Dynamic Analysis of Cage Stress in Tapered Roller Bearings Using Component-Mode-Synthesis Method

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Tomoya Sakaguchi ◽  
Kazuyoshi Harada
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Boundary Point ◽  
Axial Load ◽  
Synthesis Method ◽  
Load Condition ◽  
Component Mode Synthesis ◽  
Analysis Model ◽  
Tapered Roller ◽  
Tapered Roller Bearings

In order to investigate cage stress in tapered roller bearings, a dynamic analysis tool considering both the six degrees of freedom of motion of the rollers and cage and the elastic deformation of the cage was developed. Cage elastic deformation is equipped using a component-mode-synthesis (CMS) method. Contact forces on the elastically deforming surfaces of the cage pocket are calculated at all node points of finite-elements on it. The location and pattern of the boundary points required for the component-mode-synthesis method were examined by comparing cage stresses in a static condition of pocket forces and constraints calculated by using the finite-element and the CMS methods. These results indicated that one boundary point lying at the center on each bar is appropriate for the effective dynamic analysis model focusing on the cage stress, especially at the pocket corners of the cages, which are actually broken. A behavior measurement of a polyamide cage in a tapered roller bearing was conducted for validating the analysis model. It was confirmed in both the experiment and analysis that the cage whirled under a large axial load condition and the cage center oscillated in a small amplitude under a small axial load condition. In the analysis, the authors discussed the four models including elastic bodies having a normal eigenmode of 0, 8 or 22, and rigid-body. There were small differences among the cage center loci of the four models. These two cages having normal eigenmodes of 0 and rigid-body whirled with imperceptible fluctuations. At least approximately 8 normal eigenmodes of cages should be introduced to conduct a more accurate dynamic analysis although the effect of the number of normal eigenmodes on the stresses at the pocket corners was insignificant. From the above, it was concluded to be appropriate to introduce one boundary point lying at the center on each pocket bar of cages and approximately 8 normal eigenmodes to effectively introduce the cage elastic deformations into a dynamic analysis model.

A New Running Torque Formula for Tapered Roller Bearings Under Axial Load

1987 ◽  
Vol 109 (3) ◽  
pp. 471-477 ◽  
Author(s):  
S. Aihara
Keyword(s):  
Axial Load ◽  
Roller Bearing ◽  
Rolling Resistance ◽  
Careful Examination ◽  
Previous Theory ◽  
Load Effect ◽  
Roller Bearings ◽  
Tapered Roller ◽  
Tapered Roller Bearings ◽  
Running Torque

Conventional formula for calculating the running torque of tapered roller bearings often showed discrepancy from actual running torque, particularly under axial load. Therefore, an equation was formulated based on the knowledge of EHL rolling resistance and EHL oil film thickness. Careful examination of actual bearing running torque suggested the load dependency of EHL rolling resistance which previous theory did not include. Such load effect was confirmed by means of two disc machine and the equation was partly corrected. A new running torque formula of a tapered roller bearing under axial load was proposed and good agreement with actual bearing torque was confirmed.

A Hybrid Coordinates Component Mode Synthesis Method for Dynamic Analysis of Structures With Localized Nonlinearities

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Huan He ◽  
Tao Wang ◽  
Guoping Chen
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Synthesis Method ◽  
Nonlinear Dynamic Analysis ◽  
Higher Order ◽  
Component Mode Synthesis ◽  
Linear Component ◽  
Nonlinear Component ◽  
Order Matrix ◽  
Modal Coordinates

This paper reports on the development of the component mode synthesis (CMS) method using hybrid coordinates for a localized nonlinear dynamic system. As is well known, the CMS method is effective in reducing the degrees-of-freedom (DOF) of the system. In contrast to most existing CMS methods, which are usually developed for linear systems, a new CMS method using hybrid coordinates for nonlinear dynamic analysis has been developed in this paper. Generally, the system is divided into two parts, namely, a linear component and a nonlinear component. The equations of the linear component can be transformed into the modal coordinates using its linear vibration modes. To improve the accuracy, the equivalent higher-order matrix of the system is developed to capture the effects of the neglected higher-order modes. Quite different from early works, the flexibility attachment matrix can be obtained without using the inverse of the stiffness matrix by using an equivalent higher-order matrix, thus making it easier to deal with those components that have rigid-body freedom when formulating the residual flexibility attachment matrix. By introducing the residual flexibility attachment matrix and the retained lower-order modes, the dynamic governing equations of the linear component can be converted into the modal space and expressed by a few modal coordinates. To adopt the entire set of nonlinear terms into the final equations, the equations of the nonlinear component are kept in their original form. Compatibility conditions at the interface are used to combine the nonlinear component and the linear component to form the synthesis equations, which are expressed in hybrid coordinates. Finally, the computational efficiency and accuracy of the presented method is demonstrated using numerical examples.

