The Optimization of Surface Quality in Rapid Prototyping

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1 The Optimization of Surface Quality in Rapid Prototyping MIRCEA ANCĂU & CRISTIAN CAIZAR Department of Manufacturing Engineering Technical University of Cluj-Napoca B-dul Muncii , Cluj-Napoca ROMANIA Abstract: - Rapid Prototyping technologies are able of generating physical objects from CAD models. An important aspect of these technologies is the achieved surface quality of manufactured parts. The surface quality is strongly associated with the layered manufacturing. The surface roughness which depends by the staircase effect is a consequence of the layered manufacturing. The staircase effect vary according to the surface slope. This paper presents two different numerical methods to find out the optimal orientation of the 3D model on the working platform of the Rapid Prototyping system, so that the surface regions with higher staircase effect to be as small as possible. The first method, totally automated, find out the angles needed to rotate the 3D model around Ox and Oy axis, so that the number of the triangular facets of the 3D model in stl format, whose slope does not fulfil an initial condition, is minim. The second method involve the user intervention and is based on the visualization with a contrast colour of those triangular facets whose slope does not fulfil an initial condition. Both methods represent valuable tools in rapid prototyping processes. Key-Words: - Rapid Prototyping, Optimization, Surface Quality, Staircase Effect, Optimal Orientation 1 Introduction Rapid Prototyping (RP) technologies are able of generating physical objects from CAD models. A variety of rapid prototyping technologies have emerged including stereolithography, selective laser sintering (SLS), fused deposition manufacturing, laminated object manufacturing, 3D printing and solid ground curing (SGC). They have a common feature: the prototype is produced by adding materials, instead removing or deforming materials as in traditional manufacturing processes. In the optimization field of RP technologies, the researchers interest concentrates on few major directions such as: STL-based slicing algorithms, process parameters, modelling and simulation, part orientation, packing problem. Depending on the source data, there are two methods to slice the geometric model of a part into layers, i.e. the STLbased slicing and direct slicing based on different CAD systems with different data formats [7], [5], [4]. Compared with STL-based slicing, direct slicing avoid some approximation which exists in (STL) format file. Some researchers proposes a direct slicing method that can provide more exact laser beam paths by slicing a constructive solid geometry (CSG) representation of a part. A severe disadvantage of direct slicing is the capability among various CAD systems, in other words, it can only be used for a specific set of CAD software and machine, and is not applicable to any other CAD combinations [7]. As a matter of fact, STL-based slicing is still the commonly used method in processing the problem of layered manufacturing. The advantage of slicing a STL file is that the problem is reduced to finding plane intersections. The relationship between the main process factors and surface roughness distribution is analyzed theoretically by modelling the stair stepping effect, which results from stacking layers. Based on this investigation an optimum part orientation for fabrication is chosen [1]. While surface of stereolithography parts become rough due to the stair-stepping effect and burrs from the support structure, most parts need some finishing work for further applications. Because post-processing operations require additional time and cost, the reduction of post-processing time and cost by fabrication-direction optimization become an important concern [9]. Among the criterions taken into account by [8], it can be mentioned: minimum part height and the minimum value of the part dimensions ratio x/y (i.e. the part length considered into the direction of powder disposal on the platform must not overstep the part width). Referring only to selective laser sintering on Sinterstation 2000, [8] state that the first section of sinterized material must be less than a specific value denoted minimum specified area, in order to avoid to high values of part deformation. The problem of part orientation in the machine chamber is solved via an empiric ISBN: ISSN

