{"id":294,"date":"2025-10-31T00:25:51","date_gmt":"2025-10-31T00:25:51","guid":{"rendered":"https:\/\/vibromera.eu\/glossary\/vector-addition\/"},"modified":"2026-05-23T23:07:17","modified_gmt":"2026-05-23T23:07:17","slug":"vector-addition","status":"publish","type":"glossary","link":"https:\/\/vibromera.eu\/mr\/glossary\/vector-addition\/","title":{"rendered":"Vector Addition in Rotor Balancing Explained"},"content":{"rendered":"<h1>\u0930\u094b\u091f\u0930 \u092c\u0945\u0932\u0928\u094d\u0938\u093f\u0902\u0917\u092e\u0927\u0940\u0932 \u0935\u094d\u0939\u0947\u0915\u094d\u091f\u0930 \u092c\u0947\u0930\u0940\u091c \u0938\u092e\u091c\u0942\u0928 \u0918\u0947\u0923\u0947<\/h1>\n\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\/mr\/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\/mr\/product\/balanset-1\/\" title=\"\u092a\u094b\u0930\u094d\u091f\u0947\u092c\u0932 \u092c\u0945\u0932\u0928\u094d\u0938\u0930 \u0906\u0923\u093f \u0915\u0902\u092a\u0928 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0915 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 \u0938\u0902\u092a\u0942\u0930\u094d\u0923 \u0915\u093f\u091f \u092a\u094b\u0930\u094d\u091f\u0947\u092c\u0932 \u0938\u0902\u0924\u0941\u0932\u0915 \u0906\u0923\u093f \u0915\u0902\u092a\u0928 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0915\" 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\/mr\/product-category\/devices\/\" rel=\"tag\">Devices<\/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\/mr\/product\/balanset-1\/\" title=\"\u092a\u094b\u0930\u094d\u091f\u0947\u092c\u0932 \u092c\u0945\u0932\u0928\u094d\u0938\u0930 \u0906\u0923\u093f \u0915\u0902\u092a\u0928 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0915 Balanset-1A\">\u092a\u094b\u0930\u094d\u091f\u0947\u092c\u0932 \u092c\u0945\u0932\u0947\u0928\u094d\u0938\u0930 &#038; \u0935\u094d\u0939\u093e\u092f\u092c\u094d\u0930\u0947\u0936\u0928 \u0905\u200d\u0945\u0928\u093e\u0932\u093e\u092f\u091d\u0930 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\">&euro;<\/span>1,975.00<\/span> + VAT (\u0932\u093e\u0917\u0942 \u0905\u0938\u0932\u094d\u092f\u093e\u0938)<\/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=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=986\" data-quantity=\"1\" data-product_id=\"986\" data-product_sku=\"BS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?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=\"Add to cart: \u201cPortable balancer &amp; Vibration analyzer Balanset-1A\u201d\" rel=\"nofollow\" data-success_message=\"\u201cPortable balancer &amp; Vibration analyzer Balanset-1A\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_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\/mr\/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\/mr\/product\/vibration-sensor\/\" title=\"\u0915\u0902\u092a\u0928 \u0938\u0902\u0935\u0947\u0926\u0915\">\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 \u0915\u0902\u092a\u0928 \u0938\u0902\u0935\u0947\u0926\u0928\u0936\u0940\u0932 \u091c\u0935\u0933\u0942\u0928\" 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\/mr\/product-category\/parts\/\" rel=\"tag\">Parts<\/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\/mr\/product\/vibration-sensor\/\" title=\"\u0915\u0902\u092a\u0928 \u0938\u0902\u0935\u0947\u0926\u0915\">\u0915\u0902\u092a\u0928 \u0938\u0902\u0935\u0947\u0926\u0915<\/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\">&euro;<\/span>90.00<\/span> + VAT (\u0932\u093e\u0917\u0942 \u0905\u0938\u0932\u094d\u092f\u093e\u0938)<\/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=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=1820\" data-quantity=\"1\" data-product_id=\"1820\" data-product_sku=\"VS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=1820\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1820\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1820\" data-product_sku=\"VS-1\" aria-label=\"Add to cart: \u201cVibration sensor\u201d\" rel=\"nofollow\" data-success_message=\"\u201cVibration