Jewelry Casting Solidification Shrinkage
Computes the volumetric and linear dimensional contraction that occurs when molten precious metal solidifies inside a lost-wax investment mold.
\[ \Delta V_{shrink} = V_{liquid} \cdot \beta_{volumetric} + 3 \cdot \alpha_{linear} \cdot \Delta T \]
Plain Text Formula:
Delta_V = V_liquid * beta_volumetric + 3 * alpha_linear * Delta_T
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ \Delta V_{shrink} \] | Total Shrinkage | % volume | Net shrinkage percentage (typically 1.5% to 2.5% for gold/silver) |
| \[ \beta_{volumetric} \] | Liquid-to-Solid Phase Contraction | % | Volume drop during phase transition at melting point |
| \[ \alpha_{linear} \] | Coefficient of Thermal Expansion | 1/K | Solid state contraction coefficient during cooling to room temp |
| \[ \Delta T \] | Cooling Temperature Delta | °C | Temperature delta from solidus point to room temperature |
💡 Worked Engineering Example
Problem Statement:
Why must a jeweler enlarge a master wax model by 1.8% when casting sterling silver?
Step-by-Step Solution:
- Molten silver contracts ~1.2% during phase change
- Solid cooling from 890°C to 20°C produces additional ~0.6% contraction
- Total linear shrinkage = 1.8%
🎯 Result: Enlarging wax masters by 1.8% compensates for thermal contraction to maintain accurate ring sizing.