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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 Syst mes 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 0 005 0 69 2 48 5 28 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 crite rion recommended by ANSI and ISO standards for toler ance evaluation Fur thermore the geometric deviation of the machined surface from the nominal one was not clearly defined and the influ ence of the deformation of the tool axis trajectory surface on the change of this deviation was not quantitatively analyzed In our studies 22 23 the maximum orthogonal distance from the point on the design surface to the tool envelope surface was introduced to characterize the geometric error of the machined surface The first order gradient and sec ond order