機械鉆床外文翻譯論文中英文

1、<p><b>　　附錄</b></p><p><b>　　附錄1：外文資料</b></p><p>　　Kinematic and dynamic synthesis of a parallel kinematic high speed</p><p>　　drilling machine</p>

2、<p><b>　　Abstract</b></p><p>　　Typically, the term‘‘high speed drilling’’ is related to spindle capability of high cutting speeds. The suggested high speed drilling machine (HSDM) extends

3、this term to include very fast and accurate point-to-point motions. The new HSDM is composed of a planar parallel mechanism with two linear motors as the inputs. The paper is focused on the kinematic and dynamic synthesi

4、s of this parallel kinematic machine (PKM). The kinematic synthesis introduces a new methodology of input motion planning f</p><p>　　Keywords: Parallel kinematic machine; High speed drilling; Kinematic and d

5、ynamic synthesis</p><p>　　1. Introduction</p><p>　　During the recent years, a large variety of PKMs were introduced by research institutes and by industries. Most, but not all, of these machines

6、 were based on the well-known Stewart platform [1] configuration. The advantages of these parallel structures are high nominal load to weight ratio, good positional accuracy and a rigid structure [2]. The main disadvanta

7、ges of Stewart type PKMs are the small workspace relative to the overall size of the machine and relatively slow operation speed [3,4]. W</p><p>　　The application of the PKMs with ‘‘constant-length links’’ f

8、or the design of machine tools is less common than the type with ‘‘varying-length links’’. An excellent example of a ‘‘constant-length links’’ type of machine is shown in [6]. Renault-Automation Comau has built the machi

9、ne named ‘‘Urane SX’’. The HSDM described herein utilizes a parallel mechanism with constant-length links.</p><p>　　Drilling operations are well introduced in the literature [7]. An extensive experimental st

10、udy of highspeed drilling operations for the automotive industry is reported in [8]. Data was collected fromhundreds controlled drilling experiments in order to specify the parameters required for quality drilling. Ideal

11、 drilling motions and guidelines for performing high quality drilling were presented in [9] through theoretical and experimental studies. In the synthesis of the suggested PKM, we follow th</p><p>　　The deta

12、iled mechanical structures of the proposed new PKM were introduced in [10,11]. One possible configuration of the machine is shown in Fig. 1; it has large workspace, highspeed point-to-point motion and very high drilling

13、speed. The parallel mechanism provides Y, and Z axes motions. The X axis motion is provided by the table. For achieving highspeed performance, two linear motors are used for driving </p><p>　　the mechanism a

14、nd a highspeed spindle is used for drilling. The purpose of this paper is to describe new kinematic and dynamic synthesis methods that are developed for improving the performance of the machine. Through input motion plan

15、ning for drilling and point-to-point positioning, the machining error will be reduced and the quality of the finished holes can be greatly improved. By adding a well-tuned spring element to the PKM, the input power can b

16、e minimized so that the size the machine and </p><p>　　2. Kinematic and dynamic equations of motion of the PKM module</p><p>　　The schematic diagram of the PKM module is shown in Fig. 2. In cons

17、istent with the machine tool conventions, the z-axis is along the direction of tool movement. The PKM module has two inputs (two linear motors) indicated as part 1 and part 6, and one output motion of the tool. The posit

18、ioning and drilling motion of the PKM module in this application is characterized by (y axis motion for point-to-point positioning) and (z axis motion for drilling). Motion equations for both rigid body and elas</p&

19、gt;<p>　　2.1. Equations of motion of the PKM module with rigid links</p><p>　　Using complex-number representation of mechanisms [12], the kinematic equations of the tool unit (indicated as part 3 whic

20、h includes the platform, the spindle</p><p>　　and the tool) are developed as follows. The displacement of the tool is</p><p><b>　　and</b></p><p>　　where b is the distanc

21、e between point B and point C, r is the length of link AB (the lengths of link AB, CD and CE are equal). The velocity of the tool is</p><p><b>　　where</b></p><p>　　The acceleration o

