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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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\">Vibra\u00e7\u00f5es Lineares e N\u00e3o Lineares, Suas Caracter\u00edsticas e M\u00e9todos de Balanceamento<\/h2>\n <p>O balanceamento bem-sucedido exige compreender como um objeto reage \u00e0 adi\u00e7\u00e3o ou remo\u00e7\u00e3o de massa. Nesse contexto, os conceitos de objetos lineares e n\u00e3o lineares desempenham um papel fundamental. Compreender se um objeto \u00e9 linear ou n\u00e3o linear permite a sele\u00e7\u00e3o da estrat\u00e9gia de balanceamento correta e ajuda a alcan\u00e7ar o resultado desejado.<\/p>\n <p>Os objetos lineares ocupam um lugar especial nessa \u00e1rea devido \u00e0 sua previsibilidade e estabilidade. Eles permitem o uso de m\u00e9todos de diagn\u00f3stico e balanceamento simples e confi\u00e1veis, tornando seu estudo um passo importante na vibra\u00e7\u00e3o diagn\u00f3stica.<\/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\">O Que S\u00e3o Objetos Lineares?<\/h2>\n <p>Um objeto linear \u00e9 um sistema onde a vibra\u00e7\u00e3o \u00e9 diretamente proporcional \u00e0 magnitude do desbalanceamento.<\/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>Diferentemente dos sistemas n\u00e3o lineares, onde o comportamento de um objeto pode variar dependendo de muitos fatores, os objetos lineares permitem um alto n\u00edvel de precis\u00e3o com esfor\u00e7o m\u00ednimo.<\/p>\n <p>Al\u00e9m disso, eles servem como base para o treinamento e pr\u00e1tica de balanceadores. Compreender os princ\u00edpios dos objetos lineares ajuda a desenvolver habilidades que podem ser aplicadas posteriormente a sistemas mais complexos.<\/p>\n <\/section>\n\n <section id=\"linearity-graph\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Representa\u00e7\u00e3o Gr\u00e1fica da Linearidade<\/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=\"Gr\u00e1fico 1: A Rela\u00e7\u00e3o Entre a Amplitude de Vibra\u00e7\u00e3o (\u00b5m) e a Massa Desbalanceada (g)\" width=\"750\" height=\"589\" \/>\n <\/a>\n <p class=\"vma-caption\"><strong>Gr\u00e1fico 1: A Rela\u00e7\u00e3o Entre a Amplitude de Vibra\u00e7\u00e3o (\u00b5m) e a Massa Desbalanceada (g)<\/strong><\/p>\n <\/div>\n\n <p>O Gr\u00e1fico 1 ilustra a rela\u00e7\u00e3o entre a amplitude de vibra\u00e7\u00e3o (\u00b5m) de um objeto de balanceamento linear e a massa desbalanceada (g) do rotor. O coeficiente de proporcionalidade \u00e9 0,5 \u00b5m\/g. Basta dividir 300 por 600 para obter 0,5 \u00b5m\/g. Para uma massa desbalanceada de 800 g (MD=800 g), a vibra\u00e7\u00e3o ser\u00e1 800 g * 0,5 \u00b5m\/g = 400 \u00b5m. Observe que isso se aplica a uma velocidade constante do rotor. Em uma velocidade de rota\u00e7\u00e3o diferente, o coeficiente ser\u00e1 diferente.<\/p>\n <p>Esse coeficiente de proporcionalidade \u00e9 chamado de coeficiente de influ\u00eancia (coeficiente de sensibilidade) e tem uma dimens\u00e3o de \u00b5m\/g ou, em casos envolvendo desbalanceamento, \u00b5m\/(g*mm), onde (g*mm) \u00e9 a unidade de desbalanceamento. Conhecendo o coeficiente de influ\u00eancia (CI), tamb\u00e9m \u00e9 poss\u00edvel resolver o problema inverso, ou seja, determinar a massa desbalanceada (MD) com base na magnitude da vibra\u00e7\u00e3o. Para isso, divida a amplitude de vibra\u00e7\u00e3o pelo CI.<\/p>\n <p>Por exemplo, se a vibra\u00e7\u00e3o medida for 300 \u00b5m e o coeficiente conhecido for CI=0,5 \u00b5m\/g, divida 300 por 0,5 para obter 600 g (MD=600 g).<\/p>\n <\/section>\n\n <section id=\"influence-coefficient\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Coeficiente de Influ\u00eancia (CI): Par\u00e2metro Chave dos Objetos Lineares<\/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\">Problema Direto:<\/h3>\n <div class=\"vma-formula\">Vibration Amplitude (\u00b5m) = IC (\u00b5m\/g) * Unbalanced Mass (g)<\/div>\n\n <h3 class=\"vma-h3\">Problema Inverso:<\/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\">Fase de Vibra\u00e7\u00e3o em Objetos Lineares<\/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>Assim, conhecendo o argumento do CI e medindo a fase de vibra\u00e7\u00e3o, \u00e9 poss\u00edvel determinar o \u00e2ngulo de instala\u00e7\u00e3o da massa desbalanceada. Isso permite n\u00e3o apenas o c\u00e1lculo da magnitude da massa corretiva, mas tamb\u00e9m sua coloca\u00e7\u00e3o precisa no rotor para alcan\u00e7ar o balanceamento \u00f3timo.<\/p>\n <\/section>\n\n <section id=\"linear-balancing-steps\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Balanceamento de Objetos Lineares<\/h2>\n <p>\u00c9 importante observar que, para um objeto linear, o coeficiente de influ\u00eancia (CI) determinado dessa maneira n\u00e3o depende da magnitude ou do \u00e2ngulo de instala\u00e7\u00e3o da massa de teste, nem da vibra\u00e7\u00e3o inicial. Esta \u00e9 uma caracter\u00edstica fundamental da linearidade. Se o CI permanecer inalterado quando os par\u00e2metros da massa de teste ou a vibra\u00e7\u00e3o inicial forem alterados, pode-se afirmar com confian\u00e7a que o objeto se comporta linearmente dentro da faixa considerada de desbalanceamentos.<\/p>\n\n <h3 class=\"vma-h3\">Etapas para o Balanceamento de um Objeto Linear<\/h3>\n <ol>\n <li><strong>Medi\u00e7\u00e3o da Vibra\u00e7\u00e3o Inicial:<\/strong> O primeiro passo \u00e9 medir a vibra\u00e7\u00e3o em seu estado inicial. A amplitude e o \u00e2ngulo de vibra\u00e7\u00e3o, que indicam a dire\u00e7\u00e3o do desbalanceamento, s\u00e3o determinados.<\/li>\n <li><strong>Instala\u00e7\u00e3o de uma Massa de Teste:<\/strong> Uma massa de peso conhecido \u00e9 instalada no rotor. Isso ajuda a compreender como o objeto reage a cargas adicionais e permite que os par\u00e2metros de vibra\u00e7\u00e3o sejam calculados.<\/li>\n <li><strong>Remedi\u00e7\u00e3o da Vibra\u00e7\u00e3o:<\/strong> Ap\u00f3s instalar a massa de teste, novos par\u00e2metros de vibra\u00e7\u00e3o s\u00e3o medidos. Ao compar\u00e1-los com os valores iniciais, \u00e9 poss\u00edvel determinar como a massa afeta o sistema.<\/li>\n <li><strong>C\u00e1lculo da Massa Corretiva:<\/strong> Com base nos dados de medi\u00e7\u00e3o, a massa e o \u00e2ngulo de instala\u00e7\u00e3o da massa de corre\u00e7\u00e3o s\u00e3o determinados. Essa massa \u00e9 colocada no rotor para eliminar o desbalanceamento.