非正交可重組機床的控制

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2、a Non-Orthogonal Reconfigurable Machine Tool茲扛撅贐稗諉萬聊拔循憚唰Reuven KatzJohn YookYoram Koren廨檠紿誓清宥坦桅羅評虬鲅Received: January 3, 2003; revised: September 16, 2003爛簧倉涵賄哧笤撐夕昃熟王Abstract痢嗪鳴截抗扯錟孓篪鈺扭虍Computerized control systems for machine tools must generate coordinated movements of the separately driven axes of

3、 motion in order to trace accurately a predetermined path of the cutting tool relative to the workpiece. However, since the dynamic properties of the individual machine axes are not exactly equal, undesired contour errors are generated. The contour error is defined as the distance between the predet

4、ermined and actual path of the cutting tool. The cross-coupling controller (CCC) strategy was introduced to effectively decrease the contour errors in conventional, orthogonal machine tools. This paper, however, deals with a new class of machines that have non-orthogonal axes of motion and called re

5、configurable machine tools (RMTs). These machines may be included in large-scale reconfigurable machining systems (RMSs). When the axes of the machine are non-orthogonal, the movement between the axes is tightly coupled and the importance of coordinated movement among the axes becomes even greater.

6、In the case of a non-orthogonal RMT, in addition to the contour error, another machining error called in-depth error is also generated due to the non-orthogonal nature of the machine. The focus of this study is on the conceptual design of a new type of cross-coupling controller for a non-orthogonal

7、machine tool that decreases both the contour and the in-depth machining errors. Various types of cross-coupling controllers, symmetric and non-symmetric, with and without feedforward, are suggested and studied. The stability of the control system is investigated, and simulation is used to compare th

8、e different types of controllers. We show that by using cross-coupling controllers the reduction of machining errors are significantly reduced in comparison with the conventional de-coupled controller. Furthermore, it is shown that the non-symmetric cross-coupling feedforward (NS-CC-FF) controller d

9、emonstrates the best results and is the leading concept for non-orthogonal machine tools. 2004 ASME 詔窄浪練陛琿隼諏即盈秘锎Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, A

10、ND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division January 3, 2003; final revision September 16, 2003. Associate Editor: J. Tu. 證釗矯櫟喲餡猞慷集困到碑Keywords:machine tool, cross-coupling controller, non-orthogonal, RMT嚯倩唱康磽囊束俞各鷸娃逼升魴偶汽瓚梵謨褒膳肼那溉況賢聱垡舞勿萊大躪礞槍弟1 Introduction雇鹛乩聞鬈殺薯鯇詒鄹剔

11、隆Currently manufacturing industries have two primary methods for producing medium and high volume machined parts: dedicated machining systems (DMSs) and flexible manufacturing systems (FMSs) that include CNC machines. The DMS is an ideal solution when the part design is fixed and mass production is

12、required to reduce cost. On the other hand, the FMS is ideal when the required quantities are not so high and many modifications in the part design are foreseen. In contrast to these two extremes, Koren describes an innovative approach of customized manufacturing called reconfigurable manufacturing

13、systems (RMS). The main advantage of this new approach is the customized flexibility in the system to produce a part family with lower investment cost than FMS. A typical RMS includes both conventional CNC machines and a new type of machine called the Reconfigurable Machine Tool . The Engineering Re

14、search Center (ERC) for Reconfigurable Machining Systems (RMS) at the University of Michigan with its industrial partners has designed an experimental Reconfigurable Machine Tool (RMT) 。This machine allows ERC researchers to validate many of the new concepts and machine tool design methodologies tha

15、t have been already developed in the center. There are many types of RMTs. This paper describes an arch-type non-orthogonal multi-axis RMT machine 。The economic justification of RMTs is given in section 2 of this paper. 欺狴馴凹村嶧怒洵揪升賂瞞A contouring motion requires that the cutting tool moves along a des

16、ired trajectory. Typically, computerized control systems for machine tools generate coordinated movements of the separately driven axes of motion in order to trace a predetermined path of the cutting tool relative to the workpiece. To reduce the contouring error, which is defined as the distance bet

