外文翻譯--非正交可重組機(jī)床的控制

1、<p><b>　　附錄</b></p><p>　　Control of a Non-Orthogonal Reconfigurable Machine Tool</p><p>　　Reuven KatzJohn YookYoram Koren</p><p>　　Received: January 3, 2003; revise

2、d: September 16, 2003</p><p><b>　　Abstract</b></p><p>　　Computerized control systems for machine tools must generate coordinated movements of the separately driven axes of motion in

3、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 gener

4、ated. The contour error is defined as the distance between the predetermined and actual path of the cutting tool. The cross-coupling controller (CCC) stra</p><p>　　Contributed by the Dynamic Systems, Measure

5、ment, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Div

6、ision January 3, 2003; final revision September 16, 2003. Associate Editor: J. Tu. </p><p>　　Keywords:machine tool, cross-coupling controller, non-orthogonal, RMT</p><p>　　1 Introduction</p&

7、gt;<p>　　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 C

8、NC machines. The DMS is an ideal solution when the part design is fixed and mass production is required to reduce cost. On the other hand, the FMS is ideal when the required quantities are not so high and many modificati

9、ons in the part design are foreseen. In contrast to these two extremes, Kore</p><p>　　A contouring motion requires that the cutting tool moves along a desired trajectory. Typically, computerized control syst

10、ems 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

11、defined as the distance between the predetermined and the actual path, there have been two main control strategies. The first approach is to use feedforward co</p><p>　　In this paper, we describe three types

12、 of controllers aimed at reducing the contour 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 er

13、rors. The poor performance is due to the conflicting demands in reducing the two errors and the lack of information sharing between the two pairs of axes (X-Y and Y-Z), which are responsible for error compensation. To ov

14、ercome this problem, t</p><p>　　2 Machine Characteristics and the Control Problem</p><p>　　In this section we explain the economic advantage of the RMT, and develop the mathematical representati

15、on of the contour error and the in-depth error. </p><p>　　a Machine Characteristics</p><p>　　Typical CNC machine tools are built as general-purpose machines. The part to be machined has to

16、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 given envelope), it

17、 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</p><p>　　A conceptual

18、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, however,

19、 only three axes are needed on a new type of 3-axis non-orthogonal machine tool. Nevertheless, one may argue that it's not economical to build as product non-orthogonal machine tools for 45 deg. Therefore, we develop

20、ed a 3-axis non-orthogonal machine in which the ang</p><p>　　The designed RMT may be reconfigured into six angular positions of the spindle axis, between –15 and 60 deg with steps of 15 deg. The main axes of

21、 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

22、 machine axes comprise a non-orthogonal system of coordinates, except for the case when the spindle is in a horizontal position. Two o</p><p>　　The machine is designed to drill and mill on an inclined surfac

23、e 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 t

24、he machine drive move 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 tra<

25、;/p><p>　　b Contouring and In-Depth Errors</p><p>　　To overcome the combined error, we designed a special cross-coupling controller. In the present paper, we would like to explain some aspects

26、 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 external disturbances. </p><p>　　In-depth Error </p><p

27、>　　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 o

28、f the position errors of the 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 d

29、escribed in describes the linear relation between the error compon</p><p>　　3 Controllers Design</p><p>　　In traditional orthogonal CNC machines, the cross-coupling control strategy effecti

30、vely reduces the error between the predetermined tool path and the actual tool path. In a two-axis contouring system, the X-axis servodrive receives two inputs: one a traditional input from an X-axis servo controller tha

31、t 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 r</p><p>　　

32、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-coupling (S-CC) controller, the symmetric c

33、ross-coupling controller with additional feedforward (S-CC-FF), and a non-symmetric cross-coupling controller with feedforward (NS-CC-FF). </p><p>　　a Controllers Structures.</p><p>　　The detail

34、ed structure of the three controllers is illustrated The basic 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-dept

