Investigation of Tangential Contact Damping of Rough Surfaces From the Perspective of Viscous Damping Mechanism

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Wujiu Pan ◽  
Hongshuang Li ◽  
Haoyong Qu ◽  
Liangyu Ling ◽  
Linlin Wang
Keyword(s):  
Mathematical Model ◽  
Energy Dissipation ◽  
Dynamic Testing ◽  
Rough Surfaces ◽  
Normal Load ◽  
Three Dimensional ◽  
Contact Fatigue ◽  
Load Ratio ◽  
Point Of View ◽  
Tangential Contact

Abstract The contact damping between rough surfaces has an important influence on the wear, vibration, contact fatigue, and energy dissipation between interfaces. In this paper, based on contact theory, a tangential damping mathematical model of rough surfaces is established from the point of view of viscous contact damping energy dissipation mechanism of asperities and considering the fractal characteristics of three-dimensional topography of rough surfaces. Through the combination of micro-contact modeling and macro dynamic testing of composite beams, the analysis results show that there are important evolution rules between tangential damping and surface fractal parameters and material parameters. The nonlinear relations between them are as follows: tangential contact damping is positively correlated with normal load, load ratio, and maximum contact area of asperity, and negatively correlated with fractal roughness; tangential contact damping increases first and then decreases with the increase of three-dimensional fractal dimension. The results of computational and experimental modal analysis show that the established mathematical model is feasible for predicting tangential damping. The study of tangential contact damping between surfaces can lay a foundation for improving the performance of assembly interfaces.

Thermal Effects in Contact Fatigue Under Oscillatory Normal Load

1965 ◽  
Vol 87 (1) ◽  
pp. 177-184 ◽  
Author(s):  
R. A. Burton ◽  
J. C. Tyler ◽  
P. M. Ku
Keyword(s):  
Energy Dissipation ◽  
Dynamic Load ◽  
Normal Load ◽  
Fatigue Cracks ◽  
Thermal Transformation ◽  
Contact Fatigue ◽  
Contact Temperature ◽  
Flat Specimen ◽  
Exponential Relationship ◽  
Specimen Temperature

Experiments are reported wherein contact fatigue was brought about by the application of an oscillatory normal load between a ball and a flat specimen. Plots of the flat-specimen temperature versus time showed that a rapid temperature rise occurred in the initial stage of crack formation, and thus provided an early indication of fatigue. Thermal resistances were measured for the apparatus components as well as the specimen contact. Using these, it was possible to apply the measured flat-specimen temperature to obtain estimates of the contact temperature as well as the energy dissipation rate prior to the incidence of fatigue cracks. It was shown that the contact temperature did not rise sufficiently to produce annealing in the test specimens. Thus, toroidal rings of hardened and softened material in the stressed zone could not be attributed to thermal transformation of the bearing steel. It was also shown that energy dissipation due to cyclic loading varied in approximate exponential relationship with dynamic load, and decreased upon increase of static load when dynamic load was maintained constant.

A three-dimensional fusion prediction model for fractal rough surfaces in the sliding contact process

2014 ◽  
Vol 66 (3) ◽  
pp. 459-467
Author(s):  
Yan Lu ◽  
Zuomin Liu
Keyword(s):  
Temperature Rise ◽  
Rough Surfaces ◽  
Normal Load ◽  
Contact Process ◽  
Three Dimensional ◽  
Contact Problems ◽  
Sliding Contact ◽  
Content Type ◽  
Solution Methods ◽  
Account Temperature

Purpose – The purpose of this manuscript is to analyze the fusion micro-zone generated by typical rough surfaces and investigate the factors of thermal effects on the tribological performance of surface asperities and its results verified by the experiment. Design/methodology/approach – A three-dimensional fractal rough surfaces sliding contact model has been developed, which takes into account temperature rise and distribution. The finite-element method, Green's function method, thermal conduct theory and contact mechanics are used as the solution methods. Findings – The results yield insights into the effects of the sliding velocity, thermal properties of the material, normal load and surface roughness on the temperature rise of the sliding contact surface. It allows the specification of working conductions' properties to reduce fusion. Originality/value – The model is developed and described by using the features of the contact between one flat surface and one rough surface with varied topographies. It can be easily applied for solving the sliding contact problems with different working conditions and specified for designing the surface accuracy in the severe working condition.

