機(jī)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(dòng)力學(xué)分析</p><p><b>　　摘要</b></p><p>　　通常情況下，術(shù)語(yǔ)“高速鉆床”就是指具有較高切削速率的鉆床。高速鉆床(HSDM)也是指具有非常快的和正確的點(diǎn)到點(diǎn)運(yùn)動(dòng)的鉆床。新的HSDM是由帶有兩個(gè)直線電動(dòng)機(jī)的平面并聯(lián)機(jī)構(gòu)組成。本文主要就是對(duì)并聯(lián)機(jī)器(PKM)的動(dòng)力學(xué)分析。運(yùn)動(dòng)合成是為了介紹一種新方法，它能夠完善鉆孔操作和點(diǎn)到點(diǎn)定位

73、的準(zhǔn)確性。動(dòng)態(tài)合成旨在減少因使用彈簧機(jī)械時(shí)PKM的輸入功率。</p><p>　　關(guān)鍵詞: 并聯(lián)運(yùn)動(dòng)機(jī)床; 高速鉆床; 動(dòng)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(huì)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(tái)[1]為基礎(chǔ)結(jié)構(gòu)。這一做法的好處是高公稱(chēng)

74、的負(fù)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(diǎn)是相對(duì)小的工作空間和相對(duì)慢的操作速度 [3,4]。機(jī)床刀具的工作空間是指刀尖能夠移動(dòng)和切削材料所需要的容積。平面的斯圖爾特月臺(tái)的設(shè)計(jì)在[5]中被提到，像是對(duì)無(wú)CNC機(jī)器作翻新改進(jìn)的方法需要塑料的鑄模機(jī)制一樣。PKM[5]的設(shè)計(jì)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(zhǎng)度是以PKM受約束的順序來(lái)做幾何學(xué)的調(diào)整。</p

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

76、驗(yàn)研究在[8]中被報(bào)告。數(shù)據(jù)從數(shù)百個(gè)鉆床控制實(shí)驗(yàn)上收集起來(lái)，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(yùn)動(dòng)和制造高質(zhì)量鉆床的指導(dǎo)方針通過(guò)理論和實(shí)驗(yàn)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(xì)機(jī)械結(jié)構(gòu)在[10,11]被介紹，機(jī)器的大致結(jié)構(gòu)顯示在圖1中；它有很大的工作空間，點(diǎn)到點(diǎn)的高速運(yùn)動(dòng)和非常高的鉆速。并聯(lián)的機(jī)械裝置提供給了Y和Z軸的動(dòng)作，X

77、軸動(dòng)作是由工作臺(tái)提供的。為了達(dá)成高速的運(yùn)轉(zhuǎn)，用了兩個(gè)線性馬達(dá)來(lái)驅(qū)駛機(jī)械裝置和用一個(gè)高速的主軸來(lái)鉆孔。這篇文章的目的就是描述新的運(yùn)動(dòng)學(xué)的和動(dòng)力學(xué)合成的方法的發(fā)展，為了改良機(jī)器的運(yùn)轉(zhuǎn)。通過(guò)輸入運(yùn)動(dòng)，規(guī)劃鉆井和點(diǎn)對(duì)點(diǎn)定位，機(jī)器的誤差將會(huì)被減少，而且完成孔的質(zhì)量能被極大的提高。通過(guò)增加一個(gè)彈簧機(jī)械要素到PKM，輸入動(dòng)力就能被最小，以便機(jī)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(yùn)動(dòng)學(xué)和動(dòng)力學(xué)的運(yùn)動(dòng)方程式</p><p>　　PKM模型的概要線圖在圖2中被顯示。由于機(jī)床刀具庫(kù)的一致，Z軸是沿著工具運(yùn)動(dòng)的方向的。PKM模型有部分1和部分6二個(gè)輸入指示(二個(gè)線性電機(jī))，和一個(gè)刀具的輸出動(dòng)作。在PKM模型應(yīng)用中，定位和鉆孔運(yùn)動(dòng)分別通過(guò) ( y 軸動(dòng)作相對(duì)點(diǎn)到點(diǎn)的定位)和 (z軸動(dòng)作相對(duì)鉆孔)表示。剛體和柔性體的PKM模型運(yùn)動(dòng)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(dòng)作計(jì)劃和輸入力量還原。柔性體方程式被用來(lái)在刀具點(diǎn)到點(diǎn)定位之后的剩余振動(dòng)控制。</p><p>　　2.1.剛性連桿的PKM模型的運(yùn)動(dòng)方程式</p><p>　　機(jī)械裝置[12]的特點(diǎn)是使用了數(shù)字集成,刀具設(shè)備(含工作臺(tái)，主軸和刀具3部份)。它的運(yùn)動(dòng)學(xué)方程式的發(fā)展依下列各項(xiàng)。刀具的變位是</p><p><b>　　且</b></p

