\"nofollow\" data-success_message=\"\u201cBalanset-4\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1833\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div><div class=\"row\">\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/magnet-stand\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/magnet-stand\/\" title=\"Insize-60-kgf \u78c1\u6027\u652f\u67b6\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Magnet base.\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-1024x682.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2018\/05\/IMG-36.webp 1280w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/parts\/\" rel=\"tag\">\u96f6\u4ef6<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/magnet-stand\/\" title=\"Insize-60-kgf \u78c1\u6027\u652f\u67b6\">Insize-60-kgf \u78c1\u6027\u652f\u67b6<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>46.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1852\" data-quantity=\"1\" data-product_id=\"1852\" data-product_sku=\"MS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=1852\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1852\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1852\" data-product_sku=\"MS-1\" aria-label=\"Add to cart: \u201cMagnetic Stand Insize-60-kgf\u201d\" rel=\"nofollow\" data-success_message=\"\u201cMagnetic Stand Insize-60-kgf\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1852\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/reflective-tape\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/reflective-tape\/\" title=\"\u53cd\u5149\u8cbc\u7d19\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"\u53cd\u5149\u8cbc\u7d19\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-16x12.webp 16w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-460x306.webp 460w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-272x182.webp 272w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/parts\/\" rel=\"tag\">\u96f6\u4ef6<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/reflective-tape\/\" title=\"\u53cd\u5149\u8cbc\u7d19\">\u53cd\u5149\u8cbc\u7d19<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>10.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=2329\" data-quantity=\"1\" data-product_id=\"2329\" data-product_sku=\"rt-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=2329\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_2329\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"2329\" data-product_sku=\"rt-1\" aria-label=\"Add to cart: \u201cReflective tape\u201d\" rel=\"nofollow\" data-success_message=\"\u201cReflective tape\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_2329\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/dynamic-balancer-balanset-1a\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/zh-tw\/product\/dynamic-balancer-balanset-1a\/\" title=\"\u52d5\u614b\u5e73\u8861\u5100\u300cBalanset-1A\u300dOEM\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A kit contents with interface unit, sensors, tachometer and accessories\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-600x400.webp 600w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-300x200.webp 300w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-1024x683.webp 1024w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-768x512.webp 768w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-1536x1024.webp 1536w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-2048x1366.webp 2048w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-360x240.webp 360w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-272x182.webp 272w, https:\/\/vibromera.eu\/wp-content\/uploads\/2021\/11\/\u0411\u0430\u043b\u043a\u043e\u043c\u041a\u0438\u0442-scaled-e1732998877834.webp 708w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/>\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<div class=\"ripple-container\"><\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"content\">\n\t\t\t\t\t\t\t\t<span class=\"category\"><a href=\"https:\/\/vibromera.eu\/zh-tw\/product-category\/devices\/\" rel=\"tag\">\u8a2d\u5099<\/a><\/span>\n\t\t\t\t\t\t\t\t<h4 class=\"card-title\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"shop-item-title-link\" href=\"https:\/\/vibromera.eu\/zh-tw\/product\/dynamic-balancer-balanset-1a\/\" title=\"\u52d5\u614b\u5e73\u8861\u5100\u300cBalanset-1A\u300dOEM\">\u52d5\u614b\u5e73\u8861\u5100\u300cBalanset-1A\u300dOEM<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t<div class=\"footer\">\n\n\t\t\t\t\t\t\t\t\t<div class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">\u20ac<\/span>1,735.00<\/span> + \u589e\u503c\u7a05\uff08\u5982\u9069\u7528\uff09<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"stats\">\n\t\t\t\t\t\t\t\t\t\t<a rel=\"nofollow\" href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=4193\" data-quantity=\"1\" data-product_id=\"4193\" data-product_sku=\"BS-1OEM\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/zh-tw\/wp-json\/wp\/v2\/posts\/5199?add-to-cart=4193\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_4193\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"4193\" data-product_sku=\"BS-1OEM\" aria-label=\"Add to cart: \u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d\" rel=\"nofollow\" data-success_message=\"\u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_4193\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/section>\n\t\t<\/p>\n <\/div>\n <\/section>\n\n <section id=\"serial\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Serial balancing and stored coefficients<\/h2>\n <p>Serial balancing deserves special attention. It can significantly increase productivity, but only when applied to linear, vibration-stable objects. In such cases, influence coefficients obtained on the first rotor can be reused for subsequent identical rotors. However, as soon as support stiffness, rotational speed, or bearing condition changes, repeatability is lost and the serial approach stops working.