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黄河科技学院毕业设计 (文献综述 ) 第 1 页 QY3 型石油管道牵引机主机设计摘要摘要：石油管道牵引机研究的是在油田工地的输送油管装置的机器，此牵引机可以提供连续传输油管时的牵引力，它主要由主机部分、齿轮基座、减速装置、传动装置、输送装置等几部分组成。本课题是设计牵引机的主机部分。需要对输油管牵引机械进行特性分析、整体方案的拟定、动力机的选择等工作。关键词关键词：牵引机，主机，输送装置1.前言机械制造业是国民经济最重要的支柱产业之一，是国民经济的装备部，在国民经济中发挥着十分重要的作用。据相关资料介绍，机械制造业是国民经济最重要的支柱产业之一，机械制造业提供的装备水平对国民经济各个部门的技术进步有着相当大的影响，其规模水平是衡量一个国家国民经济实力和科学技术水平的重要尺度。 ，在经济全球化和社会信息化的大趋势下，只有通过推进企业的信息化建设，提高企业核心竞争力，才能带动整个机械制造行业的现代化发展。企业信息化的实质是增强企业的核心竞争力，通过实施信息化，加强技术创新和管理创新能力，使企业及其产品获得市场竞争优势。机械制造企业信息化是指，充分利用以现代信息技术为代表的高新技术对传统产业的渗透以及信息技术与其它专业技术的融合，在机械产品全生命周期中，通过信息技术的应用、信息资源的开发、利用、集成和共享，达到企业资源的优化配置和高效运转，从而提高机械企业的经济效益和整体竞争力，改造和提升传统的机械企业。2 输送机的发展趋势2.1 课题背景及目的在牵引机行业，牵引机械是一种应用十分广泛的产品。为了不断增大其应用范围，常常需要将其基架系统、传动系统、间隙调整系统、牵引系统进行优化改进，从而提高系统稳定性，并改善质量及性能。考虑到现代动力机械行业的机械化程度的进一步加深，这类机械的需求量还会进一步扩大，如果能设计出一种功能更加完善的新型机黄河科技学院毕业设计 (文献综述 ) 第 2 页 械，并互不干涉，不仅能节省材料消耗，降低生产成本，还能方便加工操作，提高工作效率。如何能更好的设计出来，占领这个制高点，就要求我们能很快地理解掌握同类产品，消化吸收，再加以综合优化，才能完成。我们应该把这次毕业设计当成我们在工作中的一次考核，努力并且高质量的去完成它。1） 、继续向大型化发展。大型化包括大输送能力、大单机长度和大输送倾角等几个方面。水力输送装置的长度已达 440 公里以上。带式输送机的单机长度已近 15 公里，并已出现由若干台组成联系甲乙两地的带式输送道。不少国家正在探索长距离、大运量连续输送物料的更完善的输送机结构。2） 、扩大输送机的使用范围。发展能在高温、低温条件下、有腐蚀性、放射性、易燃性物质的环境中工作的，以及能输送炽热、易爆、易结团、粘性的物料的输送机。3） 、使输送机的构造满足物料搬运系统自动化控制对单机提出的要求。如邮局所用的自动分拣包裹的小车式输送机应能满足分拣动作的要求等。4） 、降低能量消耗以节约能源，已成为输送技术领域内科研工作的一个重要方面。已将 1 吨物料输送 1 公里所消耗的能量作为输送机选型的重要指标之一。5） 、减少各种输送机在作业时所产生的粉尘、噪声和排放的废气。 3.牵引机介绍分类结构及工作原理随着我国综合国力和科技水平的提高，我们对能源的开发和利用也日趋扩大规模。然而我国能源储量有限并且分布不均，这就要求我们在开发利用能源的过程中努力实现对能源的高效、合理的开发。那么，我们就要使用领先技术，以及设备的自动化和科技化。经过我国几代人的努力，我国的机械设备制造水平已取得很大的提高。牵引机作为设备的一种可以反映我国的设备先进化。牵引机主要靠工件与其接触摩擦力来实现传动的。3.1 牵引机的分类根据结构可以讲牵引机分为两大类：履带式和滚筒式。图(1)如下：黄河科技学院毕业设计 (文献综述 ) 第 3 页 图（1）履带式牵引机主要用于小部件成批量的传送，滚筒式牵引机主要用于单件连续型设备的传送。本次设计的牵引机用于连续传送输油管时提供牵引力，因此选择滚筒式牵引机结构。3.2 滚筒式牵引机结构滚筒式牵引机主要由主机部分、齿轮基座、减速机等主要部分组成。它的传动示意图可表示如图（2）所示：图（2）3.3 输油管牵引机的组成及工作原理输油管牵引机由电机，减速部分，分动箱，辊筒，机架部分组成，根据输油管的输送要求，由齿轮带动辊筒依靠辊筒与输油管之间摩擦力完成牵引工作。牵引机的结构简图如图（2）：黄河科技学院毕业设计 (文献综述 ) 第 4 页 1:辊筒；2：机架；3：分动箱4：联轴器；5：减速机；6：电动机牵引机结构简图 （2）4.方案选择牵引机主机的动力输入有三种方案：方案一：下边三个滚筒作为主动轮，上边三个滚筒随动。结构简图如图（3）：图（3）图（3）中，油管均匀，重力为 3G，分担在下侧三个滚筒上。油管受下侧每个滚黄河科技学院毕业设计 (文献综述 ) 第 5 页 筒牵引力 F 和正压力NF，有关要带动上侧滚筒转动，受上侧滚筒静摩擦力 f 和正压力1NF。方案二：上边三个滚筒作为主动轮，下边三个滚筒随动。结构简图如图（4）：图（4）图示中，油管均匀，重力为 3G，分担在下侧三个滚筒上。油管受上侧每个滚筒牵引力 F 和正压力 FN，有关要带动下侧滚筒转动，受下侧滚筒静摩擦力 f 和正压力FN1。方案三：上下六个滚筒均作为主动轮。结构简图如图（5）：黄河科技学院毕业设计 (文献综述 ) 第 6 页 图（5）图(5)中，油管均匀，重力为 3G，分担在下侧三个滚筒上。油管受上侧每个滚筒牵引力 F 和正压力 FN，受下侧每个滚筒牵引力 F 和正压力 FN1。方案一和方案二均是牵引机主机单侧滚筒提供牵引力传送油管，其动力传递部分结构简单，尤其是分速器部分。但是其主机要产生所需牵引力，在没个主动滚筒上所要承受的正压力比较大，这对滚筒的强度刚度要求也高些。方案三中牵引机主机两侧滚筒同时提供牵引力传送输油管，虽然使传送动力的分速器结构复杂一些，但是要产生所需牵引力，分布在每个滚筒上的正压力要小得多，从而使滚筒的尺寸和强度刚度要求低一些。因此选用方案三。滚筒的组数将在设计中确定。5. 设计计算根据已知参数完成滚筒数量、尺寸大小及结构的设计计算，轴的设计及校核， 轴承的选用和校核，键的选择，轴承端盖的设计，轴承座的确定，弹簧的选定，压板的确定，支架结构设计，机身结构分析，联轴器的选择等。参考文献1余载强，张国志 玻璃钢型材料牵引机的研制J.辽林：辽林工学院，19972曹明忠 海底电缆牵引机P.山东：胜利石油化工建设有限责任公司，20033吴棕泽，机械设计手册M.北京：机械工业出版社，20024余载强 李佳奇 新式大型牵引机设计J.辽林:辽林工学院，19995濮良贵.机械设计（第七版）M.北京：高等教育出版社，20036王俊昌.王荣声.工程材料及机械制造基础M.北京：机械工业出版社，19987 王世刚.机械设计实践.哈尔滨：哈尔滨工业大学出版社，2003.8 机械设计手册编委会.机械设计手册J.第 2 卷.北京：机械工业出版社，20049.BRUNO AGARD,BERNARD PENZ. A SIMULATED ANNEALING METHOD BASED ON A CLUSTERING APPROACH TO DETERMINE BILLS OF MATERIALS FOR A LARGE PRODUCT FAMILY. INT. J. PRODUCTION ECONOMICS 117 (2009) 389401.10.R.GALAN,J.RACERO,I.EGUIA,J.M.GARCIA. A SYSTEMATIC APPROACH 黄河科技学院毕业设计 (文献综述 ) 第 7 页 FOR PRODUCT FAMILIES FORMATION IN RECONfiGURABLE MANUFACTURING SYSTEMS.ROBOTICS AND COMPUTER-INTEGRATED MANUFACTURING 23 (2007) 489502.11.SOON CHONG JOHNSON LIM,YING LIU,WING BUN LEE.A METHODOLOGY FOR BUILDING A SEMANTICALLY ANNOTATED MULTI-FACETED ONTOLOGY FOR PRODUCT FAMILY MODELLING. ADVANCED ENGINEERING INFORMATICS 25 (2011) 147161.12.JACQUES LAMOTHE,KHALED HADJ-HAMOU,MICHEL ALDANONDO. AN OPTIMIZATION MODEL FOR SELECTING A PRODUCT FAMILY AND DESIGNING ITS SUPPLY CHAIN. