In the field of sand casting foundry, the production of copper alloy worm wheel castings has long posed a challenge for riser design. Traditionally, two approaches have been employed: empirical design methods and solidification simulation techniques. However, empirical methods lack sufficient accuracy, while simulation techniques are time-consuming and require high operator expertise. There has been a clear gap in the sand casting foundry practice—a method that is both reasonably accurate and extremely convenient for daily process design. Based on my extensive experience in copper alloy casting, I have developed a nimble riser design method that systematically relates the riser shape parameters to the casting shape parameters for worm wheel castings produced in the sand casting foundry. This method not only ensures casting quality but also improves process yield and design efficiency. In this article, I will present the principle process, the mathematical relationships, and several practical case studies to illustrate the application of this method.
1. Principle Process for Worm Wheel Castings in Sand Casting Foundry
Copper alloy worm wheel castings, due to their demanding working conditions and high strength requirements, are typically made of aluminum bronze or tin bronze. In the sand casting foundry, when the gear ring wall thickness exceeds 80 mm, external chills are usually placed on the outer circumference of the gear ring to ensure densification of the tooth face. Also, chills are often placed under thicker spoke sections. For aluminum bronze worm wheels, gray iron chills are commonly used, with thickness ranging from 0.5 to 0.9 times the thickness of the area to be chilled. However, beyond a certain thickness, the effect of chills becomes almost constant; therefore, I typically control chill thickness between 40 mm and 90 mm. For tin bronze worm wheels, besides cast iron and steel chills, copper chills are also used, with thickness 0.4 to 0.7 times the thickness of the chilled area. A crucial point in the sand casting foundry is that chills placed on the inner diameter of the worm wheel should not be monolithic to avoid cracking due to lack of collapsibility and to prevent the chill from being “locked” during cooling. Therefore, I always make them segmented, with each segment length less than 300 mm and a gap of 1–5 mm between segments.
Aluminum bronze worm wheel castings are generally cast in a vertical orientation with a bottom-gating system (first closed then open), using filters. Riser(s) are placed on top of the casting. The casting shape parameters include outer diameter D, height H, gear ring wall thickness T, and maximum wall thickness (gear ring + spoke) Tmax. For large worm wheels with D > 700 mm, multiple oval risers are used (n number). For medium or small wheels with D ≤ 700 mm, a single annular through-riser is employed.
For tin bronze worm wheels, the oxidation tendency is much less than that of aluminum bronze, so simpler gating systems like shower gates are used. Tin bronze has lower linear shrinkage, thus less demand for feeding. A through-riser is usually placed on top, and the riser height is smaller than that for aluminum bronze.
2. Nimble Riser Calculation Method for Sand Casting Foundry
Based on statistical analysis of numerous production runs in our sand casting foundry, I have established the relationship between riser shape parameters and casting shape parameters for copper alloy worm wheel castings. This relationship is summarized in Table 1. The method involves calculating the riser height h, length a (or total na for multiple risers), and width b, followed by a yield check.
Table 1: Relationship between riser shape parameters and casting shape parameters for worm wheel castings in sand casting foundry
| Casting parameter | Riser calculation parameters (k1, k2, k3) | Riser verification | |||||||
|---|---|---|---|---|---|---|---|---|---|
| D (mm) | Alloy | k1 = h/H | k2 = a/D (Al bronze, ring-hub integrated) | k2 = na/D (Al bronze, ring-hub separated) | k2 = a/D (Sn bronze) | k3 = b/T (Al bronze, Tmax/T < 1.7) | k3 = b/T (Al bronze, Tmax/T ≥ 1.7) | Yield (%) Al bronze | Yield (%) Sn bronze |
| < 400 | Al | 0.75–0.85 | π | — | — | 1.0–1.2 | 1.2–1.3 | ~55 | ~65 |
| 400–700 | Al | 0.70–0.80 | π | (0.45–0.50)π | π | 1.0–1.2 | 1.2–1.3 | ~60 | ~70 |
| 700–1000 | Al | 0.70–0.80 | — | (0.45–0.50)π | π | 1.0–1.1 | 1.1–1.2 | ~65 | ~70 |
| 1000–1500 | Al | 0.65–0.75 | — | (0.45–0.45)π | π | 1.0–1.1 | 1.1–1.2 | ~65 | ~75 |
| > 1500 | Al | 0.60–0.70 | — | (0.35–0.40)π | π | 1.0–1.1 | 1.1–1.2 | ~70 | ~80 |
| < 400 | Sn | 0.20–0.30 | π | — | π | — | — | — | ~65 |
| 400–700 | Sn | 0.20–0.30 | π | — | π | — | — | — | ~70 |
| > 700 | Sn | 0.20–0.25 | π | — | π | — | — | — | ~70–80 |
Note for Table 1: For tin bronze, the riser width b is taken as b = (1.0–1.1)T when Tmax/T < 1.7, and b = (1.1–1.2)T when Tmax/T ≥ 1.7. The yield values are typical ranges; actual values depend on chill usage and casting complexity. For aluminum bronze, when the gear ring wall thickness T > 80 mm, external chills are used, and the yield tends to be higher than for equivalent sleeve castings.
