外文翻譯步進(jìn)電機(jī)的振蕩不穩(wěn)定以及控制

1、 淮 陰 工 學(xué) 院畢業(yè)設(shè)計(論文)外文資料翻譯系 （院）：江淮學(xué)院專 業(yè)：電氣工程及其自動化姓 名：學(xué) 號：外文出處：Nonlinear Dynamics18:383-404,1999(用外文寫)附 件：1.外文資料翻譯譯文；2.外文原文。指導(dǎo)教師評語： 外文資料翻譯內(nèi)容基本接近課題，具有一定的外文檢索能力，中文譯文語句基本通順，但有個別語句不符合中文習(xí)慣表達(dá)。2009年3月15日簽名： （手寫簽名） 注：請將該封面與附件裝訂成冊。附件1：外文資料翻譯譯文步進(jìn)電機(jī)的振蕩、不穩(wěn)定以及控制摘要：本文介紹了一種分析永磁步進(jìn)電機(jī)不穩(wěn)定性的新穎方法。結(jié)果表明，該種電機(jī)有兩種類型的不穩(wěn)定現(xiàn)象：中頻振蕩和

2、高頻不穩(wěn)定性。非線性分叉理論是用來說明局部不穩(wěn)定和中頻振蕩運動之間的關(guān)系。一種新型的分析介紹了被確定為高頻不穩(wěn)定性的同步損耗現(xiàn)象。在相間分界線和吸引子的概念被用于導(dǎo)出數(shù)量來評估高頻不穩(wěn)定性。通過使用這個數(shù)量就可以很容易地估計高頻供應(yīng)的穩(wěn)定性。此外，還介紹了穩(wěn)定性理論。廣義的方法給出了基于反饋理論的穩(wěn)定問題的分析。結(jié)果表明，中頻穩(wěn)定度和高頻穩(wěn)定度可以提高狀態(tài)反饋。關(guān)鍵詞：步進(jìn)電機(jī)，不穩(wěn)定，非線性，狀態(tài)反饋。1. 介紹步進(jìn)電機(jī)是將數(shù)字脈沖輸入轉(zhuǎn)換為模擬角度輸出的電磁增量運動裝置。其內(nèi)在的步進(jìn)能力允許沒有反饋的精確位置控制。 也就是說，他們可以在開環(huán)模式下跟蹤任何步階位置，因此執(zhí)行位置控制是不需要任

3、何反饋的。步進(jìn)電機(jī)提供比直流電機(jī)每單位更高的峰值扭矩;此外，它們是無電刷電機(jī)，因此需要較少的維護(hù)。所有這些特性使得步進(jìn)電機(jī)在許多位置和速度控制系統(tǒng)的選擇中非常具有吸引力，例如如在計算機(jī)硬盤驅(qū)動器和打印機(jī)，代理表，機(jī)器人中的應(yīng)用等.盡管步進(jìn)電機(jī)有許多突出的特性，他們?nèi)栽馐苷袷幓虿环€(wěn)定現(xiàn)象。這種現(xiàn)象嚴(yán)重地限制其開環(huán)的動態(tài)性能和需要高速運作的適用領(lǐng)域。 這種振蕩通常在步進(jìn)率低于1000脈沖/秒的時候發(fā)生，并已被確認(rèn)為中頻不穩(wěn)定或局部不穩(wěn)定1，或者動態(tài)不穩(wěn)定2。此外，步進(jìn)電機(jī)還有另一種不穩(wěn)定現(xiàn)象，也就是在步進(jìn)率較高時，即使負(fù)荷扭矩小于其牽出扭矩，電動機(jī)也常常不同步。該文中將這種現(xiàn)象確定為高頻不穩(wěn)定性，

