滾筒式蔬菜清洗機設(shè)計,滾筒式蔬菜清洗機設(shè)計,滾筒,蔬菜,清洗,設(shè)計 名稱：滾筒式清洗機 1 1 1 1.課題相關(guān)調(diào)查課題相關(guān)調(diào)查課題相關(guān)調(diào)查課題相關(guān)調(diào)查 2.2.2.2.方案思路設(shè)計方案思路設(shè)計方案思路設(shè)計方案思路設(shè)計 3.3.3.3.最終方案確定最終方案確定最終方案確定最終方案確定 4.4.4.4.相關(guān)參數(shù)確定相關(guān)參數(shù)確定相關(guān)參數(shù)確定相關(guān)參數(shù)確定 5.5.5.5.致謝詞致謝詞致謝詞致謝詞1.課題相關(guān)調(diào)查 隨著食品工業(yè)的發(fā)展，食品機械在食品工業(yè)中的地位越來越重要。現(xiàn)代化的食品機械不僅可以生產(chǎn)出高附加值的產(chǎn)品，而且可以提高資源的利用率。由于食品工業(yè)原料和產(chǎn)品的品種繁多，加工工藝各異，因此食品機械也相應(yīng)是門類各異，品種多樣。隨著人們對食品健康的高要求，也使得人們開始看重食品的初加工階段-清洗階段，因此對清洗機的性能提出了更高的要求，而滾筒式清洗機在同類清洗產(chǎn)品中效率還是比較高的。滾筒式清洗機是借圓形滾筒的轉(zhuǎn)動，使原料在其中不斷地翻轉(zhuǎn)，同時翻滾的原料與滾筒內(nèi)壁相互摩擦及其原料之間的相互摩擦，以達(dá)到清洗目的。用水管把泥沙由滾筒的網(wǎng)孔經(jīng)底部排出。該機適合清洗柑橘，橙，馬鈴薯等質(zhì)地較硬的物料。2.方案思路設(shè)計動力部分設(shè)計動力部分設(shè)計設(shè)計的初始數(shù)據(jù)為：滾筒轉(zhuǎn)速大約8r/min,滾筒直徑1000mm，滾筒長度約為1700mm。滾筒的速度還是很慢的，因此對電機沒有什么特殊要求，一般的三相異步電機就可以滿足要求根據(jù)初始數(shù)據(jù)計算，可以選用：Y132M-8型電動機 傳動部分設(shè)計：傳動部分設(shè)計：由俯視圖所示：動力傳動過程：由電動機通過聯(lián)軸器帶動小鏈輪轉(zhuǎn)動，然后通過鏈條帶動大鏈輪轉(zhuǎn)動，而大鏈輪與小摩擦輪在同一根軸上面，大鏈輪的轉(zhuǎn)動通過鍵連接帶動軸上面的小摩擦輪轉(zhuǎn)動，然后小摩擦輪帶動大摩擦輪轉(zhuǎn)動，大摩擦輪與滾筒焊接在一起，因此最終實現(xiàn)滾筒的轉(zhuǎn)動 滾筒部分設(shè)計：滾筒部分設(shè)計：本機采用的圓筒形鑄本機采用的圓筒形鑄鐵件鐵件 清洗部分設(shè)計：清洗部分設(shè)計：清洗部分是：螺旋導(dǎo)板通過螺栓連接在滾筒內(nèi)部，當(dāng)滾筒轉(zhuǎn)動后，螺旋導(dǎo)板會隨著滾筒一起轉(zhuǎn)動，里面的螺旋齒在轉(zhuǎn)動的過程中，會慢慢地把洗凈的食品排出1動力部分動力部分2動力傳動部分動力傳動部分由電動機經(jīng)小鏈輪帶動主軸由電動機經(jīng)小鏈輪帶動主軸上的大鏈輪低速旋轉(zhuǎn)。上的大鏈輪低速旋轉(zhuǎn)。3滾筒傳動滾筒傳動由鏈輪傳動帶動小摩擦輪帶由鏈輪傳動帶動小摩擦輪帶動大摩擦輪傳動滾筒。動大摩擦輪傳動滾筒。3.最終方案確定4.相關(guān)參數(shù)確定1.產(chǎn)品規(guī)格：1700 X 2394 X 18602.滾筒速度：8 r/min3.滾筒直徑：1000 mm4.生產(chǎn)能力：10.8 t/h致謝 為期三個多月的畢業(yè)設(shè)計已經(jīng)接近尾聲，在整個設(shè)計過程中，老師總是耐心地給我們講解有關(guān)方面的知識，及時了解我們設(shè)計中遇到的難題，使我們在短時間內(nèi)完成設(shè)計工作。在歷經(jīng)兩個多月的設(shè)計過程中，老師一直為我熱心地指導(dǎo)，經(jīng)常為我解答一系列的疑難問題，以及指導(dǎo)我設(shè)計思路。另外，本次畢業(yè)設(shè)計的圓滿結(jié)束，也離不開我們本小組其他成員的幫助。我和他們在一起做畢業(yè)設(shè)計時，經(jīng)?；ハ嘟涣?，共同探討問題，從中我也得到了他們的許多幫助。在此，我衷心地向各位指導(dǎo)老師和我同組人表示感謝！由于自己能力所限，時間倉促,設(shè)計中還存在許多不足之處，懇請各位老師同學(xué)給予批評指正。畢業(yè)設(shè)計英文翻譯 畢業(yè)設(shè)計（論文）譯文 題目名稱： 滾筒式清洗機 院系名稱： 機電學(xué)院 班 級： 機自073 學(xué) 號： 200700314307 學(xué)生姓名： 賀繼南 指導(dǎo)教師： 胡敏 2011 年03月  實驗方法 輻射黑色體理論（Chao et al., 1961）和切削表面理論（Friedman and Lenz, 1970）。隨著敏感的紅外感光膠片的發(fā)展，在一個可被記錄切削側(cè)面溫度場的工具（Boothroyd, 1961）和電視型紅外線敏感的視頻設(shè)備已被哈里斯等人使用（1980年），以熱傳感和半導(dǎo)體量子吸收的原則為基礎(chǔ)的紅外線傳感器的不斷發(fā)展，使得這些傳感器的第二敏感性大于第一次，其時間常數(shù)很小太 - 在微秒到毫秒的范圍之內(nèi)。圖5.21顯示了最新使用的第二類的例子。有兩個傳感器以及開始投入使用，一個是在1毫米至5毫米的波長范圍的敏感型銻化銦，另外一個是從6毫米至13毫米的敏感型碲鎘汞類型，通過與兩個不同的探測器信號比較可以使用溫度測量更敏感的方法。大部分金屬切削溫度已進行了調(diào)查和了解使得更好地了解這個過程。原則上，溫度測量可能用于條件監(jiān)測，例如，警告說如果是天氣太熱導(dǎo)致切割刀具后刀面磨損，然而，尤其是輻射能尺寸，在生產(chǎn)條件，校準(zhǔn)問題以及確保輻射能量途徑從傷口區(qū)到探測器不被打斷的困難，使得以溫度測量為目的方法不夠可靠切削的另一種方式是監(jiān)測聲發(fā)射，這雖然是一個間接的方法，但研究過程的狀態(tài)是一個值得考慮未來。 