The dynamic behaviour of a system that includes a rolling bearing

Wensing, J.A.; Nijen, G.C. van

doi:10.1243/1350650011543763

Cited by 7 publications

(5 citation statements)

References 11 publications

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“…In addition, there is the higher amplitude for the vibration caused by the waviness with lower order, which is supported by Wensing and Van Nijen. 2 It is easier for the inner ring waviness to arouse some additional vibrations than the outer ring waviness due to the rotation of the inner ring. The corresponding additional frequency, such as peak 5 in Figure 8, is uncertain and unpredictable, which may be changed with the operating condition.…”

Section: Resultsmentioning

confidence: 99%

“…In order to determine the relationship between the waviness amplitude and the excitation force of a ball bearing, as well as to predict the vibration frequencies due to the load deflection nonlinearity, the researches were carried out by Wardle, 1 both theoretically and experimentally. These research results have been accepted by bearing manufacturers 2 and also taken as a judgment criterion of the numerical computing results by many scholars. For roller bearings, the basic model and effect of waviness have been obtained.…”

Section: Introductionmentioning

confidence: 91%

“…As shown in Figure 3, a SRB is composed of several parts, including rollers, inner ring, outer ring, cage, and so on. While the waviness is made up of a series of sine or cosine curves, which is widely accepted for its clear physical significance in mechanism explanation and facile implementation to numerical simulation, 1–11,26 thereby there are no essential differences between the waviness model in this paper and the previous waviness models. Equations (1) and (2) are employed to characterize the waviness of inner and outer rings, respectively

Figure 3.Schematic diagram of a spherical roller bearing. …”

Section: Modelingmentioning

confidence: 99%

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Mechanical analysis of spherical roller bearings due to surface waviness

Liu

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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This work presents a theoretical model to research the vibration due to surface waviness of spherical roller bearings (SRBs), taking account of the self-aligning feature and the external axial load. The surface waviness is described by cosinoidal functions. The self-aligning features, including the variation law of the self-aligning contact angle and the interaction with the external loads, are introduced into the non-Hertzian contact model. The nonlinear equations are solved by Runge–Kutta method and the proposed model is validated by comparing with the results of the published references. The results show more characteristic frequencies will be excited under the self-aligning operating condition, whereby the improved equations proposed in this paper are recommended to instead of the previous ones to predict characteristic frequencies of the waviness vibration in an SRB. In addition, these characteristic vibrations caused by waviness are obviously influenced by the magnitude and the direction of the self-aligning contact angle. A proper pretightening load should be chosen according to the self-aligning feature or else it will lead to hidden dangers. The radial clearance and the waviness amplitude can both highlight the effect of waviness. And the vibration caused by a larger radial clearance may be fiercer than the vibration due to waviness.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

Figure 3.Schematic diagram of a spherical roller bearing. …”

Section: Modelingmentioning

confidence: 99%

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Mechanical analysis of spherical roller bearings due to surface waviness

Liu

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…; 7 x and y are the displacements along Xand Y -directions, respectively;ẋ andẏ are the velocities along Xand Ydirections, respectively;ẍ andÿ are the accelerations along Xand Y -directions, respectively; F x and F y are the components of the external force applying on the shaft; κ e is the total contact stiffness between the ball and the races. In addition, λ j is the loading zone parameter for the jth ball, which can be defined as…”

Section: Equations Of Motionmentioning

confidence: 99%

Vibration Characteristics of a Ball Bearing Considering Point Lubrication and Nonuniform Surface Waviness