35、h 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 has the same basic control structure as the contour cross-coupling controlle

36、r. In addition, a feedforward term may be used to </p><p>　　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

37、contour cross-coupling controller 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-ax

38、is movements while the in-depth cross-coupling controller compensates the in-depth error by coupling the Y and Z-axis movements. The </p><p>　　The symmetric cross-coupling feedforward (S-CC-FF) controller ha

39、s the same structure as the S-CC controller, but includes an additional feedforward term. This feedforward term gives the Z-axis information about the movement of the Y-axis. In other words, when an output from the conto

40、ur 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 controller improve<

41、/p><p>　　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 per

42、formance 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 the Z-axis to

43、 decrease the in-depth error. Namely, the coupling between the contour cross-co</p><p>　　4 Controllers Stability Analysis</p><p>　　The RMT system has tightly coupled axes and contains time-

44、varying sinusoidal parameters. In order to simplify the stability analysis, the following assumption was made: E, where , E, are contour error, axial error, and radius of curvature, respectively [15]. With this assumptio

45、n, for the stability analysis, we can approximate the sinusoidal gains by linear terms. Furthermore, in order to eliminate the complexity with time-varying parameters in the stability analysis, we analyze the linearized

46、co</p><p>　　a. Characteristic Equations of S-CC, S-CC-FF, and NS-CC-FF Controllers</p><p>　　For the linear system, = A·X + B·U, Y = C·X + D·U, the transfer function from U to

47、 Y, which is C(sI-A)–1B + D, should be examined for the stability of the system. However, if C and D are BIBO matrix, then (sI-A)–1B can be used for the stability analysis. Since the C and D matrices for the contour and

48、in-depth error of the RMT are bounded time varying gain matrices, the stability of each axis can be used for the stability analysis of the entire system. For S-CC controller the positions of each ax</p><p>　

49、　The notations Px, Py, Pz indicate the positions of the X, Y, Z-axis, respectively. Xr, Yr, Zr are the reference signals for each axis, and Ex, Ey, Ez are the errors (Ex = Xr–Px). For the S-CC-FF controller the positions

50、 are </p><p>　　Namely, the characteristic equation of the X-axis, is the same in all three controllers. However, the characteristic equations of the Y and Z-axis depend on the type of controller used. In ord

51、er to simplify the analysis the stability analysis is done for a given stable servo controllers for each axis and we investigate the stability of the system due to the cross-coupling controllers, Gr and Gz, only. </p&

52、gt;<p>　　b  Stable Region of the Cross-Coupling Controllers</p><p>　　The characteristic equations obtained in the previous section depend not only on the variable gain, C's, but also on

53、the RMT configuration angle, . Furthermore, the characteristic equation for Y with the S-CC and S-CC-FF controllers exhibit coupling between the contour and in-depth cross-coupling controllers. In order to simplify the a

54、nalysis, PI controller for Gr and P controller for Gz are used </p><p>　　Numeric values of the parameters used in this study to describe the servo controllers and the plants are presented in appendix A. Util

55、izing these values, the characteristic equation can be expressed in terms of WP, WI, WZ, C's, and . First, the configuration of the RMT system is fixed at = 60°, and the characteristic equation is calculated as

56、function of WP, WI, WZ, and C's. Using the Routh-Jury criteria, the stable regions of WP, WI, and WZ are obtained as a function of C's, and the smallest in</p><p>　　1 The stable region for S-CC and S

57、-CC-FF controllers is an area bounded by three lines (as shown in Fig. 7): Line 1, Line 2, and Line 3 while the stable region for NS-CC-FF controller is the area bounded by Line 1 and Line 3. </p><p>　　2 For

58、 higher values of the gain Wz, Line 2 moved to the left while Line 1 and Line 3 were not affected by varying Wz. It means that a higher value of the proportional controller gain Wz, will reduce the stability region. <

