Modelling and optimisation of Rapid Prototyping

Computers in Industry 47 (2002) 39±53

Modelling and optimisation of Rapid Prototyping S.H. Choi*, S. Samavedam Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Haking Wong Building, Pokfulam Road, Hong Kong, PR China Received 3 June 1999; accepted 18 August 2001

Abstract This paper proposes a Virtual Reality (VR) system for modelling and optimisation of Rapid Prototyping (RP) processes. The system aims to reduce the manufacturing risks of prototypes early in a product development cycle, and hence, reduces the number of costly design-build-test cycles. It involves modelling and simulation of RP in a virtual system, which facilitates visualisation and testing the effects of process parameters on the part quality. Modelling of RP is based on quantifying the measures of part quality, which includes accuracy, build-time and ef®ciency with orientation, layer thickness and hatch distance. A mathematical model has been developed to estimate the build-time of the Selective Laser Sintering (SLS) process. The model incorporates various process parameters like layer thickness, hatch space, bed temperatures, laser power and sinter factor, etc. It has been integrated with the virtual simulation system to provide a test-bed to optimise the process parameters. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Rapid Prototyping; Parameter optimisation; Virtual Prototyping; Simulation

1. Introduction 1.1. Rapid Prototyping Rapid Prototyping (RP) or Layer Manufacturing (LM) refers to fabrication of parts layer-by-layer. It involves adding raw material successively, in layers, to create a solid of a prede®ned shape. These parts are used in the various stages of a product development cycle. Wholers [1] conducted a survey, and found that around 23.4% of RP parts are used as visual aids, whereas 27.5% of them are used as master patterns for secondary manufacturing processes and for direct tooling. Industries use 15.6% of them for ®t and *

Corresponding author. Tel.: ‡86-852-2859-7054; fax: ‡86-852-2858-6535. E-mail address: [email protected] (S.H. Choi).

assembly tests, 16.1% for functional tests and the rest for quoting, proposal, ergonomic evaluation, etc. Fig. 1 shows the ¯ow of a typical RP process. The ®rst step is to validate the 3D CAD model of a part, i.e. to ensure it is a solid, which must be repaired otherwise. The valid model is then oriented with respect to the build chamber, by considering the build-time and the surface quality. A few models may either be merged into a one-build assembly or nested for ef®cient utilisation of the machine and the material. Based on the process requirement, support structures may be added to the model, if necessary. It is then sliced with a set of horizontal planes. Each horizontal plane yields a planar slice contour, which is crosshatched to determine the laser trajectories to control the sintering/solidi®cation process. By scanning one layer over another, the part grows incrementally to its ®nal shape. Thus, the main steps for process planning

0166-3615/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 - 3 6 1 5 ( 0 1 ) 0 0 1 4 0 - 3

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S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

Nomenclature ACH Aw B Cp db dh ds h hc hm k ` `m Ld Lh Lv MCH Nf N` Np P` R td th twd twr Tb T` Tm Ts v Vp

average cusp height (surface accuracy) surface area of workspace (mm2) build-direction specific heat (J g 1 K 1) laser beam diameter (mm) hatch space (mm) scan distance of a layer (mm) total height of the part (mm) cusp height (mm) maximum material height (mm) sinter factor layer thickness (mm) machine layer thickness (mm) laser scan distance (mm) latent heat (J g 1) laser scan velocity (mm s 1) maximum cusp height total number of facets total number of layers total number of parts laser power (W) reflectivity of the mirror material deposition time (s) time required to heat the material (s) time required for the work-bed to move down (s) time required for the work-bed to rise up (s) bed temperature (K) scan time of a layer (s) melting temperature (K) set-up time of a layer (s) velocity (mm s 1) enclosing box volume of a part (mm3)

Greek letters Z orientation efficiency r material density (g mm 3) include orientation, support structure generation if necessary, slicing and selection of process parameters. Process planning is performed to select the process parameters and to generate the control instructions to fabricate a part. In general, the designer carries out process planning by studying the part and quality requirements, which is indeed very time-consuming.

Therefore, there is a need to automate the process. This can be achieved by linking the designer's understanding and decision making with the physical process to create parts of the desired quality. Automation of process planning is also one of the fundamental aims of RP [2], which are  to build arbitrarily complex 3D shapes;  to use a generic fabrication machine which does not require part-specific fixturing or tooling;  to generate a process plan automatically, based on a CAD model;  to minimise human intervention. RP facilitates ful®lment of the ®rst two aims mentioned above. However, it requires a signi®cant amount of human intervention to produce an optimal part. The optimality depends on the functional requirements, which include accuracy, build-time, strength and ef®ciency. The quality requirements, however, vary from visual aids to master patterns for secondary processes. Hence, a signi®cant degree of expertise is required to produce parts of consistent quality. The process is, therefore, very costly and of a trial-anderror basis. The objectives of this paper are to quantify the requirements for optimisation of RP and to simulate the fabrication of prototypes for visualisation in Virtual Reality (VR). 1.2. Virtual Reality and Virtual Prototyping VR is an advanced human-computer interface that simulates a realistic environment and allows a designer to interact with it. The essence of VR is immersion and interactivity, which differentiates it from CAD systems. Immersion means to block out distractions and to focus on selective information with which the designer wants to work. Interactivity implies the ability that humans interact with events in the virtual world [3]. Applications of VR have recently gained considerable momentum in industries. Resseler [4] presented a summary of its applications in manufacturing. Dai and Gobel [5] discussed the advantages of Virtual Prototyping (VP) over physical prototyping. They considered VP as the integration of VR with product design and simulation, and listed the constraints of computer graphics that have to be solved for effective implementation of VP. They suggested the use of electronic prototyping as an

