机械工程及自动化专业外文翻译--对1PS 4TPS型混合工作机床在插补原理和方法的研究

1、机械工程及自动化专业外文翻译-对1PS+4TPS型混合工作机床在插补原理和方法的研究 外文出处: Third International Conference On Natural Computation 0-7695-2875-9/07? 2007 IEEE外文原文Study on Interpolation Principle and Method for 1PS+4TPS Type Hybrid Machine ToolShouwen Fan Xiaobing Wang Mingquan Shi Hongzhong Huang School of Mechatronics Enginee

2、ring, University of Electronic Science and Technology of China Chengdu, SiChuan, 610054, Peoples Republic of China ABSTRACTThis paper presents a novel hybrid machine tool HMT based on a 4-dof 1PS+4TPS type spatial hybrid mechanism and a x-y worktable. This type HMT enjoys some advantages relative to

3、 its conventional counterparts: large workspace, good dexterity, etc. Closed-form solutions for both the inverse displacement model and inverse kinematic model are derived. A computerized numerical control CNC system scheme for motion control of HMTs is proposed focusing on motion control characteri

4、stics of HMTs and based on research fruits of traditional numerical control machine tool. Real-time five-axis interpolator, which is composed of cutter path calculation, inverse displacement analysis model, inverse kinematic analysis model and PVT fine interpolation mode, are constructed. Cutter pat

5、h interval calculation and interpolate error analysis are also discussed, Feasibility and efficiency of above real-time interpolator are confirmed by numerical examples Keywords: Hybrid machine tool; Computerized Numerical Control; Interpolation; Error analysis; Cutter path interval 1. INTRODUCTIONP

6、arallel Machine Tool PMT is a creative application of parallel mechanism, NC technology and computer control technology in the area of machine tool 1-6. As a new-style machine tool, PMT has advantages of simple structure, low cost, low moving inertia, high velocity, agile mobility, high techniques,

7、etc. PMT complements the traditional NC machine tool perfectly and especially it is suitable for machining parts with complicated surfaces such as vane, impeller and propeller, etc2 However, as the existing PMT which only adopts parallel architecture is restrained by hinge and interfered by chain, p

8、articularly is affected by some factors such as coupling of position and orientation, the mobile platform has a limited ability to realize orientation. Therefore, it is very difficult to meet the needs of multi-coordinate NC machining with large working space and complex surface. In order to solve t

9、his problem, researchers have made efforts on exploring new architectures. Many researchers begin to pay their attention to less than 6 ,degree of freedoms DOFs PMTs, especially hybrid machine tools HMTs4, another important developing trend of PMT is that translatory DOF and rotary DOF are implement

10、ed individually by utilizing combined mechanism. This configuration not only releases the coupling between translatory control and rotary control, but also has advantages of large working space and better reconfiguration ability. Specially, as there is an analytic solution for position and orientati

11、on in forward kinematics, so it provides a great convenience for NC programming, control and error compensation 1PS+4TPS mechanism is a novel 4 DOFs hybrid mechanism8, among the abbreviations 1PS+4TPS, P represents prismical joint, S represents spherical joint, T represents hooke joint, it can imple

12、ment one translatory movement and three rotary movements. The core architecture of novel HMT is a serial and parallel compound architecture which is composed of above 4 DOFs hybrid mechanism and a x-y worktable, shown as Fig.1. Mechanism design and kinematic analysis for this novel hybrid machine to

13、ol are described first, then a CNC system scheme for HMTs is designed, a real-time five-axis interpolator for path control of HMTs is proposed. Cutter path interval calculation and interpolate error analysis are also discussed2. DESCRIPTION OF NOVEL HMTs ARCHITECTURE A 4-DOF hybrid mechanism is show

14、n in Fig. 1 A3Fig.1. Structure scheme of novel hybrid machine tool hybrid mechanism consists of five kinematic subchains, including four variable length driving legs with identical topology and one passive leg, connecting the fixed base to a moving platform. In this 4-DOF hybrid mechanism, each of t

15、he four identical legs consists of a fixed Hooke joint, an driving prismatic joint, a moving link and a spherical joint attached to the moving platform. The fifth chain, which connects the fixed base center to the moving platform center, is a passive leg with a different structure from the other fou

16、r identical chains. It consists of a prismatic joint attached to the base, a moving link and a universal joint attached to the platform. Above hybrid mechanism can be combined with two-axis systems, such as x?y tables, to form five-axis machinesINVERSE DISPLACEMENT ANALYSIS MODEL AND INVERSE KINEMAT

17、IC MODEL FOR HMTs3.1. Inverse displacement analysis modelA fixed reference coordinate system and a movable reference coordinate system are set up on the center of fixed platform and movable platform respectively, shown as Fig 2. Position of four hooke joints of fixed platform with respect to the fix