<\/p>\n <\/section>\n\n <section id=\"nonlinear-definition\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7269\u4ef6\uff1a\u7576\u7406\u8ad6\u8207\u5be6\u8e10\u80cc\u9053\u800c\u99b3\u6642<\/h2>\n <h3 class=\"vma-h3\">\u4ec0\u9ebc\u662f\u975e\u7dda\u6027\u7269\u4ef6\uff1f<\/h3>\n <p>\u975e\u7dda\u6027\u7269\u4ef6\u662f\u4e00\u7a2e\u632f\u52d5\u5e45\u5ea6\u8207\u4e0d\u5e73\u8861\u91cf\u5927\u5c0f\u4e0d\u6210\u6bd4\u4f8b\u7684\u7cfb\u7d71\u3002\u8207\u7dda\u6027\u7269\u4ef6\u4e0d\u540c\uff0c\u5f8c\u8005\u4e2d\u632f\u52d5\u8207\u4e0d\u5e73\u8861\u8cea\u91cf\u4e4b\u9593\u7684\u95dc\u4fc2\u7531\u76f4\u7dda\u8868\u793a\uff0c\u800c\u5728\u975e\u7dda\u6027\u7cfb\u7d71\u4e2d\uff0c\u9019\u7a2e\u95dc\u4fc2\u53ef\u80fd\u9075\u5faa\u8907\u96dc\u7684\u8ecc\u8de1\u3002<\/p>\n <p>\u5728\u73fe\u5be6\u4e16\u754c\u4e2d\uff0c\u4e26\u975e\u6240\u6709\u7269\u4ef6\u90fd\u8868\u73fe\u70ba\u7dda\u6027\u3002\u975e\u7dda\u6027\u7269\u4ef6\u8868\u73fe\u51fa\u975e\u76f4\u63a5\u6b63\u6bd4\u7684\u4e0d\u5e73\u8861\u8207\u632f\u52d5\u95dc\u4fc2\u3002\u9019\u610f\u5473\u8457\u5f71\u97ff\u4fc2\u6578\u4e0d\u662f\u6046\u5b9a\u7684\uff0c\u53ef\u80fd\u6703\u6839\u64da\u591a\u7a2e\u56e0\u7d20\u800c\u8b8a\u5316\uff0c\u4f8b\u5982\uff1a<\/p>\n <ul>\n <li><strong>\u4e0d\u5e73\u8861\u91cf\u5927\u5c0f\uff1a<\/strong> Increasing the imbalance can change the stiffness of the rotor's supports, leading to nonlinear changes in vibration.<\/li>\n <li><strong>\u8f49\u901f\uff1a<\/strong> \u5728\u4e0d\u540c\u7684\u8f49\u901f\u4e0b\u53ef\u80fd\u6703\u6fc0\u767c\u4e0d\u540c\u7684\u5171\u632f\u73fe\u8c61\uff0c\u5f9e\u800c\u5c0e\u81f4\u975e\u7dda\u6027\u884c\u70ba\u3002<\/li>\n <li><strong>\u6e38\u9699\u548c\u9593\u9699\u7684\u5b58\u5728\uff1a<\/strong> \u8ef8\u627f\u53ca\u5176\u4ed6\u9023\u63a5\u8655\u7684\u6e38\u9699\u8207\u9593\u9699\uff0c\u5728\u7279\u5b9a\u689d\u4ef6\u4e0b\u53ef\u80fd\u5c0e\u81f4\u632f\u52d5\u767c\u751f\u7a81\u8b8a\u3002<\/li>\n <li><strong>\u6eab\u5ea6\uff1a<\/strong> \u6eab\u5ea6\u8b8a\u5316\u6703\u5f71\u97ff\u6750\u6599\u7279\u6027\uff0c\u9032\u800c\u5f71\u97ff\u8a72\u7269\u4ef6\u7684\u632f\u52d5\u7279\u6027\u3002<\/li>\n <li><strong>\u5916\u90e8\u8ca0\u8377\uff1a<\/strong> \u4f5c\u7528\u65bc\u8f49\u5b50\u4e0a\u7684\u5916\u90e8\u8ca0\u8377\u53ef\u80fd\u6539\u8b8a\u5176\u52d5\u614b\u7279\u6027\uff0c\u4e26\u5c0e\u81f4\u975e\u7dda\u6027\u884c\u70ba\u3002<\/li>\n <\/ul>\n\n <h3 class=\"vma-h3\">\u70ba\u4f55\u975e\u7dda\u6027\u7269\u4ef6\u5177\u6311\u6230\u6027\uff1f<\/h3>\n <p>\u975e\u7dda\u6027\u6703\u70ba\u52d5\u5e73\u8861\u6821\u6b63\u904e\u7a0b\u5f15\u5165\u8a31\u591a\u8b8a\u6578\u3002\u6210\u529f\u8655\u7406\u975e\u7dda\u6027\u7269\u4ef6\u9700\u8981\u66f4\u591a\u7684\u6e2c\u91cf\u8207\u66f4\u8907\u96dc\u7684\u5206\u6790\u3002\u4f8b\u5982\uff0c\u9069\u7528\u65bc\u7dda\u6027\u7269\u4ef6\u7684\u6a19\u6e96\u65b9\u6cd5\uff0c\u5c0d\u975e\u7dda\u6027\u7cfb\u7d71\u4e26\u4e0d\u4e00\u5b9a\u80fd\u7522\u751f\u6e96\u78ba\u7684\u7d50\u679c\u3002\u9019\u9700\u8981\u66f4\u6df1\u5165\u5730\u4e86\u89e3\u904e\u7a0b\u7684\u7269\u7406\u539f\u7406\uff0c\u4e26\u4f7f\u7528\u5c08\u9580\u7684\u8a3a\u65b7\u65b9\u6cd5\u3002<\/p>\n <\/section>\n\n <section id=\"nonlinear-signs\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7684\u5fb5\u5146<\/h2>\n <p>\u975e\u7dda\u6027\u7269\u4ef6\u53ef\u900f\u904e\u4ee5\u4e0b\u5fb5\u5146\u4f86\u8b58\u5225\uff1a<\/p>\n <ul>\n <li><strong>\u975e\u6bd4\u4f8b\u632f\u52d5\u8b8a\u5316\uff1a<\/strong> \u96a8\u8457\u4e0d\u5e73\u8861\u91cf\u7684\u589e\u52a0\uff0c\u632f\u52d5\u53ef\u80fd\u6bd4\u7dda\u6027\u7269\u4ef6\u9810\u671f\u7684\u589e\u9577\u66f4\u5feb\u6216\u66f4\u6162\u3002<\/li>\n <li><strong>\u632f\u52d5\u76f8\u4f4d\u504f\u79fb\uff1a<\/strong> \u632f\u52d5\u76f8\u4f4d\u53ef\u80fd\u96a8\u8457\u4e0d\u5e73\u8861\u91cf\u6216\u8f49\u901f\u7684\u8b8a\u5316\u800c\u4e0d\u53ef\u9810\u6e2c\u5730\u6539\u8b8a\u3002<\/li>\n <li><strong>\u8ae7\u6ce2\u8207\u6b21\u8ae7\u6ce2\u7684\u5b58\u5728\uff1a<\/strong> \u632f\u52d5\u983b\u8b5c\u53ef\u80fd\u986f\u793a\u51fa\u9ad8\u6b21\u8ae7\u6ce2\uff08\u8f49\u983b\u7684\u500d\u6578\uff09\u8207\u6b21\u8ae7\u6ce2\uff08\u8f49\u983b\u7684\u5206\u6578\uff09\uff0c\u9019\u8868\u660e\u5b58\u5728\u975e\u7dda\u6027\u6548\u61c9\u3002<\/li>\n <li><strong>\u6eef\u5f8c\u73fe\u8c61\uff1a<\/strong> \u632f\u52d5\u5e45\u503c\u4e0d\u50c5\u53d6\u6c7a\u65bc\u7576\u524d\u7684\u4e0d\u5e73\u8861\u91cf\uff0c\u9084\u53ef\u80fd\u53d6\u6c7a\u65bc\u5176\u6b77\u53f2\u8b8a\u5316\u3002\u4f8b\u5982\uff0c\u7576\u4e0d\u5e73\u8861\u91cf\u589e\u52a0\u5f8c\u518d\u6e1b\u5c11\u56de\u521d\u59cb\u503c\u6642\uff0c\u632f\u52d5\u5e45\u503c\u53ef\u80fd\u4e0d\u6703\u56de\u5230\u539f\u59cb\u6c34\u5e73\u3002<\/li>\n <\/ul>\n <p>\u975e\u7dda\u6027\u6703\u70ba\u52d5\u5e73\u8861\u6821\u6b63\u904e\u7a0b\u5f15\u5165\u8a31\u591a\u8b8a\u6578\u3002\u6210\u529f\u64cd\u4f5c\u9700\u8981\u66f4\u591a\u7684\u6e2c\u91cf\u8207\u8907\u96dc\u7684\u5206\u6790\u3002\u4f8b\u5982\uff0c\u9069\u7528\u65bc\u7dda\u6027\u7269\u4ef6\u7684\u6a19\u6e96\u65b9\u6cd5\uff0c\u5c0d\u975e\u7dda\u6027\u7cfb\u7d71\u4e26\u4e0d\u4e00\u5b9a\u80fd\u7522\u751f\u6e96\u78ba\u7684\u7d50\u679c\u3002\u9019\u9700\u8981\u66f4\u6df1\u5165\u5730\u4e86\u89e3\u904e\u7a0b\u7269\u7406\u539f\u7406\uff0c\u4e26\u4f7f\u7528\u5c08\u9580\u7684\u8a3a\u65b7\u65b9\u6cd5\u3002<\/p>\n <\/section>\n\n <section id=\"nonlinear-graph\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7684\u5716\u5f62\u8868\u793a<\/h2>\n <p>\u5728\u632f\u52d5\u5c0d\u4e0d\u5e73\u8861\u91cf\u7684\u5716\u8868\u4e2d\uff0c\u975e\u7dda\u6027\u8868\u73fe\u70ba\u504f\u96e2\u76f4\u7dda\u3002\u5716\u8868\u53ef\u80fd\u5177\u6709\u5f4e\u6298\u3001\u66f2\u7387\u3001\u6eef\u5f8c\u8ff4\u5708\u53ca\u5176\u4ed6\u7279\u5fb5\uff0c\u8868\u660e\u4e0d\u5e73\u8861\u91cf\u8207\u632f\u52d5\u4e4b\u9593\u5b58\u5728\u8907\u96dc\u7684\u95dc\u4fc2\u3002<\/p>\n\n <div class=\"vma-image\">\n <a href=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2024\/11\/output-3.png\" class=\"vma-img-link\">\n <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2024\/11\/output-3-1024x816.png\" alt=\"\u5716 2. \u975e\u7dda\u6027\u7269\u4ef6\" width=\"750\" height=\"598\" \/>\n <\/a>\n <p class=\"vma-caption\"><strong>\u5716 2. \u975e\u7dda\u6027\u7269\u4ef6<\/strong><\/p>\n <p class=\"vma-caption\"><strong>50g; 40\u03bcm (yellow), 100g; 54.7\u03bcm (blue).<\/strong><\/p>\n <\/div>\n\n <p>\u6b64\u7269\u4ef6\u5448\u73fe\u5169\u500b\u7dda\u6bb5\uff0c\u5373\u5169\u689d\u76f4\u7dda\u3002\u5c0d\u65bc\u5c0f\u65bc 50 \u516c\u514b\u7684\u4e0d\u5e73\u8861\u91cf\uff0c\u5716\u8868\u53cd\u6620\u7dda\u6027\u7269\u4ef6\u7684\u7279\u6027\uff0c\u4fdd\u6301\u516c\u514b\u70ba\u55ae\u4f4d\u7684\u4e0d\u5e73\u8861\u91cf\u8207\u5fae\u7c73\u70ba\u55ae\u4f4d\u7684\u632f\u52d5\u5e45\u503c\u4e4b\u9593\u7684\u6bd4\u4f8b\u95dc\u4fc2\u3002\u5c0d\u65bc\u5927\u65bc 50 \u516c\u514b\u7684\u4e0d\u5e73\u8861\u91cf\uff0c\u632f\u52d5\u5e45\u503c\u7684\u589e\u9577\u6703\u6e1b\u7de9\u3002<\/p>\n <\/section>\n\n <section id=\"nonlinear-examples\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7269\u4ef6\u7684\u7bc4\u4f8b<\/h2>\n <p>\u5728\u52d5\u5e73\u8861\u6821\u6b63\u80cc\u666f\u4e0b\uff0c\u975e\u7dda\u6027\u7269\u4ef6\u7684\u7bc4\u4f8b\u5305\u62ec\uff1a<\/p>\n <ul>\n <li><strong>\u5e36\u6709\u88c2\u7d0b\u7684\u8f49\u5b50\uff1a<\/strong> \u8f49\u5b50\u4e0a\u7684\u88c2\u7d0b\u53ef\u80fd\u5c0e\u81f4\u525b\u6027\u767c\u751f\u975e\u7dda\u6027\u8b8a\u5316\uff0c\u9032\u800c\u5c0e\u81f4\u632f\u52d5\u8207\u4e0d\u5e73\u8861\u91cf\u4e4b\u9593\u5448\u73fe\u975e\u7dda\u6027\u95dc\u4fc2\u3002<\/li>\n <li><strong>\u5e36\u6709\u8ef8\u627f\u6e38\u9699\u7684\u8f49\u5b50\uff1a<\/strong> \u8ef8\u627f\u6e38\u9699\u5728\u7279\u5b9a\u689d\u4ef6\u4e0b\u53ef\u80fd\u5c0e\u81f4\u632f\u52d5\u767c\u751f\u7a81\u8b8a\u3002<\/li>\n <li><strong>\u5e36\u6709\u975e\u7dda\u6027\u5f48\u6027\u5143\u4ef6\u7684\u8f49\u5b50\uff1a<\/strong> Some elastic elements, such as rubber dampers, may exhibit nonlinear characteristics, affecting the rotor's dynamics.<\/li>\n <\/ul>\n <\/section>\n\n <section id=\"nonlinear-types\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7684\u985e\u578b<\/h2>\n <h3 class=\"vma-h3\">1. \u8edf\u786c\u975e\u7dda\u6027<\/h3>\n <p>\u5728\u6b64\u985e\u7cfb\u7d71\u4e2d\uff0c\u53ef\u89c0\u5bdf\u5230\u5169\u500b\u7dda\u6bb5\uff1a\u8edf\u6bb5\u8207\u786c\u6bb5\u3002\u5728\u8edf\u6bb5\u4e2d\uff0c\u884c\u70ba\u985e\u4f3c\u7dda\u6027\uff0c\u5373\u632f\u52d5\u5e45\u503c\u8207\u4e0d\u5e73\u8861\u8cea\u91cf\u6210\u6bd4\u4f8b\u589e\u52a0\u3002\u7136\u800c\uff0c\u5728\u9054\u5230\u67d0\u500b\u95be\u503c\uff08\u65b7\u9ede\uff09\u5f8c\uff0c\u7cfb\u7d71\u6703\u8f49\u63db\u70ba\u786c\u6bb5\u6a21\u5f0f\uff0c\u6b64\u6642\u5e45\u503c\u589e\u9577\u6703\u6e1b\u7de9\u3002<\/p>\n <h3 class=\"vma-h3\">2. \u5f48\u6027\u975e\u7dda\u6027<\/h3>\n <p>\u7cfb\u7d71\u5167\u652f\u6490\u6216\u63a5\u89f8\u9ede\u7684\u525b\u6027\u8b8a\u5316\uff0c\u4f7f\u632f\u52d5\u8207\u4e0d\u5e73\u8861\u91cf\u7684\u95dc\u4fc2\u8b8a\u5f97\u8907\u96dc\u3002\u4f8b\u5982\uff0c\u7576\u8de8\u8d8a\u7279\u5b9a\u8ca0\u8377\u95be\u503c\u6642\uff0c\u632f\u52d5\u53ef\u80fd\u6703\u7a81\u7136\u589e\u52a0\u6216\u6e1b\u5c11\u3002<\/p>\n <h3 class=\"vma-h3\">3. \u6469\u64e6\u8a98\u767c\u975e\u7dda\u6027<\/h3>\n <p>\u5728\u5177\u6709\u986f\u8457\u6469\u64e6\u7684\u7cfb\u7d71\u4e2d\uff08\u4f8b\u5982\u8ef8\u627f\u5167\uff09\uff0c\u632f\u52d5\u5e45\u503c\u53ef\u80fd\u96e3\u4ee5\u9810\u6e2c\u3002\u6469\u64e6\u53ef\u80fd\u5728\u67d0\u4e00\u8f49\u901f\u7bc4\u570d\u5167\u964d\u4f4e\u632f\u52d5\uff0c\u800c\u5728\u53e6\u4e00\u7bc4\u570d\u5167\u653e\u5927\u632f\u52d5\u3002<\/p>\n <\/section>\n\n <section id=\"causes\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Common causes of nonlinearity<\/h2>\n <p>The most common causes of nonlinearity are increased bearing clearances, bearing wear, dry friction, loosened supports, cracks in the structure, and operation near resonance frequencies. Often, the object exhibits so-called soft\u2013hard nonlinearity. At small unbalance levels the system behaves almost linearly, but as vibration increases, stiffer elements of the supports or casing become involved. In such cases, balancing is possible only within a narrow operating range and does not provide stable long-term results.