22、f the tool is</p><p><b>　　where</b></p><p>　　The dynamic equations of the PKM module are developed using Lagrange’s equation of the second kind [13] as shown in Eq. (7).</p>&

23、lt;p>　　where T is the total kinetic energy of the system; and are the generalized coordinates and velocities; is the generalized force corresponding to . k is the number of the independent generalized coordinates o

24、f the system. Here, k=2, q1=y1 and q2=y6. After derivation, Eq. (7) can be expressed as</p><p>　　where n is the number of the moving links; are mass and mass moment of inertia of link i; are the coordinate

25、s of the center of mass of link i; hi is the rotation angle of link i in the PKM module. The generalized force can be determined by</p><p>　　where V is the potential energy and F’i are the nonpotential forc

26、es. For the drilling operation of the PKM module, we have</p><p>　　where Fcut is the cutting force, F1 and F6 are the input forces exerted on the PKM by the linear motors. Eqs. (1) to (10) form the kinematic

27、 and dynamic equations of the PKM module with rigid links.</p><p>　　2.2. Equations of motion of the PKM module with elastic links</p><p>　　The dynamic differential equations of a compliant mecha

28、nism can be derived using the finite element method and take the form of</p><p>　　where [M], [C] and [K] are system mass, damping and stiffness matrix, respectively; {D} is the set of generalized coordinates

29、 representing the translation and rotation deformations at each element node in global coordinate system; {R} is the set of generalized external forces corresponding to {D}; n is the number of the generalized coordinates

30、 (elastic degrees of freedom of the mechanism). In our FEA model, we use frame element shown in Fig. 3 in which EIe is the bending stiffness (E is the modu</p><p>　　the original length of the element. are n

31、odal displacements expressed in local coordinate system(x, y). The mass matrix and stiffness matrix for the frame element will be 66 symmetric matrices which can be derived fromthe kinetic energy and strain energy expres

32、sions as Eqs. (12) and (13)</p><p>　　where T is the kinetic energy and U is the strain energy of the element; are the linear 1 2 3 4 5 6 and angular deformations of the node at the element local coordinate

33、system. Detailed derivations can be found in [14]. Typically, a compliant mechanism is discretized into many elements as in finite element analysis. Each element is associated with a mass and a stiffness matrix. Each ele

34、ment has its own local coordinate system. We combine the element mass and stiffness matrices of all elements a</p><p>　　where a and b are two positive coefficients which are usually determined by experiment.

35、 An alternate method [16] of representing the damping matrix is expressing [C]as</p><p>　　The element of [C’] is defined as,where signKij=(Kij/|Kij|), Kij and Mij are the elements of [K] and [M], ζis the dam

36、ping ratio of the material.</p><p>　　The generalized force in a frame element is defined as</p><p>　　where Fj and Mj are the jth external force and moment including the inertia force and moment

37、on the element acting at (xj ,yj), and m is the number of the externalforces acting on the element. The element generalized forces</p><p>　　,are then combined to formthe systemgeneralized force {R}. The seco

38、nd order ordinary differential equations of motion of the system, Eq. (11), can be directly integrated with a numerical method such as Runge-Kutta method. For the PKM we studied, each link was discreted as 15 frame eleme

39、nts. Both Matlab and ADAMS software are used for programming and solving these equations.</p><p>　　3. Input motion planning for drilling</p><p>　　Suppose we know the ideal motion function of the

40、 drilling tool. How to determine the input motor motion so that the ideal tool motion can be realized is critical for high quality drillings. The created explicit input motion function also provides the necessary informa

41、tion for machine controls. According to the study done in [9], the drilling process can be divided into three phases: entrance phase, middle phase, and exit phase. In order to increase the productivity and quality of the

42、 drilling, m</p><p>　　where vT1 is the maximum drilling velocity, T1, T2,and T3 are the times corresponding to the entrance phase, the middle phase and the exit phase. vT2 is the maximum retracting velocity.

