Authors: Đỗ Đăng Khoa - Hanoi University of Science and Technology, Phan Đăng Phong - National Research Institute of Mechanical Engineering, Đỗ Sanh - Vietnam Association of Mechanics

Published in: 10th National Conference on Mechanics – Volume 2. Dynamics and Control

Publication date: Hanoi, 8-9/12/2017

Abstract: Coulomb friction is an important issue for machine motion because it not only causes wear of machine parts but primarily causes difficulties for machine motion, especially the phenomenon of machine jamming. Frictional constraints are non-ideal constraints, a type of constraint for which no general method of treatment has been available up to now. This report proposes a treatment method: introduce constraint reactions (tangential reactions and normal reactions) into the equations of motion and  use  the ideal nature of the normal reaction to eliminate it while the tangential reactions are considered as applied forces. By this method, writing the equations of motion of a system with constraints  will not contain Lagrange multipliers. In this way, the obtained equations together with the constraint equations can be considered as the equations of motion of the mechanical system. However, these equations still contain the unknown quantities of tangential reactions.  To obtain equations that completely describe the motion of the mechanical system  an assumption about the nature of the tangential reaction, in this case the frictional force, is used. Coulomb's law of sliding friction is used  to describe the physical nature of the tangential reaction, and thereby the problem is solved: the equations describing the motion of the mechanical system are obtained. The proposed method can be applied to the general case  when  based on experiments  the physical law of tangential reactions is obtained.

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