Tool path generation for 4-axis contour EDM rough ...

International Journal of Machine Tools & Manufacture 44 (2004) 1493–1502 www.elsevier.com/locate/ijmactool

Tool path generation for 4-axis contour EDM rough machining Songlin Ding
, Ridong Jiang Institute of High Performance Computing, 1 Science Park Road, Singapore 117528, Singapore Received 22 October 2003; received in revised form 3 April 2004; accepted 17 May 2004

Abstract Contour or CNC EDM machining of free-form surfaces requires tool paths that are different from those used in mechanical milling although in geometry both processes are described by the similar model of intersection between the rotating tool and the workpiece. In this paper, special requirements on tool paths demanded by contour EDM machining are studied and a two-phase tool path generation method for 4-axis contour EDM rough milling with a cylindrical electrode is developed. In the first phase of the method, initial tool paths for virtual 3-axis milling are generated in a commercial CAD/CAM system—Unigraphics, which provides users with plenty of options in choosing suitable tool path patterns. From these tool paths, cutter contact (CC) points between electrode and workpiece are reversely calculated. In the second phase, considering the special requirements of EDM machining, which include discharging gap compensation, electrode wear compensation, DC arcing prevention, etc., the electrode is adjusted to an optimized interference-free orientation by rotating it around the CC points obtained in the previous phase. This new orientation together with the reference point of electrode is output as new tool path. The whole algorithm has been integrated into Unigraphics, machining simulations and tests have been conducted for 4-axis contour EDM rough machining. # 2004 Elsevier Ltd. All rights reserved. Keywords: EDM; Contour EDM; Tool path; Free-form surface; 4-axis; Machining

1. Introduction Electric discharge machining (EDM) technology has been widely used in industry to machine workpieces made of hard-to-cut and temperature resistive materials [1]. In the machining process extra materials are removed by plunging a 3-D profile electrode made of graphite, copper or other materials into the workpiece. Similar to mechanical milling, the whole EDM machining process can be divided into finish and rough machining as well. In finish machining, the main objective is to obtain high quality machined surfaces. For rough machining, however, unlike the rough milling process in which large volume of materials are removed, EDM rough machining suffers low machining efficiency, and the application of formed electrodes in this process is financially expensive. This is because that large material removal rate causes the formed electrode to be damaged easily due to the erosive effect of


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electric discharging on both workpiece and electrode. To increase the flexibility and expand the application areas of EDM machining, a new technology named Contour or CNC EDM milling emerged in 1980s [1–4]. Different from conventional EDM machining in which a formed electrode is used, this method applies a standard cylinder as the electrode, and its machining process is similar to that of mechanical milling with a rotating cutter in which extra materials are removed by the repeated moving of the cutter along pre-defined trajectories which are referred to as tool paths. Applications of contour EDM machining could be found in the machining of die and moulds [5], turbine disks [6] which are free-form surfaces and are made of difficult-to-machine materials. Due to the discharging property of EDM machining, tool paths generated for mechanical milling cannot be utilized directly in contour EDM milling. Modifications have to be made to make them meet some special requirements. However, few researches have been conducted in this area [5]. To solve this problem, we studied the special requirements demanded by EDM and developed a two-step tool

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path generation method for 4-axis contour EDM rough machining of free-form surfaces. In the first step of the method, considering the requirements of contour EDM, a special electrode model is constructed and initial tool paths for virtual 3-axis milling are generated by taking this model as the cutter. In order to take advantage of the rich CAM functions for mechanical milling in commercial CAD/CAM systems, a commercial system— Unigraphics (UG) is utilized and the initial tool paths are generated by using its ‘‘Cavity’’ milling template. Next, based on the initial tool paths, cutter contact (CC) points in the tool paths are reversely calculated from the geometric model and the G codes, and the electrode is adjusted to an optimized orientation which is determined by the discharging property of EDM machining. This orientation would be further modified to avoid interference should collisions be found. The new orientation together with the reference point of electrode is output as new tool paths for 4-axis contour EDM machining. The whole algorithm has been integrated into UG, machining simulation and test have been conducted for 4-axis contour EDM machining of a cavity model.