sensor\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1820\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/mr\/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\/mr\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"\u0911\u092a\u094d\u091f\u093f\u0915\u0932 \u0938\u0947\u0928\u094d\u0938\u0930 (\u0932\u0947\u091d\u0930 \u091f\u0945\u0915\u094b\u092e\u0940\u091f\u0930)\">\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=\"\u0911\u092a\u094d\u091f\u093f\u0915\u0932 \u0938\u0947\u0928\u094d\u0938\u0930 (\u0932\u0947\u091d\u0930 \u091f\u0945\u0915\u094b\u092e\u0940\u091f\u0930)\" 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\/mr\/product-category\/parts\/\" rel=\"tag\">Parts<\/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\/mr\/product\/optical-sensor-for-balanset-and-arbalance\/\" title=\"\u0911\u092a\u094d\u091f\u093f\u0915\u0932 \u0938\u0947\u0928\u094d\u0938\u0930 (\u0932\u0947\u091d\u0930 \u091f\u0945\u0915\u094b\u092e\u0940\u091f\u0930)\">\u0911\u092a\u094d\u091f\u093f\u0915\u0932 \u0938\u0947\u0928\u094d\u0938\u0930 (\u0932\u0947\u091d\u0930 \u091f\u0945\u0915\u094b\u092e\u0940\u091f\u0930)<\/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\">&euro;<\/span>124.00<\/span> + VAT (\u0932\u093e\u0917\u0942 \u0905\u0938\u0932\u094d\u092f\u093e\u0938)<\/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=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=1832\" data-quantity=\"1\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=1832\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1832\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1832\" data-product_sku=\"Tach-1\" aria-label=\"Add to cart: \u201cOptical Sensor (Laser Tachometer)\u201d\" rel=\"nofollow\" data-success_message=\"\u201cOptical Sensor (Laser Tachometer)\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1832\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/mr\/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\/mr\/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 \u0930\u094b\u091f\u0930 \u0938\u0902\u0924\u0941\u0932\u0928 \u0915\u093f\u091f: \u0935\u0939\u0928 \u0915\u0947\u0938, \u092c\u0939\u0941-\u091a\u0945\u0928\u0932 \u0938\u093f\u0917\u094d\u0928\u0932 \u0915\u0902\u0921\u093f\u0936\u0928\u0930, \u0939\u093e\u0925 \u092a\u0915\u0921\u0928\u0947 \u0935\u093e\u0932\u0940 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0915, \u091a\u0941\u0902\u092c\u0915\u0940\u092f \u0906\u0927\u093e\u0930, \u0915\u0902\u092a\u0928 \u0938\u0902\u0935\u0947\u0926\u0915, \u0906\u0923\u093f \u0915\u0949\u0907\u0932 \u0915\u0947\u092c\u0932.\" 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\/mr\/product-category\/devices\/\" rel=\"tag\">Devices<\/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\/mr\/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\">&euro;<\/span>6,803.00<\/span> + VAT (\u0932\u093e\u0917\u0942 \u0905\u0938\u0932\u094d\u092f\u093e\u0938)<\/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=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=1833\" data-quantity=\"1\" data-product_id=\"1833\" data-product_sku=\"BS-4\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=1833\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1833\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1833\" data-product_sku=\"BS-4\" aria-label=\"Add to cart: \u201cBalanset-4\u201d\" rel=\"nofollow\" data-success_message=\"\u201cBalanset-4\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1833\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div><!-- \/.row --><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\/mr\/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\/mr\/product\/magnet-stand\/\" title=\"\u092e\u0945\u0917\u094d\u0928\u0947\u091f\u093f\u0915 \u0938\u094d\u091f\u0901\u0921 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\/mr\/product-category\/parts\/\" rel=\"tag\">Parts<\/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\/mr\/product\/magnet-stand\/\" title=\"\u092e\u0945\u0917\u094d\u0928\u0947\u091f\u093f\u0915 \u0938\u094d\u091f\u0901\u0921 Insize-60-kgf\">\u092e\u0945\u0917\u094d\u0928\u0947\u091f\u093f\u0915 \u0938\u094d\u091f\u0901\u0921 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 class=\"woocommerce-Price-currencySymbol\">&euro;<\/span>46.00<\/span> + VAT (\u0932\u093e\u0917\u0942 \u0905\u0938\u0932\u094d\u092f\u093e\u0938)<\/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=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=1852\" data-quantity=\"1\" data-product_id=\"1852\" data-product_sku=\"MS-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=1852\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_1852\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"1852\" data-product_sku=\"MS-1\" aria-label=\"Add to cart: \u201cMagnetic Stand Insize-60-kgf\u201d\" rel=\"nofollow\" data-success_message=\"\u201cMagnetic Stand Insize-60-kgf\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_1852\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/mr\/product\/reflective-tape\/\" class=\"woocommerce-LoopProduct-link woocommerce-loop-product__link\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"card-image\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/mr\/product\/reflective-tape\/\" title=\"\u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0915 \u091f\u0947\u092a\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"153\" src=\"https:\/\/vibromera.eu\/wp-content\/uploads\/2023\/05\/s-l1600-230x153.webp\" class=\"attachment-woocommerce_thumbnail size-woocommerce_thumbnail\" alt=\"\u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0915 \u091f\u0947\u092a\" 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\/mr\/product-category\/parts\/\" rel=\"tag\">Parts<\/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\/mr\/product\/reflective-tape\/\" title=\"\u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0915 \u091f\u0947\u092a\">\u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0915 \u091f\u0947\u092a<\/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\">&euro;<\/span>10.00<\/span> + VAT (\u0932\u093e\u0917\u0942 \u0905\u0938\u0932\u094d\u092f\u093e\u0938)<\/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=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=2329\" data-quantity=\"1\" data-product_id=\"2329\" data-product_sku=\"rt-1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=2329\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_2329\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"2329\" data-product_sku=\"rt-1\" aria-label=\"Add to cart: \u201cReflective tape\u201d\" rel=\"nofollow\" data-success_message=\"\u201cReflective tape\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_2329\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<div class=\"col-ms-6 col-sm-6 col-md-3 shop-item\">\n\t\t\t\t\t\t<a href=\"https:\/\/vibromera.eu\/mr\/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\/mr\/product\/dynamic-balancer-balanset-1a\/\" title=\"\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915 \u092c\u0945\u0932\u0928\u094d\u0938\u0930 \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 \u0915\u093f\u091f \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0907\u0902\u091f\u0930\u092b\u0947\u0938 \u092f\u0941\u0928\u093f\u091f, \u0938\u0902\u0935\u0947\u0926\u0915, \u091f\u0945\u0915\u094b\u092e\u0940\u091f\u0930 \u0906\u0923\u093f \u0905\u0928\u0941\u0937\u0902\u0917\u0940 \u0938\u0939\" 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\/mr\/product-category\/devices\/\" rel=\"tag\">Devices<\/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\/mr\/product\/dynamic-balancer-balanset-1a\/\" title=\"\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915 \u092c\u0945\u0932\u0928\u094d\u0938\u0930 \u201cBalanset-1A\u201d OEM\">\u0921\u093e\u092f\u0928\u093e\u092e\u093f\u0915 \u092c\u0945\u0932\u0928\u094d\u0938\u0930 \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\">&euro;<\/span>1,735.00<\/span> + VAT (\u0932\u093e\u0917\u0942 \u0905\u0938\u0932\u094d\u092f\u093e\u0938)<\/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=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=4193\" data-quantity=\"1\" data-product_id=\"4193\" data-product_sku=\"BS-1OEM\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart btn btn-just-icon btn-simple btn-default\" title=\"Add to cart\" data-no-translation-title=\"\"><i