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advances in numerical modeling of manufacturing processes

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RAJIV SHIVPURI : NUMERICAL MODELING OF MANUFACTURING PROCESSES<br />

Fig. 14: Porosity location <strong>in</strong> the vent region and its relationship to die configuration<br />

Fig. 15: Analysis <strong>of</strong> the pore composition us<strong>in</strong>g SEM: Note the presense <strong>of</strong> oxygen <strong>in</strong>side the pore (picture on the right)<br />

A Box-Behnken design array with 15 runs, <strong>in</strong>clusive<br />

<strong>of</strong> 3 center runs, was chosen for this three -level /<br />

three-factor study, Fig. 16. Simulations were<br />

performed <strong>in</strong> CastView for all the runs and the results<br />

were analyzed with a view for optimization the fill<strong>in</strong>g<br />

process. An appropriate response variable was chosen<br />

with the objective to obta<strong>in</strong> a proper fill <strong>in</strong> which the<br />

region closest to the vent fills last, and the adjo<strong>in</strong><strong>in</strong>g<br />

areas fill immediately before this region, and so on.<br />

A regression model was built with the results <strong>of</strong> the<br />

analysis. The regression model was maximized us<strong>in</strong>g<br />

Micros<strong>of</strong>t Excel® s<strong>of</strong>tware, <strong>in</strong> keep<strong>in</strong>g with the<br />

objective <strong>of</strong> maximiz<strong>in</strong>g the response (the regions<br />

near the vents should fill last). The regression equation<br />

is as follows,<br />

Response Variable = 2.37523 – 10.123372 A +<br />

0.000370338 B – 0.022142558 C + 32.057016 A2<br />

+ 0.00001824 B2 – 0.0002299 C2 –0.0131143 AB<br />

+ 0.030074282 AC + 0.000019886 BC<br />

Where A refers to the fill time (sec), B refers to the<br />

gate velocity (m/s),C refers to the flow angle (degrees)<br />

The range <strong>of</strong> variation used for the parameters was<br />

as def<strong>in</strong>ed <strong>in</strong> the design array. It was found that the<br />

optimum values for maximum response correspond<br />

to the maximum value <strong>of</strong> the gate velocity, m<strong>in</strong>imum<br />

value <strong>of</strong> the fill time and flow angle <strong>in</strong> the range <strong>of</strong><br />

variation. A runner was designed for the best design<br />

alternative us<strong>in</strong>g standard NADCA guidel<strong>in</strong>es.<br />

4.4 Comparison <strong>of</strong> the new design and exist<strong>in</strong>g<br />

design us<strong>in</strong>g FLOW3D<br />

A cavity fill<strong>in</strong>g simulation us<strong>in</strong>g the new gate design<br />

parameters was performed us<strong>in</strong>g the s<strong>of</strong>tware package<br />

Flow3D (a f<strong>in</strong>ite difference s<strong>of</strong>tware for fluid<br />

dynamics) and compared with simulations performed<br />

with exist<strong>in</strong>g gate designs 45 . For this simulation the<br />

best design alternative was chosen. Us<strong>in</strong>g design<br />

357

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