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Fig. 1. RP process.

alternative to physical prototyping. However, this is not yet feasible with the present technology due to the weakness of the link between CAD systems and CAE components like FEA, kinematics and dynamics systems. Few researchers have combined the advantages of VP with RP technologies. Gibson et al. [6] investigated the contributions of VR and RP towards a more ef®cient product development in ergonomic, aesthetic and functional aspects of design. They suggested the use of VR as a complementary technology to RP with an interface accommodated through a CAD system. Fadel and co-workers [7,8] linked VR with RP to visualise the support structures of a part. They coupled RP with VR by developing the Interactive Virtual Environment for Correction of Stereolithography Tessellated List Files System (IVECS). It is a tool to perform minute surgeries on faulty tessellated models. Indeed, correcting a faulty Stereolithography Tessellated List (STL) ®le is tedious. 1.3. Process parameters of Rapid Prototyping Automation of control code generation for the desired requirements is an emerging research aspect of RP. Diane et al. [9] classi®ed RP process parameters into nuisance, constant and control parameters. Nuisance parameters include age of the laser, beam position accuracy, humidity and temperature, which are not controlled in the experimental analysis but may have some effect on a part. Constant parameters

normally include beam diameter, laser focus and material properties, etc. The control parameters will affect the output of the process and are controllable in a run. These include layer thickness, hatch space, scan pattern, part orientation, shrinkage of the material and beamwidth compensation, etc. Diane et al. [9] concluded that layer thickness, hatch space, part orientation and depth of cure are the most vital among the control parameters. They conducted experiments with hatch space, orientation, layer thickness and overcure depth, and con®rmed their in¯uence on Stereolithography (SLA) parts quality is signi®cant. Zhou and Hersovici [10] presented accuracy problems in SLA process, and established that layer thickness, hatch space, overcure, gap and the position on the build-plane of the SLA process are control factors of accuracy. They employed Taguchi method to ®nd the functional relationships between different combinations of control factors and part quality for standard surface features. However, extrapolation of these results to complex RP part surfaces is very dif®cult. Thomson and Crawford [11] chose build-time, surface ®nish and part strength for manufacturing requirements and developed numerical methods to quantify the requirements with respect to the part orientation for the Selective Laser Sintering (SLS) process. A genetic algorithm was developed by Woodzaik et al. [13] to automatically place multiple parts in a workspace to reduce build-time, and thereby, increase ef®ciency. The parts are enclosed in rectangular boxes and are rotated 908 about the z-axis to aid

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part packing, without considering the surface accuracy and the support structure requirements. Anne et al. [14] presented an integrated software system for process planning for LM under development at University of Michigan. Ablani and Bagchi [15] developed a software system to ®nd preferred orientations. It rotates a part in increments about the designer-supplied axes and slices the part to evaluate the errors due to the stair-step effect. However, they considered rotations of the part in the range from 0 to 3608, which is not entirely necessary for the estimation of surface accuracy. Due to the complexity involved, most research work has been focused on the optimisation of a single

requirement or parameter. For example, in the case of packing parts in the workspace, consideration is given only to minimising the build-time. Such algorithms are useful for solving a single requirement or optimisation of a parameter. However, they lack the ¯exibility for multiple requirements or tuning a few parameters according to the desired quality. 1.4. Modelling and optimisation of Rapid Prototyping This paper proposes a VR system for modelling and optimisation of RP. It provides a test-bed for optimising various requirements of an RP process. Fig. 2

Fig. 2. Proposed VR-based RP approach.

S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

shows the ¯owchart of the proposed approach. The designer starts with building a 3D model of a part, and subsequently performs VR simulation of the RP process to optimise the control parameters. When the desired requirements are met, they can be used for physical fabrication. If the fabrication is to be carried out by a service bureau or another department, the designer can perform virtual simulation with the control parameters. The virtual part may subsequently be sent by conventional means or through Internet to the designer/customer for assessment, as represented in dotted lines. This facilitates feedback for design improvement. Once the desired quality is obtained through virtual fabrication, physical fabrication of the part may follow. This approach will consequently reduce the time required to communicate, as well as the number of iterations. The designer may build and break as many parts as required more quickly at a relatively low cost. Thus, virtual simulation of RP parts will help reduce, if not eliminate, the number of physical prototypes required to produce a part. The designer may conveniently realise and validate the intended part before committing to manufacture.