18、ed frame can be described by ,position of four spherical joints of movable platform with respect to the movable frame can be described by ,position of four spherical joints of movable platform with respect to the fixed frame can be described by ,original point of movable frame can be described by is

19、 orientation rotation matrix of the movable platform with respect to the fixed platform described by three Euler angleThe coordineate of spherical joint in movable platform with respect to the fixed frame can be denoted by Inverse displacement analysis equation can be written as where is the 3x3 rot

20、ation transformation matrix of coordinate system which can be obtained using three sustain rotation transformation by three Euler angles and as follows shown as Fig 3. 3.2. Inverse kinematic model Definitions of parameters used in the kinematic analysis are listed as follows: length of actuating leg

21、s, input velocity of actuating legs ,angle velocity of movable platform ,velocity of center point P of movable platform ,angle velocity of actuating leg, mass center velocity of upper section of actuating legs, mass center velocity of lower section of actuating legs, distance from mass center of upp

22、er section to point ,in actuating legs, distance from mass center of lower section to point in actuating legs. Following donations are also defined: For all the donation, we adopt: i1,2,3,4because velocity of spherical joint point of movable table is equal to that of the same point in driving leg, w

23、e have Dot multipling both side of Eq.3 using , we obtain Eq.4 can be rewritten using matrix form where Then Above equation can be written separately as where Cross multipling both side of Eq.3 using derive Substituting Eq.7 into Eq.8, we obtain where Then Mass center velocity of upper section and l

24、ower section of actuating legs can be expressed as Substituting Eq.7 and Eq.10 into Eq.11, we get where Because Substituting Eq.7 into Eq.13, we obtain When input kinematic is known, the solution for velocity and angular velocity of movable platform is defined as forward velocity solution. Combining

25、 Eq.7 and Eq.14, forward velocity model equation can be expressed as Where one order influence coefficient matrix of end manipulators position and orientation velocity relative to input velocity ,If matrix is nonsingular, the inverse kinematic equation can be expressed as SCHEME OF CNC SYSTEM FOR HM

26、Ts A CNC system scheme for 1PS+4TPS type HMTs is proposed in this paper, illustrated as Fig.4. The scheme includes such design ideas as to utilize the research fruits of traditional numerical control system to ium extend, to keep good compatibility with traditional numerical control system, to keep

27、accordance with traditional numerical control system in such aspects as control system structure, technique criterion etc, and to adopt both open modular system structure and standard hiberarchy design idea. The scheme of CNC system for HMTs is compoesd of CAD layer, CAM layer, CNC layer and Servo l

28、ayer, etc. Among them, the automatic programming function modular of CAM layer can generate cutter path automatically based on surface model, cutter compensation information and velocity control information, datafiles of cutter path can be generated automatically. G code can be derived from datafile

29、 of cutter paths by post processor. G code can also be converted to graphics display of machining path by machining simulation modular, so the correctness of cutter path can be verified. The automatic programming function modular can output line and arc interpolation code directly, and then G codes

30、of interpolation are sent to interpolation layer. The interpolation layer can generate cutter path according to the precision requirement, and disperse cutter path roughly according to sample frequence provided by the hardware, then datas of cutter path are mapped into joint space via non-linear map

31、ping i.e., displacement and velocity inverse analysis model, dispersed position datas of joint space can be obtained. In joint space, a digital processor DSP based PMAC motion control card is utilized to realize precise position control for each actuating leg, by actuating hybrid mechanism, high spe

32、ed high precision cutter paths of HMTs can be realized conquentlyTraditional numerical control systems have accumulated many research fruits, above scheme inherits some system structure from traditional numerical control system, and some special requirements of motion control for HMTs are also taken

33、 into account, so above CNC system scheme is a simple and practical implementation strategy for motion control of 1PS+4TPS type HMTsSURFACE INTERPOLATION ALGORITHM 5.1. Basic principle for interpolation Nurbs Surface equation can be defined as Where:control vertex distributing as a topological recta

34、ngle array, and forming a control gridding. are weighting factors connecting with control vertex ,and are normal B spline base for parameter u and v respectively. also have If row cutting method is adapted for surface machining, parallel planes can be used for incising surface of machining part, des

35、ired cutting path can be obtained. Curve equation located in the kth plane can be expressed as Normal vector N of cutting point of machining part surface can be calculated using following equationAbove equation can be rewriten as Furthermore, unit normal of N, namely, Ne can be obtained WhereSupposi

36、ng that the axis of cutter keeps consistent with orientation of surface normal of machining parts Showen as Fig.5, so, according to geometry relationship, we have whereis position vector of cutter reference point P, is compensationvector of cutting remains ,is compensation vector of cutter radius, r

37、 is cutter radius.5.2 control of cutting velocityFeeding velocity Vu along curve direction can be defined as Where So In sampling time tkT, using Talor series and processing two order expandedness, we obtain Above equation is asymmetry iterative equation for parameter u. Feeding velocity along curve