<\/li>\n <li><strong>Verifica\u00e7\u00e3o Final:<\/strong> Ap\u00f3s instalar a massa de corre\u00e7\u00e3o, a vibra\u00e7\u00e3o deve ser significativamente reduzida. Se a vibra\u00e7\u00e3o residual ainda exceder o n\u00edvel aceit\u00e1vel, o procedimento pode ser repetido.<\/li>\n <\/ol>\n\n <div class=\"vma-note\">\n <p><span class=\"vma-kbd\">Nota:<\/span> Os objetos lineares servem como modelos ideais para estudar e aplicar praticamente m\u00e9todos de balanceamento. Suas propriedades permitem que engenheiros e diagnosticiadores se concentrem no desenvolvimento de habilidades b\u00e1sicas e na compreens\u00e3o dos princ\u00edpios fundamentais do trabalho com sistemas de rotores. Embora sua aplica\u00e7\u00e3o na pr\u00e1tica real seja limitada, o estudo de objetos lineares permanece um passo importante no avan\u00e7o da vibra\u00e7\u00e3o diagn\u00f3stica e do balanceamento.<\/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\" data-aos=\"fade-up\" >\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\/pt-br\/product\/balanset-1\/\" 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\/pt-br\/product\/balanset-1\/\" title=\"Portable balancer & Vibration analyzer Balanset-1A\">\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\/09\/77-e1693745667801-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A full kit portable balancer and vibration analyzer\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-18x12.webp 18w, 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\/pt-br\/product-category\/devices\/\" rel=\"tag\">Dispositivos<\/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\/pt-br\/product\/balanset-1\/\" title=\"Portable balancer & Vibration analyzer Balanset-1A\">Balanceador port\u00e1til & Analisador de vibra\u00e7\u00e3o 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 class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">€<\/span>1,975.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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 product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"986\" data-product_sku=\"BS-1\" aria-label=\"Adicione ao carrinho: \u201cPortable balancer & Vibration analyzer Balanset-1A\u201d\" rel=\"nofollow\" data-success_message=\"\u201cPortable balancer & Vibration analyzer Balanset-1A\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_986\" 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\/pt-br\/product\/vibration-sensor\/\" 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\/pt-br\/product\/vibration-sensor\/\" title=\"Sensor de vibra\u00e7\u00e3o\">\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\/pt-br\/product-category\/parts\/\" rel=\"tag\">Pe\u00e7as<\/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\/pt-br\/product\/vibration-sensor\/\" title=\"Sensor de vibra\u00e7\u00e3o\">Sensor de vibra\u00e7\u00e3o<\/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\">€<\/span>90.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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=\"Adicione ao carrinho: \u201cVibration sensor\u201d\" rel=\"nofollow\" data-success_message=\"\u201cVibration sensor\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/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\/pt-br\/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\/pt-br\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"Sensor \u00d3ptico (Tac\u00f4metro a Laser)\">\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=\"Sensor \u00d3ptico (Tac\u00f4metro a Laser)\" 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\/pt-br\/product-category\/parts\/\" rel=\"tag\">Pe\u00e7as<\/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\/pt-br\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"Sensor \u00d3ptico (Tac\u00f4metro a Laser)\">Sensor \u00d3ptico (Tac\u00f4metro a Laser)<\/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\">€<\/span>124.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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=\"Adicione ao carrinho: \u201cOptical Sensor (Laser Tachometer)\u201d\" rel=\"nofollow\" data-success_message=\"\u201cOptical Sensor (Laser Tachometer)\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/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\/pt-br\/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\/pt-br\/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\/pt-br\/product-category\/devices\/\" rel=\"tag\">Dispositivos<\/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\/pt-br\/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\">€<\/span>6,803.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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=\"Adicione ao carrinho: \u201cBalanset-4\u201d\" rel=\"nofollow\" data-success_message=\"\u201cBalanset-4\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/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\/pt-br\/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\/pt-br\/product\/magnet-stand\/\" title=\"Suporte Magn\u00e9tico Insize-60-kgf\">\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\/pt-br\/product-category\/parts\/\" rel=\"tag\">Pe\u00e7as<\/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\/pt-br\/product\/magnet-stand\/\" title=\"Suporte Magn\u00e9tico Insize-60-kgf\">Suporte Magn\u00e9tico Insize-60-kgf<\/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 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href=\"https:\/\/vibromera.eu\/pt-br\/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\/pt-br\/product\/dynamic-balancer-balanset-1a\/\" title=\"Balanceador din\u00e2mico \u201cBalanset-1A\u201d OEM\">\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\/pt-br\/product-category\/devices\/\" rel=\"tag\">Dispositivos<\/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\/pt-br\/product\/dynamic-balancer-balanset-1a\/\" title=\"Balanceador din\u00e2mico \u201cBalanset-1A\u201d OEM\">Balanceador din\u00e2mico \u201cBalanset-1A\u201d OEM<\/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\">€<\/span>1,735.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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=\"Adicione ao carrinho: \u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d\" rel=\"nofollow\" data-success_message=\"\u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/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\">Objetos N\u00e3o Lineares: Quando a Teoria Diverge da Pr\u00e1tica<\/h2>\n <h3 class=\"vma-h3\">O Que \u00c9 um Objeto N\u00e3o Linear?