4、因為它以比在中頻振蕩現(xiàn)象中發(fā)生的頻率更高的頻率出現(xiàn)。高頻不穩(wěn)定性不像中頻不穩(wěn)定性那樣被廣泛接受，而且還沒有一個方法來評估它。中頻振蕩已經(jīng)被廣泛地認(rèn)識了很長一段時間，但是，一個完整的了解還沒有牢固確立。這可以歸因于支配振蕩現(xiàn)象的非線性是相當(dāng)困難處理的。大多數(shù)研究人員在線性模型基礎(chǔ)上分析它1。盡管在許多情況下，這種處理方法是有效的或有益的，但為了更好地描述這一復(fù)雜的現(xiàn)象，在非線性理論基礎(chǔ)上的處理方法也是需要的。例如，基于線性模型只能看到電動機(jī)在某些供應(yīng)頻率下轉(zhuǎn)向局部不穩(wěn)定，并不能使被觀測的振蕩現(xiàn)象更多深入。事實上，除非有人利用非線性理論，否則振蕩不能評估。窗體頂端窗體底端因此，在非線性動力學(xué)上利用

5、被發(fā)展的數(shù)學(xué)理論處理振蕩或不穩(wěn)定是很重要的。值得指出的是，Taft和Gauthier3，還有Taft和Harned4使用的諸如在振蕩和不穩(wěn)定現(xiàn)象的分析中的極限環(huán)和分界線之類的數(shù)學(xué)概念，并取得了關(guān)于所謂非同步現(xiàn)象的一些非常有啟發(fā)性的見解。盡管如此，在這項研究中仍然缺乏一個全面的數(shù)學(xué)分析。本文一種新的數(shù)學(xué)分被開發(fā)了用于分析步進(jìn)電機(jī)的振動和不穩(wěn)定性。本文的第一部分討論了步進(jìn)電機(jī)的穩(wěn)定性分析。結(jié)果表明，中頻振蕩可定性為一種非線性系統(tǒng)的分叉現(xiàn)象（霍普夫分叉）。本文的貢獻(xiàn)之一是將中頻振蕩與霍普夫分叉聯(lián)系起來，從而霍普夫理論從理論上證明了振蕩的存在性。高頻不穩(wěn)定性也被詳細(xì)討論了，并介紹了一種新型的量來評估高

6、頻穩(wěn)定。這個量是很容易計算的，而且可以作為一種標(biāo)準(zhǔn)來預(yù)測高頻不穩(wěn)定性的發(fā)生。在一個真實電動機(jī)上的實驗結(jié)果顯示了該分析工具的有效性。本文的第二部分通過反饋討論了步進(jìn)電機(jī)的穩(wěn)定性控制。一些設(shè)計者已表明，通過調(diào)節(jié)供應(yīng)頻率 5 ，中頻不穩(wěn)定性可以得到改善。特別是Pickup和Russell 6，7都在頻率調(diào)制的方法上提出了詳細(xì)的分析。在他們的分析中，雅可比級數(shù)用于解決常微分方程和一組數(shù)值有待解決的非線性代數(shù)方程組。此外，他們的分析負(fù)責(zé)的是雙相電動機(jī)，因此，他們的結(jié)論不能直接適用于我們需要考慮三相電動機(jī)的情況。在這里，我們提供一個沒有必要處理任何復(fù)雜數(shù)學(xué)的更簡潔的穩(wěn)定步進(jìn)電機(jī)的分析。在這種分析中，使用的

7、是d-q模型的步進(jìn)電機(jī)。由于雙相電動機(jī)和三相電動機(jī)具有相同的d-q模型，因此，這種分析對雙相電動機(jī)和三相電動機(jī)都有效。迄今為止，人們僅僅認(rèn)識到用調(diào)制方法來抑制中頻振蕩。本文結(jié)果表明，該方法不僅對改善中頻穩(wěn)定性有效，而且對改善高頻穩(wěn)定性也有效。2. 動態(tài)模型的步進(jìn)電機(jī)本文件中所考慮的步進(jìn)電機(jī)由一個雙相或三相繞組的跳動定子和永磁轉(zhuǎn)子組成。一個極對三相電動機(jī)的簡化原理如圖1所示。步進(jìn)電機(jī)通常是由被脈沖序列控制產(chǎn)生矩形波電壓的電壓源型逆變器供給的。這種電動機(jī)用本質(zhì)上和同步電動機(jī)相同的原則進(jìn)行作業(yè)。步進(jìn)電機(jī)主要作業(yè)方式之一是保持提供電壓的恒定以及脈沖頻率在非常廣泛的范圍上變化。在這樣的操作條件下，振動和