<\/p>\n <\/section>\n\n <section id=\"instability\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Vibration instability<\/h2>\n <p>Another serious issue is vibration instability. Even a formally linear object may show changes in amplitude and phase over time. This is caused by thermal effects, changes in lubricant viscosity, thermal expansion, and unstable friction in the supports. As a result, measurements taken only minutes apart can produce different vibration vectors. Under these conditions, meaningful comparison of measurements becomes impossible, and the balancing calculation loses reliability.<\/p>\n <\/section>\n\n <section id=\"resonance\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Balancing near resonance<\/h2>\n <p>Balancing near resonance is especially problematic. When the rotational frequency coincides with, or is close to, a natural frequency of the system, even a small unbalance causes a sharp increase in vibration. The vibration phase becomes extremely sensitive to small speed variations. The object effectively enters a nonlinear regime, and balancing in this zone loses physical meaning. In such cases, the operating speed or the mechanical structure must be changed before balancing can be considered.<\/p>\n <\/section>\n\n <section id=\"high-after\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">High vibration after \u201csuccessful\u201d balancing<\/h2>\n <p>In practice, it is common to encounter situations where, after a formally successful balancing procedure, the overall vibration level remains high. This does not indicate an error of the instrument or the operator. Balancing eliminates mass unbalance only. If vibration is caused by foundation defects, loosened fasteners, misalignment, or resonance, correction weights will not solve the problem. In these cases, analyzing the spatial distribution of vibration across the machine and its foundation helps to identify the true cause.<\/p>\n <\/section>\n\n <section id=\"nonlinear-methods\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u975e\u7dda\u6027\u7269\u4ef6\u7684\u52d5\u5e73\u8861\u6821\u6b63\uff1a\u4e00\u9805\u9700\u8981\u975e\u50b3\u7d71\u89e3\u6c7a\u65b9\u6848\u4e4b\u8907\u96dc\u4efb\u52d9<\/h2>\n <p>\u975e\u7dda\u6027\u7269\u4ef6\u7684\u52d5\u5e73\u8861\u6821\u6b63\u662f\u4e00\u9805\u5177\u6311\u6230\u6027\u7684\u4efb\u52d9\uff0c\u9700\u8981\u5c08\u9580\u7684\u65b9\u6cd5\u8207\u9014\u5f91\u3002\u70ba\u7dda\u6027\u7269\u4ef6\u958b\u767c\u7684\u6a19\u6e96\u8a66\u91cd\u6cd5\uff0c\u53ef\u80fd\u7522\u751f\u932f\u8aa4\u7684\u7d50\u679c\u6216\u5b8c\u5168\u7121\u6cd5\u9069\u7528\u3002<\/p>\n\n <h3 class=\"vma-h3\">\u975e\u7dda\u6027\u7269\u4ef6\u7684\u52d5\u5e73\u8861\u6821\u6b63\u65b9\u6cd5<\/h3>\n <ul>\n <li><strong>\u9010\u6b65\u52d5\u5e73\u8861\u6821\u6b63\uff1a<\/strong> This method involves gradually reducing imbalance by installing corrective weights at each stage. After each stage, vibration measurements are taken, and a new corrective weight is determined based on the object's current state. This approach accounts for changes in the influence coefficient during the balancing process.<\/li>\n <li><strong>\u591a\u8f49\u901f\u52d5\u5e73\u8861\u6821\u6b63\uff1a<\/strong> \u6b64\u65b9\u6cd5\u89e3\u6c7a\u4e86\u4e0d\u540c\u8f49\u901f\u4e0b\u5171\u632f\u73fe\u8c61\u7684\u5f71\u97ff\u3002\u5728\u63a5\u8fd1\u5171\u632f\u7684\u6578\u500b\u8f49\u901f\u4e0b\u9032\u884c\u52d5\u5e73\u8861\u6821\u6b63\uff0c\u4f7f\u6574\u500b\u904b\u8f49\u8f49\u901f\u7bc4\u570d\u5167\u7684\u632f\u52d5\u964d\u4f4e\u66f4\u70ba\u5747\u52fb\u3002<\/li>\n <li><strong>\u4f7f\u7528\u6578\u5b78\u6a21\u578b\uff1a<\/strong> \u5c0d\u65bc\u8907\u96dc\u7684\u975e\u7dda\u6027\u7269\u4ef6\uff0c\u53ef\u63a1\u7528\u63cf\u8ff0\u8f49\u5b50\u52d5\u614b\u4e26\u8003\u616e\u975e\u7dda\u6027\u6548\u61c9\u7684\u6578\u5b78\u6a21\u578b\u3002\u9019\u4e9b\u6a21\u578b\u6709\u52a9\u65bc\u9810\u6e2c\u7269\u4ef6\u5728\u5404\u7a2e\u689d\u4ef6\u4e0b\u7684\u884c\u70ba\uff0c\u4e26\u78ba\u5b9a\u6700\u4f73\u7684\u52d5\u5e73\u8861\u6821\u6b63\u53c3\u6578\u3002<\/li>\n <\/ul>\n\n <p>The experience and intuition of a specialist play a crucial role in balancing nonlinear objects. An experienced balancer can recognize signs of nonlinearity, select an appropriate method, and adapt it to the specific situation. Analyzing vibration spectra, observing vibration changes as the object's operating parameters vary, and considering the rotor's design features all assist in making the right decisions and achieving the desired results.