外文翻譯---cnc加工加減速平穩(wěn)變化的方法

1、<p>　　中文4160字，2800單詞，1.6萬英文字符</p><p>　　出處：Jeon J W. A generalized approach for the acceleration and deceleration of CNC machine tools[C]// IEEE IECON, International Conference on Industrial Electronics,

2、 Control, and Instrumentation. 1996:1283-1288 vol.2.</p><p>　　A Generalized Approach for the</p><p>　　Acceleration and Deceleration of CNC Machine Tools</p><p>　　Jae Wook Jeon</

3、p><p>　　Department of Control and Instrumentation Engineering</p><p>　　Sungkyunkwan University</p><p>　　300 Chunchun-Dong,Jangan-Gu,Suwon City,Korea</p><p>　　Abstract—Many

4、 techniques for the acceleration and deceleration of CNC machine tools have been proposed in order to make CNC machine tools perform given machining tasks efficiently. Since they should be calculated in a limited time, m

5、ost of them are not computationally intensive. However, these previous techniques cannot generate velocity profiles having some kinds of acceleration and deceleration characteristics though they can generate velocity pro

6、files having various acceleration and decelerat</p><p>　　I. INTRODUCTION</p><p>　　The demand for better accuracy in the manufacturing of complicated parts and the desire to increase productivity

7、 have developed CNC systems so that CNC machine tools move more accurately and more quickly. Since the combined characteristics of the control and the machine tool determine the final accuracy and productivity of the CNC

8、 system, there are many factors to consider for improving these quantities. One of the important factors is efficiently generating velocity profiles which have the desi</p><p>　　machine tools. One of them is

9、 generating velocity profiles by the selection of polynomial functions [1]. This technique can generate so many kinds of velocity profiles and furthermore can make the characteristics of deceleration be independent from

10、that of acceleration. The major problem of this technique is computational load to increase almost exponentially with the order of polynomial in the acceleration or that in the deceleration. Due to time constraints, it i

11、s very difficult to apply these</p><p>　　In this paper, a generalized approach for the acceleration and deceleration of CNC machine tools is proposed. The proposed technique is as simple and efficient as the

12、 techniques based on a digital convolution and can generate velocity profiles which have more various characteristics of acceleration and deceleration than the techniques based on a digital convolution can. That is, the

13、proposed technique can generate velocity profiles of which the deceleration characteristics are independent from t</p><p>　　In section II, existing techniques for generating velocity profiles of CNC machine

14、tools will be explained. In section III, it will be explained how to generate a desired velocity profile by the proposed technique. The proposed technique and other existing techniques will be compared. In section IV, it

15、 will be shown that the proposed technique can generate some useful velocity profiles for CNC machine tools.</p><p>　　II. PREVIOUS TECHNIQUES</p><p>　　For the illustration of the previous techni

16、ques, let us consider one single-axis control system of which the maximum velocity, the maximum acceleration, and the sampling time are V max，Amax ， and Ts respectively. If this system moves the given distance S at the m

17、aximum velocity V max, then the movement time T1 in the rectangular velocity profile will be T1 = S / V max = p Ts, (1)</p><p>　　Selecting an integer n which is the

18、smallest integer among integers which are equal to or greater than p, the resulting rectangular velocity profile is constructed as in Fig. 1. The velocity and position equations for this profile are</p><p>　

19、　The position increment during each sampling time is </p><p>　　where and are the position commands at the　　and the　 sampling times respectively. That is, the position increment during every sampling t

20、ime is the same. However, since no physical system can achieve the above rectangular velocity profile due to impulse acceleration, the acceleration interval to increase velocity from the rest to a specified value and th

21、e deceleration interval to decrease velocity from the specified value to the rest are needed.</p><p>　　II-A. Selection of Polynomial Functions</p><p>　　Given an acceleration interval Ts = naTs,