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2. The virtual simulation system for Rapid Prototyping The architecture of the proposed system is shown in Fig. 3. As an initial implementation, the system is ®rst targeted at the SLS process. It may be subsequently enhanced to incorporate the characteristics of other RP processes. The input to the system is a CAD model in STL format, which is the de-facto standard in RP industry. The VR generator WorldToolKit (WTK) creates a virtual world describing the environment of the system. It also manages the geometry and rendering optimisation, and thereby, generates a VR model. Once a VR model is created, the Presentation Module makes it visible. Visualisation is based on photo-realistic rendering of the VR model. It also facilitates realistic visualisation through stereoscopic viewing. The Modelling Module allows the designer to interact with the VR model to manipulate the viewing perspectives and the part geometry. This allows the designer to view the model by navigating around it and changing the lighting, shading and rendering

Fig. 3. Architecture of the proposed virtual system for RP.

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conditions. It also enables the designer to change the shape of the part parametrically. This facilitates the designers to visually examine the intrinsic details of the part more closely. The Simulation Module performs simulation of the layer building process based on the control parameters supplied. The simulation process is mainly concerned with the realistic representation of the RP process. This is key to dynamic visualisation and analysis of the effect of different process parameters in real-time. The graphical simulation allows the designer to visualise the fabrication process of the part, particularly its topological changes with respect to the process parameters. The Evaluation Module quanti®es accuracy, buildtime and orientation ef®ciency for a given set of control parameters. It allows modi®cations of the control parameters, and subsequently facilitates the designer to visually inspect the fabricated virtual part and analyse the in¯uence of the process parameters. The Mathematical Model gets the control parameters from the designer and establishes the relationships between orientation, layer thickness, hatch space, accuracy, build-time and ef®ciency. In the development of the simulation system, it is necessary to understand and analyse the process planning stage of an RP process. The development work is, therefore, based on the following stages: (1) identi®cation of the designer requirements or objectives; (2) identi®cation of the key manufacturing parameters; and (3) veri®cation of the in¯uence of the chosen parameters on the requirements. The following sections describe the development of the RP simulation system. 2.1. Identi®cation of requirements and key manufacturing parameters The functional requirements of a manufacturing process include accuracy, strength, build-time and ef®ciency of the process. All these manufacturing requirements are also applicable to RP. Surface accuracy is gaining a greater signi®cance as more parts are used as master patterns for secondary manufacturing processes. Build-time is important in the general context of manufacturing for scheduling and cost estimation. It is particularly useful for service bureaux and their customers, as the prices of RP parts are usually quoted proportional to the build-time. Ef®ciency

denotes the utilisation of materials for fabricating a part. Earlier studies [9±12,16] have con®rmed that layer thickness, hatch space and orientation are the key control parameters for SLS and SLA. These are indeed process-independent parameters, and can be applied to other processes, such as Laminated Object Manufacturing (LOM), Fused Deposition Modelling (FDM), etc. Support structures are essential for SLA and FDM, but they are not needed for LOM and SLS processes. In the present work, orientation, layer thickness and hatch space are used to develop a simulation model for SLS, which may be subsequently enhanced to cover other processes. 2.2. Parameters versus requirements Build-time, surface accuracy and ef®ciency requirements of an RP process are largely determined by orientation, layer thickness and hatch space parameters. The orientation of an RP part affects accuracy and build-time. Orientating a part in the optimal direction will give a relatively smaller angle between the facets and the build-direction, resulting in a higher surface accuracy. The build-time of a part is proportional to its z-height in the build-direction. Orienting a part with the minimum z-height will result in fewer slices, and hence, a reduction in build-time. Layer thickness affects the surface accuracy and build-time. The surface accuracy will be improved when a part is built with a smaller thickness, but the build-time will increase inversely. On the other hand, a part will be built faster with a larger thickness that results in decreased accuracy, particularly in high curvature regions. Hatch space refers to the distance between the parallel vectors used to solidify the layer surface. A large hatch space reduces build-time. However, if it is too large, part of the material in the layer may not be sintered. Hence, it is important to set the hatch space as such that the build-time will be the minimum possible while the layer is properly sintered. 2.3. Requirement quanti®cation Developing a mathematical model that incorporates the behaviour of RP will allow the designer to estimate the part quality. This requires a detailed understanding of the effect of the control parameters on a speci®c