<\/h3>\n <p>Um objeto n\u00e3o linear \u00e9 um sistema onde a amplitude de vibra\u00e7\u00e3o n\u00e3o \u00e9 proporcional \u00e0 magnitude do desbalanceamento. Diferentemente dos objetos lineares, onde a rela\u00e7\u00e3o entre vibra\u00e7\u00e3o e massa de desbalanceamento \u00e9 representada por uma linha reta, em sistemas n\u00e3o lineares essa rela\u00e7\u00e3o pode seguir trajet\u00f3rias complexas.<\/p>\n <p>No mundo real, nem todos os objetos se comportam linearmente. Objetos n\u00e3o lineares exibem uma rela\u00e7\u00e3o entre desbalanceamento e vibra\u00e7\u00e3o que n\u00e3o \u00e9 diretamente proporcional. Isso significa que o coeficiente de influ\u00eancia n\u00e3o \u00e9 constante e pode variar dependendo de v\u00e1rios fatores, como:<\/p>\n <ul>\n <li><strong>Magnitude do Desbalanceamento:<\/strong> Increasing the imbalance can change the stiffness of the rotor's supports, leading to nonlinear changes in vibration.<\/li>\n <li><strong>Velocidade de Rota\u00e7\u00e3o:<\/strong> Diferentes fen\u00f4menos de resson\u00e2ncia podem ser excitados em velocidades de rota\u00e7\u00e3o vari\u00e1veis, resultando tamb\u00e9m em comportamento n\u00e3o linear.<\/li>\n <li><strong>Presen\u00e7a de Folgas e Espa\u00e7os:<\/strong> Folgas e jogos em rolamentos e outras conex\u00f5es podem causar mudan\u00e7as abruptas na vibra\u00e7\u00e3o sob certas condi\u00e7\u00f5es.<\/li>\n <li><strong>Temperatura:<\/strong> Mudan\u00e7as de temperatura podem afetar as propriedades dos materiais e, consequentemente, as caracter\u00edsticas de vibra\u00e7\u00e3o do objeto.<\/li>\n <li><strong>Cargas externas:<\/strong> Cargas externas atuando sobre o rotor podem alterar suas caracter\u00edsticas din\u00e2micas e levar a um comportamento n\u00e3o linear.<\/li>\n <\/ul>\n\n <h3 class=\"vma-h3\">Por que os objetos n\u00e3o lineares s\u00e3o desafiadores?<\/h3>\n <p>A n\u00e3o linearidade introduz muitas vari\u00e1veis no processo de balanceamento. O trabalho bem-sucedido com objetos n\u00e3o lineares requer mais medi\u00e7\u00f5es e an\u00e1lises mais complexas. Por exemplo, os m\u00e9todos padr\u00e3o aplic\u00e1veis a objetos lineares nem sempre produzem resultados precisos para sistemas n\u00e3o lineares. Isso exige uma compreens\u00e3o mais profunda da f\u00edsica do processo e o uso de m\u00e9todos de diagn\u00f3stico especializados.<\/p>\n <\/section>\n\n <section id=\"nonlinear-signs\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Sinais de n\u00e3o linearidade<\/h2>\n <p>Um objeto n\u00e3o linear pode ser identificado pelos seguintes sinais:<\/p>\n <ul>\n <li><strong>Mudan\u00e7as de vibra\u00e7\u00e3o n\u00e3o proporcionais:<\/strong> \u00c0 medida que o desbalanceamento aumenta, a vibra\u00e7\u00e3o pode crescer mais r\u00e1pido ou mais devagar do que o esperado para um objeto linear.<\/li>\n <li><strong>Deslocamento de fase na vibra\u00e7\u00e3o:<\/strong> A fase da vibra\u00e7\u00e3o pode mudar de forma imprevis\u00edvel com varia\u00e7\u00f5es no desbalanceamento ou na velocidade de rota\u00e7\u00e3o.<\/li>\n <li><strong>Presen\u00e7a de harm\u00f4nicos e subharm\u00f4nicos:<\/strong> O espectro de vibra\u00e7\u00e3o pode exibir harm\u00f4nicos superiores (m\u00faltiplos da frequ\u00eancia de rota\u00e7\u00e3o) e subharm\u00f4nicos (fra\u00e7\u00f5es da frequ\u00eancia de rota\u00e7\u00e3o), indicando efeitos n\u00e3o lineares.<\/li>\n <li><strong>Histerese:<\/strong> A amplitude da vibra\u00e7\u00e3o pode depender n\u00e3o apenas do valor atual do desbalanceamento, mas tamb\u00e9m de seu hist\u00f3rico. Por exemplo, quando o desbalanceamento \u00e9 aumentado e depois diminu\u00eddo de volta ao seu valor inicial, a amplitude da vibra\u00e7\u00e3o pode n\u00e3o retornar ao seu n\u00edvel original.<\/li>\n <\/ul>\n <p>A n\u00e3o linearidade introduz muitas vari\u00e1veis no processo de balanceamento. S\u00e3o necess\u00e1rias mais medi\u00e7\u00f5es e an\u00e1lises complexas para uma opera\u00e7\u00e3o bem-sucedida. Por exemplo, os m\u00e9todos padr\u00e3o aplic\u00e1veis a objetos lineares nem sempre produzem resultados precisos para sistemas n\u00e3o lineares. Isso exige uma compreens\u00e3o mais profunda da f\u00edsica do processo e o uso de m\u00e9todos de diagn\u00f3stico especializados.<\/p>\n <\/section>\n\n <section id=\"nonlinear-graph\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Representa\u00e7\u00e3o gr\u00e1fica da n\u00e3o linearidade<\/h2>\n <p>Em um gr\u00e1fico de vibra\u00e7\u00e3o versus desbalanceamento, a n\u00e3o linearidade \u00e9 evidente nos desvios de uma linha reta. O gr\u00e1fico pode apresentar curvas, curvaturas, la\u00e7os de histerese e outras caracter\u00edsticas que indicam uma rela\u00e7\u00e3o complexa entre desbalanceamento e vibra\u00e7\u00e3o.<\/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=\"Gr\u00e1fico 2. Objeto n\u00e3o linear\" width=\"750\" height=\"598\" \/>\n <\/a>\n <p class=\"vma-caption\"><strong>Gr\u00e1fico 2. Objeto n\u00e3o linear<\/strong><\/p>\n <p class=\"vma-caption\"><strong>50g; 40\u03bcm (yellow), 100g; 54.7\u03bcm (blue).<\/strong><\/p>\n <\/div>\n\n <p>Este objeto apresenta dois segmentos, duas linhas retas. Para desbalanceamentos menores que 50 gramas, o gr\u00e1fico reflete as propriedades de um objeto linear, mantendo a proporcionalidade entre o desbalanceamento em gramas e a amplitude de vibra\u00e7\u00e3o em microns. Para desbalanceamentos maiores que 50 gramas, o crescimento da amplitude de vibra\u00e7\u00e3o desacelera.<\/p>\n <\/section>\n\n <section id=\"nonlinear-examples\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Exemplos de objetos n\u00e3o lineares<\/h2>\n <p>Exemplos de objetos n\u00e3o lineares no contexto do balanceamento incluem:<\/p>\n <ul>\n <li><strong>Rotores com trincas:<\/strong> Trincas no rotor podem levar a mudan\u00e7as n\u00e3o lineares na rigidez e, como resultado, a uma rela\u00e7\u00e3o n\u00e3o linear entre vibra\u00e7\u00e3o e desbalanceamento.<\/li>\n <li><strong>Rotores com folgas nos rolamentos:<\/strong> Folgas nos rolamentos podem causar mudan\u00e7as abruptas na vibra\u00e7\u00e3o sob certas condi\u00e7\u00f5es.