Equivalent linearization of hyperelastic rubber rings in dynamic vibration absorber boring bar and simulation of its dynamic properties

Abstract

A slight perturbation in high-speed precision cutting could cause violent vibration of boring bars, resulting in unexpected wear and failure of the structures. In this paper, the dynamical characteristic of a boring bar with a dynamic vibration absorber (DVA) is investigated. Considering that the nonlinear characteristics of the rubber ring play a significant role in improving the capacity of DVA, we proposed an equivalent linearization method for modeling hyperelastic rubber rings based on the experimental data of uniaxial tensile test. The relationship between the stiffness of rubber rings and the precompression parameter δ is established for two types of rubber. The equivalent linearization model shows good accuracy and calculation efficiency while the mass of the DVA is confined to a narrow space and the assumption of small strain is inherently satisfied. Numerical results show that the time cost of the equivalent linearization model is only 5% of the full hyperelastic model. Furthermore, the effect of different spring stiffnesses and damping on the dynamic characteristics of the boring bar is compared by using the equivalent linearization model, and the vibration peak of the DVA boring bar is found to be reduced about 45%. Our findings establish a simplified modeling scheme for choosing rubber rings in design of dynamic vibration absorbers with acceptable accuracy and little time cost, which could also give some reference for modeling of metal rubber and gel-like materials.