Analysis Of Stick-slip Vibration For A Friction System Based On Time-varying Normal Load

Friction-induced vibration(FIV)is a common occurrence in mechanical systems with frictional contact pairs,such as automotive brake systems,gearing systems and wheel-rail systems.According to the vibration characteristics,FIV can be classified into many categories,among which stick-slip motion is a typical FIV phenomenon that is easily observed in mechanical applications.Stick-slip motion,which is characterized by periodic switch between the sliding and static states of two solids that are in close contact,generally happens in low speed and heavy load scenarios.The beautiful melodies produced by the violins,and the viscous motion of plates causing earthquakes are all results of the stick-slip vibrations.In addition,stick-slip vibrations can also lead to energy loss,surface wear of key components and annoying acoustic emission of mechanical equipment,therefore,a deep knowledge about the generation mechanisms and evolution behaviors of stick-slip motion must be understood to predict and evaluate the detrimental vibration,so as to find effective ways to tackle this problem.Up to now,many works have been done both theoretically and experimentally to abundant people’s knowledge on stick-slip vibrations.To simplify the analysis,the normal contact force is usually treated as a constant in theoretical and experimental studies,which does not somehow make sense as the contact force is actually fluctuating with time in real friction systems.For a more practical work that can well fit the real situation,the classical single-degree-of-freedom model was selected for this numerical study,where a sine timevarying normal force was adopted.Considering that a simplified single degree of freedom numerical model is only capable of capturing some basic features of stick-slip vibrations,meanwhile,an experimental research is also carried out to observe the characteristics of stickslip instabilities under an alternating normal loading force.Friction-induced stick-slip vibration is a typical non-smooth phenomenon with strong nonlinearities.Nonlinear analysis method of phase space reconstruction mapping the one-dimensional nonlinear time series into three dimensions was employed to better analyze and study the friction-induced nonlinear vibration.The main conclusions of this work are as follows:1.A single degree of freedom numerical model was used to perform numerical analysis by selecting two groups of static and dynamical friction coefficients.The results showed that,under a constant normal force,the vibration amplitude of the friction system increased with the increase of the normal force,while the dominant frequency with the highest energy of the system gradually decreased.The system exhibited a stable limit cycle when the difference between static and dynamical friction coefficients is small.The reduction in the dynamical friction coefficient increased the friction difference,which consequently influenced the limit cycle of the friction system.However,the motion of the friction system became extremely complicated when an alternating normal force was applied.The frequency and amplitude of the normal force are key factors influencing the system vibration,which may result in a random state of single period,multi-period and chaos solutions.When the friction difference increased,the system was more likely to enter the random vibration state where the motion is totally chaotic and unpredictable.2.The experimental results showed that the stick-slip vibration was relatively stable under the constant normal force.The increase in the normal force can intensify the stick-slip vibration of the system,while it can hardly influence the main frequency of the vibration.Under a low-frequency alternating normal force,the system was stable and showed no obvious vibration.However,as the frequency of the excitation increased to a certain value,the system was suddenly activated to vibrate.At the initial stage,the system showed no obvious vibration dominant frequency.When the excitation frequency further increased,fundamental frequencies with low energy started to emerge and transferred to the high frequency range with high energy.Keeping a low excitation frequency,the system is in stick state in the increasing phase of the normal force.While in the decreasing phase of the normal force the system showed a slip state alternating with the stick state.When the frequency of the normal force became large,high frequency self-excited vibration started to initiate in the increasing phase of the normal force.While in decreasing phase of the normal force,high frequency self-excited vibration coexisted with the low frequency stick-slip vibration.3.The experimental results showed that the vibration system shared the same period with the normal force under the alternating normal force circumstance.With the increase of the normal force amplitude,the stick-slip vibration occurred more frequently and the system vibration was intensified,what reflected from the phase diagram of the system were stacked limit cycles with rather complicated morphology.Meanwhile,the total movement distance of the friction block also increased,resulting in lower amplitude and higher frequency in the relative sliding between the friction block and the friction plate.4.When the alternating normal force is applied,the motion state of the system will be altered by increasing the frequency and the amplitude of the excitation force,which can lead to strong self-excited vibration,whose frequency was close to one of the natural frequencies of the friction system.