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Rolling element bearing dynamic behavior, which is nonlinear, is an important factor in the operation, reliability and vibration response of turbomachinery. These bearings often manifest unexpected patterns that are extremely sensitive to initial parameters and conditions.
(Photo: General Bearing Corporation)
The rolling element bearing is a complex, multi-body mechanical system with rolling elements which transmit motion and load from the inner raceway to the outer raceway. An essential part of bearing design and bearing fault detection is accurate modelling of bearing-rotor vibration response.
A model of a rotor-bearing assembly can be used as a spring-mass system, where the rotor acts as the main mass, and the raceways and rolling-elements act as nonlinear contact springs. In commonly used rolling element bearing analytical formulations, the contact between the rolling element and the raceways is considered as nonlinear springs and their stiffness are obtained by a proper nonlinear model. For example, a sophisticated version of the nonlinear “Hertzian” contact deformation model can be employed. Some modern studies have suggested including both the nonlinear “Hertzian” contact deformation and elasto-hydrodynamic fluid film (the lubrication effect) to better model all these nonlinear effects.
The elastic deformation between the race and the rolling-elements gives a nonlinear force deformation relation. Other sources of stiffness variations are the internal radial clearance, finite number of rolling-elements whose position changes periodically and the waviness at inner and outer races. They cause periodic changes in the stiffness of the bearing assembly.
Since the contact forces arise only when there is a contact deformation, nonlinear springs are required to act only in the compression. In other words, the respective spring force comes into play when the instantaneous spring length is shorter than its unstressed length, otherwise the separation between rolling-elements and the race takes place and the resulting force is set to zero.
Study, Analysis and Condition Monitoring Methods based on periodic vibration have been used to study, analysis and condition monitoring of constant-speed rolling-element bearings. A well-known example has been the “Fourier” transformation method. The “Fourier” transformation assumes that the signal is periodic; but this is not generally true for the bearing vibration as result of bearing deflections in the general form. It is not also valid for a turbomachinery with a changing speed, because the shaft speed change has the consequence of the occurrence of the impact which cannot be reproduced exactly from one cycle to another. In other words, the frequency based techniques might not be suitable for the analysis of non-stationary signals produced from bearing vibration and bearing fault monitoring of a variable-speed turbomachinery.
The variable-speed turbomachinery bearing fault signals (or generally the non-stationary signals) can be analyzed by applying time-frequency domain techniques such as the short-time “Fourier” transform, the “Wavelet” transform and the “Hilbert-Huang” transform.
The bearing stiffness is one of main factors which can influence the turbomachinery dynamic rigidity, vibrational response and turbomachinery operation. The effects of “preload” and “number of elements” are important for any turbomachinery vibration. An increase in the “preload” or “number of rolling-element” can result in stiffer rolling-element bearings. This consequently leads to a better operation and usually lower vibration.
Many observations have confirmed the appearance of instability and chaos in the dynamic response as the speed of a turbomachinery is changed. The appearance of regions of periodic, sub-harmonic and instability behavior is seen also to be strongly dependent on the radial clearance. In other words, the “speed range” and the “bearing clearance” are important for the rolling-element dynamic behavior; these are important for trouble-free operation and reliability of such machinery.
The bearing preload can be regarded as the negative internal clearance. A proper amount of negative bearing clearance is usually desirable in order to stiffen the support of turbomachinery rotor assembly. However, an inappropriate negative bearing clearance can cause excessive rolling contact stresses and eventually could lead to bearing seizure and bearing failure. Therefore, a proper internal clearance should be selected in order to prevent the bearing seizure and to improve the bearing stiffness.
The amplitude of force vibration becomes larger with smaller values of the forcing frequency. Increasing the internal radial clearance could increase the magnification factor and ultimately may reduce the forcing frequency. The result could potentially be rise in the turbomachinery vibration. Other investigations focusing on the damping have been indicated the same result.
The internal clearance is inversely proportional to the damping factor which means increasing the clearance can reduce the damping factor and eventually could increase the amplitude of vibration.
Experimental results have shown that a slight variation in bearing parameters (such as contact conditions) could result in a significant change of dynamic forces and measured vibrations (vibration acceleration and vibration velocity). In some cases, the change of vibration measurements because of a slight change in a bearing parameter could lead to a wrong monitoring result; this is often known as “false defect detection for a healthy bearing”.
The radial clearance in rolling-element bearing systems is required to compensate for dimensional changes associated with thermal expansion of various parts during operation, which may cause dimensional attrition and comprise bearing life. This thermal effect can also cause jumps in dynamic response amplitudes due to different factors mainly the unbalance excitation. These undesirable effects may be eliminated by introducing two or more loops into one of the bearing races so that at least two points of the ring circumference provide a positive zero clearance. The deviation of the outer ring with two loops, often (traditionally) known as the “ovality”, is one of the bearing distributed defects. When the ring “ovality” is introduced, the vibration spectrum in both orthogonal planes is usually no longer similar.
Too often, the vibration magnitude of the bearing load has increased in the form of repeated random impacts, between rolling-elements and rings, in the horizontal direction (the direction of maximum clearance) compared to a continuous contact along the vertical direction (the direction of positive zero clearance).
(Amin Almasi is a Chartered Professional Engineer in Australia and U.K. (M.Sc. and B.Sc. in mechanical engineering). He is a senior consultant specializing in rotating equipment, condition monitoring and reliability.)