Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres

The current work presents a different methodology for modeling the impact between elasto-plastic spheres. Recent finite element results modeling the static deformation of an elasto-plastic sphere are used in conjunction with equations for the variation of kinetic energy to obtain predictions for the coefficient of restitution. A model is also needed to predict the residual deformation of the sphere during rebound, or unloading, of which several are available and compared in this work. The model predicts that a significant amount of energy will be dissipated in the form of plastic deformation such that as the speed at initial impact increases, the coefficient of restitution decreases. This work also derives a new equation for the initial critical speed which causes initial plastic deformation in the sphere that is different than that shown in previously derived equations and is strongly dependant on Poisson’s Ratio. For impacts occurring above this speed, the coefficient of restitution will be less than a value of one. This work also compares the predictions between several models that make significantly different predictions. The results of the current model also compare well with some existing experimental data. Empirical fits to the results are provided for use as a tool to predict the coefficient of restitution.

[1]  Qiang Yu,et al.  The examination of the drop impact test method , 2004, The Ninth Intersociety Conference on Thermal and Thermomechanical Phenomena In Electronic Systems (IEEE Cat. No.04CH37543).

[2]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[3]  Hiroshi Hirayama,et al.  LOW-VELOCITY PROJECTILE IMPACT ON SPACECRAFT☆ , 2000 .

[4]  D. Bogy,et al.  An Elastic-Plastic Model for the Contact of Rough Surfaces , 1987 .

[6]  C. Thornton,et al.  Rebound behaviour of spheres for plastic impacts , 2003 .

[7]  M. Elbestawi,et al.  Three-dimensional elastoplastic finite element model for residual stresses in the shot peening process , 2004 .

[8]  Elasto-plastic hemispherical contact models for various mechanical properties , 2004 .

[9]  C. Thornton.  Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres , 1997 .

[10]  I. Green,et al.  A Finite Element Study of the Residual Stress and Deformation in Hemispherical Contacts , 2005 .

[11]  B. Bhushan,et al.  Nano-asperity contact analysis and surface optimization for magnetic head slider/disk contact , 1996 .

[12]  Subramaniam Shankar,et al.  Effect of strain hardening in elastic–plastic transition behavior in a hemisphere in contact with a rigid flat , 2008 .

[13]  I. Green,et al.  A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat , 2005 .

[14]  J. E. Field,et al.  Tackling the Drop Impact Reliability of Electronic Packaging , 2003 .

[15]  J. Barbera,et al.  Contact mechanics , 1999 .

[16]  G. Weir,et al.  The coefficient of restitution for normal incident, low velocity particle impacts , 2005 .

[17]  I. Hutchings,et al.  PLASTIC COMPRESSION OF SPHERES , 1984 .

[18]  Ian Sherrington,et al.  An evaluation of the effect of simulated launch vibration on the friction performance and lubrication of ball bearings for space applications , 2006 .

[19]  Yongwu Zhao,et al.  An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow , 2000 .

[20]  Nelson R. Deutschen,et al.  ASCC: The impact of a Silver Bullet , 1996, AT&T Tech. J..

[21]  K. Johnson.  Contact Mechanics: Frontmatter , 1985 .

[22]  D. Bogy,et al.  Some critical tribological issues in contact and near-contact recording , 1993 .

[23]  D. A. Gorham,et al.  A study of the restitution coefficient in elastic-plastic impact , 2000 .

[24]  L. Vu-Quoc,et al.  An elastoplastic contact force–displacement model in the normal direction: displacement–driven version , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  I. Green,et al.  Poisson ratio effects and critical values in spherical and cylindrical hertzian contacts , 2005 .

[26]  C. P. Diepart.  Modelling of Shot Peening Residual Stresses - Practical Applications , 1994 .

[27]  George W. Woodruff,et al.  A Transient Dynamic Analysis of Mechanical Seals Including Asperity Contact and Face Deformation , 2005 .

[28]  C. Thornton,et al.  Energy dissipation during normal impact of elastic and elastic-plastic spheres , 2005 .

[29]  L. Kogut,et al.  Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat , 2002 .

[30]  D. Marghitu.  Impact of a planar flexible bar with geometrical discontinuities of the first kind , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[31]  Colin Thornton,et al.  A theoretical model for the contact of elastoplastic bodies , 2001 .

[32]  Wen-Ruey Chang,et al.  Normal Impact Model of Rough Surfaces , 1992 .

[33]  David B. Bogy,et al.  An Asperity Contact Model for the Slider Air Bearing , 2000 .

[34]  Itzhak Green,et al.  A FINITE ELEMENT STUDY OF ELASTO-PLASTIC HEMISPHERICAL CONTACT , 2003 .

[35]  Izhak Etsion,et al.  UNLOADING OF AN ELASTIC-PLASTIC LOADED SPHERICAL CONTACT , 2005 .

[36]  J. Greenwood,et al.  Contact of nominally flat surfaces , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[37]  Christopher R. Bowen.  Shaping the future of sports equipment , 2004 .

[38]  Klaus Peikenkamp.  Modelling of processes of impact in sports , 1989 .