80、><p>　　其中b是點(diǎn)B和點(diǎn)C之間的距離,r是連桿AB的長(zhǎng)度(連桿AB、CD和CE的長(zhǎng)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(dòng)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(gè)類(lèi)型的方程式[13]。</p><p>　　其中t是系統(tǒng)的總動(dòng)能；和是總坐標(biāo)值和速度值;是總力對(duì)應(yīng)到的的值。k是坐標(biāo)系中總的獨(dú)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(dá)成</p><p>　　其中n是移動(dòng)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(biāo)；是PKM模

82、型中連桿i的旋轉(zhuǎn)角?？偭Φ闹低ㄟ^(guò)（9）決定</p><p>　　其中V是勢(shì)能， 是沒(méi)有勢(shì)能的力。為了對(duì)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(dá)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(yùn)動(dòng)學(xué)和動(dòng)力學(xué)方程式。</p><p>　　2.2.柔性連桿的PKM模型的動(dòng)作方程式</p&g

83、t;<p>　　順從的機(jī)械裝置的動(dòng)微分方程式能用有限的機(jī)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(biāo)系中的每個(gè)機(jī)械要素平移和旋轉(zhuǎn)變形表現(xiàn)的總坐標(biāo)值；{R}是總外力值，與{D}保持一致；n是坐標(biāo)的總數(shù)目值(機(jī)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(jī)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(jī)械要素的最初長(zhǎng)度。是(x,y)坐標(biāo)系統(tǒng)中表現(xiàn)的結(jié)點(diǎn)變位。機(jī)械要素的大眾基地和剛性基地將會(huì)是66個(gè)對(duì)稱(chēng)的矩陣，能從動(dòng)能和應(yīng)變能中得到，表達(dá)在公式（12）和（13）中 </p><p>　　其中t是動(dòng)能，U是機(jī)械要素的應(yīng)變能；是機(jī)械要素基本坐標(biāo)系中線性的123456和角變形節(jié)。詳細(xì)的推論能在[14]被發(fā)現(xiàn)。典型地，在有限

85、的機(jī)械要素分析中，一個(gè)順從的機(jī)械裝置是被離散成許多個(gè)機(jī)械要素的。每個(gè)機(jī)械要素與一個(gè)質(zhì)量和一個(gè)剛性母體有關(guān)。每個(gè)機(jī)械要素有它自己的基本坐標(biāo)系。我們結(jié)合機(jī)械要素質(zhì)量和所有機(jī)械要素的剛性矩陣運(yùn)行坐標(biāo)轉(zhuǎn)換時(shí)，必須把機(jī)械要素的基本坐標(biāo)系轉(zhuǎn)換成世界坐標(biāo)系，這就提供了系統(tǒng)質(zhì)量[M]和剛性[K]矩陣。在一個(gè)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(dòng)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(xiě)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(dá)所示</p><p>　　其中α和β是二個(gè)通常由實(shí)驗(yàn)決定的正系數(shù)。一個(gè)表現(xiàn)阻尼基地的交互方法[16] 表達(dá)成[C]如下</p><p>　　機(jī)械要素[C']被定義為,其中,和是[K]和[M]的機(jī)械要素, ζ是材料的阻尼比。</p><p>　　機(jī)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(dòng)作的機(jī)械要素的慣性力和力矩,m 是在機(jī)械要素上動(dòng)作的外力數(shù)目。機(jī)械要素的總力,組合構(gòu)成了系統(tǒng)總力{R}。系統(tǒng)動(dòng)作的第二次序普通微分方程式，如公式(11), 用一個(gè)數(shù)字能直接被整合的方法,就像是Runge- Kutta的方法那樣。對(duì)于我們研究的PKM,每個(gè)連桿被分離成15個(gè)機(jī)械要素結(jié)構(gòu)。Matlab和ADAMS軟件都被用來(lái)規(guī)劃和解決這些方程式。</p&

