DRAFT Proceedings of IMECE2005

2005 ASME International Mechanical Engineering Congress and Exposition November 5-11, 2005, Orlando, Florida USA

�������������

NC VERIFICATION AND RE-PROCESSING FOR COLLABORATIVE MACHINING

PeiLing Liu**, YiQiang Lu*, XiaoMing Ding*, QinRong. Fu*, ChyeBeng Lim+

*Institute of High Performance Computing 1 Science Park Road, #01-01 The Capricorn

Singapore Science Park II, Singapore 117528

**Singapore Institute of Manufacturing Technology 71 NanYang Dr, Singapore 638075

+ AMG Technologies (M) Sdn. Bhd

Abstract: Collaborative machining is becoming a common practice worldwide. In mold manufacturing industry, as the specialized workshops often do machining much faster and cheaper than big mold firms, the mold makers are sub-contracting the machining jobs to other workshops especially the specialized workshops for higher efficiency and profit. This practice causes the separation of NC data generation, verification, and re-processing which requests new ways to manage NC data. This paper investigates the collaborative machining process and identifies quick NC data verification and re-processing as critical issues. The functionalities and limitations of the commercial systems are studied and the related NC model, simulation, verification, and optimization technology are scrutinzed. A dynamic in-process stock model based on a new geometry representation is proposed, then a system for quick NC verification and re-processing is developed using OpenGL. The system has been implemented in many mold manufacturing companies and the results show that the pervasive machining modeling, simulation, verification, and re-processing can effectively optimize machining processes in collaborative machining environments. Keywords: NC verification, NC simulation, NC post-processing, Collaborative machining NOMENCLATURE IPM In-process model

LM layered manufacturing M&S modeling & simulation

1. INTRODUCTION Outsource manufacturing is a worldwide

trend. In Asia mold manufacturing industry, as the specialized workshops often do machining much faster and cheaper than big mold firms, the mold makers are sub-contracting the machining jobs to other workshops especially the specialized workshops for higher efficiency and profit. This practice causes the separation of NC data generation, verification, and re-processing which requests new ways to manage NC data. Collaborative NC programming and machining create new challenges for CAM programmers and machinist.

For example, a NC programmer may not know for certain a machine tool to post-processing NC toolpath to machine control data, such as M/G code, since the contract machine shop could use different machine tools to cut same the part, pending on the availability of the machine tool. Contract machine shop may have to switch to an available machine tool, which needs to re-post NC data through another post-processor.

When received a set of NC data files plus setup drawing, a machinist has to verify and check data integrity before start cutting. Raw material is increasingly expensive nowadays and a new order may take days to complete. Even through it is common now that original NC toolpath are verified inside CAM software, there are still many chances of NC data errors

during post-processing and NC file management, as human fatigue is the main cause. Since machinists only have a few hours to cut the part to a certain stage, there is no time to run traditional NC simulation software, which typically needs more time than cutting itself, especially for high speed machining, where blocks of M/G code can easily reach one million.

Shop floor NC programming could be one solution for this complication, where a part model and machining process plan are sending to contract machining shop. However, this will burden contract machining shop with expensive CAM software and experienced NC programmer. Separation of CAD and CAM is less effective and create some problem for process planning. Most contract machining shops are majoring only a certain process of machining, such as roughing mold base, EDM of cavity, and profile grinding of inserts. 3D in-process models (IPMs) are very essential for the integration of various activities related to manufacturing process planning, toolpath generation, and machine inspection. By sharing accurate IPMs among the related activities, engineering change could be managed in an efficient way.

Most important, for some practical consideration especially in Asia, original designers do not want to share part model with contract machining shop.

Comparing with the sharp decline of the computing cost, worldwide material and machine tool prices are upsurge significantly. Saving material and manufacturing cost through pervasive application of modeling and simulation (M&S) is not only technically possible, but also makes business sense in today’s highly increasing competitive environment. How to quick verify and re-processing NC data are becoming a critical issue in modern contracting machining.

