外文翻譯--機電一體化的做法

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1、 機電一體化的做法 機電一體化的做法 1 數(shù)控機床科普知識 數(shù)字控制機床是用數(shù)字代碼形式的信息(程序指令)，控制刀具按給定的工作程序、運動速度和軌跡進行自動加工的機床，簡稱數(shù)控機床。數(shù)控機床具有廣泛的適應性，加工對象改變時只需要改變輸入的程序指令；加工性能比一般自動機床高，可以精確加工復雜型面，因而適合于加工中小批量、改型頻繁、精度要求高、形狀又較復雜的工件，并能獲得良好的經(jīng)濟效果。 隨著數(shù)控技術的發(fā)展，采用數(shù)控系統(tǒng)的機床品種日益增多，有車床、銑床、鏜床、鉆床、磨床、齒輪加工機床和電火花加工機床等。此外還有能自動換刀、一次裝卡進行多工序加工的加工中心、車削中心等。 1948

2、年，美國帕森斯公司接受美國空軍委托，研制飛機螺旋槳葉片輪廓樣板的加工設備。由于樣板形狀復雜多樣，精度要求高，一般加工設備難以適應，于是提出計算機控制機床的設想。1949年，該公司在美國麻省理工學院伺服機構研究室的協(xié)助下，開始數(shù)控機床研究，并于1952年試制成功第一臺由大型立式仿形銑床改裝而成的三坐標數(shù)控銑床，不久即開始正式生產。 當時的數(shù)控裝置采用電子管元件，體積龐大，價格昂貴，只在航空工業(yè)等少數(shù)有特殊需要的部門用來加工復雜型面零件；1959年，制成了晶體管元件和印刷電路板，使數(shù)控裝置進入了第二代，體積縮小，成本有所下降；1960年以后，較為簡單和經(jīng)濟的點位控制數(shù)控鉆床，和直線控制數(shù)控銑床得

3、到較快發(fā)展，使數(shù)控機床在機械制造業(yè)各部門逐步獲得推廣。 為了保證機床具有很大的工藝適應性能和連續(xù)穩(wěn)定工作的能力，數(shù)控機床結構設計的特點是具有足夠的剛度、精度、抗振性、熱穩(wěn)定性和精度保持性。進給系統(tǒng)的機械傳動鏈采用滾珠絲杠、靜壓絲杠和無間隙齒輪副等，以盡量減小反向間隙。機床采用塑料減摩導軌、滾動導軌或靜壓導軌，以提高運動的平穩(wěn)性并使低速運動時不出現(xiàn)爬行現(xiàn)象。 由于采用了寬調速的進給伺服電動機和寬調速的主軸電動機，可以不用或少用齒輪傳動和齒輪變速，這就簡化了機床的傳動機構。機床布局便于排屑和工件裝卸，部分數(shù)控機床帶有自動排屑器和自動工件交換裝置。大部分數(shù)控機床采用具有微處理器的可編程序控制器，

4、以代替強電柜中大量的繼電器，提高了機床強電控制的可靠性和靈活性。 隨著微電子技術、計算機技術和軟件技術的迅速發(fā)展，數(shù)控機床的控制系統(tǒng)日益趨向于小型化和多功能化，具備完善的自診斷功能；可靠性也大大提高；數(shù)控系統(tǒng)本身將普遍實現(xiàn)自動編程。未來數(shù)控機床的類型將更加多樣化，多工序集中加工的數(shù)控機床品種越來越多；激光加工等技術將應用在切削加工機床上，從而擴大多工序集中的工藝范圍；數(shù)控機床的自動化程度更加提高，并具有多種監(jiān)控功能，從而形成一個柔性制造單元，更加便于納入高度自動化的柔性制造系統(tǒng)中。 眾所周知，一部機器的基本構成包括原動機、傳動部分、執(zhí)行部分和控制部分。其中傳動部分是絕大多數(shù)機器不可缺少的重

