Riser sizing for a gray-iron plate casting
A foundry pours a rectangular gray-iron plate 240 mm × 180 mm × 25 mm in a sand mould. The existing top riser is a plain cylinder 45 mm diameter and 67.5 mm high (H = 1.5D) with a short neck. Chvorinov's rule applies with solidification time t = k(V/A)^2, where V/A is the casting modulus. The riser must remain liquid at least 20% longer than the plate; the foundry uses a 1.2 factor on solidification time. After a batch showed shrinkage porosity near the plate centre, the pattern shop proposed simply increasing riser height to 90 mm while keeping D = 45 mm. The melting shop wants to know whether that is sufficient, and what riser size would be needed if the riser were redesigned with H = 1.5D. Pattern changes cost Rs 8,000, and the plate weighs 21 kg; riser metal is remelted with a 4% yield loss. The moulding box height limits the riser to 110 mm.
1. Compute the plate modulus and the existing riser modulus. Check whether the 1.2 solidification-time criterion is met.
Read the worked answer
Plate: V = 240×180×25 = 1,080,000 mm³. Cooling area A = 2(240×180 + 240×25 + 180×25) = 2(43,200 + 6,000 + 4,500) = 107,400 mm². Modulus M_plate = V/A = 10.06 mm.
Existing riser: D = 45 mm, H = 67.5 mm. V = πD²H/4 = π×45²×67.5/4 = 107,350 mm³. A = πD²/2 + πDH = 3,181 + 9,543 = 12,724 mm². M_riser = 107,350/12,724 = 8.44 mm.
Since t ∝ M², t_riser/t_plate = (8.44/10.06)² = 0.704. This is below 1.2, so the riser solidifies well before the plate. The shrinkage porosity is consistent with an undersized riser, not with a random moulding fault.
2. Check the proposed D = 45 mm, H = 90 mm riser. Then find the required diameter if H = 1.5D.
Read the worked answer
For D = 45 mm, H = 90 mm: V = π×45²×90/4 = 143,140 mm³. A = π×45²/2 + π×45×90 = 3,181 + 12,724 = 15,904 mm². M = 143,140/15,904 = 9.00 mm. Then t_riser/t_plate = (9.00/10.06)² = 0.800, still below 1.2. Simply increasing the height is not sufficient.
Required riser modulus: M_r = √1.2 × M_plate = 1.0954×10.06 = 11.02 mm.
For a cylinder with H = 1.5D: V = 1.1781D³ and A = 2πD², so V/A = 0.1875D. Hence D = 11.02/0.1875 = 58.8 mm and H = 88.2 mm. This is within the 110 mm moulding-box limit.
3. Compute the casting yield for the required riser and comment on the pattern-change decision.
Read the worked answer
Required riser: D = 58.8 mm, H = 88.2 mm. V_riser = π×58.8²×88.2/4 = 239,500 mm³. Plate volume is 1,080,000 mm³.
Casting yield = 1,080,000/(1,080,000 + 239,500) = 81.9%. The existing H = 90 mm riser would give 1,080,000/(1,080,000 + 143,140) = 88.3%, but it does not meet the feeding criterion. The correct riser costs about 6.4 percentage points of yield plus a 4% remelt loss on the extra metal.
That lost yield is the price of sound castings. The Rs 8,000 pattern change is small compared with a recurring shrinkage-scrap rate. The judgement is to redesign the riser to D ≈ 59 mm, H ≈ 88 mm, and verify the neck size separately; merely raising the existing riser is not an acceptable fix.