Modelling The Process of Dressing The Laps of Vibratory Finishing Machine

Abstract

Автоматизація виробничих процесів у машинобудуванні та приладобудуванні. Вип. 52. 2018 32 УДК 621.923.7 \ I. V. Kuzio, V. M. Zakharov, V. M. Korendiy doi The purpose of the paper. Substantiation of structure (design), parameters and operation modes of the improved vibratory finishing machine. Analysis of dynamical processes which occur during "lap over lap" dressing. Investigation methodology. Mathematical model of motion of the mechanical system of vibratory finishing machine was developed on the basis of Lagrange differential equations of the second order. For the purpose of describing friction between the working surfaces of the laps, the Coulomb friction model was used. Stiffness parameters of all elastic elements were modeled in accordance with the Hooke's law. Energy losses in elastic elements during their tension-compression were taken into account by corresponding coefficients of dissipation (damping). Simulation modelling of motion of the machine's mechanical oscillatory system was carried out in MathCAD software by means of solving the derived differential equations of the system's motion using the numerical methods of Runge-Kutta. Obtained results. Structural and functional peculiarities of the improved vibratory finishing machine for lapping flat surfaces of cylindric and prismatic parts were considered. Design (calculation) diagram of its mechanical oscillatory system was substantiated and differential equations of motion of oscillating masses were derived. Simulation modelling of the laps' motion during their dressing was carried out and the correspondence of the obtained results to the input modelling parameters (operation in near-resonance mode with the given oscillation amplitudes) was analyzed. Scientific novelty. For the first time we obtained following results: spatial design (calculation) diagram of mechanical oscillatory system of the improved vibratory finishing machine was proposed; mathematical model of plane-parallel motion of oscillating masses (with circular trajectories of oscillations) was developed; possibilities of performing the laps dressing using "lap over lap" method were substantiated by means of ensuring their circular oscillations. Practical value. The results of the performed investigations can be used during designing new and improving existing structures of vibratory finishing machines for finishing treatment (lapping) of flat surfaces of cylindric and prismatic parts.

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

“…Some of the lapping machines' designs have already been considered in papers [8]- [11]. Nevertheless, the papers [8]- [10] covers the issues of linear (straight-line) motion of the corresponding vibratory systems, and the paper [11] considers the process of dressing the laps, which provide planar (two-dimensional) motion (in particular, circular oscillations).…”

“…Some of the lapping machines' designs have already been considered in papers [8]- [11]. Nevertheless, the papers [8]- [10] covers the issues of linear (straight-line) motion of the corresponding vibratory systems, and the paper [11] considers the process of dressing the laps, which provide planar (two-dimensional) motion (in particular, circular oscillations). In the present paper, there will be overviewed all the possible designs of single-mass, double-mass and three-mass vibratory systems of hanger-type lapping machines both with linear (straight-line) and planar (two-dimensional) movements of the working bodies (laps).…”

Substantiation of inertial, stiffness and excitation parameters of vibratory lapping machine with linear oscillations of laps

“…Analysing the information sources on the subject of vibratory finishing treatment of flat surfaces of cylindrical and prismatic parts, we can state that the problems of dynamic analysis, substantiation of parameters and operation modes, as well as simulation modelling of vibratory lapping machines operation are not completely solved. In the papers [10]- [12], the investigations of the authors on the mentioned subject were initiated. In particular, three-and four-mass two-dimensional and three-dimensional diagrams of vibratory finishing machines were considered, the differentials equations of the working bodies' motion were derived, inertial and stiffness parameters of corresponding mechanical oscillatory systems were substantiated, and simulation modelling of the oscillatory motion of laps during their dressing was carried out.…”

“…In particular, three-and four-mass two-dimensional and three-dimensional diagrams of vibratory finishing machines were considered, the differentials equations of the working bodies' motion were derived, inertial and stiffness parameters of corresponding mechanical oscillatory systems were substantiated, and simulation modelling of the oscillatory motion of laps during their dressing was carried out. In this paper, the investigations initiated in [10]- [12] will be completed in the following directions: developing a two-dimensional design (calculation) diagram of three-mass mechanical oscillatory system of vibratory finishing machine; deriving the corresponding differential equations of the oscillating masses' motion; substantiating the inertial and stiffness parameters and the parameters of excitation of the system; dynamic analysis of periodical one-dimensional motion (linear oscillations) of the laps during their dressing; simulation modelling of the laps' motion etc.…”

“…It may be reduced to one power equation with respect to  . Since the length of the obtained equations, as well as their complexity, is very large, in major publications (for example, [6,7,[11][12][13][14]) the authors recommend to neglect the system's…”