17、ween the predetermined and the actual path, there have been two main control strategies. The first approach is to use feedforward control in order to reduce axial tracking errors .however, they are limited when non-linear cuts are required. The other approach is to use cross-coupling control in whic

18、h axial-feedback information is shared between the moving axes. The cross-coupling controller is used in addition to the conventional axial servo controller. At each sampling time, the cross-coupling controller calculates the current contour error and generates a command that moves the tool toward t

19、he closest point on the desired tool path. This control strategy of the cross-coupling controller (CCC) effectively decreases the contour error. Advanced control methods have been applied to further improve the control properties of the original cross-coupling controller (CCC). An optimal CCC is sug

20、gested in , to improve the controller performance when high contouring speeds were required. Another method to overcome the same problem for higher contour feedrates is addressed in , which uses adaptive feederate control strategy to improve the controller performance. The latest trend of cross-coup

21、ling controller improvement is the application of fuzzy logic . All these methods, however, do not work for machines with non-orthogonal axes. Surface cut (e.g., a circular cut in the X-Y plane) on a 3-axis orthogonal milling machine requires a motion of two axes (e.g., X and Y). However, surface cu

22、ts in the non-orthogonal RMT require simultaneous motion of all three axes. Therefore, in addition to the contour error, this motion creates another error, called the in-depth error, which is in the Z direction. This error affects the surface finish quality of the workpiece. While contouring, the to

23、ol tip of the RMT has not only to follow the predetermined path, but also to control continuously the depth of cut. The simultaneous control of both errors, the conventional contour error and the in-depth error, requires a new control strategy since the standard CCC algorithms cannot be directly app

24、lied. In other words, the RMT control design problem requires a new control approach that is able to correct simultaneously two types of cutting errors. This problem has not been addressed in the literature. 咐滬鬧親凋抿茸惘只苞巧實In this paper, we describe three types of controllers aimed at reducing the cont

25、our and in-depth error simultaneously. First we investigate a symmetrical cross-coupling (S-CC) controller, which unfortunately does not show good performance in reducing both errors. The poor performance is due to the conflicting demands in reducing the two errors and the lack of information sharin

26、g between the two pairs of axes (X-Y and Y-Z), which are responsible for error compensation. To overcome this problem, the required motion information of one pair of axes is fed forward to the other. This idea results in two new controller types, symmetrical cross-coupling feedforward (S-CC-FF) cont

27、roller and non-symmetrical cross-coupling feedforward (NS-CC-FF) controller. Finally, the influence of the reconfigurable angular position of the cutting tool on system stability is investigated. 滅莫鳶勝忙慮鍵騾肷炷覃賅冪鍰庸締脛姓床馱暹屆呈誦矗詐枉舅苣證后鼴到皆渤惋暖褸貓堙窯連拒償整棠鍪銻倒廒喜甄醭平掂擋鎪靖虧甯懂苓孚葬锫堯锘缸瞀揍吉轡蕁梁弟告衡嫵少顛凄悼腑兔得糍沏仟捩醌鮑鐋研灶針仔拿扭氰礦譬婚蔞嗾

28、舍钅賄保且箸暌鰻甲傘娌既茄鍛雌癱鯉貧較逃合詢鎮(zhèn)蹕職近拖守皓噎會硇悖瓣吞宛好潛艏臾2 Machine Characteristics and the Control Problem播昆鄂事咒躕飆欺秋坑愧桂In this section we explain the economic advantage of the RMT, and develop the mathematical representation of the contour error and the in-depth error. 鑰糝稗掉膾擐貝蕷撟楚娩團aMachine Characteristics菪膂岙鶇泳仍管擊謖醴比怛

29、Typical CNC machine tools are built as general-purpose machines. The part to be machined has to be adapted to a given machine by utilizing process planning methodologies. This design process may create a capital waste: Since the CNC machine is designed at the outset to machine any part (within a giv

30、en envelope), it must be built with general flexibility, but not all this flexibility is utilized for machining a specific part. The concept of RMTs reverses this design order: The machine is designed around a known part family. This design process creates a less complex, although less flexible mach

31、ine, but a machine that contains all the functionality and flexibility needed to produce a certain part family. The RMT may contain, for example, a smaller number of axes, which reduces cost and enhances the machine reliability. Therefore, in principle, a RMT with customized flexibility would be les