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 169 (2006) 10301047. 毕业设计文献综述 院（系）名称工学院机械系 专业名称机械设计制造及其自动化 学生姓名于海涛 指导教师薛东彬2012年 03 月 10 日 Journal of Mechanical Science and Technology 23 (2009) 26242634 /content/1738-494xDOI 10.1007/s12206-009-0724-6 Journal of Mechanical Science and Technology A new accurate curvature matching and optimal tool based five-axis machining algorithm Than Lin1, Jae-Woo Lee1,* and Erik L. J. Bohez2 1Aerospace Information Engineering, Konkuk University, Seoul, 143-701, Korea 2Industrial Systems Engineering, Asian Institute of Technology, Bangkok, Thailand (Manuscript Received March 28, 2008; Revised June 17, 2009; Accepted July 3, 2009) - Abstract Free-form surfaces are widely used in CAD systems to describe the part surface. Today, the most advanced machin-ing of free from surfaces is done in five-axis machining using a flat end mill cutter. However, five-axis machining re-quires complex algorithms for gouging avoidance, collision detection and powerful computer-aided manufacturing (CAM) systems to support various operations. An accurate and efficient method is proposed for five-axis CNC ma-chining of free-form surfaces. The proposed algorithm selects the best tool and plans the toolpath autonomously using curvature matching and integrated inverse kinematics of the machine tool. The new algorithm uses the real cutter con-tact toolpath generated by the inverse kinematics and not the linearized piecewise real cutter location toolpath. Keywords: Five-axis NC machining; Curvature analysis; Toolpath planning; Tool selection - 1. Introduction Free-form surface parts are widely used in the aero-space, automobile, ship-building and mold/die manu-facturing industries. CNC (computer numerical con-trol) machining of free form surfaces is an important research topic 1, 2. The ever increasing complexity of free-form parts makes the benefits of five-axis milling continuously grow by changing three-axis to five-axis milling. The whole sculptured surface mill-ing process using three-axis NC and ball end mill is inefficient as noted by 3. Due to the two additional degrees of freedom, five-axis NC machining offers many advantages over three-axis, such as better tool accessibility, faster material removal rates, reduced machining time and improved surface finish. How-ever, collisions are prone to occur in five-axis ma-chining. Collision problems in five-axis NC machin-ing can be classified into two types: local and global collision. Local collision, one of the most critical problems in free-form surface machining refers to the removal of the excess material in the vicinity of the cutter contact (CC) point due to the mismatch in cur-vature between the tool swept surface and the part surface at the CC point. It results when a high curva-ture surface is machined using larger tool diameter or by a tool improperly oriented as shown in Fig. 1.Global collision refers to the accidental contacts (i) between the surface of the tool (or tool holder) and workpiece (or machine components), (ii) between workpiece and machine components), or (iii) between the moving machine components. Free form surfaces usually have irregular curvature distribution, which causes difficulty in machining. Machining of free-form surfaces requires the assistance of sophisticated CAD/CAM software to assist the numerical control (NC) programmer in the optimal cutter orientation and selection of cutter size. Manual planning and programming for sculptured surface machining is known to be error-prone and inefficient. The free This paper was recommended for publication in revised form byAssociate Editor Jooho Choi *Corresponding