2 algorithm so that the total volume occupied by multiple parts to be minimum and in the mean time the parts to be grouped as much as possible in the near centre of the work chamber. The concepts of orientation optimization are implemented and solved with a genetic algorithm. Concerning the process parameters some researchers frequently used a statistical analysis of the rapid prototyping processes, in order to find out the combination of parameters leading to the best accuracy of the manufactured parts [3]. So, it is possible to increase the accuracy of parts setting the part process parameters to specific values. [10] used the Taguchi method, as a powerful tool to design optimization for quality, to find the optimal process parameters for fused deposition modeling. As a powerful tool for process control, the modelling and simulation of RP is based on quantifying the part quality, which includes accuracy, build-time and efficiency with orientation, layer thickness and hatch distance etc. In order to estimate the build-time, a mathematical model has been developed for selective laser sintering process [6], integrated into a virtual reality system. In the study of [12], a simulated annealing algorithm was applied to find the optimal batch configuration layout for the minimum cost of production for solid ground curing processes. They take into account three kind of objectives: fitting models into the specified container, avoiding any overlap between models and achieving high packing density, in other words, achieving the minimum overall height. A detailed study of some important build parameters which affect the quality and accuracy of the final stereolithography parts, such as the layer thickness, resultant overcure, hatch space, blade gap, and part location can be found in [13]. Their investigation suggest the best setting of these control factors for different 20 individual feature. 2 The staircase errors When we build a part layer by layer, depending on the surfaces inclination to the layer plan, is appearing a staircase effect (see Fig.1). According to [11], the size of the staircase effect st err is depending on the layer thickness and the surface angle α. For a better definition of the manufacturing errors in the RP processes, we think that the error er n measured in normal direction to the surface is more eloquent for this case. Following the definition of [11], the staircase errors decrease in conjunction with the increasing of surface angle and takes higher values at smaller surface angle. The staircase error st err is increasing together with the layer thickness (see Fig.2). st err err n h Fig.1 The staircase effect. Fig.2 The influence of layer thickness upon the staircase error. According with the above definition of staircase error, all these statements are true. In spite of the fact that the staircase error st err is increasing when the surface angle α takes smaller values, it can be noticed that for smaller values for α, the differences between the designed surface of the model and the part surface are also insignificant. We can express the error in normal direction to surface by: er n = h (sinα + cosα 1); (1) where the meaning of the variables can be seen in Fig.1. The variation of the er n is depicted in Fig.3. According to this definition there is a similitude between st err and er n behaviour, because the error in normal direction to surface increases together with the layer thickness (see Fig.3.). However, er n is α ISBN: ISSN

3 higher at α = 45 o, and decrease significantly when α get closer at 0 o or 90 o h = 0.15 where θ 0, π/2 and π [2]. The surface roughness has higher values as the surface angle θ, measured from the vertical direction (the building direction), is small, and increases while the surface angle decreases (see Fig.5). er n [mm] h = 0.10 h = 0.05 R a (θ) O Surface angle [dgr] Fig. 3. The errors variation in normal direction to surface, according to surface angle and layer thickness. θ [dgr] Fig.5 The (R a - θ) dependance. 2.1 The surface roughness definition If we follow the roughness R a definition as a function of peaks to valleys size (see Fig.4), then we can use the equation: 3 The optimum part orientation The main objective of this research is to find the optimum 3D model orientation on the RP working platform so that the surface quality will result as good as possible. We will follow two possible approaches. The first one will establish the orientation in an automate manner, while the second approach will involve human-computer interaction. Fig.4 The surface roughness as a result of layered manufacturing. l 1 Ra = y( x) y l 0 c dx; The variation of the surface roughness R a according to the inclination angle of the triangle facet, can be expressed by the equation: 2 2 π ( R1 R2 ) 1 sin( θ ) lt 4 R cos( θ ) a = 4 lt 2 (3) 2 2 π ( R1 R2 ) tan( θ ) sin( θ ); 3 l t (2) 3.1 The automated part orientation The surface of the 3D model in stl format is approximated with small triangle facets. For each facet it is known the (x,y,z) coordinates of each vertex, and the projections on the axes of the normal unit vector to the triangle surface, pointing outside the model. The position of the normal vector remains unchanged relative to the triangle position. As a consequence, if we rotate the 3D model with an angle, this will involve the rotation of all normal vectors with the same angle. To test our concepts for optimum part orientation, whose algorithm is depicted in Fig.6, we consider as example the upper case of a mobile phone as you can see in Figure 7. The drawing position was taken as reference for further orientation, according to the surface quality criterion. In order to establish optimal part orientation on the working platform of the RP system, we will give an ISBN: ISSN

