Mathematical Model of a Backlash Elimination in the New Clamping Mechanism

Abstract

A theoretical model of the operation of the electromechanical mechanism for clamping cylindrical workpieces and tools on the spindle of metalworking machines during backlash elimination is considered. The considered design of the clamping mechanism is driven by an electric motor and has a number of advantages. On the basis of the model, analytical dependencies are proposed that describe the relationship between the movements of the elements of the mechanism during the first stage of the clamping process. The proposed analytical dependencies allow taking into account stages of the functioning of the mechanism when the forces of dissipative characters prevail in its work. The presented dependencies describe the position of the elements of the mechanism depending on the generalized coordinate, which is the angle of rotation of the electric motor rotor. This allows determining the position of the elements of the mechanism depending on time. The obtained dependencies are a precondition for the development of methods for optimizing the design of mechanisms of this type.