43、 T4, T5, and T6 are corresponding to accelerating, constant velocity, and decelerating times for retracting operation. is the cycle time for a single drilling. As a numerical example, suppose we drill a 25.4 mm (1 in) d

44、eep hole with Tc=0.4s, 0.3s for drilling, 0.1s for retracting. Set T1=T3 0.06s, T4=T6=0.03s. Un</p><p>　　where vB=143.48mm/s, vC=165.77mm/s, vE=-557.36mm/s, vF=-499.44mm/s. When plotting the velocity curve w

45、ith Eq. (18), no visual difference can be found with the curve shown in Fig. 5. Eq. (18) is composed of six parts with four cycloidal functions and two linear functions. If we control the two linear motors to have the sa

46、me motion as described in Eq. (18), the drilling and retracting velocity of the tool will be almost the same as shown in Fig. 4. The absolute errors between the ideal and real to</p><p>　　errors are zero. Th

47、ese small absolute and relative errors illustrate the created input motion and are quite acceptable. The derived function is simple enough to be integrated into the control algorithmof the PKM.</p><p>　　4. I

48、nput motion planning for point-to-point positioning</p><p>　　In order to achieve fast and accurate positioning operation in the whole drilling process, the input motion should be appropriately planned so tha

49、t the residual vibration of the tool tip can be minimized. Conventionally the constant acceleration motion function is commonly used for driving the axes motions in machine tools. Although this kind of motion function is

50、 simple to be controlled, it may excite the elastic vibration of the systemdue to the sudden changes in acceleration. Take the same PK</p><p>　　realized by the two linear motors moving in the same direction.

51、 Suppose the positioning distance between the two holes is 75mm, the constant acceleration is 3g(approximated as 30m/s² here). The input motion of the linear motors with constant acceleration and deceleration is sho

52、wn in Fig. 7, in which the maximum velocity is 1500 mm/s, the positioning time is 0.1 s. Assuming the material damping ratio as 0.01, the residual vibration of the tool tip is shown in Fig. 8. In order to reduce the resi

53、du</p><p>　　where the coeffcients ci are the design variables which have to be determined by minimizing the residual vibration of the tool tip. Selecting the boundary conditions as that when t=0, sin=0, vin=

54、0, ain=0;</p><p>　　and when t=Tp, sin=h, vin=0, ain=0, where Tp is the point-to-point positioning time, the first six coeffcients are resulted:</p><p>　　Logically, set the optimization objective

55、 as</p><p>　　where c6 is the independent design variable; is the maximum fluctuation of residual vibrations of the tool tip after the point-to-point positioning. Set and start the calculation from c6=0. The

56、optimization results in c6=-10mm/s . Consequently, c5=7.5×10mm/s , c4 =-1.425×10mm/s , c3=8.5×10mm/s , c2=c1=c0=0. It can be seen that the optimization calculation brought the design variable c6 to the bou

57、ndary. If further loosing the limit for c6, the objective will continue reduce in value, but the maxi</p><p>　　5. Input power reduction by adding spring elements</p><p>　　Reducing the input powe

58、r is one of many considerations in machine tool design. For the PKM we studied, two linear motors are the input units which drive the PKM module to perform drilling and positioning operations. One factor to be considered

59、 in selecting a linear motor is its maximum required power. The input power of the PKM module is determined by the input forces multiplying the input velocities of the two linear motors. Omitting the friction in the join

60、ts, the input forces are determined f</p><p>　　balancing the drilling force and inertia forces of the links and the spindle unit. Adding an energy storage element such as a spring to the PKM may be possible

61、to reduce the input power if the stiffness and the initial (free) length of the spring are selected properly. The reduction of the maximum input power results in smaller linear motors to drive the PKM module. This will i

62、n turn reduce the energy consumption and the size of the machine structure. A linear spring can be added in the middle o</p><p>　　where l0 and k are the initial length and the stiffness of the linear spring.

