Modelling the operation of vibratory machine for single-sided lapping of flat surfaces

Abstract

Lapping is one of the finishing technological operations. It can be performed using various manual and automated techniques. One of the most efficient lapping techniques is carried out with the help of vibratory equipment. Among a great variety of vibratory lapping, polishing and grinding machines, the ones of the overhead (suspended) type with double-mass oscillatory systems are not thoroughly investigated. Therefore, the novelty of the present study consists in development and investigation of the double-mass vibratory machine for single-sided lapping of flat surfaces. It consists of the upper lap and the lower carrier connected to one another by six springs radially directed and uniformly distributed along the circle of the lap. The parts, whose upper end faces are to be treated, are fixed in the lower carrier. The lapping process is performed due to the oscillatory motion of the lap relative to the carrier. The differential equations describing the motion of the machine’s oscillatory system are derived. The analytical dependencies for calculating the stiffness coefficients of the springs ensuring the energy-efficient resonance operation mode are deduced. Based on the results of experimental studies of friction forces exerted by each moving surface on the other one during the lapping process, the numerical modelling and computer simulation of the lapping machine operation are carried out. The obtained results can be used while investigating the technological parameters (surface roughness, flatness, accuracy etc.) of the lapping process carried out with the help of vibratory equipment.