Nonlinear Objects in Rotor Balancing
Why balancing “does not work”, why influence coefficients change, and how to proceed in real field conditions
Resumen
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 “does not work”, influence coefficients change, vibration becomes unstable, and the result is not repeatable from one run to another.
Vibraciones lineales y no lineales, sus características y métodos de balanceo
Un balanceo exitoso requiere comprender cómo reacciona un objeto ante la adición o eliminación de masa. En este contexto, los conceptos de objetos lineales y no lineales desempeñan un papel clave. Comprender si un objeto es lineal o no lineal permite seleccionar la estrategia de balanceo correcta y ayuda a lograr el resultado deseado.
Los objetos lineales ocupan un lugar especial en este campo debido a su predictibilidad y estabilidad. Permiten el uso de métodos de diagnóstico y balanceo simples y confiables, lo que hace que su estudio sea un paso importante en la vibración diagnóstica.
Linear vs nonlinear objects
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.
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.
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.
¿Qué son los objetos lineales?
Un objeto lineal es un sistema donde la vibración es directamente proporcional a la magnitud del desbalance.
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.
A diferencia de los sistemas no lineales, donde el comportamiento de un objeto puede variar dependiendo de muchos factores, los objetos lineales permiten un alto nivel de precisión con un esfuerzo mínimo.
Además, sirven como base para la capacitación y práctica de los balanceadores. Comprender los principios de los objetos lineales ayuda a desarrollar habilidades que luego pueden aplicarse a sistemas más complejos.
Representación gráfica de la linealidad
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.
Gráfica 1: La relación entre la amplitud de vibración (µm) y la masa desbalanceada (g)
La Gráfica 1 ilustra la relación entre la amplitud de vibración (µm) de un objeto de balanceo lineal y la masa desbalanceada (g) del rotor. El coeficiente de proporcionalidad es 0.5 µm/g. Simplemente dividiendo 300 entre 600 se obtiene 0.5 µm/g. Para una masa desbalanceada de 800 g (MD=800 g), la vibración será 800 g * 0.5 µm/g = 400 µm. Tenga en cuenta que esto se aplica a una velocidad constante del rotor. A una velocidad de rotación diferente, el coeficiente será diferente.
Este coeficiente de proporcionalidad se llama coeficiente de influencia (coeficiente de sensibilidad) y tiene una dimensión de µm/g o, en casos que involucran desbalance, µm/(g*mm), donde (g*mm) es la unidad de desbalance. Conociendo el coeficiente de influencia (CI), también es posible resolver el problema inverso, a saber, determinar la masa desbalanceada (MD) en función de la magnitud de la vibración. Para hacerlo, divida la amplitud de vibración entre el CI.
Por ejemplo, si la vibración medida es de 300 µm y el coeficiente conocido es CI=0.5 µm/g, divida 300 entre 0.5 para obtener 600 g (MD=600 g).
Coeficiente de influencia (CI): Parámetro clave de los objetos lineales
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, µm) 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 µm/g, or, when imbalance is expressed as the product of mass and radius, µm/(g*mm).
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 – determining vibration magnitude for a given imbalance – and the inverse problem – calculating imbalance magnitude from measured vibration.
Problema directo:
Problema inverso:
Fase de vibración en objetos lineales
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:
- 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.
- 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.
Por lo tanto, conociendo el argumento del CI y midiendo la fase de vibración, es posible determinar el ángulo de instalación de la masa desbalanceada. Esto permite no solo calcular la magnitud de la masa correctiva, sino también su colocación precisa en el rotor para lograr un balanceo óptimo.
Balanceo de objetos lineales
Es importante tener en cuenta que, para un objeto lineal, el coeficiente de influencia (CI) determinado de esta manera no depende de la magnitud ni del ángulo de instalación de la masa de prueba, ni de la vibración inicial. Esta es una característica clave de la linealidad. Si el CI permanece sin cambios cuando se alteran los parámetros de la masa de prueba o la vibración inicial, se puede afirmar con confianza que el objeto se comporta de manera lineal dentro del rango de desbalances considerado.
Pasos para el balanceo de un objeto lineal
- Medición de la vibración inicial: El primer paso es medir la vibración en su estado inicial. Se determinan la amplitud y el ángulo de vibración, que indican la dirección del desbalance.
- Instalación de una masa de prueba: Se instala una masa de peso conocido en el rotor. Esto ayuda a comprender cómo reacciona el objeto a cargas adicionales y permite calcular los parámetros de vibración.
- Re-medición de la vibración: Después de instalar la masa de prueba, se miden nuevos parámetros de vibración. Al compararlos con los valores iniciales, es posible determinar cómo afecta la masa al sistema.
- Cálculo de la masa correctiva: Con base en los datos de medición, se determinan la masa y el ángulo de instalación del peso de corrección. Este peso se coloca en el rotor para eliminar el desbalance.
- Verificación final: Después de instalar el peso de corrección, la vibración debería reducirse significativamente. Si la vibración residual aún supera el nivel aceptable, el procedimiento puede repetirse.