5、要組成部分。從原動機到工作機部分的變速、改變運動方向、改變運動方式、動力與運動的傳遞分配等等功能。都是由傳動裝置完成的。在一些機器中(如機床、汽車)中傳動裝置占整機的大部分，所以機器的工作性能和運轉費用在很大程度上取決于傳動部分(傳動裝置)的優(yōu)劣。因此，為了適應市場對機械產品的要求，提高傳動裝置的設計水平具有重要的意義。 長期以來，我國在設計機械產品時，一般沿用傳統(tǒng)的設計方法，機械產品的設計是一個病態(tài)結構的、反復迭代的復雜過程，耗費設計者大量的時間和精力，因此，無論從設計性能和設計速度上均遠遠滿足不了用戶的要求，形成了先進產品要求與落后的設計方法上的矛盾。同時，市場競爭的加劇，亦要求產品朝著

6、高質量、低成本、短周期的方向發(fā)展RI。目前，機械中常用傳動的設計方法常用理論設計法。它是根據(jù)現(xiàn)有的科學技術理論及實踐知識而進行的設計，所以，常用的設計計算公式多是在某些假設的條件下進行理論推導，再引入一系列的修正系數(shù)，而得到的半理論半經(jīng)驗公式。利用這些公式手算時，需要查一系列的有關表格或線圖來確定修正系數(shù)和某些參數(shù)，過程煩瑣費時:尤其是機械設計是一個不斷修改、不斷完善的過程。無數(shù)事實證明，富有經(jīng)驗的優(yōu)秀設計師往往能比剛出校門、同樣富有才華的設計師以較快的速度設計出較好的產品來。專家系統(tǒng)技術能幫助我們實現(xiàn)專家設計經(jīng)驗的歸納和利用，使經(jīng)驗的繼承和發(fā)展大大超越了“師徒之間”的時空限制，從而大大推進了

7、設計質量和效率的提高，因而為使傳動的設計適應于產品的市場需求，開發(fā)機械傳動設計專家系統(tǒng)，使傳動設計速度快、計算準確、方案優(yōu)化成為必然的趨勢。 2 介紹 在這個文件中，機電一體化采取的是為端銑操作數(shù)控銑床制定一個數(shù)學模型，并模擬其行為。數(shù)學模型的伺服電機控制XY工作臺。其它方面的發(fā)展是同提出的為端銑操作的模型整合在一起，MATLAB是用來模擬仿真的。實驗的初衷是建立在XY工作臺上履行銑削操作。仿真的結果驗證了實驗結果。這樣的數(shù)學模型可用于評價一個新的設計。因此，一個新的設計在市場上將導致時間和成本大幅度減少。 日本在20世紀80年代已經(jīng)介紹了機電一體化技術是一個概念，盡管人民提及任何系

8、統(tǒng)都具有機械、電氣、電子元件等，例如洗衣機、復印機、數(shù)控機床等，都具有機電一體化系統(tǒng)，是一種真正的機電一體化設計原理。在傳統(tǒng)的設計方法中，系統(tǒng)的組成部分都有各自的專家來完成。例如：一名機械工程師設計機械部分，而電機工程師則設計電器元件等等。因為每個設計師都有一定的安全因素要取決于其它無知的領域的合作，從而使整體的價格變大，且系統(tǒng)變得龐大和昂貴。在機電一體化的設計方法中，整個系統(tǒng)被認為要顧及到各個部件，無論是機械、電氣、還是電子設備。由于整體的安全因素小了，因此，該系統(tǒng)的設計尺寸和費用減少了。 在這個文件中，機電控制的方法以研究數(shù)控機床為主，在援助過程中新設計了一種數(shù)控機床就座。這項研究需要模

