Chvorinov's rule
An empirical formula used to calculate the solidification time of cast metal. The rule states that t=B(V/A)ⁿ, where t is the solidification time, B is a constant whose value depends on the material properties of the cast metal, V is the volume of the cast, A is the surface area of the cast that contacts the mold, and n is a constant that is usually around 1.5 to 2.
Chvorinov's rule: solidification time from geometry
Chvorinov's rule is an empirical formula that predicts how long molten metal takes to solidify in a casting mold. The equation relates solidification time t to the geometry and thermal properties of the casting: t = B(V/A)n, where V is the casting volume, A is the surface area in contact with the mold, and B and n are material-dependent constants. The ratio V/A is called the modulus or thermal modulus; it expresses how thick or bulky the casting is relative to its cooling surface. A casting with high modulus cools slowly; one with low modulus cools fast.
The exponent n typically ranges from 1.5 to 2.0 depending on casting conditions and material system. Gray iron often follows n around 1.8, while steel and aluminum may differ slightly. The constant B reflects how readily heat flows from the metal into the mold and surrounding environment. It varies with mold material, metal temperature, casting size, and whether chills or exothermic sleeves are used. A mold made of dry silica sand gives a different B than a metal die or a bonded ceramic mold.
Foundry engineers use Chvorinov's rule during process planning to estimate whether gates, risers, and pouring temperatures will allow sound castings. A section that solidifies too quickly may have insufficient time for liquid metal to feed shrinkage in thick adjacent regions, causing porosity or cracks. Conversely, if a riser solidifies before the main body, it cannot function. By calculating moduli for different sections, designers can predict local solidification order and adjust riser placement, feeding distance, and thermal management accordingly.
The rule works best for simple geometries and steady-state cooling. Complex shapes with branches, thin sections, and unequal wall thickness introduce local thermal gradients that the simple modulus cannot capture. The formula also assumes the metal and mold reach quasi-equilibrium conditions; rapid cooling or high-velocity casting flows can invalidate the assumption. For precision predictions, computer simulation using finite-element or finite-difference methods has largely replaced hand calculation, but Chvorinov's rule remains the fastest tool for order-of-magnitude estimates and learning foundry principles.
The rule is named after Nikolai Chvorinov, a Soviet foundry researcher who published the relationship in the mid-twentieth century. Variants exist: some add a coefficient for mold permeability or use different exponents for specific alloy systems. In practice, foundries often calibrate B and n empirically by casting test blocks and measuring cooling curves, then apply those fitted values to production work.