SLS parameters optimization using the Taguchi method.

Berce, Petru ; Pacurar, Razvan ; Balc, Nicolae 等

1. INTRODUCTION

Taguchi approach uses three major steps namely, system design, parameters design and tolerance design for optimizing a process or product. In system design, scientific and engineering knowledge is applied to produce a basic functional prototype design. It contains selection of materials, components and production equipment, process parameter design, which is used to optimize the settings of process parameter values for improving quality characteristics (Pham et al., 1999). Final step of the optimization is tolerance design, used to determine and analyze tolerances around the optimal settings recommended by the parameter design (Bagchi, 1993).

Yang et al. propose compensation test pieces for the X, Y and Z axes to compensate the shape distortions caused by phase changes during the sintering process and the shrinkage rates have been measured experimentally. The scale factors obtained from the proposed building compensation test pieces of X, Y and Z axes satisfy the required dimensional accuracy, even if there are changes in the build positions and in the size of the SLS parts (Yang et al., 1998).

Figure 1 shows the simplified steps of applying the Taguchi method to the SLS process through the selection of the optimum scale factors and the build orientation. With this method it is possible to maintain the robustness to the noise factors generated by the temperature deviation in the build chamber (Yang et al., 2002).

[FIGURE 1 OMITTED]

N. Raghunath and Pulak M. Pandey propose in their paper an optimization method in order to find a relationship between the shrinkage and various process parameters of the SLS system. One case study is successfully presented to show the effectiveness of developed models for improving the accuracy of SLS plastic prototypes (Raghunath & Pandey, 2006).

The current paper presents a research developed at Technical University of Cluj-Napoca (TUCN) focused mainly on the manufacturing of the metallic parts from a dedicated material (Laserform St-100 powder) by using the Sinterstation 2000 equipment. Taguchi method has been applied successfully in this case in order to find the optimum manufacturing parameters for the SLS metal parts.

2. TAGUCHI METHOD APPLIED

Two test parts were proposed, as illustrated in Figure 2. Several pairs were manufactured on the SLS system and then measured by an optical Werth Video Check IP 250/400 machine (TUCN), on "green-stage" level and by Zeiss Eclipse CMM550 (TUCN) after the parts were post-processed in the oven. Each dimension is measured and compared to the designed one, in order to calculate the shrinkage percentage, using the following formula:

S = [L.sub.c] - [L.sub.m]/[L.sub.c] x 100 (1)

where S is the shrinkage (%), [L.sub.c] is the CAD dimension and [L.sub.m] is the measured one

[FIGURE 2 OMITTED]

In order to optimize the SLS manufacturing parameters Taguchi method has been applied. At the beginning, the most significant SLS parameters were chosen as presented in Table 1. There are so called levels of importance given for each parameter as could be observed in the same Table. In this case Level 1 is the most insignificant level and Level 5 is the maximum level.

For this experiment an L25 orthogonal array with 6 columns and 25 rows is used as presented in Table 2. To select an appropriate orthogonal array, total degrees of freedom need to be computed. The degrees of freedom are the number of comparisons to be made between designed parameters. Each parameter is assigned to each column of the orthogonal array, so 25-parameter combinations are available using [L.sub.25] array.

3. EXPERIMENTAL DATA ANALYSIS

Experimental data were analyzed using the S/N ratio by measuring the quality characteristics and meantime the deviation from the desired value. The term signal (S) represents the desirable value (mean) and the noise (N) represents the undesirable value (Standard Deviation from Mean--MSD). The S/N ratio (n) and the MSD can be defined as:

[eta] = -10 x log(MSD) (2)

MSD = 1/n [n.summation over (i=1)] [Y.sup.2.sub.i] (3)

where n is the total number of the experiments in the orthogonal array and Yi is the mean percentage shrinkage for the i-th experiment (measured dimension). S-N ratio for each dimension is calculated and presented in Table 3. The effect of a factor level is defined as the deviation it causes from the overall mean.

The overall mean S/N ratio can be calculated using the formula:

m = 1/n [n.summation over (i=1)] [[eta].sub.i] (4)

where [[eta].sub.i] is the mean S/N i-th experiment ratio.

All five levels of every factor are equally represented in 25 experiments. Thus, m is the mean of the entire experiments. Mean response is the average of quality characteristic for each parameter at different level. S/N ratio and shrinkage (%) for each parameter at each level can be calculated from mean S/N ratio and shrinkage (%) value of each of the experiment. For example, the mean percentage shrinkage for fill scanning speed at Level 1 can be calculated by averaging shrinkage (%) from the experiments 1, 7, 14, 18 and 25.