9、型的加工過程。數(shù)控端銑的特點在于以正規(guī)的序列個別消減，相當于每齒的接觸。這些消減多次強烈重疊。都是為了預知這些瞬時切削力、機械理論的運用等。在不同刀具的切削點，該力模型的發(fā)展需要工作臺中的表和刀具作為輸入?yún)?shù)，并給出了瞬時力作為輸出。機械傳動元件中組成XY工作臺的電機軸和滾珠絲杠也要考慮在內。在這個數(shù)學模型中，在機械零件的精度方面，由于剛度力學起著重要的作用，因此，他們也在考慮之列。而該模型中XY工作臺的伺服電機則來自于Kataria 和Mehta?？恐@些模型，MATLAB被用于模擬仿真。機床操作中的附件也需要設計和制作，它們附著在已有的XY工作臺上來驗證實驗的仿真結果。 3 實驗初步成立

10、 在數(shù)控銑床的研究中提出的假定是必須做的。在我們的研究中端銑通過一個可用的XY工作臺來實現(xiàn)。所以一個框架的設計和制作要能夠支持馬達和主軸。圖1顯示了在試驗中幀的設計和制作。圖2用相片顯示了一套完整的模型。附件中的主軸以這樣的一種方式來設計，其一端與交流感應電機軸連接，并由其帶動旋轉，而另一端連接在修飾銑刀用的鉆夾頭上。其它組件下次解釋。 3.0 主軸電機 在生產技術手冊中，動力所要求的端銑都做了，通過一個高速鋼刀具動力來切削鋁，主軸電機選定為：220伏特，每分鐘1440轉、250瓦特、單三相交流感應電動機。 3.1 幀 在立銑結構中，其橫向連接如圖1所示，是起決定性作用的，因

11、為在切削過程中它消減了對電機和主軸的彎曲應力。這個環(huán)節(jié)被設計為簡支梁，其橫截面選定為：35毫米*35毫米，3毫米厚，空心。 3.2 刀具夾緊裝置 在實際的數(shù)控機床中，設計條狀機械裝置是為了保證刀具。不過為了確保系統(tǒng)簡單，在這里鉆孔卡盤的改裝是為了持有刀具。 3.3 軸承 軸承安裝于車架上是為了來固定主軸的，來自于主軸上的力主要是彎曲。所以軸承承受徑向力。因此，SKF公司主要選定深溝球軸承6004 3.4 單片機 該系統(tǒng)的反應是通過觀察單片機上所用的軟件來實現(xiàn)的，而另一個DMC軟件是用來溝通控制器卡的。DMC1822是一所兩軸控制器用來控制發(fā)動機沿X軸和Y軸運動的，無論是軟件還是操作

12、工，在多組脈沖作用下均顯示錯誤結果。電機轉速和轉矩的百分比由電動機在任何時間供給。位置誤差在這里按定義之間的不同來進行編輯并取得一定位置。 4 系統(tǒng)模型 數(shù)學模型的完整建立是由組成伺服控制的XY工作臺、切削條件等等。也是本節(jié)所要介紹的。XY工作臺是由裝有PCI插槽的電腦控制的，它的所有的計算需要工作臺沿確定的路徑而離開電腦處理器的時間做其他工作的過程。該軟件是由松下來研究發(fā)展的，以便于在線監(jiān)測伺服電機。 該元素的伺服系統(tǒng)包括電機、驅動器、編碼器和控制器等，并在圖3顯示出來了，而完整的模型在圖4顯示，充分顧及到機械成分、切削力和剛度。 5 結果 在仿真的基礎上進行模擬輸出如圖4所示，在