59、/p><p>　　3 For higher values, Line 2 moves to the right while Line 1 and Line 3 are not affected. However, Line 2 can never cross Line 3 by only varying . The meaning of this observation is that horizontal spin

60、dle position represents better stability of the system. </p><p>　　4 The stability region becomes smaller with increasing sampling period. </p><p>　　The system with the NS-CC-FF controller has th

61、e largest stable region for WP, WI, and WZ. This is due to the fact that the conflict between the cross-coupling controllers has been removed by decreasing the in-depth error by Z-axis movement only. The conflict between

62、 the cross-coupling controller in S-CC and S-CC-FF controller can be seen in the transfer function shown in Eqs. (4) and (5). The subsystem for the contour error, which consists of X and Y-axis only, should contain only

63、variables rela</p><p>　　Similarly, the subsystem for the in-depth error, which consists of Y and Z-axis only, should be composed of terms related to the Y and Z-axis. Again, the in-depth subsystem contains a

64、n Ex term which will act as a disturbance to this subsystem. Unlike the transfer function of the Z-axis in Eq. (4), the one in Eq. (5) contains a feedforward term Kff. This Kff reduces the disturbance to the system resul

65、ting in a better performance for the S-CC-FF than the S-CC controller. Considering the transfer f</p><p>　　5 Simulation Results</p><p>　　The simplified RMT axial model that was used in the

66、simulation (the parameters for each axis can be found in appendix A). The cross-coupling controller parameters were chosen such that the system will operate within the stable region defined in the previous section. These

67、 parameters are not the optimal since optimization of the controller, was not a goal of this paper. For comparison purposes, all cross-coupling controller parameters are kept the same throughout the simulation. The desir

68、ed tool </p><p>　　6 Conclusions</p><p>　　The conceptual design process of crossed-coupling controllers that was described in the paper allows insight and better understanding of the RMT controll

69、er problem. Some machining processes that traditionally require four or 5 degrees-of-freedom using an orthogonal CNC machine, may be performed by a new machine-type—the reconfigurable machine tool (RMT) that has just thr

70、ee-degrees of freedom. The disadvantage of the RMT configuration is that when contour cuts are needed in the X-S plane, a new t</p><p>　　Furthermore, we also found that all three types of cross-coupling (CC)

71、 controllers reduce significantly the contour and in-depth errors. It was shown that for the control of the nonorthogonal arch-type RMT, the nonsymmetric cross-coupling feed-forward (NS-CC-FF) controller has the best per

72、formance of the three CC controllers. The symmetric cross-coupling (S-CC) controller does not adequately solve the in-depth error problem-an error that is typical to non-orthogonal RMTs. The S-CC-FF controller </p>

73、<p>　　References</p><p>　　[1] Coker SA, Shin YC. In-process control of surface roughness with tool</p><p>　　wear via ultrasonic sensing. In: Proceedings of American control</p><

74、;p>　　conference, Seattle; 1995.</p><p>　　[2] Lauderbaugh LK, Ulsoy AG. Model reference adaptive force control</p><p>　　in milling. ASME J Eng Ind 1989.</p><p>　　[3] Kim TY, Kim J

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76、ren Y. Variable-gain adaptive control systems for</p><p>　　machine tools. J Manuf Syst 1983.</p><p>　　[5] Elbestawi MA, Mohamed Y, Liu L. Application of some parameter</p><p>　　adap

77、tive control algorithms in machining. ASME J Dyn Syst Meas</p><p>　　Control 1990;</p><p>　　[6] Ulsoy AG, Koren Y. Control of machining processes. ASME J Dyn</p><p>　　Syst Meas Contr

78、ol 1993</p><p>　　[8] Park J, Ulsoy A. On-line tool wear estimation using force measure-</p><p>　　ment and a nonlinear observer. ASME J Dyn Sys Meas Control</p><p><b>　　1992<