<\/p>\n <\/section>\n\n <section id=\"nonlinear-howto-linear-tool\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u5982\u4f55\u4f7f\u7528\u70ba\u7dda\u6027\u7269\u4ef6\u8a2d\u8a08\u7684\u5de5\u5177\u4f86\u6821\u6b63\u975e\u7dda\u6027\u7269\u4ef6<\/h2>\n <p>\u9019\u662f\u500b\u597d\u554f\u984c\u3002\u6211\u500b\u4eba\u6821\u6b63\u6b64\u985e\u7269\u4ef6\u7684\u65b9\u6cd5\u59cb\u65bc\u4fee\u5fa9\u6a5f\u4ef6\uff1a\u66f4\u63db\u8ef8\u627f\u3001\u710a\u63a5\u88c2\u7d0b\u3001\u9396\u7dca\u87ba\u6813\u3001\u6aa2\u67e5\u9328\u56fa\u6216\u6e1b\u9707\u5668\uff0c\u4e26\u78ba\u8a8d\u8f49\u5b50\u672a\u8207\u975c\u6b62\u7d50\u69cb\u5143\u4ef6\u767c\u751f\u6469\u64e6\u3002<\/p>\n <p>\u63a5\u8457\uff0c\u6211\u6703\u8b58\u5225\u5171\u632f\u983b\u7387\uff0c\u56e0\u70ba\u5728\u63a5\u8fd1\u5171\u632f\u7684\u8f49\u901f\u4e0b\u7121\u6cd5\u5c0d\u8f49\u5b50\u9032\u884c\u52d5\u5e73\u8861\u6821\u6b63\u3002\u70ba\u6b64\uff0c\u6211\u4f7f\u7528\u885d\u64ca\u6cd5\u4f86\u78ba\u5b9a\u5171\u632f\u983b\u7387\uff0c\u6216\u4f7f\u7528\u8f49\u5b50\u60f0\u8f49\u964d\u901f\u5716\u3002<\/p>\n <p>Then, I determine the sensor's position on the mechanism: vertical, horizontal, or at an angle.<\/p>\n <p>\u8a66\u904b\u8f49\u5f8c\uff0c\u8a2d\u5099\u6703\u6307\u793a\u6821\u6b63\u8ca0\u8f09\u7684\u89d2\u5ea6\u8207\u91cd\u91cf\u3002\u6211\u6703\u5c07\u6821\u6b63\u8ca0\u8f09\u7684\u91cd\u91cf\u6e1b\u534a\uff0c\u4f46\u4f7f\u7528\u8a2d\u5099\u5efa\u8b70\u7684\u89d2\u5ea6\u4f86\u5b89\u88dd\u8f49\u5b50\u3002\u5982\u679c\u6821\u6b63\u5f8c\u7684\u6b98\u9918\u632f\u52d5\u4ecd\u8d85\u904e\u53ef\u63a5\u53d7\u7bc4\u570d\uff0c\u6211\u6703\u518d\u6b21\u904b\u8f49\u8f49\u5b50\u3002\u7576\u7136\uff0c\u9019\u9700\u8981\u66f4\u591a\u6642\u9593\uff0c\u4f46\u6709\u6642\u7d50\u679c\u4ee4\u4eba\u9f13\u821e\u3002<\/p>\n <\/section>\n\n <section id=\"art-science\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">\u65cb\u8f49\u8a2d\u5099\u52d5\u5e73\u8861\u6821\u6b63\u7684\u85dd\u8853\u8207\u79d1\u5b78<\/h2>\n <p>\u65cb\u8f49\u8a2d\u5099\u7684\u52d5\u5e73\u8861\u6821\u6b63\u662f\u4e00\u500b\u8907\u96dc\u7684\u904e\u7a0b\uff0c\u7d50\u5408\u4e86\u79d1\u5b78\u8207\u85dd\u8853\u7684\u5143\u7d20\u3002\u5c0d\u65bc\u7dda\u6027\u7269\u4ef6\uff0c\u52d5\u5e73\u8861\u6821\u6b63\u6d89\u53ca\u76f8\u5c0d\u7c21\u55ae\u7684\u8a08\u7b97\u8207\u6a19\u6e96\u65b9\u6cd5\u3002\u7136\u800c\uff0c\u8655\u7406\u975e\u7dda\u6027\u7269\u4ef6\u9700\u8981\u6df1\u5165\u7406\u89e3\u8f49\u5b50\u52d5\u529b\u5b78\u3001\u5206\u6790\u632f\u52d5\u4fe1\u865f\u7684\u80fd\u529b\uff0c\u4ee5\u53ca\u9078\u64c7\u6700\u6709\u6548\u52d5\u5e73\u8861\u6821\u6b63\u7b56\u7565\u7684\u6280\u5de7\u3002<\/p>\n <p>\u7d93\u9a57\u3001\u76f4\u89ba\u8207\u6301\u7e8c\u7684\u6280\u80fd\u63d0\u5347\uff0c\u662f\u8b93\u52d5\u5e73\u8861\u6821\u6b63\u4eba\u54e1\u6210\u70ba\u771f\u6b63\u5927\u5e2b\u7684\u95dc\u9375\u3002\u7562\u7adf\uff0c\u52d5\u5e73\u8861\u6821\u6b63\u7684\u54c1\u8cea\u4e0d\u50c5\u6c7a\u5b9a\u4e86\u8a2d\u5099\u904b\u8f49\u7684\u6548\u7387\u8207\u53ef\u9760\u6027\uff0c\u4e5f\u78ba\u4fdd\u4e86\u4eba\u54e1\u7684\u5b89\u5168\u3002<\/p>\n <p> <\/p>\n <\/section>\n\n <section id=\"measurement\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Measurement repeatability<\/h2>\n <p>Measurement issues also play a major role. Incorrect installation of vibration sensors, changes in measurement points, or improper sensor orientation directly affect both amplitude and phase. For balancing, it is not enough to measure vibration; repeatability and stability of measurements are critical. This is why, in practical work, sensor mounting locations and orientations must be strictly controlled.<\/p>\n <\/section>\n\n <section id=\"approach\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Practical approach for nonlinear objects<\/h2>\n <p>Balancing a nonlinear object always begins not with installing a trial weight, but with evaluating vibration behavior. If amplitude and phase clearly drift over time, change from one start to another, or react sharply to small speed variations, the first task is to achieve the most stable operating mode possible. Without this, any calculations will be random.<\/p>\n <p>The first practical step is choosing the correct speed. Nonlinear objects are extremely sensitive to resonance, so balancing must be performed at a speed as far as possible from natural frequencies. This often means moving below or above the usual operating range. Even if vibration at this speed is higher, but stable, it is preferable to balancing in a resonant zone.<\/p>\n <p>Next, it is important to minimize all sources of additional nonlinearity. Before balancing, all fasteners should be checked and tightened, clearances eliminated as much as possible, and supports and bearing units inspected for looseness. Balancing does not compensate for clearances or friction, but it may be possible if these factors are brought to a stable condition.<\/p>\n <p>When working with a nonlinear object, small trial weights should not be used out of habit. Too small a trial weight often fails to move the system into a repeatable region, and the vibration change becomes comparable to instability noise. The trial weight must be large enough to cause a clear and reproducible change in the vibration vector, but not so large that it drives the object into a different operating regime.