B. Pressure Casting
1. Results of the Statistical Experimental Design
Figures 29-31 show the comparison of the results obtained using 3-level full factorial and Box-Behnken as statistical experimental designs to determine the contribution of pressure and solids content to casting rate, cast hardness and water retention for MPP slip at 37°C. The results are quite similar.
Figure 29.Comparison of the results obtained using 3-level full factorial and Box- Behnken as statistical experimental designs to determine the impact of pressure and solids content on casting rate (mm·s-1/2) of MPP slip at 37°C.
Figure 30.Comparison of the results obtained using 3-level full factorial and Box- Behnken as statistical experimental designs to determine the impact of pressure and solids content on cast hardness (Shore A) of MPP slip at 37°C.
Figure 31.Comparison of the results obtained using 3-level full factorial and Box- Behnken as statistical experimental designs to determine the impact of pressure and solids content on water retention (%) of MPP slip at 37°C.
Figure 32 shows impact of the pressure and temperature on casting rate, cast hardness and water retention for MPP slip at 47 vol%. These results correspond to 3-level full factorial design. The trends indicate that temperature has a minor contribution on responses performance. The results are quite similar at 42 and 52 vol%.
Figures 33-35 show the comparison of the results obtained in MPP and CG slips at 37°C using Box-Behnken as statistical experimental design to determine the contribution of pressure and solids content to pressure casting. The results are quite similar in both slips.
As the pressure and solids content increase the casting rate and cast hardness increase due to the increasing packing of slip particles. The water retention level decreases as pressure and solids content increase. Higher solids content reduces water content in the cast cake.
Also, the higher pressure generates a higher water filtration rate through both the cast layer and the resin mold. Lower values of water retention lead to higher cast hardness and therefore better stiffness of the cast pieces.
Figure 32. Example of the impact of pressure and temperature on casting rate, cast hardness and water retention of MPP slip at 37°C. (A) Casting rate (mm·s-1/2); (B) Cast Hardness (Shore A); (C) Water retention (%).
Casting rate, cast hardness and water retention responses fit quadratic models for both slips (Table X). At the three evaluated temperatures, however, the results were similar for all responses (Results in Appendix E). These results indicate that heating the slips is likely unnecessary.
Table X lists the model constant and R2 value for casting rate, cast hardness and water retention equations obtained from the statistical experimental design for both slips.
The general form of the quadratic equation for casting rate, cast hardness and water retention level as follows:
Response = A + B(SC) + C(T) + D(P) + E(SC·T) + F(SC·P) + G(T·P)
+ H(SC2) + I(T2) + J(P2) (9)
where SC: solids content (vol%), T: temperature (°C) and P: pressure (kPa).
Table X. Model Constants and R2 Value for Casting Pressure Responses Equations
MPP CG MPP CG MPP CG
Constant A 1.53 3.91 214 711 -27.2 -473
SC B -0.094 -0.20 -9.08 -22.7 3.04 21.4
T C 0.027 0.033 0.33 -7.72 -1.24 -1.58
P D 1.06 x 10-4 7.87 x 10-5 -0.020 -0.054 -2.89 x 10-3 0.090 SC·T E -1.78 x 10-17 4.29 x 10-18 1.60 x 10-3 0.075 -4.30 x 10-3 7.50 x 10-3 SC·P F 1.25 x 10-6 9.38 x 10-6 1.66 x 10-4 1.90 x 10-3 3.96 x 10-5 -1.86 x 10-3 T·P G -1.25 x 10-6 -5.0 x 10-6 1.45 x 10-4 -2.93 x 10-4 -5.83 x 10-5 -9.88 x 10-5 SC2 H 1.10 x 10-3 2.19 x 10-3 0.10 0.20 -0.03 -0.22
T2 I -3.01 x 10-4 -3.50 x 10-4 -0.010 0.051 0.02 0.02 P2 J 2.24 x 10-21 -1.02 x 10-7 1.02 x 10-5 -6.03 x 10-6 3.47 x 10-7 -1.54 x 10-6
0.99 0.96 0.92 0.96 0.72 0.61
Terms/Response Casting rate Cast hardness Water retention
R2
Figure 33.Comparison of the results obtained in MPP and CG slips at 37°C using Box-Behnken as statistical experimental design to determine the impact of pressure and solids content on casting rate (mm·s-1/2).
Figure 34. Comparison of the results obtained in MPP and CG slips at 37°C using Box-Behnken as statistical experimental design to determine the impact of pressure and solids content on cast hardness (Shore A).
Figure 35. Comparison of the results obtained in MPP and CG slips at 37°C using Box-Behnken as statistical experimental design to determine the impact of pressure and solids content on water retention (%).
The slips were heated using a water bath to 37, 42 and 47°C bracketing the common temperature range used industrially for sanitary ware. The pressures commonly used in sanitary ware facilities are in the range of 600-1000 kPa even though the casting machines
are designed to reach 1400 kPa; 400, 800 and 1200 kPa were the experimental pressures.