Dynamic analysis of a tapered roller bearing

2018 ◽  
Vol 70 (1) ◽  
pp. 191-200 ◽  
Author(s):  
Sier Deng ◽  
Jinfang Gu ◽  
Yongcun Cui ◽  
Wenhu Zhang
Keyword(s):  
Friction Coefficient ◽  
Differential Equations ◽  
Dynamic Analysis ◽  
Axial Load ◽  
Roller Bearing ◽  
Radial Load ◽  
Content Type ◽  
Tapered Roller Bearing ◽  
Tapered Roller ◽  
The Impact

Purpose This study aims to analyze the roller dynamic characteristics and cage whirling of tapered roller bearing considering roller tilt and skew which provide a theoretical basis for the design and application of tapered roller bearing. Design/methodology/approach Based on rolling bearing dynamic analysis, the dynamic differential equations of tapered roller bearing are established. Fine integral method and predict correct Adams–Bashforth–Moulton multi-step method are used to solve the dynamic differential equations of tapered roller bearings. Findings Friction at the flange contact between roller and large flange is the chief factor of roller skew. In comparison to cone speed, axial loads have more visible effect on roller skew, and proper speed or axial load is beneficial to sustain cage motion and decrease cage instability. Under the combined effort of axial load and radial load, the distribution of roller skew is correlated to the roller-flange contact load. In addition, roller skew angle in loaded zone is larger than that in unloaded zone; hence, it is helpful for cage stability if an extent radial load is applied. The pocket clearance of cage has very small influence on roller skew; therefore, a reasonable pocket clearance is suggested to assure minimum instability of cage. Friction coefficient of flange contact has a large effect on roller skew, and cage whirl is found to demonstrate a circular orbit with increasing friction coefficient. Originality/value The dynamic differential equations of tapered roller bearing considering roller large end/inner ring back face rib contact under various lubrication states were established. The impact of flange friction working conditions and cage pocket clearance on cage instability and roller skew were focused on. It is the first time that the ratio of the standard deviation of the cage-center translational speed to its mean value is used to access the instability of cage in tapered roller bearing.

Dynamic Analysis of Cage Behavior in a Tapered Roller Bearing

2005 ◽  
Author(s):  
Tomoya Sakaguchi ◽  
Kazuyoshi Harada
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Simulation ◽  
Roller Bearing ◽  
Three Dimensional ◽  
Simulation Tool ◽  
Analysis Software ◽  
Traction Forces ◽  
Tapered Roller Bearing ◽  
Tapered Roller ◽  
Tapered Roller Bearings

We have developed a three-dimensional dynamic simulation tool for tapered roller bearings using commercially available analysis software, ADAMS (MSC. Software). Cage motion in six degrees was analyzed with the simulation tool and was measured by experiments. The results showed the validity of the simulation tool. Regarding the cage behavior, as the traction forces between rollers and races grew, the amplitude of the cage whirl motion increased up to the radial guide clearance between the roller and its cage pocket.

scholarly journals Gyroscopic Mode Synthesis in the Dynamic Analysis of a Multi-Shaft Rotor-Bearing System

1985 ◽  
Author(s):  
Zheng Zhao-Chang ◽  
Zhou Xiao-Ping ◽  
Li De-Bao ◽  
Zhang Lian-Xiang ◽  
Liu Ting-Yi ◽  
...  
Keyword(s):  
Dynamic Analysis ◽  
Synthesis Method ◽  
Component Mode Synthesis ◽  
Complex Mode ◽  
Numerical Examples ◽  
Complex Modes ◽  
Rotor Bearing ◽  
Bearing System

A mode synthesis method used in the dynamic analysis of multi-shaft rotor-bearing system has been developed in this paper. By introducing the idea of connecting springs and dampers, and using gyroscopic modes instead of complex modes in the mode synthesis, this method differs not only from classical component mode synthesis method, but also from complex mode synthesis. Several numerical examples show the advantages of this method.

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