For the last two decades, we have developed NC simulation using different cutting simulation method, IPMs evolved from B-rep, section method, Z map, and patented extended Z map. The novel hybrid multiple contract machining and layered manufacturing processes posed a new challenge to process planning and verification.

2. NC PROGRAM ERRORS ANALYSIS

The average scrape rate for local mould maker is 15%. There are different kinds of NC program errors.

The low quality of solid model will cause low quality NC program:

• The surface deformation is too big during to data exchange problem.

• The surface tolerance maybe as low as 0.1mm.

• There are data defects, for example the gaps between surfaces

The NC toolpath generation algorithms are unstable:

• The toolpath planning is a very difficulty task.

• The toolpath sampling method varies quite differently.

• There is no exact offset solution for curves and curved surfaces.

The lack of in-process stock IPMs causes a lot of air cut and gouging.

• The cutter may move through remaining stock too fast.

• There maybe too many conservative air cuts in semi finishing cut and finishing cut.

• Near touch condition may cause cutter wear off.

The post-processor generates arcs with several meters radius, which will cause errors in some CNC controllers. The human errors occur depending on NC programmer’s experience. The possible cases include:

• The patching up of surfaces.• Plan machining process.• Wrong part face, check face and

boundary choice. • Wrong machining set-up.• Wrong cutting parameters. 3. GENERL METHODOLOGY A. NC SIMULATOR

INTRODUCTION NC Simulation features full 3D, solid

model, shaded simulation of entire NC machine tools and material removal. This visualisation tool enables programmers and machinists alike to preview exactly what will happen on the shop floor and check for collisions. Many use NC SIMULATION for electronic shop floor documentation.

NC Verification detects problems in the NC tool path program. It is a powerful visual inspection tool, which highlights fast feed errors, gouges, and potential crashes/collisions. Programmers can detect and correct problems before prove-out. With NC Verification you can virtually eliminate NC program mistakes, greatly reduce the time spent on prove-outs, and make the move to "lights-out" machining.

NC Analysis identifies the tool path record responsible for an error. Users can quickly verify the dimensional accuracy of the entire part with a full array of 3D measurement tools. NC Analysis compares the simulated part to the design model so to ensure the machined part match the design intent.

NC Optimisation automatically determines the best feed rate for each segment of the tool path based on the machining conditions and amount of material removed. Optimizing NC feed rates greatly reduces the time it takes to machine parts and improves the quality of surface finish.

The functions of NC simulation can be summarized as follows:

• NC simulation saves time and reduces or eliminates prove-outs and save machine tool, operator, and part programming time – all of which decrease time-to-market.

• NC simulation increases quality and verifies dimensional accuracy and optimises tool paths for better finishes on surfaces and edges.

• NC simulation Save money and reduce or eliminate the cost of machine tool crashes, rework, scrapped parts, and damaged tooling, fixtures, and clamps.

• NC simulation Increase productivity by reducing machining times and interrupts production less frequently.

• NC simulation gives confidence. Through testing part programs on a computer so they run right the first time and operators don’t need to keep one hand on the "emergency stop" button.

• NC simulation conserves resources. It can reduce machine tool wear and reduce cutting tool wear so cutting tools can be used longer before needing to be reground or replaced.

• NC simulation improves safety & training. It can train programmers, operators, and students without using machine tool time or risking a dangerous, costly collision.

• NC simulation improves documentation. Enable operators and managers to preview all machining operations.

B. TRADITIONAL NC

SIMULATION METHODS ALL of the current NC verification

systems are based on view dependent extended Z-buffer pixel. The pixel model could not be zoomed from different viewpoint. It is only good for animation. Also it does not provide dynamic information about the manufacturing process.

The recent development of high speed machining (HSM) requires huge tool path to realise the constant load. The milling tool path can easily exceed a half million blocks of machine code. As the feed rate is already very high, it is almost impossible to run test cutting by increasing the feed rate. Visual tool path check is difficult as the tool path overlapping with each other. It takes a long time to run traditional simulation software. The constant load is a very important factor in HSM as the cutter will break under uneven cutting force.