5.4 聲發(fā)射 材料的活躍形變—例如裂縫的增長，變形夾雜物，快速塑性剪切，甚至晶界，位錯運動都是伴隨著彈性應(yīng)力波的排放而產(chǎn)生。這就是聲發(fā)射（AE）。排放的發(fā)生在一個很寬的頻率范圍內(nèi)，但通常是從10萬赫到1兆赫。雖然波幅度很小，但是他們可以被檢測到，通過強烈的壓電材料如鈦酸鋇或壓電陶瓷傳感器制造從，（Pb（ZrxTi1–x）O3; x = 0.5 to 0.6）。圖5.22顯示了傳感器的結(jié)構(gòu)。聲波傳送到壓力傳感器造成直接的壓力E（△L/L），其中E是傳感器的楊氏模量，L是它的長度，△L是它的長度變化。應(yīng)力產(chǎn)生電場 T = g33E(△L/L)（5.7a） g33是傳感器材料的壓電應(yīng)力系數(shù)。傳感器兩端的電壓是TL，然后 V= g33E△L（5.7b） g33和E的典型值分別是24.4 × 10-3Vm/ N和58.5GPa，以檢測電壓高達(dá)0.01毫伏，這是可能的。將這些值代入方程（5.7b）導(dǎo)致了檢測△L的長度變化的可以小到7 × 10-15米：對于一個L = 10毫米的傳感器來說，即相當(dāng)于擁有7 × 10-13 圖5.22顯示的是聲發(fā)射傳感器的結(jié)構(gòu) 實驗理論方法 的最小應(yīng)變，使用應(yīng)變傳感要比使用鋼絲應(yīng)變計更敏感，敏感的最低檢測應(yīng)變約為10-6。一個AE傳感器電信號處理可分為兩個階段。第一個是通過使用一個低噪聲前置放大器和一個帶通濾波器（≈100千赫到1兆赫）。由此產(chǎn)生的信號通常具有的基礎(chǔ)上的復(fù)雜形式，如圖5.23所示，在處理的第二階段，提取信號的主要特征，例如事件的數(shù)量，電壓超過某一閾值VL，最大電壓VT，或信號能量的脈沖頻率使用聲發(fā)射來進行狀態(tài)監(jiān)測具有許多優(yōu)點。一小部分傳感器，處于策略性部署，能調(diào)查整個機械系統(tǒng)。一個發(fā)射源可以通過不同次數(shù)的排放以到達(dá)不同的傳感器。它的高靈敏度已經(jīng)被提到。這也是很容易被記錄的;并且聲發(fā)射測量儀器重量輕而且體積小。然而，它也有一些缺點。這些傳感器必須直接連接到被監(jiān)視系統(tǒng)：這會導(dǎo)致長期的可靠性問題。在嘈雜的條件下可以使之成為不可能孤立的事件。聲發(fā)射是很容易受被監(jiān)視材料的狀態(tài)的影響，例如熱處理，預(yù)應(yīng)變和溫度。此外，由于聲發(fā)射事件和被監(jiān)視的系統(tǒng)狀態(tài)兩者關(guān)系的特點并不明顯，甚至比熱輻射測量需要更多的校準(zhǔn)或壓力測量系統(tǒng)。 在加工過程中，聲發(fā)射信號的主要來源是剪切帶，片工具和工具的工作接觸區(qū)域，切屑的破碎與碰撞，及其切削工具的特征。聲發(fā)射信號的功率比較大，一般見于范圍100千赫至300千赫。其基本性能的研究和檢測磨損工具的使用，并且切削已經(jīng)成為大量調(diào)查的主題，例如Iwata和Moriwaki（1977），Kakino（1984），Diei和Dornfeld（1987）。聲發(fā)射的使用潛力可以在圖5.24看出來。它顯示了一個后刀面磨損VB和振幅水平之間的關(guān)系 那就是AE信號會轉(zhuǎn)化0.45％的普通碳素鋼（Miwa，1981）。較大的側(cè)面磨損，較大的聲發(fā)射信號，而與具有耐磨變化切削條件的信號的變化率有關(guān)，例如切割速度。 參考文獻(xiàn) Boothroyd, G.（1961）金屬切削溫度的測定攝影技術(shù)。 英國J. Appl.物理學(xué). 12，238-242. Chao, B. T., Li, H. L. 和 Trigger, K. J.（1961）對刀腹的表面溫度分布的實驗研究Trans. ASME J. Eng. Ind. 83, 496–503. Diei，EN和Dornfeld，D. A.（1987）從端面銑削過程的聲發(fā)射—過程變量的影響。Trans ASME J. Eng. Ind. 109, 92–99. Friedman, M. Y. and Lenz, E.（1970）切屑表面溫度場的測定。 機械工程研究所19（1），395-398. 實驗理論方法 Harris, A., Hastings, W. F.和Mathew, P.（1980）切削溫度的試驗測量。 見于：Proc. Int. Conf. on Manufacturing Engineering,墨爾本，8月25-27日，第30-35。 Iwata, I. and Moriwaki, T.（1977）對聲發(fā)射中的應(yīng)用工具傳感進程的 磨損。機械工程研究所26（1），21-26。 Kakino, K.（1984）金屬切削和磨削過程聲發(fā)射監(jiān)測3，108-116。 Miwa,Y., Inasaki, I. and Yonetsu, S.（1981）用聲發(fā)射信號故障檢測工具的過程，Trans JSME 47, 1680–1689. Reichenbach, G. S.（1958）實驗的金屬切削溫度分布測量。 Trans ASME 80, 525–540. Schwerd, F. (1933) Uber die bestimmung des temperaturfeldesbeimspanablauf. Zeitschrift VDI 77, 211–216. Shaw, M. C. (1984) 金屬切削原理。牛津：Clarendon出版社。 Trent, E. M. (1991) 金屬切削第三版。牛津：北海海涅曼。 Ueda, T., Sato, M. and Nakayama, K. (1998) 單晶鉆石刀具溫度的轉(zhuǎn)變。 CIRP 47(1), 41–44. Williams, J. E, Smart, E. F. and Milner, D. (1970)冶金的加工，第一部分. Metallurgia 6 力學(xué)進展 6.1簡介 第2章介紹了最初的機械，熱及摩擦學(xué)加工過程的報告。