The calculation procedure in this sand casting foundry method is as follows:
- Given D, H, T, and Tmax, determine the ratio Tmax/T.
- From Table 1, read k1 based on D and alloy type. Then riser height: $$ h = k_1 \cdot H $$
- From Table 1, read k2 based on D and casting shape (ring-hub integrated or separated for Al bronze; for Sn bronze always use k2 = π for through-riser). Then total riser length: $$ na = k_2 \cdot D $$ where n is the number of risers (for multiple oval risers, n is chosen typically 4, 6, or 8). For a single through-riser, n=1 and a = πD (the circumference).
- From Table 1, read k3 based on D and Tmax/T. Then riser width: $$ b = k_3 \cdot T $$ For tin bronze, k3 is taken from the appropriate column.
- After obtaining riser dimensions, I calculate the total riser volume and compare with the casting volume to estimate the process yield. The yield should fall within the ranges given in Table 1; if not, I adjust the riser dimensions within the allowed coefficient ranges.
This method is extremely simple and fast, making it ideal for daily use in a sand casting foundry. It has been validated by numerous production orders and supplemented by occasional solidification simulations for critical parts.
3. Case Studies in Sand Casting Foundry
Case 1: Large Machine Tool Worm Wheel (Aluminum Bronze)
Outer diameter D = 1068 mm, height H = 176 mm, gear ring wall thickness T = 144 mm, maximum thickness Tmax = 234 mm. The spoke is offset to one side, protruding 90 mm beyond the gear ring. Since Tmax = 234 mm < 280 mm, centrifugal casting is possible but the order quantity is only 3 pieces, so I chose sand casting to avoid high mold cost. The gear ring thickness > 80 mm, so I placed gray iron chills on the outer circumference with thickness 90 mm (12 segments per circle, gap 2 mm). Also, chills were placed under the spoke region. I used a bottom-gating system with four filters. Based on D = 1068 mm, H = 176 mm, T = 144 mm, Tmax/T = 1.63 < 1.7, from Table 1 (Al bronze, D between 1000 and 1500 mm): k1 = 0.65–0.75, k2 = (0.40–0.45)π (for separated ring-hub, as the spoke is integrated but the riser is placed on top with multiple ovals), k3 = 1.0–1.1. I chose n = 4 oval risers.
Calculations:
$$ h = (0.65 \text{ to } 0.75) \times 176 = 114 \text{ to } 132 \text{ mm}; \text{ take } h = 125 \text{ mm} $$
$$ na = (0.40 \text{ to } 0.45)\pi \times 1068 = 1342 \text{ to } 1510 \text{ mm}; \text{ with } n=4, a = 336 \text{ to } 378 \text{ mm}; \text{ take } a = 360 \text{ mm} $$
$$ b = (1.0 \text{ to } 1.1) \times 144 = 144 \text{ to } 158 \text{ mm}; \text{ take } b = 150 \text{ mm} $$
Yield check: casting mass = 700 kg, riser mass = 335 kg, gating system = 70 kg, yield = 700/(700+335+70) = 63.3%, which is within the expected range (~65% for this size). The castings produced were sound.
Case 2: Large Aluminum Bronze Worm Wheel with Thick Spoke
D = 1666 mm, H = 213 mm, T = 83 mm, Tmax = 270 mm, ratio Tmax/T = 3.25 (> 1.7). The gear ring is relatively thin but the spoke is very thick in two steps. I placed chills on the outer circumference with thickness 90 mm (18 segments, gap 3 mm), and L-shaped chills on the bottom and side of the spoke with thickness 60 mm (to support the core). Because the feeding path from the riser to the gear ring is narrow, I added a pad (taper) at the root of the riser to increase the local thickness of the gear ring to 100 mm. n = 6 oval risers.
From Table 1 for D > 1500 mm and Tmax/T ≥ 1.7: k1 = 0.60–0.70, k2 = (0.35–0.40)π, k3 = 1.1–1.2.
$$ h = 0.60 \times 213 = 127.8 \text{ mm}; \text{ but due to strong chilling, I took } h = 130 \text{ mm} $$
$$ na = 0.35\pi \times 1666 = 1832 \text{ mm}; \text{ } n=6, a = 305 \text{ mm}; \text{ I took } a = 300 \text{ mm} $$
$$ b = 1.1 \times 83 = 91.3 \text{ mm}; \text{ considering the large hot spot, I took } b = 100 \text{ mm} $$
Yield: casting 1370 kg, risers 210 kg, gating 120 kg → yield = 1370/(1370+210+120) = 80.6%, which is high but acceptable because of the extensive chills. Solidification simulation (not shown) confirmed no shrinkage defects.