13、進行的試驗中，立銑刀應符合以下規(guī)格：高速鋼刀具的直徑為12毫米，螺旋角刀具直徑為30，耙角工具直徑為11，工件材料則包括鋁和有機玻璃。在實驗中，參數(shù)的不同則視進給和切削深度而定。以每分鐘300毫米的進給速度和2毫米的切削深度切割圓形槽樣的有機玻璃塊時，得出的加工路線如圖5所示。當切削直槽時。錯誤也需要衡量，也可能觀察不到太大的變化。所以這種類型對定位精度和進給率可能沒有太大的影響。在切削直槽或圓槽時。降低進給速度來減少誤差。 另一方面，錯誤也出自如圖6所示的脈沖模型上，如果切削條件仍然與圖5那樣，則誤差范圍有所變化，他們是相似的。因此，數(shù)學模型代表著一個現(xiàn)實模型應用于端銑操作的銑床上。 6

14、 結論 在本文提出了數(shù)學模型為端銑操作，這是結合仿真模型的伺服裝置來控制XY工作臺的。這是在實驗初建成的，在真正的端銑切削加工中，它們都附著在現(xiàn)有的XY工作臺上。在編程和完成定位時，定位誤差是不同的。無論是從仿真模擬還是實驗設定，都是為了獲得表。結果配合密切，正如在圖5與圖6所顯示的那樣。因此，在沒有做出真正的原型時，這樣的一個數(shù)學模型是有用的業(yè)績考核的一種新的設計，不過這樣即費時且費用昂貴。因此，無論是時間還是投資上，把一個新產品投入市場將引起激烈的競爭。因此，在設計者中機電一體化的設計研究已經(jīng)被越來越多的人所接受。 7 一種新的制造技術----采用高速銑削 與一些好處的超高速銑削的方

15、法相比，傳統(tǒng)的銑可列為如下：增加切割速度，切割動力和芯片體積，改善表面質量。由于較低水平負載的工具和機床工具的熱量從切削區(qū)傳遞給晶片，是為了減少切削力而確保更好的精度，使工件溫度相對較低，從而減少了加工時間和加工費用。很多時候，與傳統(tǒng)方法相比高速加工被認為是一種由于高的切割速度而提高了生產率。它很少強調提高精度和更好的表面光潔度能提高產品質量。 這項研究主要是由赫爾辛基科技大學和芬蘭的VTT技術研究中心來證明的，他們?yōu)椴煌愋偷牟牧虾彤a品測試是否適合高速切削。結果由HUT和VTT密切合作共同研究工業(yè)狀況來證實的。這項測試是對7200個垂直型加工中心海事處進行研究證實的。其主軸是裝有深溝球軸承

16、，并能達到最高時速每分鐘4500轉，功率為5千瓦，X軸和Y軸最大進給速度為每分鐘24米，Z軸最大進給速度為每分鐘20米，數(shù)值控制選擇的是海德漢跨國公司的415. 耐磨性的刀具材料已被視為是限制切削速度的最重要的因素，高速鋼和涂層由于他們低的耐磨性已經(jīng)證實了我們的研究測試。高切削速度的硬質合金的刀具壽命眾所周知是短的。不過，它們可用于加工軟材料，金屬陶瓷是被提供的整理的鋼。像立方氮化硼和聚晶金剛石這種超硬刀具材料，自然是被視為屬于改集團的高速加工刀具材料。 該刀具適用于高速銑削，并可分為單銑和多銑。在我們這個領域的活動中，我們的實驗室還包括了制造業(yè)的復雜工件，如制造模具等。在那個領域，主要應

17、用于固體銑刀。根據(jù)我們的經(jīng)驗，高速加工的刀具都具有標準的幾何形狀。 應用最廣的高速銑削加工是加工鋼材，因為他們是在工程中應用最廣泛的材料。無論是工件中冷點、熱點和塑料模具鋼，它們在完成硬化狀態(tài)后會得到許多鋼材。采用高速銑削也可用于加工淬硬鋼。它通常用于在整理模具溶洞中作代替放電操作。立方氮化硼工具也通常被使用，主要是因為它們有很多優(yōu)點，例如它給出了一個替代碳化物。 這個問題涉及到由于缺乏有關切削參數(shù)為硬質材料的參數(shù)方面的知識，使得超高速銑削鋼已不能勝任工具的耐磨性。刀具材料和刀具幾何形狀的發(fā)展將使之采用高速銑削不同的鋼材的調查可能履行。甚至在一定的鍛煉條件下使用高合金工具鋼。 Mec

