【機械類畢業(yè)論文中英文對照文獻翻譯】評價為微型工廠設(shè)計的微型機床的尺度效應(yīng),機械類畢業(yè)論文中英文對照文獻翻譯,機械類,畢業(yè)論文,中英文,對照,對比,比照,文獻,翻譯,評價,微型,工廠,設(shè)計,機床,尺度,效應(yīng) 英文資料 Evaluation of Size Effect on Micro-machine-tools Design for Microfactory M. Yamanaka1, S. Hirotomi2 and K. Inoue3 1Tohoku University, 6-6-01, Aramaki-Aoba, Sendai 980-8579, Japan, yamanaka@elm.mech.tohoku.ac.jp 2Shimano Inc, Japan 3Tohoku University, Japan Abstract. A micro lathe with a machine base size of 150×100 mm (postcard size) was developed by the authors. It has a good cutting performance for brass test workpieces. To know the developed machine is most suitable size for machining the given workpiece size, the error functions, which affect the cutting performance, are examined how to change to the machine tool size. The calculation method and a simple size effect of error functions are proposed and their usefulness is examined by some calculation results. Keywords: Microfactory, Machine tools, Lathe, Machine design, Size effect 1. Introduction Ordinary production systems use enlarged machine tools aiming at high rigidity regardless of the size of the parts produced. The concept of microfactory is to use small machine tools corresponding to the miniaturization of workpieces. This is useful for saving resources, space, and energy. Some prototypes were developed to realize this concept [1]. Okazaki developed an NC micro lathe which is 32×28×30 mm in size [1]. Park developed a miniaturized 3-axis milling machine of 200×300×200 mm [2]. The authors are developing micro lathes aiming at the practical use in mass production systems of small/micro parts for optics, IT and electronics, until now [3]. The machine with a base size of 150×100 mm (postcard size) has been developed and the relation between machine characteristics and cutting performance are evaluated to clarify advantage/disadvantage of the developed lathe [4]. To design micro machine tools, it is important to properly understand the merits and demerits of downsizing. Mishima proposed a design tools [5] combined with the form-shaping theory of machine tools[6] and Taguchi method [7]. It offers a simplified method to consider the deformation of machine tool structures and the component errors. The developed micro lathe has a good cutting performance for the test workpiece. However, it is obscure that the developed machine is most suitable size for machining the given workpiece size. It is impossible to make many sizes of machine tools and evaluate their performances. In this paper, the outline of developed micro lathe is introduced, and the influence of accuracies according to the machine size to the cutting performance is examined in a simulation. The calculation method considering the size effect on micro machine tools design is discussed with the calculation results. 2. Micro Lathe The maximum size of target workpiece was assumed to beφ5 ×10 mm and the lathe was designed. The size of the machine base was decided to be of A6 size (150×100 mm) for its foot print area considering the degree of miniaturization, its practicality, assembly and, in particular, a sufficient rigidity. Each device of the machine was designed with this restriction. The developedmicro lathe MTS 2 (product of Nano Corporation, Japan) is shown in Fig. 1.1. X and Z-axis tables, which use the same modules, are guided by