2. Related work Since 1980s a large number of researches have been carried out on contour or CNC EDM machining and many results have been achieved in this area [1–4,7–13]. However, most of these researches are on principles of contour EDM machining, few of them focus on tool path generation methods. In 1994, systematic investigations on the use of cylindrical electrodes for the production of 3-D complex shapes on CNC EDM machines were conducted by Bayramoglu and Duffill [8,9]. In their research, flat and ball end cylindrical electrodes with 10 and 15 mm diameter were used. The effects of tool path, pick feed and rotation of electrode were discussed. The tool paths they used were 2D contours, but no detailed descriptions were presented. Another contour EDM system was designed by Mizugaki [10]. In the system, tool paths were generated by the offsetting algorithm, which is a common approach in CAD/CAM fields. In the tool path generation process, first, an offset surface of the workpiece surface with the parallel distance between the two equivalent to the radius of the ball-nosed cylindrical electrode was generated. Next, spatial tool paths for the electrode are generated on this offset surface by projecting tool paths designed on a plane. However, similar to the tool path generation process in mechanical milling, sometimes it is difficult to obtain an implicitly or explicitly defined offset surface and there is not a robust method to get one. For example, the offset surface of a bicubic surface does not necessarily take

the form of ‘‘bicubic’’. It may contain self-intersections and/or gaps, which must be detected and eliminated. Unfortunately, it is not a trivial task to remove these anomalies when they appear on the offset surface. Kaneko et al. [4,11–13] designed a system that included mechanisms of automatic measurement and compensation of the electrode deformation. The system processed various free curves as objective contours. In the calculation of compensation values for electrode deformation, the free curve of the objective contour was approximated by a combination of small inclined straight lines. However, how the tool paths were generated had not been introduced. Similar systems can also be found in [2,7], but similar to above discussed systems, there were no introductions of how tool paths for contour EDM machining were generated. A detailed tool path generation method for 5-axis contour EDM machining of die and mould was presented by Yun et al. [5] recently. In their algorithm, cylindrical electrode was used for flank machining of free-form surfaces. Electrode wear compensation was also considered in the system. But this method is for flank machining only, how to apply cylindrical electrode for end-machining which is a more common method was not covered. With the advance of high speed machining/milling (HSM), which can be utilized to cut hard materials with high speed, applications of EDM for roughing in some industries such as mold and die become not so widely used because of the ‘‘one product one piece’’ characters of these industries. However, due to the high costs of applying HSM, especially in mass production, it is not able to replace contour EDM machining.

3. Special requirements on tool paths in contour EDM machining Because of the different machining principles of contour EDM and mechanical milling, although both processes are realized by the similar movements of a cylindrical rotating tool, the tool path generation methods and the resulted tool paths used in the two processes are different. Several special factors have to be considered in the tool path generation for contour EDM machining. Those include the discharging gap compensation, electrode wear compensation, DC arcing prevention and global interference detection. 3.1. Discharging gap compensation EDM machining is non-contact due to the electric discharging. The gap between electrode and workpiece which is referred to as discharging gap is a variable that changes dynamically with machining parameters [14].

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Fig. 1. Discharging gap in contour EDM machining with a ball end electrode.

