車床轉盤零件機械加工工藝規(guī)程及銑夾具設計【車外圓端面+銑燕尾】 長227【含6張CAD圖紙+PDF圖】

喜歡這套資料就充值下載吧。。。資源目錄里展示的都可在線預覽哦。。。下載后都有，，請放心下載，，文件全都包含在內，，【有疑問咨詢QQ:414951605 或 1304139763】

青島理工大學 機械加工工藝過程卡片 產(chǎn)品型號 零件圖號 產(chǎn)品名稱 車床轉盤 零件名稱 車床轉盤 共1頁 第1頁 材料 牌號 HT200 毛坯種類 鑄件 毛坯外形尺寸 每毛坯可制件數(shù) 1 每臺件數(shù) 1 備注 工序號 工序名稱 工序內容 車間 工段 設備 工藝設備 工時/s 準終 單件 1 銑削 粗銑燕尾面M、H及空刀面和凹臺面，以底面P為主要定位基準，兩側面K為第二定位基準。 X51立式銑床 專用夾具 138.9 2 銑削 粗銑+半精銑轉盤的兩個端面Q和R，以M、H面以及未加工面N為定位基準。 X61臥式銑床 專用夾具 69 3 車削 粗車+半精車+精車加工轉盤底面P、外圓面N、端面L等以已加工面M、H、Q面定位，實現(xiàn)完全定位。 C620-1臥式車床 專用夾具 4.8 4 銑削 粗銑+半精銑加工轉盤的196mm圓弧面和尺寸132mm的兩側面K，以底面P、外圓面N、燕尾面H定位。 X51立式銑床 專用夾具 52 6 銑削 精銑燕尾面M、H及空刀面和凹臺面，以已加工面底面P為主要定位基準，以已加工兩側面K為第二定位基準。 X51立式銑床 專用夾具 21.3 7 鉆孔 鉆、擴、鉸孔 Z550型立式鉆床 專用夾具 15.66 8 鉆孔 鉆2孔 Z550型立式鉆床 專用夾具 24 9 倒角、去毛刺 倒角、去毛刺 C620-1臥式車床 專用夾具 10 檢驗 檢查 LATHE The basic machines that are designed primarily to do turning, facing and boring are called lathes. Very little turning is done on other types of machine tools, and none can do it with equal facility. Because lathe can do boring, facing, drilling, and reaming in addition to turning, their versatility permits several operations to be performed with a single setup of the workpiece. These accounts for the fact that lathes of various types are more widely used in manufacturing than any other machine tool. Lathes in various forms have existed for more than two thousand years. Modem lathes date from about 1797, when Henry Maudsley developed one with a lea&crew. It provided controlled, mechanical feed of the tool. This ingenious Englishman also developed a changegear system that could connect the motions of the spindle and lea&crew and thus enable threads to be cut. Lathe Construction. The essential components of a lathe are depicted in the block diagram. These are the bed, headstock assembly, tailstock assembly, carriage assembly, quick-change gear box, and the lea&crew and feed rod. The bed is the backbone of a lathe. It usually is made of well-normalized or aged gray or nodular cast iron and provides a heavy, rigid frame on which all the other basic components are mounted. Two sets of parallel, longitudinal ways, inner and outer, are contained on the bed, usually on the upper side. Some makers use an inverted V-shape for all four ways, whereas others utilize one inverted V and one flat way in one or both sets. Because several other components are mounted and/or move on the ways they must be made with precision to assure accuracy of alignment. Similarly, proper precaution should be taken in operating a lathe to assure that the ways are not damaged. Any inaccuracy in them usually means that the accuracy of the entire lathe is destroyed. The ways on most modem lathes are surface hardened to offer greater resistance to wear and abrasion. The headstock is mounted in a fixed position on the inner ways at one end of the lathe bed. It provides a powered means of rotating the work at various speeds. It consists, essentially, of a hollow spindle, mounted in accurate bearings? And a set of transmission gears similar to a truck transmission through which the spindle can be rotated at a number of speeds. Most lathes provide from eight to eighteen speeds, usually in a geometric ratio, and on modem lathes all the speeds can be obtained merely by moving from two to four levers. An increasing trend is to provide a continuously variable speed range through electrical or mechanical drives. Because the accuracy of a lathe is greatly dependent on the spindle, it is of heavy construction and mounted in heavy bearings, usually preloaded tapered roller or ball types, a longitudinal hole extends through the spindle so that long bar stock can be fed through it. The size of this hole is an important size dimension of a lathe because it de termines the maximum size of bar stock that can be machined when the material must be fed through the spinale. The inner end of the spindle protrudes from the gear box and