Nota: Los objetos lineales sirven como modelos ideales para estudiar y aplicar prácticamente los métodos de balanceo. Sus propiedades permiten a ingenieros y diagnostistas centrarse en desarrollar habilidades básicas y comprender los principios fundamentales del trabajo con sistemas de rotores. Aunque su aplicación en la práctica real es limitada, el estudio de los objetos lineales sigue siendo un paso importante para avanzar en la vibración diagnóstica y el balanceo.
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Serial balancing and stored coefficients
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.
Objetos no lineales: cuando la teoría se desvía de la práctica
¿Qué es un objeto no lineal?
Un objeto no lineal es un sistema donde la amplitud de vibración no es proporcional a la magnitud del desbalance. A diferencia de los objetos lineales, donde la relación entre la vibración y la masa de desbalance se representa mediante una línea recta, en los sistemas no lineales esta relación puede seguir trayectorias complejas.
En el mundo real, no todos los objetos se comportan de manera lineal. Los objetos no lineales exhiben una relación entre el desbalance y la vibración que no es directamente proporcional. Esto significa que el coeficiente de influencia no es constante y puede variar dependiendo de varios factores, como:
- Magnitud del desbalance: Increasing the imbalance can change the stiffness of the rotor's supports, leading to nonlinear changes in vibration.
- Velocidad de rotación: Diferentes fenómenos de resonancia pueden excitarse a velocidades de rotación variables, lo que también resulta en un comportamiento no lineal.
- Presencia de juegos y holguras: Los juegos y holguras en los rodamientos y otras conexiones pueden provocar cambios bruscos en la vibración bajo ciertas condiciones.
- Temperatura: Los cambios de temperatura pueden afectar las propiedades de los materiales y, en consecuencia, las características de vibración del objeto.
- Cargas externas: Las cargas externas que actúan sobre el rotor pueden alterar sus características dinámicas y provocar un comportamiento no lineal.
¿Por qué los objetos no lineales son un desafío?
La no linealidad introduce muchas variables en el proceso de balanceo. El trabajo exitoso con objetos no lineales requiere más mediciones y un análisis más complejo. Por ejemplo, los métodos estándar aplicables a objetos lineales no siempre arrojan resultados precisos para sistemas no lineales. Esto requiere una comprensión más profunda de la física del proceso y el uso de métodos de diagnóstico especializados.
Señales de no linealidad
Un objeto no lineal puede identificarse por las siguientes señales:
- Cambios de vibración no proporcionales: A medida que aumenta el desbalance, la vibración puede crecer más rápido o más lento de lo esperado para un objeto lineal.
- Desplazamiento de fase en la vibración: La fase de la vibración puede cambiar de manera impredecible con las variaciones en el desbalance o la velocidad de rotación.
- Presencia de armónicos y subarmónicos: El espectro de vibración puede presentar armónicos superiores (múltiplos de la frecuencia de rotación) y subarmónicos (fracciones de la frecuencia de rotación), lo que indica efectos no lineales.
- Histéresis: La amplitud de la vibración puede depender no solo del valor actual del desbalance, sino también de su historial. Por ejemplo, cuando el desbalance se aumenta y luego se disminuye nuevamente a su valor inicial, la amplitud de la vibración puede no regresar a su nivel original.
La no linealidad introduce muchas variables en el proceso de balanceo. Se requieren más mediciones y un análisis complejo para una operación exitosa. Por ejemplo, los métodos estándar aplicables a objetos lineales no siempre arrojan resultados precisos para sistemas no lineales. Esto requiere una comprensión más profunda de la física del proceso y el uso de métodos de diagnóstico especializados.
Representación gráfica de la no linealidad
En una gráfica de vibración frente a desbalance, la no linealidad es evidente en las desviaciones de una línea recta. La gráfica puede presentar curvas, curvaturas, bucles de histéresis y otras características que indican una relación compleja entre el desbalance y la vibración.
Gráfica 2. Objeto no lineal
50g; 40μm (yellow), 100g; 54.7μm (blue).
Este objeto presenta dos segmentos, dos líneas rectas. Para desbalances menores a 50 gramos, la gráfica refleja las propiedades de un objeto lineal, manteniendo la proporcionalidad entre el desbalance en gramos y la amplitud de vibración en micrones. Para desbalances mayores a 50 gramos, el crecimiento de la amplitud de vibración se ralentiza.
Ejemplos de objetos no lineales
Los ejemplos de objetos no lineales en el contexto del balanceo incluyen:
- Rotores con grietas: Las grietas en el rotor pueden provocar cambios no lineales en la rigidez y, como resultado, una relación no lineal entre la vibración y el desbalance.
- Rotores con juego en los rodamientos: Los juegos en los rodamientos pueden provocar cambios bruscos en la vibración bajo ciertas condiciones.
- Rotores con elementos elásticos no lineales: Some elastic elements, such as rubber dampers, may exhibit nonlinear characteristics, affecting the rotor's dynamics.