38、 direction during machining process can be controlled by adjusting increment of parameter u, and feeding velocity along curve direction can be made to keep constant. So, smooth cutting characteristic can be achieved 5.3. Fine interpolation algorithmPVT fine interpolation mode of pmac motion card is

39、also called position, velocity, time motion mode. Under such PVT mode, interpolation period is set to be a constant, and acceleration is a linear function of time. Based on constrain condition of position and velocity of start point and end point, a smooth continuous spline curve can be obtained usi

40、ng Hermite interposition. So, acceleration velocity position of joint space under atain time can be expressed asWhere5.4 cutter path interval calculationfig .6a shows the situation, in which machined surface is a plane. Suppose radius of cutter is R, cutter path interval is L, remains height is h, b

41、ased on geometry relationship in Fig.6a, we have In order to make the remains height less than the allowed height H0, following condition must be met Fig 6b shows the situation ,in which machined surface is a protruding surfaceSuppose curvature radius of surface is , based on geometry relationship i

42、n Fig.6b, we have Expand above equation using taylor series,the simplified equation can be expressed as In order to make the remains height less than the allowed height H0, following condition must be met Fig 6c shows the situation which machined surface is a concave surface. Based on geometry relat

43、ionship in Fig.6c, we have Expand above equation using taylor series ,the simplified equation can be expressed as In order to make the remains height less than the allowed height H0, following condition must be met 6 ERROR ANALYSIS AND SIMULATION CALCULATIONBased on derivation of above interpolation

44、 algorithm ,it ca be seen that interpolation point always located on section curve of machining surface, there is not direction keeps constant. Interpolation error mainly comes forth from radial error of chord and curve, shown as Fig. 7. Suppose length of chord is L, curvature radius is , error is ,

45、 based on error relationship between chord and arc, we havefeed speed of HMT is 10m/min, interpolation period of CNC system is 2ms, based on Eq.36, it can be calculated that the interpolation error is 0.278m. So, it can be concluded that even the machining speed is very high, above interpolation alg

46、orithm can also implement high precise machining with machining error less than 1m.Interpolation algorithm, we proceeded a calculationsimulation. In order to simulate machining process, cutter motion is displayed dynamicly on computer screen, simulation program is designed using Delphi 6.0 computer

47、language. Fig. 8 shows simulation results of cutter motion path and cutter motion orientation represented using cutter axis line, in order to display simulation results clearly, cutter motion path and cutter motion orientation are displayed after an interval of row, in Fig. 8, cutter axis line keeps

48、 perpendicular to maching plane. Graph display result and data sampling analysis result show that interpolation algorithm proposed in this paper is correct and feasible CONCLUSIONS AND DISCUSSION Closed from inverse displacement analysis model and inverse kinematic model for main feed mechanism of 1

49、PS+4TPS type HMTs are established. Focusing on characteristics of 1PS+4TPS type HMTs such as highly nonlinear, tightly coupled and uncertain, we designed a CNC system scheme for 1PS+4TPS type HMTs based on research fruits of traditional numerical control machine tool. Real-time five-axis interpolato

50、r, which is composed of cutter path calculation, inverse displacement analysis model, inverse kinematic analysis model and PVT fine interpolation mode, are constructed. Cutter path interval calculation and interpolate error analysis are also discussed, Feasibility and efficiency of above real-time i

51、nterpolator are confirmed by numerical example. With the development of parallel machine toochnology, new configurations for parallel machine tool with less than 6 axis degree of freedom would be more appropriate, so hybrid machine tool has shown its technical potential, 1PS+4TPS type HMTs, which co

52、mbines advantages of parallel structure with that of serial structure, possesses good kinematic characteristic, high stiffness, large workspace, is a promising structure type for numerical control machine tool. Development and application of this type HMT are meanful and valuable in theoretic and ap

53、plication aspect for development of high speed, high precision, high efficiency numerical control machine toolREFERENCES中文译文对1PS+4TPS型混合工作机床在插补原理和方法的研究 范守文,王小斌,师明全,黄鸿忠 中国电子科技大学成都,四川,610054, 中华人民共和国摘要 本文基于 4 dof 的1PS ,设计了新型的混合工作机器 (HMT)+4TPS 键入空间的混合机制和 a x-y 的工作台。这一类型 HMT与它的传统相比有一些优势: 大的工作空间、较好的灵活度等等。可以实现倒转的换置模型和倒转的运动学模型的关闭。对应HMTs运动控制的CNC方案是运动控制特性和基于传统的数字控制机器的研究成果。即时的五轴插补器,它包括切削路径计算,倒转的换置分析模型,倒转的运动学的分析模型和 PVT插补模态,事实证明他们可以构建。 通过切削路径间隔计算和插补错误分