Dimensionless Analysis for Investigating the Quality Characteristics of Aluminium Matrix Composites Prepared through Fused Deposition Modelling Assisted Investment Casting
Abstract
:1. Introduction
2. Materials and Methods
- The alternative feedstock filaments (FP) have been prepared using PA, Al2O3, and Al in different %wt. proportions with the help of single screw extrusion process.
- The formed filaments were used for the development of sacrificial patterns of cubical shape with three different volumes (VP), such as 17,576 mm3, 27,000 mm3, and 39,304 mm3. They were produced at low, high, and solid density of FDM process (DP) by using uPrint-SE system of Stratasys Inc. (Edina, MN, USA). In the works, reported previously, it has been seen that the change in the in-fill density affects the mechanical and tribological performances of the developed AMCs [1,2,3]. The prime reason behind the selection of FDM technology is due to its affordability and suitability for hybridization within the IC process [23,24,41]. Further, the selection of the process parametric levels from previous studies has been judicially selected, based on the pilot studies.
- Prior to shell moulding, the barrel finishing (BF) process was performed on the samples, for the refurbishment of resulted surface finish [31]. Here, barrel finishing time (BFT) and barrel finishing media weight (BFW) have been selected as input process parameters.
- Then, the IC moulds were prepared by coating the trees (consisting of riser, pouring basin, gating, and also the FDM printed sacrificial pattern) with refractory layers of silica. The number of IC slurry layers (NSL) has also varied in accordance to Table A1 in the Appendix A.
- Autoclaving and baking were performed in one step at 1150 °C (by maintaining the pouring sprue in a vertical up position so that the Al2O3 filler particles could be arrested within the cavity only). At this range of temperature, the matrix of the sacrificial patterns evaporates, immediately, without causing mould cracks.
- Finally, pouring of molten Al-6063 has been carried out.
3. Dimensionless modelling: Buckingham Pi Approach
- First of all, the units of the input and the output process parameters have been unified and converted into physical quantities (such as M, L, and T). Further, it is of utmost importance to highlight that any kind of categorical parameter, either input or output, is not suitable for the modelling. Moreover, upon such conversions, it should be considered that the replacement could be represented in-terms of M, L, and T formats. Therefore, in present work, the original Table A1 in the Appendix A has been modified in order to balance the units, as well as to convert the qualitative parameters into quantitative. For instance, the parameter “filament proportion” has been quantified in-terms of its tensile strength; density of the FDM pattern has been considered in terms of mass and volume; mould wall thickness has been converted from a number of layers to thickness of the wall, etc. Table 1 is the final prepared modified version of Table A1.The obtained dimensions of input and output parameters would be:Hardness (H) as ML−1T−2,Dimensional accuracy as L,Surface roughness as L,Filament proportion (P) in-terms of tensile strength of filament as MLT−2,Volume of FDM reinforced pattern (V) as L3,Density of FDM pattern (ρ) as ML−3,BF cycle time (t) as T,BF media weight (W) as M and the Number of IC slurry layers (l) resulting into mould wall thickness as L.
- Then, it is mandatory to find out the significance level of the input process parameters for the measured outcomes. In the present case, ANOVA has been implemented with the help of MINITAB-17 based statistical software in order to identify the significance and contribution of input parameters. Table 2 shows the contribution percentage of input process parameters for surface hardness, dimensional accuracy, and surface roughness.
- Before starting to formulate the π equations (let us say ‘x’), it is necessary to identify the ‘x − 1’ top performing input parameters. For instance, in the case of surface hardness, when ‘x’ is equal to 4 that allows to develop 4 π-equations, three top performing input parameters have to be identified.
- Now, the top performing input parameters and the output parameters being analyzed represent the π equations.
- After calculating the π equations, the π1 (related to the output parameter) is solved as a function of other πs (π2, π3, and π4, consisted of input parameters).
- Once the step-v is completed, a constant ‘K’ has been considered whose value has been driven from a second order quadratic equation of the fitness curve that connect the output response and the most contributing input parameter.
- Further, the fitness curve should be plotted between the measured output values and the corresponding values of the most significant input parameter, while keeping the rest of the parameters constant. Alternatively, in the present case, the plots have been drawn between the three levels of the input process parameters and the average of the corresponding output result. For instance, in case of Figure 4, the average of hardness for experiment #1, #4, #7, #10, #13, and #16 has been plotted against first level of FD (5.12 × 10−6 N/mm3) and the average of hardness for experiment #2, #5, #8, #11, #14, and #17 has been plotted against second level of FD (7.63 × 10−6 N/mm3). Similar procedure has been adopted for the third level of the FD.
