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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Contração volumétrica de solidificação
Quando um metal passa do estado líquido para o sólido, ele encolhe — porque, na maioria dos metais, a estrutura cristalina ordenada do sólido empacota os átomos de forma mais compacta (mais densa) que o arranjo desordenado do líquido. A contração volumétrica de solidificação mede essa redução: ΔV = (ρ_sólido − ρ_líquido) ÷ ρ_líquido × 100%, calculada a partir das densidades do metal nos dois estados. Essa contração — distinta da contração líquida (do líquido esfriando) e da contração sólida (do sólido esfriando até a ambiente) — é a vilã principal da sanidade interna das peças fundidas: ao solidificar, o metal 'falta', e se não houver suprimento de metal líquido adicional para preencher esse déficit, forma-se um rechupe (uma cavidade de contração), geralmente na última região a solidificar (o ponto quente). É exatamente essa contração que os massalotes precisam alimentar: o volume do massalote deve ser suficiente para repor toda a contração de solidificação da peça (critério de volume), além de solidificar depois dela (critério de módulo). Os valores variam muito: aço ~3%, alumínio ~6,6% (alta, exigindo bons massalotes), cobre ~5%, magnésio ~4%. O ferro fundido cinzento é a notável exceção: durante a solidificação, a grafita que se forma tem volume maior e expande, compensando parte da contração da matriz — por isso o ferro cinzento precisa de massalotes muito menores (ou nenhum), uma das razões de seu sucesso industrial. Conhecer a contração de solidificação é essencial para dimensionar o volume dos massalotes e prever o risco de rechupes. Informe as densidades do metal sólido e líquido.
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.
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