S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

process. The in¯uences of the control parameters on the requirements vary from one process to another. As an initial step, it will be useful to start with a relatively simple mathematical model, which incorporates process-independent parameters only, and subsequently enhanced with the characteristics of individual processes. There are different approaches to quantifying the requirements with regard to the control parameters. The following sections discuss the measurement of each requirement. 2.3.1. Accuracy Surface accuracy can be de®ned as the deviation of the geometry from the progenitor CAD model to the part. The loss of accuracy is mainly due to (1) preprocess errors; (2) process planning errors; and (3) post-process errors. 2.3.1.1. Pre-process errors. These errors are inherent due to the representation of a part in a CAD system for data exchange purposes. The part surface is normally represented in the STL format, which is a collection of tessellated triangular facets. To generate a STL model, a tolerable chordal error has to be set, as shown in Fig. 4. Thus, to represent highly curved surfaces accurately, a small tolerance value is needed. This results in an increased number of facets, and hence, the file size, which may have to be compromised with the accuracy of the part surface. 2.3.1.2. Process planning errors. In RP, each layer is generated as an extrusion of a planar contour by processing the material on the interior of a 2D slice. A slice is generated by the intersection of a horizontal plane with a faceted STL model. Extrusion of a slice to form a layer results in stepped approximation of the boundary of the original CAD model. Consequently, all

Fig. 4. The stair-step effect due to layer thickness.

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parts generated by RP exhibit a ``stair-step'' effect, as shown in Fig. 4, and such effect becomes more obvious on slanted and curved surfaces. This error can be quantified by cusp height, which is the distance between the intended and approximated surface at each facet. For each facet, the surface normal indicates the angle that the facet makes with the build-direction. If the surface normal is not perpendicular to the builddirection, the facet will exhibit some stair-step effect. For a given facet, with (a±c) as vertices as shown in Fig. 4, the error can be evaluated as cusp height …hc † ˆ bc cos y

(1)

maximum cusp height …MCH† ˆ max…hc † P Nf hci average cusp height …ACH† ˆ iˆ1 Nf

(2) (3)

The average cusp height represents the mean of the linear deviations of all facets, while the maximum cusp height is the maximum linear deviation among the facets. However, the dimensional error may also be represented as the volumetric deviation, which can be evaluated by calculating the volumetric error for each layer that can be summed up to give the overall volumetric deviation. Determining the volumetric error would be computationally intensive. Hence, in the present approach, the average cusp height is adopted for measuring the surface accuracy. Post-process errors include process, shrinkage and warpage errors. Process errors are mainly due to laser delivery mechanism and the induced angle with the part surface. Shrinkage error is mainly due to solidi®cation of the part. For RP processes that employ heat energy to solidify/sinter the material, the subsequent prototypes tend to shrink after cooling, resulting in dimensional deviations from the original design. Warpage is another kind of inaccuracy caused by uneven distributions of heat energy and the resultant binding force. These dimensional errors vary with the part geometry and the characteristics of RP processes. Indeed, shrinkage and warpage are complex thermal processes, which are beyond the scope of the present work. However, when thermodynamics and binding force models for estimation of shrinkage and warpage become available, they may be incorporated into the system to enhance the overall surface accuracy of prototypes.

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2.3.2. Build-time Build-time can be de®ned as the time required for building a physical part. STLtime [16] estimates build-time based on the part volume, height and surface area. Kamesh and Flyn [17] developed a buildtimer that evaluates build-time as a function of the total scan length and the laser speed. They derived the laser speed from statistical observations, which can predict build-time approximately. As the speed is derived statistically, the in¯uence of process parameters is not incorporated. Thus, these models have inadequacies in analysing the effects of process parameters on build-time. A more detailed study was performed by Chen and Sullivan [18]. They considered the actual scan vectors for each layer, the theoretical laser velocity and overcure for SLA. Hitherto, build-time estimators are available for SLA only. Indeed, there are not build-time estimators for other processes like SLS and LOM. This factor motivated us to develop an accurate build-time estimator for these machines. Amongst LOM and SLS, the latter is widely used and is capable of producing moulds directly. Furthermore, it is vital that an RP machine is available to conduct experiments and test the mathematical model. The faculty has a Sinterstation 2000 SLS machine, which is very suitable for testing and veri®cation of the simulation system. Although the SLS machine has an integrated build-time estimator, it is highly inaccurate. These reasons, thus, led us to develop a build-time estimator for the SLS process, which may subsequently be modi®ed for other processes using laser heads. The build-time estimator evaluates the time as a function of the laser velocity, scan distance and layer thickness. For SLS, the laser velocity derived from [19] is shown in Eq. (4). Velocity …v† ˆ

P` …1 rdb `m ‰Cp …Tm

R† Tb † ‡ kLh Š

(4)

The build-time of a part can be obtained by summing up the time taken for each layer, as shown in Eq. (8), which is derived from Eq. (5). The time taken for building a layer can be divided into the scan time and the set-up time. The set-up time can be obtained from the machine manual, and it is normally constant for all layers. The time required for scanning a layer varies along the z-axis and can be obtained as a ratio of the scan distance to the scan velocity from Eq. (6). The total scan distance within a layer can be obtained from

the hatch ®le. The velocity can be estimated based on the process. For example, it can be estimated from Eq. (4) for the SLS process. Build-time of a part ˆ

