Research on the Identification Methods of Friction in Kinematical Joints of Mechanical Systems

This paper describes two approaches for the simultaneous identification of the coulomb and viscous parameters in kinematical joints. One is a time-domain method (TDM) and the other is a frequency-domain method (FDM). Simulation shows that both of the two methods have good performances in identifying friction at high SNR (90dB). But at low SNR (20dB), the estimation accuracy of the frequency-domain method is higher than that of the time-domain method. A field experiment employing a linkage mechanism driven by motor is also carried out. The experimental results obtained by the two approaches are almost identical under different experiment conditions. It has been concluded that the presented identification methods of friction in kinematical joints are correct and applicable. INTRODUCTION Kinematical joint is an absolutely necessary structural connection in mechanical systems. The kinematical joint is responsible for transferring energy to a remote site, and may change the type of motion, as needed. The characteristics of kinematical joints have been studied in many papers [1,2]. Friction is an inevitable and complicated phenomenon in kinematical joints when the system works. Many friction models have been presented for friction identification, such as the viscous plus coulomb memoryless model [3,4], the stickslip model [5] and LuGre model [6] etc. When the system runs stably, these friction models tend to be the same friction model, i.e., the viscous plus coulomb memoryless model [3]. Therefore, it is important to study the viscous plus coulomb friction model in mechanical systems. METHODS 1 The time-domain method We denote the rotor angular position by θ , its inertia by J , and the friction torque by . The viscous plus coulomb memoryless model is adopted in this paper, i.e., f ) sgn(θ θ & & c v K K f + = (1) where, is the viscous parameter, and is the coulomb parameter. According to the Newton’s second law, the free vibration differential equation of a SDOF rotor system is 0 > v K 0 > c K f J − = θ& & (2) In this paper only the rotational speed decrement movement of the rotor at initial angular velocity is studied. So the sign function is omitted. According to the equation , the Eq. (2) is transformed to ) sgn(θ& v = θ& 0 = + + c v K v K v J & (3) The initial angular velocity of the rotor is 0 at time v 0 = t in Eq.(3). The analytic solution of Eq.(3) based on the ordinary differential equation theory is ( ) v c J t K v c K K e K K v v v / / / 0 − + = − (4) The expressions of coulomb and viscous parameters are obtained by the least square method: ) 1 ( / ) )( ( 1 1 0 i v i v i v t J K n