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http://dx.doi.org/10.9725/kts.2020.36.6.324

Critical Wedging Coefficient in Frictional Elastic System Considering Separation State  

Kim, Sangkyu (Dept. of Mechanical Engineering, Yonsei University)
Jang, Yong Hoon (School of Mechanical Engineering, Yonsei University)
Publication Information
Tribology and Lubricants / v.36, no.6, 2020 , pp. 324-331 More about this Journal
Abstract
Wedging in a frictional elastic system is defined if the state of stick exists after the external loading on the system is removed. This paper presents a method to determine the critical coefficient of wedging for an elastic frictional system by considering the separation state. Wedging is always possible if the coefficient of friction exceeds a critical value known as the critical wedging coefficient. This method requires two concepts: a necessary and sufficient condition for wedging, which can be interpreted as positive spanning sets of constraint vectors existing in the wedged system, and the minimal positive basis that enables a minimum wedging coefficient. The algorithm based on the positive spanning concept is repeatedly executed after eliminating nodes from the contact stiffness matrix, for which the separation states are impending. The simulation results show that once a node enters the separation state, it never returns to the contact state again and the critical wedging coefficient reduces during repeated algorithm execution. The benefit of this method is that the computation time permits handling models with large numbers of contact nodes. The algorithm can also numerically find the critical wedging coefficient, thereby contributing to fastening and assembly performance improvements in mechanical systems.
Keywords
wedging; critical wedging coefficient; positive spanning; discrete frictional system; separation state;
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  • Reference
1 Bickford, J.H., Introduction to the Design and Behavior of Bolted Joints: Non-Gasketed Joints, 4th Edition, CRC Press, Boca Raton, 2007.
2 Mosemann M., Wahl F. M., "Automatic decomposition of planned assembly sequences into skill primitives", IEEE Trans. Robotics Automation, 2001, Vol. 17, pp.709-718, 2001.   DOI
3 Sturges, R.H., Laowattana, S., "Virtual wedging in three-dimensional peg insertion tasks", J. Mech. Design, Vol. 118, pp.99-105, 1996.   DOI
4 Falkenberg A., Drummen P., Morlock M.M., Huber G., "Determination of local micromotion at the stem-neck taper junction of a bimodular total hip prosthesis design", Med. Engrg. Phys., Vol. 65, pp.31-38, 2019.   DOI
5 Hild P., "Non-unique slipping in the Coulomb friction model in two dimensional linear elasticity", Quarter J. Mech. Appl. Math. Vol.57, pp.225-235, 2004.   DOI
6 Ahn, Y.J., Bertocchi, E., Barber, J.R., "Shakedown of coupled two-dimensional discrete frictional systems", J. Mech. Phys. Solids., Vol. 56, pp. 3433-3440, 2008.   DOI
7 Hassani R., Hild P., Ionescu I.R., Sakki N.-D., "A mixed finite element method and solution multiplicity for Coulomb frictional contact", Comput. Methods Appl. Mech. Engrg., Vol.192, pp.4517-4531, 2003.   DOI
8 Hild P., "On finite element uniqueness studies for Coulomb's frictional contact model", Int. J. Appl. Math. Comp. Sci. Vol.12, pp.41-50, 2002.
9 Barber, J.R., Hild, P., "On wedged configurations with Coulomb friction," in: Peter, W., Udo, N. (Eds.), Analysis and Simulation of Contact Problems. Springer, Berlin pp. 205-221, 2006.
10 Fujita R., Kanno Y., "Enumeration of all wedged equilibrium configurations in contact problem with Coulomb friction", Comput. Methods Appl. Mech. Engrg. Vol.199, pp.1202-1215, 2010.   DOI
11 Pinto da Costa A., "Assessing the complete solution set of the planar frictional wedging problem", Comput. Methods Appl. Mech. Engrg. 205-208, 139-148, 2012.   DOI
12 Regis R.G., "On the properties of positive spanning sets and positive bases", Optim. Engng., vol. 17, pp.229-262, 2016.   DOI
13 Kim S., Jang Y.H., Barber J.R., "Wedging of frictional elastic systems", FACTA Univ. Series: Mech. Engng., Vol.17, pp.141-148, 2019.   DOI
14 Kim S., Jang Y.H., "Determination of critical wedging coefficient for full-contact frictional systems using positive spanning", Int. J. Mech. Sci., Vol.177, 105576, 2020.   DOI
15 Barber, J.R., Contact mechanics, Chap. 8, Springer, 2018. (ISBN 978-3-319-70938-3)
16 Davis C., "Theory of positive linear dependence", Amer. J. Math. Vol.76, pp.733-746, 1954.   DOI
17 Hills D. A., A. Sackfield, and D. Nowell. Mechanics of elastic contacts. pp.40-41, Oxford : Butterworths, 1993. (ISBN 978-0-750-60540-3)
18 Conn A.R., Scheinberg, K., Vicente, L.N., Introduction to Derivative-Free Optimization, SIAM, 2009.