Usually its value is in the range from 10 to several 100 lm [15]. When electric parameters of power supply and other relevant machining parameters are constant, the statistic average of discharging gap can be taken as constant. In contour EDM in which a ball end electrode is applied for end-machining, the discharging area can be effectively described as an offset ball [15], as illustrated in Fig. 1, where the solid lines present the electrode while the dashed ones describe the effective area of discharging. In machining process, materials of workpieces within this area will be removed by electric discharging. There are two ways to compensate the discharging gap: on-line and off-line. The on-line method uses the geometry of electrode directly to calculate tool paths. The discharging gap is not considered in the tool path generation phase. It is compensated in the machining process by offsetting the electrode at each cutter location (CL) point along the normal direction of the surface by a distance g, where g is measured or calculated according to the machining parameters by a realtime module [5,15]. This method is of high precision, but the complicity makes it less widely used in rough machining. In off-line method, tool paths are calculated by effectively taking the dashed envelope of the electrode as the cutter (Fig. 1). The gap information is thus included in tool paths and no further processing is needed. The benefit of applying this method is the simplicity. However, when electric parameters are changed, the gap will change accordingly, tool paths should be recalculated. Applying original tool paths will import errors to the machining process. 3.2. Electrode wear compensation Unlike the mechanical milling process in which tool wear is very small and could be neglected in most cases, in contour EDM especially in rough machining, because of the erosive effect of discharging, wear of electrode is

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significant that could be up to several millimeters per minute. It has to be compensated in real-time. In the end-machining process wear of electrode occurs at the end portion of the cylindrical electrode in both radial and axial directions. It is symmetrical because electrode is rotating. The wear in axial direction causes the electrode to become shorter while in radial direction the flat end of the cylindrical electrode becomes tapered, filleted or torus shapes. In practice, there are three types of methods to compensate the length of electrode: off-line method, on-line method and semi-online method. In the off-line method, compensation of the length of electrode is conducted based on an anticipated value, which is determined for each segment of tool path prior to machining. In 3-axis and some types of 4-axis machining, this value is added directly to the Z coordinate to compensate the wear in axial direction. The determination of this compensation value is based on the ‘‘same removal volume’’ theory which means that the wear of electrode in machining process is of the same volume as that in the preparing process when same volume of materials are removed [4,16]. The on-line method adopts the real-time wear compensation strategy [13,16]. It consists of two steps: realtime wear measurement and real-time compensation. The wear of electrode is measured directly by sensors [17] or indirectly by indicators that use electric pulse analysis [13]. The measured value is compensated to the length of electrode on-line through servo systems. The advantage of this method is its precision and capability of being adaptive to different machining environments, but those are achieved by applying additional measuring equipments and at the cost of modifying servo systems. The semi-online method uses periodically measured wear as the anticipated value for the off-line method. As machining is performed in successive layers, the measuring of electrode length and correction of the anticipated wear compensation are usually performed after each layer [16]. The measuring could be conducted by regularly putting the electrode in contact with a reference probe [4,16] or through optical measurement systems made of area CCD sensors [13]. 3.3. DC arching prevention In mechanical milling, when a ball end mill is applied, the mill can be at any orientation with respect to the workpiece surface in 3-D space provided that there is no local gouging and global interference. The surface finish will not be of much difference for different tool orientations. However, in contour EDM the case is different. Since discharging gap is very sensitive to the distance between electrode and workpiece [14,15], an abrupt change of electrode orientation may

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cause this distance changed, this may lead to DC arcing which results in large holes on the surface (Fig. 2). To reduce the chances of arching, the change of orientation of electrode with respect to workpiece surface should be minimized, their relative orientation should be kept constant as much as possible. 3.4. Global interference detection In mechanical milling, global interference occurs between the cutter shaft and workpiece when the distance between them is smaller than the tool radius [18]. It would be certain that there is no interference should the distance be greater than the radius of the cutter. Suppose V is the tool axis vector (Fig. 3(a)), C is a CC point on the surface, D is the center point of the bottom plane of the flat end mill, F is a possible collision point on the surface, d is its distance to tool axis, r is the radius of cutter, h is the height of cutter, and l is the height of the projection point E. In triangle DFE, d ¼ jDF jsinh ¼

jV  DF j jV j

ð1Þ

where DF ¼ F ðx;y;zÞ  Dðx;y;zÞ.

Fig. 3. (a) Interference detection. (b) Discharging gap in global interference detection.