Currently there is no way to check this before the operation. There are strong requirements from industry for a real dynamic simulation to optimize feed/speed.

NC simulation could be classified by their geometrical models, which are sometimes called in-process model (IPM) since it is deformable. The in-process model represents the state of the product at each step in the machining process. It is represented as a 3D geometry that reflects the results of the machining operations. This model allows the user to visually verify that the machining operations which have been defined accurately and ensure their sequence is correct. This 3D model can be automatically re-generated when there are changes in the product design, machining parameters or sequence of the machining operations [1]. In following sections, the geometric representation techniques of IPMs for the traditional manufacturing simulation are presented. B-rep

The first choice of IPM should be naturally B-rep, which is the typical geometrical model of commercial CAD system. The benefits of using the same geometrical model of CAD as the IPM are obvious. The CAD geometrical model is matured and available through CAD development kit, so there is little need to develop a new geometrical model kernel. Sharing common geometrical model with CAD, the IPM facilitates seamless integration of CAD-CAPP-CAM.

The author of this paper developed an automatic forging design and manufacture system in 1986, in which pre-form forging IPMs were same as the CAD system CV/MUDUSA running on VAX-11/750 computer [5-6]. The creation of pre-form forging IPMs took days of calculation and often failed due to Boolean operation failure. It is very difficulty to deform a B-rep model other than traditional Boolean operation, where the topologies of B-rep model are altered and more faces are added. Boolean operations have to loop through all the faces to trim blank body with tool body. Localization of Boolean has been tried with limited success.

With great research efforts in the last two decades, the B-rep geometrical model has been improved a lot in term of Boolean operation stability, but the B-rep based IPMs are still

limited to 2.5 axis milling (Figure 1). S. C. Park reported a prismatic IPM generation method that employed a polygon extrusion algorithm, which could be used to sweep a ball-nose cutter [1]. Section Method

Since the integrated B-rep IPMs can not be created inside a CAD geometrical model, the ad-hoc cross-section-wire-frame based approach is proposed in a new concept forging die CAD/CAM system [5]. The idea is to use a series of paralleled cross section drawing as representation of 3D shapes (Figure 1).

The cross section IPM is widely used in many commercial CAD/CAM systems. I-DEAS from SDRC uses water level cross section as IPM for generative machining. In a traditional NC programming environment, a significant amount of time is spent trying to visualize the in-process stock as it goes through various process stages. With I-DEAS, the IPM - in-process stock model can be created for downstream applications such as toolpath generation, process planning, fixture designing, and clamp positioning.

A part can be sectioned along XYZ axis. The Z-axis section is usually called water level section. For 3-axis milling, the water level section could have many loops, which will make the set operation between sections complicated. X and Y sections are single half loops and the Z value is unique for every points.

Fig. 1 section representation and regulated

section A working system of using IPM for pre-

forging design was described in [5]. A section drawing sheet of part section was created first using BACIS command language of CV/MEDUSA CAD system. Since there were many sections in a drawing sheet, the section wire frame was assigned to different layers according to their Y distance, and a certain number of sections could be looped through layers. Then the cutter sections were moved to

the cutter location and compared with the part sections. The overlap between the cutter section and the part section was removed from the part section and a real milling IPM was obtained from the collection of the result sections.

The display of sections was line segment and could be confusing when there were too many lines. There was a need to render IPM as a realistic 3D image. In order to calculate the surface normal, which was needed for rendering, we divided the section wire frame along X direction by the same step over of Y direction. A so-called regulated section was formed to facilitate the calculation of surface normal and interpolation of points between the sections. A certain node in one section was linked to a certain node in the next section. A node’s normal could be calculated by the four neighboring nodes.

The regulated section can also be used to accelerate set operation between cutter section and part section. The calculation of intersection, trimming between two sections and the re-ordering of the line segments are very time consuming. This can be improved with the regulated sections, where the line segments were indexed in both cutter section and part section. Only the line segments with the same index were compared and trimmed. There is no need to loop through every segments of the section. If all the line segments fall on the regulated nodes, there is no need to trim two line segments. The set operation could be simplified to the comparison of two Z values. The comparison of two values could be very fast and stable. The so called Z map representation of IPM was born [6].