79、;/b></p><p>　　[9] Glass K, Colbaugh R. Real-time tool wear estimation using cutting</p><p>　　force measurements. In: Proceedings of the 1996 IEEE international</p><p>　　conferenc

80、e on robotics and automation; 1996</p><p>　　[10] Li X, Li HX, Guan XP, Du R. Fuzzy estimation of feed-cutting force</p><p>　　from current measurement–A case study on intelligent tool wear</p&

81、gt;<p>　　condition monitoring. IEEE Trans Syst Man Cybernet – Part</p><p><b>　　2004;</b></p><p>　　非正交可重組機(jī)床的控制</p><p><b>　　摘要</b></p><p>　

82、　為了準(zhǔn)確預(yù)定刀具相對(duì)于工件的軌跡，機(jī)床計(jì)算機(jī)控制系統(tǒng)必須協(xié)調(diào)各運(yùn)動(dòng)機(jī)構(gòu)運(yùn)轉(zhuǎn)軸的動(dòng)作。不過(guò),由于各機(jī)械軸的運(yùn)動(dòng)軌跡不盡相同的情況下,產(chǎn)生了偶然的誤差。誤差的范圍是指與刀具實(shí)際預(yù)定軌跡的距離。交叉耦合控制(CCC)戰(zhàn)略的實(shí)施,有效地減少了正交機(jī)床常規(guī)誤差范圍。這篇文章,涉及一類(lèi)新的非正交可重組機(jī)床(RMTs)。這種機(jī)床可列入大規(guī)?？芍亟M加工系統(tǒng)(RMSS)。當(dāng)機(jī)械軸非正交時(shí)，軸線(xiàn)之間的運(yùn)動(dòng)必須是緊密結(jié)合，各運(yùn)動(dòng)軸協(xié)調(diào)的重要性變得更大。在非

83、正交可重組機(jī)床加工中,除了形狀誤差之外,加工誤差也是非正交機(jī)床引起的。這項(xiàng)研究的重點(diǎn)是減少新型交叉耦合控制的非正交機(jī)床形狀和加工誤差的概念設(shè)計(jì)。各種交叉耦合控制,對(duì)稱(chēng)和非對(duì)稱(chēng),有沒(méi)有前饋,是需要研究的?？刂葡到y(tǒng)的穩(wěn)定性調(diào)查,使用模擬比較不同類(lèi)型控制。我們證明與傳統(tǒng)的去耦控制相比用交叉耦合控制時(shí)，機(jī)械誤差大為減少。此外,它顯示了非對(duì)稱(chēng)交叉耦合前饋(NS-CC-FF)控制顯示最好成績(jī)是主要的概念和非正交機(jī)床。</p><

84、p>　　關(guān)鍵詞：機(jī)床刀具，交叉耦合控制，非正交，可重組加工系統(tǒng)</p><p><b>　　1.概述</b></p><p>　　目前制造行業(yè)中主要有兩種進(jìn)行批量生產(chǎn)的方法:加工專(zhuān)用系統(tǒng)(DMSS)和數(shù)控柔性制造系統(tǒng)。DMS是一個(gè)理想的在設(shè)計(jì)、量產(chǎn)定需降低成本時(shí)的解決方法。另一方面,FMS是在零件設(shè)計(jì)要求不是很高,數(shù)量很多時(shí)的理想方法。與這兩個(gè)極端相比,Kore

85、n描述了一種要求可重組設(shè)計(jì)制造制造系統(tǒng)(RMS)的新辦法。這一新方法的主要優(yōu)點(diǎn)是靈活性系統(tǒng)設(shè)計(jì)制作了比FMS投資成本低的"零件庫(kù)"。典型的RMS一般包括傳統(tǒng)的和可重組的新型數(shù)控機(jī)床。美國(guó)密西根大學(xué)可重組加工系統(tǒng)(RMS)工程研究中心(ERC)與產(chǎn)業(yè)合作伙伴設(shè)計(jì)了實(shí)驗(yàn)用可重組機(jī)床(RMT)。這種機(jī)床使ERC研究中心的研究人員機(jī)床設(shè)計(jì)和驗(yàn)證方法得到了發(fā)展。有許多種RMTs。這篇文章主要是描述原型非正交多軸RMT機(jī)床。RM