演示實驗的報告研究表明，在剪切面角，摩擦角和前角之間沒有獨特的的關(guān)系;證據(jù)表明這部分可能受主剪切帶加工硬化;切削速度與高溫之間的關(guān)系和高應(yīng)力條件下使摩擦面的摩擦角條件不足的影響。3至5章集中描述了工件和刀具材料的性能，刀具磨損和故障的本質(zhì)和加工后的實驗方法過程。這使得針對描述力學(xué)進展的背景下，導(dǎo)致有能力來預(yù)測從機械加工行為和物理性質(zhì)的工作及其工具。 本章安排了除本介紹之外的三個部分：滑移線場模型，從而使成連續(xù)切屑形成具有很大的啟示，但這最終是令人沮喪的，因為它最終沒有提供去刪除以上所指非唯一性的辦法;考慮到建模的工作流引入應(yīng)力變化的影響這消除了非唯一性，即使只通過一個近似的方式；第一個實例，以對切屑形成的正交模型來擴展更多的一般的三維（非正交）的條件。這是一個第2章與現(xiàn)代數(shù)值（有限元）制作經(jīng)典材料之間的過渡章節(jié)第7章。 6.2滑線場模擬 第2章介紹了兩個早期的平面的剪切角依賴摩擦和斜角的理論。根據(jù)Merchant（1945）（方程（2.9））切屑的形成發(fā)生在一個給定摩擦最低能量的條件下。據(jù)Lee和Shaffer（1951年）（方程（2.10）），剪切面的夾角是由在第二剪切帶相關(guān)的塑性流動摩擦角規(guī)則。Lee和Shaffer的貢獻(xiàn)首次是在slipline的切屑形成磁場模型。 6.2.1 滑移線場理論 滑移線場理論適用于平面應(yīng)變（二維）的塑性流動。材料的力學(xué)性能被簡化為剛性，完全塑料。這就是說，它的彈性模量被認(rèn)為是不定的（剛性）及其塑性流動時發(fā)生的應(yīng)用是最大剪應(yīng)力達(dá)到某一臨界值，k，它不隨條件，如應(yīng)變，應(yīng)變率和溫度流動的變化而變化。對于這樣一個在平面上的理想化材料，應(yīng)變塑性狀態(tài)，滑移線場理論發(fā)展的壓力和速度如何可以改變規(guī)則。這些被認(rèn)為是在詳細(xì)附錄1之中。一個簡短的部分在這里給出了摘要，足以使該理論應(yīng)用到加工中。 首先：什么是滑移線和滑移線場;以及他們有用嗎？一個平面材料的應(yīng)力應(yīng)變加載的分析結(jié)論是，在任何一點上都有兩個正交方向，其中剪應(yīng)力方向為最大值。此外，在這些方向直接應(yīng)力是平等的（和平等的靜水壓力）。然而，這些方向可以從一個點到另一個點而改變。如果材料是加載塑性，應(yīng)力狀態(tài)完全是所描述的最大剪應(yīng)力常數(shù)K值，以及方向和靜水壓力各不相同的點。 A線，一般彎曲，沿其長度最大剪應(yīng)力方向都被稱為滑移線。一個滑移線是正交曲線滑移在塑料地帶現(xiàn)有生產(chǎn)線配套?；€場理論是構(gòu)建在特定情況下的滑移線場（例如規(guī)則加工）和計算領(lǐng)域內(nèi)的靜水壓力的變化之上。 該文章摘自：Metal MachiningTheory and Applications Thomas Childs University of Leeds,UK Katsuhiro Maekawa Ibaraki University,Japan Toshiyuki Obikawa Tokyo Institute of Technology,Japan Yasuo Yamane Hiroshima University,Japan http://www.arnoldpublishers.com Copublished in North,Central and South America by John Wiley & Sons Inc.,605 Third Avenue, New York,NY 10158–0012  Experimental methods (Chao et al.,1961) and on the chip surface (Friedman and Lenz,1970). With the development of infrared sensitive photographic film,temperature fields on the side face of a chipand tool have been recorded (Boothroyd,1961) and television type infrared sensitive video equipment has been used by Harris et al. (1980). Infrared sensors have continued to develop,based on both heat sensing and semiconductor quantum absorption principles. The sensitivity of the second of these is greater than the first,and its time constant is quite small too in the range of ms to ms. Figure 5.21 shows a recent example of the use of the second type. Two sensors,anInSb type sensitive in the 1 mm to 5 mm wavelength range and a HgCdTetype,sensitive from 6 mm to 13 mm, were used:more sensitive temperature measurements may be made by comparing the signals from two different detectors. Most investigations of temperature in metal cutting have been carried out to understand the process better. In principle,temperature measurement