[FIGURE 3 OMITTED]

4. CONCLUSION

Further on, by following the same algorithm as presented above, the effect of process parameters in X, Y and Z direction is obtained as illustrated in Figure 3. Finally, the optimum SLS manufacturing parameters for minimum shrinkage were obtained, as the ones presented in Table 4.

5. REFERENCES

Bagchi, T. P. (1993). Taguchi Methods Explained, PrenticeHall, ISBN 0-87692-808-4, India.

Pham, D. T. et al., (1999). Selective laser sintering: applications and technological capabilities. Journal of Engineering Manufacture, Vol. 213, No. 5 (1999), 435-449, ISSN 0954-4054.

Raghunath, N. & Pandey, P. M., (2006). Improving accuracy through shrinkage modeling by using Taguchi method in selec t ive laser sintering. International Journal of Machine Tools and Manufacture, Vol. 47, No. 6 (2006), 985-995, ISSN 0890-6955.

Yang, H.-J. et al. (2002), A study on shrinkage compensation of the SLS process by using the Taguchi method. International Journal of Machine Tools and Manufacture, Vol. 42, No.11 (2002), 1203-1212, ISSN 0890-6955.

Yang, W. H. et al., (1998). Design optimization of cutting parameters for turning operations based on the Taguchi method. Journal of Materials Processing Technology, Vol. 84, No. 1 (1998), 122-129, ISSN 0924-0136.

Tab. 1 Parameters levels of importance

No Parameter Level 1 Level 2 Level 3

1 Fill laser power [W] 24 25 26
2 Fill scan speed [mm/s] 1200 1300 1400
3 Outline scan speed [mm/s] 50 100 200
4 Slicer fill scan spacing [mm] 0.074 0.076 0.078
5 Part bed temperature [[degrees]C] 90 92 94
6 Powder layer thickness [mm] 0.074 0.076 0.078

No Parameter Level 4 Level 5

1 Fill laser power [W] 27 28
2 Fill scan speed [mm/s] 1500 1600
3 Outline scan speed [mm/s] 300 400
4 Slicer fill scan spacing [mm] 0.08 0.082
5 Part bed temperature [[degrees]C] 96 98
6 Powder layer thickness [mm] 0.08 0.082

Tab. 2 Taguchi L25 orthogonal array

Exp
No Columns

 Factor 1 Factor 2 Factor 3

1 1 1 1
2 1 2 2
3 1 3 3
4 1 4 4
5 1 5 5
6 2 2 1
7 2 1 2
8 2 4 5
9 2 5 3
10 2 3 4
11 3 3 2
12 3 2 3
13 3 5 1
14 3 1 4
15 3 4 5
16 4 4 3
17 4 3 4
18 4 1 2
19 4 2 5
20 4 5 1
21 5 5 4
22 5 4 5
23 5 2 3
24 5 3 1
25 5 1 2

Exp
No Columns

 Factor 4 Factor 5 Factor 6

1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 3 4 5
7 4 5 3
8 2 3 1
9 1 2 4
10 5 1 2
11 4 5 1
12 5 1 4
13 3 4 2
14 2 3 5
15 1 2 3
16 5 1 2
17 1 2 5
18 4 5 3
19 3 4 1
20 2 3 4
21 1 2 3
22 2 3 1
23 5 1 4
24 4 5 2
25 3 4 5

Tab. 3. S-N ratio

 Measured dimensions

Ex
No X Y Z

1 5,07 5,06 25,18
2 15,13 15,10 20,20
... ... ... ...
25 45,07 45,01 4,99

Ex MSD
No X Y Z

1 0,068 0,044 0,009
2 0,023 0,011 0,023
... ... ... ...
25 0,001 1,21 1,01

Ex
No X Y Z

1 -8,336 6,515 0,279
2 -3,775 0,428 3,684
... ... ... ...
25 17,497 13,76 3,457
m 2,115 3,328 5,443

Tab. 4. Optimum parameters obtained for the SLS process

No. Parameter Measuring Value
 unit

1 Fill laser power W 28
2 Fill scan speed mm/s 1500
3 Outline scan speed mm/s 300
4 Slicer fill scan spacing mm 0.08
5 Part bed temperature [degrees]C 90
6 Powder layer thickness mm 0.08