63、 The input power of the linear motors is determined by</p><p>　　In order to reduce the input power, we set the optimization objective as follows:</p><p>　　where v is a vector of design variables

64、 including the length and the stiffness of the </p><p>　　spring, . For the PKM module we studied, the mass properties are listed in Table 1. The initial values of the design variables are set as . The domain

65、s for design variables are set as [lmin;lmax]=[400, 500 ]mm, [kmin; kmax]=[1,20 ]N/mm. The PKM module is driven by the input motion function described as Eq. (18). Through minimizing objective (24), the optimal spring pa

66、rameters are obtained as and k=14.99 N/mm. The input powers of the linear motors with and without the optimized spring are shown </p><p>　　6. Conclusions</p><p>　　The paper presents a new type

67、of high speed drilling machine based on a planar PKM module. The study introduces synthesis technology for planning the desirable motion functions of the PKM. The method allows both the point-to-point positioning motion

68、and the up-and-down motion required for drilling operations. The result has shown that it is possible to reduce substantially the residual vibration of the tool tip by optimizing a polynomial motion function. Reducing re

69、sidual vibration is critical w</p><p>　　In order to better understand the properties of the HSDM and to complete its design, further study is required. It will include error analysis of the machine as well a

70、s the control strategies and control design of the system.</p><p>　　7. Acknowledgements</p><p>　　The authors gratefully acknowledge the financial support of the NSF Engineering Research Center f

71、or Reconfigurable Machining Systems (US NSF Grant EEC95-92125) at the University of Michigan and the valuable input fromthe Center’s industrial partners.</p><p><b>　　中文翻譯</b></p><p>

72、　　高速鉆床的動力學(xué)分析</p><p><b>　　摘要</b></p><p>　　通常情況下，術(shù)語“高速鉆床”就是指具有較高切削速率的鉆床。高速鉆床(HSDM)也是指具有非?？斓暮驼_的點到點運動的鉆床。新的HSDM是由帶有兩個直線電動機的平面并聯(lián)機構(gòu)組成。本文主要就是對并聯(lián)機器(PKM)的動力學(xué)分析。運動合成是為了介紹一種新方法，它能夠完善鉆孔操作和點到點定位

73、的準確性。動態(tài)合成旨在減少因使用彈簧機械時PKM的輸入功率。</p><p>　　關(guān)鍵詞: 并聯(lián)運動機床; 高速鉆床; 動力學(xué)的合成</p><p><b>　　1.介紹</b></p><p>　　在最近的幾年里，研究所和工業(yè)協(xié)會介紹了各式各樣的PKM。其中大部分（但不是所有）,以眾所周知的斯圖爾特月臺[1]為基礎(chǔ)結(jié)構(gòu)。這一做法的好處是高公稱

74、的負載重量比，良好的位置精度和結(jié)構(gòu)剛性[2]。斯圖爾特式PKM的主要缺點是相對小的工作空間和相對慢的操作速度 [3,4]。機床刀具的工作空間是指刀尖能夠移動和切削材料所需要的容積。平面的斯圖爾特月臺的設(shè)計在[5]中被提到，像是對無CNC機器作翻新改進的方法需要塑料的鑄模機制一樣。PKM[5]的設(shè)計允許可以調(diào)整幾何學(xué)已經(jīng)被規(guī)定了的最佳的再配置的任何路徑。 一般的，改變一根或較多連桿的長度是以PKM受約束的順序來做幾何學(xué)的調(diào)整。</p

75、><p>　　在機床設(shè)計中，“定長度連桿”的PKM應(yīng)用比“不定長度連桿”的共同點要少的多。一個優(yōu)秀“定長度連桿”型的機器例子被顯示在[6]。Renault-Automation Comau已經(jīng)建造叫做“Urane SX”的機器。在此HSDM被描述成是一個采用“定長度連桿”組成的并聯(lián)機械裝置。</p><p>　　鉆床操作在文學(xué)[7]中被很好的介紹了。汽車工業(yè)中，一項關(guān)于高速鉆孔的操作的廣泛的實