contains a means for mounting various types of chucks, face plates, and dog plates on it. Whereas small lathes often employ a threaded section to which the chucks are screwed, most large lathes utilize either cam-lock or key-drive taper noses. These provide a large-diameter taper that assures the accurate alignment of the chuck, and a mechanism that permits the chuck or face plate to be locked or unlocked in position without the necessity of having to rotate these heavy attachments. Power is supplied to the spindle by means of an electric motor through a V-belt or silent-chain drive. Most modem lathes have motors of from 5 to15 horsepower to provide adequate power for carbide and ceramic tools at their high cutting speeds. The tailstock assembly consists, essentially, of three parts. A lower casting fits on the inner ways of the bed and can slide longitudinally thereon, with a means for clamping the entire assembly in any desired location. An upper casting fits on the lower one and can be moved transversely upon it on some type of keyed ways. This transverse motion pemfits aligning the tailstock and headstock spindles and provides a method of tuming tapers. The third major component of the assembly is the tailstock quill. This is a hollow steel cylinder, usually about 2 to sinches in diameter, that can be moved several inches longitudinally in and out of the upper casting by means of a handwheel and screw. The open end of the quill hole terminates in a morse. Taper in which a lathe center, or various tools such as drills, can be held. A graduated scale, several inches in length, usually is engraved on the outside of the quill to aid in controlling its motion in and out of the upper casting. A locking device permits clamping the quill in any desired position. The carriage assembly provides the means for mounting and moving cutting tools. The carriage is a reianvely fiat H-shaped casting that rests and moves on the outer set of ways on the bed. The transverse bar of the carriage contains ways on which the cross slide is mounted and can be moved by means of a feed screw that is controlled by a small handwheel and a graduated dial. Through the cross slide a means is provided for moving the lathe tool in the direction normal to the axis of rotation of the work. On most lathes the tool post actually is mounted on a compound rest. This consists of a base, which is mounted on the cross slide so that it can be pivoted about a vertical axis, and an .upper casting. The upper casting is mounted on ways on this base .so that it can be moved back and forth and controlled by means of a short lead screw operated by a handwheel and a calibrated dial. Manual and powered motion for the carriage, and powered motion for the cross slide, is provided by mechanisms within the apron, attached to the front of the carriage. Manual movement of the carriage along the bed is effected by turning a handwheel on the front of the apron, which is geared to a pinion on the back side. This pinion engages a rack that is attached beneath the upper front edge of the bed in an inverted position. To impart powered movement to the carriage and cross slide, a rotating feed rod is provided. The feed rod, which contains a keyway throughout most of its length, passes throughthe two reversing bevel pinions and is keyed to them. Either pinion cam be brought into mesh with a mating bevel gear by means of the reversing lever on the front of the apron and thus provide "forward" or "reverse" power to the carriage. Suitable clutches connect either the rack pinion or the cross-shde screw to provide longitudinal motion of the carriage or transverse motion of cross slide. For cutting threads, a second means of longitudinal drive is provided by a lead screw. Whereas motion of the carriage when driven by the feed-rod mechanism takes place through a friction clutch in which shppage is