Investigation of the frictional damping in friction induced vibration

Abstract

Some phenomena of friction induced vibration can be illustrated using negative damping theory, basing on the assumption that the frictional damping of friction induced vibration is constant. The frictional damping of friction induced vibration, however, has not been investigated in details yet. In order to address this problem, a test rig is developed in this research to provide a constant sliding velocity underneath the block. In order to acquire the frictional damping of friction induced vibration, force and vibration should be measured simultaneously. As Fibre Bragg Grating sensing technology can measure distributed systems simultaneously, it is applied to develop the force sensor and acceleration sensor. The natural frequencies of these two sensors designed by finite element method are much higher than the vibration frequency of the test rig acquired with analytical method, ensuring the accuracy of measurement. The force and vibration are measured by the force sensor and acceleration sensor that connected together via one fibre, and the results show that measured dominant frequencies of force and vibration are consistent at various sliding velocities when the block vibrates steadily. In comparison, the dominant vibration frequencies of the test rig acquired by experimental method are slightly lower than the vibration frequency acquired by analytical method due to the existence of frictional damping at the contact interface. A mathematical method for the frictional damping at various sliding velocities is developed, and the results show that the frictional damping is constant when sliding velocity is beyond a certain value, which can verify the assumption that the frictional damping of friction induced vibration is constant, thus complementing negative damping theory.

Investigation of the effect of longitudinal creepage on wheel squeal

“…According to equation (11), the effective system damping can be expressed as the summation of structural damping, friction damping and negative damping. As the structural damping and frictional damping of friction induced vibration mode are consistent at various sliding velocities (Liu et al, 2022), the negative damping should decrease with longitudinal creepage with reference to Figure 10. As a result, it can be inferred that the reason why longitudinal creepage can mitigate wheel squeal is that the negative damping decreases when more longitudinal creepage is introduced at wheel/rail interface, so it is less likely to overcome the structural damping and frictional damping so as to generate wheel squeal.…”

“…The real part of eigenvalue a i is an important parameter to estimate the stability of a system given that the effective damping ratio of a system is determined by a i , that iswhen the real part a i is larger than zero, the effective damping ratio ξi is negative, indicating that the vibration displacement x ( t ) tends to increase with time, and that the wheel/rail system is unstable and tends to generate wheel squeal. In particular, the effective system damping Ceff proportional to the effective damping ratio ξi can be expressed as (Liu et al, 2022)where structural damping Cs is normally a constant value; frictional damping Cf is likely to remain constant in the experiment (Liu et al, 2022) and negative damping Cn is determined by the contact mechanics at the contact point. As Ceff is proportional to ξi, the decrease of ξi means a decrease of Ceff, which can infer the decrease of negative damping Cn.…”

“…when the real part a i is larger than zero, the effective damping ratio ξ i is negative, indicating that the vibration displacement x (t) tends to increase with time, and that the wheel/rail system is unstable and tends to generate wheel squeal. In particular, the effective system damping C eff proportional to the effective damping ratio ξ i can be expressed as (Liu et al, 2022)…”

“…where structural damping C s is normally a constant value; frictional damping C f is likely to remain constant in the experiment (Liu et al, 2022) and negative damping C n is determined by the contact mechanics at the contact point.…”

Dynamics and Entropy Analysis of a Frictionally Loaded Pendulum

“…In technical drive structures, friction is unavoidably present [ 4 ]. Friction occurring between the contact surfaces of a rotating shaft and pendulum-like sliding objects may induce vibration.…”