76、驗研究在[8]中被報告。數(shù)據(jù)從數(shù)百個鉆床控制實驗上收集起來，是為了具體指定鉆床質(zhì)量所必須的參數(shù)。理想的鉆床運動和制造高質(zhì)量鉆床的指導(dǎo)方針通過理論和實驗的研究被呈現(xiàn)在[9]中。在被建議的PKM綜合中，我們遵循[9]中的結(jié)論。</p><p>　　新推出的PKM的詳細機械結(jié)構(gòu)在[10,11]被介紹，機器的大致結(jié)構(gòu)顯示在圖1中；它有很大的工作空間，點到點的高速運動和非常高的鉆速。并聯(lián)的機械裝置提供給了Y和Z軸的動作，X

77、軸動作是由工作臺提供的。為了達成高速的運轉(zhuǎn)，用了兩個線性馬達來驅(qū)駛機械裝置和用一個高速的主軸來鉆孔。這篇文章的目的就是描述新的運動學(xué)的和動力學(xué)合成的方法的發(fā)展，為了改良機器的運轉(zhuǎn)。通過輸入運動，規(guī)劃鉆井和點對點定位，機器的誤差將會被減少，而且完成孔的質(zhì)量能被極大的提高。通過增加一個彈簧機械要素到PKM，輸入動力就能被最小，以便機器的尺寸和能量損耗降低。數(shù)字模擬的正確查證和熱交換率的方法呈現(xiàn)在這篇文章中。</p><p

78、>　　2.PKM模型的運動學(xué)和動力學(xué)的運動方程式</p><p>　　PKM模型的概要線圖在圖2中被顯示。由于機床刀具庫的一致，Z軸是沿著工具運動的方向的。PKM模型有部分1和部分6二個輸入指示(二個線性電機)，和一個刀具的輸出動作。在PKM模型應(yīng)用中，定位和鉆孔運動分別通過 ( y 軸動作相對點到點的定位)和 (z軸動作相對鉆孔)表示。剛體和柔性體的PKM模型運動方程式都被發(fā)展了。剛體方程式被用于合成輸入

79、鉆床的動作計劃和輸入力量還原。柔性體方程式被用來在刀具點到點定位之后的剩余振動控制。</p><p>　　2.1.剛性連桿的PKM模型的運動方程式</p><p>　　機械裝置[12]的特點是使用了數(shù)字集成,刀具設(shè)備(含工作臺，主軸和刀具3部份)。它的運動學(xué)方程式的發(fā)展依下列各項。刀具的變位是</p><p><b>　　且</b></p

80、><p>　　其中b是點B和點C之間的距離,r是連桿AB的長度(連桿AB、CD和CE的長度是相等的)。刀具的速度是</p><p><b>　　其中</b></p><p><b>　　刀具的加速度是</b></p><p><b>　　其中</b></p><

81、p>　　PKM模型的動力學(xué)方程式的發(fā)展如方程（7）所示，使用了拉格朗日的第二個類型的方程式[13]。</p><p>　　其中t是系統(tǒng)的總動能；和是總坐標值和速度值;是總力對應(yīng)到的的值。k是坐標系中總的獨立數(shù)目。在這里,k=2，q1= y1和q2=y6，引出之后，公式(7)可被表達成</p><p>　　其中n是移動連桿的數(shù)目；是連桿i的大量慣性矩；是連桿i的質(zhì)量中心坐標；是PKM模

82、型中連桿i的旋轉(zhuǎn)角?？偭Φ闹低ㄟ^（9）決定</p><p>　　其中V是勢能， 是沒有勢能的力。為了對PKM模型的鉆孔操作，我們有</p><p>　　其中是切削力, F1和F6是線性馬達在PKM上輸入的力。情緒商數(shù)。公式(1)到公式(10)構(gòu)成了剛性連桿PKM模型的運動學(xué)和動力學(xué)方程式。</p><p>　　2.2.柔性連桿的PKM模型的動作方程式</p&g