8、不穩(wěn)定的問題通常會出現(xiàn)。圖1.三相電動機(jī)的圖解模型 用qd框架參考轉(zhuǎn)換建立了一個三相步進(jìn)電機(jī)的數(shù)學(xué)模型 。下面給出了三相繞組電壓方程va = Ria + L*dia /dt M*dib/dt M*dic/dt + dpma/dt ,vb = Rib + L*dib/dt M*dia/dt M*dic/dt + dpmb/dt ,vc = Ric + L*dic/dt M*dia/dt M*dib/dt + dpmc/dt , (1) 其中R和L分別是相繞組的電阻和感應(yīng)線圈，并且M是相繞組之間的互感線圈。pma, pmb and pmc 是應(yīng)歸于永磁體 的相的磁通，且可以假定為轉(zhuǎn)子位置的正弦函數(shù)

9、如下pma = 1 sin(N),pmb = 1 sin(N 2 QUOTE /3),pmc = 1 sin(N - 2 QUOTE /3), (2)其中N是轉(zhuǎn)子齒數(shù)。本文中強調(diào)的非線性由上述方程所代表，即磁通是轉(zhuǎn)子位置的非線性函數(shù)。使用Q ,d轉(zhuǎn)換，將參考框架由固定相軸變換成隨轉(zhuǎn)子移動的軸（參見圖2）。矩陣從a,b,c框架轉(zhuǎn)換成q,d框架變換被給出了8 (3)例如，給出了q,d參考里的電壓 (4)在a,b,c參考中，只有兩個變量是獨立的（ia + ib + ic = 0），因此，上面提到的由三個變量轉(zhuǎn)化為兩個變量是允許的。在電壓方程（1）中應(yīng)用上述轉(zhuǎn)換，在q,d框架中獲得轉(zhuǎn)換后的電壓方程為v

10、q = Riq + L1*diq/dt + NL1id + N1,vd = Rid + L1*did/dt NL1iq, (5) 圖2，a,b,c和d,q參考框架其中L1 = L + M，且是電動機(jī)的速度。有證據(jù)表明,電動機(jī)的扭矩有以下公式T = 3/2N1iq . (6)轉(zhuǎn)子電動機(jī)的方程為J*d/dt = 3/2*N1iq Bf Tl , (7) 如果Bf是粘性摩擦系數(shù)，和Tl代表負(fù)荷扭矩（在本文中假定為恒定）。為了構(gòu)成完整的電動機(jī)的狀態(tài)方程，我們需要另一種代表轉(zhuǎn)子位置的狀態(tài)變量。為此，通常使用滿足下列方程的所謂的負(fù)荷角8D/dt = 0 , (8) 其中0是電動機(jī)的穩(wěn)態(tài)轉(zhuǎn)速。方程（5），（

11、7），和（8）構(gòu)成電動機(jī)的狀態(tài)空間模型，其輸入變量是電壓vq和vd.如前所述，步進(jìn)電機(jī)由逆變器供給，其輸出電壓不是正弦電波而是方波。然而，由于相比正弦情況下非正弦電壓不能很大程度地改變振蕩特性和不穩(wěn)定性（如將在第3部分顯示的，振蕩是由于電動機(jī)的非線性），為了本文的目的我們可以假設(shè)供給電壓是正弦波。根據(jù)這一假設(shè)，我們可以得到如下的vq和vdvq = Vmcos(N) ,vd = Vmsin(N) , (9) 其中Vm是正弦波的最大值。上述方程，我們已經(jīng)將輸入電壓由時間函數(shù)轉(zhuǎn)變?yōu)闋顟B(tài)函數(shù)，并且以這種方式我們可以用自控系統(tǒng)描繪出電動機(jī)的動態(tài)，如下所示。這將有助于簡化數(shù)學(xué)分析。根據(jù)方程（5），（7），