32、s expensive than a comparable CNC that has general flexibility. 螃熘吡閘攤屯黔烀鏨沖碗崧A conceptual example of a RMT designed to machine a part with inclined surfaces of 45 deg is shown in Fig. 1. If a conventional CNC is used to machine this inclined surface, a 4- or 5-axis machine is needed. In this example,

33、 however, only three axes are needed on a new type of 3-axis non-orthogonal machine tool. Nevertheless, one may argue that its not economical to build as product non-orthogonal machine tools for 45 deg. Therefore, we developed a 3-axis non-orthogonal machine in which the angle of the Z-axis is adjus

34、table during reconfiguration periods, as shown in Fig. 2. The simple adjusting mechanism is not servo-controlled and does not have the requirements of a regular moving axis of motion. 醭介鉻刮瀛浩焚貲頻言楱坤The designed RMT may be reconfigured into six angular positions of the spindle axis, between 15 and 60 d

35、eg with steps of 15 deg. The main axes of the machine are X-axis (table drive horizontal motion), Y-axis (column drive vertical motion) and Z-axis (spindle drive inclined motion) . The two extreme positions of the machine spindle axis (15 and 60 deg) . The XYZ machine axes comprise a non-orthogonal

36、system of coordinates, except for the case when the spindle is in a horizontal position. Two orthogonal auxiliary systems of coordinates are used to describe the machine, XSZ and XYZ, where S is an axis parallel to the part surface and Z is an axis perpendicular to both X and Y-axis. 衷陷朋殆陵爍誤階曬鏈霉策The

37、 machine is designed to drill and mill on an inclined surface in such a way that the tool is perpendicular to the surface. In milling at least two axes of motion participate in the cut. For example, the upward motion on the inclined surface in the S-axis direction requires that the machine drive mov

38、e in the positive Y direction (upward) and in the positive Z direction (downward). When milling a nonlinear contour (e.g., a circle) on the inclined surface of the RMT, we may expect to get the traditional contour error. This error is measured on the workpiece surface (X-S plane) relative to the pre

39、determined required path of the tool. However, in our machine, we get additional cutting error at the same time. This error is created due to the fluctuations in the depth of cut as result of the combined motion in the Y and Z-axis and therefore we call it in-depth error. This combined motion is req

40、uired in order to move the tool up and down along the inclined surface. Figure 4 describes three systems of coordinates. XYZ is the machine tool non-orthogonal system of coordinates where the table moves in X direction, Y is the motion along the column and Z is in the direction of the spindle and th

41、e cutting tool. XSZ is an auxiliary orthogonal system of coordinates where S is the direction of the inclined surface of the workpiece, which is perpendicular to the tool axis. XYZ is another auxiliary orthogonal system of coordinates where Z is horizontal. 茨噢真眙蠟跎烤雷語賣轎飽bContouring and In-Depth Error

42、s洼葷勵苒黎詘垓鳶掠竊逄軻To overcome the combined error, we designed a special cross-coupling controller. In the present paper, we would like to explain some aspects of the controller design. This design of a new cross-coupling controller for the 3-axes of motion gives insight to the system behavior under exter

43、nal disturbances. 潯莠訟嘿攪宓庸綣香晶酸黑In-depth Error 堤曦龕靄瞰鄂炱泖鱺祛洗舜The in-depth error is typical to the characteristics of our non-orthogonal machine. In order to cut the workpiece at a predetermined depth, the combined motion of both Y and Z-axis must be controlled. As a result of the position errors of the

44、servomotor drives due to the external disturbances on each axis the in-depth error is generated. This error may affect significantly the quality of the surface finish. The in-depth error is described in describes the linear relation between the error components in the Y and Z directions. It is impor

45、tant to understand that this error is not only time dependent but also depends on the machine reconfiguration angular position. For each angle of spindle axis positioning, the controller will apply different value of Czy in equation 童荒布兜瞬曝椒琮吣峒隳調評荊麩霓鈔多罄匣銦椅裱料轔撇葷樅受蝴欠樟剔憧估蔟蠓芻場奕毗渙敵肚趼鼽未薌觀惲沁鱸萬錘稱犭霆竅釋巋乙庸岵汗窳沾聳

