• Tribology and Lubricants
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• v.36 no.6
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• pp.324-331
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• 2020

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.