86、Ts的經(jīng)濟(jì)因素在本文的第二部分給出。</p><p>　　做等直線(xiàn)運(yùn)動(dòng)的要求規(guī)定刀具要沿著理想的軌跡運(yùn)動(dòng)。通常,機(jī)床的計(jì)算機(jī)控制系統(tǒng)各軸的協(xié)調(diào)運(yùn)動(dòng)議案是為了追蹤相對(duì)于刀具的預(yù)定的軌跡。為了減少造型錯(cuò)誤,即指在預(yù)定的和實(shí)際的軌跡。有兩個(gè)主要的控制策略。第一種方式是使用前饋控制,以減少實(shí)驗(yàn)跟蹤誤差。然而，當(dāng)需要非線(xiàn)性切削時(shí)他們是有限的。其他方法是使用交叉耦合控制實(shí)驗(yàn)中移動(dòng)軸共享的反饋信息。除了使用在傳統(tǒng)伺服控制軸之外

87、，交叉耦合控制還被使用著。每次采樣時(shí)，交叉耦合控制計(jì)算當(dāng)前形狀誤差,并產(chǎn)生指導(dǎo)刀具沿著預(yù)定軌跡運(yùn)動(dòng)的指令。這種交叉耦合控制（CCC）的控制策略有效地減少了誤差范圍。先進(jìn)的控制方法已應(yīng)用于使原有交叉耦合控制(CCC)的控制性能更進(jìn)一步提高。當(dāng)要求高速度時(shí)，最佳的（CCC）建議改善控制性能。另一種克服形狀高饋送率這個(gè)問(wèn)題的方法,是用適應(yīng)的饋送率控制策略,以提高控制性能。最新趨勢(shì)交叉耦合控制改善即為應(yīng)用模糊邏輯。但是，所有這些方法都不用于非正

88、交軸線(xiàn)機(jī)床。在三軸正交銑床上的表面切削(如，在X-Y坐標(biāo)面的循環(huán)切削)需要兩個(gè)坐標(biāo)軸的坐標(biāo)運(yùn)動(dòng)(如X和Y)。然而,在非正交RMT內(nèi)的表面切削同時(shí)要求三軸坐標(biāo)。因此,除了形狀誤差之外,這造成了另一種在Z方</p><p>　　在這篇文章中,描述了三種量的控制,以同時(shí)減少外形和深度誤差。首先調(diào)查對(duì)稱(chēng)交叉耦合(S-CC)控制,不幸的是它不能良好的同時(shí)減少誤差。表現(xiàn)不佳的原因是同時(shí)減少兩個(gè)誤差的矛盾需求和缺乏信息交流的兩

89、個(gè)坐標(biāo)面(X-Y和Y-Z),其中的誤差相互補(bǔ)償了。為解決這個(gè)問(wèn)題,就要求各坐標(biāo)軸間相互傳送信息。這種觀念導(dǎo)致兩個(gè)新的控制類(lèi)型：對(duì)稱(chēng)交叉耦合前饋(S-CC-FF)控制和非對(duì)稱(chēng)交叉耦合前饋(NS-CC-FF)控制。后,對(duì)系統(tǒng)穩(wěn)定刃具可重組性的影響需要調(diào)查。</p><p>　　2機(jī)床特性和控制問(wèn)題</p><p>　　在本節(jié)里我們說(shuō)明的是RMT的經(jīng)濟(jì)優(yōu)勢(shì),并制定了精確的代表性誤差范圍和深度誤差