Sliding Contact Analysis of Layered Elastic/Plastic Solids With Rough Surfaces

2001 ◽  
Vol 124 (1) ◽  
pp. 46-61 ◽  
Author(s):  
Wei Peng ◽  
Bharat Bhushan
Keyword(s):  
Surface Deformation ◽  
Rough Surfaces ◽  
Normal Load ◽  
Three Dimensional ◽  
Sliding Contact ◽  
Fast Fourier Transformation ◽  
Maximum Pressure ◽  
Asperity Contact ◽  
Elastic Plastic ◽  
Von Mises

A three-dimensional numerical model is presented to investigate the quasi-static sliding contact behavior of layered elastic/plastic solids with rough surfaces. The model is applicable for both single-asperity contact and multiple-asperity contacts. The surface deformation is obtained based on a variational principle. The surface and subsurface stresses in the layer and the substrate are determined with a Fast Fourier transformation (FFT) based scheme and von Mises and principal tensile stresses are computed accordingly. Contact statistics, such as fractional contact area, maximum pressure/E2 and relative meniscus force are predicted. The results are used to investigate the effect of the contact statistics on friction, stiction, and wear problems such as debris generation, brittle failure, and delamination of layered media. Optimum layer parameters are identified. It allows the specification of layer properties, according to the contact statistics, to reduce friction, stiction, and wear of materials. A normalization procedure is presented to apply the results on various combinations of surface roughness, material properties, and normal load.

A Reconstruction and Contact Analysis Method of Three-Dimensional Rough Surface Based on Ellipsoidal Asperity

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Yuqin Wen ◽  
Jinyuan Tang ◽  
Wei Zhou ◽  
Lin Li
Keyword(s):  
Rough Surface ◽  
Rough Surfaces ◽  
Minimum Mean Square Error ◽  
Three Dimensional ◽  
Contact Fatigue ◽  
Contact Analysis ◽  
Analysis Method ◽  
Surface Asperity ◽  
Surface Contact ◽  
Rough Surface Contact

Abstract The 3D rough surface modeling and contact analysis is a difficult problem in the study of rough surface contact. In this paper, a new method for reconstruction and contact analysis of asperities on 3D rough surfaces is proposed based on real rough surfaces. Watershed algorithm is used to segment and determine the area of asperities on the rough surface. According to the principle of minimum mean square error, ellipsoid fitting is carried out on asperities. Based on the elastic-plastic contact model of a single ellipsoidal asperity, a stable and efficient method for 3D rough surface contact analysis and calculation is proposed. Compared with existing calculating methods, the present method has the following characteristics: (1) the constructed surface asperity is closer to the real asperity in contact, and the calculation of asperity parameters has better stability under different sampling intervals and (2) the contact pressure, contact area, and other contact parameters of the 3D rough surface are calculated with high accuracy and efficiency, and the calculation convergence is desirable. The reconstruction and contact analysis method of the 3D rough surface asperity proposed in this paper provides a more accurate reconstruction and calculation method for the study of contact fatigue life and wear failure of rough surfaces.

Moment and Friction Force in Three Dimensional Elastic Contact of Two Rectangular Rough Surfaces

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Friction Force ◽  
Half Plane ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Compressive Load ◽  
Angular Misalignment ◽  
Tangential Contact ◽  
Applied Forces

It is reasonable to expect that when two nominally flat rough surfaces are brought into contact by an applied resultant force, they must support, in addition to the compressive load, an induced moment. The existence of a net applied moment would imply non-even distribution of contact force so that there are more asperities in contact over one region of the nominal area. In this paper we consider the contact between two rectangular rough surfaces that provide normal and tangential contact force as well as contact moment to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop slight angular misalignment and through this contact moment is derived. Through this scheme it is possible to also define elastic contribution to friction since the half-plane tangential contact force on one side of an asperity is no longer balanced by the half-plane tangential force component on the opposite side. The elastic friction force however is shown to be of a much smaller order than the contact normal force.

