Abstract
This study presents an analytical method for the solution of dynamic frictional contact problem between a rigid punch and an isotropic elastic solid. Rigid flat punch moves over the isotropic elastic solid at a constant subsonic speed and friction force develops based on Dahl’s friction law instead of Coulomb’s dry friction law. Dahl’s dynamic friction model is adopted since this model is one of the well-known dynamic friction models in the literature. According to this model, friction force depends only on a displacement rather than the speed of the punch since viscous effects are ignored. Influences of the parameters describing Dahl’s friction model on contact stress at slow and high speed sliding cases are examined. Analytical solution is conducted by means of Galilean and Fourier transformations. Friction force is computed numerically by the use of 4th order Runge–Kutta method for various displacements of the punch. Formulation for the contact problem is reduced to a singular integral equation and normal stress over the surface of elastic half-plane is determined. Obtained contact stresses are compared with those generated through finite element method and results display a high degree of accuracy. The influences of direction of motion, Coulomb’s coefficient of friction, pre-sliding displacement, asperity stiffness and shape factor of hysteresis loop upon contact stresses and stress intensity factors are revealed.
Highlights
Contact mechanics of solids have been an attractive topic of research for many years since it concerns the maintenance of mechanical and structural elements
The friction force developed is calculated by Dahl’s friction model [44] which belongs to the earliest dynamic friction models; it was designated to simulate a symmetrical hysteresis loops observed in bearings subjected to sinusoidal excitations with small amplitudes
The motion of the rigid punch is controlled by a pilot node which is created at the center of the punch
Summary
Contact mechanics of solids have been an attractive topic of research for many years since it concerns the maintenance of mechanical and structural elements. The main idea behind the Dahl’s friction model is that when the applied load is not adequate to exceed static friction, the asperities at the contact surface will deform which results in a pre-sliding motion. Thorough examination of the available literature showed that there is no similar work pertaining to the contact mechanics analysis of elastic bodies under the effect of Dahl’s dynamic friction model. After verification of the analytical method, influences of the direction of the motion, pre-sliding displacement, coefficient of friction, asperity stiffness and hysteresis loop’s shape factor on contact stresses are examined. The analytical formulations for contact mechanics of elastic solids based on using Dahl’s dynamic friction model are provided in Sect.
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