An Improved Analytical Model of Friction and Ball Motion in Linear Ball Bearings With Application to Ball-to-Ball Contact Prediction

2018 ◽  
Author(s):  
Bo Lin ◽  
Molong Duan ◽  
Chinedum E. Okwudire ◽  
Jason S. Wou
Keyword(s):  
Analytical Model ◽  
Analytical Formula ◽  
Point Contact ◽  
Friction Model ◽  
Linear Velocity ◽  
Contact Forces ◽  
Ball Bearings ◽  
Friction Behavior ◽  
Rolling Ball ◽  
Ball Contact

The friction behavior of rolling ball machine components like linear ball bearings is very important to their functionality. For instance, differences in linear velocity of balls induces ball-to-ball contact in certain circumstances, resulting in significant increases and variations in friction. In this paper, an improved analytical formula for determining the linear velocity of balls in four-point-contact linear ball bearings is derived as a function of contact angle deviations and contact forces. The analytical formula is validated against a comprehensive friction model in the literature and shown to be in good agreement, while an oversimplified analytical model proposed by the authors in prior work is shown to be inaccurate. A case study is presented where insights gained from the derived analytical formula are used to mitigate velocity difference of balls in a linear ball bearing which otherwise would experience ball-to-ball contact.

A Simplified Analytical Model of Rolling/Sliding Behavior and Friction in Four-Point-Contact Ball Bearings and Screws

2017 ◽  
Author(s):  
Bo Lin ◽  
Molong Duan ◽  
Chinedum E. Okwudire ◽  
Jason S. Wou
Keyword(s):  
Analytical Model ◽  
Contact Point ◽  
Point Contact ◽  
Contact Angles ◽  
Friction Model ◽  
Contact Forces ◽  
Ball Bearings ◽  
Contact Points ◽  
Pure Rolling ◽  
Coulomb Friction Model

Four-point contact between ball and raceways is common in machine elements like ball bearings and ball screws. The ideal four-point-contact machine element is designed with pure rolling (i.e., no sliding at contact points) to minimize friction. However, this ideal may not always be achieved, leading to sliding and higher frictional forces. In this paper, a simplified analytical model for rolling/sliding behavior and friction in four-point contact is developed, based on Coulomb friction model and rigid body assumption. It is found that pure rolling is only possible when the contact-point geometry satisfies a certain relationship. When pure rolling condition fails to hold, the sliding contact point(s) can be determined analytically as a function of contact forces and contact angles. Case studies are presented to demonstrate how the proposed model could elucidate the roles of misalignments, manufacturing errors and loading conditions on rolling/sliding behavior and friction.

Analytical and Low-Order Numerical Modeling of Ball-to-Ball Contact Friction in Linear Ball Bearings and Ball Screws

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Bo Lin ◽  
Molong Duan ◽  
Chinedum E. Okwudire
Keyword(s):  
Case Studies ◽  
Numerical Models ◽  
Experimental Studies ◽  
Point Contact ◽  
Ball Screw ◽  
Contact Friction ◽  
Ball Bearings ◽  
Friction Behavior ◽  
Ball Contact ◽  
Low Order

Analytical and low-order numerical models are very useful for studying friction behavior of rolling element machine components like ball bearings and ball screws. This is because they provide generalizable insights into friction behavior at much lower computational costs compared with high-order numerical models like finite element analysis (FEA). While analytical and low-order numerical models in the literature are mainly focused on ball-to-groove contact friction, experimental studies have shown that ball-to-ball contact friction is also very important. This is especially true for linear ball bearings/guideways and ball screws which, unlike rotary ball bearings, do not typically make use of caged balls to prevent ball-to-ball contact. Therefore, in this paper, low-order numerical models for ball-to-ball contact friction in linear ball bearings and ball screws are developed. Furthermore, an analytical model for ball-to-ball contact friction in four-point contact linear ball bearing is derived by making simplifications to its low-order numerical model. Compared with ball-to-ball friction predictions from FEA models developed in ansys, the proposed numerical models are shown in case studies to be accurate within 7%, while computing at least three orders of magnitude faster. Moreover, case studies are used to demonstrate how the developed models can be used in practice, e.g., for the mitigation of ball-to-ball contact friction in linear ball bearings and the prediction of friction variation during the operation of a ball screw.

scholarly journals Modelling elastic structures with strong nonlinearities with application to stick–slip friction

2014 ◽  
Vol 470 (2161) ◽  
pp. 20130593 ◽  
Author(s):  
Robert Szalai
Keyword(s):  
Point Contact ◽  
Linear Structure ◽  
Transformation Method ◽  
Friction Model ◽  
Contact Forces ◽  
Stick Slip ◽  
Lipschitz Continuous ◽  
Contact Points ◽  
Dimensional Equation ◽  
Low Dimensional