possible, motion through the lead screw is by a direct, mechanical connection between the apron and the lead screw, s This is achieved by a split nut. By means of a clamping lever on the front of the apron, the split nut can be closed around the lead screw. With the split nut closed, the carriage is moved along the lead screw by direct drive without possibility of slippage. Modern lathes have a quick-change gear box. The input end of this gear box is driven from the lathe spindle by means of suitable gearing. The output end of the gear box is connected to the feed rod and lead screw. Thus, through this gear train, leading from the spindle to the quick-change gear box, thence to the lead screw and feed rod, and then to the carriage, the cutting tool can be made to move a specific distance, either longitudinally or transversely, for each revolution of the spindle. A typical lathe provides, through the feed rod, forty-eight feeds ranging from 0.002 inch to 0.118 inch per revolution of the spindle, and, through tne lead screw, leads for cutting forty-eight different threads from 1.5 to 92 per inch. On some older and some cheaper lathes, one or two gears in the gear train between the spindle and the change gear box must be changed in order to obtain a full range of threads and feeds. 車床 用與車外圓、端面和鏜孔等加工的機床叫車床。車削很少在其他種類的機床上進行，因為其他機床都不能像車床那樣方便地進行車削加工。由于車床除了用于車外圓外還能用于鏜孔、車端面、鉆孔和鉸孔，車床的多功能性可以使工件在一次定位安裝中完成多種加工。這就是在生產(chǎn)中普遍使用各種車床比其他種類的機床都要多的原因。 兩千多年前就已經(jīng)有了車床?，F(xiàn)代車床可以追溯到大約1797年，那時亨利·莫德斯利發(fā)明了一種具有絲杠的車床。這種車床可以控制工具的機械進給。這位聰明的英國人還發(fā)明了一種把主軸和絲杠相連接的變速裝置，這樣就可以切削螺紋。 車床的主要部件：床身、主軸箱組件、尾架組件、拖板組件、變速齒輪箱、絲杠和光杠 床身是車床的基礎件。它通常是由經(jīng)過充分正火或時效處理的灰鑄鐵或者球墨鑄鐵制成，它是一個堅固的剛性框架，所有其他主要部件都安裝在床身上。通常在床身上面有內外兩組平行的導軌。一些制造廠生產(chǎn)的四個條導軌都采用倒“V”形，而另一些制造廠則將倒“V”形導軌和平面導軌相結合。由于其他的部件要安裝在導軌上并(或)在導軌上移動，導軌要經(jīng)過精密加工，以保證其裝配精度。同樣地，在操作中應該小心，以避免損傷導軌。導軌上的任何誤差，常常會使整個機床的精度遭到破壞。大多數(shù)現(xiàn)代車床的導軌要進行表面淬火處理，以減小磨損和擦傷，具有更大的耐磨性。主軸箱安裝在床身一端內導軌的固定位置上。它提供動力，使工件在各種速度下旋轉。它基本上由一個安裝在精密軸承中的空心主軸和一系列變速齒輪——類似于卡車變速箱所組成，通過變速齒輪，主軸可以在許多種轉速下旋轉。大多數(shù)車床有8—18種轉速，一般按等比級數(shù)排列。在現(xiàn)代車床上只需扳動2～4個手柄，就能得到全部擋位的轉速。目前發(fā)展的趨勢是通過電氣的或機械的裝置進行無級變速。 由于車床的精度在很大程度上取決于主軸，因此主軸的結構尺寸較大，通常安裝在緊密配合的重型圓錐滾子軸承或球軸承中。主軸中有一個貫穿全長的通孔，長棒料可以通過該孔送料。主軸孔的大小是車床的一個重要尺寸，因為當工件必須通過主軸孔供料時，它確定了能夠加工棒料毛坯的最大外徑尺寸。 主軸的內端從主軸箱中凸出，其上可以安裝多種卡盤、花盤和擋塊。而小型的車床常帶有螺紋截面供安裝卡盤之用。很多大車床使用偏心夾或鍵動圓錐軸頭。這些附件組成了一個大直徑的圓錐體，以保證對卡盤進行精確地裝配，并且不用旋轉這些笨重的附件就可以鎖定或松開卡盤或花盤。 主軸由電動機經(jīng)V帶或無聲鏈裝置提供動力。大多數(shù)現(xiàn)代車床都裝有5—15馬力的電動機，為硬質合金和金屬陶瓷合金刀具提供足夠的動力，進行高速切削。 尾座組件主要由三部分組成。底座與床身的內側導軌配合，并可以在導軌上做縱向移動，底座上有一個可以使整個尾座組件夾緊在任意位置上的裝置。尾座安裝在底座上，可以沿鍵槽在底座上橫向移動，使尾座與主軸箱中的主軸對中并為切削圓錐體提供方便。尾座組件的第三部分是尾座套筒，它是一個直徑通常在2～3英寸之間的鋼制空心圓柱軸。通過手輪和螺桿，尾座套筒可以在尾座體中縱向移入和移出幾英寸?；顒犹淄驳拈_口一端具有莫氏錐度，可以用于安裝頂尖或諸如鉆頭之類的各種刀具。通常在活動套筒的外表面刻有幾英寸長的刻度，以控制尾座的前后移動。鎖定裝置可以使套筒在所需要的位置上夾緊。 拖板組件用于安裝和移動切削工具。拖板是一個相對平滑釣H形鑄件，安裝在床身外側導軌上，并可在上面移動。大拖板上有橫向導軌，使橫向拖板可以安裝在上面，并通過絲杠使其運動，絲杠由一個小手柄和刻度盤控制。橫拖板可以帶動刀具垂直于工件的旋轉軸線切削。 大多數(shù)車床的刀架安裝在復式刀座上，刀座上有底座，底座安裝在橫拖板上。可繞垂直軸和上刀架轉動；上刀架安裝在底座上，可用手輪和刻度盤控制一個短絲杠使其前后移動。溜板箱裝在大拖板前面，通過溜板箱內的機械裝置可以手動和動力驅動大拖板以及動力驅動橫拖板。通過轉動溜板箱前的手輪，可以手動操作拖板沿床身移動。手輪的另一端與溜板箱背面的小齒輪連接，小齒輪與齒條嚙合，齒條倒裝在床身前上邊緣的下面。利用光杠可以將動力傳遞給大拖板和橫拖板。光杠上有一個幾乎貫穿于整個光杠的鍵槽，光杠通過兩個轉向相反并用鍵連接的錐齒輪傳遞動力。通過溜板箱前的換向手柄可使嚙合齒輪與其中的一個錐齒輪嚙合，為大拖板提供“向前”或“向后”的動力。適當?shù)碾x合器或者與齒條小齒輪連接或者與橫拖板的螺桿連接，使拖板縱向移動或使橫拖板橫向移動。 對于螺紋加工，絲杠提供了第二種縱向移動的方法。光杠通過摩擦離合器驅動拖板移動，離合器可能會產(chǎn)生打滑現(xiàn)象。而絲杠產(chǎn)生的運動是通過溜板箱與絲杠之間的直接機械連接來實現(xiàn)的，對開螺母可以實現(xiàn)這種連接。通過溜板箱前面的夾緊手柄可以使對開螺母緊緊包合絲杠。當對開螺母閉合時，可以沿絲杠直接驅動拖板，而不會出現(xiàn)打滑的可能性。 現(xiàn)代車床有一個變速齒輪箱，齒輪箱的輸入端由車床主軸通過合適的齒輪傳動來驅動。齒輪箱的輸出端與光杠和絲杠連接。主軸就是這樣通過齒輪傳動鏈驅動變速齒輪箱，再帶動絲杠和光杠，然后帶動拖板，刀具就可以按主軸的轉數(shù)縱向地或橫向地精確移動。一臺典型的車床的主軸每旋轉一圈，通過光杠可以獲得從0．叩2到0．118英寸尺寸范圍內的48種進給量；而使用絲杠可以車削從1．5到92牙／英寸范圍內的48種不同螺紋。一些老式的或價廉的車床為了能夠得到所有的進給量和加工出所有螺紋，必須更換主軸和變速齒輪箱之間的齒輪系中的一個或兩個齒輪。 