It is clear that interference will not occur when d > r (0 < l < h). However, this criterion of detecting global interference is not valid in contour EDM machining. Interference could occur even when the distance is equal to or larger than the cutter radius, as shown in Fig. 3(b). Due to the influence of discharging gap between electrode and workpiece as discussed in Section 3.1, materials of workpiece within the dashed lines will be removed by electric discharging. This will damage adjacent surfaces and should be avoided. Compensation of discharging gaps in shaft portion of the electrode should also be considered in global interference detection.

4. Tool path generation for 4-axis contour EDM rough machining

Fig. 2. Large holes caused by arcing on the surface.

In 4-axis and 5-axis mechanical milling, in order to reduce large variations of tool orientation, many constrictions are applied on tool axes. For examples, the tool axis may be required to be perpendicular to workpiece surfaces, to pass through or towards a point in 3-D space, to pass through or towards a straight line,

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etc. In our research tool paths generated by all those methods cannot satisfy the special requirements of contour EDM machining; a different tool path generation method is needed. For this purpose, considering the factors introduced in Section 3, a two-step algorithm is developed. In the first step, a geometric model of electrode is constructed and initial tool paths for 3-axis milling are generated in UG by taking this model as the cutter. CC points in tool paths are reversely calculated from the resultant G codes and the electrode model. Secondly, orientations of electrode are determined by minimizing the tool swing as much as possible. Should collisions be found, the electrode would be further adjusted to an interference-free orientation so to make the tool path applicable in 4-axis machining. 4.1. Discharging gap compensation As discussed in Section 3, the advantage of off-line method is the simplicity. In our research, which is about rough machining, this off-line method is adopted. The effective diameter of the cutter is: D ¼ d þ 2g

ð2Þ

d is the diameter of the electrode, g is the discharging gap, which is stable when machining parameters are constant. However, because the discharge gap is a function of machining parameters, if parameters of power supply are changed, g will change accordingly and D will not be correct any longer. 4.2. Electrode wear compensation In roughing, layer-by-layer machining is a commonly used strategy. Electrode wear occurs in both axial and radial directions of the electrode. If the cutting depth is not large, for example, smaller than 2 mm, the wear in both directions may reach a dynamic balance, i.e., both the edge and the bottom of the flat end of the electrode are worn away together continuously; the worn shape at the end looks nearly unchanged while wearing process is going on. Hence the real-time radial-wear compensation can thus be implemented on the electrode length, and the radial-wear compensation can be introduced by replacing the flat end of the electrode with a static torus or fillet geometry. In our system, a semionline electrode wear compensation strategy which is similar to that used in [2,16] is utilized. A real-time module is designed to add compensation values to Z coordinate in each layer. 4.3. Geometric model of electrode The simplest electrode is a cylinder. Because of the erosive effect of discharging, the sharp edges between the flat end plane and the cylinder become obtuse [19].

Fig. 4.

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Geometric model of the electrode.

Considering the end plane, the electrode cannot be described by a simple cylinder any longer. More precisely it is approximated by a cylindrical cutter with a torus end as shown in Fig. 4. r in Fig. 4 is the radius of the circle of torus that is related to discharging gap and cutting depth. Its value is determined by real machining tests. In rough machining it could be approximated as equaling to the cut depth if the depth is small, for example, smaller than 2 mm. 4.4. Tool path generation strategy In a user designed CAM system which is different from commercial ones, usually there are two ways to generate the required tool paths. The first one is to process the entire cutting and noncutting parameters used in tool path generation by user themselves, for example, the tolerance, the scallop height or side steps, the design of engage and retract methods. The benefit of this method is that the users can modify parameters of interest according to their own requirements. However, because of large amount of computations, it is almost impossible to design a full functional system which can support the entire cutting and non-cutting parameters, for example, to include different tool path patterns such as zigzag tool path, spiral tool path or boundary conformed tool paths. The second way is to generate tool paths by taking advantage of commercial CAD/CAM systems [20]. First, initial tool paths that are of the desired pattern but do not fully comply with user’s requirements are generated by a commercial system. To make them meet the final requirements, further modifications of those tool paths are followed in the second step. The benefit of this method is that the rich CAM functions of commercial systems become transparent to external users. This makes the user designed system more robust and the user’s developing work be simplified significantly as well. In our research the second method is adopted. The tool path generated directly by UG is for mechanical

