Patterns, pattern allowances and core making

Why it matters

Every sand casting starts as a pattern, and every error in the pattern is copied into every casting made from it. Getting the allowances right decides whether a pump casing or engine block can be machined to size or ends up as scrap, and correct core design decides whether internal passages come out where the drawing puts them.

Key ideas

Pattern. A pattern is a replica of the casting, used to make the mould cavity in sand. It is not the same size as the casting: it carries allowances, and it carries core prints that do not appear on the casting at all. Pattern materials are wood (cheap, easy to shape, for small batches), metal such as aluminium or cast iron (long life, for machine moulding and large batches), plastics/epoxy, and expendable materials (wax for investment casting, expanded polystyrene for full-mould/lost-foam casting).

Types of pattern.

• Single-piece (solid) — simplest, for simple shapes and few castings.
• Split pattern — made in two halves along the parting line, one half in the cope and one in the drag; used when the shape cannot be withdrawn in one piece.
• Match-plate pattern — cope and drag halves mounted on the two faces of one plate, with gates and runners; used on moulding machines for many small castings.
• Cope-and-drag pattern — halves on separate plates so two workers or machines can make the cope and drag separately; used for large castings.
• Gated pattern — several patterns joined by the gating system, for many small castings per mould.
• Loose-piece, sweep, skeleton and follow-board patterns — for overhangs, large symmetric shapes (sweep), and very large castings where a full pattern would be too costly (skeleton).

Pattern allowances. A metal contracts in three stages as it cools: liquid contraction (pouring temperature to liquidus), solidification shrinkage (liquid to solid), and solid contraction (solidus to room temperature). Only the solid contraction is compensated by the pattern; liquid and solidification shrinkage are fed by risers (see the riser-design topic). The allowances are:

• Shrinkage (contraction) allowance — pattern made larger by the linear solid contraction of the metal. Typical values (take exact values from your data book): grey cast iron about 1%, steel about 2%, aluminium alloys about 1.3%, brass about 1.5%. Pattern makers use a "shrink rule" graduated with this allowance built in.
• Machining (finish) allowance — extra metal on every surface that will be machined, to remove scale, sand and surface defects. It is added on each machined face, so a dimension machined on both ends gets twice the face allowance.
• Draft (taper) allowance — a taper on vertical faces so the pattern can be drawn out without breaking the sand. Typically 0.5°–2° on external faces, more on internal faces (pockets), because the sand inside a pocket grips the pattern as it contracts onto it.
• Shake (rapping) allowance — rapping the pattern to loosen it enlarges the cavity slightly, so the pattern is made slightly smaller. It is the only negative allowance.
• Distortion (camber) allowance — long, thin or U-shaped castings warp because sections cool at different rates; the pattern is bent the opposite way so the casting straightens as it cools.

Cores. A core is a separately made body of sand (or metal, or salt) placed in the mould to form an internal cavity or an undercut. A good core needs green and dry strength to survive handling and metal pressure, refractoriness, permeability to vent the gases generated when the binder burns, and collapsibility so it breaks down as the casting contracts around it (otherwise hot tears) and can be knocked out afterwards.

• Green-sand core — formed from the moulding sand itself, by the pattern; weak, only for simple shapes.
• Dry-sand core — silica sand with a core binder (linseed oil, cereal, or resin), rammed in a core box and baked; the common type.
• Shell, CO₂ and cold-box cores — resin- or sodium-silicate-bonded cores hardened by heat, CO₂ gas or an amine gas, for accuracy and high production.

Core prints and chaplets. Core prints are projections on the pattern that make seats in the sand to locate and support the core; they are not part of the casting. When a core is long or overhanging and the prints cannot carry the load, metal chaplets support it; they are made of a metal compatible with the casting so they fuse into it.

Buoyancy on a core. Molten metal is much denser than sand, so a core immersed in it is pushed upward. The prints (or chaplets) must resist this force, and it is a standard numerical.

Formulas

L_p = L_c × (1 + α)

• L_p = pattern dimension (mm), L_c = casting dimension before shrinkage compensation (mm), α = linear shrinkage allowance (fraction, e.g. 0.02). This is the usual textbook and GATE convention. If α is instead defined as a fraction of the pattern dimension, L_p = L_c / (1 − α); the difference is tiny for α of 1–2%.

