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? Science China Press and Springer-Verlag Berlin Heidelberg 2010 Review Mechanical Engineering SPECIAL TOPIC: Huazhong University of Science and Technology October 2010 Vol.55 No.30: 3408?3418 doi: 10.1007/s11434-010-3247-7 Tool path generation and simulation of dynamic cutting process for five-axis NC machining DING Han 1* , BI QingZhen 2 , ZHU LiMin 2 2 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China Received October 9, 2009; accepted December 29, 2009 Five-axis NC machining provides a valid and efficient way to manufacture the mechanical parts with complex shapes, which are widely used in aerospace, energy and national defense industries. Its technology innovations have attracted much attention in re- cent years. In this paper, the state-of-the-art techniques for five-axis machining process planning are summarized and the chal- lenging problems are analyzed from the perspectives of tool path generation, integrated geometric/mechanistic simulation and machining stability analysis. The recent progresses in accessibility-based tool orientation optimization, cutter location (CL) plan- ning for line contact and three-order point contact machining, shape control of cutter envelope surface and milling stability pre- diction are introduced in detail. Finally, the emerging trends and future challenges are briefly discussed. five-axis machining, tool path generation, integrated geometric/mechanistic simulation, dynamics simulation Citation: Ding H, Bi Q Z, Zhu L M, et al. Tool path generation and simulation of dynamic cutting process for five-axis NC machining. Chinese Sci Bull, 2010, 55: 3408?3418, doi: 10.1007/s11434-010-3247-7 In conventional three-axis NC machining only the transla- tion motions of the cutter are permitted while the cutter ori- entation is allowed to change in a five-axis machine tool because of the two additional rotational axes. The advan- tages of five-axis NC machining mainly depend on the con- trol of tool orientations: (1) The collision between the part and the cutter can be avoided by selecting the accessible tool orientation, which provides the ability to machine the complicated shapes such as aerospace impeller, turbo blade and marine propeller. (2) A large machining strip width can be obtained if the tool orientation is properly planed so that the tool tip geometry matches the part geometry well. Also, the highly efficient flank milling can be applied to machine aerospace impeller by using a five-axis machine tool. (3) The cutting conditions can be improved in five-axis ma- chining. For example, it is possible to shorten the tool overhang length if the tool orientation is optimized. Deter- mining the safe and shortest tool length is very helpful when *Corresponding author (email: dinghan@) the surface is machined in a confined space, in which only the small-diameter cutters can be used. The cutting area of a cutter, which affects the cutting force, cutter wear and ma- chined surface quality can also be controlled by changing the cutter orientation. Besides the above advantages, there exist several chal- lenging problems in five-axis machining. Since the tool orientation is adjustable, it is hard to image the complicated spatial motion of the tool. Thus, it is much more difficult to generate the collision-free and high efficient tool paths, which limits its wide application. Furthermore, the cutting force prediction and dynamics simulation are more complex because the involved cutting parameters are time-varying during the machining process. Current works about five- axis machining fall into three categories [1]: tool path gen- eration, integrated geometric/mechanistic simulation and dynamics simulation, as shown in Figure 1. Tool path gen- eration is the process to plan the cutter trajectory relative to the part based on the part model, machining method and tolerance requirement. The cutter trajectory affects greatly DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3409 the cutting efficiency and quality. It is also the foundation of integrated geometric/mechanistic simulation, which de- pends on the cutting geometry and cutting force modeling techniques. The cutting geometry reflects the meshing state between the cutter and the workpiece during the material removing process. By integrating the cutting geometry and cutting force models, the transient cutting force can be pre- dicted. The cutting force then can be applied to dynamics simulation, feedrate scheduling, and prediction and com- pensation of deformation. The goal of dynamics simulation is to predict the cutting stability and the machined surface profile based on the cutting force and the dynamics charac- teristics of the machine tool-cutter-fixture system. Dynam- ics simulation is helpful to optimize the cutting parameters and the tool path. The literatures on five-axis NC machining are enormous. A