author. Tel.: +82 2 450 3461, Fax.: +82 2 3437 3548 E-mail address: jwleekonkuk.ac.kr KSME & Springer 2009 T. Lin et al. / Journal of Mechanical Science and Technology 23 (2009) 26242634 2625 Fig. 1. Local Tool Interference. form surface machining with more than three degrees of freedom needs high end commercial CAD/CAM system for the cutter location (CL) and orientation data 4. Milling the surface is divided into three phases: roughing, semi-roughing and finishing. Careful plan-ning is required to determine the five-axis toolpath for the finish machining of sculptured surfaces. In the finishing process of five-axis machining for free-form surface, there are drawbacks, such as complex tool movements, tool interference and tool undercut prob-lem. Thus it is necessary to find a method to select the optimal cutter size and tool orientation for the se-lected toolpath (i.e., spiral, zigzag, zig). Five-axis machining requires consideration of tool orientation, tool size, optimizing tool paths, avoiding interfer-ences, and improving the metal removal rate. If the undercut and overcut material left by the finish ma-chining operation are controlled, then the amount of grinding and polishing can be reduced or eliminated. The objective of this paper is to develop an inte-grated automatic toolpath generation algorithm based on curvature matching for obtaining higher metal removal rate and surface finish using the best tool cutter size and optimal inclination angles (, ). A new integrated automatic toolpath generation algo-rithm has been implemented in Mathematica. A virtual Maho-600e five-axis CNC machine which is implemented in VeriCut is used for virtual cutting. Unlike the traditional graphical verification and user-interactive correction of toolpath generation, the pro-posed algorithm selects the best tool and plans the toolpath autonomously based on curvature matching for free-form surfaces. The inverse kinematics of the machine tool is integrated in the toolpath computation. The paper is organized as follows. A review of re-lated work is presented in Section 2. Section 3 pre-sents curvature matching and optimal tool based five-axis machining and an integrated automatic toolpath generation algorithm. The proposed algorithm fol-lowed by an example is presented in Section 4 and the last section is the conclusion. 2. Literature review The CAD/CAM technologies for five-axis machin-ing complex parts such as turbine blades or impellers are investigated in 5-7. The commercial CAD/CAM systems have well developed ball end machining capacities. Ball end machining is widely used in sculptured surface machining. When using a flat end mill to machine a free-form surface, the conventional practice has been fix the inclination angle of the tool relative to the surface. This machining process is re-ferred to as a Sturz milling method used in 8. The tool is inclined at a fixed angle from the surface nor-mal as the cutter moves along the surface of the part. In industry, a typical inclination angle between 5 and 15 is chosen to minimize the local gouging. The problem for this method is that the local gouging may occur when the cutter is not inclined far enough from the surface. A manufactured part is produced by an NC pro-gram containing a series of coded instructions called NC code that directly affects the accuracy and cost of manufactured parts. In the aerospace industry, it takes tens or even hundreds of hours to machine a free-form surface part from a solid block in preparing detailed operation plans and NC part programs for sculpture surface machining. It is difficult for human planners to select the optimal machining strategies due to complex