关键词: 单边约束, 多体系统, 库仑摩擦, 蛙式打夯机, 线性互补

Abstract: The modeling and numerical simulation of frog-hammer are typical questions about multibody system dynamics with frictional unilateral constraints. With rational assumptions on frog-hammer and its working environment, simplified multibody model of frog-hammer is established. Dynamics equations are derived by means of Lagrange’s equations of first kind. They are constrained by two unilateral constraints with friction. Time-stepping impulse-velocity schemes and corresponding linear complementarity formulas, which is equivalent to the stick-slip transition conditions, are adopted to simulate the whole working process of frog-hammer. The numerical results perfectly depict the stick-slip phenomenon in advancing process and periodic lift off-ramming process. With numerical results, two important frog-hammer performance parameters, i.e., the advancing velocity of frog-hammer and ramming energy absorbed by the ground per impact, are calculated.

Key words: Coulomb friction, Frog-hammer, Linear complementarity, Multibody system, Unilateral constraint