cross-roller ways, and driven by a φ2-triangle screw thread and an AC 15-mm in square servomotor. The size of the table is about 50×80 mm (excluding motor). The weight including the motor is 585 g. The headstock is fixed on the X-axis table and the tool post is mounted on the Z-axis table. Figure 1.1. Appearance of developed micro lathe MTS2 (Nano Corporation, Japan, base size: 150x100 mm) A micro motor of 16 mm diameter is used to drive the work spindle in the headstock from the balance with the table. A rotary speed of more than 10000 min-1 is necessary to obtain a cutting speed of about 150 m/min for small-diameter workpieces. Because of this, a direct drive is preferred, but a reducer is required to drive the workpiece because the motor torque of a φ16 mm class motor is extremely small (only a few mNm), which is generally not enough to obtain a sufficient cutting power. The rotary speed is secured as much as possible by selecting a high-speed motor. The planetary roller reducer using traction drives is adopted for this work spindle. The reduction ratio is 4. The size and weight of the headstock is 75×40×30 mm, its weight is 230 g (include motor). 3. Calculation of Error in Consideration of Size Effect There are many error functions, which affect the cutting performance. Here, only four error functions, namely the assembly error, the motion error, the deformation by cutting force and the thermal deformation, are considered, and how they change to the machine tool size is examined. Then we propose the calculation method of error in consideration of size effect. The model with dimensions of above-mentioned micro lathe and those of enlarged/reduced are used to calculate by using the formshaping theory. The deviation from the target position of the tool point is obtained and the proposed method is evaluated. 3.1 Calculation method The above-mentioned micro lathe is modeled as shown in Fig. 1.2. The model consists of eight elements. The numbers from 0 to 7 are given to the reference point in coordinate transformation on each element. Though the bed is actually one solid component, it is divided into two parts virtually to consider the influence of the bed’s rigidity. The target position in the tool point is apart from the point 0 to h in Z-direction and R in X-direction, respectively. An orthogonal coordinate system Si corresponding to an element i is defined. The transformation from Si to Si+1 is represented by the coordinate transformation, which is represented by the homogeneous transformation matrices Ai. Vector rw represents the relative displacement between the workpiece and the tool, and vector rT represents the position of the tool point. The relation between rw and rT is given by Eq. (1), and rw is defined as the form-shaping function. The error between element i and i+1 is represented by another homogeneous transformation matrix εi as follows. The form-shaping function considering the error is defined as r’w expressed by The form-shaping error function re, which expresses the error as a quantitative deviation from the target position, is defined as Eq. (4). The error between elements of the micro lathe is represented by 6 components, which are translational and rotational motions along the X, Y and Z axes, as δx, δy, δz, α, β, and γ, respectively. The limited four error functions may affect