<\/li>\n <li><strong>Rotores com elementos el\u00e1sticos n\u00e3o lineares:<\/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\">Tipos de n\u00e3o linearidade<\/h2>\n <h3 class=\"vma-h3\">1. N\u00e3o linearidade macia-r\u00edgida<\/h3>\n <p>Nesses sistemas, observam-se dois segmentos: macio e r\u00edgido. No segmento macio, o comportamento assemelha-se \u00e0 linearidade, onde a amplitude da vibra\u00e7\u00e3o aumenta proporcionalmente \u00e0 massa de desbalanceamento. No entanto, ap\u00f3s um certo limite (ponto de quebra), o sistema transita para um modo r\u00edgido, onde o crescimento da amplitude desacelera.<\/p>\n <h3 class=\"vma-h3\">2. N\u00e3o linearidade el\u00e1stica<\/h3>\n <p>Mudan\u00e7as na rigidez dos apoios ou contatos dentro do sistema tornam a rela\u00e7\u00e3o vibra\u00e7\u00e3o-desbalanceamento complexa. Por exemplo, a vibra\u00e7\u00e3o pode aumentar ou diminuir subitamente ao cruzar limiares espec\u00edficos de carga.<\/p>\n <h3 class=\"vma-h3\">3. N\u00e3o linearidade induzida por atrito<\/h3>\n <p>Em sistemas com atrito significativo (por exemplo, em rolamentos), a amplitude da vibra\u00e7\u00e3o pode ser imprevis\u00edvel. O atrito pode reduzir a vibra\u00e7\u00e3o em uma faixa de velocidade e amplific\u00e1-la em outra.<\/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\">Balanceamento de objetos n\u00e3o lineares: uma tarefa complexa com solu\u00e7\u00f5es n\u00e3o convencionais<\/h2>\n <p>O balanceamento de objetos n\u00e3o lineares \u00e9 uma tarefa desafiadora que requer m\u00e9todos e abordagens especializados. O m\u00e9todo padr\u00e3o de massa de teste, desenvolvido para objetos lineares, pode produzir resultados err\u00f4neos ou ser totalmente inaplic\u00e1vel.<\/p>\n\n <h3 class=\"vma-h3\">M\u00e9todos de balanceamento para objetos n\u00e3o lineares<\/h3>\n <ul>\n <li><strong>Balanceamento passo a passo:<\/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>Balanceamento em m\u00faltiplas velocidades:<\/strong> Este m\u00e9todo aborda os efeitos de fen\u00f4menos de resson\u00e2ncia em diferentes velocidades de rota\u00e7\u00e3o. O balanceamento \u00e9 realizado em v\u00e1rias velocidades pr\u00f3ximas \u00e0 resson\u00e2ncia, permitindo uma redu\u00e7\u00e3o mais uniforme da vibra\u00e7\u00e3o em toda a faixa de velocidade de opera\u00e7\u00e3o.<\/li>\n <li><strong>Uso de modelos matem\u00e1ticos:<\/strong> Para objetos n\u00e3o lineares complexos, podem ser empregados modelos matem\u00e1ticos que descrevem a din\u00e2mica do rotor, levando em conta os efeitos n\u00e3o lineares. Esses modelos ajudam a prever o comportamento do objeto sob v\u00e1rias condi\u00e7\u00f5es e a determinar os par\u00e2metros de balanceamento ideais.<\/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\">Como balancear objetos n\u00e3o lineares usando uma ferramenta projetada para objetos lineares<\/h2>\n <p>Esta \u00e9 uma boa pergunta. Meu m\u00e9todo pessoal para balancear tais objetos come\u00e7a com a repara\u00e7\u00e3o do mecanismo: substitui\u00e7\u00e3o de rolamentos, soldagem de trincas, aperto de parafusos, verifica\u00e7\u00e3o de \u00e2ncoras ou isoladores de vibra\u00e7\u00e3o e confirma\u00e7\u00e3o de que o rotor n\u00e3o atrita contra elementos estruturais estacion\u00e1rios.<\/p>\n <p>Em seguida, identifico as frequ\u00eancias de resson\u00e2ncia, pois \u00e9 imposs\u00edvel balancear um rotor em velocidades pr\u00f3ximas \u00e0 resson\u00e2ncia. Para isso, utilizo o m\u00e9todo de impacto para determina\u00e7\u00e3o da resson\u00e2ncia ou um gr\u00e1fico de parada por in\u00e9rcia do rotor.<\/p>\n <p>Then, I determine the sensor's position on the mechanism: vertical, horizontal, or at an angle.<\/p>\n <p>Ap\u00f3s as rodadas de teste, o dispositivo indica o \u00e2ngulo e o peso das cargas de corre\u00e7\u00e3o. Reduzo pela metade o peso da carga de corre\u00e7\u00e3o, mas utilizo os \u00e2ngulos sugeridos pelo dispositivo para a coloca\u00e7\u00e3o no rotor. Se a vibra\u00e7\u00e3o residual ap\u00f3s a corre\u00e7\u00e3o ainda ultrapassar o n\u00edvel admiss\u00edvel, realizo outra rodada do rotor. Naturalmente, isso leva mais tempo, mas os resultados \u00e0s vezes s\u00e3o inspiradores.<\/p>\n <\/section>\n\n <section id=\"art-science\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">A Arte e a Ci\u00eancia do Balanceamento de Equipamentos Rotativos<\/h2>\n <p>O balanceamento de equipamentos rotativos \u00e9 um processo complexo que combina elementos de ci\u00eancia e arte. Para objetos lineares, o balanceamento envolve c\u00e1lculos relativamente simples e m\u00e9todos padr\u00e3o. No entanto, o trabalho com objetos n\u00e3o lineares exige um profundo entendimento da din\u00e2mica de rotores, a capacidade de analisar sinais de vibra\u00e7\u00e3o e a habilidade de escolher as estrat\u00e9gias de balanceamento mais eficazes.<\/p>\n <p>Experi\u00eancia, intui\u00e7\u00e3o e melhoria cont\u00ednua das habilidades s\u00e3o o que fazem de um balanceador um verdadeiro mestre de sua arte. Afinal, a qualidade do balanceamento n\u00e3o apenas determina a efici\u00eancia e a confiabilidade da opera\u00e7\u00e3o do equipamento, mas tamb\u00e9m garante a seguran\u00e7a das pessoas.<\/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\/pt-br\/wp-json\/wp\/v2\/posts\/5199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/comments?post=5199"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/posts\/5199\/revisions"}],"predecessor-version":[{"id":20911,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/posts\/5199\/revisions\/20911"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/media\/5200"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/media?parent=5199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/categories?post=5199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/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\">Conte\u00fado<\/div>\n <ol>\n <li><a href=\"#intro\">Vis\u00e3o Geral<\/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\">Vis\u00e3o Geral<\/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\">Vibra\u00e7\u00f5es Lineares e N\u00e3o Lineares, Suas Caracter\u00edsticas e M\u00e9todos de Balanceamento<\/h2>\n <p>O balanceamento bem-sucedido exige compreender como um objeto reage \u00e0 adi\u00e7\u00e3o ou remo\u00e7\u00e3o de massa. Nesse contexto, os conceitos de objetos lineares e n\u00e3o lineares desempenham um papel fundamental. Compreender se um objeto \u00e9 linear ou n\u00e3o linear permite a sele\u00e7\u00e3o da estrat\u00e9gia de balanceamento correta e ajuda a alcan\u00e7ar o resultado desejado.