An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low-dimensional equation with memory. The method is general and well suited to problems with isolated discontinuities such as friction and impact at point contact. It is assumed that the structure is composed of two parts: a continuum but linear structure and finitely many discrete but strong nonlinearities acting at various contact points of the elastic structure. The localized nonlinearities include discontinuities, e.g. the Coulomb friction law. Despite the discontinuities in the model, we demonstrate that contact forces are Lipschitz continuous in time at the onset of sticking for certain classes of structures. The general formalism is illustrated for a continuum elastic body coupled to a Coulomb-like friction model.

Nonlinear Normal Modes and the LuGre Friction Model Parameter Identification

2014 ◽  
Author(s):  
Abdallah Hadji ◽  
Njuki Mureithi
Keyword(s):  
Contact Region ◽  
Signal Reconstruction ◽  
Superposition Principle ◽  
Harmonic Balance Method ◽  
Friction Model ◽  
Contact Forces ◽  
Fourier Series Expansion ◽  
Model Parameters ◽  
Harmonic Forms ◽  
Friction Behavior

A Hybrid friction model has recently been developed by Azizian and Mureithi [1] to simulate the general friction behavior between surfaces in contact. However, identification of the model parameters remains an unresolved problem. To identify the parameters of the friction model, the following quantities are required: contact forces (friction and impact forces), the slip velocity and displacement in the contact region. Direct measurement of these quantities is difficult. In the present work, a beam clamped at one end and simply supported with the consideration of friction effect at the other is used as a mechanical amplifier of the friction effects at the microscopic level. Using this simplified approach, the contact forces, the sliding velocity and the displacement can be indirectly obtained by measuring the beam vibration response. A new method based on nonlinear modal analysis to calculate the contact forces is developed in the present work. The method is based on the modal superposition principle and Fourier series expansion. For the harmonic balance method, two approaches were tested. The approach based on sub-harmonic forms gave the best results. Signal reconstruction made it possible to accurately identify the parameters of the hybrid friction model with a multiple step approach.

An improved nonlinear model considering relative velocity for the friction behavior between untwisted glass-fiber tow and roller

2021 ◽  
pp. 004051752110308
Author(s):  
Yang Liu ◽  
Zhong Xiang ◽  
Xiangqin Zhou ◽  
Zhenyu Wu ◽  
Xudong Hu
Keyword(s):  
Friction Coefficient ◽  
Glass Fiber ◽  
Relative Velocity ◽  
Friction Model ◽  
Woven Fabric ◽  
Test Results ◽  
Application Process ◽  
Friction Behavior ◽  
Improved Model

Friction between the tow and tool surface normally happens during the tow production, fabric weaving, and application process and has an important influence on the quality of the woven fabric. Based on this fact, this paper studied the influence of tension and relative velocity on the three kinds of untwisted-glass-fiber tow-on-roller friction with a Capstan-based test setup. Furthermore, an improved nonlinear friction model taking both tension and velocity into account was proposed. According to statistical test results, firstly, the friction coefficient was found to be positively correlated with tension and relative velocity. Secondly, tension and velocity were complementary on the tow-on-roller friction behavior, with neither being superior to the other. Thirdly, an improved model was found to present well the nonlinear characteristics between friction coefficient and tension and velocity, and predicational results of the model were found to agree well with the observations from Capstan tests.

Finite Element Analysis of Large-Size Yaw Bearings with Supporting Structure in Wind Turbine

2014 ◽  
Vol 672-674 ◽  
pp. 1550-1553
Author(s):  
Zhen Guo Shang ◽  
Zhong Chao Ma ◽  
Zhen Sheng Sun
Keyword(s):  
Finite Element ◽  
Wind Turbine ◽  
Point Contact ◽  
Element Model ◽  
Contact Forces ◽  
Element Analysis ◽  
Supporting Structure ◽  
Rolling Elements ◽  
Yaw Bearing ◽  
Compression Springs

A procedure for obtaining the load distribution in a four point contact wind turbine yaw bearing considering the effect of the structure’s elasticity is presented. The inhomogeneous stiffness of the supporting structures creates a variation in the results obtained with a rigid model. A finite element model substituting the rolling elements with nonlinear compression springs has been built to evaluate the effect of the supporting structure elasticity on the contact forces between the rolling elements and the raceways.