between elements shown in Fig. 1.3. The assembly error appears between all elements except between the bed 1 and the bed 2, which are divided into two parts. The motion error appears between the elements that move relatively during cutting. Because force and heat propagate through an element, the deformations by cutting force and heat appear between all elements. Moreover, as shown in Table 1, it was analyzed and classified which error components are affected by above-mentioned four error functions. For example, the motion error between the workpiece and the work spindle depends on the runout of the work spindle. Because the workpiece rotates around the Z-axis, the translational error in X and Y except Z-axes are considered. The assembly error can not define the direction to appear, and is assumed to appear in all 6 components. The deformations by cutting force and heat are assumed to appear in 3 components of translationalerror. 3.2 Size effect of error Table 2 shows to what extent the amount of error of each item in Table 1 changes when the size of the machine tool is changed n times, which is examined by other reports [8,9] and the calculation. It is thought that the difficulty of assembly is constant regardless of the machine size. Therefore, the size effect of the assembly error is 1. The motion error depends on the accuracies of guides in a slide table or bearings in a work spindle. Here, it is considered that the machine element of same absolute accuracy can be selected regardless of the size, and the size effect of the motion error is assumed to be 1 as well as the assembly error. The cutting force is divided in 3 directions, namely principle, the thrust and the feed force. A simple bend and compression of beam according to the direction of applied force on each element is considered, the size effect of deformation by cutting force is assumed to be 1/n and 1/n2, respectively. If the temperature increases, generally a material expands. The deformation δt of a member having a length ? can be calculated using the formula where, αt is the linear coefficient of thermal expansion and ΔT is the temperature rise of the member. Therefore, the size effect of thermal deformation is considered as n. The dimensions of each element of the model in Fig. 1.2 are required to calculate the error. The real dimensions of the developed micro lathe shown in Fig. 1.1, and these are used as that of a model for n= 1. Then the model is enlarged n times and the error in Eq. (4) is calculated by the method mentioned above using the size effect of errors shown in Table 1.2. And how the error changes according to n is examined changing n from 0.5 to 10. However, the dimensions of workpiece and tool are assumed to be constant regardless of n, where R is 2.5 mm, h is 10 mm and t is 8 mm. In this method, actual values of error are required for the calculation. Hence, the magnitude of each error for n= 1 is decided as shown in Table 1.1. The assembly and the motion errors were decided in consideration of actual micro lathe. Both errors can take a positive or negative value, and are expressed with the sign of + or -. The deformations by cutting force and heat are obtained by FEM. The deformation of workpiece and tool were not considered. The element 7 is fixed and the magnitude of deformation of each element is