83、t;<p>　　順從的機械裝置的動微分方程式能用有限的機械要素方法和以下的公式得到</p><p>　　其中[M]、[C]和[K]分別是系統(tǒng)質(zhì)量，阻尼和剛性母體；{D}是在全球同等坐標系中的每個機械要素平移和旋轉(zhuǎn)變形表現(xiàn)的總坐標值；{R}是總外力值，與{D}保持一致；n是坐標的總數(shù)目值(機械裝置的柔性自由度)。在我們的FEA模型中，我們使用在圖3中被顯示的機械要素結(jié)構(gòu)，其中EIe是彎曲剛性(E是材料

84、的柔性系數(shù),Ie是慣性矩),ρ是物質(zhì)的密度,le是</p><p>　　機械要素的最初長度。是(x,y)坐標系統(tǒng)中表現(xiàn)的結(jié)點變位。機械要素的大眾基地和剛性基地將會是66個對稱的矩陣，能從動能和應(yīng)變能中得到，表達在公式（12）和（13）中 </p><p>　　其中t是動能，U是機械要素的應(yīng)變能；是機械要素基本坐標系中線性的123456和角變形節(jié)。詳細的推論能在[14]被發(fā)現(xiàn)。典型地，在有限

85、的機械要素分析中，一個順從的機械裝置是被離散成許多個機械要素的。每個機械要素與一個質(zhì)量和一個剛性母體有關(guān)。每個機械要素有它自己的基本坐標系。我們結(jié)合機械要素質(zhì)量和所有機械要素的剛性矩陣運行坐標轉(zhuǎn)換時，必須把機械要素的基本坐標系轉(zhuǎn)換成世界坐標系，這就提供了系統(tǒng)質(zhì)量[M]和剛性[K]矩陣。在一個順從的系統(tǒng)中捕獲阻尼特性不是這么順利的。即使, 在許多應(yīng)用中，阻尼可能很小，但是它能作用在系統(tǒng)安全性和動力的頻率響應(yīng)中，尤其在共振區(qū)域中,可能是重要

86、的。阻尼基地[C]能被寫做一種質(zhì)量和剛性矩陣[15]的線性結(jié)合，構(gòu)成比例阻尼[C]如下式表達所示</p><p>　　其中α和β是二個通常由實驗決定的正系數(shù)。一個表現(xiàn)阻尼基地的交互方法[16] 表達成[C]如下</p><p>　　機械要素[C']被定義為,其中,和是[K]和[M]的機械要素, ζ是材料的阻尼比。</p><p>　　機械要素結(jié)構(gòu)中的總力被定

87、義為</p><p>　　其中和是的外力和力矩，包括在上動作的機械要素的慣性力和力矩,m 是在機械要素上動作的外力數(shù)目。機械要素的總力,組合構(gòu)成了系統(tǒng)總力{R}。系統(tǒng)動作的第二次序普通微分方程式，如公式(11), 用一個數(shù)字能直接被整合的方法,就像是Runge- Kutta的方法那樣。對于我們研究的PKM,每個連桿被分離成15個機械要素結(jié)構(gòu)。Matlab和ADAMS軟件都被用來規(guī)劃和解決這些方程式。</p&

88、gt;<p>　　3.為鉆床輸入動作計劃</p><p>　　假如我們知道鉆床理想的動作功能。高質(zhì)量鉆床的關(guān)鍵是如何決定輸入電動機動作以便刀具的理想動作能被了解。創(chuàng)建明白的輸入動作功能時也為機器控制提供了必需的數(shù)據(jù)。依照研究在[9]中所做的,鉆孔的過程能分為三個時期: 入口期,中間期和出口期。為了增加生產(chǎn)能力和鉆孔的質(zhì)量，許多操作限制，例如最小刀具的壽命限制，孔位置誤差限制,退出毛邊限制,鉆頭扭轉(zhuǎn)破