<\/p>\n <p>Os objetos lineares ocupam um lugar especial nessa \u00e1rea devido \u00e0 sua previsibilidade e estabilidade. Eles permitem o uso de m\u00e9todos de diagn\u00f3stico e balanceamento simples e confi\u00e1veis, tornando seu estudo um passo importante na vibra\u00e7\u00e3o diagn\u00f3stica.<\/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\">O Que S\u00e3o Objetos Lineares?<\/h2>\n <p>Um objeto linear \u00e9 um sistema onde a vibra\u00e7\u00e3o \u00e9 diretamente proporcional \u00e0 magnitude do desbalanceamento.<\/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>Diferentemente dos sistemas n\u00e3o lineares, onde o comportamento de um objeto pode variar dependendo de muitos fatores, os objetos lineares permitem um alto n\u00edvel de precis\u00e3o com esfor\u00e7o m\u00ednimo.<\/p>\n <p>Al\u00e9m disso, eles servem como base para o treinamento e pr\u00e1tica de balanceadores. Compreender os princ\u00edpios dos objetos lineares ajuda a desenvolver habilidades que podem ser aplicadas posteriormente a sistemas mais complexos.<\/p>\n <\/section>\n\n <section id=\"linearity-graph\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Representa\u00e7\u00e3o Gr\u00e1fica da Linearidade<\/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=\"Gr\u00e1fico 1: A Rela\u00e7\u00e3o Entre a Amplitude de Vibra\u00e7\u00e3o (\u00b5m) e a Massa Desbalanceada (g)\" width=\"750\" height=\"589\" \/>\n <\/a>\n <p class=\"vma-caption\"><strong>Gr\u00e1fico 1: A Rela\u00e7\u00e3o Entre a Amplitude de Vibra\u00e7\u00e3o (\u00b5m) e a Massa Desbalanceada (g)<\/strong><\/p>\n <\/div>\n\n <p>O Gr\u00e1fico 1 ilustra a rela\u00e7\u00e3o entre a amplitude de vibra\u00e7\u00e3o (\u00b5m) de um objeto de balanceamento linear e a massa desbalanceada (g) do rotor. O coeficiente de proporcionalidade \u00e9 0,5 \u00b5m\/g. Basta dividir 300 por 600 para obter 0,5 \u00b5m\/g. Para uma massa desbalanceada de 800 g (MD=800 g), a vibra\u00e7\u00e3o ser\u00e1 800 g * 0,5 \u00b5m\/g = 400 \u00b5m. Observe que isso se aplica a uma velocidade constante do rotor. Em uma velocidade de rota\u00e7\u00e3o diferente, o coeficiente ser\u00e1 diferente.<\/p>\n <p>Esse coeficiente de proporcionalidade \u00e9 chamado de coeficiente de influ\u00eancia (coeficiente de sensibilidade) e tem uma dimens\u00e3o de \u00b5m\/g ou, em casos envolvendo desbalanceamento, \u00b5m\/(g*mm), onde (g*mm) \u00e9 a unidade de desbalanceamento. Conhecendo o coeficiente de influ\u00eancia (CI), tamb\u00e9m \u00e9 poss\u00edvel resolver o problema inverso, ou seja, determinar a massa desbalanceada (MD) com base na magnitude da vibra\u00e7\u00e3o. Para isso, divida a amplitude de vibra\u00e7\u00e3o pelo CI.<\/p>\n <p>Por exemplo, se a vibra\u00e7\u00e3o medida for 300 \u00b5m e o coeficiente conhecido for CI=0,5 \u00b5m\/g, divida 300 por 0,5 para obter 600 g (MD=600 g).<\/p>\n <\/section>\n\n <section id=\"influence-coefficient\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Coeficiente de Influ\u00eancia (CI): Par\u00e2metro Chave dos Objetos Lineares<\/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\">Problema Direto:<\/h3>\n <div class=\"vma-formula\">Vibration Amplitude (\u00b5m) = IC (\u00b5m\/g) * Unbalanced Mass (g)<\/div>\n\n <h3 class=\"vma-h3\">Problema Inverso:<\/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\">Fase de Vibra\u00e7\u00e3o em Objetos Lineares<\/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>Assim, conhecendo o argumento do CI e medindo a fase de vibra\u00e7\u00e3o, \u00e9 poss\u00edvel determinar o \u00e2ngulo de instala\u00e7\u00e3o da massa desbalanceada. Isso permite n\u00e3o apenas o c\u00e1lculo da magnitude da massa corretiva, mas tamb\u00e9m sua coloca\u00e7\u00e3o precisa no rotor para alcan\u00e7ar o balanceamento \u00f3timo.<\/p>\n <\/section>\n\n <section id=\"linear-balancing-steps\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Balanceamento de Objetos Lineares<\/h2>\n <p>\u00c9 importante observar que, para um objeto linear, o coeficiente de influ\u00eancia (CI) determinado dessa maneira n\u00e3o depende da magnitude ou do \u00e2ngulo de instala\u00e7\u00e3o da massa de teste, nem da vibra\u00e7\u00e3o inicial. Esta \u00e9 uma caracter\u00edstica fundamental da linearidade. Se o CI permanecer inalterado quando os par\u00e2metros da massa de teste ou a vibra\u00e7\u00e3o inicial forem alterados, pode-se afirmar com confian\u00e7a que o objeto se comporta linearmente dentro da faixa considerada de desbalanceamentos.<\/p>\n\n <h3 class=\"vma-h3\">Etapas para o Balanceamento de um Objeto Linear<\/h3>\n <ol>\n <li><strong>Medi\u00e7\u00e3o da Vibra\u00e7\u00e3o Inicial:<\/strong> O primeiro passo \u00e9 medir a vibra\u00e7\u00e3o em seu estado inicial. A amplitude e o \u00e2ngulo de vibra\u00e7\u00e3o, que indicam a dire\u00e7\u00e3o do desbalanceamento, s\u00e3o determinados.<\/li>\n <li><strong>Instala\u00e7\u00e3o de uma Massa de Teste:<\/strong> Uma massa de peso conhecido \u00e9 instalada no rotor. Isso ajuda a compreender como o objeto reage a cargas adicionais e permite que os par\u00e2metros de vibra\u00e7\u00e3o sejam calculados.<\/li>\n <li><strong>Remedi\u00e7\u00e3o da Vibra\u00e7\u00e3o:<\/strong> Ap\u00f3s instalar a massa de teste, novos par\u00e2metros de vibra\u00e7\u00e3o s\u00e3o medidos. Ao compar\u00e1-los com os valores iniciais, \u00e9 poss\u00edvel determinar como a massa afeta o sistema.<\/li>\n <li><strong>C\u00e1lculo da Massa Corretiva:<\/strong> Com base nos dados de medi\u00e7\u00e3o, a massa e o \u00e2ngulo de instala\u00e7\u00e3o da massa de corre\u00e7\u00e3o s\u00e3o determinados. Essa massa \u00e9 colocada no rotor para eliminar o desbalanceamento.<\/li>\n <li><strong>Verifica\u00e7\u00e3o Final:<\/strong> Ap\u00f3s instalar a massa de corre\u00e7\u00e3o, a vibra\u00e7\u00e3o deve ser significativamente reduzida. Se a vibra\u00e7\u00e3o residual ainda exceder o n\u00edvel aceit\u00e1vel, o procedimento pode ser repetido.