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.

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.

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.

Ball Motion and Sliding Friction in a Four-Contact-Point Ball Bearing

2007 ◽  
Vol 129 (4) ◽  
pp. 801-808 ◽  
Author(s):  
Alexandre Leblanc ◽  
Daniel Nelias
Keyword(s):  
Ball Bearing ◽  
Sliding Friction ◽  
Contact Point ◽  
Friction Model ◽  
Operating Conditions ◽  
Published Data ◽  
Contact Points ◽  
Coulomb Friction Model ◽  
Gyroscopic Effects ◽  
Control Criterion

An analysis of double arched ball bearing, which considers centrifugal forces and gyroscopic effects, is performed. Based on operating conditions of a five DOF inner ring and Coulomb friction model, the conventional bearing theory is extended from two to three or four-contact points. The commonly used control criterion of ball bearing by the inner or outer raceway is debatable and is known to fit with difficulty with experimental data. In addition, when more than two-contact points are involved, it becomes obsolete. The paper presents a mathematical model to describe the complex ball bearing internal kinematics under the effect of the external working conditions. Lubricant thickness is taken into account in geometrical equations and the nonlinear system of this quasistatic model is solved by a Newton-Raphson method. The model is first validated through comparisons with published data for conventional or single arched ball bearings. Results are also compared to those provided by the commercial software RBL4. The analysis of a double arched ball bearing is finally performed and the complex motion of the ball highlighted.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

Multi-Agent Form Closure Capture of a Generic 2D Polygonal Object Based on Projective Path Planning

2006 ◽  
Author(s):  
Pankaj Sharma ◽  
Anupam Saxena ◽  
Ashish Dutta
Keyword(s):  
Path Planning ◽  
Contact Point ◽  
Point Contact ◽  
Object Boundary ◽  
Actual Object ◽  
Contact Points ◽  
Correct Orientation ◽  
Novel Approach ◽  
Form Closure ◽  
Multi Agent

The study of multi-agent capture and manipulation of an object has been an area of active interest for many researchers. This paper presents a novel approach using Genetic Algorithm to determine the optimal contact points and the total number of agents (mobile robots) required to capture a stationary generic 2D polygonal object. After the goal points are determined the agents then reach their respective goals using a decentralized projective path planning algorithm. Form closure of the object is obtained using the concept of accessibility angle. The object boundary is first expanded and the robots reach the expanded object goal points and then converge on the actual object. This ensures that the agents reach the actual goal points at the same time and have the correct orientation. Frictionless point contact between the object and robots is assumed. The shape of the robot is considered a circle such that it can only apply force in outward radial direction from its center and along the normal to the object boundary at the contact point. Simulations results are presented that prove the effectiveness of the proposed method.

Isothermal Modeling of Meniscus Oscillation in the Continuous Strip Casting Process

2010 ◽  
Author(s):  
Kevin W. Wilcox ◽  
A. Gordon L. Holloway ◽  
Andrew G. Gerber
Keyword(s):  
Natural Frequency ◽  
Analytical Model ◽  
Cold Work ◽  
Casting Process ◽  
Contact Angles ◽  
Strip Casting ◽  
Water Model ◽  
Working Fluid ◽  
Contact Points ◽  
Continuous Strip

In the continuous strip casting process a meniscus forms a compliant boundary between the casting nozzle and transporting conveyor. Movement of this meniscus during casting has been shown to create surface defects, which require extensive cold work to remove and limit the minimum thickness for which sections may be cast. This paper discusses experimental work conducted to test an analytical model of the meniscus oscillation. A high frame rate shadowgraph technique was used on an isothermal water model of the casting process to observe meniscus motion, and thus allowing the calculation of meniscus frequency, amplitude, contact points and contact angles. Both natural frequency and flow excited tests were conducted. Natural frequency tests were also conducted using mercury as the working fluid, having a non-wetting contact angle, typical of molten metals. The experimental results were found to be in good agreement with the predictions of theory for both wetting and non-wetting conditions. The experimentally verified analytical model for meniscus motion is valuable to the design of the continuous casting process, because it offers an opportunity to mitigate the effects of boundary motion on surface quality.

scholarly journals Dynamic Responses of Planar Multilink Mechanism considering Mixed Clearances

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Xiulong Chen ◽  
Shuai Jiang ◽  
Yu Deng
Keyword(s):  
Great Influence ◽  
Friction Model ◽  
Contact Forces ◽  
Dynamic Responses ◽  
Prototype Model ◽  
Planar Mechanisms ◽  
Coulomb’S Friction ◽  
Revolute Joints ◽  
Friction Models ◽  
Coulomb Friction Model

Translational and revolute joints are the main kinds of joints in planar multilink mechanisms. Translational and revolute clearance joints have great influence on dynamical responses of planar mechanisms. Most research studies mainly focused upon revolute clearance of planar mechanisms based upon the modified Coulomb friction model, some studies investigated clearance of the pin-slot joint, and few studies researched mixed clearances (considering both translational clearance and revolute clearance) based on the LuGre friction model. Dynamic response of the 2-DOF nine-bar mechanism considering mixed clearances based on the LuGre model is investigated in this work. The dynamic model with mixed clearances is built by the Lagrange multipliers. Dynamic responses including motion output of the slider, driving torques, contact forces, shaft center trajectories at revolute clearance pairs, and slider trajectory inside the guide are analyzed, respectively. Influences of different friction models on dynamic responses are studied, such as LuGre and modified Coulomb’s friction models. Effects of different clearance values and different driving speeds on dynamic responses with mixed clearances are both analyzed. Virtual prototype model considering mixed clearances is carried out through ADAMS to verify correctness.