89、壞限制等等，一定要考慮而且要滿意。在這些條件之下，刀具的補給速度在入口期應(yīng)該是慢的，以減少孔位置的誤差。刀具的速度在出口期也應(yīng)該是慢的，以減少出口毛邊。在中央期,刀具的鉆速應(yīng)該很快速并且保持持續(xù)。刀具在完成鉆孔之后的退回應(yīng)該被做的盡可能的快，以增加生產(chǎn)能力。基于這些考慮, 我們采取了公式（17）中得到的理想鉆床和刀具的退回速度。</p><p>　　其中是最大的鉆孔速度，T1、T2和T3是分別對應(yīng)入口期，中間期和

90、出口期的時間。vT2是退回的最大速度。T4 、T5和T6對應(yīng)的分別是加速的，持續(xù)的速度,和縮回操作時減速的時間。是一個單一鉆孔的周期。用一個數(shù)字為例,我們打算利用鉆一個25.4mm(1 在)深的孔，0.3s用來鉆孔，0.1s用來刀具退回。設(shè)定T1=T3=0.06s,T4=T6=0.03s。在這些條件下，。圖4顯示了理想刀具運動的圖解式。如果PKM中連桿長度r=500mm，在鉆孔出發(fā)點時的角β =53 °，與理想刀具動作相關(guān)的對

91、應(yīng)輸入電動機的速度顯示在圖5中。一般的，曲線裝配方法能用來產(chǎn)生輸入運動的函數(shù)，但是依照圖5中顯示的曲線形狀，我們創(chuàng)建的線性馬達速度函數(shù)詳盡的顯示在公式(18)中</p><p>　　其中。當(dāng)按公式（18）計畫速度曲線時,沒有不同的曲線能被發(fā)現(xiàn)，通過圖（5）中顯示的曲線。公式(18)由四個旋輪線的函數(shù)和兩個線性函數(shù)共六個函數(shù)組成。假如我們像公式（18）中描述的那樣控制兩個線性電動機就會有相同的動作,那么刀具鉆孔和退

92、回的速度將幾乎是與在圖4中顯示的相同。 在理想的和真正的刀具速度之間的絕對誤差在圖6中被顯示,圖中最大的誤差不足8mm/s,相對誤差不足1.5%，在鉆孔的開始和結(jié)束的位置,誤差是等于零的。這</p><p>　　些小的絕對和相對的誤差說明了輸入動作的產(chǎn)生并且容易接受。這些已知的函數(shù)能非常簡單被整合進PKM的控制運算法則里。</p><p>　　4.輸入點到點的定位動作計劃</p>

93、;<p>　　為了在整個的鉆孔過程中達到快速的和正確的定位運動,應(yīng)該適當(dāng)?shù)赜媱澼斎雱幼鳎员愕毒呒舛说氖Ｓ嗾駝幽鼙蛔钚』?。照慣例加速度運動函數(shù)在機床中能被普遍用來驅(qū)動軸的運動。雖然這種動作函數(shù)很容易被控制, 但是由于它在加速度中的突然變化可能引起系統(tǒng)的柔性振動。舉個早先使用相同的PKM例子來說。 一個FEA模型是通過有機械要素結(jié)構(gòu)的ADMAS建造起來的。定位動作是Y軸的動作, 也就是在同一方向上通過兩個線性電動機的運動實現(xiàn)

94、的。</p><p>　　假如在二個孔之間的定位距離是75mm,等加速度是3g(接近30m/s²)。等加速度和減速度的線性電動機的輸入動作在圖7中被顯示,其中最大的速度是 1500mm/s，定位時間為0.1s。 假定材料的阻尼率為0.01,則刀具尖端的剩余振動顯示在圖8中。</p><p>　　為了要減少剩余振動和定位動作的平穩(wěn),建了一個輸入動作的六次多元函數(shù)如(19)所示<

95、;/p><p>　　其中系數(shù)Ci必須是由刀具尖端的最小剩余振動決定的設(shè)計變數(shù)。選擇接口條件為，時，其中是點到點的定位時間，就產(chǎn)生了最初六個系數(shù)如下：</p><p>　　合乎邏輯地,設(shè)立最佳目的如下</p><p>　　其中C6是獨立的設(shè)計變數(shù)，是刀具尖端在點到點定位之后的剩余振動的最大變動。設(shè)定</p><p>　　并從C6=0開始計算，最佳導(dǎo)