12、和（8），電動機(jī)的狀態(tài)空間模型可以如下寫成矩陣式 = F(X,u) = AX + Fn(X) + Bu , (10) 其中X = iq id T, u = 1 Tl T 定義為輸入，且1 = N0 是供應(yīng)頻率。輸入矩陣B被定義為矩陣A是F(.)的線性部分，如下Fn(X)代表了F(.)的線性部分，如下輸入端u獨立于時間，因此，方程（10）是獨立的。在F(X,u)中有三個參數(shù)，它們是供應(yīng)頻率1，電源電壓幅度Vm和負(fù)荷扭矩Tl。這些參數(shù)影響步進(jìn)電機(jī)的運行情況。在實踐中，通常用這樣一種方式來驅(qū)動步進(jìn)電機(jī)，即用因指令脈沖而變化的供應(yīng)頻率1來控制電動機(jī)的速度，而電源電壓保持不變。因此，我們應(yīng)研究參數(shù)1的影

13、響。3.分叉和中頻振蕩，設(shè)=0，得出方程（10）的平衡且是它的相角， = arctan(1L1/R) . (16) 方程（12）和（13）顯示存在著多重均衡，這意味著這些平衡永遠(yuǎn)不能全局穩(wěn)定。人們可以看到，如方程（12）和（13）所示有兩組平衡。第一組由方程（12）對應(yīng)電動機(jī)的實際運行情況來代表。第二組由方程（13）總是不穩(wěn)定且不涉及到實際運作情況來代表。在下面，我們將集中精力在由方程（12）代表的平衡上。 附件2：外文原文 Oscillation, Instability and Control of Stepper MotorsLIYU CAO and HOWARD M. SCHWARTZ

14、Department of Systems and Computer Engineering, Carleton University, 1125 Colonel By Drive,Ottawa, ON K1S 5B6, Canada(Received: 18 February 1998; accepted: 1 December 1998)Abstract. A novel approach to analyzing instability in permanent-magnet stepper motors is presented. It is shown that there are

15、two kinds of unstable phenomena in this kind ofmotor: mid-frequency oscillation and high-frequency instability. Nonlinear bifurcation theory is used to illustrate the relationship between local instability and midfrequencyoscillatory motion. A novel analysis is presented to analyze the loss of synch

16、ronism phenomenon, which is identified as high-frequency instability. The concepts of separatrices and attractors in phase-space are used to derive a quantity to evaluate the high-frequency instability. By using this quantity one can easily estimate the stability for high supply frequencies. Further

17、more, a stabilization method is presented. A generalized approach to analyze the stabilization problem based on feedback theory is given. It is shown that the mid-frequency stabilityand the high-frequency stability can be improved by state feedback. Keywords: Stepper motors, instability, nonlinearit

18、y, state feedback.1. IntroductionStepper motors are electromagnetic incremental-motion devices which convert digital pulse inputs to analog angle outputs. Their inherent stepping ability allows for accurate position control without feedback. That is, they can track any step position in open-loop mod

19、e, consequently no feedback is needed to implement position control. Stepper motors deliver higher peak torque per unit weight than DC motors; in addition, they are brushless machines and therefore require less maintenance. All of these properties have made stepper motors a very attractive selection

20、 in many position and speed control systems, such as in computer hard disk drivers and printers, XY-tables, robot manipulators, etc.Although stepper motors have many salient properties, they suffer from an oscillation or unstable phenomenon. This phenomenon severely restricts their open-loop dynamic

21、 performance and applicable area where high speed operation is needed. The oscillation usually occurs at stepping rates lower than 1000 pulse/s, and has been recognized as a mid-frequency instability or local instability 1, or a dynamic instability 2. In addition, there is another kind of unstable p

22、henomenon in stepper motors, that is, the motors usually lose synchronism at higher stepping rates, even though load torque is less than their pull-out torque. This phenomenon is identified as high-frequency instability in this paper, because it appears at much higher frequencies than the frequencie

23、s at which the mid-frequency oscillation occurs. The high-frequency instability has not been recognized as widely as mid-frequency instability, and there is not yet a method to evaluate it.Mid-frequency oscillation has been recognized widely for a very long time, however, a complete understanding of