lot of related commercial systems have been developed, such as the general-purpose CAM softwares UG and CATIA, the special CAM software Max-AB for machining impeller and Turbosoft for machining blade, and the dy- namics simulation software CutterPro. European Commis- sion supported a project about flank milling optimization that is called “Flamingo”. Because of the obvious advan- tages of flank milling in cutting efficiency and surface qual- ity, a number of famous companies (SNECMA, Rolls Royce, Dassault Systèmes) and a university (Hannover) participated in this project. The researches on five-axis high-efficiency and high-precision machining have also been carried out in some famous companies, such as United Technologies, Pratt it is difficult to automatically generate the opti- mum tool orientations that consider simultaneously all the Figure 1 Three challenging problems in five-axis NC machining. objectives required by the practical cutting process, such as collision avoidance, large effective cutting width, globally cutter orientation smoothness and shorter tool length. Also, most of the existing works about dynamics simulation aim to three-axis machining. Models and algorithms applicable to five-axis machining need to be explored. 1 Tool path generation Tool path generation is the most important technology in NC programming. The critical problem in five-axis ma- chining is to plan cutter orientations. Theoretically, the tool orientation can be any point on the Gauss Sphere. In fact, the feasible tool orientations are only a limited area on the Gauss Sphere because of the constraints of global collision avoidance and machine joint angle limits. To improve ma- chining efficiency and quality, the tool orientation of each cutter location (CL) data should be optimized by consider- ing the important factors related to a practical cutting proc- ess. The factors consist of geometrical constraints, kine- matic constraints, dynamic characteristics and physical fac- tors. How to take into account these factors is the most challenging issue in the research of tool path generation. 1.1 Collision avoidance Collision avoidance must be first considered in the process of tool path generation. There are mainly two kinds of ideas to avoid interference: (1) First generating and then adjusting cutter orientation to avoid collision. (2) Access-based tool path generation. With the former idea, cutter orientations are first planned according to some strategies. A collision detection method is then used to detect the collision be- tween the tool and the parts. If collision occurs, the tool orientations must be changed as shown in Figure 2. With the latter idea, the cutter orientations are generated directly in the accessibility cones as shown in Figure 3. The research about the first idea focuses on the algo- rithms to improve the collision detection efficiency and ad- just cutter orientations to avoid collision. In practical appli- cations, tool paths are usually composed of thousands to hundred thousands of tool positions. The collision detection often requires large computation time and resource. There- fore lots of algorithms have been proposed to improve the computation efficiency of collision detection [2,3]. When machining a complex shape, the detection and adjustment processes usually repeat several times. Collision avoidance is of first concern. It is difficult to consider other factors affect- ing the cutting process when adjusting cutter orientations. The access-based tool path generation method consists of two steps. Collision-free cutter orientations at every cutter contact (CC) point are first computed. The set of colli- sion-free cutter orientations is called accessibility cone. The cutter orientations are then generated in the accessibility 3410 DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 Figure 2 Detecting and adjusting cutter orientation to avoid collision [2]. (a) Collision detection; (b) adjust cutter orientation. Figure 3 Access-based collision-free tool path generation. (a) Accessi- bility cone; (b) collision-free tool path. cones. The most obvious merit of this method is that the iterative process of adjusting cutter orientations can almost be avoided. Based on the accessibility cone, the manufac- turability can be directly determined. Furthermore, the cut- ter orientation optimization can be carried out in the colli- sion-free space. Other objectives such as cutting forces and velocity smoothness may also be considered. The problem with this idea is the difficulty in efficiently computing ac- cessibility cones. Usually computing accessibilities will cost large computation time because complex shape may consist of hundreds of thousands of polygonal meshes. Some algo- rithms were proposed to improve computation efficiency such as the C-space (Configuration Space) methods [4,5] and visibility-based methods [6?10]. Though C-space is an