Z Map Representation

If all the section line segments fall on the nodes, the object surface can be represented by the Z values of the nodes. A map of Z values represents the object geometry. (A Z map can also be seen as a forest of uniformed planted trees, where the heights of trees represent the geometry of the forest.) Mathematically, Z map could expressed as a two-dimension array Z[i, j], where i represents the index in X direction and j represents the index in Y direction. The XY position of the Z map can be calculated by i or j times grid size.

The best way to describe a Z map is using a needle bed sample, where needles are

uniformly distributed over XY plane. The height of every needle touches the object surface that it represents. The milling simulation can be seen as the tool cutting through needle bed. These needles can be described in math term as z axis aligned vectors, passing through the grid points on the XY plane. Z map representation can be effectively used for the surface that is always visible from above in the direction parallel to the Z axis. Since 3-axis milling parts are composed of surfaces visible in the z direction, they can be effectively expressed by the Z map representation. With the Z map representation, the machining process can be simulated through cutting the Z map vectors by the cutter.

Fig. 2 classic Z Map and display The vector in Z map has direction and

length. The vector in Z map is infinitely thin without volume. The top of the vector is just a point and has no shape at all. Only at this point the Z map and the object meet with each other. Z map mode could not give accurate object geometry besides these points. There are many ways of interpolating the geometry between grid points. For example, triangle needs to be formed by tri neighboring Z values to render a Z map model.

Fig. 3 NS simulation based on Z Map The extended Z map representation

method comprises the steps of providing geometric data of an object having a surface,

the object constituting one of a physical object and a virtual object, and the geometric data being indicative of the surface of the object. As shown in Fig 4, firstly it generates a reference plane with z-axis being perpendicular to the reference plane, then constructs a z-map grid, the z-map grid being planar and coincident with the reference plane, after that constructs a first z-map of a first portion of the surface of the object which is generated with reference to the z-map grid, finally constructs a second z-map of a second portion of the surface of the object which is generated with reference to the z-map grid. Z map could be expended with another Z value to represent an object with top and bottom surface.

Fig. 4 Extend Z map to top and bottom faces

This Z map has many alias or hybrid

cousins such as ray casting, Z buffer etc. When a group of virtually light rays pass through an object from Z direction, there will be intersections between the light ray and the object. These top and bottom Z values are stored in the depth buffers of the graphics card and used for hidden surface removal algorithm. This process was called ray casting or tracing technology and is used for many graphics application such as volume rendering. The detailed description of the extended Z map method can be found in two patents [12]. Dexel or extended Z buffer extends Z map to multi segments and positions it along screen normal, so a faster cutting animation could be achieved but it is view dependent.

Fig. 5 extended Z buffer Dexel model

Z map can not approximate vertical wall very well since it always has a slope as showed in Fig 7. This is not a big problem for forging die design since there always are draft angles in forging parts. This is a big problem for milling parts since profiling always creates vertical walls.

Fig. 6 classic Z Map cannot model vertical

walls precisely It is obvious that the XY resolution of the

Z map grid is the precision of Z map model. The smaller grid has the better precision but needs greater memory. For a part of 1000mm*1000mm, the size of the Z map is 1000*1000 if the precision is 1mm, but it increases to 2000*2000 if the precision is 0.5mm. Reducing the model size and achieving suitable precision appears to be a critical issue on Z map.

Because of its simplicity in the data structure and fast computation time, Z map model is used by most commercial CAM software [7-9]. One of the solutions is to balance Z precision and XY precision. One invention in [12] is to use integer array to replace the float array of Z map, which reduces the Z map size by half, and at the same time improves the boolean operation speed because the comparison of integers is much faster than the comparison of floats. The memory of Z map is further reduced it by half through compressing Z map file section by section.