24、 it has not been well established. This can be attributed to the nonlinearity that dominates the oscillation phenomenon and is quite difficult to deal with.384 L. Cao and H. M. SchwartzMost researchers have analyzed it based on a linearized model 1. Although in many cases, this kind of treatments is

25、 valid or useful, a treatment based on nonlinear theory is needed in order to give a better description on this complex phenomenon. For example, based on a linearized model one can only see that the motors turn to be locally unstable at some supplyfrequencies, which does not give much insight into t

26、he observed oscillatory phenomenon. In fact, the oscillation cannot be assessed unless one uses nonlinear theory.Therefore, it is significant to use developed mathematical theory on nonlinear dynamics to handle the oscillation or instability. It is worth noting that Taft and Gauthier 3, and Taft and

27、 Harned 4 used mathematical concepts such as limit cycles and separatrices in the analysis of oscillatory and unstable phenomena, and obtained some very instructive insights into the socalled loss of synchronous phenomenon. Nevertheless, there is still a lack of a comprehensive mathematical analysis

28、 in this kind of studies. In this paper a novel mathematical analysis is developed to analyze the oscillations and instability in stepper motors.The first part of this paper discusses the stability analysis of stepper motors. It is shown that the mid-frequency oscillation can be characterized as a b

29、ifurcation phenomenon (Hopf bifurcation) of nonlinear systems. One of contributions of this paper is to relate the midfrequency oscillation to Hopf bifurcation, thereby, the existence of the oscillation is provedtheoretically by Hopf theory. High-frequency instability is also discussed in detail, an

30、d a novel quantity is introduced to evaluate high-frequency stability. This quantity is very easyto calculate, and can be used as a criteria to predict the onset of the high-frequency instability. Experimental results on a real motor show the efficiency of this analytical tool.The second part of thi

31、s paper discusses stabilizing control of stepper motors through feedback. Several authors have shown that by modulating the supply frequency 5, the midfrequencyinstability can be improved. In particular, Pickup and Russell 6, 7 have presented a detailed analysis on the frequency modulation method. I

32、n their analysis, Jacobi series was used to solve a ordinary differential equation, and a set of nonlinear algebraic equations had to be solved numerically. In addition, their analysis is undertaken for a two-phase motor, and therefore, their conclusions cannot applied directly to our situation, whe

33、re a three-phase motor will be considered. Here, we give a more elegant analysis for stabilizing stepper motors, where no complex mathematical manipulation is needed. In this analysis, a dq model of stepper motors is used. Because two-phase motors and three-phase motors have the same qd model and th

34、erefore, the analysis is valid for both two-phase and three-phase motors. Up to date, it is only recognized that the modulation method is needed to suppress the midfrequency oscillation. In this paper, it is shown that this method is not only valid to improve mid-frequency stability, but also effect

35、ive to improve high-frequency stability.2. Dynamic Model of Stepper MotorsThe stepper motor considered in this paper consists of a salient stator with two-phase or threephase windings, and a permanent-magnet rotor. A simplified schematic of a three-phase motor with one pole-pair is shown in Figure 1

36、. The stepper motor is usually fed by a voltage-source inverter, which is controlled by a sequence of pulses and produces square-wave voltages. Thismotor operates essentially on the same principle as that of synchronous motors. One of major operating manner for stepper motors is that supplying volta

37、ge is kept constant and frequencyof pulses is changed at a very wide range. Under this operating condition, oscillation and instability problems usually arise.Figure 1. Schematic model of a three-phase stepper motor.A mathematical model for a three-phase stepper motor is established using qd framere

38、ference transformation. The voltage equations for three-phase windings are given byva = Ria + L*dia /dt M*dib/dt M*dic/dt + dpma/dt ,vb = Rib + L*dib/dt M*dia/dt M*dic/dt + dpmb/dt ,vc = Ric + L*dic/dt M*dia/dt M*dib/dt + dpmc/dt ,where R and L are the resistance and inductance of the phase windings

39、, and M is the mutual inductance between the phase windings. _pma, _pmb and _pmc are the flux-linkages of thephases due to the permanent magnet, and can be assumed to be sinusoid functions of rotor position _ as followpma = 1 sin(N),pmb = 1 sin(N 2 QUOTE /3),pmc = 1 sin(N - 2 QUOTE /3),where N is nu

