Outer Race Waviness Research Articles

Dynamic characteristics of high-speed angular contact ball bearings considering the coupling of outer race waviness and local defects

This paper proposes a novel four degrees of freedom model of angular contact ball bearings (ACBBs) under high-speed effect, in order to characterize the dynamic behavior of rolling bearings with coupling waviness and local defects on the outer race in detail. Firstly, based on bearing quasi-static model, considering centrifugal force, gyroscope moment, the bearing contact stiffness is calculated. Then, the representation model of outer race waviness and the time-varying displacement excitation expression of the bearing with local defects are put forward respectively. On the basis, a dynamic model of ACBBs with coupling factors is built. Finally, the vibration characteristics of the bearing with faults are investigated, the model is verified by the existing experimental results and the influence of different parameters on the bearing dynamics is analyzed. The results show that the bearing fault characteristic frequency is unchanged when the high-speed effect is considered, but the vibration amplitude is smaller than that without the high-speed effect. With the increase of speed, the bearing fault characteristic frequency and vibration amplitude increase. When considering the coupling of outer race waviness and local defects, with the increase of the two factors, the bearing fault characteristic frequency remains unchanged but the vibration amplitude increase.

An improved model for investigating the vibration characteristics of ball bearing owing to outer race waviness under high speed

In this study, an improved model for a ball bearing is established to investigate the vibration response characteristics owing to outer race waviness under an axial load and high speed. The mathematical ball bearing model involves the motions of the inner ring, outer ring, and rolling elements in the radial XY plane and axial z direction. The 2Nb + 5 nonlinear differential governing equations of the ball bearing are derived from Lagrange's equation. The influence of rotational speed and outer race waviness is considered. The outer race waviness is modeled as a superposition of sinusoidal function and affects both the contact deformation between the outer raceway and rolling elements and initial clearance. The MATLAB stiff solver ODE is utilized to solve the differential equations. The simulated results show that the axial vibration frequency occurred at l fc and the radial vibration frequencies appeared at l fc fc when the outer race waviness of the order (l) was the multiple of the number of rolling elements (k Nb) and that the principal vibration frequencies were observed at l fc fc in the radial x direction when the outer race waviness of the order (l) was one higher or one lower than the multiple of the number of rolling elements (k Nb 1). At last, the validity of the proposed ball bearing model was verified by the high-speed vibration measurement tests of ball bearings.

Nonlinear vibration response analysis of a double-row self-aligning ball bearing due to surface imperfections

This work attempts to study the vibration response of a double-row self-aligning ball bearing due to surface and localized imperfections. For the contact deformation at the ball–race interactions, the Hertzian load–deflection relation is used for the evaluation of time-varying contact stiffness. The elastohydrodynamic theory is applied to find out the central film thickness. For both the inner and outer race waviness cases, the system response is observed as periodic (with vibrations of high amplitude) at [Formula: see text], i.e. multiples of Nb and its vicinity, but gradually turns to quasi-periodic as the value of waviness order reach some intermediate value. In the case of a localized defect, the double impulse phenomenon marks the entry and exit events of the rolling element in and out of the rectangular spall. Hence, this analysis can be used as a diagnostic tool with system dynamic characteristics for distributed and localized defect identification.

Vibration analysis of dynamically loaded bearing with distributed defect based on defect induced excitation

In the present study an investigation has been carried out to determine distributed defect induced excitations in a bearing subjected to an external load which is a combination of static and dynamic load. The dynamic component of external load has been considered to be harmonic in nature and may be due to the shaft unbalance. The race surface waviness in radial direction has been taken in to account as the distributed defects in bearings. The race waviness is modeled mathematically, as sinusoidal functions of different orders and superposition of sinusoidal functions as well. Equal and random amplitudes of different orders have been considered. Kinematic and dynamic parameters as well as contact forces resulted due to race-rolling element interaction as obtained from published literature have been modified and extended to consider radial waviness and external dynamic loading. The frequency spectra of nonlinear contact forces causing excitations have been obtained. For static radial loading, these spectra are in accordance with those obtained for responses of linear dynamic models. For external dynamic loading, however, additional spectral components as sidebands at shaft frequency about the significant frequencies corresponding to external static loading have been observed for both inner and outer race surface waviness, when modeled as sinusoidal function of any order. Additional spectral components have also been observed for outer race waviness when formulated as superposition of different orders whereas for inner race, there are some amplitude variations in spectral components compared to that of static loading. Variation in amplitudes of spectral components has also been resulted when random values were assigned to different orders of waviness.