might be used for condition monitoring,for example to warn if tool flank wear is leading to too hot cutting conditions. However,particularly for radiant energy measurements and in production conditions,calibration issues and the difficulty of ensuring the radiant energy path from the cutting zone to the detector is not interrupted,make temperature measurement for such a purpose not reliable enough. Monitoring the acoustic emissions from cutting is Fig. 5.21 Experimental set-up for measuring the temperature of a chip’s back surface at the cutting point, using a diamond tool and infrared light, after Ueda et al. (1998) Acoustic emission 155 anotherway,albeit an indirect method,to study the state of the process,and this is considered next. 5.4Acoustic emission The dynamic deformation of materials – for example the growth of cracks,the deformation of inclusions,rapid plastic shear,even grain boundary and dislocation movements is accompanied by the emission of elastic stress waves. This is acoustic emission (AE).Emissions occur over a wide frequency range but typically from 100kHz to 1MHz.Although the waves are of very small amplitude,they can be detected by sensors madefrom strongly piezoelectric materials,such as BaTiO3 or PZT (Pb(ZrxTi1–x)O3; x = 0.5 to0.6). Figure 5.22 shows the structure of a sensor. An acoustic wave transmitted into thesensor causes a direct stressE(DL/L) where E is the sensor’s Young’s modulus, L is itlength and DL is its change in length. The stress creates an electric field T = g33E(DL/L)(5.7a) where g33 is the sensor material’s piezoelectric stress coefficient. The voltage across thesensor,TL,is then V = g33EDL (5.7b) Typical values of g33 and E for PZT are 24.4 × 10–3 Vm/N and 58.5GPa. It is possible,withamplification,to detect voltages as small as 0.01 mV. These values substituted intoequation (5.7b) lead to the possibility of detecting length changes DL as small as 7 × 10–15m:for a sensor with L = 10mm,that is equivalent to a minimum strain of 7 × 10–13. AE Fig. 5.22 Structure of an AE sensor 156 Experimental methods Fig. 5.23 An example of an AE signal and signal processingstrain sensing is much more sensitive than using wire strain gauges,for which the minimum detectable strain is around 10–6. The electrical signal from an AE sensor is processed in two stages. It is first passedthrough a low noise pre-amplifier and a band-pass filter (≈100kHz to 1MHz). The resulting signal typically has a complicated form,based on events,such as in Figure 5.23. In thesecond stage of processing,the main features of the signal are extracted,such as thenumber of events,the frequency of pulses with a voltage exceeding some threshold valueVL,the