obtained. The tangent force applied to a workpiece is calculated by the rated torque of the motor of the work spindle, and it is assumed to be the principal cutting force. The ratio among 3-divided cutting forces is decided by the reference [8]. The deformation of each element when the atmosphere rises by 20 K is calculated as the thermal deformation. Because the target is a cylindrical component, the errors ΔR in cutting radius and Δz in longitudinal direction are defined as the evaluation function of error. R’ and R are the actual and instructed cutting radii, respectively. ΔR is given as follows. The assembly and motion errors take positive or negative values in Table 1.1, and the number of those items is 44. If the case of plus/minus in each item is combined, there are 244 patterns to calculate. This combination is so large that the orthogonal table in Taguchi method [7] is applied and the calculation is held in small combinations. Here, the orthogonal table of L64 is used to obtain re by Eq. (4) and the evaluation functions are calculated in 64 cases. The relation between the machine size n and the average of evaluation function is shown in Fig. 1.4. The max/min values are also plotted in the figure. The magnitude of ΔR increases as n increases. The difference between the maximum and the minimum values increases too. The assembly error and the thermal deformation may be the reason for this. Though the magnitude of assembly error does not depend on n, as shown in Table 1.2, the movement in coordinate transformation becomes large as n increases, so that re becomes large. The thermal deformation increases because of its size effect. As for Δz, there is the minimum value near n = 1.5. Δz increases as well as ΔR when n increases more than it. When n becomes small, Δz increases slightly by the size effect of the deformation by cutting force. This suggests that an optimum size of this kind of machine exists for a given size of workpiece. Here, R is set as 2.5 so that R >> Δx, Δy and ΔR is almost constant from Eq. (6) though n becomes small. Each mean value for n is normalized by dividing by that for n= 1 to know the tendency of change of evaluation function to n. The result is shown in Fig. 1.5. ΔR and Δz become 8 and 3.4 times as large as at n= 10. It can be said that the sensitivity of ΔR to the machine size is higher. The calculation result by the proposed method changes greatly by the values of error and the size effect shown in Tables 1.1 and 1.2. In this study, though, the size effect of error functions was simplified, more examination is necessary to improve the accuracy of calculation. 4. Conclusions The influence of accuracies according to machine size on cutting performance is examined. The conclusions may be summarized as follows: 1. The error function, which affects the cutting performance, is examined. Then the calculation method of error in considerlation of size effect is proposed applying the form-shaping theory. 