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1、附录 英文文献翻译Modeling and design of servo system of CNC machine toolsJinxing Zheng Mingjun Zhang and Qingxin Meng Department of Mechanical and Electrical Engineering Harbin Engineering University Harbin,HeiLongJiang,150001 Chinazhengjinxing, &zhangmingjun &mengqingxinAbstract Accurate modeling of the fe
2、ed drives dynamics is an crucial step in designing a high performance CNC system. This paper presented a comprehensive dynamic model of CNC feed drive system. The friction model was established analyzing the nonlinear characters of machine tool movement. And a trapezoidal velocity control algorithm
3、was presented due to friction dependence of velocity. As verification of the controller, tracking and contouring simulation were implemented. Index Terms Servo system modeling;Nnonlinear characters; PID control; Contour error; Velocity generation profileI. INTRODUCTIONThe feed servo system of machin
4、e tools is defined as a control system whose purpose is to make the position and the speed of worktable follow the command from numerical control unit. The servo system compares the real position signal by using sensor feedback measurements with the desired command information, then drives the drivi
5、ng units to make the worktable move to the direction of minimizing errors in order to obtain the more accurate workpiece in size. So the design of servo controllers is crucial to the high performance of machine tools. The design of a high performance feed drive control system requires accurate knowl
6、edge of the axis dynamics 1-2. Looking more closely into the design, though many modern control design techniques are now available, most machine tool servo designs are still based on the well-known PID control architecture, only considering more delicate factors to eliminate the effect of backlash
7、and friction, etc. The feedback controllers need to be designed to impose the same closed loop response on all axes, in order to avoid contouring errors in linear motion. This paper presents a method for modeling the dynamics of feed drives. A more comprehensive mathematic model of feed servo system
8、 is presented considering the dominant nonlinear effects of friction. A friction model is incorporated into the axis dynamics. Then a trapezoidal velocity profile for acceleration and deceleration based on varying interpolationduration is considered due to the viscous friction force is proportion to
9、 velocity of feed. The remaining of this paper is organized as follows: modeling of the linear dynamics, as well as nonlinear friction effects are presented in Section. This is continued by trapezoidal velocity generation algorithm in Section . A block of PID control system is given and simulations
10、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 sy
11、stem design, mechanical subsystem servo-motor 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 common motors used in the feed drives are dire
12、ct 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 complex, the motor is frequently
13、 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 well-known DC motor equations are Where Vm is voltage applied to the motors circuit, Ia is the armature current, Rm is the a
14、rmature resistance, Lm is the armature inductance, Kemf is the motors voltage back e.m.f. 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 Kt.The total dynamic torque de
15、livered by the motor is spent in accelerating the inertia of the motor (Jm ) and overcoming the motor shafts viscous damping (Bm), and the external load torque Td which includes the torque to drive the ball-bearing leadscrew and table as well as workpiece (TL), and the disturbance torque due to nonl
16、inear 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 Mathema
17、tical models of the mechanical subsystem are generally constructed by developing equations of motion between the motor and components 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 composed of the motor rotor,
18、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 mechani
19、cal component. R is a conversion ratio of linear-to-rotational motion. Kl is the equivalent axial stiffness composed. of the ballscrew, nut and support bearing stiffnesses. K is the equivalent torsional stiffness composed of the ballscrew and the coupling. Ff is the friction force on the guideways o
20、f 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 Fig.1, the block diagram of a servo physical system model between the control signal Vcfrom controller which is usually implemented by compu
21、ter and worktable real position xt is derived as Fig.2. Where Kv is a gain of signal amplifier and power amplifier. Td is disturbance torque which is composed of friction force on the guideways and cutting force. Kbv is a tachometer gain and Kbp is linear position sensor gain. C. Nonlinear character
22、istic analysis and friction model of feed system of machine toolsDue to several inherent nonlinearities, the stick-slipphenomena appear when the machine tools move more slowly.It has strongly nonlinear dynamic behaviours in the vicinity ofzero velocity. The main reasons are: 1) Stribeck friction exi
23、sts 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
24、 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 compensation techniques of dealing with it. The typical friction ch
25、aracteristics 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
26、 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
27、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
28、. 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, wh
29、ich allows a lubricant film to be formed. At this stage, the film is not thick enough to completely separate the two surfaces, and the contacts at some asperities still affect the friction force. This regime is named as partial fluid lubrication. As partial fluid lubrication increases, solid to soli
30、d contact between the boundary layers decreases, which results in the reduction of friction force with increasing velocity. Partial fluid lubrication is inherently an unstable regime; with increasing velocity, the lubricant film gets thicker, hence reducing the friction force,and causing the velocit
31、y to increase further. This regime is difficult to model, as it involves the interaction of elasto-hydrodynamic phenomena with surface roughness properties.4-5. After sliding velocity reaches a certain level, a continuous fluid film is formed which completely separates the two surfaces. In this regi
32、me, referred to as full fluid lubrication the viscosity of the lubricant is dominant on the friction force.So the expression for friction torque Tf may be written as, Where is very small and positive number, Ta is what remains of the motor torque Tm after a part of it has been used to overcome the e
33、ffect of cutting forces Tc. Tstat and Tcoul are the static friction and the coulomb frition torque respectively. ()t is critical Stribeck velocity, usually a sempirical coefficient, and is an exponent, usually equals to 2. Sinece the effect of viscous damping is included in the axis dynamics in Fig.