7 International Journal of Machine Tools received in revised form 2 October 2000; accepted 6 October 2000 Abstract Gears are crucial components for modern precision machinery as a means for the power transmission mechanism. Due to their complexity and unique characteristics, gears have been designed and manufactured by a special type of machine tools, such as gear hobbing and shaping machines. In this paper, we attempt to manufacture the spiral bevel gear (SBG: the most complex type among the gear products) by a three- axis CNC milling machine interfaced with a rotary table. This consists of (a) geometric modeling of the spiral bevel gears, (b) process planning for NC machining, (c) a tool path planning and execution algorithm for both 4-axis and 3/4-axis (three out of four axes) controls. Experimental cuts were made to ascertain the validity and effectiveness of the presented method with a CNC milling machine controlled by the 3/4- axis control mode. 2001 Published by Elsevier Science Ltd. Keywords: Gear manufacturing; Spiral bevel gear; Geometric modeling of gears; Sculptured surface machining; Rotary table application; Additional-axis machining technology 1. Introduction Gears are efficient and precision mechanisms for industrial machinery as a means for power transmission. Among the various types of gears (Fig. 1), the spiral bevel gears (SBG) are the most complex type and are used to transmit the rotational motion between angularly crossed shafts. Previous studies on gears have been mainly concerned with the design and analysis of gears. The geometric characteristics and design parameters of SBGs have been studied extensively * Corresponding author. Fax: +82-54-279-5998. E-mail address: shspostech.ac.kr (S.H. Suh). 0890-6955/01/$ - see front matter 2001 Published by Elsevier Science Ltd. PII: S0 890-6955(00)00104-8 834 S.H. Suh et al. / International Journal of Machine Tools (2) by the SSM method, a broad range Fig. 2. Special machine tools and cutters for manufacturing SBGs. 835S.H. Suh et al. / International Journal of Machine Tools (3) a special type of gear, for instance “huge” gears of diameter over 1000 mm, and “crown” gears can be machined by the SSM method, which cannot be done by the dedicated gear machine tools, except in very limited cases. In view of the above, special attention is given to the capability of the SSM method in terms of geometric accuracy and surface quality together with machining time. If the performance is comparable, except for the production rate, the SSM method can be applied in industrial practice for NC machining of huge SBGs, while the production rate is not emphasized. This paper presents comprehensive technology including geometric modeling, process planning, tool path algorithms, and experimental validation. 2. Geometric modeling of the SBGs Typically, geometric specification of SBGs is given by a set of parameters. These parameters are provided with an engineering drawing, as shown in Fig. 3. Some parameters (principal parameters) are required for defining the geometry, while others (auxiliary parameters) can be derived based on a formula. Table 1 summarizes some of the crucial parameters including relation- ships among parameters 2. Using the parameters, the surface model can be derived as follows. As illustrated in Fig. 4, the surface between two teeth is modeled by the large section curve swept along the spiral curve. The section curve is decomposed into five fragments; S i (u i , i P 1:5, where u i P 0, u max i ) is the parameter for fragment i. Denoting w by the parameter along the spiral curve, the surface model can be represented by S i (u, w), i P 1:5 as shown in Fig. 4. S i and S 5 are the involute surfaces, and S 2 and S 4 the filleted surfaces, and S 3 the bottom surface. Fig. 3. An engineering drawing. 836 S.H. Suh et al. / International Journal of Machine Tools (b) only three axes out of the four axes can be controlled simultaneously. The latter is called the additional-axis machine system, which can often be found in industrial practice where the rotary table is controlled by the fourth axis of the three-axis machine tool controller (see 11 for details). In this paper, we present a tool path algorithm for both configurations. 