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milling and cannot be used in EDM machining, further modifications are needed. Based on Open APIs provided in UG, the overall tool path generation process consists of following three parts. 4.4.1. Generation of initial tool paths for 3-axis milling in UG 4-axis milling machine tool has one more rotating axis than 3-axis machine. This extra axis causes the tool path generation for 4-axis milling more complicated than that for 3-axis due to constrains used to control tool axis. In this research, initial tool paths for virtual 3-axis milling are generated in UG by taking the effective electrode as the cutter. These tool paths are utilized to calculate CL points later. No electrode orientation or interference problems are considered in this phase. 4.4.2. Reverse determination of CC points from CL points Because tool paths generated in above step are for 3-axis machining and no interference is checked, they cannot be used in 4-axis machining and further modifications are needed. To adjust the orientation of electrode so to obtain the optimized one in contour EDM milling, CC points between workpiece and electrode should be determined first of all. However, the CL source file or G code file output from CAD/CAM systems contains data of CL only, no CC information is available. CC data has to be reversely calculated from the CL data by users themselves. The usual tool path generation procedure is to calculate CC points first, CL points are obtained from these CC points through a series of geometric computation in the second step. Therefore, calculating CC points from CL points is actually a reverse process of calculating CL points from CC data. To obtain these data, a distance calculation method is designed. With this method, points on the workpiece surface that have zero distance or a value within a prescribed tolerance to the electrode are regarded as CC points. The electrode has been modeled as a fillet or torus end mill. For most cases in machining the slant walls of a pocket, the effective cutting edge used to determine the tool path is the rounded portion of the torus or the fillet, not the bottom plane. Thus, it is similar to a ball end mill, there are no ambiguous CC points. However, if the CL point is at the flat bottom plane, the entire bottom will cut into the workpiece, which makes it impossible to reversely find a unique CC point. In this case, as the cutting edge is the bottom plane, it means that the tool is vertical to the surface. This is an idea machining orientation, which is even better than keeping an angle with the surface and no further adjustment is needed. If interference occurs at this orientation, the electrode can be adjusted by rotating around the CL point to avoid collisions. The error

caused is at the same level of that in rotating around the CC point. 4.4.3. Adjustment of electrode orientations Similar to milling, to avoid interference in contour EDM machining, the electrode should be adjusted to an interference-free orientation. Meanwhile, to avoid abrupt changes of electrode orientations so to reduce the possibilities of arcing, i.e., to get smooth tool paths as introduced in Section 3.4, the relative orientation of electrode with respect to the workpiece surface should be kept constant as much as possible. Geometrically this relative orientation could be measured by the angle between electrode and the tangent plane of the surface at CC point. However, because a 4-axis machine is used here, the adjustment of electrode in 3-D space can only be realized by rotating the electrode around CC point in B direction, B is the fourth rotating axis of the machine tool. This leads to the risk that the angle cannot be kept constant along the whole tool paths because the electrode cannot rotate freely in 3-D space. For those points at which the constant angle cannot be formed, or those for which large rotating is needed to form the angle, the orientation of electrode at previous point is inherent to reduce large changes of electrode orientations between two consecutive points. Suppose the electrode rotates around X axis, i.e., rotates in YZ plane (Fig. 5). A is the rotated angle, P is the CC point, N is the normal vector of the tangent plane, T is the vector of electrode axis, Proj_t is the projected line of T on the tangent plane along the reverse direction of N, which is obtainable by intersecting the tangent plane with the plane that consists of N

Fig. 5.

Calculation of angles between electrode and tangent plane.