Force Optimization Approaches for Common Anthropomorphic Grasps

2016 ◽  
Author(s):  
Aimee Cloutier ◽  
James Yang
Keyword(s):  
Point Contact ◽  
Contact Forces ◽  
Applied Force ◽  
Linear Matrix ◽  
Human Hand ◽  
Numerical Examples ◽  
Contact Points ◽  
Force Optimization ◽  
Grasping Forces ◽  
Grasping Force

A smart choice of contact forces between robotic grasping devices and objects is important for achieving a balanced grasp. Too little applied force may cause an object to slip or be dropped, and too much applied force may cause damage to delicate objects. Prior methods of grasping force optimization in literature have mostly assumed grasp only at the fingertips but have rarely considered how the whole hand grasps more common to anthropomorphic hands affect the optimization of grasping forces. Further, although numerical examples of grasping force optimization methods are routinely provided, it is often difficult to compare the performance of separate methods when they are evaluated using different parameters, such as the type of grasping device, the object grasped, and the contact model, among other factors. This paper presents three optimization approaches (linear, nonlinear, and nonlinear with linear matrix inequality (LMI) friction constraints) which are compared for an anthropomorphic hand. Numerical examples are provided for three types of grasp commonly performed by the human hand (cylindrical grasp, tip grasp, and tripod grasp) using both soft finger contact and point contact with friction models. Contact points between the hand and the object are predetermined. Results are compared based on their accuracy, computational efficiency, and other various benefits and drawbacks unique to each method. Future work will extend the problem of grasping force optimization to include consideration for variable forces and object manipulation.

Isothermal Modeling of Meniscus Oscillation in the Continuous Strip Casting Process

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Kevin W. Wilcox ◽  
A. Gordon L. Holloway ◽  
Andrew G. Gerber
Keyword(s):  
Natural Frequency ◽  
Analytical Model ◽  
Cold Work ◽  
Casting Process ◽  
Contact Angles ◽  
Strip Casting ◽  
Water Model ◽  
Geometrical Parameters ◽  
Contact Points ◽  
Continuous Strip

In the continuous strip casting process a meniscus forms a compliant boundary between the casting nozzle and transporting conveyor. Movement of this meniscus during casting has been shown to create surface defects, which require extensive cold work to remove and limit the minimum thickness for which sections may be cast. This paper discusses experimental work conducted to test an analytical model of the meniscus oscillation. A high frame rate shadowgraph technique was used on an isothermal water model of the casting process to observe meniscus motion, and thus allow the calculation of meniscus frequency, amplitude, contact points and contact angles. Both natural frequency and flow excited tests were conducted. Natural frequency tests were also conducted using mercury which has a nonwetting contact angle typical of molten metals. The experimental results were found to be in good agreement with the predictions of theory for both wetting and nonwetting conditions. The experimentally verified analytical model for meniscus motion is valuable to the design of a continuous casting process because it describes the effect of geometrical parameters on meniscus motion and thus provides an opportunity to mitigate the effects of boundary motion on surface quality.

An Analytical Model of Four-Point Contact Rolling Element Ball Bearings

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Jacob D. Halpin ◽  
Anh N. Tran
Keyword(s):  
Analytical Model ◽  
Ball Bearing ◽  
Minimum Energy ◽  
Point Contact ◽  
Contact Angles ◽  
State Theory ◽  
Operating Conditions ◽  
Rolling Element Bearing ◽  
Design Guideline ◽  
Rolling Element

The purpose of this work is to establish an analytical model and standard way to predict the performance characteristics of a four-point contact, or gothic arch type, rolling element ball bearing. Classical rolling element bearing theory, as developed by Jones, has been extended to include the complex kinematics of the four-point contact bearing; thereby providing complete elementwise attitude and internal load distribution of the bearing under operating conditions. Standard performance parameters, such as element contact stresses, contact angles, inner ring deflections, nonlinear stiffness's, torque, and L10 life, are solved explicitly via standard Newton–Raphson techniques. Race control theory is replaced with a minimum energy state theory to allow both spin and slip to occur at the ball-to-raceway contact. The developed four-point model was programed within the orbis software program. Various test cases are analyzed and key analytical results are compared with the Jones four-point contact ball bearing analysis program, the Wind Turbine Design Guideline, DG03, and traditional two-point (angular contact) analysis codes. Model results for the internal distribution of ball loads and contact angles match the Jones program extremely well for all cases considered. Some differences are found with the DG03 analysis methods, and it is found that modeling a four-point contact bearing by overlaying two opposed angular contact bearings can result in gross errors.

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