Solidification Volumetric Shrinkage
Calculate the volumetric shrinkage on solidification of a metal, ΔV = (ρ_solid − ρ_liquid) ÷ ρ_liquid × 100%, from the metal densities in the solid and liquid states. The result, in %, is the volume reduction that occurs when the metal goes from liquid to solid — because the solid is denser (more compact) than the liquid. This shrinkage is the main cause of shrinkage cavities (internal voids) and is exactly what risers must feed with extra molten metal. Each metal has its solidification shrinkage: steel ~3%, aluminum ~6.6%, copper ~5%. Gray cast iron is an exception (graphite expands, reducing the liquid shrinkage). Enter the solid and liquid metal densities.
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Solidification volumetric shrinkage
When a metal goes from the liquid state to the solid state, it shrinks — in most metals the ordered crystal structure of the solid packs the atoms more compactly (more densely) than the disordered arrangement of the melt. The solidification volumetric shrinkage measures that reduction: ΔV = (ρ_solid − ρ_liquid) ÷ ρ_liquid × 100%, computed from the densities of the metal in the two states. This shrinkage — distinct from liquid contraction (the melt cooling down before it freezes) and from solid contraction (the casting cooling to room temperature) — is the main culprit behind internal soundness defects in castings: as the metal freezes, metal 'goes missing', and if no extra liquid metal is fed in to make up that deficit, a shrinkage cavity (a pipe or void) forms, normally in the last region to solidify, the hot spot. It is exactly this shrinkage that risers (feeders) have to supply: the riser volume must be enough to replace all the solidification shrinkage of the casting (volume criterion), and the riser must freeze after the casting (modulus criterion). Typical figures vary a lot: steel ~3%, aluminium ~6.6% (high, demanding generous risers), copper ~5%, magnesium ~4%. Grey cast iron is the notable exception: while it freezes, the graphite that forms takes up more volume and expands, offsetting part of the contraction of the matrix — which is why grey iron needs far smaller risers, or none at all, one of the reasons behind its industrial success. Knowing the solidification shrinkage is essential to size riser volume and to anticipate the risk of shrinkage cavities. Enter the densities of the metal in the solid and liquid states.
Related Tools
Riser Modulus
Calculate the minimum modulus of a riser (feeder) by the modulus rule, M_riser = 1.2 × M_part, from the part's cooling modulus. The result, in cm, is the modulus the riser must have to solidify after the part (about 20% slower) and feed it with molten metal during solidification shrinkage, avoiding shrinkage cavities. The riser is a metal reservoir placed over the thickest region of the part; if it solidifies first, it fails its purpose. From the modulus, the riser geometry is sized. It is a fundamental rule of casting design. Enter the part's cooling modulus.
Casting Cooling Modulus
Calculate the cooling modulus (or geometric modulus) of a casting, M = V ÷ A, dividing the volume V by the surface area A in contact with the mold. The result, in cm (length unit), is the parameter governing solidification speed: the larger the modulus, the slower the solidification (Chvorinov's rule says the time is proportional to the modulus squared). It is the basis of riser sizing in foundry — the modulus rule requires the riser modulus to be about 1.2 times that of the part, so it solidifies later and feeds the shrinkage, avoiding shrinkage cavities. Enter the part volume and area.
Slurry Volumetric Concentration
Calculate the solids volumetric concentration in a slurry, C_v = (ρ_m − ρ_w) ÷ (ρ_s − ρ_w), from the mixture density ρ_m, the solids density ρ_s and the water density ρ_w (kg/m³). Volumetric concentration is the fraction of total slurry volume occupied by solids — the fundamental hydraulic-transport parameter. It is the inverse of the mixture-density calculation: in practice the slurry density in the pipe is measured (with a nuclear gauge, measuring gamma-ray attenuation through the pipe) and, knowing the water and solid densities, the solids concentration being transported is computed in real time. Volumetric concentration defines a dredge's or pipeline's PRODUCTION (solids volume transported = flow × C_v), and it is the parameter the operator seeks to MAXIMIZE (more solids per pumped water = more production and less energy per tonne) without exceeding the limits that cause clogging or excessive wear. Typical dredging volumetric concentrations are 10-30%; in optimized pipelines, up to 40-50%. Concentration control is the heart of hydraulic-transport operation. Enter the mixture density, the solids density and the water density.
Casting Metal Yield
Calculate the metal yield of a casting process, η = (part mass ÷ total poured mass) × 100%, dividing the finished part mass by the total poured metal (part + risers + runners + spills). The result, in %, measures the metal utilization efficiency: the rest (runners, risers, flash) is remelted, but consumes energy and adds cost. Typical yields range from 50 to 80%, depending on the part and gating complexity. Maximizing yield (well-sized risers, optimized gating) cuts energy and remelting costs. Enter the part mass and the total poured mass.
Shrinkage Allowance
Calculate the pattern (mold) dimension accounting for solidification shrinkage, dimension = part dimension × (1 + shrinkage ÷ 100), from the desired final part dimension and the metal's linear shrinkage coefficient (%). The result is the larger dimension the pattern must have so that, upon solidifying and cooling, the part shrinks to the correct size. Each metal has its linear solidification shrinkage: steel ~2%, gray cast iron ~1%, aluminum ~1.3%, bronze ~1.5%. Patternmakers use shrink rules ('contraction rules') already scaled up. Ignoring shrinkage results in undersized parts. Enter the part dimension and the shrinkage coefficient.
Solidification Time (Chvorinov)
Calculate the solidification time of a casting by Chvorinov's rule, t = B × (V ÷ A)², from the mold constant B (min/cm², depending on the mold material and metal) and the ratio of the part's volume V to its surface area A. The result, in minutes, is the time for the metal to fully solidify. The rule shows that parts with a higher volume/area ratio (more 'massive') solidify more slowly — a fundamental casting design principle: risers (metal reservoirs) must have a larger modulus than the part to solidify last and feed the shrinkage. Enter the mold constant, the volume and the part area.
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