Sand casting: patterns, moulds, gating and risers

Why it matters

Sand casting is still the cheapest way to make large, complex metal parts such as pump housings, engine blocks, machine-tool beds and gearbox casings. Most casting defects (blowholes, shrinkage cavities, cold shuts, sand inclusions) trace back to a wrong pattern allowance, a poor gating design or an undersized riser, so these three decisions decide whether the part is sound.

Key ideas

Pattern. A replica of the part used to form the mould cavity. It is made of wood, metal, plastic or wax and is deliberately not the same size as the finished part. Pattern allowances:

• Shrinkage (contraction) allowance – the pattern is made larger to cover the solid contraction from solidus to room temperature. It is a linear percentage that depends on the metal (cast iron about 1%, steel about 2%; take exact values from your data book). Liquid and solidification shrinkage are not covered by the pattern; the riser feeds them.
• Machining allowance – extra metal on surfaces that will be machined.
• Draft allowance – a taper (typically 0.5–2°) on vertical faces so the pattern can be withdrawn without breaking the mould.
• Distortion allowance – a deliberate counter-shape for parts that warp (long thin sections, U-shapes).
• Shake allowance – a negative allowance, because rapping the pattern loose enlarges the cavity slightly.

Pattern types: single-piece, split, match-plate, cope-and-drag, loose-piece, sweep and skeleton patterns. Cores (baked sand, held by core prints) make internal cavities; a core in liquid metal feels a buoyant force equal to (ρ_metal − ρ_core)·g·V_core, which chaplets or core prints must resist.

Mould. A green-sand mould is silica sand + clay (bentonite) binder + water, rammed in a two-part flask: the cope (top) and drag (bottom), split along the parting line. Important sand properties are permeability (lets gases escape), green strength, refractoriness, collapsibility (lets the casting contract without hot tearing) and flowability. Vent holes help release steam and gases.

Gating system. Pouring basin → sprue → sprue well → runner → ingates → cavity. Its jobs: fill the cavity before the metal freezes, keep flow smooth (low velocity, little turbulence), trap slag and sand, and set up favourable temperature gradients.

• The sprue is tapered (narrower at the bottom). Metal accelerates as it falls, so by continuity the cross-section must shrink; a straight sprue would let the stream pull away from the wall and aspirate air.
• Top gating fills fast and gives good temperature gradients but the falling metal splashes and erodes the mould. Bottom gating fills quietly but takes longer because the head reduces as the metal rises, and the hottest metal ends up at the bottom. Parting-line gating is the common compromise.
• Gating ratio = sprue : runner : ingate area. A pressurised system (e.g. 1 : 0.75 : 0.5) keeps the system full and limits aspiration; an unpressurised one (e.g. 1 : 2 : 2) gives lower ingate velocity, used for oxidation-prone metals such as aluminium and magnesium.

Riser (feeder). A reservoir of liquid metal that feeds the casting while it shrinks during solidification. To work it must (a) freeze after the casting, (b) hold enough metal to cover the volumetric shrinkage, and (c) be connected to the heavy section it feeds. A riser is usually sized by the modulus method: modulus M = V/A (volume ÷ cooling surface area), and solidification time grows with M² (Chvorinov's rule, next topic). A common design rule is M_riser ≥ 1.2·M_casting, i.e. the riser freezes about 1.44 times later. The best riser shape is a sphere (largest V/A); a cylinder with H ≈ D is used in practice. Insulating sleeves and exothermic toppings raise the riser's effective modulus. Chills placed at the far end of a section promote directional solidification towards the riser.

Formulas

Pattern size = (casting size + machining allowance) × (1 + shrinkage allowance)

• sizes in mm; shrinkage allowance as a fraction (from data book for the metal).

v = √(2·g·h)

• v = velocity at the sprue base (m/s), g = 9.81 m/s², h = height of liquid head above that point (m). Bernoulli with no losses; real velocities are lower.

A_top·√h_top = A_bottom·√h_bottom

• sprue taper by continuity; A = sprue cross-section (m²), h = head measured from the free surface in the pouring basin (m).

t_f = V / (A_g·√(2·g·h_t)) (top gating)

• t_f = filling time (s), V = cavity volume (m³), A_g = ingate (choke) area (m²), h_t = sprue height (m).

t_f = (A_m / A_g)·(2 / √(2·g))·(√h_t − √(h_t − h_m)) (bottom gating)

• A_m = plan area of the mould cavity (m²), h_m = height of the cavity (m), h_t = sprue height above the bottom gate (m).