22、 a deceleration interval Td= ndTs where na= nd, and a distance S, a trapezoidal velocity profile which has the linear acceleration and deceleration characteristics can be constructed as in Fig.2. If this profile has the

23、constant velocity interval, then n=[S/(VmaxTs)] is larger than na . The velocity and position equations for this profile are</p><p><b>　　And</b></p><p>　　Fig .1.A rectangular veloci

24、ty profile for moving a distance S</p><p>　　Fig .2.A trapezoidal velocity profile for moving a distance S</p><p>　　In the above derivation, it is assumed that the acceleration interval is the sa

25、me as the deceleration interval and the constant velocity interval is present. In the case that the acceleration interval is different from the deceleration interval or the constant velocity interval is not present, simi

26、lar equations are possible to derive. This trapezoidal velocity profile which has the linear acceleration and deceleration characteristics is particularly effective for controlling a machine tool havin</p><p&g

27、t;　　jerk quantity have been proposed [1]. Given position, velocity, and acceleration at the initial and final positions, a class of polynomial functions for satisfying these conditions is selected. One approach is to spe

28、cify a seventh-degree polynomial for each axis. Another approach is to split the entire trajectory into several trajectory segments so that different polynomials of a lower degree can be used in each trajectory segment.

29、The most common methods are 4-3-4 trajectory, 3-5-3 trajectory, </p><p>　　II-B. Digital Convolution Techniques</p><p>　　Given an acceleration interval Ta=naTs (which determines the decelerati

30、on interval Td = ndTs = naTs because two intervals cannot be different in velocity profiles generated by digital convolution techniques) and a desired distance S, a trapezoidal velocity profile which has the linear ac

31、celeration and deceleration characteristics can be constructed by digital convolution techniques. The position increment during each sampling time in a trapezoidal velocity profile δPl(kTs) is constructed b</p>&l

32、t;p>　　, 　　 　 (7)</p><p>　　where　　 　 　 (8)</p><p>　　as in Fig. 3. The relationship between δP0 and δP1 is expressed as the following recursive eq

33、uation [2]</p><p>　　Equation (9) provides the basic information for the trapezoidal velocity profile. Based on (9), we can design the hardware system for trapezoidal velocity profiles as in Fig. 4, where buf

34、fer registers act as delay elements [4]. A second-order velocity profile which has the parabolic acceleration and deceleration characteristics can also be constructed by digital convolution techniques. The position incre

35、ment in a second-order velocity profile </p><p>　　can be obtained by successive convolutions as in Fig. 5</p><p>　　Where 　 . (10)</p><p>　　The shape of second-order vel

36、ocity profile can be determined by the values of m1 and m2 [2,4]. The relationship between and is expressed as the following recursive equations [2].</p><p>　　Fig.3.A digital convolution for a trapezoidal

37、velocity profile</p><p>　　Fig.4.A hardware structure for a trapezoidal velocity profile</p><p>　　Fig.5.Successive digital convolutions for a second-order velocity profile</p><p>　　S

38、imilarly, the position increment of a smooth velocity profile which has the high-order acceleration and deceleration characteristics can be obtained by several successive convolutions as in Fig. 6 where each sequence has

39、 the similar meaning as in (10). The shape of the smooth velocity profile can be determined by the values of ml,m2,...,mq, and q [2,4]. The relationships between and are expressed as the following recursive eq

40、uations [2]:</p><p>　　The velocity profiles generated by (13) have the property that the moving distances during the acceleration interval and during the deceleration interval are same. These distances are a

41、lso same as the moving distance of trapezoidal velocity profile during the acceleration interval under the same condition.</p><p>　　In order to generate an arbitrary shape velocity profile, the position incr

42、ement during each sampling time in the desired velocity profile can be generated from the following convolution [2,4]</p><p>　　From the appropriate of choice ai , for i = 1,2,...,m, the desired velocity p

43、rofile can be obtained. The hardware system based on (14) for generating an arbitrary velocity profile can be designed as in Fig. 7. The acceleration and deceleration interval T, is given by </p><p>　　Ta =

