Mathematical model of shock-vibration mechanism

This article considers a mathematical model of the operation of a shock-vibration mechanism for compacting bulk materials (including those that are difficult to deform) based on a four-link mechanism that includes an Archimedes lever. The schematic diagram of the shock-vibration mechanism, the principle of operation and its advantages, relative to similar compaction mechanisms, formulas for calculating the coefficients of increasing the driving force of the drive are given. A mathematical model of the mechanism consisting of geometric, kinematic and dynamic calculations is described. The necessary initial data for the calculation of the mathematical model are highlighted: the dimensions of the links of the mechanism (the radii of the crank and rocker arm, the length of the connecting rod), the masses and moments of inertia of these links, the compaction force. In the geometric calculation, the positions of the links of the mechanism in space are determined depending on the angle of rotation of the crank, the angles of deflection of the rocker arm, the connecting rod relative to the initial position during operation of the mechanism, as well as the positions of the links in space. Kinematic calculation includes the determination of angular velocities and accelerations by differentiating the angles of deviation of the links relative to the initial position, as well as linear velocities and accelerations of the links of the mechanism and at special points. Based on the dynamic calculation, the necessary torque and power are determined, taking into account the force required for pressing, inertial forces and moments, and gravity. During the work, the following operating conditions of the mechanism were highlighted, namely, the maximum lifting angle of the working plate should not exceed 20°, the optimal position of the crank at the end of the working stroke to achieve maximum pressing force, it is necessary to install a flywheel to prevent sudden fluctuations and peak loads.