Statistical modelling and optimization of surface

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Statistical modelling and optimization of surface roughness in the selective laser sintering process P B Bacchewar, S K Singhal, and P M Pandey* Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, India The manuscript was received on 13 June 2006 and was accepted after revision for publication on 2 October 2006. DOI: 10.1243/09544054JEM670

Abstract: Selective laser sintering (SLS) is a layered manufacturing process that builds prototypes by selective sintering of materials in powder form, like thermoplastic polymer powder (Polyamide 2200), using a CO2 laser. Prototypes made by SLS are widely used in product development as they can be used for product testing. SLS prototypes, therefore, should have a very good surface finish for functional performance as well as aesthetics. However, prototypes made by the SLS process have comparatively high surface roughness due to the stair stepping effect. Surface roughness of the prototypes also depends on the various process parameters. This paper attempts to study the effect of process parameters, namely build orientation, laser power, layer thickness, beam speed, and hatch spacing, on surface roughness. Central rotatable composite design (CCD) of experiments was used to plan the experiments. Analysis of variance (ANOVA) was used to study the significance of process variables on surface roughness. In the case of upward-facing surfaces, build orientation and layer thickness have been found to be significant parameters. In downwardfacing surfaces, other than build orientation and layer thickness, laser power has also been found to be significant. Empirical models have been developed for estimating the surface roughness of the parts. A trust-region-based optimization method (standard module of MATLAB) has been employed to obtain a set of process parameters for obtaining the best surface finish. A confirmation experiment has been carried out at an optimum set of parameters and predicted results were found to be in good agreement with experimental findings. A case study of a standard part ‘Truncheon’ is also presented. Keywords:

1

selective laser sintering (SLS), surface roughness, CCD, ANOVA

INTRODUCTION

Diverse customer needs have resulted in a tremendous reduction in the life cycle of a product. For the development of new products, time reduction has become a significant issue. The application of rapid prototyping (RP) technology has greatly reduced design manufacturing cycle time and, hence, reduced the cost of the product in global competition [1]. RP is a layer-by-layer material additive process capable of producing complex objects directly from the computer-aided design (CAD) model. Stereolithography (SLA), laminated object manufacturing (LOM), fused deposition modelling *Corresponding author: Department of Mechanical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India. email: [email protected]

JEM670 IMechE 2007

(FDM), and selective laser sintering (SLS) are the popular RP systems commercially available today. SLS is one of the most rapidly growing RP processes, mainly due to its ability to process various materials, such as polymers, metals, ceramics, and composites. Commercial SLS systems (EOS P 380) build parts through the selective solidification of thermoplastic polymer powder by a CO2 laser. First, a tessellated CAD model is sliced with layer thicknesses ranging from 0.1 to 0.3 mm. Powder is spread on the machine bed with the help of a re-coater. The powder is preheated to about 4–5 C below its melting point to keep the amount of energy contributed by laser as low as possible. This is done by means of four heat radiators present in the build chamber. The laser sinters powder and leads to a local solidification of the material. In the sintering process, the temperature of the powder is raised to

Proc. IMechE Vol. 221 Part B: J. Engineering Manufacture

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P B Bacchewar, S K Singhal and P M Pandey

a point of fusion without actual melting. After allowing sufficient time for the sintered layer to cool down without causing significant internal stresses, the part bed moves down by one layer thickness and powder is again spread by a re-coater. The sintered material forms the part while the un-sintered powder remains in its place to support the structure and is cleaned away once the build is complete. RP models are no longer used only for the design verification. Currently, prototypes built utilizing layer manufacturing technology can be employed as functional prototypes and as patterns or tools for different manufacturing processes, such as vacuum casting, investment casting, injection moulding, die casting, and sand casting. Therefore, the surface finish of the part should be good enough to ensure the functional requirements. However, layer-by-layer deposition in SLS leads to a staircase effect on the part’s surface and detracts from the part’s surface finish, similar to other RP processes like FDM [2]. Due to non-availability of the information related to surface roughness as a function of process parameters, the designers use their intuition based on experience to orient the part during deposition to control the surface roughness at critical locations. Several attempts have been made to model the surface roughness of RP parts. Tumer et al. [1] showed experimentally that layer thickness and part orientation affect the surface quality of the SLS parts. Parameters varied in their experiments were laser power, layer thickness, and build orientation. For the purpose of determining the effect of the process parameters on the surface finish, a factorial experimental design was used. An empirical model was developed by regression to predict the root mean square surface roughness. Reeves and Cobb [3] presented a mathematical model to predict the surface roughness of stereolithography parts in terms of layer thickness, surface angle, and layer profile. They proposed two different expressions to predict surface roughness of upwardand downward-facing surfaces. For downwardfacing surfaces, an effect known as print through helps in improving the surface finish. Onuh and Hon [4] found the effect of layer thickness, hatch style, hatch spacing, and hatch over cure on the surface finish by using Taguchi method for stereolithography. Based on their studies, two new hatch styles were proposed for improving overall surface finish. Perez et al. [5, 6] developed an analytical model to predict the surface roughness of stereolithography parts assuming the edge profile as filleted. They reported that the theoretical model agrees well in the case of stereolithography. However, the model needs correction when slopes are close to 0 and 90 . They also explored the possibilities of