N` X T`i ‡ Ts N`

(5)

iˆ1

Scan time …T` † ˆ

Ld Lv

(6)

Set-up time refers to the time that the SLS machine takes to spread a thin and even layer of powder to be sintered for the next slice. It refers to everything the machine does when it is not sintering. The set-up time for SLS is shown in Eq. (7). Set-up time …Ts † ˆ twd ‡ td ‡ twr ‡ th (7) P N`   h dsi …`=`m † Build-time of a part ˆ Ts ‡ iˆ1 `m Lv (8) The present algorithm is a useful step in developing a build-time estimator for SLS machines. Unlike the previously available algorithms, the present one includes the material properties, process parameters like layer thickness and hatch space and the machine parameters like work-bed temperature, power and laser re¯ectivity. 2.3.3. Orientation ef®ciency In an RP process, the work-bed is lowered and the material is deposited on it before the laser starts scanning. The preparation time and the material deposited for each layer is always constant, regardless of the number of parts being built and the area of the work-bed used. This prompts the designer to increase the ef®ciency by building a number of parts together, which may ®ll the largest work area and volume possible, as stacking one part over another will lead to a higher ef®ciency. However, utilisation of the maximum workspace is not always feasible. For example, the RP process may not support packing along the z-axis; or the batch size required may be small; or there may be limitations on the CAD system, such as the dif®culty in slicing a number of STL models due to the limitations of computer memory. Ef®ciency may be obtained as a ratio of volume of the parts with the total volume of the workspace. However, as packing along the z-axis is in general not

S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

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Fig. 5. Comparison of total volume and volume in-use.

necessary, the volume in use should be considered instead of the total workspace volume. Fig. 5 illustrates the volume and the height of material deposition, and that of the workspace of the RP machine. The workspace volume occupied by a part may vary with its orientation. For example, the volume occupied by a rectangular box oriented at 458 is more than when it is oriented at 908 or 08 to its base. It is, therefore, necessary to construct a rectangular box around the part to yield a volume that will envelop the part for a given orientation. The resulting measure will indicate the maximum material utilised for the given orientation. This relative measure of orientation ef®ciency is given in Eq. (9). It presents the designer with the maximum material utilised for the part in the given orientation. This is different from other measures, which consider ef®ciency as the total workspace utilisation. Orientation ef®ciency signi®es the material utilised for a single part or for a number of parts nested or packed in the workspace volume. Hence, it provides a better estimation of material consumed and the cost involved to fabricate the part. P Np Vpi Orientation efficiency …n† ˆ iˆ1 (9) h m Aw 3. Implementation of the system A system that simulates the layer building process of a part to estimate the surface accuracy and buildtime has been developed. It reads a product model in STL format and adopts uniform slicing to process layers for simulation of the RP fabrication. Though

some new developments such as adaptive slicing and direct slicing have been reported, most RP machines still support only uniform slicing of STL ®les. The present system consists of the following modules, which include: (1) model display; (2) orientation and slicing; (3) layer processing; and (4) virtual fabrication. The system is developed on a Pentium II 400 MHz PC with Windows NT, WTK from Sense 8, Visual C‡‡ and interfaces with AutoCAD and Solidworks. To achieve cost and functionality trade-off, a semiimmersed VR system with CrystalEyes glasses and a Mitsubishi 2100 monitor are used. The CrystalEyes glasses ®lter the images on the monitor for the left and right eyes alternatively to provide the designer with stereoscopic views of the part. 3.1. Model display The model display module reads a product model represented in STL format and displays it in a virtual world. A STL format approximates the model with triangles, and each triangle consists of three vertices and a normal vector describing its orientation. The module reads in all the triangles of the model and constructs a bounding box of it. The bounding box is used for translation and scaling purposes to display the model in the middle of the virtual world. Interface utilities have been developed to facilitate the designer to view a model from different perspectives, and hence, analyse it by inspecting both the external geometry and the interior structure. For complex prototypes, it may be necessary to analyse the interior of the part for layout, visibility and accessibility.

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The designer can view and analyse the interior of the virtual prototype with a realistic feeling. Virtual models not only show the shape and the surface derived from the CAD data, but also offer some physical features, such as shinnies, (high-lights, colours, re¯ection) and contour changes for ¯exible parts. In the current system, a part can be displayed in wire-frame or rendered mode. Texture mapping further enhances realistic representation of the model, which is vital to aesthetic design of the product. Fig. 6A shows a bottle in rendered mode, while Fig. 6B displays it in stereoscopic mode. Upon activating the stereoscopic mode, the images generated from left and right eyes, respectively will be stretched towards each other and offset slightly. The CrystalEyes glasses close and occlude vision to left eye and the right eye alternatively. The brain fuses the two

images to create depth perception. This visualisation of a product model in a realistic display enhances the designer's imagination upon viewing and manipulation, which facilitates re®ning the design. 3.2. Orientation and slicing This module orients a part in STL format in a direction such that the desired requirements can be achieved. The optimal build-orientation is determined based on either the build-time or the surface accuracy criterion. The algorithm reads the STL part on a facetby-facet basis and determines the minimum and the maximum x-, y- and z-coordinates of the part. These minimum and maximum coordinates are used to build a bounding box around the part. In the present work, the part is sliced with a constant layer thickness, so the

Fig. 6. VR display of a bottle.