4. QUICK NC SIMULATION

METHODS 4.1 Sub-cell Since the precision of Z map is decided

mainly by the XY resolution along the vertical walls, how to increase the resolution along these walls and reduce memory becomes a critical issue. Viewing from top, the vertical walls only cover a small percentage of Z direction projection, how can we use finer resolution along the vertical walls while

maintain a rough resolution in the planar area? This was the initial idea of extended Z map.

In this study, at least one grid on a z-map is segregated into sub-cells. Only grids corresponding to intricate features on the surface of an object are assigned sub-cells to improve representation of object features. Figure 7a shows the front sectional view, while Figure 7b illustrates the plan view of the z-map grid with sub-cells 52.

Fig. 7 extend Z Map with sub-cells along

vertical walls The size of the grid can be reduced

through using sub-cells. But the precision of XY dimension is still limited by the size of sub-cells. For a sub-cell of 0.1mm, the best precision is 0.1mm in XY plane. There is a need to represent XY dimension precisely. Instead of using vectors in the sub-cells, we use sticks in the sub-cells that have volumes and surface geometry. A B-rep surface model can be represented precisely using a map of B-rep sticks.

Fig. 8 stick method and a sample display Milling simulation in stick method

involves Boolean operation of cutter and stick. Figure 10 shows different stick shape after cutting. The experiments with B-rep stick model are very slow and create a huge B-rep model. To simplify stick and Boolean operation, polygon instead of real surface is used in a stick cell. This can greatly increase simulation speed. The data structure of polygon is much simpler than that of B-rep which needs a group of complicated pointers to maintain a double wing data structure.

Fig. 9 different shapes of stick elements The real world objects are not always

uniform in XY dimension and can be any shape. Nodes are used to enhance sub-cell’s precisions in representation of object face. For example, one edge of the sub-cell may have two overlapping nodes to represent a vertical face. The nodes of a sub-cell may not be uniformly distributed over XY plane. Figure 11 shows an exploded plan view of a portion of the z-map grid with nodes 54. Figure 12 shows how stick method represents a circular hole and vertical walls.

Fig. 10 extended sub-cells to approximate

vertical wall 4.2 Color index In addition, a color index is assigned to

each grid point on the z-map grid and stored in a reference list containing cells corresponding to each grid point on the z-map. A computer model of the object is pre-rendered using the reference list onto a plurality of display lists corresponding to different portions of the computer model of the object. By recalling the required display list for display when the computer model is virtually displaced, the time lag for displaying the computer model to a user is substantially reduced.

The system starts with a solid model of the machined part and quickly simulates and optimizes machining processes. NC code could be selectively reverse post processed into 3D tool path graphics display and interactively viewed, edited, and optimized.

44 52 52 52

The user can highlight or hide operation, tool path, or layer. The user also can display and edit a certain layer of toolpath. Tool paths and cutting results can be viewed from any viewpoint and checked automatically. The machined part and the design part are compared for the remaining stock and over cut. Error-free tool paths are created, eliminating the need for a time-consuming test cut. Quick and simple post processors export the optimized toolpath to NC code.

4.3 Applications We developed several practical

applications for mould manufacturers. These include QuickSeeNC and PartingAdviser, which provide “What You See is What You Cut” functionality for shop floor machine operators and designers. It could be integrated with other CAM software such as UG through a native APT adapter.

The actual application example of a steel insert of discman mould comes from last author’s company. The steps to do simulation is described below: Step 1 was to setup stock size as 3300*220*100mm; Step 2 was to open APT toolpath discman.cls. There were 16 operations in this CLS file that contains almost half million of NC blocks. QuickSeeNC loaded in half million lines in seconds and displayed toolpath in different colours according to operation. User could control the display by layers or operation, depending on the editing needs.