manufacturing stereolithography parts with constant slice thickness, or with surface roughness confined within given values of surface roughness with variable layer thickness. Kattethota and Anderson [7] studied the surface roughness of FDM parts considering layer thickness, part orientation, layer edge profile, layer composition, and sub-parameters composition as parameters. They developed software based on collected data for surface roughness to determine a composite set of good orientation and layer thickness. Vasudevarao et al. [8] presented an experimental design technique for determining the optimal surface finish of a part built in FDM. They carried out fractional factorial design of experiments considering build orientation, layer thickness, road width, air gap, and model temperature as the parameters. They concluded that layer thickness and part orientation are the significant factors in determining the surface quality of the part. Model temperature, air gap, and road width did not have a significant influence on the surface finish of the part. Anitha et al. [9] used the Taguchi method to understand the influence of the process parameters on the surface roughness of FDM prototypes. Layer thickness, road width, and speed of deposition were considered as process parameters in their work. They reported that all three parameters affect the surface roughness of FDM parts significantly. Pandey et al. [2] proposed a stochastic model to predict surface roughness of FDM parts. They considered layer thickness and build orientation as the two most significant process variables. Parts with different build orientation were fabricated on FDM1650 to study the surface roughness characteristics. They measured surface profiles of the different faces using Surf Analyzer 5000. Based on the actual surface profiles, they proposed the surface roughness model. Campbell et al. [10] presented a computer-graphics-based visualization system for the surface roughness of RP parts (SL 250, Actua 2100, FDM 1650, LOM 1015, and Z 402). A part named ‘Truncheon’ was fabricated using different RP processes with constant slice thickness. Surface roughness values were measured using a contact Talysurf system. Experimentally obtained surface roughness values were used to generate the graphical output. It is evident from the literature review that most of the previous work is concentrated towards FDM and stereolithography. A surface roughness model for SLS with polyamide as a material has not yet been reported in the literature to the best of authors’ knowledge. In SLS, there are many input parameters that can be changed to get the desired surface quality of the parts. Some of these input variables are laser power, beam speed, build orientation, hatch


JEM670 IMechE 2007

Surface roughness in the selective laser sintering process

spacing, part bed temperature, layer thickness, scan length, etc. Laser power determines the severity of the temperature gradient and due to this temperature rise sintering of the powder takes place. Hence, the level of power has a significant effect on the surface quality. Beam speed also decides the amount of energy input during the sintering and hence contributes towards the surface quality of the part. Orientation and layer thickness cause stair stepping in SLS parts, which leads to bad surface finish. Hatch spacing was also found to affect the surface roughness of the SLS prototypes [11]. Therefore, this present work aimed to find out the effect of parameters, namely, laser power, beam speed, hatch spacing, build orientation, and layer thickness, on surface roughness. Experiments were planned using the central rotatable composite design (CCD) of experiments. Typical parts were built in various orientations to correspond to the experimental factors and levels using the EOS P 380 workstation at IIT Delhi. Surface roughness measurements were done using a Form Talysurf instrument. The surface roughness of upward- and downward-facing surfaces was considered to be the response for two analyses. Analysis of variance (ANOVA) was used to analyse the main effects and to obtain the significant parameters. Two different second-order empirical models were developed for predicting the surface roughness of ‘upward’- and ‘downward’-facing surfaces. Optimum process parameters were obtained by using trust-region-based optimization methods utilizing the MATLAB 7 optimization toolbox. Parts were fabricated with the optimum parameters and it was found that the predicted surface roughness values were in good agreement with the experimental results. A case study of a typical part, called ‘Truncheon’, is also presented. 2

RESPONSE SURFACE METHODOLOGY

A well-designed experiment can substantially reduce the number of trials. In classical methods of experimental planning (factorial designs, fraction factorial designs, etc.), a large number of experiments have to be carried out as the number of the process parameters increases, which is difficult and time consuming and also results in higher cost as is the case with RP. In order to determine the equations of the response surface, several experimental designs exist that approximate the equation using the smallest number of experiments possible. The most preferred classes of design are the orthogonal firstorder design and the central composite secondorder design. The first-order model is acceptable over a narrow range of variables; therefore, the experiments are conducted to obtain the second-order