<\/li>\n <\/ol>\n\n <div class=\"vma-note\">\n <p><span class=\"vma-kbd\">Nota:<\/span> Os objetos lineares servem como modelos ideais para estudar e aplicar praticamente m\u00e9todos de balanceamento. Suas propriedades permitem que engenheiros e diagnosticiadores se concentrem no desenvolvimento de habilidades b\u00e1sicas e na compreens\u00e3o dos princ\u00edpios fundamentais do trabalho com sistemas de rotores. Embora sua aplica\u00e7\u00e3o na pr\u00e1tica real seja limitada, o estudo de objetos lineares permanece um passo importante no avan\u00e7o da vibra\u00e7\u00e3o diagn\u00f3stica e do balanceamento.<\/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\" data-aos=\"fade-up\" >\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\/pt-br\/product\/balanset-1\/\" 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\/pt-br\/product\/balanset-1\/\" title=\"Portable balancer & Vibration analyzer Balanset-1A\">\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\/09\/77-e1693745667801-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Balanset-1A full kit portable balancer and vibration analyzer\" srcset=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-230x153.webp 230w, https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/09\/77-e1693745667801-18x12.webp 18w, 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\/pt-br\/product-category\/devices\/\" rel=\"tag\">Dispositivos<\/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\/pt-br\/product\/balanset-1\/\" title=\"Portable balancer & Vibration analyzer Balanset-1A\">Balanceador port\u00e1til & Analisador de vibra\u00e7\u00e3o 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 class=\"price\"><h4><span class=\"woocommerce-Price-amount amount\"><span class=\"woocommerce-Price-currencySymbol\">€<\/span>1,975.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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 product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"986\" data-product_sku=\"BS-1\" aria-label=\"Adicione ao carrinho: \u201cPortable balancer & Vibration analyzer Balanset-1A\u201d\" rel=\"nofollow\" data-success_message=\"\u201cPortable balancer & Vibration analyzer Balanset-1A\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_986\" 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\/pt-br\/product\/vibration-sensor\/\" 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\/pt-br\/product\/vibration-sensor\/\" title=\"Sensor de vibra\u00e7\u00e3o\">\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\/pt-br\/product-category\/parts\/\" rel=\"tag\">Pe\u00e7as<\/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\/pt-br\/product\/vibration-sensor\/\" title=\"Sensor de vibra\u00e7\u00e3o\">Sensor de vibra\u00e7\u00e3o<\/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\">€<\/span>90.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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=\"Adicione ao carrinho: \u201cVibration sensor\u201d\" rel=\"nofollow\" data-success_message=\"\u201cVibration sensor\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/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\/pt-br\/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\/pt-br\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"Sensor \u00d3ptico (Tac\u00f4metro a Laser)\">\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=\"Sensor \u00d3ptico (Tac\u00f4metro a Laser)\" 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\/pt-br\/product-category\/parts\/\" rel=\"tag\">Pe\u00e7as<\/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\/pt-br\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"Sensor \u00d3ptico (Tac\u00f4metro a Laser)\">Sensor \u00d3ptico (Tac\u00f4metro a Laser)<\/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\">€<\/span>124.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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=\"Adicione ao carrinho: \u201cOptical Sensor (Laser Tachometer)\u201d\" rel=\"nofollow\" data-success_message=\"\u201cOptical Sensor (Laser Tachometer)\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/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\/pt-br\/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\/pt-br\/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\/pt-br\/product-category\/devices\/\" rel=\"tag\">Dispositivos<\/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\/pt-br\/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\">€<\/span>6,803.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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=\"Adicione ao carrinho: \u201cBalanset-4\u201d\" rel=\"nofollow\" data-success_message=\"\u201cBalanset-4\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/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\/pt-br\/product\/magnet-stand\/\" class=\"woocommerce-LoopProduct-link 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class=\"woocommerce-Price-currencySymbol\">€<\/span>46.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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\" 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src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"Fita refletiva\" 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\/pt-br\/product-category\/parts\/\" rel=\"tag\">Pe\u00e7as<\/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\/pt-br\/product\/reflective-tape\/\" title=\"Fita refletiva\">Fita refletiva<\/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\">€<\/span>10.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" class=\"fas fa-cart-plus\" 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href=\"https:\/\/vibromera.eu\/pt-br\/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\/pt-br\/product\/dynamic-balancer-balanset-1a\/\" title=\"Balanceador din\u00e2mico \u201cBalanset-1A\u201d OEM\">\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\/pt-br\/product-category\/devices\/\" rel=\"tag\">Dispositivos<\/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\/pt-br\/product\/dynamic-balancer-balanset-1a\/\" title=\"Balanceador din\u00e2mico \u201cBalanset-1A\u201d OEM\">Balanceador din\u00e2mico \u201cBalanset-1A\u201d OEM<\/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\">€<\/span>1,735.00<\/span> + IVA (se aplic\u00e1vel)<\/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=\"\/pt-br\/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=\"Adicionar ao carrinho\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Adicionar ao carrinho\" 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=\"\/pt-br\/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=\"Adicione ao carrinho: \u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d\" rel=\"nofollow\" data-success_message=\"\u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d foi adicionado ao seu carrinho\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Adicionar ao carrinho<\/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\">Objetos N\u00e3o Lineares: Quando a Teoria Diverge da Pr\u00e1tica<\/h2>\n <h3 class=\"vma-h3\">O Que \u00c9 um Objeto N\u00e3o Linear?