maximum voltage VT,or the signal energy. The use of acoustic emission for condition monitoring has a number of advantages. Asmall number of sensors,strategicallyplaced,can survey the whole of a mechanicalsystem. The source of an emission can be located from the different times the emissiontakes to reach different sensors. Its high sensitivity has already been mentioned. It is alsoeasy to record; and acoustic emission measuring instruments are lightweight and small.However,it also has some disadvantages. The sensors must be attached directly to thesystem being monitored:this leads to long term reliability problems. In noisy conditions itcan become impossible to isolate events. Acoustic emission is easily influenced by thestate of the material being monitored,its heat treatment,pre-strain and temperature. Inaddition,because it is not obvious what is the relationship between the characteristics ofacoustic emission events and the state of the system being monitored,there is even moreneed to calibrate or train the measuring system than there is with thermal radiationmeasurements. In machining,the main sources of AE signals are the primary shear zone,the chip–tooland tool–work contact areas,the breaking and collision of chips,and the chipping andfracture of the tool. AE signals of large power are generally observed in the range 100kHzto 300kHz. Investigations of their basic properties and uses in detecting tool wear andchipping have been the subject of numerous investigations,for example Iwata andMoriwaki (1977),Kakino (1984) and Diei and Dornfeld (1987). The potential of using AE is seen in Figure 5.24. It shows a relation between flank wear VB and the amplitude level References 157 Fig. 5.24 Relation between flank wear VB and amplitude of AE signal, after Miwa et al. (1981)of an AE signal in turning a 0.45% plain carbon steel (Miwa,1981). The larger the flankwear,the larger the AE signal,while the rate of change of signal with wear changes withthe cutting conditions,such as cutting speed. References Boothroyd,G. (1961) Photographic technique for the determination of metal cutting temperatures.British J. Appl. Phys. 12,238–242. Chao,B.T.,Li,H.L. and Trigger,K.J. (1961) An experimental investigation of temperature distribution at tool flank surface. Trans. ASME J. Eng. Ind. 83,496–503. Diei,E.N. and Dornfeld,D.A. (1987) Acoustic emission from the face milling process – the effectsof process variables. Trans ASME J. Eng. Ind. 109,92–99. Friedman,M.Y. and Lenz,E. (1970) Determination of temperature field on upper chip face. AnnalsCIRP 19(1),395–398. 