S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

minimum part height along the build-direction results in the minimum number of layers. As discussed in the build-time estimation, the orientation that results in the minimum number of layers will lead to the minimum build-time. The number of layers to be built is determined by dividing the part height along the builddirection by the layer thickness. To determine an optimal orientation for the minimum build-time, the algorithm ®rst rotates the part such that its height is the minimum possible, and the vertical axis is ®xed as the z-axis along the builddirection. Then, the algorithm rotates the parts about the x- and/or y-axis within a given range at a speci®c interval to determine the surface accuracy. Rotation of the part about the z-axis is not necessary, as it will not change the angle between the facet normal and the build-direction. For each orientation, the algorithm determines the cusp factor. The product of the cusp factor and the layer thickness gives the cusp height, and subsequently the average cusp and the maximum cusp heights are estimated. If the maximum cusp height exceeds the given value, that orientation is not considered. The orientation that gives the minimum average of these values is the preferred orientation of the part for the minimum build-time while achieving good surface accuracy. In addition to estimating the accuracy, the algorithm also estimates the build-time and ef®ciency for each rotation. On the other hand, if the maximum surface accuracy is the main criterion, the algorithm does not attempt to ®nd the minimum part height along the build-direction. Instead, it rotates the part about the three axes within a given range at a speci®c interval to determine the surface accuracy. However, in the case that the part geometry is relatively simple, such as the one that has square edges, rotation is not always required for the above calculations. The slicing algorithm slices a STL part into a number of layers of a uniform thickness speci®ed by the designer. It is indeed the kernel of an RP process. By determining the intersection points of the slicing plane and the facets, the contours of each layer is generated. All these layer contours are stored in a data ®le, which will be further processed to represent the virtual system. The layer thickness can be regarded as the resolution of an RP part, and may be varied to optimise its surface accuracy and build-time.

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3.3. Layer processing This module is used to process the layer data ®le generated by the slicing algorithm for display in the virtual system. A layer is formed by extrusion of the contour polygon. A contour ®le is an unordered list of contours. Any two contours selected at random within the layer may form the following combinations, namely (1) external-and-external, and (2) externaland-internal. In the external-and-external case, both contours are independent of each other, i.e. disjoint. The externaland-internal case occurs when a given contour is either contained or surrounded by the other one. The algorithm stores the internal and the external contours separately, by considering the arrangement of the contour points. External contours are clockwise, while internal contours are anti-clockwise. Each external contour is checked with all the internal contours to ®nd whether they are contained or disjoint. If they are contained, the points of an internal contour are inserted into the external contour to form a closed loop with imaginary lines linking various contours. The algorithm employs the forward-trace and backward-trace processes to rearrange the data and integrate the contours to form a single polygon. This new contour is again checked for the remaining internal contours to ®nd other internal contours. If no more internal contour remains, the process is repeated for the next external contour. After arranging the contours, the next step is to generate a layer. A layer is formed by the extrusion of the contours to the desired thickness. Each external contour with its internals is treated as a child node within the layer node. 3.4. Virtual fabrication This module simulates layer fabrication process in a VR environment. The designer can interactively view the building of a single layer or multiple layers. Once the simulation is completed, the designer can rotate the virtual part to view it or to map the surface texture to visualise the physical part that the RP machine will subsequently deliver. Visualisation, in general, is a method of extracting meaningful information from complex data sets through the use of interactive graphics and imaging. It facilitates seeing and navigating

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S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

through the unseen, thereby, enriching the existing scienti®c methods. It also provides a mechanism that facilitates exploring the internal and opaque structures of the part. Hence, the designer can conveniently move around the layers and analyse the stair-step effect. The algorithm calculates the average surface/contour deviation and the maximum surface deviation based on the cusp heights from Eqs. (2) and (3). Visual presentation of the part along with the numerical values of the surface accuracy gives the designer a better illustration of the stair-step effect. The average and the maximum surface deviations represent the mean and the largest surface inaccuracies of the part, respectively. If these values are desirable, the part may be fabricated. Otherwise, it is simulated again with a different layer thickness. Fig. 7 demonstrates the RP layer building process. Fig. 7A shows a virtually fabricated human face, and Fig. 7B a spider. The designer can feel the difference between the intended

part and the stepped approximation after visualising the ®nal product in the virtual system. The designer can, thus, make qualitative judgement about the product by manipulating the prototype and viewing its geometric changes. Virtually fabricating the part helps avoid manufacturing bottlenecks and facilitates tuning the control parameters for physical fabrication. This reduces the manufacturing costs and the development time involved. It increases the designer's responsiveness, i.e. the ability to respond to customer demands is signi®cantly enhanced. 4. Case studyÐfabrication simulation of a part To demonstrate the application of the system, fabrication of a turbine fan on a Sinterstation 2000 SLS machine with nylon was simulated, and the result is

Fig. 7. Two virtually fabricated parts.

