Sand casting: patterns, moulds, gating and risers

Why it matters

Cylinder blocks, cylinder heads, brake drums, differential housings and manifolds are still made largely by sand casting because it handles complex internal passages at low tooling cost. Whether a casting comes out sound or full of porosity, cold shuts and shrinkage cavities is decided long before pouring – by the pattern allowances, the sand, the gating that fills the mould and the risers that feed it. Gating and riser calculations are standard numerical questions.

Key ideas

The sequence. Make a pattern → ram moulding sand around it in a flask (drag below, cope above, separated by the parting line) → withdraw the pattern → set cores in core prints → close the mould → pour → solidify → shake out → fettle (remove gates and risers, clean) → inspect.

Patterns. A pattern is a replica of the casting, not of the finished part, so it carries allowances:

• Shrinkage (contraction) allowance – the pattern is made larger to cover solid contraction from the solidus to room temperature. Liquid and solidification shrinkage are fed by risers, not by the pattern. Typical values: grey cast iron about 1 %, steel about 2 %, aluminium alloys about 1.3 % – take exact values from a data book.
• Machining allowance – extra metal on surfaces to be machined; more on the cope side, where inclusions float.
• Draft (taper) – about 0.5–3° on vertical faces so the pattern can be withdrawn; internal surfaces need more.
• Distortion (camber) allowance – for long, thin or U-shaped castings that warp on cooling.
• Shake (rapping) allowance – a negative allowance, because rapping enlarges the cavity slightly. Pattern types: solid (single piece), split, match-plate (for machine moulding of small parts in volume), cope-and-drag, loose-piece, gated, sweep and skeleton patterns. Materials: wood (cheap, short runs), metal such as aluminium or cast iron (long runs), plastics, wax (investment casting) and expanded polystyrene (lost-foam).

Moulding sand. Silica sand + binder (clay and water for green sand; resins or sodium silicate for dry, no-bake and CO₂ moulds) + additives (coal dust for surface finish, cereal binders). Key properties: permeability (lets gases escape), green and dry strength, refractoriness, collapsibility (lets the casting shrink without hot tears), flowability. Fine grains give better finish but lower permeability – a classic trade-off.

Cores form internal cavities (water jackets, oil passages). They are made of bonded sand, baked or resin-cured for strength and collapsibility, and sit in core prints. Molten metal exerts a buoyant force on a core; if it exceeds what the prints can support, chaplets (metal supports that fuse into the casting) are used.

Gating system. Pouring basin → sprue (vertical) → sprue well → runner (horizontal, often in the cope or drag) → ingates → mould cavity. It must fill the mould before the metal freezes, avoid turbulence and air aspiration, trap slag and promote directional solidification.

• The sprue is tapered (narrower at the bottom) because the stream accelerates as it falls; a straight sprue would let the stream separate from the walls and draw in air.
• Gating ratio sprue : runner : ingate (by area). Pressurised systems (e.g. 1 : 0.75 : 0.5) keep the system full and give higher yield; unpressurised systems (e.g. 1 : 2 : 2, common for aluminium) lower velocities and turbulence.
• Top gating fills quickly but causes splashing and mould erosion; bottom gating fills quietly but slowly and leaves the hottest metal at the bottom, which works against directional solidification; parting-line gating is a compromise.

Risers (feeders). Metal shrinks in volume as it cools in the liquid and freezes; the riser stores liquid metal and must (1) solidify after the casting, (2) hold enough metal to feed the shrinkage, and (3) be placed so a feed path exists (directional solidification towards the riser). Chills, insulating sleeves and exothermic toppings are used to help. Riser solidification time follows Chvorinov's rule (developed in the next topic). Riser types: top or side, open or blind.

Typical defects (cause in brackets): blowholes and gas porosity (low permeability, moisture), shrinkage cavity (inadequate feeding), misrun and cold shut (low fluidity, slow pouring, low temperature), hot tear (poor collapsibility), sand inclusion and scab (erosion), mould shift (misaligned cope and drag), swell, fins.

Formulas

v = √(2·g·h) Velocity of metal at the bottom of the sprue (m/s); g = 9.81 m/s², h = effective head from the free surface in the basin (m). Assumes no friction losses.