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and T. So the angle between the electrode and tangent plane is B:   T Proj t B ¼ arcos ð3Þ jT jjProj tj The optimized value of this angle should be determined according to experiments. 4.5. Error analysis Initial tool paths for 3-axis machining are generated in UG according to preset tolerances. Additional overcut or undercut is caused when the electrode rotates towards or away from workpiece surfaces based on these tool paths. This introduces extra errors to the system. Assume the surface in the vicinity of CC point could be approximated by a plane [21], as shown in Fig. 6. Suppose the largest overcut caused by rotating the electrode towards workpiece surface is e, O and Oi are center points of the circles of the torus before and after rotating, r is the radius, B is the rotated angle. The maximum distance which electrode over cuts into workpiece therefore is: e ¼ rð1  cosBÞ

ð4Þ v

Suppose r is 2 mm, B is 10 , then the error e ¼ 2  2cos10 ¼ 0:03 mm. In rough machining, it is small enough and could be neglected. 4.6. Tool path generation algorithm The proposed tool path generation algorithm is a two-phase process in which optimized orientations of

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electrode are calculated from initial tool paths for 3-axis milling. The first step of the algorithm is to obtain initial tool paths and corresponding CC points. Those initial tool paths are generated within UG. CC points are calculated based on the geometric model and previous tool path information. In the second step, further modifications of tool paths are performed to adjust the electrode to an optimized and interferencefree orientation. In the adjustment, a course-fine adjusting strategy is adopted. The course adjustment, which is followed by a fine one is to increase the calculating speed. The fine one on the other hand, is to obtain the more precise orientation. The detailed algorithm is as follows. Algorithm: Generating new tool path at an initial CL point Input: Surface model, G codes for 3-axis milling, effective diameter of electrode, radius of torus, constant angle B Output: G codes for 4-axis contour EDM machining Begin: Read in G codes, surface model Calculate the distance between electrode and each surface patch; find the CC point which has 0 distances to the electrode Adjust the electrode to an interference-free orientation Calculate surface parameters at CC point, generate the tangent plane Calculate the projected line of electrode on the tangent plane: Proj_t Calculate the angle between electrode and the projected line: N While (((N < B)|| (N > B)) && (No interference)) { if (N < B) { Rotate electrode towards the normal direction of surface } if (N>B) { Rotate electrode away from the direction of normal to the surface } Detect interference Calculate Proj_t Calculate N } Calculate new reference Output tool path

Fig. 6. Overcut caused by the rotation of electrode.

End

point of

electrode

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Fig. 7.

Solid model of workpiece.

Feed rate is also an important factor for the successful application of contour EDM machining. However, different with milling, the feed rate in EDM is related with many electric parameters such as current, voltage, width of electric pulse, etc. It is beyond the scope of this paper and will not be elaborated.

5. The implementation for 4-axis contour EDM rough machining The proposed tool path generation algorithm for 4-axis contour EDM rough machining is implemented with Visual C++ and has been integrated into UG by using the Open APIs UG provides. 5.1. CAD model The model to be machined is a cubic with a cavity in the middle. Left and right walls of the cavity are two pieces of free-form surfaces that have concave and convex portions in both directions, as shown in Fig. 7. 5.2. Initial tool paths for virtual 3-axis milling Initial tool paths for 3-axis milling are mainly used to provide CL points from which CC points can be calculated. They are generated by applying the ‘‘Cavity’’ template of UG, as shown in Fig. 8(a). Because some areas of the surface are concave, actually this model cannot be machined by 3-axis milling. To avoid collision, the system automatically offsets tool paths outward, which causes undercut areas on the workpiece. To eliminate these undercuts, i.e., to machine the con-

Fig. 8. (a) Tool path for 3-axis milling generated by UG. (b) Interference occurs between the electrode and workpiece.

cave parts of the surface, more precise tool paths are created by turning off the ‘‘tolerant machining’’ selection button in UG. This causes the tool interfere with the workpiece, as shown in Fig. 8(b). However, since the purpose of this process is to obtain CL points only, these abnormal tool paths are not directly used for machining, so no further correction is needed.