44、mTs [2,4]. In [3], a similar convolution technique which can generate velocity </p><p>　　profiles which has several acceleration and deceleration characteristics is derived. While the computational load for

45、generating smooth velocity profile by these digital convolution techniques is much less than that for the selection of polynomial techniques, the deceleration characteristic generated by these techniques is determined fr

46、om the acceleration characteristics. That is, the deceleration characteristic cannot be made to be independent from the acceleration characteristic by using di</p><p>　　Fig.6.Successive digital convolutio

47、ns for a higher-order velocity profile</p><p>　　III. PROPOSED TRAJECTORY GENERATION TECHNIQUE</p><p>　　As in section II, let us consider one single-axis control system of which the maximum v

48、elocity, the maximum acceleration, and the sampling time are Vmax, Amax, and Ts respectively. Given an acceleration interval Ta =naTs , a deceleration interval Td =ndTs , and a distance S , a velocity profile which has

49、 the desired characteristics of acceleration and deceleration can be constructed by the proposed technique.</p><p>　　III-A. Linear Acceleration and Deceleration</p><p>　　In the technique selecti

50、ng polynomial functions, the velocity equation which has the linear acceleration and deceleration characteristics is calculated by (5). The coefficients of (5) may vary according to given conditions. But the ratio betwe

51、en the position increment during each sampling time in the acceleration interval is fixed. That is, </p><p>　　in Fig. 8. Similarly, the ratio between each position increment in the deceleration interval is f

52、ixed. Therefore, the velocity profile which has the linear acceleration and deceleration characteristics can be calculated as the following:</p><p>　　(i) The velocity after the acceleration Vm is determined

53、 as </p><p>　　Fig.7.The hardware structure of arbitrary acceleration and deceleration</p><p>　　where (16)</p><p>　　(ii) Then the positio

54、n increment during each sampling time is calculated as</p><p><b>　　if ,</b></p><p><b>　　if , </b></p><p>　　According to the acceleration and deceleration

55、 interval, the coefficients</p><p>　　and in (17)and (18) can be calculated and be </p><p>　　stored in advance. Therefore a velocity profile which has the linear acceleration and deceleration c

56、haracteristics is able to be efficiently calculated for a given distance.</p><p>　　III-B. Arbitrary Acceleration and Deceleration</p><p>　　Let us consider a velocity profile V(t) which has file

57、acceleration characteristic and the deceleration characteristic represented by and respectively,</p><p>　　where both of and are differential on and are continuous on , and Tc is the time to start de

58、celeration and Vm is the velocity after acceleration. Then the position increment during each sampling time in the acceleration interval can be represented as</p><p>　　and it can be written as </p>

59、<p>　　where is the coefficients which can be calculated from fa(u) and na=Ta /Ts and be stored. Similarly, the position increments during each sampling time in the deceleration interval can be represented as</p

60、><p>　　Fig.8.The position increment during each sampling time</p><p>　　in the acceleration interval of a trapezoidal velocity</p><p>　　Where dγk is the coefficients which can be calc

61、ulated from fd(u) and nd = Td / Ts and be stored. The area Sa under fa during the acceleration interval and the area Sd under　fd during the deceleration interval can be represented as</p><p>　　where

62、can be calculated from and , and be stored. Similarly, can be calculated from and and be stored. In the technique selecting polynomial functions, the velocity equation which has the acceleration and deceleration chara

63、cteristics represented by and respectively is calculated by appropriate polynomial functions. The coefficients of the polynomial function may vary according to given conditions. But the ratio between the position increm

64、ent during each sampling time in the acceleration inte</p><p>　　(i) For an acceleration interval Ta =naTs and a deceleration interval Td =ndTs, the　corresponding coefficients and

65、 are retrieved.</p><p>　　(ii) For moving a distance S, the velocity after the acceleration Vm is determined as</p><p>　　where </p&g