interactions among tools size, part shapes, and tool trajectories 9. Today, many commercially available CAM soft-wares for five-axis machining such as Mastercam, UGS NX, CATIA, Delcams PowerMILL and Open Minds hyperMILL, provide gouge detection and correction. However, an intensive user interaction is still needed while using this software to avoid colli-sions. These CAM systems are unable to accomplish the collision avoidance autonomously 10. A new five-axis cutter orientation algorithm is pro-posed based on curvature matching between the cutter and local machined surface regions by applying dif-ferential geometry techniques 11, 12. A technique is developed to determine the flat-end cutter orientation based on slope and curvature matching for five-axis machining 12, 13. The curvature radius is consid-ered as a function of both inclination and tilt angles, 2626 T. Lin et al. / Journal of Mechanical Science and Technology 23 (2009) 26242634 and the curvatures are similarly compared to detect local gouging. An automatic tool selection method developed by 14 has been implemented using C-language on the existing ROBLINE system. A cutter selection algo-rithm for fillet-end cutters is based on curvature matching machining, in which local-gouging, rear-gouging, and global-collision are considered. A multi-axis tool path generation algorithm is described in 15 where tool orientation is adapted to avoid ma-chine collisions and to increase material removal. The developed modules are integrated within an existing CAM system. Although references 14 and 15 pro-vide an algorithm for curvature matching, it is highly inaccurate because the linearized tool path is used. The correct way to compute the real tool path is dis-cussed in detail in 16. Many of the above methods are based on curvature matching in only one direction. In this paper, an accu-rate and efficient method is proposed for five-axis CNC machining of free-form surfaces. A new algo-rithm proposed in this study selects the best tool and plans the toolpath autonomously using curvature matching and integrated inverse kinematics of the machine tool. With regard to the local gouging avoid-ance, curvature matching techniques are employed such that the two curvature radii of the effective tool cutting shape, one along the feeding direction and another one perpendicular to the feeding direction, are smaller than those of the corresponding curves on the free-form surface. 3. Curvature matching and optimal tool based five-axis machining Free-form surfaces usually have irregular curvature distribution, which causes difficulty in machining. To mill a surface, the CAD/CAM system moves the cut-ter along a number of curves, usually iso-parametric curves or projection curves on the surfaces. Scallops are produced between the successive tracks machined on the surface. The term “scallop” refers to ridges, cusps and other surface protrusions left between adja-cent overlapping tool passes that extend above a de-sign surface profile. It depends on the type of cutting tool, tool size, tool orientation and the distance be-tween the cutter paths. The ability to classify the sculptured surfaces into different regions can be applied to determine the op-timal tools in free-form surface machining. If the surface is locally convex, the cutter may be oriented with its axis in the direction of surface normal without gouging. If the surface is locally concave or saddle, gouging will occur. It is required to orient the tool by using curvature matching. The local surface shape around the point can be divided into convex, concave and saddle. Surface curvature plays a key role in se-lecting a cutter size and orientation