<\/p>\n <p>Measurements should be performed quickly and under identical conditions. The less time passes between measurements, the higher the chance that the dynamic parameters of the system remain unchanged. It is advisable to perform several control runs without changing the configuration to confirm that the object behaves consistently.<\/p>\n <p>It is very important to fix vibration sensor mounting points and their orientation. For nonlinear objects, even a small sensor displacement can cause noticeable changes in phase and amplitude, which may be mistakenly interpreted as the effect of the trial weight.<\/p>\n <p>In calculations, attention should be paid not to exact numerical agreement, but to trends. If vibration consistently decreases with successive corrections, this indicates that balancing is moving in the right direction, even if influence coefficients do not formally converge.<\/p>\n <p>It is not recommended to store and reuse influence coefficients for nonlinear objects. Even if one balancing cycle is successful, during the next start the object may enter a different regime and the previous coefficients will no longer be valid.<\/p>\n <p>It should be remembered that balancing a nonlinear object is often a compromise. The goal is not to achieve the lowest possible vibration, but to bring the machine into a stable and repeatable condition with an acceptable vibration level. In many cases, this is a temporary solution until bearings are repaired, supports are restored, or the structure is modified.<\/p>\n <p>The main practical principle is to stabilize the object first, then balance it, and only after that evaluate the result. If stabilization cannot be achieved, balancing should be considered an auxiliary measure rather than a final solution.<\/p>\n <\/section>\n\n <section id=\"reduced-correction\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Reduced correction weight technique<\/h2>\n <p>In practice, when balancing nonlinear objects, another important technique often proves effective. If the instrument calculates a correction weight using a standard algorithm, installing the full calculated weight frequently makes the situation worse: vibration may increase, the phase may jump, and the object may shift into a different operating mode.<\/p>\n <p>In such cases, installing a reduced correction weight works well \u2014 two or sometimes even three times smaller than the value calculated by the instrument. This helps avoid \u201cthrowing\u201d the system out of the conditionally linear region into another nonlinear regime. In effect, the correction is applied gently, with a small step, without causing a sharp change in the dynamic parameters of the object.<\/p>\n <p>After installing the reduced weight, a control run must be performed and the vibration trend evaluated. If the amplitude steadily decreases and the phase remains relatively stable, the correction can be repeated using the same approach, gradually approaching the minimum achievable vibration level. This step-by-step method is often more reliable than installing the full calculated correction weight at once.<\/p>\n <p>This technique is especially effective for objects with clearances, dry friction, and soft\u2013hard supports, where full calculated correction immediately drives the system out of the conditionally linear zone. Using reduced correction masses allows the object to remain in the most stable operating regime and makes it possible to achieve a practical result even where balancing is formally considered impossible.<\/p>\n <p>It is important to understand that this is not an \u201cinstrument error\u201d, but a consequence of the physics of nonlinear systems. The instrument correctly calculates for a linear model, while the engineer adapts the result in practice to the real behavior of the mechanical system.<\/p>\n <\/section>\n\n <section id=\"conclusion\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Final principle<\/h2>\n <p>Ultimately, successful balancing is not merely about calculating a weight and an angle. It requires understanding the dynamic behavior of the object, its linearity, vibration stability, and distance from resonance conditions. The Balanset-1A provides all necessary tools for measurement, analysis, and calculation, but the final result is always determined by the mechanical condition of the system itself. This is what distinguishes a formal approach from real engineering practice in vibration diagnostics and rotor balancing.<\/p>\n <\/section>\n\n <section id=\"faq\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Questions & answers<\/h2>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why do vibration amplitude and phase change unpredictably after installing a trial weight, and why does the correction weight calculation give a poor result?<\/div>\n <p class=\"vma-a\">This is a sign of a nonlinear object. In a linear object, vibration amplitude is proportional to the amount of unbalance, and the phase changes by the same angle as the angular position of the weight. When these conditions are violated, the influence coefficient is no longer constant and the standard balancing algorithm starts to produce errors. Typical causes are bearing clearances, loosened supports, friction, and operation near resonance.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is a linear object from the balancing point of view?