40、mber of rotor teeth. The nonlinearity emphasized in this paper is represented by the above equations, that is, the flux-linkages are nonlinear functions of the rotor position.By using the q; d transformation, the frame of reference is changed from the fixed phase axes to the axes moving with the rot

41、or (refer to Figure 2). Transformation matrix from the a; b; c frame to the q; d frame is given by 8For example, voltages in the q; d reference are given byIn the a; b; c reference, only two variables are independent (ia C ib C ic D 0); therefore, the above transformation from three variables to two

42、 variables is allowable. Applying the abovetransformation to the voltage equations (1), the transferred voltage equation in the q; d frame can be obtained asvq = Riq + L1*diq/dt + NL1id + N1,vd=Rid + L1*did/dt NL1iq, (5)Figure 2. a, b, c and d, q reference frame.where L1 D L CM, and ! is the speed o

43、f the rotor.It can be shown that the motors torque has the following form 2T = 3/2N1iqThe equation of motion of the rotor is written asJ*d/dt = 3/2*N1iq Bf Tl ,where Bf is the coefficient of viscous friction, and Tl represents load torque, which is assumed to be a constant in this paper.In order to

44、constitute the complete state equation of the motor, we need another state variable that represents the position of the rotor. For this purpose the so called load angle _ 8 is usually used, which satisfies the following equationD/dt = 0 ,where !0 is steady-state speed of the motor. Equations (5), (7

45、), and (8) constitute the statespace model of the motor, for which the input variables are the voltages vq and vd. As mentioned before, stepper motors are fed by an inverter, whose output voltages are not sinusoidal but instead are square waves. However, because the non-sinusoidal voltages do not ch

46、ange the oscillation feature and instability very much if compared to the sinusoidal case (as will be shown in Section 3, the oscillation is due to the nonlinearity of the motor), for the purposes of this paper we can assume the supply voltages are sinusoidal. Under this assumption, we can get vq an

47、d vd as followsvq = Vmcos(N) ,vd = Vmsin(N) ,where Vm is the maximum of the sine wave. With the above equation, we have changed the input voltages from a function of time to a function of state, and in this way we can represent the dynamics of the motor by a autonomous system, as shown below. This w

48、ill simplify the mathematical analysis.From Equations (5), (7), and (8), the state-space model of the motor can be written in a matrix form as follows = F(X,u) = AX + Fn(X) + Bu , (10)where X D Tiq id ! _UT , u D T!1 TlUT is defined as the input, and !1 D N!0 is the supply frequency. The input matri

49、x B is defined byThe matrix A is the linear part of F._/, and is given byrepresents the nonlinear part of F._/, and is given byThe input term u is independent of time, and therefore Equation (10) is autonomous.There are three parameters in F.X;u/, they are the supply frequency !1, the supply voltage

50、 magnitude Vm and the load torque Tl . These parameters govern the behaviour of the stepper motor. In practice, stepper motors are usually driven in such a way that the supply frequency !1 is changed by the command pulse to control the motors speed, while the supply voltage is kept constant. Therefo

51、re, we shall investigate the effect of parameter !1.3. Bifurcation and Mid-Frequency OscillationBy setting ! D !0, the equilibria of Equation (10) are given asand is its phase angle defined by = arctan(1L1/R) . (16) Equations (12) and (13) indicate that multiple equilibria exist, which means that th

52、ese equilibria can never be globally stable. One can see that there are two groups of equilibria as shown in Equations (12) and (13). The first group represented by Equation (12) corresponds to the real operating conditions of the motor. The second group represented by Equation (13) is always unstab

53、le and does not relate to the real operating conditions. In the following, we will concentrate on the equilibria represented by Equation (12).付：外文翻譯 電火花加工 電火花加工法對加工超韌性的導(dǎo)電材料（如新的太空合金）特別有價值。這些金屬很難用常規(guī)方法加工，用常規(guī)的切削刀具不可能加工極其復(fù)雜的形狀，電火花加工使之變得相對簡單了。在金屬切削工業(yè)中，這種加工方法正不斷尋找新的應(yīng)用領(lǐng)域。塑料工業(yè)已廣泛使用這種方法，如在鋼制模具上加工幾乎是任何形狀的模腔。 電