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20、sing small quantities, modified frequent, high-precision , The shape and the more complicated parts, and access to good economic results. With the development of numerical control technology, the use of CNC machine tools increasing varieties, lathes, milling machines, boring machine, drilling, grin

21、ding machines, machine tools and processing gear EDM machine, and so on. There is also the tool change automatically, with a multi-card processing operations of the processing centres, turning centres and so on. 1948, the United States to accept the U.S. Air Force commissioned by the Parsons Corpor

22、ation, the outline of the development model of aircraft propeller blades of the processing equipment. As example of complex and varied forms, high-precision, difficult to adapt to ordinary processing equipment, therefore proposed the idea of computer-controlled machine tools. 1949, the company in th

23、e U.S. Massachusetts Institute of Technology Research servo institutions, with the assistance of CNC machine tools began research and trial production in 1952 by the first successful large-scale copying of vertical milling machine converted the 3-D CNC milling machine, Soon start production. At tha

24、t time, the NC devices using tube components, size, is expensive, only a few in the aviation industry and other sectors with special needs for processing of complex components; 1959, made a transistor components and printed circuit boards, NC Entered a second-generation devices, reducing size, cost

25、has decreased in 1960 after a relatively simple and economic point of control NC drilling machine, CNC milling machine and line control by rapid development so that the NC machine tools in the machine manufacturing industry Gradually promote the various departments. In order to ensure a great machi

26、ne to process performance and ability to work for stability, structural design of CNC machine tools are characterized by sufficient rigidity, accuracy, anti-vibration, heat and maintain the stability and accuracy. Feed the mechanical transmission systems linked by ball screw, screw and non-static sp

27、ace gear, so as to minimize reverse gap. Machine tools used by motorized plastic rails, rolling or static guide rails to enhance the smooth movement of low-speed and movement when there is no creeping phenomenon. As a result of a wide speed range of feed-speed servo motor and the main motor, you ca

28、n not drive or less used and Gear Shift, which simplifies the machine's drive mechanism. Paixie facilitate the distribution of machine tools and parts handling, with automatic part of NC machine tools and auto parts Paixie exchange device. Most of CNC machine tools used with the microprocessor PLC,

29、strong, to replace the large number of counters in the relay, raising the machine-control, reliability and flexibility. With micro-electronics technology, computer technology and software technology is developing rapidly, the NC machine tool control system at the growing tendency of small-scale and

30、 multi-functional, have improved self-diagnostic features, reliability and greatly improve the system itself will generally NC Automatic programming. The type of CNC machine tools the future will be more diversified, multi-processing operations on the more and more varieties of NC machine tools, las

31、er processing technology will be implemented in cutting machine tools, thereby increasing the number of processes on the scope of the NC machine tool automation Further improve the level and a variety of monitoring, thus forming a flexible manufacturing unit, makes it easy to incorporate highly auto

32、mated flexible manufacturing systems. It is well known, a machine basic constitution including machine, transmission part, and execution part and control section. Transmission part is the overwhelming majority machine essential important constituent. From machine to working machine partial speed ch

33、anges, change heading, change mode of motion, power and movement transmission assignment and so on function. All is completes by the transmission device. In some machines (for example machine, automobile) center the transmission device occupies the entire machine majority, therefore the machine oper

34、ating performance and the operation cost are decided are partial (transmission device) to the transmission the fit and unfit quality in the very great degree. Therefore, in order to adapt the market to the mechanical product request enhances the transmission device the design level to have the vital

35、 significance. Since long ago, our country when design mechanical product, generally continues to use traditional the design method, the mechanical product design is the complex process which a morbid state structure, repeatedly iterates, costs the designer massive time and the energy, therefore,