96、致C6=-10mm/s。因</p><p>　　此 。可以看見最佳化計算使得變數(shù)C6的設(shè)計到了極限。如果給c6深層的釋放極限,那么目的將會在價值中連續(xù)減少,但是輸入動作的加速度的最大價值將會變成太大。最佳化后的最佳輸入動作在圖9中被顯示。對應(yīng)的刀具尖端的剩余振動在圖10中被顯示。比較圖8和圖10，可以看到，在最佳化之后，振幅和刀具尖端的剩余振動被減少到了30次。較小的剩余振動將會對增加定位精度非常有用。這里應(yīng)當(dāng)注

97、意，只有柔性連桿被包含在上述的計算之中。剩余振動在最佳化后將會仍然非常小，如果柔度是來自其他的來源，如壓力和驅(qū)動系統(tǒng)，會比在圖10中顯示的結(jié)果高的10倍。</p><p>　　5.通過增加彈簧機械要素減少輸入動力</p><p>　　減少輸入動力是機床刀具設(shè)計中的眾多考慮之一。對于我們研究的PKM,兩個線性馬達是使PKM模型做鉆孔運動和定位運動的輸入設(shè)備。在選擇一個線性馬達時要考慮的一個因

98、數(shù)就是它需要的最大動力。PKM模型的輸入動力是由輸入力乘以二個線性的電動機輸入速度決定的。省略接觸處的磨擦, 輸入力是通過平衡鉆削力和連桿與主軸設(shè)備的慣性力決定的。增加一個能量儲存的機械要素，例如加一個彈簧到PKM上，如果彈簧的剛性和最初的(自由的) 長度被適當(dāng)?shù)剡x擇，或許能夠減少輸入動力。減小最大輸入動力導(dǎo)致用比較小的線性電動機驅(qū)動PKM模</p><p>　　型。這將會依次減少能量的損失和機床的結(jié)構(gòu)尺寸。一個

99、線性的彈簧可以被把加到二個連桿的中央如圖11(a)所示，或者在B點和C點加入兩個減震彈簧如圖11（b）所示。我們將會像舉例子一樣討論線性彈簧來說明設(shè)計程序。公式（10）中的總力有以下形式：</p><p>　　其中和 k 是線性彈簧的初始長度和彈性模量。 線性馬達的輸入動力取決于</p><p>　　為了要減少輸入動力，我們依下列各項設(shè)定最佳數(shù)值:</p><p>

100、　　其中v是一個設(shè)計變數(shù)的矢量，包括彈簧長度和彈性模量。</p><p>　　對于我們研究的PKM模型,大量的數(shù)值在表1中被列出。 設(shè)計變數(shù)的初始數(shù)值被設(shè)定為。設(shè)計變數(shù)的范圍被設(shè)定為，。PKM模型是通過公式（18）描述的輸入動作函數(shù)驅(qū)動的。經(jīng)過數(shù)值(24)的最小化，最佳的彈簧參數(shù)和k=14.99N/mm被得到。有優(yōu)化彈簧的線性電動機</p><p>　　和沒有優(yōu)化彈簧的線性電動機的輸入動力

101、如圖12所示,圖中實線表示沒有彈簧的</p><p>　　輸入動力，虛線表示用了優(yōu)化彈簧的輸入動力。從結(jié)果中可以看出，右邊線性馬達的最大輸入動力從122.37降到了70.43W，減少量達到了42.45%。對于左邊的線性馬達,最大的輸入動力從114.44降到了62.72W，減少量達到了45.19%。通過增加一個彈簧機械要素來減少機器輸入動力，實現(xiàn)熱交換的方法被證實了。減震彈簧可能被用來減少慣性作用和彈簧附屬件的尺寸