elegant concept to deal with collision avoidance, the free C-space cannot be explicitly and efficiently computed. Wang et al. [5] showed that the elapsed time to compute an accessibility cone for a part composed of only 10000 trian- gles would be 1190.33 min. Furthermore, the algorithm did not consider the collision of the tool holder. A cutter can be abstracted as a light ray that emits from the CL point if its radius is ignored. Then the problem of collision avoidance is transformed into that of visibility. We [6?8] described cutter’s visibility cone using the concept of C-space and proposed three strategies to accelerate the computation speed using the hidden-surface removal techniques in com- puter graphics. The manufacturability of a complex surface was also analyzed based on the visibility cone. However, the conventional visibility is only the necessary condition of accessibility because a milling tool usually consists of sev- eral cylindrical shapes with finite radii. The real accessible directions cannot be directly obtained from the visibility cone, and secondary collision checking and avoidance strat- egies are still needed [9]. The accessibility will be equal to the visibility if both the machined surface and the interfer- ence checking surface are replaced by their offset surfaces [10]. However, the offset surface is usually not easy to ob- tain and the collision avoidance of the tool holder cannot be guaranteed. Furthermore, the method only applies to ball- end cutters and cannot be extended to other types of cutters. We [11,12] proposed a high-efficient algorithm to compute the accessibility cone using graphics hardware. The algo- rithm has almost linear time complexity and applies to both flat-end and torus-end cutters. Generally, the CL point can be specified by the CC point, outward normal direction of the machined surface and cutter orientation. If the viewing direction is opposite to the cutter orientation, the global ac- cessibility of the cutter is then equal to the complete visi- bilities of the involved cylinders and cones. This equiva- lence provides an efficient method for detecting the acces- sibility of the milling cutter by using the occlusion query function of the graphics hardware. The computation effi- ciencies of the three algorithms are compared in Table 1. It is found that the computation time of our algorithm is less than 2% of that in [9] even though both the number of tri- angles and the number of cutter orientations are greater than 10 times of those in [9]. The average computation time for one cutter orientation at one contact point is less than 2‰ of that in [9]. The average computation time is also much less than that in [3] even though the number of inputted triangles is much greater than that in [3]. 1.2 Cutting efficiency Nowadays, ball-end cutters are widely employed for five-axis NC machining. The major advantages of ball-end milling are that it applies to almost any surface and it is Table 1 The comparison of computation time Inputted models Method Computation platform Triangle Cutter center point Cutter orientations Computation time Average computa- tion time Ref. [9] SGI work station, Dual CPU 250M 10665 1500 80 51.63 m 2.58×10 ?2 s Ref. [3] CPU 2.4G, RAM 512M 12600 50000 1 61.61s 1.23×10 ?3 s Our method [12] CPU 2.4G, RAM 512M 139754 2000 1026 60.53 s 2.95×10 ?5 s DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3411 relatively easy to generate the tool path. From the manufac- turer’s point of view, however, the main disadvantage of ball-end milling is that it is very time consuming. It may require more finish passes and each pass removes only a small amount of material. Compared with ball-end cutter, non-ball-end cutter possesses more complex geometry, and exhibits different “effective cutting profiles” at different locations. Thus, it is possible to position the cutter so that its “effective cutting profile” well matches the design surface, which results in a great improvement of the machining strip width. Hence, increasing attention has been drawn onto the problem of tool path optimization for milling complex sur- faces with non-ball-end cutters. In five-axis machining, the machined surface is formed by the swept envelope of the cutter surface. The true ma- chining errors are the deviations between the design surface and the cutter envelope surface. It is well known that the shape of the cutter envelope surface cannot be completely determined unless all the cutter positions are given [13,14]. Due to the difficulty and complexity in locally modeling the cutter envelope surface, most works adopted the approxi- mate or simplified models, which formulate the problem of optimal cutter positioning as that of approximating the cut- ter surface to the design surface in the neighborhood of the current CC point [15]. These optimization models do not characterize the real machining process. Also, they