angles (, ) (See Fig. 2) to avoid gouging. In five-axis machining with a flat-end milling cutter, the tool axis orientations can be adjusted to avoid gouging. Gouging is the main problem in finishing a free-form surface. Finishing removes the final layers of material to obtain a sur-face with a certain distance. Cutter interference has to be controlled. Cutter interference may occur when the free-form surface has high curvature. Traditionally, the orientation of the flat end mill has remained fixed (being set to an angle that ranges from 5 to 15 degrees of the principal spindle axis) during tool motion. The traditional fixed-orientation practice cannot effec-tively prevent gouging problems during toolpath plan-ning. Ball end mills have been widely used in curved-surface machining because historically these have been easy to position with three-axis machines and require simple cutter compensation. However, com-pared to the flat end-mill, the ball end mill produces poor geometry matching between cutter and surface and has zero cutting speed at the axis of rotation. Fig. 2 shows the terminology in five-axis machining with a flat end mill tool. A local coordinate system and tool coordinate sys-tem are defined to analyze the cutting operation. The tool coordinate system should have the axis XL tan-gent to the real CC tool path (XL, YL and ZL form a Frenet system) shown in Fig. 2. The tool coordinate system Xt, Yt, Zt passes through the CC point and the tool center line. Fig. 3 shows the error when the linear approximate toolpath (along LXaxis) is used instead of the real curved CC toolpath (along XL axis). Several researchers have developed techniques to avoid local gouging by calculating the effective cut-ting curvature of the tool swept surface and compar-ing it to the normal curvature of the surface at the CC point 17-23. The traditional steps adopted to detect and avoid local gouging are (1) determining the effec-tive cutting shape E () (referred to as a tool swept section); and comparing the curvature of the effective cutting shape (referred to effective cutting curvature) the normal curvature of the surface in the plane of T. Lin et al. / Journal of Mechanical Science and Technology 23 (2009) 26242634 2627 tool swept section. Changing tool orientation affects the effective cutting shape E () as shown in Fig. 4. The effective cutting radius on the XY plane and ZY plane of cutter with tool orientation can be deter-mined by using Eqs. (1) and (2). To avoid gouging, the effective radius Reff,XL and Reff,ZL in XL and ZL Fig. 2. Inclined tool by rotating along YL and ZL. Fig. 3. Convex/Concave Part- CC and CL points. Fig. 4. Effective cutting shape. directions should be no larger than the radius of the local surface curvature. LLLLXLeffrrgRsin)(cos),( 12,= (1) LLLLZLeffrrgRsin)(sin),(22,= (2) Fig. 5 shows a flow chart for integrated automatic toolpath generation algorithm which is implemented in Mathematica 24. In this study, surface curvature information is first evaluated to determine the optimal tool diameter size and orientation angles (, ) which are based on the curvature matching. The inverse kinematics of the machine tool is integrated in the toolpath computation. For the CL data generated by this method it is as-sumed that the tool path between two CL points is a straight line relative to the workpiece. The solid curved lines in Fig. 3 show the real CL and CC point patch. In five-axis machining the real toolpath be-tween two CL-points is not linear but curved. 