Mechanical Power Losses of Ball Bearings: Model and Experimental Validation

2021 ◽  
pp. 1-29
Author(s):  
Ahmet Dindar ◽  
Amit Chimanpure ◽  
Ahmet Kahraman
Keyword(s):  
Dynamic Model ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Mechanical Power ◽  
Ball Bearings ◽  
Power Losses ◽  
Euler Parameters ◽  
Surface Shear ◽  
Axial Forces ◽  
Set Up

Abstract A tribo-dynamic model of ball bearings is proposed to predict their load-dependent (mechanical) power losses. The model combines (i) a transient, point contact mixed elastohydrodynamic lubrication (EHL) formulation to simulate the mechanics of the load carrying lubricated ball-race interfaces, and (ii) a singularity-free dynamics model, and establishes the two-way coupling between them that dictates power losses. The dynamic model employs a vectoral formulation with Euler parameters. The EHL model is capable of capturing two-dimensional contact kinematics, velocity variations across the contact as well as asperity interactions of rough contact surfaces. Resultant contact surface shear distributions are processed to predict mechanical power losses of example ball bearings operating under combined radial and axial forces. An experimental set-up is introduced for measurement of the power losses of rolling-element bearings. Sets of measurements taken by using the same example ball bearings are compared to those predicted by the model to assess its accuracy in predicting mechanical power loss of a ball bearing within wide ranges of axial and radial forces.

Numerical Investigation of Size Effect on Dry Friction Behavior in Micro Upsetting Process

2014 ◽  
Vol 997 ◽  
pp. 321-324
Author(s):  
Wei Zheng ◽  
Guang Chun Wang ◽  
Bing Tao Tang ◽  
Xiao Juan Lin ◽  
Yan Zhi Sun
Keyword(s):  
Friction Coefficient ◽  
Size Effect ◽  
Dry Friction ◽  
Normal Pressure ◽  
Friction Model ◽  
Strain Hardening Exponent ◽  
Forming Process ◽  
Friction Behavior ◽  
Initial Yield Stress ◽  
Coulomb’S Friction

After modifying the Wahime/Bay friction model, a new friction model suitable for micro-forming process without lubrication is established. In this model, it is shows that the friction coefficient is a function of strain hardening exponent, the normal pressure and the initial yield stress of material. Based on the experimental data, the micro-upsetting process is simulated using the proposed friction model. The simulation results are used to investigate the size effect on the dry friction behavior. It is found that the Coulomb’s friction coefficient is dropping with miniaturization of specimens when the amount of reduction is not too large.

Oil Film Thickness and Rolling Friction in Elastohydrodynamic Point Contact

1971 ◽  
Vol 93 (3) ◽  
pp. 371-379 ◽  
Author(s):  
R. Gohar
Keyword(s):  
Film Thickness ◽  
Tungsten Carbide ◽  
Material Properties ◽  
High Pressures ◽  
Glass Plate ◽  
Point Contact ◽  
Rolling Friction ◽  
Significant Alteration ◽  
Oil Film ◽  
Rolling Ball

The effect of material properties upon the film thickness in elastohydrodynamic point contact is demonstrated with a rolling ball and plate machine. A 220 fold range of Young’s modulus is employed and a maximum Hertzian pressure of 5 × 105 lb f/in2 is reached. The oil film, which is measured by interferometry, shows no significant alteration at such high pressures, and is also fairly insensitive to the choice of bounding materials. Using a technique similar to that employed by Crook, the rolling friction between a tungsten carbide and a glass plate is found and compared with theory. The effect of spin is investigated and found to be slight.

A friction based approach for modeling wire bonding

2013 ◽  
Vol 2013 (1) ◽  
pp. 000208-000212 ◽  
Author(s):  
Simon Althoff ◽  
Jan Neuhaus ◽  
Tobias Hemsel ◽  
Walter Sextro
Keyword(s):  
Contact Area ◽  
Copper Wire ◽  
Point Contact ◽  
Welding Process ◽  
Friction Model ◽  
Ultrasonic Power ◽  
Physical Effects ◽  
Wedge Bonding ◽  
Work Done ◽  
Do So

A model approach for wedge/wedge bonding copper wire is presented. The connection between wire and substrate is based on a variety of physical effects, but the dominant one is the friction based welding while applying ultrasound. Consequently, a friction model was used to investigate the welding process. This model is built up universal and can be used to describe the formation of micro welds in the time variant contact area between wire and substrate. Aim of the model is to identify the interactions between touchdown, bond normal force, ultrasonic power and bonding time. To do so, the contact area is discretized into partial areas where a Point Contact Model is applied. Based on this approach it is possible to simulate micro and macro slip inside the contact area between wire and substrate. The work done by friction force is a main criterion to define occurring micro joints which influence the subsequent welding.

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