36、regardless of by far could not satisfy user's request from the design performance and the design speed, has formed the advanced product request and in backwardness design method contradiction. At the same time, market competition intensifying, also requests the product to face, the low cost, and the

37、 short cyclical direction high grade is developing RI. At present, in machinery commonly used transmission design method commonly used theoretical design law. It is the design which carries on according to the existing science and technology theory and the practice knowledge, therefore, the commonly

38、 used design calculation formula are many is carries on the theory inferential reasoning in under certain suppositions conditions, again introduces aeries of correction coefficient, but obtains half theory semi-rational formula. Calculates using these formulas time, needs to look up a series of rela

39、ted forms or the graph determined the correction coefficient and certain parameters, the process is troublesome time-consuming: The machine designing is a process in particular which unceasingly revises, unceasingly consummates. The innumerable facts proved that, the experienced outstanding designer

40、 often could compared to just leave the school gate, the similarly rich talent designer to design a better product by a quicker speed to come. The expert system technology can help us to realize the expert to design the experience the induction and the use, causes the experience the continuation and

41、 development had greatly surmounted” between the priests and disciples" space and time limit, thus greatly advanced the design quality and the efficiency enhancement, thus for causes the transmission the design to adapt in the product market demand, develops the mechanical drive to design the expert

42、 system, quickly causes the transmission design speed, the computation to be accurate, the plan optimizes into the inevitable tendency. 2 INTRODCUTION A mechatronics approach is developing a mathematical model for the end milling operations on a CNC milling machine to simulate its behavior, is

43、 taken up in this paper. The mathematical model of the servomotor controlled XY table, developed elsewhere, is integrated with the proposed model for the end milling operations. Simulations are performed using SIMULINK of MATLAB. An experimental set-up was built to perform end milling operation on a

44、n existing XY table. SIMULINK results are validated with the experimental results. Such mathematical models are useful for evaluation of a new design. Hence, the lead time and cost to bring a new design in the market will be drastically reduced. Mechatronics is a concept introduced in Japan in 1980

45、s. Even though people refer to any system having mechanical, electrical, electronics components, for example, washing machine,photocopiers, CNC machines, etc., as mechatronics systems, truly `mechatronics!ˉ is a design philosophy. In conventional design approach, components of a system are designed

46、by respective experts. For example, a mechanical engineer designs the mechanical components, whereas the electrical engineer designs the electrical components, and so on. Since every designer leaves certain factor of safety (FOS) due to the ignorance of the other fields, the overall FOS is large and

47、 the system becomes bulky and expensive. In mechatronics design approach, the whole system is treated as one by taking care of all the components, be it a mechanical, electrical or electronics. As a result overall factor of safety is small and, hence, the system’s size and cost are reduced. In t

48、his paper, the mechatronics approach to the study of end milling in a CNC machine is taken up to aid the process of new design of a CNC machine table. The study requires the model of the machining process. The characteristics of end milling lies in the regular sequence of individual cuts, correspond

49、ing to each successive tooth engagements. These cuts many times are strongly overlapped. To predict the instantaneous cutting forces, mechanistic theory (Fuh and Hwang, 1997) is used. The force model developed here takes the feed of table and rpm of cutter as input parameters and gives the instantan

50、eous force as output at different cutter flutes locations. Mechanical transmission elements of the XY table comprising of motor axes and ball screws are also considered. Since stiffness of the mechanical elements plays an important role in accuracy of machined parts they are also taken into account

51、in the mathematical model, whereas the models of the PMBLDC servo motors of the XY table are taken from Kataria and Mehta (2001). Based on these models, simulations are performed using SIMULINK of MATLAB. An attachment for the end milling operation is also designed and fabricated, which is attached