3.1 Finding optimal tool orientation In programming for five-axis machining, it is com-mon to predefine the cutter orientation (, ) as goug-ing is affecting the machining accuracy. In this sec-tion, the surface curvature is used to calculate the cutter orientation by matching curvature in XL and ZL direction. To avoid local gouging, it must be ensured that the effective cutting curvature (also referred to as the curvature of effective cutting shape) is not less than the effective surface curvature. 3.1.1 Finding tool inclination angle ( ) In five-axis machining, it is easier to define the tool orientation based on the local surface property than that based on the machine global coordinate system. A local coordinate system is defined to analyze the cutting operation. Fig. 2 shows the local coordinate system, inclination angle and tilt angle represented by XL, YL and ZL axes. The minimum tool inclination angle L can be de-fined by avoiding over cutting on both the ZY plane and XY plane. Initially, tilt angle L is set to be 0. As shown in Fig. 6, if the curvature KXL on XY plane is non-positive (KXL 0), which means the surface is convex or saddle, the tool inclination angle L is set to a small default angle. If the surface is concave (KXL 2628 T. Lin et al. / Journal of Mechanical Science and Technology 23 (2009) 26242634 Fig. 5. A flow chart for integrated automatic toolpath generation algorithm. T. Lin et al. / Journal of Mechanical Science and Technology 23 (2009) 26242634 2629 Fig. 6. The inclination angle L in ZL XL. Fig. 7. Adjust tilt angle L to avoid local gouging (Cutting direction out from the paper). 0), the tool inclination angle L to avoid over cutting on the XY plane can be calculated by using Eq. (3) according to the local surface curvature KXL. =XLLr11sin if r XL and KXL 0 (3) To avoid gouging on the YL ZL plane, the incli-nation angle L is calculated by Eq. (4). =ZL12sinrL if r ZL and KZL 0 (4) The minimum tool inclination angle L is deter-mined with equation (5) below. ,21LLLMax= (5) L is selected by using Eq. (3), (4) and (5). To get a real solution of L, the radius should be no larger than the radius of curvature (r ). If the cutter size r is larger than the local radius of curvature, searching for a new tilt angle L is needed to ensure the effective cutting radius Reff Limit), the inclination angle L is set to Limit. The new tilt angle can be determined by using Eq. (6) (7).This new tilt angle in (6) and (7) has to make the effective radius smaller than the radius of curvature in both XY and ZY directions. =XLitLrK)sin(coslim11 )0(/1)sin(limXLXLitKandKrifK (6) =ZLitLrK)sin(coslim12 )0(/1)sin(limZLZLitKandKrifK (7) 21min,LLLMax= (8) 3.2 Calculation of maximum cutter size and opti-mum orientation angles A maximum effective cutter radius selection is a critical problem before the toolpath generation is car-ried out for free-form surface machining. The objec-tive is to maximize the removal of material with the largest feasible cutter that does not cause local goug-ing. In general, the larger the cutter diameter is, the better the removal of material. However, a large cut-ter may inevitably cause gouging and/or collision at certain points on given surface. Smaller the gouging with curvature matching can be corrected in two ways: 1. Change the inclination angle () and tilt angle (). 