88、gt;<p>　　3.為鉆床輸入動(dòng)作計(jì)劃</p><p>　　假如我們知道鉆床理想的動(dòng)作功能。高質(zhì)量鉆床的關(guān)鍵是如何決定輸入電動(dòng)機(jī)動(dòng)作以便刀具的理想動(dòng)作能被了解。創(chuàng)建明白的輸入動(dòng)作功能時(shí)也為機(jī)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(guò)程能分為三個(gè)時(shí)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(bǔ)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?；谶@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(duì)應(yīng)入口期，中間期和

90、出口期的時(shí)間。vT2是退回的最大速度。T4 、T5和T6對(duì)應(yīng)的分別是加速的，持續(xù)的速度,和縮回操作時(shí)減速的時(shí)間。是一個(gè)單一鉆孔的周期。用一個(gè)數(shù)字為例,我們打算利用鉆一個(gè)25.4mm(1 在)深的孔，0.3s用來(lái)鉆孔，0.1s用來(lái)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(yùn)動(dòng)的圖解式。如果PKM中連桿長(zhǎng)度r=500mm，在鉆孔出發(fā)點(diǎn)時(shí)的角β =53 °，與理想刀具動(dòng)作相關(guān)的對(duì)

91、應(yīng)輸入電動(dòng)機(jī)的速度顯示在圖5中。一般的，曲線裝配方法能用來(lái)產(chǎn)生輸入運(yùn)動(dòng)的函數(shù)，但是依照?qǐng)D5中顯示的曲線形狀，我們創(chuàng)建的線性馬達(dá)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(jì)畫(huà)速度曲線時(shí),沒(méi)有不同的曲線能被發(fā)現(xiàn)，通過(guò)圖（5）中顯示的曲線。公式(18)由四個(gè)旋輪線的函數(shù)和兩個(gè)線性函數(shù)共六個(gè)函數(shù)組成。假如我們像公式（18）中描述的那樣控制兩個(gè)線性電動(dòng)機(jī)就會(huì)有相同的動(dòng)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(duì)誤差在圖6中被顯示,圖中最大的誤差不足8mm/s,相對(duì)誤差不足1.5%，在鉆孔的開(kāi)始和結(jié)束的位置,誤差是等于零的。這</p><p>　　些小的絕對(duì)和相對(duì)的誤差說(shuō)明了輸入動(dòng)作的產(chǎn)生并且容易接受。這些已知的函數(shù)能非常簡(jiǎn)單被整合進(jìn)PKM的控制運(yùn)算法則里。</p><p>　　4.輸入點(diǎn)到點(diǎn)的定位動(dòng)作計(jì)劃</p>

93、;<p>　　為了在整個(gè)的鉆孔過(guò)程中達(dá)到快速的和正確的定位運(yùn)動(dòng),應(yīng)該適當(dāng)?shù)赜?jì)劃輸入動(dòng)作，以便刀具尖端的剩余振動(dòng)能被最小化。照慣例加速度運(yùn)動(dòng)函數(shù)在機(jī)床中能被普遍用來(lái)驅(qū)動(dòng)軸的運(yùn)動(dòng)。雖然這種動(dòng)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(dòng)。舉個(gè)早先使用相同的PKM例子來(lái)說(shuō)。 一個(gè)FEA模型是通過(guò)有機(jī)械要素結(jié)構(gòu)的ADMAS建造起來(lái)的。定位動(dòng)作是Y軸的動(dòng)作, 也就是在同一方向上通過(guò)兩個(gè)線性電動(dòng)機(jī)的運(yùn)動(dòng)實(shí)現(xiàn)

94、的。</p><p>　　假如在二個(gè)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(dòng)機(jī)的輸入動(dòng)作在圖7中被顯示,其中最大的速度是 1500mm/s，定位時(shí)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(dòng)顯示在圖8中。</p><p>　　為了要減少剩余振動(dòng)和定位動(dòng)作的平穩(wěn),建了一個(gè)輸入動(dòng)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(dòng)決定的設(shè)計(jì)變數(shù)。選擇接口條件為，時(shí)，其中是點(diǎn)到點(diǎn)的定位時(shí)間，就產(chǎn)生了最初六個(gè)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(dú)立的設(shè)計(jì)變數(shù)，是刀具尖端在點(diǎn)到點(diǎn)定位之后的剩余振動(dòng)的最大變動(dòng)。設(shè)定</p><p>　　并從C6=0開(kāi)始計(jì)算，最佳導(dǎo)

