Gating system design and pouring time

Why it matters

The gating system decides how the metal enters the mould: too slow and it freezes before the cavity is full (misruns, cold shuts); too fast or turbulent and it erodes the sand, entrains air and oxide films and carries slag into the casting. Gating design is one of the few places in casting where a short hand calculation — Bernoulli and continuity — directly fixes real defects.

Key ideas

Elements of the gating system (in flow order):

• Pouring basin (cup) — receives the stream from the ladle, keeps a steady head, and lets slag float off before metal enters the sprue.
• Sprue — vertical channel. It is tapered, narrower at the bottom, because the falling stream accelerates and contracts; a straight sprue lets the stream pull away from the walls, creating low pressure that sucks air and gas in through the permeable sand (aspiration).
• Sprue well (base) — a small enlargement at the sprue bottom that cushions the falling stream and turns it gently into the runner.
• Runner — horizontal channel, usually in the drag, that carries metal to the gates. A runner extension beyond the last gate traps the first, cold, dirty metal.
• Ingates (gates) — the openings into the cavity. Skim bobs and strainer cores/ceramic filters trap slag and dross.

Choke. The smallest cross-section in the system is the choke. It sets the flow rate for a given head; it is usually at the sprue bottom (in a pressurised system the gates act as the choke).

Types of gate by position.

• Top gate — metal falls directly into the cavity from the top. Fast filling and favourable temperature gradient for feeding from the top, but the falling metal erodes the mould and oxidises; suited to ferrous metals in simple shapes, not to aluminium.
• Bottom gate — metal enters at the bottom and rises quietly. Minimum turbulence and erosion, but the effective head falls as the cavity fills, so filling is slower, and the hottest metal ends up at the bottom — an unfavourable gradient for top risers.
• Parting-line (side) gate — a compromise, the most widely used in practice.

Gating ratio = sprue (choke) area : total runner area : total ingate area.

• Non-pressurised (for example 1 : 2 : 2) — areas increase downstream, velocities fall, low turbulence; preferred for oxidation-prone aluminium and magnesium. Runners must be designed carefully so all gates flow.
• Pressurised (for example 1 : 0.75 : 0.5) — gates are the choke, the system stays full of metal and back-pressured, which avoids aspiration and gives even flow from multiple gates, but gate velocities are high; used for ferrous castings.

Assumptions behind the formulas. The standard GATE model treats the metal as an ideal fluid (no friction, no heat loss), uses Bernoulli's equation between the free surface in the basin and the gate, and assumes the basin level is held constant. Real systems have friction losses, accounted for with a discharge coefficient (about 0.8–0.9) if the question gives one.

Pouring time. Too short means turbulence and sand erosion; too long means cold metal, misruns and cold shuts. Empirical pouring-time rules for different metals (for example, t = K·√W type relations) exist in data books — use the constants given in the question.

Formulas

v = √(2·g·h) — velocity at the sprue bottom or gate (m/s); g = 9.81 m/s², h = metal head above that point (m).

Q = A·v — continuity; Q = volume flow rate (m³/s), A = area at the choke (m²).

t_f = V / (A_g·v_g) — top gating filling time (s); V = mould cavity volume (m³), A_g = gate area (m²), v_g = √(2·g·h_t) with h_t = sprue height (constant head, m).

t_f = (A_m / A_g) × (2/√(2g)) × (√h_t − √(h_t − h_m)) — bottom gating filling time (s); A_m = plan area of the mould cavity (m²), h_m = cavity height (m), h_t = sprue height measured from the gate (m). Derived by integrating A_m·dh = A_g·√(2g(h_t − h))·dt, because the head falls as metal rises.

A_top / A_bottom = √(h_bottom / h_top) — sprue taper to avoid aspiration; h_top = metal head at the sprue top (depth of metal in the basin), h_bottom = head at the sprue bottom (basin depth + sprue length).

Re = ρ·v·d / μ — Reynolds number in a channel; above about 2000 the flow is turbulent. Gating systems usually run turbulent; the aim is to keep it moderate (below about 20 000).

Worked examples

Example 1 (standard — top gating). A mould cavity of volume 1.5 × 10⁻³ m³ (200 × 100 × 75 mm) is top-gated through a sprue 200 mm high. The gate (choke) area is 200 mm². Find the filling time.

1. v = √(2 × 9.81 × 0.2) = 1.981 m/s.
2. Q = A_g·v = 200 × 10⁻⁶ × 1.981 = 3.962 × 10⁻⁴ m³/s.
3. t_f = V / Q = 1.5 × 10⁻³ / 3.962 × 10⁻⁴ = 3.79 s.

Answer: t_f ≈ 3.8 s.

Example 2 (GATE level — bottom gating). The same cavity (plan 200 × 100 mm, height 75 mm) is bottom-gated with the same 200 mm² gate, the top of the sprue being 200 mm above the gate. Find the filling time and compare with Example 1.

1. A_m = 0.2 × 0.1 = 0.02 m², A_m/A_g = 0.02 / 2 × 10⁻⁴ = 100.
2. 2/√(2g) = 2 / 4.429 = 0.4515 s/m^0.5.
3. √h_t − √(h_t − h_m) = √0.2 − √0.125 = 0.4472 − 0.3536 = 0.0936.
4. t_f = 100 × 0.4515 × 0.0936 = 4.23 s.

Answer: t_f ≈ 4.2 s, about 12% longer than top gating, because the effective head falls as the metal rises in the cavity.

Example 3 (sprue taper). The basin holds 50 mm of metal above the sprue top; the sprue is 200 mm long and its bottom (choke) area is 200 mm². Find the area at the sprue top.

1. h_top = 0.05 m, h_bottom = 0.05 + 0.2 = 0.25 m.
2. A_top = A_bottom × √(h_bottom/h_top) = 200 × √(0.25/0.05) = 200 × 2.236.

Answer: A_top ≈ 447 mm².

Common mistakes

• Using the sprue height as the head in bottom gating throughout the fill. The head falls from h_t to h_t − h_m; use the integrated formula.
• Using the total cavity volume divided by cavity height wrongly — A_m is the plan (horizontal) area of the cavity.
• Inverting the sprue taper: the sprue is wider at the top, narrower at the bottom.
• Measuring the head from the wrong point — h is measured from the free surface of metal in the basin to the point where velocity is required.
• Forgetting to convert mm² to m² (factor 10⁻⁶) and mm to m before using g = 9.81 m/s².
• Saying the pressurised system has the largest gate area; in a pressurised system the gates are the smallest (the choke).

For GATE PI

This topic gives frequent two-mark numericals: filling time for top and bottom gating, the ratio of bottom- to top-gating time, sprue top area from the taper relation, flow velocity and flow rate at the choke, and occasionally a Reynolds-number check. One-mark questions ask which gating ratio is pressurised, why sprues are tapered, and which gate type gives the least turbulence. Practise the bottom-gating derivation once so you can rebuild it if you forget the formula.

Quick check

1. Why is a sprue tapered?
2. Which takes longer to fill the same cavity with the same gate and sprue height: top or bottom gating?
3. In a gating ratio 1 : 2 : 2, which element is the choke?
4. Head at a gate = 0.3 m. What is the ideal metal velocity there?
5. Which gating ratio type suits aluminium alloys, and why?

Answers: 1. To follow the contracting stream and avoid aspiration of air and gas. 2. Bottom gating. 3. The sprue. 4. √(2 × 9.81 × 0.3) ≈ 2.43 m/s. 5. Non-pressurised — low velocities reduce turbulence and oxide (dross) formation.