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model. The expression for the second order central composite design is given by [12] Y ¼ b0 þ

k X

bi xi þ

i¼1

k X

bii xi2 þ

XX

bij xi xj þ "

ð1Þ

i F 0.01, 3, 28 Model is adequate and lack of fit is insignificant

Radown ¼ 168:08 10:2891X1 0:0223X2 0:8642X3 þ 0:399X4 þ 1152X5 þ 0:1437X12 0:0000014621X22 0:001093X32 0:002294X42 8826:7X52 þ 0:0002X1 X2 0:005X1 X3 0:0021X1 X4 þ 29:2596X1 X5 þ 0:000019X2 X3 þ 0:00016X2 X4 0:084X2 X5 þ 0:0058X3 X4 þ 3:73X3 X5 7:65X4 X5

ð6Þ

ANOVA for the above-mentioned model is presented in Table 6. The F-value of the model shows that the model is adequate at a 99 per cent confidence level. Although the model is adequate, it has many terms and can be simplified by eliminating the terms that are less significant based on the F-values presented in Fig. 7. Terms with F-values less than 4.5 are eliminated from the



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Fig. 5 Response surface for the surface roughness (upward-facing surfaces)

Fig. 6 Percentage contribution of the factors and interactions on the surface roughness (upward-facing surfaces) Table 6

ANOVA for developed response surface given by equation (6)

Source

DF

SS

Adj. SS

Adj. MS

F

Remark

Regression Linear Square Interactions

20 5 5 10

212.84 93.032 69.243 50.569

212.843 93.032 69.243 50.569

10.6422 18.6063 13.8485 5.0569

6.31

F

Residual error Lack-of-fit Pure error Total

11 6 5 31

18.541 15.493 3.048 231.385

18.541 15.493 3.048

1.6856 2.5821 0.6096

model. The modified surface roughness model is therefore given as follows. Radown ¼ 185 9:52X1 0:834X3 0:157X4 þ 0:15X12 0:00099X32 þ 0:0058X3 X4

ð7Þ


0.01, 20, 11

¼ 4.1

F > F 0.01, 20, 11 Model is adequate and lack of fit is insignificant

ANOVA of this response surface is presented in Table 7. It can be seen from Table 7 that this model is also adequate at 99 per cent confidence level. Plots of response surfaces for this model are presented in Fig. 8. Percentage contributions for


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Fig. 7 F-values (downward-facing surfaces). Table 7 ANOVA for developed response surface given by equation (7) Source Regression Linear Square Interactions Residual error Lack-of-fit Pure error Total

DF

SS

Adj. SS

Adj. MS

F

Remark

6 3 2 1

179.49 87.64 64.61 27.24

179.49 80.86 64.61 27.24

29.915 26.934 32.306 27.241

14.41

F

25 8 17 31

51.89 16.62 35.27 231.385

51.89 16.62 35.27

2.076 2.078 2.075

each term in the model are shown in Fig. 9. The figure clearly shows that laser power and build orientation are the two dominant parameters that affect surface roughness of downward faces. 4.3

Precision of the models

Due to experimental error, the estimated parameters and, hence, the estimated surface roughness are subject to uncertainty. The precision of surface roughness has been estimated by calculating the confidence interval. The confidence interval for the predicted response is Ra DRa, where DRa is given by pffiffiffiffiffiffi DRa ¼ ta=2;DF Ve

ð8Þ

Here, t is the value of the horizontal coordinate on t-distribution corresponding to specified degree of

JEM670 IMechE 2007

0.01, 6, 25

¼ 3.63

F > F 0.01, 6, 25 Model is adequate and lack of fit is insignificant

freedom (DF), a is the level of confidence interval, and Ve is the variance of error of the predicted response. DRa values for upward- and downward-facing surfaces are calculated using the values of error variance from Tables 5 and 7. The value of a is taken as 0.05. The values of DRa for upward- and downward-facing surface roughness models are calculated as 5.2 mm and 2.93 mm, respectively. 4.4

Effect of process parameters on surface roughness

Figure 10 shows that, in the case of upward-facing surfaces, laser power does not affect the surface finish. This may be due to the fact that the filleting effect, which is observed in case of downward-facing surfaces and is affected by laser power, is not



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Fig. 8 Response surfaces for the surface roughness (downward-facing surfaces)