scholarly journals NONLINEAR MATHEMATICAL MODEL OF PEDAGOGICAL SYSTEM FUNCTIONING

2020 ◽  
Vol 34 (4) ◽  
pp. 93-98
Author(s):  
Irina V. Konopleva ◽  
◽  
Anna R. Sibireva ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Modeling ◽  
Differential Equations ◽  
Dimensional Space ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Stability Limit ◽  
Point Of View ◽  
Social Phenomena ◽  
System Functioning

The purpose of this article is to study the crisis in pedagogical systems from the point of view of an internal observer. The aim of the work is to build and investigate a mathematical model describing the course of crises in pedagogical systems. When building the model, a synergetic methodology, system and process approaches are used. For the mathematical analysis of various social phenomena, systems of differential equations are used to investigate the dynamics of the process. The paper considers a system of nonlinear differential equations in three-dimensional space that describes the functioning of the pedagogical system during the crisis. Numerical and topological methods of nonlinear dynamics, the method of Lyapunov characteristic exponents and the theory of strange attractors by Lorentz were used to study it. Numerical modeling of system solutions for various sets of control parameters (system coefficients) makes it possible to determine the region of stability (asymptotic stability), limit cycles, bifurcation points, and describe possible trajectories of development of the pedagogical system. Mathematical modeling deepens the knowledge about the essence of crises, the peculiarities of their course, makes it possible to study qualitative and numerical modeling, and also allows predicting possible effective measures to combat crisis phenomena and develop new approaches in the management of pedagogical systems.

A Numerical Three-Dimensional Model for the Contact of Layered Elastic/Plastic Solids With Rough Surfaces by a Variational Principle

2000 ◽  
Vol 123 (2) ◽  
pp. 330-342 ◽  
Author(s):  
Wei Peng ◽  
Bharat Bhushan
Keyword(s):  
Variational Principle ◽  
Rough Surfaces ◽  
Normal Load ◽  
Three Dimensional ◽  
Fast Fourier Transformation ◽  
Three Dimensional Model ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Influence Coefficients ◽  
Elastic Perfectly Plastic

A new numerical model for the three-dimensional contact analysis of a layered elastic–perfectly plastic half space with another rough surface is presented. The model is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. A quasi-Newton method is used to find the minimum. The influence coefficients matrix is determined using the Papkovich–Neuber potentials with fast Fourier transformation. The model is extended to elastic–perfectly plastic contacts in dry and wet conditions. Contact analyses have been performed to predict contact statistics of layered elastic/plastic solids with rough surfaces using this model. The effects of the stiffness of the layer and the substrate, layer thickness, as well as normal load are studied. Optimum layer parameters are identified to provide low friction/stiction and wear.

Combined Force and Moment in a Three Dimensional Model of Elastic Contact of Nominally Flat Rough Surfaces

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Half Plane ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Three Dimensional Model ◽  
Tangential Contact ◽  
Applied Forces ◽  
Approximate Equations

In this paper we consider the contact between two rectangular rough surfaces that provide normal and tangential contact force as well as contact moment to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop slight angular misalignment and thereby contact moment is derived. Through this scheme it is possible to also define elastic contribution to friction since the half-plane tangential contact force on one side of an asperity is no longer balanced by the half-plane tangential force component on the opposite side. The elastic friction force however is shown to be of a much smaller order than the contact normal force. Approximate closed form equations are found for contact force and moment as functions of separation, asperity radius of curvature sum, mean plane slope and nominal contact dimension. The approximate equations are shown to give error within seven percent.

A Real-Time Mathematical Model for Three-Dimensional Tidal Flow and Water Quality

1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Real Time ◽  
Control Volume ◽  
Tidal Flow ◽  
Three Dimensional ◽  
River Estuary ◽  
Pearl River Estuary ◽  
Practical Application ◽  
The Pearl River

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.

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