66、t;<p>　　(iii) Then the position increment during each sampling time is calculated as</p><p><b>　　if </b></p><p><b>　　if </b></p><p>　　Since the co

67、efficients and can be calculated and be stored in advance according to the acceleration and deceleration intervals, file velocity profile which has arbitrary acceleration and deceleration characteristics is able to be

68、 efficiently calculated for a given distance.</p><p>　　In digital convolution techniques as in (14) and Fig. 7, the shape of a velocity profile is determined by the values of ai for i = 1,2,...,m where m det

69、ermines the acceleration and deceleration intervals which are same na = nd = m. This means that the values of ai determine the above coefficients and where na = nd. Therefore, the coefficients in velocity profiles g

70、enerated by digital convolution techniques cannot be made to be independent from the coefficients . The deceleration characteris</p><p>　　IV. GENERATION OF SOME VELOCITY PROFILES</p><p>　　While

71、a number of velocity profiles can be generated by the digital convolution techniques [2-6], some velocity profiles cannot be generated by them. Velocity profiles</p><p>　　Fig.9.The position increment during

72、each sampling time</p><p>　　in the acceleration interval of a velocity profile</p><p>　　which cannot be generated by the digital convolution techniques are illustrated in Fig. 10 where the accel

73、eration characteristic is represented by and the deceleration characteristics is represented by ．Let us consider one single-axis linear motion control system of which the maximum velocity, the sampling time, the decele

74、ration interval, and the coupling ratio are Vmax = 3000rpm, Ts= 2msec , Td = 40Ts = 80msec , and P=10 tums/in respectively. Given linear distances L1= 0.5 in. and L2 = 1 i</p><p>　　V. CONCLUSION</p>

75、<p>　　A generalized approach for the acceleration and deceleration of CNC machine tools has been proposed. Given a machining task in a CNC system, the appropriate acceleration characteristic, the deceleration char

76、acteristic, the acceleration interval, and the deceleration interval can be determined. According to the acceleration characteristic, the deceleration characteristic, the acceleration interval, and the deceleration inter

77、val, some coefficients are calculated and are stored. By using these coef</p><p>　　Fig.10-a.A velocity profile for L1=0.5 in .=40,and =40</p><p>　　Fig.10-b.A velocity profile for L2=1 in . =40,a

78、nd =40</p><p>　　Fig.10-c.A velocity profile for L1=0.5 in . =50,and =40</p><p>　　Fig.10-d.A velocity profile for L2=1 in . =50 , and =40</p><p>　　REFERENCES</p><p>　　

79、1. K. S. Fu, R. C. Gonzalez, and C. S. G. Lee, Robotics: Control, Sensing,Vision and Intelligence, McGraw-Hill, 1987.</p><p>　　2. D. I. Kim, J. W. Jeon, and S. Kim, "Software acceleration/deceleration m

80、ethods for industrial robots and CNC machine tools," Mechatronics, Vol. 4, No. 1, pp. 37-53, 1994.</p><p>　　3. D. S. Khalsa, "High Performance Motion Control Trajectory Commands Based on The Convol

81、ution Integral and Digital Filtering" Proceedings of Intelligent Motion, pp. 54-61, Oct. 1990.</p><p>　　4. United States Patent, Patent Number 4,555,758, Nov. 26, 1985.</p><p>　　5. Masory O

82、. and Korea Y., "Reference-Word Circular Interpolators for CNC Systems," Trans. of ASME, J. Eng. Ind., vol 104, pp. 400-405, 1982.</p><p>　　6. Koren Y., Computer Control of Manufacturing ,Systems,

83、McGraw-Hill Inc. 1988.</p><p>　　CNC數(shù)控加工加減速平穩(wěn)變化的方法</p><p>　　Jac Wook Jcon </p><p>　　Sungkyunkwan大學(xué) 控制和儀器控制工程系</p><p>　　300 Chunchun-Dong、 Jangan-Gu 、 Suwon市,韓國</p>