rel=\"tooltip\" data-original-title=\"Add to cart\" class=\"fas fa-cart-plus\" data-no-translation-data-original-title=\"\"><\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a><a href=\"\/mr\/wp-json\/wp\/v2\/glossary\/294?add-to-cart=4193\" aria-describedby=\"woocommerce_loop_add_to_cart_link_describedby_4193\" data-quantity=\"1\" class=\"button product_type_simple add_to_cart_button ajax_add_to_cart\" data-product_id=\"4193\" data-product_sku=\"BS-1OEM\" aria-label=\"Add to cart: \u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d\" rel=\"nofollow\" data-success_message=\"\u201cDynamic balancer \u201cBalanset-1A\u201d OEM\u201d has been added to your cart\" data-no-translation=\"\" data-trp-gettext=\"\" data-no-translation-aria-label=\"\" data-no-translation-data-success_message=\"\">Add to cart<\/a>\t<span id=\"woocommerce_loop_add_to_cart_link_describedby_4193\" class=\"screen-reader-text\">\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/section>\n\t\t\n<p><strong>\u0938\u0926\u093f\u0936 \u091c\u094b\u0921\u0923\u0947<\/strong> is the mathematical operation of combining two or more vectors into a single resultant vector. In <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/balancing\/\">\u0930\u094b\u091f\u0930 \u0938\u0902\u0924\u0941\u0932\u0928<\/a>, vibration is treated as a vector because it carries two pieces of information at once: a magnitude (its <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/amplitude\/\">amplitude<\/a>) and a direction (its <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/phase\/\">\u092b\u0947\u091c \u0915\u094b\u0928<\/a>). This matters enormously, because separate sources of <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/unbalance\/\">unbalance<\/a> combine <em>\u0935\u094d\u0939\u0947\u0915\u094d\u091f\u0930\u0930\u093f\u0924\u094d\u092f\u093e<\/em>, not algebraically \u2014 their phase relationships count for just as much as their sizes. A firm grasp of vector addition is therefore what lets an engineer read balancing data correctly and predict how a <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/correction-weight\/\">\u0926\u0941\u0930\u0941\u0938\u094d\u0924\u0940 \u0935\u091c\u0928<\/a> will reshape the vibration of the whole rotor system.<\/p>\n<h2>1. Why Vibration Must Be Treated as a Vector<\/h2>\n<p>The vibration produced by unbalance is a rotating force that repeats exactly once per revolution. Measured at any one sensor location it has two inseparable properties:<\/p>\n<ul>\n<li><strong>\u0906\u092f\u093e\u092e:<\/strong> the magnitude or strength of the motion, usually in mm\/s, in\/s or microns.<\/li>\n<li><strong>\u092b\u0947\u091c:<\/strong> the angular instant at which the peak occurs relative to a reference mark on the rotor, read in degrees from 0\u00b0 to 360\u00b0 and timed from the <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/keyphasor\/\">keyphasor<\/a> pulse.<\/li>\n<\/ul>\n<p>Because phase is decisive, vibration amplitudes can never simply be summed. Picture two unbalances that each generate 5 mm\/s: the total can be anything from 0 mm\/s \u2014 if they sit 180\u00b0 apart and cancel \u2014 to 10 mm\/s, if they are in phase and reinforce. Everything in between is possible depending on the angle. Only vector addition, which respects both amplitude and phase, gives the right answer.<\/p>\n<h2>2. The Mathematical Basis of Vector Addition<\/h2>\n<p>A vector can be written in two equivalent forms, and balancing uses both, converting freely between them.<\/p>\n<h3>Polar form (magnitude and angle)<\/h3>\n<p>Here the vector is an amplitude <em>A<\/em> at a phase angle <em>\u03b8<\/em> \u2014 for example, 5.0 mm\/s \u2220 45\u00b0. This is the most natural form for a technician because it maps directly onto what the instrument displays and onto a <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/polar-plot\/\">\u0927\u094d\u0930\u0941\u0935\u0940\u092f \u0906\u0932\u0947\u0916<\/a>.