Development of a discreet-continuous mathematical model of a percussion device with parameters of influence on the characteristics of an impact pulse

Abstract

A study of a model of a discrete-continuous type of impactor in the energy transfer phase during the impact of a striker and a tool is presented. The device is used to destroy rocks, in construction equipment, and in the oil industry. In the mathematical model, the tool is represented by a rod with a variable profile, and the striker is a discrete element with a consolidated mass. The presence of rigid and dissipative connections models the impact interaction. The motion of the interacting elements of the impactor is described by a system of differential equations linked by boundary and initial conditions. The model allows determining the parameters of influence on the characteristic of the shock pulse at variable resistance of the working medium. The force of impact of a discrete element and the contact end of the rod is represented as a power law dependent on the difference in displacements of the contacting elements. The finite difference method is used to solve the initial boundary value problem. The parameters of the difference scheme were determined through modelling problems and were as follows: time step (1, ..., 5)·10-5 s; length step – (0.1...0.3) of the tool length, and for the mixed scheme – within 0.5...0.8. It was found that the time of striker-to-tool co-impact, depending on the stiffness coefficient, was 200...300 μs. With a load of up to 90 kN in the time range of 0...4 ms, the normal stresses in the tool sections at different times were 200...250 MPa. The combination of discrete and continuous elements simplifies the calculation scheme. It allows to determine the distribution of force characteristics in the cross-sections of the tool, the force and time of impact, and the influence of the working environment on these parameters. The developed model can be used to design impactors and optimize their parameters