Experimental observations and dynamic modeling of vibration characteristics of a cylindrical roller bearing with roller defects
Introduction
Rolling element bearings (REBs) play an important role in the safety and reliability of a machine system. As REB faults largely affect the vibrations of a bearing, vibration-based condition monitoring and fault diagnosis for REBs have been studied widely [1], [2] to diagnose the bearing faults. Based on the impulse characteristics of accelerations in defective REBs, many powerful signal processing techniques have been proposed to extract the fault features and to diagnose the fault effectively, such as wavelet transformation [3], [4], time–frequency analysis [5], empirical mode decomposition [6], cyclostationarity analysis [7], spectral kurtosis method [8] and sparsity-based method [9].
Dynamic models of REBs with localized defects are powerful tools for investigating and predicting the vibration characteristics of REBs with localized defects [2]. The predicted vibrations can provide theoretical proof for the verification of signal processing techniques for the fault diagnosis of REBs. By now, many dynamic models for defective REBs have been proposed to investigate the vibration of a bearing with race defects. Sawalhi [10], [11] proposed a dynamic model for gear-bearing systems with localized and distributed bearing race defects. Relative slippage at contact surfaces was considered in [10], [11]. Sopanen [12], [13] proposed a dynamic model for a deep-groove ball bearing with localized defects on races by using the commercial multi-body dynamics software ADAMS. Kiral [14] investigated the vibration of a REB with a localized defect on the outer race by using the finite element method. The effects of the localized race defect on the force–deflection relationship and on the motions of bearing components were investigated by Ashtekar [15], [16]. Patil [17] modeled the localized race defect as a part of a sinusoidal wave. Patel [18] proposed a model for the dynamics of deep groove ball bearings with single and multiple defects. Liu [19] proposed a piecewise response function to describe the impulse caused by a defect on a race. Cao [20] investigated the effect of a localized defect on vibrations of a spindle system by using a quasi-static model considering centrifugal force and the gyroscopic moment. The effect of the defect shape on the impulse waveform was investigated by Liu [21] by using the finite element method. Singh [22], [23] investigated the effect of an outer race defect on the vibration response of a REB by using the explicit dynamics finite element software LS-DYNA. El-Thalji [24], [25] proposed a dynamic model to investigate the wear evolution in a REB. Kogan [26] modeled the outer race defect by a sinus function for single and duplex ball bearings. Moazen Ahmadi [27], [28] investigated the effect of an outer race defect by considering the finite size of a rolling element. Petersen [29] investigated the vibrations of double-row rolling element bearings with race defects. Liu investigated the effects of time-varying contact stiffness [30] and edge topographies of a defect [31] in a ball bearing with race defects. Khanam investigated the magnitude and duration of the impact force caused by an outer race defect and an inner race defect [32], [33]. Wang [34] investigated the dynamics of a cylindrical roller bearing with race defects. Niu [35] proposed a dynamic model for high speed rolling ball bearings with localized defects on races. Relative slippage was considered in Ref. [35]. Later, Niu [36] extended their model [35] by considering the cage and the finite size of a ball to investigate the ball passing frequencies systematically. Based on dynamic modeling of REBs, the defect size prediction (i.e., the quantitative diagnosis of REBs) was investigated by Cui [37], [38] and Chen [39]. In addition, a deep groove ball bearing with race defects was modeled by Gomez [40] to investigate the effect of instantaneous angular speed variations. More recently, the effect of localized defects on the rotating speed fluctuation in a tapered roller bearing was investigated by Bourdon [41].
The models discussed above were mainly focused on race defects. Besides the effect of race defects on the vibration response of a bearing, many researchers also investigated the influence of rolling element defect on the vibration response of a bearing. Choudhury [42] proposed a lumped-mass model to obtain the vibration responses of a REB with defects on various bearing components including rolling elements and races. Sassi [43] modeled the vibration of a REB with localized defects on rolling elements and races by using the system kinetic energy. Sawalhi [10], [11] also proposed a dynamic model for gear-bearing systems with rolling element defects. In Sawalhi’s model, the relative slippage was considered. Cao [44] proposed a dynamic model for double-row spherical roller bearings with localized defects on various bearing components. In Cao’s model, the dynamic equations were established by Lagrange equations. Arslan [45] investigated the vibrations of a shaft-bearing system with localized bearing defects. The nonlinear dynamic behavior of a REB with localized defects on rolling elements and races was investigated by Rafsanjani [46]. Yuan [47] proposed a dynamic model for ball bearing-rotor system with single and compound defects. Mishra [48] investigated the dynamics of ball bearing with ball defects using bond graph method. More recently, a dynamic model considering the 3D motion of ball defect was proposed by Niu [49] based on Gupta’s dynamic model of high-speed ball bearings [50], [51].
Compared to the investigation on race defects, the dynamics of a bearing with rolling element defect has not been studied deeply. It is known that the vibration responses of the bearing as a rolling element defect goes around a race are essential to the fault diagnosis of the bearing defect. Indeed, the path of a roller as it travels around a race defect has been widely investigated [10], [11], [22], [23], [27], [28], [29]. These studies show that the vibration responses as a roller travels around a race defect have important information about the defect size. Compared to race defect conditions, the path of a rolling element and the vibration responses of a bearing as the rolling element defect rolls around a race has not been investigated deeply. In order to investigate this topic, a dynamic model considers the rolling element defect should be proposed.
