建模和数控机床的伺服系统的设计工具毕业论文外文翻译

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 Harbin,HeiLongJiang,150001 ChinaAbstract Accurate modeling of the feed drives dynamics is an crucial step in designing a high perfo

2、rmance 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 was presented due to friction dependence of velocity. As verifi

3、cation 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 machine tools is defined as a control system whose purpose is to make

4、 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 driving units to make the worktable move to the direction of minimiz

5、ing 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 knowledge of the axis dynamics 1-2. Looking more closely into the de

6、sign, 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 and friction, etc. The feedback controllers need to be designed

7、 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 is presented considering the dominant nonlinear effects of fri

8、ction. 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 velocity of feed. The remaining of this paper is organized as

9、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 are implemented in Section . Conclusions are described in Secti

10、on .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 servo-motor drive subsystem a

11、nd 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 direct current (DC) motor since they allow a wide range of operatin

12、g 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 modelled as an equivalent DC motor using vector transformation

13、 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 armature resistance, Lm is the armature inductance, Kemf is the

14、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 delivered by the motor is spent in accelerating the inertia of th

15、e 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 nonlinear static and Coulomb friction in the guide way (Tf) and cut

16、ting 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 construc

17、ted 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, coupling and ballscrew inertias. m and s are rotational angles

18、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 component. R is a conversion ratio of linear-to-rotational

19、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 of machine tools. The equivalent inertia Jeq and stiffness Keq o

20、f 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 computer and worktable real position xt is derived as Fig.2. Where K

21、v 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 characteristic analysis and friction model of feed system of machine too

22、lsDue 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 exists for the metallic surfaces in contacton the machine tool sli

23、dway; 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

24、 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 characteristics for lubricated metallic surfaces in contact can b

25、e 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

26、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

27、 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 layer

28、s 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 fi

29、lm 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 solid contact between the boundary layers decreases, which results

30、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 velocity to increase further. This regime is difficult to model, as it

31、 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 regime, referred to as full fluid lubrication the viscosity of the

32、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 effect of cutting forces Tc. Tstat and Tcoul are the static fric

33、tion 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. 2, the friction torque expression in (5) neglects viscous damp

34、ing 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 torque.III.TRAPEZOIDALVELOCITYCOMMANDGENERATIONBASEDONVARYINGIN

35、TERPOLATION 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, but must also smooth kinematical profiles in order to maintain h

36、igh 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 interpolation duration is presented.The feed f is provided by the NC

37、 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 during machining by a feed-override switch or a sensor-based mac

38、hining 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 of Ti,N is always rounded to the next higher even integer for

39、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 deceleration is presented in this paper, which is simple to im

40、plement, 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 path length (l1) traveled during the acceleration period iswhich

41、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 not reached because of a short tool path, that is N20, then N2=0

42、,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 during acceleration and deceleration where the velocity changes is

43、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 positions in the x and y drives are automatically defined by the alg

44、orithm. 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 and friction forces. And in order to widen the axis tracking band

45、width, 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 machine tools are identified and list in table.A reference circl

46、e 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 generated by using trapezoidal velocity algorithm and the desired circ

47、le 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 the comprehensive servo axis dynamical model and friction mode

48、l 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.

49、 The intelligent method tuning the parameters of PID and more complicated friction model will help improve the tracking and contour accuracy.V. CONCLUSIONThis paper has presented the detail modeling process of servo drive system of CNC machine tools. A dynamic servo model has been combined with a fr

50、iction model. And the novel velocity control algorithm has been presented and implanted based on the varying periods. A serial of simulations verified the high performance of PID controller based on the comprehensive model and reasonable friction compensation. REFERENCES1 Y.Koren, Computer Control o

51、f Manufacturing Systems, McGraw-Hill, New York, 1983 2 A.T.Elfizy, et al, “Model-based controller design for machine tool direct feed drive, International Journal of Machine Tools and Manufacturing,vol. 41, 2001, pp. 1637-1658. 3 Min-Seok Kim, Sung-chong Chung, “A systematic approach to design high-

52、performance feed drive systems, International Journal of Machine Tools and Manufacturing, vol. 45, 2005, pp. 1421-1435 4 Kann Erkorkmaz, Yusuf. Altintas, “High speed CNC system desigh. Part , International Journal of Machine Tools and Manufacturing, vol. 41, 2001, pp. 1487-1509. 5 Kann Erkorkmaz, Yu

53、suf. Altintas, “High speed CNC system desigh. Part , International Journal of Machine Tools and Manufacturing, vol. 41, 2001, pp. 1637-1658. 6 Y. Altintas, Manufacturing Automation: Metal cutting Mechanics, Machine Tool Vibrations, and CNC design, Cambridge University Press, Cambridge, 2000. nd7 Liu

54、 Jinkun, Advanced PID control and MATLAB simulation,2 ed, Publishing House of Electronics Industry, Beijing, 20042006年IEEE的程序在机电工程与自动化国际会议6月25日 - 2006 28，中国洛阳建模和数控机床的伺服系统的设计工具郑金星张明君萌清新机电工程系 哈尔滨工程大学 黑龙江省哈尔滨市，150001中国 摘 要在进给驱动“动态精确建模是在设计一个高性能数控系统的关键一步。本文提出的数控进给的综合动态模型驱动系统，建立了摩擦模型分析机床运动的非线性字符，和梯形速度控制算法