34、 2, the friction torque expression in (5) neglects viscous damping component. And the friction model is integrated into the axis dynamics is shown in Fig. 4. In this case, as the equations of motion are written according to the motor shaft, the friction is considered to be a part of the disturbance
35、torque.III.TRAPEZOIDALVELOCITYCOMMANDGENERATIONBASEDONVARYINGINTERPOLATION DURATIONAn interpolation algorithm in which reference trajectories are generated plays a key role to the performance of the feed drive systems. Generated trajectories must not only describe the desired tool path accurately, b
36、ut must also smooth kinematical profiles in order to maintain high tracking accuracy. Due to the friction is relating to the feedrate of the servo system, which is strongly influence the performance of designing the controller and machine tools, a novel velocity generation based on the varying inter
37、polation duration is presented.The feed f is provided by the NC part program, and the minimum interpolation period Tmin is set within the CNC control software. The interpolation step size is calculated as LFT . The step size L is kept constant until Tmin or Fminis changed. When the feed is changed d
38、uring machining by a feed-override switch or a sensor-based machining process control module, L is kept constant but the interpolation time Ti is updated as 7 Assuming that the total displacement along an arbitrary path is L, the interpolation task is executed N times at interpolation time intervals
39、 of Ti,N is always rounded to the next higher even integer for computational efficiency. The total number of iterations (N) is divided into a number of stages depending on the type of velocity profile used for trajectory generation. For simplicity, a trapezoidal velocity profile for acceleration and
40、 deceleration is presented in this paper, which is simple to implement, computationally advantageous. The total number of interpolation steps (N) is divided into acceleration (N1), constant velocity (N2) and deceleration (N3) zones shown in Fig. 5, that is. If the 123 initial feed is f0, the tool pa
41、th length (l1) traveled during the acceleration period iswhich leads toSimilarly, if the system decelerates from feed F to fe, thenumber of interpolation periods during deceleration:where A is acceleration and D deceleration. The counters N,N1,N2,and N3 are rounded integers. If the desired feed is n
42、ot reached because of a short tool path, that is N20, then N2=0,N1=N3=N/2, assuming A=D. Since the traveled tool path segment L is kept constant, the following expression can be written between interpolation periods: By substitutingTk() t t ,t fk()/At, fk( 1)/A, the ikkk 11kinterpolation period duri
43、ng acceleration and deceleration where the velocity changes is found at each increment as If we take a two-axis motion in the x and y directions, the resulting velocities of the x and y drives,Hence, once L, interpolation time Ti, and N1,N2,and N3 are calculated, the velocities and incremental posit
44、ions in the x and y drives are automatically defined by the algorithm. IV.SIMULATION AND RESULTS ANALYSISThere are a significant number of control laws to be implemented in CNC servo system. Typically, PID controllers are used to compensate for steady-error and disturbances such as external loads an
45、d friction forces. And in order to widen the axis tracking bandwidth, a simple feed forward friction method is applied to prevent from degrading the tracking and contouring performance. The parameters in the feedforward compensator are from the experimental knowledge. The parameters of one axis in m
46、achine tools are identified and list in table.A reference circle toolpaths is used in contour machining simulation tests 7. The commands of position and velocity of each axis are generated in CNC units based on the trapezoidal velocity control algorithm presented here. The contour profile is generat
47、ed by using trapezoidal velocity algorithm and the desired circle shown in Fig.6. The generating velocity profiles are shown in Fig. 7. The actual each axis position and velocity are shown in Figs.8-11. The performance of classical PID controller adding the feedforward friction compensation based on
48、 the comprehensive servo axis dynamical model and friction model is illustrated in these figures. The actual contour toolpaths compared with the desired towpaths is shown in Fig. 12. the dash thick curve is actual contour under the PID controller, and the solid thin curve is desired contour. There are still contour errors due to the simple friction compensator. The in