S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

51

Fig. 8. A virtually fabricated turbine fan.

shown in Fig. 8. The laser diameter was 0.04 mm, while the hatch space and the layer thickness were both set as 0.1 mm. The turbine fan has different features like a hollow cylinder and several freeform surfaces around it. Depending on the distribution of the facets, the surface accuracy, build-time and ef®ciency could be different for different orientations.

Tables 1 and 2 indicate the surface accuracy, buildtime, orientation ef®ciency and the number of layers when the part was rotated about the x- and y-axes, respectively. The surface accuracy was mainly dependent on the cosine of the angle between the facet normal and the build-direction. Thus, it was only necessary to rotate the part between 0 and 908. The

Table 1 Simulation results of the turbine fan at various orientations about the x-axis Orientation (8) 0

10

20

Layer thickness (`) ˆ 0.1 mm, hatch space (dh) ˆ 0.1 mm Number of layers (N` ) 127 186 240 Surface accuracy, ACH (mm) 0.033 0.042 0.044 Build-time (h) 0.71 0.98 1.21 Efficiency, Z (%) 1 1 1.5

30

40

50

60

70

80

90

287 0.047 1.34 2

325 0.049 1.57 2

354 0.051 1.69 2

371 0.052 1.76 2

377 0.052 1.78 1.5

372 0.051 1.76 1

365 0.050 1.74 1

30

40

50

60

70

80

90

287 0.047 1.34 2

325 0.049 1.57 2

354 0.050 1.69 2

371 0.050 1.76 2

377 0.051 1.78 1.5

372 0.050 1.76 1

365 0.049 1.74 1

Table 2 Simulation results of the turbine fan at various orientations about the y-axis Orientation (8) 0

10

20

Layer thickness (`) ˆ 0.1 mm, hatch space (dh) ˆ 0.1 mm 127 186 240 Number of layers (N` ) Surface accuracy, ACH (mm) 0.033 0.042 0.044 Build-time (h) 0.71 0.98 1.21 Efficiency, Z (%) 1 1 1.5

52

S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

Table 3 The results when the layer thickness and hatch space were varied

Layer thickness (`) ˆ 0.15 mm, hatch space (dh) ˆ 0.1 mm Layer thickness (`) ˆ 0.1 mm, hatch space (dh) ˆ 0.2 mm

part at orientation of 08 gave the minimum build-time of 0.71 h and the surface accuracy of 0.033 mm. The possibilities of reducing the build-time while achieving the best surface accuracy possible at this orientation were, thus, further considered. Simulations were also performed to reduce the build-time by increasing the layer thickness to 0.15 mm and the hatch space to 0.2 mm while keeping all the other values constant. The simulation results are shown in Table 3. It was observed that a change in the layer thickness had no effect on the ef®ciency. The surface accuracy changed from 0.033 to 0.049 mm. However, the buildtime was reduced from 0.71 to 0.51 h. It is as expected, since the number of layers was also reduced from 127 to 84. Despite the fact that the scan distance per layer was not changed, the total laser scan time was reduced, because the number of layers scanned was reduced. A change in the hatch space did not affect the surface accuracy and ef®ciency. However, it is evident that an increase in the hatch space reduces the total scan distance, and hence, the build-time. It was demonstrated the build-time was reduced from 0.71 to 0.60 h, when the hatch space was increased from 0.1 to 0.2 mm. 5. Limitations and further development A limitation of the present system is that there is a decrease in the speed when it processes layer contours for simulation of relatively large and complex models. To improve this, effort is now devoted to developing a methodology to simplify the contour hierarchy of complex layers. Another possible improvement of the system is the incorporation of shrinkage and warpage effects to enhance accuracy estimation. Effort is now focused on the development of a dexel-based RP modelling technique. A dexel may be regarded as a solid strip of a ®nite size. Subsequently, a dexel-based virtual proto-

Number of layers (N` )

Surface accuracy, ACH (mm)

Build-time (h)

Efficiency, Z (%)