4 incremental rotation to the 3D model around Ox and Oy axis. alfay = 0.0; while (alfay pi) alfax = 0.0; while (alfax pi) Rotate normal vectors around Oy with the angle alfay n = 0; for i=0 to i < facetnumber Rotate normal vectors around Ox with the angle alfax Calculate the angle teta made by the normal vector with horizontal direction if (teta tetamin && teta tetamax) n++; if (n < nmin) nmin = n; alfaxmin = alfax; alfaymin = alfay; increase alfax with the increment; increase alfay with the increment; Fig.6 The algorithm for part rotation. number of triangular facets whose slope is between some initial established limits. Only those values which corresponds to a minimum number of facets which respects initial conditions, will be taken. Facet number Rotation angle around Oy [dgr] Fig.8 Optimal position of the 3D model (α x = 135 o, α y = 135 o, n min = 4958). So, for the model from Fig.7, the position which corresponds to the minimum number of triangular facets whose slope is included within the preestablished initial limits, according to the surface roughness variation from Fig.5, is α x = 135 o and α y = 135 o. According to the reference position of the model as in the Fig.7, for the numerical established position corresponds n min = 4958 (see Fig.8). The plot from the Fig.8 corresponds for an angle of 135 degrees around Ox axis. The rotation of the model around Ox and Oy axis was made with an angular increment of 3 degrees. Fig.7 The 3D model of mobile phone case. For each incremental position we will calculate the 3.2 The manual part orientation Some surfaces need a better roughness due to its functional task, while others need the same roughness values for aesthetic purpose. In every case the engineer have the mission to decide in this problem. Despite engineers experience, when the part has a complicated geometry, is difficult to appreciate which is the most appropriate orientation so that some surfaces will result with some prescribed roughness. We need an instrument to identify those triangular facets which have a specific slope, for a given orientation of the 3D model. That specific slope will produce a roughness above the input limits. This is why we made a program which shows the triangular facets with a specific slope in a different contrast colour than the other facets, so that these facets may be easy identified. Fig.9 shows the 3D model ISBN: ISSN

regions with a roughness due to the staircase effect, higher than that specified by the user. a) b) Fig.9. The front (a) and the back (b) of the mobile phone upper case.

Both faces of the 3D model have triangular facets with a slope which involve a roughness higher than that the admissible roughness.

on the back side of the model do not matter if we are interested only in the surface quality on the front surface. Fig.

5 regions with a roughness due to the staircase effect, higher than that specified by the user. a) b) Fig.9. The front (a) and the back (b) of the mobile phone upper case. With a contrast color are displayed the triangular facets whose slope coresponds to a higher staircase effect. Both faces of the 3D model have triangular facets with a slope which involve a roughness higher than that the admissible roughness. If there is an automate process which count the number of these facets, then will be taken into account all the facets which do not satisfy the criterion of slope value, even if the facets situated on the back side of the model do not matter if we are interested only in the surface quality on the front surface. Fig.10 shows the facets which do not satisfy the criterion of slope value, if the part orientation is made automatically. Fig.10 The 3D model with automated orientation. It can be simply seen that at an orientation of 135o rotation around Ox and also 135o around Oy, that even if the facet number which will result with a higher staircase effect is minimum, their placement is asymmetric. This situation will involve asymmetric surfaces which will require postprocessing, which may lead to geometric errors. This is why, a manual orientation of the part on the RP system working platform is almost always essential. 4 Conclusion There exists an interdependence between the surface roughness and the staircase effect in RP processes. The staircase effect greatly depends on the layer thickness. As a consequence, the decrease of the layer thickness will decrease the staircase effect and will improve the surface roughness. The decreasing of the layer thickness will lead implicitly at a considerably reduction of RP process productivity. The surface quality in RP processes depends on the 3D model orientation on the working platform. For different 3D model orientation on the working platform of the RP system, will result different surfaces quality. Also, the regions which will have a roughness higher than that imposed by the designer, have a variable size and location. As a consequence, to find out the optimal orientation of the 3D model on the working platform of the RP system, is a requirement. This paper presented two different alternatives to find out the optimal orientation of the 3D model on the working platform of the RP system. The first variant is an entirely computerized one. The method is base on the minimum number of the triangular facets whose slope accomplishes an initial condition. The main disadvantage of the automated method is the fact that it does not take into account that some surfaces are very important concerning the functional or aesthetic role, while other surfaces are not. The second variant proposed by this research require the manual part orientation by the designer. This is why a computer program which shows in a contrast colour those triangular facets whose slope angle fulfil an initial condition, was made. By rotation of the model around its horizontal axis, those regions of the surfaces which will result with a higher staircase effect, can be easy visualized. So the designer can easy decide which is the optimal orientation of the 3D model, while taking into consideration the importance of the surfaces by functional or aesthetic role. Both of the presented methods are useful in the RP processes. None of the methods does exclude each other. Contrary, the methods completes each other. ISBN: ISSN