158 Experimental methods Harris,A.,Hastings,W.F. and Mathew,P. (1980) The experimental measurement of cutting temperature. In: Proc. Int. Conf. on Manufacturing Engineering,Melbourne,25–27 August,pp. 30–35. Iwata,I. and Moriwaki,T. (1977) An application of acoustic emission to in-process sensing of toolwear. Annals CIRP 26(1),21–26. Kakino,K. (1984) Monitoring of metal cutting and grinding processes by acoustic emission. J.Acoustic Emission 3,108–116. Miwa,Y.,Inasaki,I. and Yonetsu,S. (1981) In-process detection of tool failure by acoustic emissionsignal. Trans JSME 47,1680–1689. Reichenbach,G.S. (1958) Experimental measurement of metal cutting temperature distribution.Trans ASME 80,525–540. Schwerd,F. (1933) Uber die bestimmung des temperaturfeldesbeimspanablauf. Zeitschrift VDI 77,211–216. Shaw,M.C. (1984) Metal Cutting Principles. Oxford:Clarendon Press.Trent,E.M. (1991) Metal Cutting,3rd edn. Oxford:Butterworth Heinemann.Ueda,T.,Sato,M. and Nakayama,K. (1998) The temperature of a single crystal diamond tool inturning. Annals CIRP 47(1),41–44. Williams,J.E,Smart,E.F. and Milner,D. (1970) The metallurgy of machining,Part 1. Metallurgia 6 Advances in mechanics 6.1Introduction Chapter 2 presented initial mechanical,thermal and tribological considerations of themachining process. It reported on experimental studies that demonstrate that there is nounique relation between shear plane angle,friction angle and rake angle; on evidence thatpart of this may be the influence of workhardening in the primary shear zone; on hightemperature generation at high cutting speeds; and on the high stress conditions on the rakeface that make a friction angle an inadequate descriptor of friction conditions there.Chapters 3 to 5 concentrated on describing the properties of work and tool materials,thenature of tool wear and failure and on experimental methods of following the machiningprocess. This sets the background against which advances in mechanics may be described,leading to the ability to predict machining behaviours from the mechanical and physicalproperties of the work and tool. This chapter is arranged in three sections in addition to this introduction:an account ofslip-line field modelling,which gives much insight into continuous chip formation butwhich is ultimately frustrating as it offers no way to remove the non-uniqueness referredto above; an account of the introduction of work flow stressvariation effects intomodelling that removes the non-uniqueness,even though only in an approximate manner in thefirst instance; and an extension of modelling from orthogonal chip formation to moregeneral three-dimensional (non-orthogonal) conditions. It is a bridging chapter,betweenthe classical material of Chapter 2 and modern numerical (finite element) modelling inChapter 7. 