M = V / A, design rule M_riser ≥ 1.2·M_casting

• M = modulus (m), V = volume (m³), A = area through which heat is lost (m²). Cube of side a: M = a/6. Cylinder with H = D cooling on all faces: M = D/6.

Worked examples

Example 1 – pattern size (standard). A steel block is 200 mm long after machining. Each end face gets a 3 mm machining allowance. Take shrinkage allowance = 2% (data-book value for steel). Find the pattern length.

1. Casting length before machining = 200 + 2 × 3 = 206 mm.
2. Formula: Pattern size = (casting size) × (1 + shrinkage allowance).
3. Pattern length = 206 × 1.02 = 210.12 mm. Pattern length ≈ 210.1 mm

Example 2 – filling time, top vs bottom gate (GATE level). A mould cavity is 500 mm × 300 mm in plan and 100 mm high. The sprue height is 200 mm and the ingate area is 5 cm². Take g = 9.81 m/s² and neglect losses. Find the filling time for (a) top gating, (b) bottom gating.

1. V = 0.5 × 0.3 × 0.1 = 0.015 m³; A_m = 0.5 × 0.3 = 0.15 m²; A_g = 5 × 10⁻⁴ m².
2. (a) Velocity at the gate: v = √(2 × 9.81 × 0.2) = 1.981 m/s.
3. Flow rate Q = A_g·v = 5 × 10⁻⁴ × 1.981 = 9.905 × 10⁻⁴ m³/s.
4. t_f = V/Q = 0.015 / 9.905 × 10⁻⁴ = 15.1 s (top gating).
5. (b) t_f = (A_m/A_g)·(2/√(2g))·(√h_t − √(h_t − h_m)) = (0.15 / 5 × 10⁻⁴) × (2 / 4.429) × (√0.2 − √0.1) s
6. = 300 × 0.4516 × (0.4472 − 0.3162) = 300 × 0.4516 × 0.1310 = 17.7 s (bottom gating). Bottom gating is slower because the effective head falls as the cavity fills.

Example 3 – riser size by the modulus method. A steel cube casting of side 100 mm is fed by a cylindrical side riser with H = D. Use M_riser = 1.2·M_casting.

1. M_casting = a/6 = 100/6 = 16.67 mm.
2. M_riser = 1.2 × 16.67 = 20.0 mm.
3. For the riser, M = D/6, so D = 6 × 20.0 = 120 mm. Riser D = H = 120 mm; it freezes about 1.2² = 1.44 times later than the casting.

Common mistakes

• Thinking the shrinkage allowance covers all shrinkage. It covers only solid contraction; liquid and solidification shrinkage are fed by the riser.
• Applying shrinkage to the finished size and then adding machining allowance. The machining allowance is added first, then the whole casting size is scaled.
• Making the sprue straight or wider at the bottom, which aspirates air.
• Using the total cavity surface for a riser that sits on the casting: the face in contact with the casting does not lose heat and is left out of A.
• Forgetting that the shake allowance is negative.
• Mixing mm and m in √(2gh); keep h in metres when g = 9.81 m/s².

For GATE ME

Expect numericals on filling time for top and bottom gating, sprue taper from continuity, sprue-base velocity, riser sizing by the modulus method (often combined with Chvorinov's rule), the buoyancy force on a core, and pattern dimensions with allowances. Conceptual MCQs cover pattern allowances, sand properties, the purpose of each gating element and casting defects. Practise deriving the bottom-gating formula once so you can rebuild it under pressure.

Quick check

1. Which pattern allowance is negative?
2. Why is a sprue tapered?
3. For the same sprue height, which fills faster: top or bottom gating?
4. What is the modulus of a 60 mm cube cooling on all faces?
5. Does the shrinkage allowance compensate for solidification shrinkage?

Answers: 1. Shake (rapping) allowance. 2. To match the shrinking stream area as the metal speeds up and prevent air aspiration. 3. Top gating. 4. 10 mm. 5. No; the riser feeds it, the shrinkage allowance covers only solid contraction.