3.2. Machining strategy The workpiece is premachined as a conic form by turning operation. The volume to be removed is the swept volume of the cross-section CUIW along the spiral curve defined by S i (u, w), i P 1:5). The volume is removed by several processes: (1) rough cut with several flat endmills; (2) semi-finished cut with several ball endmills; and (3) finish cut with a ball endmill. To minimize the machining time, a larger tool is desired for the rough cut and semi-finish cut. The finish cut allowance is set (for instance 0.3 mm), and the semi-finish cut removes the uneven surface (resulting from the rough cut). During the finish cut, the whole surface is machined by a single ball endmill of diameter D=0.8I (this is based on a heuristic), where I is the chodal length between the two points defining the S 3 curve in the small section curve (see Fig. 4). This is to prevent any cutter marks on the surface due to tool change. Tool path algorithms for rough and semi-finished cuts are omitted for the brevity of the paper. 3.3. Tool path planning for finish cut The surface model S 1 (u, w) is machined by a ball endmill of radius R. As mentioned earlier, the involute surfaces S 1 and S 5 are the most important surfaces, the accuracy of which should be strictly controlled. Our method is based on the CC-parametric scheme, where the CC-points are sampled from the parametric surface model, equally distanced on the parametric plane. For the sake of machining efficiency, tool motion along the w direction is chosen. In what follows, inter- ference-free CL-data for S 5 (u, w) is presented, as the same can be applied for S 1 (u, w). 841S.H. Suh et al. / International Journal of Machine Tools and (b) finding a feasible range of the interference-free tool axis, followed by selecting an interference-free axis. We take the second approach. In what follows, we present a computationally efficient method for finding a feasible range defined by the two bounding axes A 1 and A r for the given CC-point S 1 (u, w) as shown in Fig. 8. Suppose the tool center point and its unit normal vector are given by C and N C . Then, the tool motion in the four-axis configuration is defined on the CL-plane: P C =PuP x =C x , where C x is the x value of C. Let C 1i , i P 1:m, C 2j , j P 1:n be the offset points on the CL-plane (Fig. 9). Noting that T 1 P C 1i , T 2 P C 2i , consider the problem of finding T i . Define the reference axis (Fig. 9(a) as V5CC 11 3N C (11) Fig. 7. TBI in the boundary region. 842 S.H. Suh et al. / International Journal of Machine Tools A5 uCT 2 uCT 1 +uCT 1 uCT 2 uCT 2 uCT 1 +uCT 1 uCT 2 (16) In general, the tool axis vector is not aligned with the spindle axis (Z). In the four-axis con- figuration where the workpiece is oriented by the rotary table, it is necessary to align the tool axis vector with the spindle axis. The rotation angle to access a CC-point S 5 (u, w) is determined such that the tool axis vector A(u, w) is parallel to the XZ-plane. Decomposing the tool axis vector into A x , A y , A z the rotation angle (Fig. 10) is Fig. 10. Tool-axis determination for four-axis control. 844 S.H. Suh et al. / International Journal of Machine Tools 2. convert the rotational angle range into the y i value y min i , y max i by Eq. (17). Step 2: Determine y* as follows: set I=1, where I is the number of groups in the CC-path 1. find y min i , y max i =intersection of y min i , y max i , for i P I; 2. if the intersection range is found, then y =y min +y max /2, and exit; 3. otherwise, divide the CC-points into I+1 groups and go to Step 2.2. 845S.H. Suh et al. / International Journal of Machine Tools (b) Adjacent pitch error, (c) Accumulated pitch error. 