Fig. 11 almost half million of NC block The system abstract toolpath and cutter

info from cls file and created NC data file that could be sent to shop floor:

NC Program Data Sheet core_insert_nc

No. Program Name Cutter SOL Time 1 V64C61CA D20.00 R0.000 L75 96m 2 V61CA1 D20.00 R0.000 L75 11m 3 V64C61CB D12.00 R6.000 L75 31m 4 V64C61CC D6.000 R3.000 L75 45m 5 V64C61CD D6.000 R3.000 L75 153m 6 V64C61CE D4.000 R2.000 L75 33m 7 V61CE1 D4.000 R2.000 L75 11m 8 V64C61CF D20.00 R0.000 L75 2m 9 V61CF1 D20.00 R0.000 L75 1m 10 V64C61CG D8.000 R0.000 L75 6m 11 V61CG1 D8.000 R0.000 L75 7m 12 V61CG2 D8.000 R0.000 L75 7m 13 V61CG3 D8.000 R0.000 L75 7m 14 V61CG4 D8.000 R0.000 L75 7m 15 V64C61CH D16.00 R0.000 L75 13m 16 V61CH1 D16.00 R0.000 L75 14m Total NC Program = 16 Machine time = 7 hours 23 minutes In step 3 a user studied the operation using

toolpath manager. The red colour shows the current toolpath. cutting simulation from start to finish could be completed in less than one minute. After scrutiny the IPM, 16 operations was scheduled to different machine tools and quick post out to NC code, with all the cutter and process info inserted on the top of the NC data file.

Fig. 12 Extended Z map IPM

5. TOWARDS A UNIFIED MODEL FOR

MULTIPLE MACHINING AND LM SIMULATION

The term voxel represents a volume

element in space decomposition geometrical model schema, just like the term pixel denotes a picture element in raster graphics. Voxelization is the process of converting a 3D object into a voxel model. After analyzing the voxel model, the authors of this paper believe the voxel-based volume modeling is a very promising approach to the unified IPM for multiple machining and layered manufacturing

simulation. As a natural clone of the LM technology, the voxel model of an object and the object fabricated using an LM closely resemble each other since both are made of layers of small cells. It eliminates the STL format and eases accomplishments of tasks such as estimation of errors in the physical parameters of the fabricated objects, tolerance and interference detection. Furthermore, voxel based models permit the designer to analyze the LM object and modify it at the voxel level leading to the design of custom composites of arbitrary topology.

Volume graphics, voxelization and volume rendering have attracted considerable research in recent years. However, all of this works are directed at the display of volume data, mainly for medical applications. In this paper we propose a simplified voxel-based IPM to unite the new LM and traditional machining processes simulation.

The memory requirements of traditional voxel models are enormous. There is a need to store the voxel array in compressed form and use algorithms that will operate directly on the compressed data, specially when the material is homogenous, where internal voxel could represented by boundary voxel extension. It is possible to convert the voxel array into some other more compact representation and reconvert into voxels when required. However, this could be mainly used for storage purpose. We keep the original geometric representation and use voxelization algorithms when necessary. This is especially valuable since design data are mainly generated from conventional CAD system.

A voxel-based system should be able to update the display at interactive rates. Current graphics rendering systems cannot provide a level of rendering performance on voxel models that is comparable to their polygon-rendering performance. Parallel algorithms and hardware support for volume rendering are the focus of current research efforts. Only boundary voxel needs to be rendered by a patented color list, which effectively avoid expensive ray-casting of huge internal voxels. The rendering of voxel model is easily achieved by rendering a points cloud. However, internal voxel display is not possible with this method and needs more study.

Voxel based LM simulation could be achieved by the voxelization of the road shapes, which are similar to a pipe along the

LM toolpath. Boolean addition between the road shape voxel and the base voxel is fast and stable, independent of the model shape, which is a critical issue with B-rep. One layer of road shapes would make B-rep based solid modeler very slow, since B-rep Boolean operation is dependent on model shape.

During a combined LM and machining manufacturing, such as shape deposition manufacturing, a LM part needs to be inserted with a electronic device and milled to a certain shape. The unified LM-machining simulation displays the machining process in which the initial LM generated workpiece is incrementally converted into the finished part. The voxel representation is used to model efficiently the state of IPM, which is generated by successively subtracting tool swept volumes from the workpiece. The voxel representation also simplifies the computation of regularized Boolean set operations and of material removal volumes. By using the material removal rate measured by the number of removed voxels, the feedrate can be adjusted adaptively to increase the machining productivity.