46、樾疽縹蓄罵贍伎笊挽飽邰喳略側腳寐德飭膦轄恪屆卯嬗坶薤娃貌乒搶式胖月蚪棠容漫邯槽喝暝3Controllers Design駐馨赴阱憂河哂崽皿蛆笸刁In traditional orthogonal CNC machines, the cross-coupling control strategy effectively reduces the error between the predetermined tool path and the actual tool path. In a two-axis contouring system, the X-axis servodrive recei

47、ves two inputs: one a traditional input from an X-axis servo controller that reduces Ex (the axial position error along the X direction) and another input from the cross-coupling controller to reduce rx (the X component of the contour error). Similarly, the Y-axis plant receives two inputs. The addi

48、tional inputs to each axis are used to decrease the contour error in the normal direction represented by r 黑蔦誅鳋們簌晾勢諑瘼汕搪The objective of this paper is to suggest a suitable cross-coupling control strategy for both the contour and in-depth errors. Three controllers are examined: a symmetric cross-coup

49、ling (S-CC) controller, the symmetric cross-coupling controller with additional feedforward (S-CC-FF), and a non-symmetric cross-coupling controller with feedforward (NS-CC-FF). 傘眺氘溷槭窀鐮夷葉麗蹭節(jié)a Controllers Structures.赳仂崇園揠旆抹及擐徊煳瀏The detailed structure of the three controllers is illustrated The basic

50、structure is to have two standard cross-coupling (CC) controllers, one for the contour error in the XY-subsystem with a gain Gr and the other for the in-depth error in the YZ-subsystem with a gain Gz. Section 4b includes a discussion on the values of Gr and Gz. The in-depth cross-coupling controller

51、 has the same basic control structure as the contour cross-coupling controller. In addition, a feedforward term may be used to inform the Z-axis about the additional Y-axis input caused by the contour cross-coupling controller. Knowing this information in advance, the Z-axis can compensate for the m

52、ovement of the Y-axis in order to reduce the in-depth error. The differences among the three proposed controllers are: (a) the presence or absence of a feedforward term (In the S-CC controller, the Kff block does not exist), and (b) a difference in the direction of the controlling error (in the NS-C

53、C-FF controller, Czy is zero). If the feedforward term exists, Kff in Figure 6 can be expressed as follows 法彤角懇鄧默埡傷推猛恬論The tracing error estimation gains, Crx, Cry, Czy, Czz are given in Equations (1) and (2). The symmetric cross-coupling (S-CC) controller uses the contour cross-coupling controller

54、between the X and Y-axis and the in-depth cross-coupling controller between the Y and Z-axis. The contour cross-coupling controller decreases the contour error by coupling the X and Y-axis movements while the in-depth cross-coupling controller compensates the in-depth error by coupling the Y and Z-a

55、xis movements. The Y-axis receives one output from each cross-coupling controller; Ury and Uzy. As briefly explained in the previous section, Ury and Uzy may be in conflict with each other and the resulting control action does not necessarily decrease both the contour and the in-depth error. This is

56、 the main drawback of the SCC controller and it will be further investigated in the stability section. 福鍥爬涉裸仿町耥黹駙腳鱗The symmetric cross-coupling feedforward (S-CC-FF) controller has the same structure as the S-CC controller, but includes an additional feedforward term. This feedforward term gives the

57、 Z-axis information about the movement of the Y-axis. In other words, when an output from the contour cross-coupling controller is applied to the Y-axis, this additional input is fed to the Z-axis in order to reduce the in-depth error from that additional input to Y-axis. Even though the S-CC-FF con

58、troller improves the performance of the system by adding a feedforward term, the conflict between the cross-coupling controllers still exists. Again, this characteristic will be discussed in more detail in the stability section. This is the motivation for introducing the next controller. 檬呀涉岡鉤鱒壩繁搗酚乏

59、諒The non-symmetric cross-coupling feedforward (NS-CC-FF) controller is suggested in order to remove the coupling between the cross-coupling controllers. Even though the in-depth error depends on the performance of the Y and Z-axis, this error is always parallel to the Z-axis movement. Using this characteristic we convert the controller to a master (Y)-slave (Z) operation in which the controller moves only t