84、<p>　　摘要 ： 為了使CNC機(jī)床有效率地完成預(yù)定的數(shù)控加工任務(wù)，人們提出了許多數(shù)控機(jī)床加減速的方法。因?yàn)闄C(jī)床要在限定時(shí)間完成任務(wù), 而這些方法并不能準(zhǔn)確的計(jì)算。然而，這些早先的技術(shù)不能夠形成某些加減速度特性的速度分布圖，盡管他們能形成很多種加減速度特性的速度分布圖。這篇文章提出了一個(gè)早先的技術(shù)并不能做到的形成速度分布圖的一般方法，這些。根據(jù)需要達(dá)到的加減速特性，計(jì)算出各個(gè)系數(shù)并存儲(chǔ)，對(duì)CNC系統(tǒng)設(shè)定一個(gè)移動(dòng)距離，一個(gè)

85、加速度時(shí)間和一個(gè)減速度時(shí)間，運(yùn)用這些系數(shù)就可以形成所需求的加減速特性的速度分布圖。下面將詳細(xì)說明用這個(gè)技術(shù)形成典型的速度分布圖的方法。</p><p><b>　　一、引言</b></p><p>　　生產(chǎn)復(fù)雜零件的精確度要求和提高生產(chǎn)力的要求改進(jìn)了CNC系統(tǒng)，使得CNC機(jī)床運(yùn)作的快速精確。因?yàn)榭刂破鞯慕M合特性和工作母機(jī)決定了CNC系統(tǒng)的最終精確度和生產(chǎn)率，所以有許多

86、因素需要考慮。其中一個(gè)重要因素就是如何有效的形成給定加工任務(wù)所需求的加減速特性的速度分布圖。許多研究者提出了CNC機(jī)床形成速度分布圖的技術(shù)。其中一個(gè)就是通過多項(xiàng)式功能選擇來完成速度分布圖[1]。這項(xiàng)技術(shù)能夠形成很多種速度分布圖，此外還將減速度特性從加速度中獨(dú)立出來。這項(xiàng)技術(shù)的主要問題是計(jì)算負(fù)荷將隨加減速多項(xiàng)式的需求成指數(shù)增長。因?yàn)闀r(shí)間的限制，用這些技術(shù)控制CNC系統(tǒng)非常困難。之前其他形成速度分布圖的其他技術(shù)都是基于數(shù)字回旋 [2-6]。

87、這些技術(shù)比多項(xiàng)式功能選擇技術(shù)更加有效，用硬件也更加容易實(shí)現(xiàn)。但是，在這些技術(shù)形成的速度分布圖過程中，加速度時(shí)間總是和減速時(shí)間相等，而且加速度特性決定了減速度特性。因此，這樣有些速度分布圖是不能用這些方法實(shí)現(xiàn)的。</p><p>　　這篇論文提出數(shù)控機(jī)床加減速的一般途徑。這種技術(shù)的難易程度和數(shù)字回旋相當(dāng)，并且能形成比它更多種加減速特性。換句話說，這種技術(shù)能夠產(chǎn)生減速度特性獨(dú)立于加速度特性的速度分布圖。首先，根據(jù)加速

88、特性、減速特性、加速時(shí)間，減速時(shí)間計(jì)算出一些系數(shù)并存儲(chǔ)。然后給定需要移動(dòng)距離，通過計(jì)算經(jīng)過每個(gè)采樣時(shí)間的位移增量就產(chǎn)生了所需特性的速度分布圖。每個(gè)采樣時(shí)間的位移增量可以通過</p><p>　　將存儲(chǔ)的系數(shù)和采樣時(shí)間與加速后速度的乘積相乘得到。</p><p>　　在第二部分中，將會(huì)對(duì)數(shù)控機(jī)床產(chǎn)生速度分布圖的現(xiàn)有技術(shù)進(jìn)行說明。第三部分將說明怎樣運(yùn)用這個(gè)技術(shù)產(chǎn)生所需求的速度分布圖。這種技術(shù)將