Case 3: Medium Boiler Worm Wheel (Aluminum Bronze, Ring-Hub Integrated)
D = 510 mm, H = 235 mm, T = 77 mm, Tmax = 150 mm, ratio = 1.95 (> 1.7). I used a single cylindrical through-riser. Chills on outer circumference (60 mm thick, 12 segments) and on the lower part of the gear ring (50 mm thick, 8 segments).
From Table 1 for D = 400–700 mm (Al bronze): k1 = 0.70–0.80, k2 = π (through-riser), k3 = 1.2–1.3 (since Tmax/T > 1.7).
$$ h = 0.75 \times 235 = 176 \text{ mm}; \text{ I took } h = 180 \text{ mm} $$
$$ a = \pi \times 510 = 1602 \text{ mm} \text{ (circumference of riser)} $$
$$ b = 1.25 \times 77 = 96 \text{ mm}; \text{ I took } b = 92 \text{ mm} $$
Yield: casting 193 kg, riser 118 kg, gating 10 kg → yield = 193/(193+118+10) = 60.1%, consistent with Table 1 (~60% for this size).
Case 4: Medium Worm Wheel with Two Sleeves (Aluminum Bronze)
A complex worm wheel: D = 535 mm, H = 340 mm, T = 50 mm (gear ring), Tmax = 198 mm (hub), ratio = 3.95. The casting has a double-sleeve shape: an outer gear ring and an inner hub connected by a thin web (24 mm). The web cannot provide adequate feeding from a single top riser to the gear ring. Therefore, I placed a main cylindrical through-riser on the hub (height reduced) and four auxiliary oval risers on the gear ring. The auxiliary risers were taller (265 mm) than the main riser (170 mm).
For the main riser on the hub (hub wall thickness 67.5 mm), using a virtual single-riser approach for comparison: k1 = 0.70–0.80, k2 = π, k3 = 1.2–1.3 → h=250 mm, b=85 mm (with pad). But I reduced the main riser height to 170 mm thanks to the auxiliary risers. For each auxiliary riser: a=80 mm, b=50 mm, h=265 mm.
Mass breakdown: casting 195 kg, main riser 70 kg, four auxiliary risers 71 kg, gating 10 kg → yield = 195/(195+70+71+10) = 56.4%, slightly lower than typical but necessary for this complex shape. The castings were defect-free.
Case 5: Large Tin Bronze Worm Wheel Rim (Single Piece)
D = 1128 mm, H = 145 mm, T = 85 mm, Tmax = 135 mm, ratio = 1.59 (< 1.7). Centrifugal casting was considered but the order was single piece, so I chose sand casting with steel chills on the outer circumference (65 mm thick, 12 segments) and graphite chills on the inner diameter. I used a shower gating system. The riser is a through-riser around the top.
From Table 1 for Sn bronze with D between 1000 and 1500 mm: k1 = 0.20–0.25, k2 = π, k3 = 1.0–1.1 (since ratio < 1.7).
$$ h = 0.25 \times 145 = 36 \text{ mm}; \text{ I took } h = 35 \text{ mm} $$
$$ a = \pi \times 1128 = 3544 \text{ mm} $$
$$ b = 1.0 \times 85 = 85 \text{ mm}; \text{ no pad needed} $$
Yield: casting 420 kg, riser 91 kg, gating (which entered the riser) not counted; yield ≈ 420/(420+91) = 82.2%, very high. Solidification simulation confirmed soundness.
4. Conclusion
Through many years of practice in the sand casting foundry, I have developed and refined a nimble riser design method specifically for copper alloy worm wheel castings. The method is based on a set of simple empirical coefficients that correlate riser dimensions (height, total length, width) with casting parameters (outer diameter, height, wall thickness, and maximum thickness ratio). It eliminates the guesswork of pure experience and the time burden of full solidification simulations, providing a practical tool for rapid and reliable process design in any sand casting foundry. The five case studies demonstrate how this method is applied to various worm wheel geometries—large and small, aluminum bronze and tin bronze, simple and complex. In every case, the calculated riser sizes have led to castings free of shrinkage defects while maintaining high process yields, often exceeding 60% and reaching 80% in favorable conditions. I encourage my colleagues in the sand casting foundry industry to adopt this method as a standard for copper alloy worm wheel production.