6.2Slip-line field modeling Chapter 2 presented two early theories of the dependence of the shear plane angle on thefriction and rake angles. According to Merchant (1945) (equation (2.9)) chip formationoccurs at a minimum energy for a given friction condition. According to Lee and Shaffer(1951) (equation (2.10)) the shear plane angle is related to the friction angle by plastic flowrules in the secondary shear zone. Lee and Shaffer’s contribution was the first of the slipline field models of chip formation. 160 Advances in mechanics 6.2.1Slip-line field theory Slip-line field theory applies to plane strain (two-dimensional) plastic flows. A material’smechanical properties are simplified to rigid,perfectly plastic. That is to say,its elasticmoduli are assumed to be infinite (rigid) and its plastic flow occurs when the applied maximum shear stress reaches some critical value, k,which does not vary with conditions ofthe flow such as strain,strain-rate or temperature. For such an idealized material,in a planestrain plastic state,slip-line field theory develops rules for how stress and velocity can vary from place to place. These are considered in detail in Appendix 1. A brief and partialsummary is given here,sufficient to enable the application of the theory to machining tobe understood. First of all:what are a slip-line and a slip-line field; and how are they useful? The analysis of stress in a plane strain loaded material concludes that at any point there are two orthogonal directions in which the shear stresses are maximum. Further,the direct stresses are equal(and equal to the hydrostatic pressure) in those directions. However,those directions can varyfrom point to point. If the material is loaded plastically,the state of stress is completelydescribed by the constant value k of maximum shear stress,and how its direction and thehydrostatic pressure vary from point to point. A line,generallycurved,which is tangentialall along its length to directions of maximum shear stress is known as a slip-line. A slip-linefield is the complete set of orthogonal curvilinear slip-lines existing in a plastic region. Slip-line field theory provides rules for constructing the slip-line field in particular cases (such asmachining) and for calculating how hydrostatic pressure varies within the field. Article from ：Metal MachiningTheory and Applications Thomas Childs University of Leeds,UK Katsuhiro Maekawa Ibaraki University,Japan Toshiyuki Obikawa Tokyo Institute of Technology,Japan Yasuo Yamane Hiroshima University,Japan http://www.arnoldpublishers.com Copublished in North,Central and South America by John Wiley & Sons Inc.,605 Third Avenue, New York,NY 10158–0012 16