54、火花加工法是一種受控制的金屬切削技術(shù)，它使用電火花切除（侵蝕）工件上的多余金屬，工件在切削后的形狀與刀具（電極）相反。切削刀具用導(dǎo)電材料（通常是碳）制造。電極形狀與所需型腔想匹配。工件與電極都浸在不導(dǎo)電的液體里，這種液體通常是輕潤滑油。它應(yīng)當(dāng)是點的不良導(dǎo)體或絕緣體。 用伺服機(jī)構(gòu)是電極和工件間的保持0.00050.001英寸（0.010.02mm）的間隙，以阻止他們相互接觸。頻率為20000Hz左右的低電壓大電流的直流電加到電極上，這些電脈沖引起火花，跳過電極與工件的見的不導(dǎo)電的液體間隙。在火花沖擊的局部區(qū)域，產(chǎn)生了大量的熱量，金屬融化了，從工件表面噴出融化金屬的小粒子。不斷循環(huán)著的不導(dǎo)電的液體

55、，將侵蝕下來的金屬粒子帶走，同時也有助于驅(qū)散火花產(chǎn)生的熱量。 在最近幾年，電火花加工的主要進(jìn)步是降低了它加工后的表面粗糙度。用低的金屬切除率時，表面粗糙度可達(dá)20.10vin)。用高的金屬切除率如高達(dá)15in3/h(245.8cm3/h)時，表面粗糙度為1000vin.(25vm)。 需要的表面粗糙度的類型，決定了能使用的安培數(shù),電容,頻率和電壓值?？焖偾谐饘伲ù智邢鳎r，用大電流,低頻率,高電容和最小的間隙電壓。緩慢切除金屬（精切削）和需獲得高的表面光潔度時，用小電流,高頻率,低電容和最高的間隙電壓。 與常規(guī)機(jī)加工方法相比，電火花加工有許多優(yōu)點。 1 . 不論硬度高低，只要是導(dǎo)電材料都能對

56、其進(jìn)行切削。對用常規(guī)方法極難切削的硬質(zhì)合金和超韌性的太空合金，電火化加工特別有價值。 2 . 工件可在淬火狀態(tài)下加工，因克服了由淬火引起的變形問題。 3 . 很容易將斷在工件中的絲錐和鉆頭除。 4 . 由于刀具（電極）從未與工件接觸過，故工件中不會產(chǎn)生應(yīng)力。 5 . 加工出的零件無毛刺。 6 . 薄而脆的工件很容易加工，且無毛刺。 7 . 對許多類型的工件，一般不需第二次精加工。 8 .隨著金屬的切除，伺服機(jī)構(gòu)使電極自動向工件進(jìn)給。 9 .一個人可同時操作幾臺電火花加工機(jī)床。 10.能相對容易地從實心坯料上，加工出常規(guī)方法不可能加工出來的極復(fù)雜的形狀。 11.能用較低價格加工出較好的模具。12

57、.可用沖頭作電極，在陰模板上復(fù)制其形狀，并留有必須的間隙。Electrical discharge machiningElectrical discharge machining has proved especially valuable in the machining of super-tough, electrically conductive materials such as the new space-age alloys. These metals would have been difficult to machine by conventional methods, but

58、 EDM has made it relatively simple to machine intricate shapes that would be impossible to produce with conventional cutting tools. This machining process is continually finding further applications in the metal-cutting industry. It is being used extensively in the plastic industry to produce caviti

59、es of almost any shape in the steel molds. Electrical discharge machining is a controlled metal removal technique whereby an electric spark is used to cut (erode) the workpiece, which takes a shape opposite to that of the cutting tool or electrode. The cutting tool (electrode) is made from electrica

60、lly conductive material, usually carbon. The electrode, made to the shape of the cavity required, and the workpiece are both submerged in a dielectric fluid, which is generally a light lubricating oil. This dielectric fluid should be a nonconductor (or poor conductor) of electricity. A servo mechani