A multi-mesh MPM for simulating the meshing process of spur gears

Abstract A numerical scheme is presented to simulate the meshing process of spur gears, based on the material point method (MPM). To allow engagements at successive contact points and subsequent separation between neighboring gear teeth, a contact/sliding/separation procedure in a multi-mesh environment without using master/slave nodes is proposed so that the no-slip contact constraint inherent in the existing MPM can be released. Individual drive members rotate around corresponding axes, through which simulated angular velocity transmission is in good agreement with the analytical solution. It appears from the simulation results presented here that the multi-mesh MPM could become a robust spatial discretization tool for gear design problems that involve large rotation, contact/sliding and separation.

[1]  K. Bathe,et al.  Stability and patch test performance of contact discretizations and a new solution algorithm , 2001 .

[2]  N. K. Anifantis,et al.  Numerical simulation of conjugate spur gear action , 2001 .

[3]  K. Bathe.  Finite Element Procedures , 1995 .

[4]  Robert L. Norton,et al.  Machine Design: An Integrated Approach , 1996 .

[5]  D. Sulsky,et al.  A particle method for history-dependent materials , 1993 .

[6]  Shaker A. Meguid,et al.  On the contact stress analysis of spur gears using variational inequalities , 1995 .

[7]  Rebecca M. Brannon,et al.  An evaluation of the MPM for simulating dynamic failure with damage diffusion , 2002 .

[8]  A. Seireg,et al.  Computer Simulation of Dynamic Stress, Deformation, and Fracture of Gear Teeth , 1973 .

[9]  Michael Ortiz,et al.  Adaptive mesh refinement in strain localization problems , 1991 .

[10]  E. Buckingham.  Analytical mechanics of gears , 1949 .

[11]  Shijian Zhou,et al.  Simulation of geomembrane response to settlement in landfills by using the material point method , 1999 .

[12]  M.Ananda Rao,et al.  Dynamic analysis of spur gear teeth , 1988 .

[13]  N. Ganesan,et al.  A Study Of Dynamic Stresses In A Spur Gear Under A Moving Line Load And Impact Load Conditions By A Three-dimensional Finite Element Method , 1993 .

[14]  D. Sulsky.  Erratum: Application of a particle-in-cell method to solid mechanics , 1995 .

[15]  J. Brackbill,et al.  The material-point method for granular materials , 2000 .

[16]  Klaus-Jürgen Bathe,et al.  On the constraint function method for contact problems , 1997 .