89、和現(xiàn)有的技術(shù)做個(gè)比較。在第四部分，將會(huì)說明這種技術(shù)能夠產(chǎn)生一些對(duì)CNC機(jī)床有用的速度分布圖。</p><p><b>　　二、 先前的技術(shù)</b></p><p>　　為了說明的技術(shù)，就以單軸控制系統(tǒng)為例，它的最大速度、最大加速度、采樣時(shí)間分別是Vmax, Amax, 和Ts。如果系統(tǒng)以最大速度Vmax移動(dòng)給定的距離S，則矩形速度分布圖中的運(yùn)動(dòng)時(shí)間 T1 將是

90、 </p><p><b>　　(1)</b></p><p>　　選取一個(gè)大于等于p最小整數(shù)n，則形成如圖１的矩形速度分布圖。圖形的速度和位移方程如下：</p><p>　　每個(gè)采樣時(shí)間的位移增量是</p><p>　　, (4)</p><p>　　其中　和　　分別是

91、采樣點(diǎn)為　 和 位移。也就是說，每個(gè)采樣時(shí)間的位置增量相同。然而沒有一個(gè)物理系統(tǒng)可以通過推進(jìn)加速度來完成上面所講的矩形速度分布圖，需要加速時(shí)間內(nèi)將速度由零升到一個(gè)特定階段而減速時(shí)間內(nèi)將當(dāng)前速度降為零。</p><p>　　1.多項(xiàng)式函數(shù)的選擇</p><p>　　給定加速度時(shí)間 , 減速時(shí)間 這里 距離為S，</p><p>　　則形成如圖２所示的具

92、有線性加減速度特性的梯形速度分布圖。如果有恒速度時(shí)段，那么</p><p>　　。速度和位置方程如下：</p><p><b>　　另外</b></p><p>　　圖１　移動(dòng)距離?。印〉木匦嗡俣确植紙D</p><p>　　圖２ 移動(dòng)距離　Ｓ　的梯形速度分布圖</p><p>　　根據(jù)上文所說，假

93、定加速度時(shí)間和減速度時(shí)間相等,當(dāng)前速度恒定。在加減速度不等，現(xiàn)有速度不是恒定的情況下，就會(huì)得到一些類似的方程。這種有線性加減速度特性的梯形速度分布圖特別適用于控制剛性強(qiáng)的機(jī)床。然而，梯形圖連接點(diǎn)的大的進(jìn)給可能將鐵屑聚集還會(huì)可能影響機(jī)床的剛性。因?yàn)槠交乃俣确植紙D有更高的要求加減速度特性，在頂點(diǎn)處不會(huì)產(chǎn)生大的進(jìn)給，這些速度分布圖常被應(yīng)用在數(shù)控機(jī)床上[1-6]，于是提出了一些選擇多項(xiàng)式函數(shù)來產(chǎn)生速度分布圖的技術(shù)方法[1]。給定位置，速度以及

94、在起始和終了位置的加速度，就選擇了一類滿足這些條件的多項(xiàng)式函數(shù)。一個(gè)方法就是對(duì)每個(gè)軸列入一個(gè)第7次多項(xiàng)式。另一個(gè)方法就是將一個(gè)完整的軌跡分成一些軌跡片段，這樣不同多相式的低次數(shù)就可以用于軌跡片段。最普通的方法就是4-3-4分段法，3-5-3分段法還有5-立方分段法。用選擇多項(xiàng)式函數(shù)的方法產(chǎn)生速度分布圖的主要問題就是計(jì)算的負(fù)荷。產(chǎn)生一個(gè)平滑的速度分布圖所需要的時(shí)間在增加次數(shù)后成指數(shù)的增長。因此，在CNC系統(tǒng)的控制中，用這些技術(shù)產(chǎn)生任意平滑