6. CONCLUSIONS Numerical Control Machining is the

cutting edge of modern manufacturing technology. NC errors could destroy work pieces, even damage machine tool. One NC error could make the workpiece a waste and take days to rework a new workpiece. The machining errors eat into profit. In the age of small batch production, there is no time for trial and errors. Verifying and optimizing precision NC machining make profits.

In the age of high speed (HSM) precision machining, the fast moving and expensive cutter is very easy to be broken. However, traditional NC simulation only checks geometry errors which is not good enough. The dynamic machining load will greatly affect cutter life, geometry accuracy and surface finishing.

The challenges also come from huge tool path of HSM. Million lines of NC code are common practice in today’s shop floor. The traditional NC verification is so slow that even HSM itself is faster than verification. The size of the program combined with a high feed rate makes it almost impossible to run test simulations prior to cutting metal.

3D IPMs is very essential for collaborative machining and the integration of various activities related to manufacturing process planning, toolpath generation, and machine inspection. By sharing accurate IPMs among the related activities, engineering change could be managed in an efficient way. We generated the machining IPMs through different cutting simulation method, evolved from B-rep, section method, Z map, and patented extended Z map. The novel hybrid multiple machining and layered manufacturing processes posed a new challenge to process planning and verification. Towards the vision of pervasive modeling & simulation, we proposed a unified voxel-based in-process geometrical model for multiple machining and layered manufacturing simulations. REFERENCE:

[1] SANG C. PARK, GOPALAN

MUKUNDAN, SHUXIN GU and GUSTAV J. OLLING, “IN-PROCESS MODEL GENERATION FOR THE PROCESS PLANNING OF A PRISMATIC PART”, Journal of Advanced Manufacturing Systems, Vol. 2, No. 2 (2003) 147–162

[2] D. Qiu, N. Langrana, S. C. Danforth, A.

Safari, M. Jafari, "Development of Multi-material Virtual Layered Manufacturing Simulation", the Proceedings of Third Pacific Rim International Conference on Advanced Materials and Processing, Hawaii, July, 1998.

[3] Choi, S.H., and Cheung , H.H., 2005,

A multi-material virtual prototyping system, Computer-Aided Design 130 (37)123–136

[4]www.imti21.org/msam/UnitProcess.pdf [5] Liu P.L et al, a New Concept

Integrated CAD/CAM System for Complicated Die & Mold, ADVANCES IN COMPUTER SCIENCE APPLICATION TO MACHINERY, International Academic Publisher, 1991.8, ISBN 7-8003-154-3/TH.2, pp.90-95

[6] Liu P.L et al, 3D Complicated Parts

Design Based on the Automatic Shape Generation, CHINESE JOURNAL OF MECHNAICAL ENGINEERING (English Edition), Volume 5 Number 2, 1992, pp88-92.

[7] R. B. Jerard, S. Z. Hussaini, R. L.

Drysdale and B. Schaudt, “Approximate methods for simulation and verification of numerically controlled machining programs”, Visual Computer, 5(4), pp. 329–348, 1989.

[8] S. Stifter, “Simulation of NC

machining based on the dexel model: a critical analysis”, International Journal of Advanced Manufacturing Technology, 10(3), pp. 149–157, 1995.

[9] Seung Ryol Maenga,b, Nakhoon

Baekc,*, Sung Yong Shinb, Byoung Kyu Choid, “A Z-map update method for linearly moving tools”, Computer-Aided Design 35 (2003) 995–1009

[10] Vijay Chandru , Swami Manohar , C.

Edmond Prakash, Voxel-Based Modeling for Layered Manufacturing, IEEE Computer

Graphics and Applications (1995), v.15 n.6 [11] Donggo Jang, Kwangsoo Kim, and

Jungmin Jung ,Voxel-based Virtual Multi-axis Machining Int. Journal of Advanced Manufacturing Technology 16(10), 709-713, 2000

[12] Liu P.L et al, 2002, An object

representation method, WO04032001A1.