<\/p>\n<h3>Rectangular (Cartesian) form (X and Y components)<\/h3>\n<p>Here the vector is split into a horizontal (X) and a vertical (Y) component using trigonometry:<\/p>\n<ul>\n<li>X = A \u00d7 cos(\u03b8)<\/li>\n<li>Y = A \u00d7 sin(\u03b8)<\/li>\n<\/ul>\n<p>Addition then becomes trivial: sum all the X components, sum all the Y components, and you have the resultant&#8217;s components, which can be turned back into polar form whenever a magnitude-and-angle answer is wanted.<\/p>\n<h3>A worked example<\/h3>\n<p>Take two vibration vectors:<\/p>\n<ul>\n<li>\u0935\u094d\u0939\u0947\u0915\u094d\u091f\u0930 1: 4.0 mm\/s \u2220 30\u00b0<\/li>\n<li>\u0935\u094d\u0939\u0947\u0915\u094d\u091f\u0930 2: 3.0 mm\/s \u2220 120\u00b0<\/li>\n<\/ul>\n<p>Convert each to rectangular form:<\/p>\n<ul>\n<li>\u0935\u094d\u0939\u0947\u0915\u094d\u091f\u0930 1: X\u2081 = 4.0 \u00d7 cos(30\u00b0) = 3.46, Y\u2081 = 4.0 \u00d7 sin(30\u00b0) = 2.00<\/li>\n<li>Vector 2: X\u2082 = 3.0 \u00d7 cos(120\u00b0) = \u22121.50, Y\u2082 = 3.0 \u00d7 sin(120\u00b0) = 2.60<\/li>\n<\/ul>\n<p>Add the components:<\/p>\n<ul>\n<li>X_total = 3.46 + (\u22121.50) = 1.96<\/li>\n<li>Y_total = 2.00 + 2.60 = 4.60<\/li>\n<\/ul>\n<p>Convert back to polar form:<\/p>\n<ul>\n<li>\u0905\u0945\u092e\u094d\u092a\u094d\u0932\u093f\u091f\u094d\u092f\u0942\u0921 = \u221a(1.96\u00b2 + 4.60\u00b2) = 5.00 mm\/s<\/li>\n<li>\u092b\u0947\u091c = arctan(4.60 \/ 1.96) = 66.9\u00b0<\/li>\n<\/ul>\n<p>Result: the combined vibration is <strong>5.00 mm\/s \u2220 66.9\u00b0<\/strong>. Notice that two vectors of 4.0 and 3.0 mm\/s did <em>not<\/em> add to 7.0; because they were 90\u00b0 apart they combined to exactly 5.0, the familiar 3-4-5 right triangle. That gap between the naive sum and the true result is precisely why phase cannot be ignored. If you want to combine your own measured vectors without hand arithmetic, the <a href=\"https:\/\/vibromera.eu\/mr\/calculators\/vibration-phase-angle\/\">\u0915\u0902\u092a\u0928 \u092b\u0947\u091c \u0905\u0901\u0917\u0932 \u0915\u0945\u0932\u094d\u0915\u094d\u092f\u0941\u0932\u0947\u091f\u0930<\/a> performs the conversion and addition directly.<\/p>\n<h2>3. The Graphical Tip-to-Tail Method<\/h2>\n<p>Vector addition can also be done by drawing, which gives an immediate visual feel for how vectors combine and is easily sketched on a polar plot:<\/p>\n<ol>\n<li><strong>Draw the first vector:<\/strong> from the origin, with its length set to the amplitude and its direction set to the phase.<\/li>\n<li><strong>Position the second vector:<\/strong> place its tail at the tip of the first, keeping its own correct length and angle.<\/li>\n<li><strong>Draw the resultant:<\/strong> a line from the origin to the tip of the second vector is the sum.<\/li>\n<\/ol>\n<p>This construction is handy for quickly estimating the effect of adding or removing a correction weight, and for sanity-checking the numbers an instrument produces.<\/p>\n<h2>4. Practical Application in Balancing<\/h2>\n<p>Vector addition is not a side calculation \u2014 it is woven through every stage of the balancing workflow.<\/p>\n<h3>Combining original unbalance and trial weight<\/h3>\n<p>\u091c\u0947\u0935\u094d\u0939\u093e \u090f\u0916\u093e\u0926\u093e <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/trial-weight\/\">trial weight<\/a> is fitted, the new reading is the vector sum of the original unbalance vibration (O) and the trial weight&#8217;s effect (T). The instrument measures (O+T) directly; to isolate T alone it performs vector subtraction: T = (O+T) \u2212 O.<\/p>\n<h3>Calculating the influence coefficient<\/h3>\n<p>The <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/influence-coefficient\/\">\u092a\u094d\u0930\u092d\u093e\u0935 \u0917\u0941\u0923\u093e\u0902\u0915<\/a> is found by dividing the trial weight&#8217;s vector effect by the trial mass, so it too is a vector quantity \u2014 an amount of vibration per unit of weight, at a characteristic angle. The <a href=\"https:\/\/vibromera.eu\/mr\/calculators\/influence-coefficient-calculator\/\">\u092a\u094d\u0930\u092d\u093e\u0935 \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u0945\u0932\u094d\u0915\u094d\u092f\u0941\u0932\u0947\u091f\u0930<\/a> automates this single-plane case.