<\/h3>\n <p>Um objeto n\u00e3o linear \u00e9 um sistema onde a amplitude de vibra\u00e7\u00e3o n\u00e3o \u00e9 proporcional \u00e0 magnitude do desbalanceamento. Diferentemente dos objetos lineares, onde a rela\u00e7\u00e3o entre vibra\u00e7\u00e3o e massa de desbalanceamento \u00e9 representada por uma linha reta, em sistemas n\u00e3o lineares essa rela\u00e7\u00e3o pode seguir trajet\u00f3rias complexas.<\/p>\n <p>No mundo real, nem todos os objetos se comportam linearmente. Objetos n\u00e3o lineares exibem uma rela\u00e7\u00e3o entre desbalanceamento e vibra\u00e7\u00e3o que n\u00e3o \u00e9 diretamente proporcional. Isso significa que o coeficiente de influ\u00eancia n\u00e3o \u00e9 constante e pode variar dependendo de v\u00e1rios fatores, como:<\/p>\n <ul>\n <li><strong>Magnitude do Desbalanceamento:<\/strong> Increasing the imbalance can change the stiffness of the rotor's supports, leading to nonlinear changes in vibration.<\/li>\n <li><strong>Velocidade de Rota\u00e7\u00e3o:<\/strong> Diferentes fen\u00f4menos de resson\u00e2ncia podem ser excitados em velocidades de rota\u00e7\u00e3o vari\u00e1veis, resultando tamb\u00e9m em comportamento n\u00e3o linear.<\/li>\n <li><strong>Presen\u00e7a de Folgas e Espa\u00e7os:<\/strong> Folgas e jogos em rolamentos e outras conex\u00f5es podem causar mudan\u00e7as abruptas na vibra\u00e7\u00e3o sob certas condi\u00e7\u00f5es.<\/li>\n <li><strong>Temperatura:<\/strong> Mudan\u00e7as de temperatura podem afetar as propriedades dos materiais e, consequentemente, as caracter\u00edsticas de vibra\u00e7\u00e3o do objeto.<\/li>\n <li><strong>Cargas externas:<\/strong> Cargas externas atuando sobre o rotor podem alterar suas caracter\u00edsticas din\u00e2micas e levar a um comportamento n\u00e3o linear.<\/li>\n <\/ul>\n\n <h3 class=\"vma-h3\">Por que os objetos n\u00e3o lineares s\u00e3o desafiadores?<\/h3>\n <p>A n\u00e3o linearidade introduz muitas vari\u00e1veis no processo de balanceamento. O trabalho bem-sucedido com objetos n\u00e3o lineares requer mais medi\u00e7\u00f5es e an\u00e1lises mais complexas. Por exemplo, os m\u00e9todos padr\u00e3o aplic\u00e1veis a objetos lineares nem sempre produzem resultados precisos para sistemas n\u00e3o lineares. Isso exige uma compreens\u00e3o mais profunda da f\u00edsica do processo e o uso de m\u00e9todos de diagn\u00f3stico especializados.<\/p>\n <\/section>\n\n <section id=\"nonlinear-signs\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Sinais de n\u00e3o linearidade<\/h2>\n <p>Um objeto n\u00e3o linear pode ser identificado pelos seguintes sinais:<\/p>\n <ul>\n <li><strong>Mudan\u00e7as de vibra\u00e7\u00e3o n\u00e3o proporcionais:<\/strong> \u00c0 medida que o desbalanceamento aumenta, a vibra\u00e7\u00e3o pode crescer mais r\u00e1pido ou mais devagar do que o esperado para um objeto linear.<\/li>\n <li><strong>Deslocamento de fase na vibra\u00e7\u00e3o:<\/strong> A fase da vibra\u00e7\u00e3o pode mudar de forma imprevis\u00edvel com varia\u00e7\u00f5es no desbalanceamento ou na velocidade de rota\u00e7\u00e3o.<\/li>\n <li><strong>Presen\u00e7a de harm\u00f4nicos e subharm\u00f4nicos:<\/strong> O espectro de vibra\u00e7\u00e3o pode exibir harm\u00f4nicos superiores (m\u00faltiplos da frequ\u00eancia de rota\u00e7\u00e3o) e subharm\u00f4nicos (fra\u00e7\u00f5es da frequ\u00eancia de rota\u00e7\u00e3o), indicando efeitos n\u00e3o lineares.<\/li>\n <li><strong>Histerese:<\/strong> A amplitude da vibra\u00e7\u00e3o pode depender n\u00e3o apenas do valor atual do desbalanceamento, mas tamb\u00e9m de seu hist\u00f3rico. Por exemplo, quando o desbalanceamento \u00e9 aumentado e depois diminu\u00eddo de volta ao seu valor inicial, a amplitude da vibra\u00e7\u00e3o pode n\u00e3o retornar ao seu n\u00edvel original.<\/li>\n <\/ul>\n <p>A n\u00e3o linearidade introduz muitas vari\u00e1veis no processo de balanceamento. S\u00e3o necess\u00e1rias mais medi\u00e7\u00f5es e an\u00e1lises complexas para uma opera\u00e7\u00e3o bem-sucedida. Por exemplo, os m\u00e9todos padr\u00e3o aplic\u00e1veis a objetos lineares nem sempre produzem resultados precisos para sistemas n\u00e3o lineares. Isso exige uma compreens\u00e3o mais profunda da f\u00edsica do processo e o uso de m\u00e9todos de diagn\u00f3stico especializados.<\/p>\n <\/section>\n\n <section id=\"nonlinear-graph\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Representa\u00e7\u00e3o gr\u00e1fica da n\u00e3o linearidade<\/h2>\n <p>Em um gr\u00e1fico de vibra\u00e7\u00e3o versus desbalanceamento, a n\u00e3o linearidade \u00e9 evidente nos desvios de uma linha reta. O gr\u00e1fico pode apresentar curvas, curvaturas, la\u00e7os de histerese e outras caracter\u00edsticas que indicam uma rela\u00e7\u00e3o complexa entre desbalanceamento e vibra\u00e7\u00e3o.<\/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=\"Gr\u00e1fico 2. Objeto n\u00e3o linear\" width=\"750\" height=\"598\" \/>\n <\/a>\n <p class=\"vma-caption\"><strong>Gr\u00e1fico 2. Objeto n\u00e3o linear<\/strong><\/p>\n <p class=\"vma-caption\"><strong>50g; 40\u03bcm (yellow), 100g; 54.7\u03bcm (blue).<\/strong><\/p>\n <\/div>\n\n <p>Este objeto apresenta dois segmentos, duas linhas retas. Para desbalanceamentos menores que 50 gramas, o gr\u00e1fico reflete as propriedades de um objeto linear, mantendo a proporcionalidade entre o desbalanceamento em gramas e a amplitude de vibra\u00e7\u00e3o em microns. Para desbalanceamentos maiores que 50 gramas, o crescimento da amplitude de vibra\u00e7\u00e3o desacelera.