L_c = L_finished + Σ machining allowances on the faces that bound that dimension

• Apply machining allowance first, then shrinkage to the total.

Increase in width per side due to draft = h × tan θ

• h = height (depth) of the vertical face (mm), θ = draft angle. For a round boss the diameter at the parting line exceeds the diameter at the far end by 2·h·tan θ.

F_b = V_c × (ρ_m − ρ_c) × g

• F_b = net upward (buoyant) force on the core (N), V_c = volume of core immersed in metal (m³), ρ_m = density of liquid metal (kg/m³), ρ_c = density of core sand (kg/m³), g = 9.81 m/s². If the question asks for the buoyant force alone (ignoring core weight), use V_c·ρ_m·g.

Volumetric allowance ≈ 3α (for small α) — relates linear and volumetric solid contraction.

Worked examples

Example 1 (standard). A steel shaft blank must be 300 mm long after machining. Both end faces are machined with an allowance of 3 mm per face. Steel shrinkage allowance is 2%. Find the pattern length.

1. Casting length needed: L_c = 300 + 2 × 3 = 306 mm.
2. Pattern length: L_p = L_c × (1 + α) = 306 × 1.02.
3. L_p = 312.12 mm.

Answer: L_p ≈ 312.1 mm (using the 1/(1 − α) convention gives 312.2 mm — state which you use).

Example 2 (draft). A cylindrical boss 80 mm in diameter at its far end is 150 mm deep in the drag. A draft of 1.5° is given. Find the pattern diameter at the parting line.

1. Increase per side: h·tan θ = 150 × tan 1.5° = 150 × 0.02619 = 3.93 mm.
2. Diameter at the parting line: 80 + 2 × 3.93 = 87.86 mm.

Answer: ≈ 87.9 mm.

Example 3 (GATE level — core buoyancy). A cylindrical sand core 100 mm in diameter and 300 mm long lies horizontally, fully surrounded by molten grey cast iron. Density of liquid iron = 7200 kg/m³, density of core sand = 1600 kg/m³. Find the net upward force the core prints must resist.

1. Core volume: V_c = (π/4) × 0.1² × 0.3 = 2.356 × 10⁻³ m³.
2. Buoyant force: V_c·ρ_m·g = 2.356 × 10⁻³ × 7200 × 9.81 = 166.4 N.
3. Core weight: V_c·ρ_c·g = 2.356 × 10⁻³ × 1600 × 9.81 = 37.0 N.
4. Net upward force: F_b = 166.4 − 37.0 = 129.4 N.

Answer: ≈ 129 N upward. If the prints cannot carry this (sand bearing strength is limited), chaplets are added.

Common mistakes

• Adding the machining allowance only once when both faces of a dimension are machined.
• Applying shrinkage to the finished dimension and then adding machining allowance — shrinkage acts on the whole casting, so apply it to the dimension including machining stock.
• Thinking the pattern compensates for all shrinkage. Liquid and solidification shrinkage are fed by risers; the pattern handles only solid contraction.
• Treating shake allowance as positive. Rapping enlarges the cavity, so the pattern is made smaller.
• Using the buoyant force V·ρ_m·g when the question asks for the net force (subtract the core weight), or vice versa.
• Forgetting that core prints add length to the pattern but not to the casting.
• Mixing up the draft on one side with the change in diameter (which is twice the per-side value).

For GATE PI

Expect one-mark conceptual questions on which allowance is negative, which shrinkage the pattern compensates, the purpose of core prints and chaplets, and matching pattern types to production situations. Numericals ask for the pattern dimension with shrinkage and machining allowances combined, draft-corrected dimensions, and the buoyant or net force on a core. Practise doing allowances in the right order and keeping track of how many machined faces bound a dimension.

Quick check

1. Which pattern allowance is negative, and why?
2. Which of the three stages of contraction does the shrinkage allowance cover?
3. A 200 mm cast-iron casting dimension, shrinkage 1%: what is the pattern dimension?
4. What two properties let a core vent gas and avoid hot tears in the casting?
5. What supports a long core when core prints are not enough?

Answers: 1. Shake (rapping) allowance — rapping enlarges the cavity, so the pattern is made smaller. 2. Solid contraction only. 3. 202 mm. 4. Permeability and collapsibility. 5. Metal chaplets that fuse into the casting.