5. Concluding remarks In this paper we attempted to manufacture the spiral bevel gear using the CNC milling machine based on the sculptured surface machining method. For such a purpose, we investigated surface modeling and the tool path computing algorithm. The surface model accepts the gear parameters as input and outputs the bi-parametric surface model so that it can be directly used for deriving the tool path via the CC-parametric scheme. Note that almost all previous works have been con- cerned with the design aspect, and the bi-parametric surface model has not been explicitly derived. The tool path algorithm presented in this paper was based on the CC-parametric scheme. In developing the tool path algorithm, geometric accuracy and surface quality were addressed, 850 S.H. Suh et al. / International Journal of Machine Tools & Manufacture 41 (2001) 833850 together with machine tool configuration. By the tool path algorithm. the involute surface can be accurately machined without tool interference due to tool size and the tool axis for both four- axis and 3/4-axis control. Also, we tried to reduce the computational complexity by exploiting the geometric characteristics of the gear. The validity of the surface model was verified via comparison with the genuine product (manufactured by dedicated machine tools). The result showed good conformity, as the bi-para- metric model was derived based on the definition of the gear parameters. Even if there is slight unconformity, the performance of a pair of gears is practically acceptable. Also, the machined pair of gears was tested via a gear-mating machine, showing a smooth motion without noise. Distinguished from the conventional method by the dedicated machine tools, the presented method can produce any type and size of SBGs, so long as the geometric model is provided. Hence, it can be practically applied, especially to produce huge gears with crowns which cannot be machined by the dedicated machine tool. Elaboration of the machining strategy and feedrate optimization for the reduction of machining time is left for further study. Acknowledgements The research work in this paper was in part supported by a grant from the National Research Laboratory for STEP-NC Technology, and the Korea Research Fund under Contract No. 1998- 018-E00152. References 1 D. Dudley, Practical Gear Design, MacMillan, New York, 1954. 2 D. Dudley, Gear Handbook, MacMillan, New York, 1962. 3 A. Sloane, Engineering Kinematics, Dover, New York, 1966. 4 R. Huston, J. Coy, Ideal spiral bevel gears a new approach to surface geometry, ASME Journal of Mechanical Design 103 (1) (1981) 127133. 5 R. Huston, J. Coy, Surface geometry of circular cut spiral bevel gears, ASME Journal of Mechanical Design 104 (4) (1982) 743748. 6 Y. Tsai, P. Chin, Surface geometry of straight and spiral bevel gears, ASME Journal of Mechanisms, Trans- missions, and Automation in Design 109 (4) (1987) 443449. 7 M. Al-Daccak, I. Angeles, M. Gonzalez-Palacios, The modeling of bevel gears using the exact spherical involute, ASME Journal of Mechanical Design 116 (1994) 364368. 8 M. Shunmugam, S. Narayana, V. Jayapraksh, Establishing gear tooth surface geometry and normal deviation. Part I cylindrical gears, Journal of Mechanism and Machine Theory 33 (5) (1998) 517524. 9 M. Shunmugam, B. Rao, V. Jayapraksh, Establishing gear tooth surface geometry and normal deviation. Part II bevel gears, Journal of Mechanism and Machine Theory 33 (5) (1998) 525534. 10 S. Suh, J. Kang, Process planning for multi-axis NC machining of free surfaces, International Journal of Production Research 33 (10) (1995) 27232738. 11 S. Suh, J. Lee, Multi-axis machining with additional-axis NC system, International Journal of Advanced Manufac- turing Technology 14 (1998) 865875. 12 S. Sub et al., Development of 4-axis surface manufacturing technology using CNC milling machine, Technical report TR-IE-99012, POSTECH, April 1999.