only apply to certain surfaces or cutters. Only a few works have addressed the cutter positioning problem from the perspective of local approximation of cutter envelope surface to design surface [15?17]. For a flat-end or disk cutter, Wang et al. [15] and Rao et al. [16] developed the third- and second-order approximate models of the cutter envelope surface, respectively. However, for such a cutter, its envelope surface is swept by the cutting circle, which is not a rotary surface. Therefore, the two me- thods cannot be applied to other types of rotary cutters. Re- cently, Gong et al. [17] developed a mathematical model that describes the second-order approximation of the enve- lope surface of a general rotary cutter in the neighborhood of the CC point, and then proposed a cutter positioning strategy that makes the cutter envelope surface have a con- tact of second-order with the design surface at the CC point. However, theoretically speaking, a third-order contact be- tween the cutter envelope surface and the design surface could be achieved by adjusting the cutter orientation. This means that the cutter location planning based on the sec- ond-order model does not take full advantage of the effi- ciency and power that the five-axis machining offers. The above models are not compatible with each other. Also, the optimal CL is determined by solving two equations derived from the second- and third-order contact conditions. Due to the constraints of machine joint angle limits, global colli- sion avoidance and tool path smoothness, maybe there is no feasible solution to this system of equations. In our recent works [18,19], the geometric properties of a pair of line contact surfaces were investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and the design surface along the characteristic curve and cutter contact (CC) path, respec- tively, a mathematical model describing the third-order ap- proximation of the cutter envelope surface according to just one given cutter location (CL) was developed. It was shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section could be de- termined by those of the cutter surface and the design sur- face. This model characterizes the intrinsic relationship among the cutter surface, the cutter envelope surface and the design surface in the vicinity of the CC point. On this basis, a tool positioning strategy was proposed for effi- ciently machining free-form surfaces with non-ball-end cutters. The optimal CL was obtained by adjusting the in- clination and tilt angles of the cutter until its envelope sur- face and the design surface had the third-order contact at the CC point, which resulted in a wide machining strip. The strategy can handle the constraints of joint angle limits, global collision avoidance and tool path smoothness in a nature way, and applies to general rotary cutters and com- plex surfaces. Numerical examples demonstrated that the third-order point contact approach could improve the ma- chining strip width greatly as compared with the recently reported second-order one. A comparison of the machining strip widths using different CLs for the five-axis machining of a helical surface with a toroidal cutter is summarized in Table 2. The values of the tool parameters chosen for simu- lation are: radius of the torus R=10 mm, and radius of the corner r=2.5 mm. Compared with the point milling, the flank milling can increase the material removal rate, lower the cutting forces, eliminate necessary hand finish and ensure improved com- ponent accuracy. It offers a better choice for machining slender surfaces. Lartigue et al. [20] proposed an approach to globally optimize the tool path for flank milling. The basic idea is to deform the tool axis trajectory surface so that the tool envelope surface fits the design surface ac- cording to the least-squares criterion. To simplify the com- putation, an approximate distance measure was employed. For a cylindrical cutter, Gong et al. [21] presented the error propagation principle, and transformed the problem into that of least-squares (LS) approximation of the axis trajectory surface to the offset surface of the design surface. In these two works, not the local geometric error, but the geometric Table 2 Comparison of the machining strip widths for different CLs Tolerance (mm) Ball-end cutter (R = 5.5 mm) Toroidal cutter (Second order contact) Toroidal cutter (Third order contact) δ = 0.005 0.69 2.48 5.28 δ = 0.01 0.98 3.12 6.14 3412 DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 error between the envelope surface of the cutter and the design surface, was of the first concern. Thus it was called the global optimization method. Although the LS method was easy for implementation and efficient in computation, it could not incorporate readily the non-over- cut constraint required by semi-finish milling, and more importantly, it did not conform to the minimum zone c