The rolling-element bearing operation and behaviour (such as the nonlinear dynamic behaviour)are important factors for operation, reliability and vibration response of different machineries in industrial plants.
The behaviour of a nonlinear rolling-element bearing often demonstrates unexpected patterns that are extremely sensitive to initial parameters and conditions. The effect of rolling-element bearing parameters(such as the internal radial clearance and the preload) on the machinery vibrations is investigated. Theoretically, the main part of the bearing vibration could occur at the rolling-element passage frequency. The harmonics of the rolling-element passage frequency may also be present. The bearing preload can be regarded as the negative internal clearance.
The amplitudes of machinery vibrations are considerably reduced if the internal radial clearance(and the preload) of bearing is correctly selected. An increase in the preload or the number of rolling-element can result in stiffer rolling-element bearings and lower vibrations.
The rolling-element bearings are among the most important and frequently-used machinery components in industrial plants. They are employed for machineries in the small and medium size ranges and also some special large machinery. The rolling-element bearings could be affected by manufacturing errors, mounting defects or operational damages. Such bearing errors (or damages) can cause vibration, noise, and even failure of the whole machinery. The rolling-element bearings are important potential sources of vibration in industrial plants.
The major dynamic forces of rolling-element bearings, which can generate the machinery noise and vibration, are time-varying nonlinear contact forces, which exist between various components of bearings particularly the rolling-elements, races and the shaft.
Different and complex effects could appear in the fault detection and the vibration analysis of rolling-element bearings, such as:
- The nonlinear effects.
- The effects caused by force-deformation relationships.
- The effects caused by axial load variations.
- The effects and the fault diagnostic in the case of combined axial and radial loads.
- The problems and difficulties associated with the fault detection (particularly the early fault detection).
- The determination of monitoring limits like the smallest detectable fault.
- A nonlinear damping, the rolling-element inertia, and the rolling-element sliding.
- The different interface nonlinear (stiffness) effects such as the interfaces of bearing/shaft and bearing/support.
- The complicated thermal and lubrication effects.
- The contact properties are very complex and should be described with detailed geometrical properties. Even small changes in the contact stiffness should betaken into account for an accurate modelling.
- The “Brinell” damage and the “False Brinelling” damage (the “False Brinelling” is damage caused by fretting). Other damages because of corrosion, fretting,material deformation, etc.
The rolling-element bearing stiffness is nonlinear. In addition, the bearing forces depend upon velocities and motions, so an accurate dynamic modelling of machineries using rolling-element bearings could be highly nonlinear.
The rolling-element bearing is a multi-body complex mechanical system with rolling-elements that transmit motion and load from the inner raceway to the outer raceway. An important step in the bearing design and the bearing-fault detection would be an accurate model for the bearing-rotor vibration response. A model of a rotor-bearing assembly can be used as a spring-mass system, where the rotor assembly acts as the main mass and the raceways and rolling-elements act as the 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 the elasto-hydrodynamic fluid film (the lubrication effect).
The elastic deformation between the race and the rolling-elements gives a nonlinear force deformation relation. Other sources of the stiffness variation are the internal radial clearance, the finite number of rolling-elements whose position changes periodically and the waviness at the 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, the 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 the rolling-element and the race takes place and the resulting force is set to zero.
The bearing stiffness is one of the main factors that can influence the machinery dynamic rigidity (and the vibrational response and the machinery operation). The effects of the “preload” and the “number of elements”are important for the machinery vibration. An increase in the preload or the number of rolling-element can result in stiffer rolling-element bearings.
Many observations have confirmed the appearance of instability and chaos in the dynamic response as the speed of a machinery is changed. The appearance of regions of periodic, sub-harmonic and instability behaviour 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 behaviour (the trouble-free operation and the reliability).
The bearing preload can be regarded as the negative internal clearance. A proper amount of negative bearing clearance is desirable in order to stiffen the support of machinery rotor assemblies. However, an inappropriate negative bearing clearance can cause excessive rolling element contact stresses and eventually could lead to bearing seizure. Therefore, a proper internal clearance should be selected in order to prevent the bearing seizure and to improve the bearing stiffness.
The amplitude of a forced vibration could become larger with smaller values of 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 machinery 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 the bearing parameters (such as contact conditions) could result in a significant change of the dynamic force and the measured vibration (the vibration acceleration and the vibration velocity). In some cases, the change of the vibration measurements because of a slight change in a bearing parameter could lead to a wrong monitoring result (false defect detection for a healthy bearing).