The casting time was fixed at 10.3 minutes. The measured responses were casting rate, cast hardness and water retention.
The impact of the apparent viscosity on casting rate, cast hardness and water retention level was determined by measuring the MPP and CG slips viscosity at 37, 42 and 47°C, as well as at room temperature (18°C). Casting rate, cast hardness and water retention level data were obtained by casting both slips at mentioned temperatures at 400, 800 and 1200 kPa of pressure.
An interesting observation arises from Figure 36 showing that, in general hardness increases as casting rate increases but cast hardness is not solely dependent on casting rate.
In addition, it is evident that at the same casting rate, a broad range of hardness values are measured.
Casting Rate (mm·s-1/2)
0.10 0.15 0.20 0.25 0.30 0.35 0.40
Hardness (Shore A)
0 2 4 6 8 10 12 14 16 18
MPP 400 kPa MPP 800 kPa MPP 1200 kPa CG 400 kPa CG 800 kPa CG 1200 kPa R2=0.69
Figure 36. Cast hardness as a function of casting rate for MPP and CG slips at 400, 800 and 1200 kPa of pressure casting.
The water retention level and pore volume correlate directly with either cast hardness or casting rate (Figures 37 and 38). Pore volume and water retention are directly connected. Equation (6) was used to calculate pore volume.
MPP scatter data in Figures 37 and 38 is broader than CG likely because of the broader range of solids content.
The general trends in Figure 37 indicate that as water retention and pore volume decrease as casting rate increases as expected. The general trends also indicate that casting rate increases with pressure.
Casting Rate (mm·s-1/2)
0.10 0.15 0.20 0.25 0.30 0.35 0.40
Water Retention (%)
18 20 22 24 26 28
M PP 400 kPa M PP 800 kPa M PP 1200 kPa CG 400 kPa CG 800 kPa CG 1200 kPa
A.
Casting Rate (mm·s-1/2)
0.15 0.20 0.25 0.30 0.35
Pore Volume (%)
30 32 34 36 38 40
MPP 400 kPa MPP 800 kPa MPP 1200 kPa CG 400 kPa CG 800 kPa CG 1200 kPa
B.
Figure 37. (A) Water retention as a function of casting rate for MPP and CG and;
(B) pore volume as a function of casting rate. At 400, 800 and 1200 kPa of pressure casting for both slips.
The general trends in Figure 38 show that cast hardness reduces as water retention and pore volume reduce. The cast hardness of the cast piece is a subjective measurement since there are no established standards. The proposed value for cast hardness (10 Shore
A) is based on both the observations during the pressure casting tests in this work and the industrial experience of the author.
Water Retention (%)
18 20 22 24 26 28
Hardness (Shore A)
0 2 4 6 8 10 12 14 16 18
M PP 400 kPa M PP 800 kPa M PP 1200 kPa CG 400 kPa CG 800 kPa CG 1200 kPa
y = -2.04x + 49.5 R² = 0.17
y =-5.26x + 135.8 R² = 0.89 A.
Pore Volume (%)
32 34 36 38
Hardness (Shore A)
0 2 4 6 8 10 12 14 16 18
MPP 400 kPa MPP 800 kPa MPP 1200 kPa CG 400 kPa CG 800 kPa CG 1200 kPa B.
Figure 38. (A) Cast hardness as a function of water retention and; (B) Cast hardness as a function of pore volume. At 400, 800 and 1200 kPa of pressure casting for both slips.
The pressure casting results has shown that cast hardness and casting rate increase as pressure and solids content increase. It also has been shown that as pressure and solid content increase pore volume and water retention decrease. (as would be expected as cast hardness is function of particle packing). The result is an increasing in density when increasing pressure with a corresponding increasing in flow rate of fluid through the cast layer.
When pressure is applied through the liquid, as is the case with pressure casting, a hydrostatic pressure scenario is assumed as illustrated in Figure 39A. In this situation, there is no directional pressure applied to the system so there should be no increase in cast cake density with increasing pressure (An applied uniaxial pressure would crush the cast cake increasing the cake density as observed in previous work).13 The increase in cake density with increasing pressure and the corresponding increase in casting rate can only occur if there is an oriented force on the particle network that would facilitate particle rearrangement and packing efficiency. It is proposed that this force is the net force applied to the particles via fluid flow and drag on the particles in the network, as illustrated in Figure 39B. As the volumetric flow increases with increasing pressure, particles within the packed bed network experience a net directional force facilitating compaction. A higher flow rate (obtained by increased casting pressure) would result in a higher cake density.
The increase in cast cake density observed with higher solids loading would indicate a greater velocity of water through the cast layer creating a greater directional force on the particle network.
Figure 39. Schematic of (A) hydrostatic and (B) isostatic pressure on suspension particles.