In the models of rolling element defect discussed above, the rotation speed of the rolling element is assumed as a constant value which is calculated based on pure rolling assumptions, and the relative slippage at the contacting surface is not considered. Although the relative slippage is taken into account in Refs. [10], [11], the slippage is modeled as random numbers and does not depend on the real dynamics of the REB.
Moreover, in most of the published models, the rolling element was modeled as a point mass, and the additional clearance induced by defect does not rely on the dynamics of a REB. However, the geometric interaction between the rolling element defect and the race varies when the defect rolls around the race and largely depends on the REB dynamics, which means that the finite size of a rolling element should be considered when modeling the defect (the concept of the finite size of a rolling element was firstly proposed by Moazen Ahmadi when modeling the outer race defect in [27]). In order to clearly illustrate these two concepts (i.e., the point mass model and the finite size of a rolling element), the geometric interaction between a rolling element defect and an outer race is schematically shown in Fig. 1. In Fig. 1, the rolling element defect is denoted as AB (point A denotes the back edge and point B denotes the front edge of the defect) and the rolling element defect is in contact with the outer race. In the point mass model, the interaction between the rolling element defect and the race is checked only along the line connecting the mass center of the rolling element and that of the outer race . However, when the rolling element defect rolls around a race, the race may be in contact with the defect edge A which is not along the line . As for the race-rolling element defect interaction shown in Fig. 1, the defect is not in contact with the race if the point mass model is used, however, the defect is in contact with the race at the back edge A if the effect of finite size of rolling element is considered. As a result, the contact point between the rolling element defect and the race should be found at the surface of the rolling element (not just along the line ), which means that the finite size of the rolling element should be considered.
Additionally, when the rolling element defect contacts with the race, the direction of the contact force changes, and the contact force at defect-race can be decomposed into a normal component and a tangential component relative to the line as schematically shown in Fig. 1. The change of the contact force direction largely influences the rotation speed of the rolling element. However, in most of the published models, the change of the contact force direction was not considered.
From the above discussions it can be found that, in order to predict the vibrations of REBs with localized defects on rolling elements more reasonably, the relative slippage, the finite size of a rolling element, and the change of the contact force direction at defect-race should be considered in the dynamic model.
In this paper, the path of a roller and the vibration responses of a bearing as the roller defect rolls around a race in a cylindrical roller bearing are investigated both experimentally and theoretically. In order to investigate this topic, a dynamic model of cylindrical roller bearing considering roller defect is proposed. In the proposed model, the relative slippage, the finite size of a roller, and the change of the contact force direction at roller defect-race are all considered.
The reminder part of the current paper is organized as follows. Firstly, an experiment was carried out to observe the vibration characteristics as a roller defect travels around a race (Section 2). Then, a dynamic model considering roller defects is proposed (Section 3). The proposed model is verified in Section 4. Based on the proposed dynamic model, the vibration characteristics when a roller defect goes around a race is investigated (Section 5). Finally, the conclusion is given in Section 6.
Section snippets
Experimental observations.
In order to investigate the fault diagnosis techniques of cylindrical roller bearings, an experiment was carried out. The test rig is shown in Fig. 2(a). The outer ring of the tested bearing is installed inside the bearing housing, and the housing is bolted to the base plate. Two accelerometers are used to measure the vibrations of the bearing in the and axes, as shown in Fig. 2(b). The accelerometers are 8763B50AB type Kistler ceramic shear triaxial IEPE accelerometers. The tested bearing
Dynamic modeling
In order to study the dynamic characteristics of a cylindrical roller bearing with roller defects, a dynamic model considering roller defect is proposed. First, a dynamic model of healthy bearing is proposed. Then, the roller defect is modeled and integrated into the healthy bearing model.
Model verification.
In this section, the proposed dynamic model is verified with the experiment results given in Section 2. All the parameters of the cylindrical roller bearing in simulation are listed in Table 2. Moreover, as the lubricant characteristics is not the main focus of the current investigation, a simple four-parameter traction model is used to simulate the relationship between the relative sliding velocity and the traction coefficient (i.e., the traction model) as shown in Fig. 12 [54]. The
Vibration characteristics when a roller defect rolls around a race
In this section, the vibration characteristics of the bearing as a roller defect rolls around races (i.e., the defect edges successively roll through the line connecting the roller and race centers) are discussed by the simulation results. In order to discuss this topic, the contact forces at roller-races and the acceleration of the bearing housing in the direction are analyzed. In addition, as discussed in previous sections, the defect may be in contact with the corresponding race when
Conclusion
In this paper, the vibration characteristics when a roller defect rolls around a race are investigated, and the multi-impulse phenomenon is studied by dynamic modeling. The following conclusions are drawn on the basis of the current investigation.
- •
The process when a roller defect goes around a race can be divided into three stages. The first stage is the stage that the front edge of the roller defect rolls through the line connecting the roller and the race centers. The second stage is the
Author contributions
Linkai Niu developed the dynamic model and wrote the manuscript.
Hongrui Cao designed the experiment.
Huipeng Hou helped Linkai Niu to draw some of the figures in the manuscript.
Bing Wu helped Linkai Niu to write the computer codes.
Yuan Lan helped Linkai Niu to analyze the vibration signals.
Xiaoyan Xiong helped Hongrui Cao to carry out the experiment.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
Special thanks to Prof. Zhengjia He for his great contributions to start this research project. This work was supported by the National Natural Science Foundation of China (Grant No. 51705351) and the Natural Science Foundation of Shanxi Province (Grant No. 201701D221141).
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