Tipos de no linealidad
1. No linealidad blanda-rígida
En estos sistemas, se observan dos segmentos: blando y rígido. En el segmento blando, el comportamiento se asemeja a la linealidad, donde la amplitud de la vibración aumenta proporcionalmente a la masa de desbalance. Sin embargo, después de un cierto umbral (punto de quiebre), el sistema transita a un modo rígido, donde el crecimiento de la amplitud se ralentiza.
2. No linealidad elástica
Los cambios en la rigidez de los soportes o contactos dentro del sistema hacen que la relación vibración-desbalance sea compleja. Por ejemplo, la vibración puede aumentar o disminuir repentinamente al cruzar umbrales de carga específicos.
3. No linealidad inducida por fricción
En sistemas con fricción significativa (por ejemplo, en rodamientos), la amplitud de la vibración puede ser impredecible. La fricción puede reducir la vibración en un rango de velocidades y amplificarla en otro.
Common causes of nonlinearity
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–hard 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.
Vibration instability
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.
Balancing near resonance
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.
High vibration after “successful” balancing
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.
Balanceo de objetos no lineales: una tarea compleja con soluciones no convencionales
El balanceo de objetos no lineales es una tarea desafiante que requiere métodos y enfoques especializados. El método estándar de peso de prueba, desarrollado para objetos lineales, puede arrojar resultados erróneos o ser completamente inaplicable.
Métodos de balanceo para objetos no lineales
- Balanceo paso a paso: 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.
- Balanceo a múltiples velocidades: Este método aborda los efectos de los fenómenos de resonancia a diferentes velocidades de rotación. El balanceo se realiza a varias velocidades cerca de la resonancia, lo que permite una reducción más uniforme de la vibración en todo el rango de velocidades de operación.
- Uso de modelos matemáticos: Para objetos no lineales complejos, se pueden emplear modelos matemáticos que describan la dinámica del rotor teniendo en cuenta los efectos no lineales. Estos modelos ayudan a predecir el comportamiento del objeto bajo diversas condiciones y a determinar los parámetros óptimos de balanceo.
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.
Cómo balancear objetos no lineales utilizando una herramienta diseñada para objetos lineales
Esta es una buena pregunta. Mi método personal para balancear este tipo de objetos comienza con la reparación del mecanismo: reemplazar rodamientos, soldar grietas, apretar pernos, verificar anclajes o aisladores de vibración y comprobar que el rotor no roce contra elementos estructurales fijos.
A continuación, identifico las frecuencias de resonancia, ya que es imposible realizar el balanceo de un rotor a velocidades cercanas a la resonancia. Para ello, utilizo el método de impacto para la determinación de la resonancia o un gráfico de paro por inercia del rotor.
Then, I determine the sensor's position on the mechanism: vertical, horizontal, or at an angle.
Después de las pruebas de funcionamiento, el dispositivo indica el ángulo y el peso de las cargas de corrección. Reduzco a la mitad el peso de la carga de corrección, pero utilizo los ángulos sugeridos por el dispositivo para la colocación en el rotor. Si la vibración residual después de la corrección aún supera el nivel aceptable, realizo otra prueba de funcionamiento del rotor. Naturalmente, esto toma más tiempo, pero los resultados a veces son inspiradores.
El arte y la ciencia del balanceo de equipos rotativos
El balanceo de equipos rotativos es un proceso complejo que combina elementos de ciencia y arte. Para objetos lineales, el balanceo implica cálculos relativamente simples y métodos estándar. Sin embargo, trabajar con objetos no lineales requiere una comprensión profunda de la dinámica de rotores, la capacidad de analizar señales de vibración y la habilidad para elegir las estrategias de balanceo más efectivas.
La experiencia, la intuición y la mejora continua de las habilidades son lo que hacen de un balanceador un verdadero maestro de su oficio. Después de todo, la calidad del balanceo no solo determina la eficiencia y confiabilidad del funcionamiento del equipo, sino que también garantiza la seguridad de las personas.
Measurement repeatability
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.
Practical approach for nonlinear objects
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Reduced correction weight technique
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.
In such cases, installing a reduced correction weight works well — two or sometimes even three times smaller than the value calculated by the instrument. This helps avoid “throwing” 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.
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.
This technique is especially effective for objects with clearances, dry friction, and soft–hard 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.
It is important to understand that this is not an “instrument error”, 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.
Final principle
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.
Questions & answers
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.
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.
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–hard supports, or the engagement of stiffer structural elements.
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.
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.
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.
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.
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.
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.
There are inherent structural instability, slow “creeping” instability, variation from start to start, warm-up-related instability, and resonance-related instability when operating near natural frequencies.
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.
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.
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.
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.
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.
Correct conversion is possible only for single-frequency harmonic vibration. For complex vibration spectra, such conversions provide only approximate results.
Possible reasons include resonance, foundation defects, loosened fasteners, bearing wear, misalignment, or object nonlinearity. Balancing removes unbalance only, not other defects.
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.
Incorrect sensor installation distorts amplitude and phase, reduces measurement repeatability, and can lead to incorrect diagnostic conclusions and erroneous balancing results.
Vibration is distributed unevenly throughout the structure. Stiffness, masses, and mode shapes differ, so amplitude and phase can vary significantly from point to point.
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.
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.
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.
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.
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.
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