<\/p>\n<h3>Determining the correction weight<\/h3>\n<p>The correction weight vector is the negative (a 180\u00b0 phase shift) of the original vibration, divided by the influence coefficient. Sized this way, its effect \u2014 when vectorially added back to the original unbalance \u2014 cancels it, driving the vibration toward zero.<\/p>\n<h3>Predicting final vibration<\/h3>\n<p>Once the correction is fitted, the expected <a href=\"https:\/\/vibromera.eu\/mr\/glossary\/residual-unbalance\/\">residual vibration<\/a> can be forecast by adding the original vibration vector to the calculated effect of the correction. Comparing that prediction with the measured outcome is a powerful quality check on the whole job.<\/p>\n<h2>5. Vector Subtraction<\/h2>\n<p>Vector subtraction is nothing more than vector addition with the second vector reversed (rotated 180\u00b0). To subtract vector B from vector A:<\/p>\n<ul>\n<li>Reverse B by rotating it 180\u00b0 \u2014 or, in rectangular form, simply negate both its components.<\/li>\n<li>Add the reversed B to A with ordinary vector addition.<\/li>\n<\/ul>\n<p>As noted above, this is the operation that isolates a trial weight&#8217;s effect, T = (O+T) \u2212 O, where O is the original vibration and (O+T) is the reading with the trial weight installed.<\/p>\n<h2>6. Common Mistakes and Misconceptions<\/h2>\n<p>Most balancing errors that trace back to vector maths fall into three traps:<\/p>\n<ul>\n<li><strong>Adding amplitudes directly:<\/strong> treating 3 mm\/s + 4 mm\/s as 7 mm\/s ignores phase entirely; as the worked example showed, the true result depends on the angle between them.<\/li>\n<li><strong>Ignoring phase information:<\/strong> attempting to balance on amplitude alone, with no phase reference, almost never converges to a good result.<\/li>\n<li><strong>Inconsistent angle convention:<\/strong> mixing clockwise and counter-clockwise conventions, or measuring from the wrong reference, sends correction weights to the wrong position on the rotor.<\/li>\n<\/ul>\n<h2>7. Modern Instruments Handle the Vector Maths<\/h2>\n<p>Although understanding the mathematics is essential for any balancing professional, the arithmetic itself is now done automatically by the instrument. A portable analyser such as the <a href=\"https:\/\/vibromera.eu\/mr\/product\/balanset-1\/\">Balanset-1A<\/a> collects amplitude and phase from both channels, carries out every vector addition, subtraction and division internally, displays the results numerically and graphically on polar plots, and reports the final correction weight mass and angular location ready to fit. Yet the underlying theory still earns its keep: an engineer who understands it can verify the instrument&#8217;s output, diagnose anomalies when a result looks wrong, and grasp why certain balancing strategies converge faster than others.<\/p>\n<hr>\n<p><a href=\"https:\/\/vibromera.eu\/mr\/glossary\/\">\u2190 \u092e\u0941\u0916\u094d\u092f \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u0915\u093e\u0902\u0915\u0921\u0947 \u092a\u0930\u0924<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>Learn about vector addition, the mathematical method used in balancing to combine vibration vectors with both amplitude and phase, essential for calculating correction weights accurately.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[109,111],"tags":[],"class_list":["post-294","glossary","type-glossary","status-publish","hentry","category-glossary","category-rotor-balancing"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/mr\/wp-json\/wp\/v2\/glossary\/294","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/mr\/wp-json\/wp\/v2\/glossary"}],"about":[{"href":"https:\/\/vibromera.eu\/mr\/wp-json\/wp\/v2\/types\/glossary"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/mr\/wp-json\/wp\/v2\/glossary\/294\/revisions"}],"predecessor-version":[{"id":101467,"href":"https:\/\/vibromera.eu\/mr\/wp-json\/wp\/v2\/glossary\/294\/revisions\/101467"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/mr\/wp-json\/wp\/v2\/media?parent=294"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/mr\/wp-json\/wp\/v2\/categories?post=294"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/mr\/wp-json\/wp\/v2\/tags?post=294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}