<\/p>\n <\/section>\n\n <section id=\"nonlinear-examples\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">Exemplos de objetos n\u00e3o lineares<\/h2>\n <p>Exemplos de objetos n\u00e3o lineares no contexto do balanceamento incluem:<\/p>\n <ul>\n <li><strong>Rotores com trincas:<\/strong> Trincas no rotor podem levar a mudan\u00e7as n\u00e3o lineares na rigidez e, como resultado, a uma rela\u00e7\u00e3o n\u00e3o linear entre vibra\u00e7\u00e3o e desbalanceamento.<\/li>\n <li><strong>Rotores com folgas nos rolamentos:<\/strong> Folgas nos rolamentos podem causar mudan\u00e7as abruptas na vibra\u00e7\u00e3o sob certas condi\u00e7\u00f5es.<\/li>\n <li><strong>Rotores com elementos el\u00e1sticos n\u00e3o lineares:<\/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\">Tipos de n\u00e3o linearidade<\/h2>\n <h3 class=\"vma-h3\">1. N\u00e3o linearidade macia-r\u00edgida<\/h3>\n <p>Nesses sistemas, observam-se dois segmentos: macio e r\u00edgido. No segmento macio, o comportamento assemelha-se \u00e0 linearidade, onde a amplitude da vibra\u00e7\u00e3o aumenta proporcionalmente \u00e0 massa de desbalanceamento. No entanto, ap\u00f3s um certo limite (ponto de quebra), o sistema transita para um modo r\u00edgido, onde o crescimento da amplitude desacelera.<\/p>\n <h3 class=\"vma-h3\">2. N\u00e3o linearidade el\u00e1stica<\/h3>\n <p>Mudan\u00e7as na rigidez dos apoios ou contatos dentro do sistema tornam a rela\u00e7\u00e3o vibra\u00e7\u00e3o-desbalanceamento complexa. Por exemplo, a vibra\u00e7\u00e3o pode aumentar ou diminuir subitamente ao cruzar limiares espec\u00edficos de carga.<\/p>\n <h3 class=\"vma-h3\">3. N\u00e3o linearidade induzida por atrito<\/h3>\n <p>Em sistemas com atrito significativo (por exemplo, em rolamentos), a amplitude da vibra\u00e7\u00e3o pode ser imprevis\u00edvel. O atrito pode reduzir a vibra\u00e7\u00e3o em uma faixa de velocidade e amplific\u00e1-la em outra.<\/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\">Balanceamento de objetos n\u00e3o lineares: uma tarefa complexa com solu\u00e7\u00f5es n\u00e3o convencionais<\/h2>\n <p>O balanceamento de objetos n\u00e3o lineares \u00e9 uma tarefa desafiadora que requer m\u00e9todos e abordagens especializados. O m\u00e9todo padr\u00e3o de massa de teste, desenvolvido para objetos lineares, pode produzir resultados err\u00f4neos ou ser totalmente inaplic\u00e1vel.<\/p>\n\n <h3 class=\"vma-h3\">M\u00e9todos de balanceamento para objetos n\u00e3o lineares<\/h3>\n <ul>\n <li><strong>Balanceamento passo a passo:<\/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>Balanceamento em m\u00faltiplas velocidades:<\/strong> Este m\u00e9todo aborda os efeitos de fen\u00f4menos de resson\u00e2ncia em diferentes velocidades de rota\u00e7\u00e3o. O balanceamento \u00e9 realizado em v\u00e1rias velocidades pr\u00f3ximas \u00e0 resson\u00e2ncia, permitindo uma redu\u00e7\u00e3o mais uniforme da vibra\u00e7\u00e3o em toda a faixa de velocidade de opera\u00e7\u00e3o.<\/li>\n <li><strong>Uso de modelos matem\u00e1ticos:<\/strong> Para objetos n\u00e3o lineares complexos, podem ser empregados modelos matem\u00e1ticos que descrevem a din\u00e2mica do rotor, levando em conta os efeitos n\u00e3o lineares. Esses modelos ajudam a prever o comportamento do objeto sob v\u00e1rias condi\u00e7\u00f5es e a determinar os par\u00e2metros de balanceamento ideais.<\/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\">Como balancear objetos n\u00e3o lineares usando uma ferramenta projetada para objetos lineares<\/h2>\n <p>Esta \u00e9 uma boa pergunta. Meu m\u00e9todo pessoal para balancear tais objetos come\u00e7a com a repara\u00e7\u00e3o do mecanismo: substitui\u00e7\u00e3o de rolamentos, soldagem de trincas, aperto de parafusos, verifica\u00e7\u00e3o de \u00e2ncoras ou isoladores de vibra\u00e7\u00e3o e confirma\u00e7\u00e3o de que o rotor n\u00e3o atrita contra elementos estruturais estacion\u00e1rios.<\/p>\n <p>Em seguida, identifico as frequ\u00eancias de resson\u00e2ncia, pois \u00e9 imposs\u00edvel balancear um rotor em velocidades pr\u00f3ximas \u00e0 resson\u00e2ncia. Para isso, utilizo o m\u00e9todo de impacto para determina\u00e7\u00e3o da resson\u00e2ncia ou um gr\u00e1fico de parada por in\u00e9rcia do rotor.<\/p>\n <p>Then, I determine the sensor's position on the mechanism: vertical, horizontal, or at an angle.<\/p>\n <p>Ap\u00f3s as rodadas de teste, o dispositivo indica o \u00e2ngulo e o peso das cargas de corre\u00e7\u00e3o. Reduzo pela metade o peso da carga de corre\u00e7\u00e3o, mas utilizo os \u00e2ngulos sugeridos pelo dispositivo para a coloca\u00e7\u00e3o no rotor. Se a vibra\u00e7\u00e3o residual ap\u00f3s a corre\u00e7\u00e3o ainda ultrapassar o n\u00edvel admiss\u00edvel, realizo outra rodada do rotor. Naturalmente, isso leva mais tempo, mas os resultados \u00e0s vezes s\u00e3o inspiradores.<\/p>\n <\/section>\n\n <section id=\"art-science\" class=\"vma-anchor\">\n <h2 class=\"vma-h2\">A Arte e a Ci\u00eancia do Balanceamento de Equipamentos Rotativos<\/h2>\n <p>O balanceamento de equipamentos rotativos \u00e9 um processo complexo que combina elementos de ci\u00eancia e arte. Para objetos lineares, o balanceamento envolve c\u00e1lculos relativamente simples e m\u00e9todos padr\u00e3o. No entanto, o trabalho com objetos n\u00e3o lineares exige um profundo entendimento da din\u00e2mica de rotores, a capacidade de analisar sinais de vibra\u00e7\u00e3o e a habilidade de escolher as estrat\u00e9gias de balanceamento mais eficazes.<\/p>\n <p>Experi\u00eancia, intui\u00e7\u00e3o e melhoria cont\u00ednua das habilidades s\u00e3o o que fazem de um balanceador um verdadeiro mestre de sua arte. Afinal, a qualidade do balanceamento n\u00e3o apenas determina a efici\u00eancia e a confiabilidade da opera\u00e7\u00e3o do equipamento, mas tamb\u00e9m garante a seguran\u00e7a das pessoas.<\/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\/pt-br\/wp-json\/wp\/v2\/posts\/5199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/comments?post=5199"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/posts\/5199\/revisions"}],"predecessor-version":[{"id":20911,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/posts\/5199\/revisions\/20911"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/media\/5200"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/media?parent=5199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/categories?post=5199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/pt-br\/wp-json\/wp\/v2\/tags?post=5199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}