- Noticeably, the regression (R2) ~ 1 indicates the best fitness of the data.
3.1. Hardness
3.2. Dimensional Accuracy
3.3. Surface Roughness
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Exp. No. | FP | VP (mm3) | DP | BFT | BFW | NSL | Ra (µm) | S/N ratio (dB) | Δd (mm) | S/N ratio (dB) | HV | S/N ratio (dB) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | C1 | 26 × 26 × 26 | Low density | 20 | 10 | 7 | 4.762 | −13.55 | 0.026 | 31.34 | 89.5 | 39.01 |
2 | C1 | 26 × 26 × 26 | High density | 40 | 15 | 8 | 5.151 | −14.27 | 0.03 | 29.45 | 91.8 | 39.18 |
3 | C1 | 26 × 26 × 26 | Solid | 60 | 20 | 9 | 4.778 | −13.58 | 0.02 | 33.30 | 115 | 41.18 |
4 | C1 | 30 × 30 × 30 | Low density | 20 | 15 | 8 | 4.371 | −12.82 | 0.06 | 23.37 | 80.3 | 38.06 |
5 | C1 | 30 × 30 × 30 | High density | 40 | 20 | 9 | 5.582 | −14.93 | 0.063 | 23.80 | 86.5 | 38.72 |
6 | C1 | 30 × 30 × 30 | Solid | 60 | 10 | 7 | 6.094 | −15.69 | 0.053 | 25.32 | 115 | 41.22 |
7 | C1 | 34 × 34 × 34 | Low density | 40 | 10 | 9 | 5.368 | −14.59 | 0.043 | 27.06 | 77.1 | 37.73 |
8 | C1 | 34 × 34 × 34 | High density | 60 | 15 | 7 | 5.658 | −15.05 | 0.08 | 21.89 | 91.9 | 39.25 |
9 | C1 | 34 × 34 × 34 | Solid | 20 | 20 | 8 | 6.404 | −16.13 | 0.016 | 35.22 | 100.4 | 39.92 |
10 | C2 | 26 × 26 × 26 | Low density | 60 | 20 | 8 | 4.709 | −13.45 | 0.016 | 35.22 | 93.4 | 39.38 |
11 | C2 | 26 × 26 × 26 | High density | 20 | 10 | 9 | 4.573 | −13.20 | 0.076 | 22.29 | 95.9 | 39.62 |
12 | C2 | 26 × 26 × 26 | Solid | 40 | 15 | 7 | 4.658 | −13.36 | 0.056 | 24.72 | 134.3 | 42.60 |
13 | C2 | 30 × 30 × 30 | Low density | 40 | 20 | 7 | 5.297 | −14.48 | 0.033 | 29.45 | 95.3 | 39.56 |
14 | C2 | 30 × 30 × 30 | High density | 60 | 10 | 8 | 5.889 | −15.40 | 0.050 | 25.90 | 93.8 | 39.41 |
15 | C2 | 30 × 30 × 30 | Solid | 20 | 15 | 9 | 6.845 | −16.70 | 0.060 | 24.35 | 104.5 | 40.37 |
16 | C2 | 34 × 34 × 34 | Low density | 60 | 15 | 9 | 8.564 | −18.65 | 0.033 | 29.20 | 84.1 | 38.29 |
17 | C2 | 34 × 34 × 34 | High density | 20 | 20 | 7 | 5.721 | −15.15 | 0.043 | 27.06 | 102.4 | 40.20 |
18 | C2 | 34 × 34 × 34 | Solid | 40 | 10 | 8 | 5.894 | −15.40 | 0.046 | 26.44 | 106.2 | 40.48 |
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Exp. No. | Tensile Strength, N/mm2 | Volume of Fused Deposition Modelling (FDM) Reinforced Pattern (mm3) | Density of FDM Pattern, N/mm3 | BF Cycle Time (sec) | BF Media Weight (N) | Mould Wall Thickness Obtained, mm | H, N/mm2 (Converted from HV with a Multiplying Factor of 9.807) | Δd, mm | Ra, mm (Converted from µm with a Dividing Factor of 0.001) |
---|---|---|---|---|---|---|---|---|---|
1 | 21.65 | 17576 | 5.12 × 10-6 | 1200 | 98 | 11.5 | 877.72 | 0.026 | 4762 |
2 | 21.65 | 17576 | 7.63 × 10−6 | 2400 | 147 | 13 | 900.28 | 0.033 | 5151 |
3 | 21.65 | 17576 | 9.16 × 10−6 | 3600 | 196 | 15 | 1127.80 | 0.02 | 4778 |