2. The calculation model is built by using the dimensions of the actual micro lathe. The relation between machine size and error is obtained. The assembly error and the thermal deformation have the strongest influence. References [1] Okazaki, Y., et al., (2004) Microfactory: Concept, historyand developments. Trans. ASME, J. ManufacturingScience and Engineering 126: 837-844 [2] Park, J. K., et al., (2006) A precision meso scale machine tools with air bearings for microfactory. Proc 5th Int.Workshop on Microfactories, Besancon, France (CDROM) [3] Iijima, D, et al., (2004) Micro Turning System 3 (MTS3): A practical CNC lathe for microfactories. Proc. 4th Int. Workshop on Microfactories, Shanghai, China 1: 50-55 [4] Yamanaka, M, et al., (2006), Relation between mechanical characteristic and cutting performance of micro lathe. Proc 5th Int. Workshop on Microfactories, Besancon, France(CD-ROM) [5] Mishima, N., (2003) Design of a Miniature Manufactuirng System for Micro-fabrication. Proc 10th Annual Conf. for Concurrent Engineering, Modeira, Pirtugal 1129-1135 [6] Reshtov, D. N., Portman, V. T., (1988) Accuracy of machine tools. ASME Press, New York [7] Taguchi, G., Konishi, S., (1994) Quality engineering series. ASI Press [8] Sugita, T., et al., (1984) Fundamentals of cutting (in Japanese). Kyoritsu Publish. 中文翻譯 評價為微型工廠設(shè)計的微型機床的尺度效應(yīng) M. Yamanaka1, S. Hirotomi2 and K. Inoue3 1Tohoku University, 6-6-01, Aramaki-Aoba, Sendai 980-8579, Japan, yamanaka@elm.mech.tohoku.ac.jp 2Shimano Inc, Japan 3Tohoku University, Japan 摘要: 一種微型機床總體尺寸為150×100 mm(明信片大小)現(xiàn)在發(fā)展起來。它在切割黃銅制品的實驗中表現(xiàn)出良好的性能。根據(jù)所給工件的大小，誤差函數(shù)，這些影響切削性能的方面來確定機床的大小。受計算方法和簡單的尺寸的影響的誤差函數(shù)的提出是為審查通過一些計算結(jié)果。 關(guān)鍵詞：微型工廠 ，機床，車床，機械設(shè)計，尺寸效應(yīng) 1.導(dǎo)言 普通生產(chǎn)系統(tǒng)的使用大機床是針對高剛性，不論零件大小。微型工廠的概念是用小機床相應(yīng)的小型化工件。這是對于節(jié)省資源，空間和能源是有益的。一些原型的開發(fā)就是為了實現(xiàn)這種觀念[1]。岡崎研制出一種微型數(shù)控車床大小為32×28×30mm[1]。開發(fā)的一種微型三軸銑床為200×300×200mm[2]。作者正在開發(fā)的微型車床著眼于實際使用在大規(guī)模生產(chǎn)系統(tǒng)中的小型/微型光學(xué)部件，信息技術(shù)和電子產(chǎn)品，截至目前為止[3]。已經(jīng)研制成功的一種機床包括基座面積為150×100mm（明信片大?。谧鰴C床的機械特性與切削加工性能兩者之間關(guān)系的評價，以徹底弄清這種車床的優(yōu)劣[4] 。 設(shè)計微型機床時正確認識到小型化所帶來優(yōu)點和缺點是非常重要的。三島提出了一個設(shè)計工具[5] 結(jié)合機床的仿型刨原理[6]和田口原理[7]。它提供了一種簡化方法去考慮機床的結(jié)構(gòu)變形和組件的誤差。發(fā)展起來的微型車床對于測試工件表現(xiàn)出良好的切削加工性能。但是，所研制的機床大小對于工件尺寸是否是最合適模糊不清。也不可能設(shè)計許多大小不同的型號的機床來評估它們的表現(xiàn)。 在這篇論文中介紹的微型車床，對于機器的大小相對應(yīng)的切削加工性能對于精度的影響已經(jīng)在一個仿真中測試。設(shè)計微型機床時考慮到尺寸效應(yīng)的計算方法與計算結(jié)果已經(jīng)被討論。 2 .微型車床 車床設(shè)計時目標工件的最大尺寸假設(shè)為Φ5×10mm。機床底座被設(shè)計為A6尺寸（150×100mm）考慮到它的小型化程度和實用性。機器的每個部件都用此限制。這種微型車床MTS2（由日本Nano公司生產(chǎn)），引進Fig.1.1 X和Z 軸工作臺，這種工作臺使用相同的模塊，用交叉輥子導(dǎo)向，用Φ2三角螺紋與15mm方形交流伺服電機驅(qū)動。工作臺大小是約50×80mm（不包括電機 。包括電機的重量為585g。主軸箱固定在X軸上，刀架裝在Z軸上。 圖1.1微型車床MTS2外觀（Nano公司，日本，基座面積：150x100mm） 裝在主軸箱里的工作主軸是由16毫米直徑微電機驅(qū)動，主軸箱與工作臺相連。轉(zhuǎn)速超過10000轉(zhuǎn)/分鐘對于切削小直徑工件時要取得切削速度約150米/分鐘是很必要的。正因為如此，直接驅(qū)動是首選，但是需用減速機驅(qū)動工件，因為16毫米級電動機的轉(zhuǎn)矩是非常小的（只有幾mNm ），一般不足夠提供足夠的切削功率。旋轉(zhuǎn)的速度可以保障的，可以選擇轉(zhuǎn)速盡可能高的電機。行星輥減速器用來驅(qū)動主軸。該減速器減速比是4 。尺寸為75×40×30mm，它的重量是230 g（包括電動機）。 3 .考慮到尺寸效應(yīng)的計算誤差 有許多誤差函數(shù)會影響到切削性能。在這里，只考慮四個誤差函數(shù)，即裝配誤差，運動誤差，切削力導(dǎo)致的變形和熱變形，以及它們?nèi)绾斡绊憴C床尺寸已經(jīng)被計算。那么，我們提出的計算誤差的方法應(yīng)考慮尺寸效應(yīng)。上文提到的微型車床和那些擴大/減少車床的模型的尺寸是用仿型刨理論來計算的。計算出了刀尖偏離目標的距離，并且評價了這種理論。 3.1計算方法 上文提到的微型車床的模型見圖1.2 。該模型分為8個部分。號碼從0到7是個部分進行坐標變換時的參考點。雖然基座實際上是一個整體組成，考慮到剛度的影響，它分為兩個部分。目標位置在工具的一點是，原點O至刀尖點在Z方向是h，在X方向是R。 圖1.2.微型車床計算模型 定義一個正交坐標系Si相當于部分i.從Si到Si+1的坐標轉(zhuǎn)換，是由奇次變換矩陣Ai所代表。矢量Rw代表工件和刀具之間相對位移，向量RT代表刀具位置。Rw和RT的關(guān)系有等式（1）給出，RW是定義為仿型刨函數(shù)。 部分i和i+1之間的誤差由以下齊次變換矩陣?i所示。 考慮到誤差的仿型刨函數(shù)定義為r'w，表達如下 仿型刨誤差函數(shù)re，它體現(xiàn)了誤差作為一個定量偏離了目標位置，是由等式（4）定義。 微型車床個組件之間的誤差有6部分組成，它們分別是沿X、Y、Z軸平移和繞它們旋轉(zhuǎn)，記為δx,δy,δz,α,β,γ. 有限的四個誤差函數(shù)可能會影響如圖1.3所示各部分。