Analysis of a Ball Bearing With Waviness Considering the Centrifugal Force and Gyroscopic Moment of the Ball

2003 ◽  
Vol 125 (3) ◽  
pp. 487-498 ◽  
Author(s):  
G. H. Jang ◽  
S. W. Jeong
Keyword(s):  
Centrifugal Force ◽  
Contact Force ◽  
Ball Bearing ◽  
Vibration Frequencies ◽  
Governing Equations ◽  
Equilibrium Equations ◽  
Gyroscopic Moment ◽  
Rolling Elements ◽  
Force Contact ◽  
Force Displacement

This research presents an analytical method to calculate the characteristics of the ball bearing under the effect of the waviness in its rolling elements and the centrifugal force and gyroscopic moment of ball. The waviness of rolling elements is modeled by using sinusoidal function, and the centrifugal force and gyroscopic. moment of ball are included in the kinematic constraints and force equilibrium equations to produce the nonlinear governing equations. To improve the convergence of the numerical solution of the nonlinear governing equations, it includes the derivatives of the gyroscopic moment and load-deflection constant of each race in the Newton-Raphson formulation. The accuracy of this research is validated by comparing with the prior research, i.e., (i) the contact force, contact angle in case of considering only the centrifugal force and gyroscopic moment of ball, and (ii) the contact force and vibration frequencies in case of considering only the waviness, respectively. It investigates the stiffness, contact force, displacement and vibration frequencies of the ball bearing, considering not only the centrifugal force and gyroscopic moment of ball but also the waviness of the rolling elements.

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

2021 ◽  
Vol 69 (2) ◽  
pp. 89-101
Author(s):  
Pingping Hou ◽  
Liqin Wang ◽  
Zhijie Xie ◽  
Qiuyang Peng
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Vibration Measurement ◽  
Vibration Frequencies ◽  
Outer Race ◽  
Response Characteristics ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Initial Clearance ◽  
Improved Model

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.

Contact force analysis on two-fingered robot grasping

2020 ◽  
pp. 146441932096402
Author(s):  
Jiun-Ru Chen ◽  
Wei-En Chen ◽  
CH Liu ◽  
Yin-Tien Wang ◽  
CB Lin ◽  
...  
Keyword(s):  
Kinetic Analysis ◽  
Contact Force ◽  
Numerical Procedure ◽  
Spherical Body ◽  
Solution Procedure ◽  
The Body ◽  
Contact Forces ◽  
Grasping Forces ◽  
Robot Grasping ◽  
Force Displacement

A procedure for inverse kinetic analysis on two hard fingers grasping a hard sphere is proposed in this study. Contact forces may be found for given linear and angular accelerations of a spherical body. Elastic force-displacement relations predicted by Hertz contact theory are used to remove the indeterminancy produced by rigid body modelling. Two types of inverse kinetic analysis may be dealt with. Firstly, as the fingers impose a given tightening displacement on the body, and carry it to move with known accelerations, corresponding grasping forces may be determined by a numerical procedure. In this procedure one contact force may be chosen as the principal unknown, and all other contact forces are expressed in terms of this force. The numerical procedure is hence very efficient since it deals with a problem with only one unknown. The solution procedure eliminates slipping thus only nonslip solutions, if they exist, are found. Secondly, when the body is moving with known accelerations, if the grasping direction of the two fingers is also known, then the minimum tightening displacement required for non-sliding grasping may be obtained in closed form. In short, the proposed technique deals with a grasping system that has accelerations, and in this study the authors show that indeterminancy may be used to reduce the complexity of the problem.

Noise calculation method of deep groove ball bearing caused by vibration of rolling elements considering raceway waviness

2021 ◽  
pp. 095440622110458
Author(s):  
Minjie Sun ◽  
Haojie Xu ◽  
Qi An
Keyword(s):  
Ball Bearing ◽  
Axial Direction ◽  
Rolling Bearing ◽  
Mechanical Analysis ◽  
Machining Accuracy ◽  
Surface Waviness ◽  
Random Surface ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Rolling Elements