5.3. Reverse calculation of CC points To calculate CC points from CL data, a distance calculation process is carried out at each CL point. The criterion of determining whether a point is CC point or not is: the point on the wall surface that has zero distance or a value within a prescribed tolerance to the electrode is taken as CC point. In the implementation, this calculation is conducted by the UG function which is used internally to calculate the distance between solids and sheet bodies: UF_MODL_ask_minimum_dist( ).

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Fig. 9.

Manufacturing simulation.

5.4. Adjustment of electrode orientation In 4-axis machining because the orientation of electrode can only be changed by rotating the electrode around one axis, when constant angle B (Fig. 5) cannot be formed or a large change of angle A is needed to keep B constant, to guarantee a smooth transition of electrode, large charge of A should be avoided, the A left from previous CC point or that but having only a small difference is used for current position provided that there are no interferences. As result, B can only be kept near the constant value as much as possible. On the other hand, if B is obtained but interference occurs at the same time, the electrode should be further adjusted also to avoid interference. 5.5. Interference detection Interference detection is conducted by directly applying the UG Open function: UF_MODL_check_ interference( ). In this application, the electrode is taken as the single object and the workpiece surfaces are taken as a group of objects. 5.6. Machining simulation and test The simulation of 4-axis contour EDM rough milling process with tool paths generated by the previously introduced method is shown in Fig. 9. The diameter of electrode is 7 mm, cutting depth is 1.5 mm, radius of the circle of torus at the end of electrode is 1.5 mm which equals to the cutting depth approximately, discharging gap is taken as 0.5 mm. The angle between v tangent plane and electrode is set as 6 .

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Fig. 10. (a) Wear of the electrode. (b) The surface after rough EDM machining.

The machining is conducted by a layer-by-layer process. Fig. 8 shows the trace of electrode when one layer is machined. Electrode wear is compensated at the start of each layer by the semi-online method, which is for the left and right wall respectively. Compensation values for each segment are obtained from a model which is designed to simulate the functions of semionline wear measurement as discussed in Section 3.2. Fig. 10(a) illustrates the electrode used in the machining. It could be seen clearly that the end becomes a part of torus. Fig. 10(b) demonstrates the surface after rough contour EDM machining. 5.7. Discussion This algorithm is for rough contour EDM machining, there are undercut left on the bottom of the pocket. Also, because the semi-online compensation strategy is adopted, there will be compensation errors in each compensating segment of tool path. The error increases with the length of the segment. All those could be eliminated in following finish machining processes. The feed rate for milling and EDM is totally different. Because the feed rate of EDM is related with the choice of electric parameters such as current, pulse width, voltage, it is beyond the topic of this paper.

6. Conclusions Being a special application of conventional EDM, contour or CNC EDM machining of free-form surfaces is a new technology emerged in recent years. Due to its special machining properties, although the electrode

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moves in the same way as a cutter in mechanical milling, tool paths generated for milling cannot be used directly in contour EDM machining. Discharge gap compensation, electrode wear compensation and many other factors have to be considered in the tool path generation process. The proposed tool path generation method for contour EDM machining consists of two steps. In the first step, considering electric discharging gap, the electrode is approximated by a cutter that has the shape of a cylinder but with a torus end. Disregarding global interference between the tool and workpiece, initial tool paths and corresponding G codes for virtual 3-axis mechanical milling with this cutter are generated by a commercial CAD/CAM system—UG. Next, CC points in the tool paths are reversely calculated based on the geometric model and the previously generated G codes. The orientations of electrode are determined by the ‘‘constant angle’’ principle to obtain better surface finish by avoiding sharp changes in electrode orientations. This orientation will be further adjusted to an interference-free one should collisions be detected between electrode and workpiece so to make tool paths applicable in 4-axis machining. This method has been integrated into UG, machining simulation and test for 4-axis contour EDM machining has been conducted.

Acknowledgements The authors would like to thank Dr. R. Yuan and Mr. Z. Li of General Electric Company for their help in this research.

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