4 | 21.65 | 27000 | 5.12 × 10−6 | 1200 | 147 | 13 | 787.50 | 0.056 | 4371 |
5 | 21.65 | 27000 | 7.63 × 10−6 | 2400 | 196 | 15 | 848.30 | 0.063 | 5582 |
6 | 21.65 | 27000 | 9.16 × 10−6 | 3600 | 98 | 11.5 | 1127.80 | 0.053 | 6094 |
7 | 21.65 | 39304 | 5.12 × 10−6 | 2400 | 98 | 15 | 756.11 | 0.043 | 5368 |
8 | 21.65 | 39304 | 7.63 × 10−6 | 3600 | 147 | 11.5 | 901.26 | 0.08 | 5658 |
9 | 21.65 | 39304 | 9.16 × 10−6 | 1200 | 196 | 13 | 984.62 | 0.016 | 6404 |
10 | 21.53 | 17576 | 5.12 × 10−6 | 3600 | 196 | 13 | 915.97 | 0.016 | 4709 |
11 | 21.53 | 17576 | 7.63 × 10−6 | 1200 | 98 | 15 | 940.49 | 0.076 | 4573 |
12 | 21.53 | 17576 | 9.16 × 10−6 | 2400 | 147 | 11.5 | 1317.08 | 0.056 | 4658 |
13 | 21.53 | 27000 | 5.12 × 10−6 | 2400 | 196 | 11.5 | 934.60 | 0.033 | 5297 |
14 | 21.53 | 27000 | 7.63 × 10−6 | 3600 | 98 | 13 | 919.89 | 0.05 | 5889 |
15 | 21.53 | 27000 | 9.16 × 10−6 | 1200 | 147 | 15 | 1024.83 | 0.06 | 6845 |
16 | 21.53 | 39304 | 5.12 × 10−6 | 3600 | 147 | 15 | 824.76 | 0.033 | 8564 |
17 | 21.53 | 39304 | 7.63 × 10−6 | 1200 | 196 | 11.5 | 1004.23 | 0.043 | 5721 |
18 | 21.53 | 39304 | 9.16 × 10−6 | 2400 | 98 | 13 | 1041.50 | 0.046 | 5894 |
Source | Surface Hardness (H) | Dimensional Accuracy (Δd) | Surface Roughness (Ra) |
---|---|---|---|
FP | 7.69% | 0.76% | 4.16% |
VP | 8.85% | 16.95% | 43.84% * |
DP | 65.75% * | 19.83% | 3.03% |
BFT | 1.03% | 3.30% | 6.45% |
BFW | 0.8 % | 31.71% * | 2.94% |
NSL | 14.14% | 8.97% | 5.72% |
Residual Error | 1.74% | 18% | 33.86% |
Total | 100% | 100% | 100% |
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Singh, S.; Prakash, C.; Antil, P.; Singh, R.; Królczyk, G.; Pruncu, C.I. Dimensionless Analysis for Investigating the Quality Characteristics of Aluminium Matrix Composites Prepared through Fused Deposition Modelling Assisted Investment Casting. Materials 2019, 12, 1907. https://doi.org/10.3390/ma12121907
Singh S, Prakash C, Antil P, Singh R, Królczyk G, Pruncu CI. Dimensionless Analysis for Investigating the Quality Characteristics of Aluminium Matrix Composites Prepared through Fused Deposition Modelling Assisted Investment Casting. Materials. 2019; 12(12):1907. https://doi.org/10.3390/ma12121907
Chicago/Turabian StyleSingh, Sunpreet, Chander Prakash, Parvesh Antil, Rupinder Singh, Grzegorz Królczyk, and Catalin I. Pruncu. 2019. "Dimensionless Analysis for Investigating the Quality Characteristics of Aluminium Matrix Composites Prepared through Fused Deposition Modelling Assisted Investment Casting" Materials 12, no. 12: 1907. https://doi.org/10.3390/ma12121907
APA StyleSingh, S., Prakash, C., Antil, P., Singh, R., Królczyk, G., & Pruncu, C. I. (2019). Dimensionless Analysis for Investigating the Quality Characteristics of Aluminium Matrix Composites Prepared through Fused Deposition Modelling Assisted Investment Casting. Materials, 12(12), 1907. https://doi.org/10.3390/ma12121907