2. Change tool diameter. The maximum and minimum of the inclination an-gle and tilt angle are not only limits of the machine but also workpiece and collision. Local gouging oc-curs when the curvatures between the cutter and sur-face at the point do not match each other. An initial 2630 T. Lin et al. / Journal of Mechanical Science and Technology 23 (2009) 26242634 cutter radius (r), minimum and maximum values of inclination angles () and () are inputs for an algo-rithm. Use KXL and KZL (based on XL and ZL direc-tion) by choosing the minimum positive value (con-cave) and tool radius to calculate tool inclination an-gles. The lead angle is defined in a plane parallel to the feed direction. Compare the tool inclination angle with the maximum lead angle that we have set. If the tool inclination angle is greater than the maximum lead angle, we need to select a new smaller tool di-ameter. If the effective cutter radius is smaller than the radius of curvature, set an inclination angle equal to the inclination that we have calculated and set a tilt angle equal zero, else calculate a tilt angle. If the tilt angle is greater than the maximum tilt angle we need to select a new smaller tool diameter; if not, set an inclination angle and tilt angle equal to the angle that we have calculated. It can be considered only a criti-cal point (the point that has the maximum positive curvature) because this point is the most serious point which will cause gouging first, or consider all points for dynamically changing the lead and tilt angles dur-ing tool path generation. The algorithm computes all CC points of surface in XL and ZL directions. Finally, the optimum tool radius (the largest tool radius) is calculated on all CC points of the surface. Inclination angles () and tilt angles () are computed for each the CC point of the given surface. See algorithm de-tails in Fig. 5. 4. An example In this section, a convex/concave surface shown in Fig. 8 is presented. Fig. 8. A convex/concave part surface. A free-form surface is derived by parametric sur-face Eqs. (9), (10) and (11). Equations below are plot-ted in Mathematica 24 for a surface (Fig. 8). Table 1 shows the input setup parameters of this example using the proposed new algorithm (see Fig. 5). 10050xu= (9) 50100 =vy (10) 234(3.5514.821.159.9 )(1)100/( 0.2) 72zuuuu vv=+ (11) 4.1 Toolpath generation The simple tool path that use in this study is the Zig (one way) tool path which cuts the workpiece in one direction (along v direction). It starts from the u = 0, v =0 to u=1, v=1 as shown in Figure 8 by specifying path interval (0.5). First, all the CC points and radius of curvature in u and v directions are computed by algorithm. The value of the path interval is the value of u inter-val .The ideal method is specifying the interval value of both u and v as small as possible in order to get properties data, i.e., surface curvature of every point on the surface, but in practice we cannot get all points on the surface so the value of the interval should rep-resent the surface accurately. In other words, specify-ing the interval value of both u and v is smaller than the minimum surface curvature. 4.2 Machining simulation Vericut simulation software 25 is used for ma-chining simulation. A virtual five-axis model is im-plemented by using real five-axis Maho 600e CNC machine parameters. The NC file generated using the algorithm is uploaded to Vericut for geometric mate-rial removal. By selecting tool type, tool size and Table 1. Input setup parameters. Setup parameters in proposed new algorithm in Mathematica Setup Parameters in a virtual machine simulation in VericutParametric Equation (9,10,11) A block of 100x100x100 mm Step-size (mm) 0.5 Tool length 179.512 mm Min-Max () (Deg)- 0.01- 60 Min-Max () (Deg)- 0.01-60 Tool-Radius (mm) (100) Workpiece coordinate See Fig. 9 T. Lin et al. / Journal of Mechanical Science and Technology 23 (2009) 26242634 2631 Fig. 9. Maho600e Virtual Machine in Vericut. Fig. 10. A cut model using proposed algorithm. workpiece, setup parameters, the five-axis virtual machine maho600e is simulated (See Fig. 9). An optimal tool radius of 6 mm computed by the algorithm is used for cutting the