Liu¹,

Shi²,

Shao³

2018

The International Journal of Acoustics and Vibration

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Surface waviness is one of the main geometrical errors in ball bearings. Time-varying contact stiffness excitations (TCSEs) produced by the uniform and nonuniform waviness on races of a lubricated ball bearing cannot be accurately described by the previous uniform waviness models considering the time-varying displacement excitation (TDE) in the literature. To overcome this problem, a new dynamic modelling method coupling both the TDE and TCSE produced by the uniform and nonuniform waviness on the races of a lubricated ball bearing is proposed. Effects of the amplitude and nonuniform distribution of waviness on the contact stiffness between one ball and races of the lubricated and unlubricated bearings are investigated, as well as vibrations of the bearings produced by the uniform and nonuniform waviness. Numerical results show that the proposed model can describe the TDE and TCSE produced by the uniform and nonuniform waviness on the races of the lubricated bearing, which cannot be described by the previous uniform waviness models. The results also show that the peak frequencies of spectra of accelerations of the bearing with the waviness will be changed by the lubricating film oil. It seems that the proposed model can provide a new dynamic modelling method for formulating the vibrations of a lubricated bearing with the uniform and nonuniform waviness on its races. NOMENCLATURE c Damping coefficient, N m/s D i Diameter of the normal inner race, mm D o Diameter of the normal outer race, mm d Diameter of the ball, mm E 1 and E 2 Elastic modulus of the two contact components, Pa E * Equivalent elastic modulus of the contact components, Pa F x and F y Components of the external force applying on the shaft, N G Dimensionless material parameter H c Dimensionless central film thickness h c Central film thickness, mm h ij Central film thickness between the ball and inner race, mm h oj Central film thickness between the ball and outer race, mm j jth ball K d Total contact stiffness between one ball and two races, N/mn K id Contact stiffness between the ball and normal unlubricated inner race, N/mn K od Contact stiffness between the ball and normal unlubricated outer race, N/mn K wi Contact stiffness between the ball and abnormal unlubricated inner race, N/mn K wo Contact stiffness between the ball and abnormal unlubricated outer race, N/mn K doi Contact stiffness between the ball and lubricated inner race, N/mn K doo Contact stiffness between the ball and lubricated outer race, N/mn

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“…Lynagh et al (2000) used an analytical model to investigate vibration responses of an angular contact ball bearing with the surface waviness in a high speed routing spindles. Wensing and Nijen (2001) used a new method including the time-dependent stiffness and mass properties of a rolling element bearing application to investigate effects of the damping of the rolling element bearing on parametric excitations in a real bearing application. Jang and Jeong (2002) used a dynamic rigid rotor model with five degree of freedom to investigate the effect of the surface waviness of mating components of a angular contact ball bearing on principal frequencies of system vibration responses and their harmonics.…”

Section: Introductionmentioning

confidence: 99%

Vibration modelling of nonuniform surface waviness in a lubricated roller bearing

Liu

Shao

2016

Journal of Vibration and Control

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Surface waviness is one important source of vibrations in a roller bearing. When the surface waviness occurs on the surface of the inner or outer race of a roller bearing, a time-varying deflection excitation and a time-varying contact stiffness excitation can be generated due to the changes in the curvature radii of the race with surface waviness at the contact position between the roller and the race of the roller bearing. In this paper, a new dynamic model (TDCE model) considering both the time-varying deflection excitation, the time-varying contact stiffness excitation, and the lubricating oil film is proposed to investigate vibration responses of a lubricated roller bearing with a uniform and a nonuniform surface waviness on its races, which cannot be accurately modelled by the previous time-varying deflection excitation (PTDE) model in the literature. Effects of the number, the maximum amplitude, and the nonuniform distribution of the surface waviness on the contact stiffness between one roller and the race with surface waviness are investigated, as well as the vibration responses of a lubricated roller bearing. Numerical results from the proposed model are compared with those from the PTDE model in the literature, which shows that the proposed TDCE model can provide more accurate impulses generated by the surface waviness on the races of the roller bearing. Moreover, the results show that the proposed method can provide a new vibration modelling method for a lubricated roller bearing with the uniform and nonuniform surface waviness on its races.

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The dynamic behaviour of a system that includes a rolling bearing

Cited by 7 publications

References 11 publications

Mechanical analysis of spherical roller bearings due to surface waviness

Mechanical analysis of spherical roller bearings due to surface waviness

Vibration Characteristics of a Ball Bearing Considering Point Lubrication and Nonuniform Surface Waviness

Vibration modelling of nonuniform surface waviness in a lubricated roller bearing

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