Vibration Reduction Analysis of a Dry Friction Constrained Longitudinal Vibration System Considering the Maximum Mises Stress and the Magnitude and Distribution of the Normal Load

In this paper, on account of an exponential-type velocity-dependent friction coefficient model, the difference between dynamic and static friction coefficients is considered to improve the one-dimensional micro-slip model. Incorporating with the finite element method, the corresponding dry friction contact element is developed to solve the frictionally constrained longitudinal vibration system with a distributed normal load. As high cycle fatigue failure is caused by excessive vibration stress, the maximal Mises stress instead of the displacement, energy or average power of the system is introduced to evaluate the vibration reduction effect of the system. Meanwhile, the normal load distribution coefficient is proposed to measure its convexity and concavity degree of the distribution of the normal load and the optimal normal load is redefined considering both the magnitude and distribution of the normal load. With Newmark- \(\beta \) method, influences of both the magnitude and distribution of the normal load on the reduction rate and location of the maximal Mises stress of the dry friction constrained longitudinal vibration system are detailly studied. Numerical results indicate that considering the difference between the dynamic and static friction coefficients in the micro-slip model and introducing the maximum Mises stress to evaluate the vibration reduction effect are valuable in dynamical analysis of the dry friction constrained systems. A stress-based criterion for vibration reduction of the dry friction longitudinal vibration system is established.