95、的速度分布圖幾乎是不可能的。</p><p><b>　　2.數(shù)字回旋技術(shù)</b></p><p>　　給定加速度時(shí)間 Ta=naTs （它決定了減速度時(shí)間 Td = ndTs = naTs ，因?yàn)閿?shù)字回旋技術(shù)產(chǎn)生的速度分布圖的加減速時(shí)間不可能不同）給定距離 S， 通過數(shù)字式回旋技術(shù)就會(huì)構(gòu)造出一個(gè)有線性加減速特性的梯形速度分布圖。公式（4）中顯示梯形分布圖中每個(gè)

96、采樣時(shí)間的關(guān)系，梯形速度分布圖中每個(gè)采樣時(shí)間里的位置增量 由位置增量 的反饋構(gòu)成，次序 H(kTs ) 由以下得到：</p><p>　　, (7)</p><p>　　這里 (8)</p><p>　　圖3顯示δP0 和 δP1

97、 的關(guān)系可以表達(dá)成如下遞歸方程[2]：</p><p>　　方程(9)提供給梯形速度分布圖基礎(chǔ)信息。根據(jù)方程（9），我們可以為梯形速度分布圖設(shè)計(jì)硬件系統(tǒng)如圖４，緩沖寄存器充當(dāng)延時(shí)元件［４］。有假想加減速度特性的2級(jí)速度分布圖也能夠用數(shù)字回旋技術(shù)構(gòu)造。二次分布圖的位置增量 可從連續(xù)的反饋后得到，如圖5。</p><p>　　這里 　　

98、 (10)</p><p>　　二級(jí)速度分布圖的輪廓由m1 和 m2 的值決定[4]。 和 的關(guān)系可以由下面的遞歸方程[2]表示：</p><p>　　圖3 梯形速度分布圖的數(shù)字反饋</p><p>　　圖 4 梯形速度分布圖的硬件組成</p><p>　　圖 5 第2次速度分布圖的連續(xù)數(shù)字反饋</p><p>

99、;　　同樣的，具有高速加減速特征的平滑速度分布圖的位置增量可由幾次回旋得到例圖6。每次回旋都有相似的意義。平滑速度分布圖的輪廓可以由,決定，q[2，4]。 和 的關(guān)系可以用下面的遞歸方程表示[2]：</p><p>　　由公式（13）產(chǎn)生的速度分布圖有這樣的特性：加速度和減速度時(shí)間內(nèi)的位移相等。在相同條件下也和梯形速度分布圖在相同加速度時(shí)間內(nèi)的位移相等。</p><p>　　為了形成任意

100、形速度分布圖，所需的速度分布圖中每段采樣時(shí)間的位置增量 </p><p>　　都可以由以后的回饋產(chǎn)生[2，4]：</p><p>　　選擇合適的 ，,就會(huì)獲得所需的速度分布圖。根據(jù)公式（14）設(shè)計(jì)的為產(chǎn)生任意速度分布圖的硬件系統(tǒng)可設(shè)計(jì)成如圖 7 所示。加速度和減速時(shí)間 由公式 得出。在[3]中，可得到有多次加減速的速度分布圖，這種變化圖可由一種相似的反饋技術(shù)得到。而用反饋技術(shù)產(chǎn)生平

101、滑速度分布圖的計(jì)算負(fù)荷則比用多項(xiàng)式技術(shù)少的多，這個(gè)方法產(chǎn)生的減速度特性由加速度特性決定。換句話說，用數(shù)字反饋技術(shù)產(chǎn)生的減速度特性不可能獨(dú)立于加速度特性。因此，一些對(duì)CNC機(jī)床有益的速度分布圖就不能用這些反饋技術(shù)形成。</p><p>　　圖6 更高次速度分布圖的連續(xù)數(shù)字反饋</p><p>　　三、關(guān)于軌跡形成技術(shù)</p><p>　　如第二部分所說，讓我們考慮下單