Analysis and improvement of design diagrams and mathematical models of vibratory lapping machines

Abstract

Problem statement. The development of energy-efficient and high-performance vibratory lapping machines demands the improvement of their design diagrams and calculation techniques. Purpose. The main objectives of this research consist in detailed analysis of existent design diagrams and mathematical models of vibratory lapping machines; designing the three-mass hanger-type structures of such machines providing circular oscillations of laps; derivation of differential equations describing the motion of their oscillatory systems. Methodology. The technique of the research is based on fundamental concepts of engineering mechanics, strength of materials and theory of mechanical vibrations. Findings (results). The improved design diagrams of vibratory lapping machines with circular oscillations of laps are proposed and the corresponding differential equations describing the motion of the working elements are derived. Originality (novelty). The mathematical model of circular oscillations of the three-mass mechanical oscillatory system of vibratory lapping machine is developed. The possibilities of performing the double-side lapping of cylindrical and prismatic parts are considered. Practical value. The results of the performed investigations can be used during creating new designs and improving existent structures of vibratory finishing machines for lapping flat surfaces of cylindrical and prismatic parts. Scopes of further investigations. In further investigations, it is necessary to perform the numerical modelling of the system’s motion using the derived differential equations, and to compare the obtained theoretical results with the results of experimental investigations.

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

“…Depending on the operational requirements set for a part and the surfaces to be treated, these processes can be divided into two basic types -single-sided [1] and double-sided ones [2][3][4][5]. Considering the drives of technological machines for finishing treatment, most of them are equipped by electric motors and mechanical transmissions [1][2][3][4][5], while a relatively small number of such machines use vibration excitation for setting the working members into motion [6][7][8][9][10].…”

“…Despite numerous advantages of the electromechanically-driven finishing machines, their main drawbacks consist in design complexity due to application of several electrical drives that must be synchronized; reduced reliability caused by the use of several mechanical transmissions; relatively low degree of dimensional accuracy of the finished parts etc. The mentioned drawbacks can be partially avoided in the designs of finishing machines driven by electromagnetic vibration exciters [6][7][8][9][10]. In the work [6], the authors proposed the mathematical model of the bowl-type vibratory finishing machine, studied the dynamics of its excitation system, and analyzed the machine's performance.…”

“…In [8], there has been modelled the kinematics of the treating media, and the material removal intensity during the finishing process. Unlike numerous existing investigations, in [9,10], as well as in the present paper, the authors made an attempt to propose the improved designs, to derive the mathematical models, and to study the dynamic behavior of vibratory finishing machines with circular oscillations of laps. The novelty of the present paper consists in development and investigation of the double-mass vibratory machine of the overhead (suspended) type for single-sided lapping of flat surfaces.…”