Raceway waviness error is the main reason to cause rolling elements to vibrate along axial direction and emit noise. In this paper, the mechanical analysis on deep groove ball bearing is carried out. With auto-correlation function, random surface waviness of both inner and outer raceways is simulated. A contact model of rolling elements and raceways considering surface waviness is established. Combining with the theory of acoustic equation, a calculation model is established for the noise caused by vibration of rolling elements and inner ring. The results show that with the decrease of machining accuracy, the noise of rolling elements increases due to axial vibration; with the increase of rotation speed, the noise also increases. Besides, the spectrum of radiation noise of inner raceway with different waviness amplitudes is given. The results indicate that the 3-D waviness on raceway surface has an influence on the vibration and the noise emitted by both rolling elements and inner ring, and provide guidance for sound control in deep groove rolling bearing.

scholarly journals A Study of Prevention of Fretting of Ball Bearing Using the Revolution of Rolling Elements

2011 ◽  
Vol 77 (779) ◽  
pp. 2894-2904
Author(s):  
Shoji NOGUCHI ◽  
Kazuaki MATSUO ◽  
Satoshi YOSHIKAWA ◽  
Takashi NOGI
Keyword(s):  
Ball Bearing ◽  
Rolling Elements ◽  
The Revolution

Contact Stress FEM Analysis of Deep Groove Ball Bearing Based on ANSYS Workbench

2014 ◽  
Vol 574 ◽  
pp. 21-26 ◽  
Author(s):  
Hua Rong Xin ◽  
Lin Zhu
Keyword(s):  
Contact Stress ◽  
Ball Bearing ◽  
Fem Analysis ◽  
Bearing Contact ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Rolling Elements ◽  
Practical Engineering ◽  
Stress And Deformation ◽  
Ansys Workbench

The 3D nonlinear contact model of a deep groove ball bearing was established in ANSYS Workbench software. With the reasonable setting of the boundary conditions,the contact stress and deformation are calculated in Static Structural (ANSYS) by using the finite element method,and the contact stress and deformation of the inner ring, the outer ring and the rolling elements were obtained. Furthermore, the computational values are consistent with the Hertz values. The results show that solving the bearing contact problem with ANSYS Workbench software is feasible and it coincides with the stress and deformation of the actual situation. The FEM results provide reference for the design,optimization and failure analysis of rolling bearings and have practical engineering value.

Effect of Centrifugal Force on Frequency Characteristic of Rotating Hollow Cylinders Using a Newly Designed Cylindrical Super Element

2006 ◽  
Author(s):  
M. Bonakdar ◽  
M. T. Ahmadian
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Centrifugal Force ◽  
Natural Frequencies ◽  
Rotating Cylinder ◽  
Finite Cylinder ◽  
Vibration Frequencies ◽  
Hollow Cylinders ◽  
Special Case

A sixteen node cylindrical super element is presented for evaluating the free vibration characteristics of a rotating laminated cylinder with conventional boundary conditions. It is shown that the natural frequencies are affected considerably when the centrifugal force is also taken into account. The vibration frequencies of rotating finite cylinder, obtained by conventional finite element are used to evaluate the accuracy of this approach. The special case of a stationary cylinder with zero spinning velocity is also considered as a check on this method. Results indicate only few number of cylindrical super elements are capable of predicting the natural frequency of the rotating cylinder within the same limit as many elements used in the conventional finite element method.

Identification of Contact Conditions from Contact Force and Moment - Experimental Verification in Effective Sensing Strategy -

2009 ◽  
Vol 21 (2) ◽  
pp. 236-244 ◽  
Author(s):  
Takayoshi Yamada ◽  
◽  
Tetsuya Mouri ◽  
Akira Tanaka ◽  
Nobuharu Mimura ◽  
...  
Keyword(s):  
Contact Force ◽  
Contact Line ◽  
Contact Conditions ◽  
Contact Type ◽  
Degree Of Separation ◽  
Direction Of Movement ◽  
Force Contact ◽  
The Difference ◽  
Contact Position ◽  
Small Eigenvalues

This paper discusses an effective sensing strategy for identification of contact conditions by using experiments. The contact conditions include contact position, contact force, contact type, direction of contact normal, and direction of contact line. To distinguish contact type more quickly and accurately, we must raise the degree of separation of large and small eigenvalues of a covariance matrix for estimating contact moment. Firstly, several sensing strategies are investigated through experiments. The difference of these strategies is the origin and direction of movement because the contact moment, which expresses the characteristic of contact type, is generated at a contact frame. Secondly, a more effective sensing movement is suggested from experimental results. Finally, it is pointed out that these strategies are related to sensing movement by a human being.

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