52、to the already available XY table for experimental verifications of some of the simulation results. 3 EXPERIMENTAL SET-UP The study of proposed end milling operation is assumed to be done in a CNC milling machine. In our study, end milling was carried out on an available XY table. So a frame was d

53、esigned and fabricated which supports motor and locates the spindle. Figure 1 shows the frame designed and fabricated to carryout the experiments, whereas Fig. 2 shows the photograph of the complete set-up. The spindle of the attachment is designed in such a way that its one end is connected with th

54、e AC induction motor shaft providing rotation, whereas the other end is connected to a drilling chuck which is modified to hold the end mill cutter . Fig. 1 End milling attachment 2.0 Spindle motor . Power requirements for end mill

55、ing are done as per the production technology handbook . Based on the power to cut Aluminum by an HSS tool, spindle motor is selected as: 220V, 1440RPM, 250W, single-phase AC induction motor. 2.1 Frame The horizontal link of the frame in the end mill attachment, as shown in Fig. 1, is the critica

56、l one as it supports the motor and the spindle against bending forces induced during cutting. This link is designed as simple supported beam. Link cross-section is chosen as: 35mm x 35mm, 3mm thickness, hollow. 2.2 Tool holding device In actual CNC milling machines, draw bar mechanism is used t

57、o secure the cutting tool. However, to keep the system simple, here a drilling chuck was modified to serve the purpose of holding the end mill cutter. 2.3 Bearing Bearing is fixed on the frame which houses the spindle. The forces coming on the spindle are predominantly of bending. So, bearings h

58、ave to withstand radial forces. Hence, the SKF deep groove ball bearings 6004 are selected. 2.4 Panaterm The system response was observed by using the software package PANATERM , whereas DMCterm is another software was used to communicate with the Galil DMC1822 controller card (Galil, 2000). D

59、MC1822 is a two-axis controller which controls the PMBLDC motors along X and Y axes. Both the software allow online monitoring of the driver, which show errors in terms of the number of pulses, motor RPM, and torque percentage supplied by the motors at any time instant. The positional errors are de

60、fined here as the difference between the programmed and achieved positions. 3 SYSTEM MODELLING The mathematical model of the complete set-up, comprising of the servo controlled XY table, cutting conditions, etc., is presented in this section. The controller of the XY table is mounted on the PCI

61、 slot of the PC, which does all the calculations necessary to move the table along a pre-determined path leaving computer processor time free to do other jobs. The software package PANATERM developed by Panasonic facilitates the online monitoring of the servomotors. The elements of servo system i

62、ncluding motor, driver, encoder and the controller are modelled and shown in Fig. 3, whereas the complete model is shown in Fig. 4 that takes care of the mechanical elements, cutting forces and stiffness . Fig. 3 Functional elements of the controller.

63、 Fig. 4 Complete SIMULINK (in MATLAB) model. 4 RESULTS Simulations are performed in SIMULINK based on the model shown in Fig. 4 and experiments were conducted using an end milling cutter with the following specifications: HSS tool with straight shank of diameter 12mm; Helix angle of too

64、l 30 ; Rake angle of the tool 11 . Work materials are considered as Aluminum and Perspex (polymethyl methalcralyte). For experiments, the parameters varied are feed and depth of cut. For the cutting of a circular slot on Perspex block at 300mm/min feed rate with 2mm depth of cut, errors obtained fr

65、om PANATERM are shown in Fig. 5. Errors were also measured while cutting straight slot but not much variations were observed. So the type of paths may not have much influence on the positional accuracy, whereas the feed rate has. Lowering the feed rate has reduced the variation of errors during str

66、aight or circular slots. On the hand, errors from the SIMULINK model is shown in Fig. 6, where the cutting conditions remained same as in Fig. 5. Note the range of error variations, which is similar, i.e., +/- .075mm. Hence, the mathematical model represents the a realistic model for the end milling operation on a milling machine. 5 CONCLUSIONS Mathematical model for the end milling operation is proposed in this paper, which is integrated w