<\/div>\n <p class=\"vma-a\">A linear object is a rotor system in which, at the same rotational speed, vibration amplitude is directly proportional to the magnitude of unbalance, and the vibration phase strictly follows the angular position of the unbalanced mass. For such objects, the influence coefficient is constant and does not depend on the mass of the trial weight.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is considered a nonlinear object in balancing?<\/div>\n <p class=\"vma-a\">A nonlinear object is a system in which the proportionality between vibration and unbalance and\/or the constancy of the phase relationship is violated. Vibration amplitude and phase begin to depend on the mass of the trial weight. Most often this is associated with bearing clearances, wear, dry friction, soft\u2013hard supports, or the engagement of stiffer structural elements.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Is it possible to balance a nonlinear object using an instrument designed for linear systems?<\/div>\n <p class=\"vma-a\">Yes, but the result is unstable and depends on the operating mode. Balancing is possible only within a limited range where the object behaves conditionally linearly. Outside this range, influence coefficients change and result repeatability is lost.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is the influence coefficient in simple terms?<\/div>\n <p class=\"vma-a\">The influence coefficient is a measure of vibration sensitivity to changes in unbalance. It shows how much the vibration vector will change when a known trial weight is installed in a given plane at a given speed.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does the influence coefficient change from one measurement to another?<\/div>\n <p class=\"vma-a\">The influence coefficient is unstable if the object is nonlinear, if vibration is unstable over time, or if resonance, thermal warm-up, loosened fasteners, or changing friction conditions are present. In such cases, repeated starts produce different amplitude and phase values.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">When can stored influence coefficients be used?<\/div>\n <p class=\"vma-a\">Stored influence coefficients may be used only for identical rotors operating at the same speed, under the same installation conditions and support stiffness. The object must be linear and vibration-stable. Even a slight change in conditions makes the old coefficients unreliable.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does vibration change during warm-up even without a change in unbalance?<\/div>\n <p class=\"vma-a\">During warm-up, bearing clearances, support stiffness, lubricant viscosity, and friction level change. This alters the dynamic parameters of the system and, as a result, changes vibration amplitude and phase.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is vibration instability and why does it interfere with balancing?<\/div>\n <p class=\"vma-a\">Vibration instability is a change in amplitude and\/or phase over time at a constant rotational speed. Balancing relies on comparing vibration vectors, so when vibration is unstable, the comparison loses meaning and the calculation becomes unreliable.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What types of vibration instability exist?<\/div>\n <p class=\"vma-a\">There are inherent structural instability, slow \u201ccreeping\u201d instability, variation from start to start, warm-up-related instability, and resonance-related instability when operating near natural frequencies.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why is it impossible to balance a rotor in the resonance zone?<\/div>\n <p class=\"vma-a\">In the resonance zone, even a small unbalance causes a sharp increase in vibration, and the phase becomes extremely sensitive to small changes. Under these conditions, the object becomes nonlinear and the balancing results lose physical meaning.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">How can one tell that the balancing speed is close to a resonant speed?<\/div>\n <p class=\"vma-a\">Typical signs are a sharp increase in vibration with small speed changes, unstable phase, broad humps in the spectrum, and high sensitivity of vibration to minor RPM variations. A vibration maximum is often observed during run-up or coast-down.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does high vibration not always mean large unbalance?<\/div>\n <p class=\"vma-a\">High vibration can be caused by resonance, loosened structures, foundation defects, or bearing problems. In such cases, balancing will not eliminate the cause of vibration.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is the difference between vibration displacement, vibration velocity, and vibration acceleration?<\/div>\n <p class=\"vma-a\">Vibration displacement characterizes the motion amplitude, vibration velocity characterizes the speed of this motion, and vibration acceleration characterizes the acceleration. These quantities are related, but each is better suited to detecting certain types of defects and frequency ranges.