RESEARCH OF THE CHANGE IN THE CONSOLIDATED MASS IN FLAT MULTI-LINK MECHANISMS

Abstract

Purpose. Determination of the equation of motion of the crank-connecting mechanism using the methods of researching the motion of flat multi-link mechanisms. Development of the dependence using the theorem on the change in kinetic energy of the mechanical system for determining the total mass of flat mechanisms when the angle of rotation of the driving link of the flat mechanism changes.
 Research methods. Dynamic analysis of the mechanism. The method of reducing forces and masses. Mathematical determination of the kinetic energy depending on the angle of rotation of the crank of a flat mechanism. Regression processing of the obtained calculation results and their subsequent correlation analysis were carried out using computer software for the analysis and visualisation of scientific and statistical data – «SigmaPlot» from the company «Jandel Corporation».
 Results. A calculated formula for the change in the combined mass depending on the angle of rotation of the crank was obtained. The existence of a sinusoidal relationship between the calculated parameters (crank angle and reduced mass) was established. The correlation analysis of the obtained function showed a sufficiently high degree of relationship between the calculated data and the mathematical dependence, while the correlation coefficient was r = 0.972. The graph of the determined mathematical dependence also showed a fairly high correlation between the specified parameters. The resulting equation can be used for systems with one degree of freedom. For mechanisms with several degrees of freedom, the law of change of the combined mass will be different for each degree of freedom.
 Scientific novelty. Using the calculated formulas of kinetic energy for planar mechanisms, the law of change of the reduced mass in planar mechanisms, which takes into account the rotation of the crank around its own axis, is obtained.
 Practical value. When designing flat crank mechanisms, it is necessary to take into account the effect of inertial forces, the value of which depends on the mass and acceleration. This makes it possible to calculate correctly the dynamic loads on the parts of the flat mechanism (bearings, etc.). The obtained mathematical dependence of the change in the combined mass on the angle of rotation of the leading link of the mechanism makes it possible to analyse the change in the combined moment of inertia, which in turn affects the change in torque.