Theoretically, for a new and healthy bearing, the main part of the bearing vibration could occur at the rolling-element passage frequency.The harmonics of the rolling-element passage frequency can also be present.Both the sub-harmonics and the super-harmonic can be generated. The vibration spectrum and the amplitude of a harmonics of the rolling-element passage frequency could depend on the radial load, the radial clearance (and the preload), the speed and the order of harmonics.
By selecting the correct number of rolling-elements and amount of preload in a bearing, the vibration (at the rolling-element passage frequency and other frequencies) could be reduced. Increasing the number of rolling-elements means increasing the number of rolling-elements supporting the shaft therefore increasing the system stiffness and reducing the vibration amplitudes. For a small number of rolling-elements, peak amplitudes of vibrations at the rolling-element passage frequency are more significant. In other words, increasing the number of rolling-elements, the peak amplitude of vibration decreases and the vibration frequency is pushed to a higher value.For example, for a rolling–element bearing, when the number of rolling-elements increased from 5 to 11, the rolling-elements passage frequency increased from 100 Hz to 220 Hz and the peak vibration (at the rolling-elements passage frequency) reduced to less than 40%. The vibration amplitudes (at the rolling-elements passage frequency and its harmonics) are nonlinear functions of the bearing clearance (and the preload) and the number of rolling-elements.
The damping of a rolling-element bearing is relatively small. This damping is present because of the friction, the structural damping and a small amount of lubrication (lubrication oil or grease). An estimation of the damping of a rolling-element bearing is very difficult, since it is highly nonlinear and originated from different sources. A low damping can usually result in a low decay rate of a bearing vibration.
Important defects related to rolling-element bearings are “a dent on a rolling-element”, “a localised defect on a race”, the “off-size rolling-element”, the “waviness of rolling-element” and the “waviness of the races”. Many other defects could affect the rolling-element bearing operation.Examples are the surface roughness and various localised and distributed defects. The rolling-element bearing defects usually present complex and unexpected behaviour patterns.
The manufacturer’s error could be prevented by extensive inspections and testing programs. At an early stage of the bearing’s operation,almost only local defects are present, for instance, because of the improper mounting of the bearing which will cause a dent due to the plastic deformation of the rolling surface. Another local defect may be present in the bearing due to debris, since grease or lubricant in the bearing can contain particle contaminants. Such particle contaminant can be modelled as a local defect with the exception that the particle is free to move within the bearing.
The detailed geometry of local defects is usually modelled as an impressed-ellipsoid on bearing races and as a fattened sphere for the rolling-elements.
Any defect can potentially cause new cases of the resonances and high vibrations. For example, when the number of rolling-elements and the waves (for a waviness fault) are equal, there would be severing vibrations. As another example, for the outer race waviness, a significant vibration could occur when the rolling-element passage frequency or its harmonics coincide with a natural frequency. In addition of the above mentioned effect, the dynamic effects of the bearing defects should be carefully studied.
As a consequence of a localised fault (such as a dent), the vibration could increase. Another important aspect of the localised faults is that due to the different geometry of the contact between the localised fault and the bearing component, the contact-stiffness can change because of the different geometrical properties in the contact zones. On the other hand, a damaged bearing (particularly a small damage at an early stage of damage development)usually produces small amplitudes of vibration in high frequency bands as the response of bearing and the housing to the impact that is caused by the fault.A defect on a rolling-element can produce the vibration at two-times of the rolling-element’s rotational frequency (2 × rolling-element’s rotational frequency).
Axial loads could result in an increase of the vibration amplitudes because of a fault. In other words, there would be significant vibration components because of localized defects on the outer race, the inner race or on a rolling-element under an axial load. The rise can be caused by varying contact conditions and load distributions in a rolling-element bearing.However, it should be mentioned that axial loads do not always lead to an increase of vibration amplitudes. This could depend on contact conditions between rolling-element and faulty region.
Thermal Effects on Bearings
The radial clearance in rolling-element bearing systems is required to compensate for dimensional changes associated with thermal expansion of the various parts during operation, which may cause dimensional attrition and comprise bearing life. This thermal effect can also cause jumps in dynamic responses to 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 (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).