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why are vibration limits usually specified in terms of vibration velocity?<\/div>\n <p class=\"vma-a\">Vibration velocity reflects the energy level of vibration over a wide frequency range and is convenient for assessing the overall condition of machines according to ISO standards.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Is it possible to directly convert vibration displacement to vibration velocity and vice versa?<\/div>\n <p class=\"vma-a\">Correct conversion is possible only for single-frequency harmonic vibration. For complex vibration spectra, such conversions provide only approximate results.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does vibration remain high after balancing?<\/div>\n <p class=\"vma-a\">Possible reasons include resonance, foundation defects, loosened fasteners, bearing wear, misalignment, or object nonlinearity. Balancing removes unbalance only, not other defects.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">How can one tell that the problem is not in the rotor but in the foundation?<\/div>\n <p class=\"vma-a\">If mechanical defects are not detected and vibration does not decrease after balancing, it is necessary to analyze the vibration distribution over the machine and the foundation. Typical signs are high vibration of the casing and base, and phase shifts between measurement points.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why is correct installation of vibration sensors important?<\/div>\n <p class=\"vma-a\">Incorrect sensor installation distorts amplitude and phase, reduces measurement repeatability, and can lead to incorrect diagnostic conclusions and erroneous balancing results.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why do different measurement points show different vibration levels?<\/div>\n <p class=\"vma-a\">Vibration is distributed unevenly throughout the structure. Stiffness, masses, and mode shapes differ, so amplitude and phase can vary significantly from point to point.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Is it possible to balance a rotor with worn bearings?<\/div>\n <p class=\"vma-a\">As a rule, no. Wear and increased clearances make the object nonlinear. Balancing becomes unstable and does not provide a long-term result. Exceptions are possible only with design clearances and stable conditions.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does the balancing result differ after each start?<\/div>\n <p class=\"vma-a\">Starting creates high dynamic loads. If the structure is loosened, the relative positions of elements change after each start, leading to changes in vibration parameters.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">When is serial balancing using influence coefficients acceptable?<\/div>\n <p class=\"vma-a\">Serial balancing is possible for identical rotors installed under identical conditions, with vibration stability and absence of resonance. In this case, influence coefficients from the first rotor can be applied to subsequent ones.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">Why does the result suddenly stop being repeatable during serial balancing?<\/div>\n <p class=\"vma-a\">This is usually due to changes in support stiffness, assembly differences, changes in rotational speed, or transition of the object into a nonlinear operating regime.<\/p>\n <\/div>\n\n <div class=\"vma-qa\">\n <div class=\"vma-q\">What is the main criterion for successful balancing?<\/div>\n <p class=\"vma-a\">Reduction of vibration to a stable level while maintaining repeatability of amplitude and phase from start to start, and the absence of signs of resonance or nonlinearity.<\/p>\n <\/div>\n <\/section>\n <\/div>\n <\/main>\n <\/div>\n<\/body>\n<\/html>\n\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Nonlinear Objects in Rotor Balancing: Causes, Symptoms, and Practical Approach Nonlinear Objects in Rotor Balancing Why balancing \u201cdoes not work\u201d, why influence coefficients change, and how to proceed in real field conditions Contents Overview Linear & nonlinear vibrations Linear vs nonlinear objects What are linear objects? Graph of linearity Influence […]<\/p>\n","protected":false},"author":2,"featured_media":5200,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ai_generated_summary":"","footnotes":""},"categories":[4,113,9,5,110],"tags":[],"class_list":["post-5199","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-example","category-measurement","category-rotors","category-solutions","category-vibration-diagnostics"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/posts\/5199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/comments?post=5199"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/posts\/5199\/revisions"}],"predecessor-version":[{"id":20911,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/posts\/5199\/revisions\/20911"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/media\/5200"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/media?parent=5199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/categories?post=5199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/zh-tw\/wp-json\/wp\/v2\/tags?post=5199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}