96、致C6=-10mm/s。因</p><p>　　此 ?？梢钥匆?jiàn)最佳化計(jì)算使得變數(shù)C6的設(shè)計(jì)到了極限。如果給c6深層的釋放極限,那么目的將會(huì)在價(jià)值中連續(xù)減少,但是輸入動(dòng)作的加速度的最大價(jià)值將會(huì)變成太大。最佳化后的最佳輸入動(dòng)作在圖9中被顯示。對(duì)應(yīng)的刀具尖端的剩余振動(dòng)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(dòng)被減少到了30次。較小的剩余振動(dòng)將會(huì)對(duì)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(jì)算之中。剩余振動(dòng)在最佳化后將會(huì)仍然非常小，如果柔度是來(lái)自其他的來(lái)源，如壓力和驅(qū)動(dòng)系統(tǒng)，會(huì)比在圖10中顯示的結(jié)果高的10倍。</p><p>　　5.通過(guò)增加彈簧機(jī)械要素減少輸入動(dòng)力</p><p>　　減少輸入動(dòng)力是機(jī)床刀具設(shè)計(jì)中的眾多考慮之一。對(duì)于我們研究的PKM,兩個(gè)線性馬達(dá)是使PKM模型做鉆孔運(yùn)動(dòng)和定位運(yùn)動(dòng)的輸入設(shè)備。在選擇一個(gè)線性馬達(dá)時(shí)要考慮的一個(gè)因

98、數(shù)就是它需要的最大動(dòng)力。PKM模型的輸入動(dòng)力是由輸入力乘以二個(gè)線性的電動(dòng)機(jī)輸入速度決定的。省略接觸處的磨擦, 輸入力是通過(guò)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(gè)能量?jī)?chǔ)存的機(jī)械要素，例如加一個(gè)彈簧到PKM上，如果彈簧的剛性和最初的(自由的) 長(zhǎng)度被適當(dāng)?shù)剡x擇，或許能夠減少輸入動(dòng)力。減小最大輸入動(dòng)力導(dǎo)致用比較小的線性電動(dòng)機(jī)驅(qū)動(dòng)PKM模</p><p>　　型。這將會(huì)依次減少能量的損失和機(jī)床的結(jié)構(gòu)尺寸。一個(gè)

99、線性的彈簧可以被把加到二個(gè)連桿的中央如圖11(a)所示，或者在B點(diǎn)和C點(diǎn)加入兩個(gè)減震彈簧如圖11（b）所示。我們將會(huì)像舉例子一樣討論線性彈簧來(lái)說(shuō)明設(shè)計(jì)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(zhǎng)度和彈性模量。 線性馬達(dá)的輸入動(dòng)力取決于</p><p>　　為了要減少輸入動(dòng)力，我們依下列各項(xiàng)設(shè)定最佳數(shù)值:</p><p>

100、　　其中v是一個(gè)設(shè)計(jì)變數(shù)的矢量，包括彈簧長(zhǎng)度和彈性模量。</p><p>　　對(duì)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(jì)變數(shù)的初始數(shù)值被設(shè)定為。設(shè)計(jì)變數(shù)的范圍被設(shè)定為，。PKM模型是通過(guò)公式（18）描述的輸入動(dòng)作函數(shù)驅(qū)動(dòng)的。經(jīng)過(guò)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(dòng)機(jī)</p><p>　　和沒(méi)有優(yōu)化彈簧的線性電動(dòng)機(jī)的輸入動(dòng)力

101、如圖12所示,圖中實(shí)線表示沒(méi)有彈簧的</p><p>　　輸入動(dòng)力，虛線表示用了優(yōu)化彈簧的輸入動(dòng)力。從結(jié)果中可以看出，右邊線性馬達(dá)的最大輸入動(dòng)力從122.37降到了70.43W，減少量達(dá)到了42.45%。對(duì)于左邊的線性馬達(dá),最大的輸入動(dòng)力從114.44降到了62.72W，減少量達(dá)到了45.19%。通過(guò)增加一個(gè)彈簧機(jī)械要素來(lái)減少機(jī)器輸入動(dòng)力，實(shí)現(xiàn)熱交換的方法被證實(shí)了。減震彈簧可能被用來(lái)減少慣性作用和彈簧附屬件的尺寸