55、，呈现出摩擦速度的依赖。验证控制器，跟踪和轮廓模拟得到实施。关键词 ： 伺服系统建模; Nnonlinear字符; PID控制;轮廓误差;速度生成配置文件第一章 引言机床的进给伺服系统被定义为一个控制系统，其目的是使该位置与工作台速度从数值按照命令控制单元。伺服系统比拟实际位置通过使用传感器反应的测量与期望的信号命令的信息，然后驱动所述驱动单元以使工作台移动到最大限度地减少错误的方向订购的尺寸，以获得更准确的工件。所以，伺服控制器的设计是非常重要的高性能机床。高性能进给驱动器的设计控制系统需要轴线准确的知识动态1-2。在寻找更紧密地融入设计中，尽管许多现代控制设计技术现已有售，最机床的伺服设计

56、仍然是基于对知PID控制架构，只考虑更细腻因素来消除齿隙和摩擦等的影响反应控制器需要被设计为在施加对所有的轴相同的闭环回路响应，以防止在轮廓直线运动的错误。本文提出了建模动态的方法的进给驱动。一个更全面的数学模型进给伺服系统，提出考虑的主导摩擦的非线性效应。摩擦模型结合成轴的动力。然后一对梯形速度曲线根据不同的插值加速和减速持续时间被认为是由于粘性摩擦力比例为饲料的速度。其余本文是安排如下：线性动力学建模，以及作为非线性摩擦影响列于第。这是继续在梯形速度生成算法节。 第二章 伺服系统的综合预测模型进给驱动系统由几个子系统组成，如动力传动机构，传动器，传感器，控制器和放大器。构成伺服系统设计的视

57、图机械子系统伺服电机驱动子系统和控制器子系统均包括在内。的精确模型机械和控制子系统是不可或缺的圆满完成了系统设计。2.1 伺服电机M在进给驱动装置中最常用的电动机是直流DC电机，因为它们允许范围广泛的运行速度与足够大的扭矩传递由机床所需。最近，大局部进给驱动执行器机的工具是交流电AC伺服电机。由于交流电机的模型是复杂的，电机经常建模为一个等效直流电动机采用矢量改造或根均方。所以下面伺服电机的建模是基于直流伺服解释电机。一组著名的直流电动机方程为 其中Vm为施加到电动机的电路电压，1a是对电枢电流，Rm为电枢电阻，Lm是电枢电感，Kemf是电机的电压的反电动势常数，m是角速度电机。磁场产生电机动

58、态转矩Tm，这是成正比到电枢电流Ia的电机转矩常数Kt。由电机交付的总动态扭矩都花在了加快电机JM的惯性，克服电动机轴的粘性阻尼BM，和外部负载扭矩TD其中包括驱动球轴承的转矩丝杠和表以及工件TL，以及由于非线性静力和库仑扰动力矩摩擦的导轨TF和切削力TC。 角速度的电机轴m和的电枢电压Vm和外部负载转矩TL可以表现在拉普拉斯域： 2.2 进给系统的机械子系统的线性模型机床 机械子系统的数学模型一般建造，开发的运动方程电机和进给驱动系统的部件之间出了机械子系统的freebody图。 在图1，JM是旋转的组成元件的惯性 电机转子，联轴器和滚珠丝杠的惯量。 m和s是电机轴和滚珠丝杠的旋转角度， T

59、m是电动机的驱动转矩。 XS和XT都横向距离上的螺母，表中MT是表质量的Fd是作用在驱动力机械部件。 R是直链对转化率旋转运动。 KL是由等效轴向刚度。K是等效扭转刚度由滚珠丝杠和的耦合。 FF是对的导轨的摩擦力机床。 图一 进给驱动系统的物理组件图进给驱动器的等效惯量JEQ和刚度KEQ 系统被描述为3和4，分别为 从上面的等式和图1中，a的框图控制信号Vc之间的伺服系统的物理模型从控制器，它是由计算机通常被实现并工作台的实际位置XT推导图2。凡Kv值是增益信号放大器和功率放大器。 TD是干扰，它是由摩擦力对导轨的力矩和切削力。 KBV是一个测速发电机增益和KBP是线性的位置传感器的增益。图二

60、 进给驱动器的物理系统模型框图2.3 非线性特性分析和摩擦模型机床进给系统如果一个切向力施加到外表上，其将第一工作，以弹性变形的凹凸结。这现象被称为presliding位移和摩擦力是在静摩擦区。如果切向力超过一定阈值时，称为最大静摩擦力，该路口将打破，导致滑动启动。一旦脱离发生时，润滑膜将不能在非常低的速度接触外表之间建立起来的。在这种情况下，滑动将固体边界层之间发生润滑剂的被粘在金属外表上。这个政权的斯特里贝克曲线，被称为边界润滑。如两个外表之间的滑动速度增大，更润滑剂被吸入到接触区，它允许将要形成的润滑膜。在这个阶段，电影是不厚足以完全分开的两个外表上，并且在一些粗糙的接触仍影响摩擦力。这