A study on waviness induced vibration of ball bearings based on signal coherence theory

This paper focuses on the effects of waviness on vibration of ball bearings. An experimental analysis method is developed by adopting signal coherence theory of multiple-inputs/single-output (MISO) system. The inputs are waviness excitations of the inner and outer races, and the output is vibration response of the outer ring. Waviness excitation signals are first derived from the manufacturing deviations, and found to be strongly coherent in low frequency range. Virtual input signals are then introduced by the method of orthogonalization. In both cases of vibration acceleration and speed responses, the cumulated virtual input–output coherence function verifies that the first peak region of vibration spectrum is mainly induced by the waviness excitations. In order to distinguish the contributions of the inner and outer races, coherence functions of the virtual inputs with real inputs are calculated, and the results indicate that the outer race waviness contributes more to vibration than the inner race waviness does in the example. Further, a multi-body dynamic model is constructed and employed to frequency response analyses. It is discovered that the waviness induced spectral peak frequency is close to the natural frequency of bearing.

Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered

A rotor system supported by roller bearings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincarè maps, the spectrum diagrams and the axis orbit of responses of the system. The results show that the system is liable to undergo instability caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases. Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces—all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.

Dynamic model of ball bearings with internal clearance and waviness

In this paper, a general dynamic model is presented for studying the dynamic properties of rotor system supported by ball bearings under the effects of both internal clearance and bearing running surface waviness. The ball bearing model includes the high-speed effects of ball centrifugal force and gyroscopic moment. The cage speed is considered a time-variation parameter related with the orbital speed of balls. Numerical results of this research are in good agreement with prior authors’ experimental researches and already existing models. Then the model is employed to investigate the effects of clearance, waviness, preload and radial force on the nonlinear stability and vibration behavior of a rotor bearing system at high speed. It is shown that the clearance, axial preload and radial force play a significant role in affecting the system stability. The effect of outer race waviness on cage speed variation is more considerable than that of inner race and ball waviness.

A Theoretical Model to Predict the Vibration Response of Rolling Bearings in a Rotor Bearing System to Distributed Defects Under Radial Load

A theoretical model to predict the vibration response of rolling element bearing in a rotor bearing system to distributed defects under radial load has been developed. The rotor bearing system has been considered as a three degrees of freedom model. The distributed defects considered are, the waviness of outer and inner races, and off size rolling element. The model predicts discrete spectrum with specific frequency components for each order of waviness. For outer race waviness, the spectrum has components at outer race defect frequency and its harmonics. In the case of inner race waviness, the waviness orders equal to number of rolling elements and its multiples give rise to spectral components at inner race defect frequency and its multiples. Other orders of waviness generate sidebands at multiples of shaft frequency about these peaks. The model predicts the amplitudes of the spectral components due to outer race waviness to be much higher as compared to those due to inner race waviness. In the case of an off-size rolling element, the model predicts discrete spectra having significant components at multiples of cage frequency. [S0742-4787(00)00603-2]

Analysis of Ball Bearing Vibrations Caused by Outer Race Waviness

An analytical investigation of the shaft vibration caused by a ball bearing is presented in this paper. Bearing vibration could be caused by a number of factors, such as defects occurring on the race track or the rolling elements. A common problem with defective bearings is the generation of waviness on the outer race track during the manufacturing process. The vibration of an automobile drive shaft caused by rolling elements rolling over the waviness surface is transmitted to the passenger cabin, and produces undesirable noise. In this paper an analytical study is undertaken to evaluate the effect of waviness number, radial gap and shaft imbalance on the bearing vibration. An experimental investigation was carried out to confirm the analytical study. The results show that the analytical study and experimental investigation agree very well.

Theoretical analysis of shaft vibration supported by a ball bearing with small sinusoidal waviness

This paper describes theoretical analysis of radial vibration of a rigid shaft supported by a ball bearing with form errors. Assuming a small sinusoidal waviness of n-th order on the inner race, outer race or rotating balls, the displacement of the shaft center while rotating is numerically calculated. The frequency and amplitude of the shaft vibration are analyzed by numerical FFT. From consideration of the generating mechanism of the shaft vibration, it is found that the outer race waviness of the order n=jZ+1 (j: integer, Z: total ball number) generates a backward exciting force and vibration with frequency of jZf/sub c/ (f/sub c/: cage speed), while that of n=jZ-1 generates forward ones of the same frequency. The inner race waviness of n=jZ+1 generates a forward exciting force and vibration with frequency of jZ(f/sub r/-f/sub c/)+f/sub r/ (f/sub r/: inner race speed), while that of n=jZ-1 generates backward ones with frequency of jZ(f/sub r/-f/sub c/)-f/sub r/. It is also found that small amplitude vibrations with frequencies jZfc and jZ(f/sub r/-f/sub c/)/spl plusmn/f/sub r/ can be generated by the waviness of the order number different from n=jZ/spl plusmn/1, when the ball number Z is a prime number, e.g. 7. A good qualitative agreement between calculated and experimental Campbell diagrams for shaft vibration is obtained.