Q = A·v A₁·v₁ = A₂·v₂ Volume flow rate (m³/s) and continuity; A = area (m²).

A_top / A_bottom = √(h_bottom / h_top) Sprue taper; h measured from the free surface in the pouring basin to each section (m).

t_f = V / (A_g·√(2·g·h_t)) Filling time for top gating (s); V = mould volume (m³), A_g = gate (choke) area (m²), h_t = sprue height (m).

t_f = (A_m / A_g)·(2 / √(2·g))·(√h_t − √(h_t − h_m)) Filling time for bottom gating (s); A_m = mould plan area (m²), h_m = mould cavity height (m).

L_pattern = L_casting·(1 + s) (approximately) s = linear shrinkage allowance (fraction).

F_b = V_c·(ρ_m − ρ_c)·g Net buoyant force on a core (N); V_c = core volume in the metal (m³), ρ_m and ρ_c = densities of metal and core sand (kg/m³).

t_s = B·(V / A)² (Chvorinov) Solidification time (s); V/A = casting modulus (m); B = mould constant (s/m²) from data.

Worked examples

Example 1 (standard) – filling time, top vs bottom gating. A mould cavity 0.3 m × 0.2 m in plan and 0.1 m high is filled through a gate of area 500 mm² with a sprue height of 0.2 m.

1. V = 0.3 × 0.2 × 0.1 = 0.006 m³; A_m = 0.06 m²; A_g = 5 × 10⁻⁴ m².
2. Top gating: v = √(2 × 9.81 × 0.2) = 1.981 m/s; t_f = 0.006/(5 × 10⁻⁴ × 1.981) = 6.06 s.
3. Bottom gating: t_f = (0.06/5 × 10⁻⁴) × (2/√19.62) × (√0.2 − √0.1) = 120 × 0.4515 × 0.1310 = 7.10 s. Bottom gating is slower because the effective head falls as metal rises in the mould.

Example 2 (GATE level) – riser size. A 100 mm steel cube is fed by a cylindrical riser with height = diameter. Treat all surfaces of both as cooling surfaces and require the riser to take 25 % longer to freeze than the casting.

1. Cube modulus: (V/A)_c = a³/(6a²) = a/6 = 16.67 mm.
2. Riser modulus with H = D: V = πD³/4, A = πD² + 2(πD²/4) = 1.5πD², so (V/A)_r = D/6.
3. Chvorinov with the same B: t_r/t_c = [(V/A)_r/(V/A)_c]² = 1.25 ⇒ (V/A)_r = 16.67 × √1.25 = 18.63 mm.
4. D = 6 × 18.63 = 111.8 mm, H = 111.8 mm.

Example 3 – sprue taper. The free surface in the basin is 50 mm above the sprue top; the sprue is 200 mm long, and its top area is 700 mm². Bottom area = 700 × √(50/250) = 313 mm².

Common mistakes

• Giving shrinkage allowance for the full volumetric shrinkage. The pattern covers only solid contraction; risers feed liquid and solidification shrinkage.
• Applying shake allowance as positive – it is negative.
• Using the sprue length instead of the head from the free surface in Bernoulli and taper calculations.
• Using the top-gating formula for bottom gating (the head is not constant in bottom gating).
• Computing riser modulus with surfaces that touch the casting counted as cooling area, or vice versa – read which surfaces the question treats as cooling.
• Writing Q = ρ·c·ΔT as "heat energy" in joules – that is energy per unit volume; multiply by volume and add latent heat to get the heat removed in casting.

For GATE ME

Typical items: matching allowances, sand properties, pattern types and defects with causes; numericals on filling time (top and bottom gating), sprue taper, flow rate, riser sizing by Chvorinov's rule (cylinders, cubes, plates, side and top risers), and buoyancy on cores. Practise moduli of simple shapes and the bottom-gating integral until they are automatic.

Quick check

1. Which allowance is negative?
2. Why is a sprue tapered?
3. What is the modulus V/A of a 60 mm cube with all faces cooling?
4. Which gating gives the least turbulence but slowest fill?
5. What is the role of a chaplet?

Answers: 1. Shake (rapping) allowance; 2. To match the accelerating stream so air is not aspirated; 3. 10 mm; 4. Bottom gating; 5. To support a core against metal buoyancy.