whole surface. Fig. 10 shows a cut model simulated with our proposed algorithm. The proposed method is compared with a traditional method by using UGS NX. Fig. 11 shows a simulated cut model using UGS NX. Fig. 12 shows a flowchart of using UGS NX. A comparison table shown in Table 2 was constructed to prove our proposed algorithm and compare the material removal, accuracy and preparation time be-tween the two methods. UGS NX computes the curvature match based on a piecewise linear CC point toolpath. It is much less accurate than our integrated approach as shown by the simulation results in Table 2. Fig. 11. A cut model using UGS NX. Fig. 12. Flowchart five-axis toolpath generation in UGS NX. 2632 T. Lin et al. / Journal of Mechanical Science and Technology 23 (2009) 26242634 Table 2. A comparison of two methods applied. UGS NX Integrated Automatic Toolpath Generation algorithm Proposed NC program preparation time (hr) 10 1 Tool diameter (mm) 8 (estimated value base on minimum radius of curvature checked in UGS NX) 12 (computed by algorithm) Inclination angle () (Deg) 10 (Fixed) 015 (Variable) Tilt angle () (Deg) 0 (Fixed) 01 (Variable) Type of toolpath One way One way Step size (mm) 0.5 0.5 Feed rate (mm per min) 800 800 Maximum size of undercut (mm) 4.98 2.74 Total number of undercuts 4098 1316 Maximum size of over-cut (mm) 4.98 3.98 Total number of over-cuts 4095 3684 Rt (maximum height between peak and valley) (mm) 9.96 6.72 5. Conclusion An accurate and efficient method is presented for five-axis CNC machining of free-form surfaces. In this approach, the surface is first analyzed and classi-fied into convex, concave, and saddle. A developed integrated automatic toolpath generation algorithm selects the best tool and plans the toolpath autono-mously using curvature matching. The proposed inte-grated automatic tool path generation algorithm has been implemented using Mathematica. A virtual five-axis maho600e CNC implemented in VeriCut is used for virtual cutting simulation and checking accu-racy. The new approach uses the real curved CC tool-path and not the piecewise linear approximation re-sulting in a much higher accuracy. With the use of the proposed approach, the accu-racy of undercut and overcut can be adjusted to meet the required accuracy by changing the step size. As a result, if we can use a bigger cutter, then we can have higher material removal rate; thus we can save the cutting time. The proposed algorithm can be custom-ized for a wide range of applications in three-, four- or five-axis machine, and it can be used to automate the programming of the toolpath for the machining of a free-form surface. Acknowledgment This work was supported by the Korea Foundation for International Cooperation of Science & Technol-ogy (KICOS) through a grant provided by the Korean Ministry of Science & Technology (MOST) in pro-ject reference K20610010001-07E0101-00100 and Brain Korea-21 program (BK21). The authors are greatly appreciative to Mr. Cho Guk-Hyun, for his assistance in this paper. References 1 Y. Wang and X. Tang, Five-Axis NC Machining of Sculpture Surfaces, Int. J. Adv. Manufacturing. Tech. 15 (1999) 7-14. 2 S. Ding, C. H. Daniel and Z. Han, Flow Line Ma-chining of Turbine Blades, Proc. of the 2004 Inter-national Conference on Intelligent Mechatronics and Automation, Chengdu, China. (2004) 140-145. 3 G. W. Vickers and K. W. Quan , Ball-mills versus end-mills for curved surface machining, J. Eng In-dustry. 111 (1989) 22-26. 4 T. Chen, Y. Zhong and J. Zhou, Determination of cutter orientation for Five-axis sculptured surface machining with a filleted-end cutter, Int. J. Adv. 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