6 Both methods represent important tools in the rapid prototyping and manufacturing processes. Future research will take into consideration the productivity of RP processes as a very important optimization criterion. References: [1] Ahn, D., Kim, H., Lee, S. Fabrication direction optimization to minimize post-machining in layered manufacturing. International Journal of Machine-Tools & Manufacture, Vol. 47, 2007, p [2] Byun, H.S., Lee, K.H. Determination of the optimal build direction for different rapid prototyping processes using multi-criterion decision making. Robotics and Computer- Integrated Manufacturing, Vol. 22, 2006, p [3] Campanelli, S.L. et al. Statistical analysis of the stereolithographic process to improve the accuracy. Computer-Aided Design, Vo.39, 2007, p [4] Cao, W., Myiamoto, Y. Direct slicing from AutoCAD solid models for rapid prototyping, Int. J. Adv. Manuf. Technol. Vol.21, 2003, p [5] Chang, C.C. Direct slicing and G-code contour for rapid prototyping machine of UV resin spray using PowerSOLUTION macro commands, Int. J. Adv.Manuf. Technol. Vol.23, 2004, p [6] Choi, S.H., Samavedam, S. Modelling and optimisation of Rapid Prototyping. Computers in Industry, Vol.47, 2002, p [7] Haipeng, P., Tianrui, Z. Generation and optimization of slice profile data in rapid prototyping and manufacturing. Journal of Materials Processing Technology, Vol , 2007, p [8] Hur, S.M., Choi, K.H., Lee, S.H., Chang, P.K. Determination of fabricating orientation and packing in SLS process. Journal of Materials Processing Technology, Vol.112, 2001, p [9] Kim, H.C., Lee, S.H. Reduction of postprocessing for stereolithography systems by fabrication-direction optimization. Computer- Aided Design, Vo.37, 2005, p [10] Lee, B.H., Abdullah, J., Khan, Z.A. Optimization of rapid prototyping parameters for production of flexible ABS object. Journal of Materials Processing Technology, Vol.169, 2005, p [11] Li, L. et al. Mathematical Modelling of Geometrical Error Transformation Process in Additive Rapid Prototyping/Manufacturing, Proceedings of the 7 th European Conference on Rapid Prototyping and Manufacturing, Aachen, 1998, pp [12] Zhang, X., Zhou, B., Zeng, Y., Gu, P. Model layout optimization for solid ground curing rapid prototyping processes. Robotics and Computer Integrated Manufacturing, Vol.18, 2002, p [13] Zhou, J.G., Herscovici, D., Chen, C.C. Parametric process optimization to improve the accuracy of rapid prototyped stereolithography parts. Int. J. Machine Tools & Manufacture, Vol.40, 2000, p ISBN: ISSN

THE EFFECTIVENESS OF MULTI-CRITERIA OPTIMIZATION IN RAPID PROTOTYPING

THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 15, Number 4/214, pp. 362 37 THE EFFECTIVENESS OF MULTI-CRITERIA OPTIMIZATION IN RAPID PROTOTYPING Mircea