90、。</p><p><b>　　A 機(jī)床特點(diǎn) </b></p><p>　　典型數(shù)控機(jī)床被建成通用機(jī)械。機(jī)械部分必須符合規(guī)劃的利用特定機(jī)器方法的過(guò)程。這個(gè)設(shè)計(jì)過(guò)程中可能造成資金浪費(fèi): 由于數(shù)控機(jī)床首先設(shè)計(jì)的是機(jī)床的一部分，它必須建立在一般的靈活性,但這種靈活性不是全部用于加工特定部分。RMTS概念顛倒了設(shè)計(jì)的順序：機(jī)床設(shè)計(jì)圍繞著已知的部分零件庫(kù). 這造成了較復(fù)雜的

91、設(shè)計(jì)過(guò)程中,雖然是柔性機(jī)床,但是一種機(jī)床包含了所有必要的功能性和柔性，這就需要一定的零件庫(kù)。例如，RMT可能要包括減少軸的數(shù)量,降低成本和提高機(jī)器可靠性。因此,原則上,一個(gè)專(zhuān)用的RMT與一臺(tái)類(lèi)似的柔性數(shù)控機(jī)床價(jià)格差不多。RMT設(shè)計(jì)了一個(gè)概念性的例子,即一個(gè)與零件表面成45度的機(jī)床。如果用傳統(tǒng)的數(shù)控機(jī)床加工傾斜表面的零件就需要4或5根軸。但是，這個(gè)例子在新型三軸非正交機(jī)床上只需要三根軸。然而,人們可能會(huì)認(rèn)為自己的產(chǎn)品非正交45度機(jī)床是不經(jīng)

92、濟(jì)的。因此,我們制定了三軸非正交角度機(jī)床,在重組期間機(jī)床Z軸是可調(diào)節(jié)的。簡(jiǎn)單的調(diào)整機(jī)制不影響伺服控制,而且也沒(méi)有經(jīng)常移動(dòng)軸的要求。在步驟15中在60-15度之間，RMT設(shè)計(jì)可重新設(shè)計(jì)成六個(gè)方向軸角位置。機(jī)床的主軸是X-軸()、Y-軸(驅(qū)動(dòng)垂直方向的運(yùn)動(dòng))和Z-軸(驅(qū)動(dòng)傾</p><p>　　B 形狀和深度誤差 </p><p>　　為了克服結(jié)合的誤差，我們?cè)O(shè)計(jì)一個(gè)特殊的交叉耦合的控制。 在

93、現(xiàn)在的論文中，我們?cè)敢饨忉屢恍┛刂圃O(shè)計(jì)的方面。 這運(yùn)動(dòng)的3軸的一個(gè)新的交叉耦合的控制的設(shè)計(jì)把洞察力給外部干擾下的系統(tǒng)行為。 </p><p>　　形狀誤差： 形狀誤差在許多報(bào)文中被描述了。 被一個(gè)形狀誤差被定義為的一個(gè)即時(shí)的圓接近的一條一般的非線(xiàn)性曲線(xiàn)由Lo [ 15 ]給。 數(shù)字5a顯示形狀和“徹底”誤差。 數(shù)字5b顯示一個(gè)彎曲的形狀誤差。 在RMT機(jī)器中的形狀誤差方程</p><p>

94、　　由于在30°和105°,之間變化Cry的特異性不需要考慮。 </p><p>　　深度誤差： 誤差對(duì)深度是典型的是我們的非直角的機(jī)器所特有的。 為了切削一個(gè)預(yù)定的深度的工作件，必須被控制Y和Z路線(xiàn)的結(jié)合的運(yùn)動(dòng)。 由于伺服機(jī)構(gòu)驅(qū)動(dòng)因?yàn)殛P(guān)于每一路線(xiàn)的外部干擾的位置誤差誤差深度被產(chǎn)生。我這誤差可能在相當(dāng)大的程度上影響表面結(jié)束的質(zhì)量。 誤差在數(shù)字5c中深度被描述了。 方程( 2 )描述Y和Z方向中