84 127

0.0495 0.033

0.51 0.60

1 1

type has similar geometric characteristics to its physical prototype. Such a virtual prototype may, thus, provide a convenient vehicle to model the energy density and the binding force distribution based on the heat dissipation of individual dexels, which facilitate subsequent prediction of shrinkage and warpage. By predicting these effects, it would be possible to modify the model design to compensate for the dimensional changes. Consequently, fabrication of high precision prototypes would become possible. 6. Conclusions This paper proposes a virtual system to aid a designer to select process parameters for RP. The system adopts surface accuracy, build-time and orientation ef®ciency as the key manufacturing requirements. Part orientation, layer thickness and hatch space were identi®ed as the key control parameters that in¯uence the requirements signi®cantly. A mathematical model was developed to relate the requirements with key control parameters. Preliminary implementation of the system has been completed. The system facilitates evaluation of surface accuracy and build-time. It also provides utilities for the designer to visualise and analyse the surface accuracy to perform a number of trials with the control parameters for a given part. The virtually fabricated parts may be made available in VRML format for effective communication via Internet between the designer and the customers. Acknowledgements The authors would like to thank the Research Grants Council of the Hong Kong SAR Government and the CRCG of the University of Hong Kong for their ®nancial support for this project. Thanks are also

S.H. Choi, S. Samavedam / Computers in Industry 47 (2002) 39±53

due to Dr. I. Gibson and his colleagues for providing access to the Sinterstation 2000 SLS machine. References [1] T. Wholers, Rapid Prototyping State of The IndustryÐ1999 World Wide Progress Report, RPA-SME Publication, 1999. [2] D.L. Bourell, J.J Beaman, H.L. Marcus, J.W. Barlow, Solid freeform fabrication: an advanced manufacturing approach, in: Proceedings of the SFF Symposium, 1990, pp. 1±7. [3] S.L. Springer, R. Gadh, State of the art Virtual Reality hardware for computer-aided design, Journal of Manufacturing Systems 7 (1996) 457±465. [4] S. Resseler, Applying Virtual Environments to Manufacturing, NISTIR, p. 5343. [5] F. Dai, M. Gobel, Virtual PrototypingÐan approach using VR techniques, Computer in Engineering 1 (1994) 311±316. [6] I. Gibson, D. Brown, S. Cobb, R. Eastgate, Virtual Reality and Rapid Prototyping, in: Proceedings of IEE workshop on Virtual Reality in Engineering (1993) 51±63. [7] G.M. Fadel, D. Crane, L. Dooley, R. Geist, Support structure visualisation in a Virtual Reality environment, in: Proceedings of the Sixth International Conference on Rapid Prototyping, Dayton, 1995. [8] S.M. Morvan, G.M. Fadel, IVCES: interactively correcting STL ®les in a virtual environment, in: Proceedings of the 1996 ASME Design Engineering Technical Conference, 1996. [9] A.S. Diane, K.-R. Chu, D.C. Montgomery, Optimising Stereolithography throughput, Journal of Manufacturing Systems 16 (4) (1997) 290±303. [10] J.G. Zhou, D. Hersovici, Parameter tuning and optimisation for SLA Rapid Prototyping manufacturing processes, in: Proceedings of the International Conference on Manufacturing Automation (ICMA'97), Vol. 2, 1997, pp. 894±902. [11] D.C. Thomson, R.H. Crawford, Optimising part quality with orientation, in: Proceedings of the Solid Freeform Fabrication Symposium, 1995, pp. 362±368. [12] D.C. Thomson, R.H. Crawford, Computational quality measures for evaluation of part orientation in freeform fabrication, Journal of Manufacturing Systems 16 (4) (1997) 273±289.

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[13] J.R. Woodzaik, G.M. Fadel, C. Kirschman, A genetic algorithm for optimising multiple part placement to reduce build-time, in: Proceedings of the Fifth International Conference on Rapid Prototyping, 1994. [14] A.L. Marsan, S. Allen, P. Kulkarni, D. Dutta, An integrated software system for process planning for layered manufacturing, in: Proceedings of the Solid Freeform Fabrication Symposium, 1997, pp. 661±668. [15] M. Ablani, A. Bagchi, Quanti®cation of errors in Rapid Prototyping processes, and determination of preferred orientation of parts, Transactions of the North American Manufacturing Research Institution of SME, Vol. XXIII, 1995, pp. 319±324. [16] Build-time Estimator Program, STLTime, Clemson University, Clemson, 1994. [17] T. Kamesh, D. Flyn, Build-time Estimator for Stereolithography MachinesÐA Preliminary Report, Prototype Express. [18] C.C. Chen, P.A. Sullivan, Predicting total build-time and the resultant cure depth of the 3D Stereolithography process, Rapid Prototyping Journal 2 (4) (1996) 27±40. [19] W.M. Steen, 1998, Laser Material Processing, Springer, Berlin. S.H. Choi is associate professor in the IMSE Department at the University of Hong Kong. He obtained both his BSc and PhD degrees at the University of Birmingham. He worked in computer industry as CADCAM consultant before joining the University of Hong Kong. His current research interests include CADCAM, advanced manufacturing systems and VP technology.

S. Samavedam got his degree in mechanical engineering from the Nagarjuna University, India, in 1994. He is now a research student in the IMSE Department at the University of Hong Kong, and his research interest is in the development of VR for RP.