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Fig. 9 Percentage contributions of factors and interactions on the surface roughness (downward-facing surfaces)

Fig. 10

Main effect plots

geometrically meaningful in the case of upwardfacing surfaces. Figure 11 shows that, with increase in laser power, there is improvement in surface finish initially, but after a certain value of laser power,

JEM670 IMechE 2007

surface finish deteriorates. This is due to the fact that, with an increase in laser power, the filleting effect increases initially, which leads to the improvement of surface finish. However, beyond a certain



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Fig. 11

Variation of surface roughness with laser power (downward-facing surfaces)

Fig. 12

Fig. 13

Filleting effect while sintering layers (downward-facing surfaces)

Variation of surface roughness with orientation at different layer thicknesses (downward-facing surfaces)

value of laser power, the penetration of laser increases and causes the surface finish to deteriorate, as shown in Fig. 12. A similar phenomenon has also been reported in the stereolithography process [3]. The main effect plots of Figs 10(a) and (b) show that beam speed does not affect surface roughness significantly. It can be seen from Fig. 10 that build orientation is the most significant factor that affects the surface finish in both upward- and downward-facing surfaces. Stair stepping effect is due to the build


orientation and is the main cause of poor surface finish [2, 5–8]. Figure 13 shows that, at higher build orientation, when layer thickness is small, better finish is obtained as compared to higher layer thickness. This can be explained with the help of Fig. 14. At small layer thicknesses, the filleting effect helps in the improvement of the surface finish; however, at higher layer thicknesses, this effect is not that dominant for constant energy density required for sintering. It can be seen from Fig. 15 that surface roughness increases with an increase in layer thickness


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Fig. 14

Fig. 15

Possible phenomenon of filleting for thin and thick layers with constant laser intensity at high build orientations

Variation of surface roughness with build orientation and layer thickness (upward-facing surfaces)

for the upward-facing surfaces. With an increase in layer thickness, the stair stepping effect increases, which deteriorates surface finish. However, in the case of downward-facing surfaces, as shown in Fig. 16, there is a decrease in surface roughness at smaller build orientations with the increase in layer thickness. This may be because, at higher layer thickness, penetration of laser is such that it tends to improve the surface finish by filleting, as shown in Fig. 17(a). However, for smaller layer thicknesses, penetration of laser of

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the same order of energy density may cause over-sintering and hence deteriorate surface finish (Fig. 17(b)). Another possible reason may be due to the movement of the stylus while carrying out surface roughness measurement for a given cutoff length. When the part is built with smaller layer thickness, more numbers of layer are measured and when the stylus crosses one layer to another, a jerk is recorded. This effect is less when the layer thickness is more. Therefore, a better surface finish is observed with thicker layers.



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Fig. 16

Variation of surface roughness with layer thicknesses at different build orientations (downward-facing surfaces) Subjected to 0 6 X3 6 90 150ðmmÞ 6 X4 6 190ðmmÞ

For downward-facing surfaces Minimize ðRadown Þ Subjected to 25ðW Þ 6 X1 6 37ðW Þ 0 6 X3 6 90 150ðmmÞ 6 X4 6 190ðmmÞ

Fig. 17

Possible phenomenon of filleting for thin and thick layers with constant laser intensity at low build orientations

It can be seen from the main effect plots (Fig. 10) that the hatch spacing does not influence the surface roughness to a great extent. This may be due to the fact that laser scanning takes place in the XY plane, while the surface roughness measurement is done on the external surface of the part. It is a general observation that average surface roughness on the downward-facing surface is lower than the average surface roughness on the upward-facing surfaces. This is mainly due to the filleting effect observed on downward-facing surfaces.

The trust region method for non-linear minimization is used to find the optimum levels of the parameters. The optimization tool box of MATLAB 7 is used for carrying out the optimization. Details of the trust region method are described below. 5.1

Trust region method for non-linear minimization

In the trust-region method [13], the objective function f (x) is approximated by a simpler function q(x), which reasonably reflects the behaviour of function f in a neighbourhood N around the point x. The function f (x) takes vector argument and returns scalar. This neighbourhood is known as the trust region. A trial step s is computed by minimizing q(s) (or approximately minimizing) over N. This is the trust region sub-problem and is mathematically given by minfqðsÞ; s 2 N g s

5

OPTIMIZATION OF SURFACE ROUGHNESS

Surface roughness can be minimized by setting process parameters at optimum levels. The problem of surface roughness minimization is formulated and is given below. For upward-facing surfaces Minimize ðRaup Þ


ð9Þ

The current point is updated to be x þ s if f (x þ s)