95、的誤差組成部分之間的線(xiàn)性的關(guān)系。 理解這誤差是重要，不僅記時(shí)依賴(lài)也依賴(lài)于機(jī)器再可重組角度的位置。 對(duì)于每一主軸路線(xiàn)定位的角度，控制將在方程( 2 )中應(yīng)用Czy的不同的價(jià)值。注意到Y(jié)路線(xiàn)Ey的位置誤差在兩Eqs上出現(xiàn)是重要(1)和( 2 )。 這深度意味著嚴(yán)緊連接形狀誤差和誤差。 RMT控制應(yīng)該有效地減少兩個(gè)誤差。 </p><p><b>　　3控制設(shè)計(jì)</b></p>&l

96、t;p>　　在傳統(tǒng)的直角的CNC機(jī)器中，交叉耦合的控制策略有效地減少預(yù)定的工具路徑和實(shí)際的工具路徑之間的誤差。 在兩路線(xiàn)形狀系統(tǒng)中，X路線(xiàn)伺服傳動(dòng)裝置收到兩種輸入： 從從交叉耦合的控制減少減少rx (形狀誤差)的X組成部分的一X路線(xiàn)伺服機(jī)構(gòu)控制的一傳統(tǒng)的輸入前(沿著X方向)的軸的位置誤差和另一個(gè)輸入。 同樣地，Y路線(xiàn)植物收到兩種輸入。 每一路線(xiàn)的附加的輸入用來(lái)朝著被代表的正常的方向減少形狀誤差圖5b中的r。</p>

97、<p>　　本文的目標(biāo)是為了形狀和深度誤差建議一個(gè)適合的交叉耦合的控制策略。 三個(gè)控制被檢查： 一個(gè)對(duì)稱(chēng)的交叉耦合( S-CC )的控制，的對(duì)稱(chēng)的交叉耦合的控制附加向前饋 ( S-CC-FF )，和帶有( NS-CC-FF )的一個(gè)非對(duì)稱(chēng)的交叉耦合的控制。</p><p><b>　　a 控制構(gòu)造 </b></p><p>　　三個(gè)控制的詳盡的結(jié)構(gòu)在基本

98、的結(jié)構(gòu)是有兩個(gè)標(biāo)準(zhǔn)的交叉耦合( CC )的控制圖6.中被說(shuō)明了，一個(gè)個(gè)由于XY-輔助系統(tǒng)中的形狀誤差獲得Gr和其它深度YZ-輔助系統(tǒng)的誤差獲得Gz。 段4b包括關(guān)于Gr和Gz的價(jià)值的一次討論。 深度交叉耦合控制作為形狀交叉耦合的控制有同樣基本的控制結(jié)構(gòu)。 此外，一個(gè)前饋的期間可能被用來(lái)告知Z路線(xiàn)關(guān)于關(guān)于被輸入的附加的Y路線(xiàn)之事宜由形狀造成交叉耦合的控制。 知道這信息提前，為了減少誤差Z路線(xiàn)能彌補(bǔ)Y路線(xiàn)的運(yùn)動(dòng)深度。三個(gè)所提出的控制中的區(qū)別

99、是： (a)一個(gè)前饋的期間( S -CC控制，Kff塊不存在)存在或者缺乏， ( b )朝著控制的誤差( NS-CC-FF控制，Czy是零)的方向的一種區(qū)別。 如果前饋的期間存在，數(shù)字6的Kff能被表達(dá)如下</p><p>　　追蹤誤差評(píng)價(jià)獲得，Crx，Cry，Czy，Czz被提交方程( 1 )和( 2 )。 對(duì)稱(chēng)的交叉耦合( S-CC )的控制使用X和Y路線(xiàn)之間的形狀交叉耦合的控制和在Y和Z路線(xiàn)之間深度交叉耦合