誤差會出現(xiàn)各要素之間除了被分為兩部分的基座1和基座2。該運動誤差出現(xiàn)在各部分在切削過程中的相對運動中。因為力和熱量會傳播，由切削力和熱引起的變形會在各部件之間傳播。此外，如表1所示，它分析和歸類了受上述四項誤差函數(shù)影響的誤差項組成。舉例來說，工件和工作主軸之間的運動誤差取決于工作主軸的跳動。由于工件圍繞Z軸旋轉(zhuǎn)要考慮Z軸除外的沿X和Y軸的直線運動誤差。誤差出現(xiàn)的地方不能確定，有可能出現(xiàn)在所有6個組成部分。切削力和熱導(dǎo)致的變形假定出現(xiàn)在平移誤差的3個組成部分。 3.2誤差的尺寸效應(yīng) 表1.1在n=1時，誤差函數(shù)對誤差個組成部分的影響和實際值 表1.1 n=1時，誤差函數(shù)對誤差各個組成部分的影響和實際值 表2顯示，當機床大小改變了N倍時，表1中的各項的誤差是在何種程度上變化，這些已經(jīng)被其他報告[8，9]計算和檢驗過。裝配難度是恒定的，與機器尺寸無關(guān)。 因此，尺寸效應(yīng)的裝配誤差是1 。該運動誤差取決于安裝在工作主軸上的導(dǎo)軌和軸承的精度。這里，認為機器的部件的精度可以選擇，不論尺寸大小，而且運動誤差的尺寸效應(yīng)和裝配誤差一樣被假設(shè)為1。切削力分為三方向，即原發(fā)法向力，推力和進給力。 一個簡單的彎曲和壓縮的梁依照每一個元素的應(yīng)力方向，由切削力導(dǎo)致的變形引起的尺寸效應(yīng)分別假設(shè)為1/n和1/，如果溫度升高，一般的，金屬會膨脹，長度l的形變可以用以下公式計算 這里的α表示一個熱膨脹的線性系，T表示溫度的增量。因此，熱變形的尺寸效應(yīng)用n表示。 圖1.3 微型車床的誤差產(chǎn)生 表1.2 誤差函數(shù)的尺寸效應(yīng) 3.3結(jié)果與討論 維度的每個單元的模型圖 1.2 須計算誤差。高級的微型車床實際尺寸用圖。 1.1顯示 ，而這些都是n = 1 的模型。那么該模型被放大n倍與Eq誤差。 （ 4 ）用上述在表1.2中提到的使用尺寸效應(yīng)誤差的方法計算。以及如何通過改變n從0.5至10 來改變誤差。然而，工件和刀具的尺寸都被假定為恒不論n ，其R是2.5毫米， h是10毫米t是8毫米。在此方法中，誤差的實際值是計算所必需的。因此，對于n=1，每個誤差的大小正如表1.1所示是確定的。裝配和運動誤差是由微型車床來確定的。這兩個錯誤，可以采取正或負的價值，并表達為符號+或-。由切削力和熱引起的變形被FEM獲得。工件和刀具的變形沒有考慮到。元件7被確定和每個元件的變形大小也被獲得了。應(yīng)用于工件的接觸力 是通過計算工作主軸的發(fā)動機的額定扭矩得來的，它是假定位主要的切削力。 該3個被分開的切削力通過被提及的[8]來決定。當大氣壓升高到20K時每一個元件的變形被按照熱變形來計算。因為目標是一個圓柱形的零件，切削半徑誤差δ R和軸向誤差δ z被定義誤差的評價函數(shù)。R '和R分別是實際的和指示的切削半徑。δR 按照下面給出。 裝備和運動誤差采用表1.1中的正或負的值，那些項目的數(shù)量是44。如果在每個項目的加/減情況被結(jié)合，2個形態(tài)來計算。這結(jié)合是如此之大以致正交的工作臺 在這里，直交的L64工作臺通過Eq來獲得r和評價函數(shù)用64種情況來計算。 加工尺寸n (a)半徑誤差δH 加工尺寸n 縱向誤差δz 圖1.4 關(guān)系的評價職能和機器大小 加工尺寸n 圖1.5規(guī)格化評估函數(shù)的改變趨勢 \ 關(guān)系機器尺寸N和有關(guān)平均評價函數(shù)平均值之間的關(guān)系表現(xiàn)在圖1.4里 。該最高/最低值也在圖表中表示出來了?！鱎增長隨著n的增長而變化。最高值和最低值之間的差值也增大。裝配誤差和熱變形的可能是出現(xiàn)這一現(xiàn)象的原因。雖裝配誤差不能完全隨著n值變化而變，如表1.2所示 ，隨著n值的增加坐標變化幅度也開始變大，進而re 也變大。熱變形增加，是因為尺寸的影響。至于△ z ， 有有一個最小值接近于n=1.5 。當n>1.5時△R和△z同時增大。當n 變小時，△z只是由于切削力產(chǎn)生輕微的影響。這意味著這種機器存在著一種合適的尺寸加工特定的工件。這里，R為2.5所以R〉△X，盡管n變成小了△Y和△R幾乎保持一致，如表（ 6 ）所示。 結(jié)果如表1.5所示。當N=10的時候△R和△z的數(shù)值為8和3.4 。可以說△R對于機器尺寸的敏感度比較高。誤差和尺寸的影響對計算結(jié)果的影響是相當大的，見圖表1.1和1.2。在這個研究中，錯誤功能對尺寸的影響被簡化。還需要更多的研究去完善結(jié)論的精確性。 4 結(jié)論 研究中，檢驗了切削表現(xiàn)對切削精度的影響程度。結(jié)論歸納如下： 1 .影響切削性能的錯誤功能被檢查到。對于錯誤尺寸影響的計算結(jié)論可以應(yīng)用于成型理論。 2 .理論是建立在度量實際的微型車床的基礎(chǔ)之上的，也獲得了誤差和機床尺寸之間的關(guān)系。計算理論錯誤和熱變形是對機床產(chǎn)生最嚴重影響的因素。 參考文獻: [1] Okazaki, Y., et al., (2004) Microfactory: Concept, history and developments. Trans. ASME, J. Manufacturing Science and Engineering 126: 837-844 [2] Park, J. K., et al., (2006) A precision meso scale machine tools with air bearings for microfactory. Proc 5th Int.Workshop on Microfactories, Besancon, France (CDROM) [3] Iijima, D, et al., (2004) Micro Turning System 3 (MTS3): A practical CNC lathe for microfactories. Proc. 4th Int. Workshop on Microfactories, Shanghai, China 1: 50-55 [4] Yamanaka, M, et al., (2006), Relation between mechanical characteristic and cutting performance of micro lathe. Proc 5th Int. Workshop on Microfactories, Besancon, France(CD-ROM) [5] Mishima, N., (2003) Design of a Miniature Manufactuirng System for Micro-fabrication. Proc 10th Annual Conf. for Concurrent Engineering, Modeira, Pirtugal 1129-1135 [6] Reshtov, D. N., Portman, V. T., (1988) Accuracy of machine tools. ASME Press, New York [7] Taguchi, G., Konishi, S., (1994) Quality engineeringseries. ASI Press [8] Sugita, T., et al., (1984) Fundamentals of cutting (inJapanese). Kyoritsu Publish