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.doc

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 &Abstract Accurate modeling of the feed 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 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 machine 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 driving 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 knowledge 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 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 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 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 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 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 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 complex, 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 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 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 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 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 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 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 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 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 computer 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 characteristic 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 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 compensation 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 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 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 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 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 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. 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 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, but 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 interpolation 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 during 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 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 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 path 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 not 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 during 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 positions 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 and 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 machine 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 generated 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 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 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 friction 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. 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Altintas, Manufacturing Automation: Metal cutting Mechanics, Machine Tool Vibrations, and CNC design, Cambridge University Press, Cambridge, 2000. nd7 Liu 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 zhengjinxing，与zhangmingjunmengqingxin 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，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。伺服系统比较实际位置通过使用传感器反馈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馈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，以避免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