【正文】 tinued by trapezoidal velocity generation algorithm in Section . A block of PID control system is given and simulations are implemented in Section . Conclusions are described in Section .II. COMPREHENSIVE MODELOFSERVOSYSTEMOFMACHINETOOLSWITHNONLINEARCHARACTERSFeed drive systems consist of several subsystems such as power transmission mechanism, actuators, sensors, controllers and amplifiers. Form the view of servo system design, mechanical subsystem servomotor drive subsystem and controller subsystem are included. Accurate models of the mechanical and control subsystem are indispensable to perform the systematic design satisfactorily. A. Servo motor model The most mon motors used in the feed drives are direct current (DC) motor since they allow a wide range of operating speeds with the sufficiently large torque delivery required by machine tools. Recently, most feed drive actuators of machine tools are alternating current (AC) servo motors. Because an AC motor model is plex, the motor is frequently modelled as an equivalent DC motor using vector transformation or root mean squares. So the following modelling of servo motor is explained based on DC servo motors. A set of wellknown DC motor equations are Where Vm is voltage applied to the motor’s circuit, Ia is the armature current, Rm is the armature resistance, Lm is the armature inductance, Kemf is the motor’s voltage back . constants, m is the angular velocity of motor. The magnetic field produces motor dynamic torque Tm, which is proportional to the armature current Ia with the motor torque constant total dynamic torque delivered by the motor is spent in accelerating the inertia of the motor (Jm ) and overing the motor shaft’s viscous damping (Bm), and the external load torque Td which includes the torque to drive the ballbearing leadscrew and table as well as workpiece (TL), and the disturbance torque due to nonlinear static and Coulomb friction in the guide way (Tf) and cutting forces (Tc).The angular velocity of the motor shaft m and the armature voltage Vm and the external load torque TL can be expressed in Laplace domain as: B. Linear model of mechanical subsystem of feed system in machine tools Mathematical models of the mechanical subsystem are generally constructed by developing equations of motion between the motor and ponents of the feed drive system. Fig. 1 shows a freebody diagram of the mechanical subsystem. In Fig. 1, Jm is the inertia of rotating elements posed of the motor rotor, coupling and ballscrew inertias. m and s are rotational angles of the motor shaft and the ballscrew, respectively. Tm is the driving torque of the motor. xs and xt are transverse distances of the nut and the table, respectively. And Mt is the table mass, Fd is the driving force acting on the mechanical ponent. R is a conversion ratio of lineartorotational motion. Kl is the equivalent axial stiffness posed. of the ballscrew, nut and support bearing stiffnesses. K is the equivalent torsional stiffness posed of the ballscrew and the coupling. Ff is the friction force on the guideways of machine tools. The equivalent inertia Jeq and stiffness Keq of the feed drive system are described as (3) and (4), respectively. From the above equations and , the block diagram of a servo physical system model between the control signal Vcfrom controller which is usually implemented by puter and worktable real position xt is derived as . Where Kv is a gain of signal amplifier and power amplifier. Td is disturbance torque which is posed of friction force on the guideways and cutting force. Kbv is a tachometer gain and Kbp is linear position sensor gain. C. Nonlinear characteristic analysis and friction model of feed system of machine toolsDue to several inherent nonlinearities, the stickslipphenomena appear when the machine tools move more has strongly nonlinear dynamic behaviours in the vicinity ofzero velocity. The main reasons are: 1) Stribeck friction exists for the metallic surfaces in contacton the machine tool slidway。 2) The flexibility of the coupling between the servo motorand the ballscrew mechanism makes it impossible to restrainthe Stribeck friction.3) the backlash exists in the ballscrew transmission。 Since effects of friction are dominant in the nonlinear characters, some of the significant points of friction are summarized and a friction model is presented. Armstrong et al. have presented an excellent survey on the physics behind the friction phenomenon, as well as pensation techniques of dealing with it. The typical friction characteristics for lubricated metallic surfaces in contact can be described by the Stribeck curve, as shown in Fig. 3. The typical friction characteristics for lubricated metallic surfaces in contact can be described by the Stribeck curve. The stribeck curve consists of four different regions: static friction zone, boundary lubrication zone, partial lubrication zone, and full fluid lubrication zone. If a tangential force is applied to the surfaces, it will first work to elastically deform the asperity junctions. This phenomenon is referred to as presliding displacement and friction force is in static friction zone. If the tangential force exceeds a certain threshold, referred to as maximum static friction force, the junctions will break, causing sliding to start. Once the breakaway occurs, a film of lubricant will not be able to build up between the contact surfaces at very low velocities. In this case, sliding will occur between solid boundary layers of lubricant that are stuck to the metal surfaces. This regime of the Stribeck curve, is referred to as boundary lubrication. As the sliding velocity between the two surfaces increases, more lubricant is drawn into the contact zone, which allows a lubricant film to be formed. At this stage, the film is not thick enough to pletely separate the