Substantiation of Parameters and Analysis of Operational Characteristics of Oscillating Systems of Vibratory Finishing Machines

Abstract

The calculation diagrams of oscillating systems and operation features of vibratory finishing machines are considered. The mathematical models of three-mass and four-mass oscillating systems are presented. The amplitude values of the oscillating masses displacements are derived. The functions of inertial and stiffness parameters optimization are formed. The optimization problems are solved with a help of MathCAD software. On the basis of synthesized inertial and stiffness parameters, the amplitude-frequency characteristics of the oscillating systems of vibratory finishing machines are formed and analyzed. In order to verify the validity of the proposed theoretical approaches, the simulation of the mathematical model of the oscillating system motion is carried out by means of numerical solving of the system of differential equations of the oscillating masses motion. The proposed structural diagrams and the operation schemes of the vibratory finishing machine, as well as the derived analytical formulas may be used by designers, researchers and technologists while improving existent and developing new equipment for vibro-finishing treatment.

Searching for the two­frequency motion modes of a three­mass vibratory machine with a vibration exciter in the form of a passive auto­balancer

“…It should be noted that three-mass vibratory machines are widely used in various industries [10][11][12][13][14][15][16][17][18].…”

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

“…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…”

“…The larger is the value n , the weaker (safer) is the mechanical interaction between the oscillating system and the fixed frame of the machine. Its minimal value is 3...4 n  [11,13]. Vibration isolators are to be calculated according to the single-mass scheme consisting of one rigid body with the mass equal to the total mass of the whole structure and of the elastic element of certain stiffness representing the isolator.…”

“…2. Thus, for calculating (analysing) the parameters of the mechanical oscillating system of vibratory finishing machine we can use the following formulas: In order to find the steady-state solution of the differential equations (1) and to simulate the system's motion, let us prescribe the parameters of the oscillating system of vibratory lapping machine: 1 c c  , we have proved the assumption about "zero stiffness" phenomenon and in-phase motion of reactive and intermediate masses [11,13]. The obtained values ensure one of the most efficient modes of "lap over lap" dressing.…”

“…Due to occurring the in-phase motion, the air gap in electromagnetic vibration exciter can be minimal because in such a case there is no relative displacements between two adjacent masses. This allows significant decreasing of the value of current flowing in the winding of the vibration exciter, as well as the power consumed [11,13].…”