A Spiral Hoop Gear is a large-diameter helical ring gear — also called a spiral girth gear — that wraps around a rotating drum and meshes with one or two driven pinions to transmit torque. You see it on the shell of a FLSmidth ball mill, a Polysius rotary cement kiln, or a heavy turntable on a Pittler PV SL vertical lathe. The helix angle spreads tooth load across multiple teeth at once, which lets the gear carry MW-class torque at low RPM without shock. The result is smooth, quiet drive of equipment weighing hundreds of tonnes.
Spiral Hoop Gear Interactive Calculator
Vary helix angle, face width, tooth pitch, and base contact ratio to see how many teeth share load in a spiral hoop gear mesh.
Equation Used
The calculator estimates helical overlap contact ratio from face width, helix angle, and transverse circular pitch. Adding the base transverse contact ratio gives the effective number of teeth sharing load. Higher helix angle increases load sharing, but also raises axial thrust on the pinion bearings.
- Uses transverse circular pitch p_t for the helical overlap estimate.
- Load is assumed to divide evenly across the effective teeth in mesh.
- Axial thrust trend is shown as F_a / F_t = tan(beta).
- Defaults are selected so the 8 deg worked diagram gives about 2-3 teeth in contact.
Inside the Spiral Hoop Gear
A Spiral Hoop Gear is bolted directly to the outside of a drum, kiln shell, or turntable using a flanged spring-plate connection that lets the shell expand thermally without stressing the gear rim. The teeth are cut at a helix angle — typically 6° to 12° on cement and mining girth gears — so that as the ring rotates, more than one tooth on the pinion is in contact at any instant. That overlap is what gives the spiral hoop its load-carrying advantage over a straight-cut ring. If the helix angle goes too low you lose contact ratio and the drive starts hammering. Too high and axial thrust on the pinion shaft climbs past what the thrust bearing can hold, and you start chewing the bearing at a measurable rate.
Most spiral hoop gears are built as split rings — two halves bolted together at site — because nobody ships a 12 m diameter forging. The split joint has to be machined to within roughly 0.05 mm of perfect circularity once torqued, otherwise you get a periodic clunk twice per revolution as each pinion crosses the joint. Tooth contact pattern is set by jacking the pinion bearing housing on shims. You want a contact band covering 70-80% of the face width, biased slightly to the centre. If contact runs hard on one end of the tooth — the classic symptom is bluing or polish only on the drive side root — your pinion is misaligned in pitch and you will pit teeth within months, not years.
Lubrication is open-gear spray. The system pulses a high-viscosity asphaltic or synthetic adhesive lubricant onto the gear flanks every 5-15 minutes through a manifold of nozzles. Run it dry for an 8-hour shift and you can scrap a half-million-dollar girth gear from scuffing damage on the active flanks.
Key Components
- Helical Ring (Hoop): The split forged or cast ring carrying the helical teeth. Typical diameters run 4 m to 14 m, face widths 400 mm to 1000 mm, made from cast steel grades like GS-42CrMo4 or forged 42CrMo4 with through-hardened or surface-hardened tooth flanks at 280-320 HB.
- Pinion: The driven gear that meshes with the hoop. Typically case-hardened 18CrNiMo7-6 at 58-62 HRC, sized for a face width 5-10 mm wider than the ring to accommodate axial float. Single-pinion drives feed up to ~6 MW; dual-pinion drives split torque for installations above that.
- Spring-Plate Mount: Flexible mounting flange between the ring and the drum or kiln shell. Allows radial thermal growth of up to 25 mm on a hot kiln without distorting the gear pitch circle. Bolted with fitted high-tensile bolts torqued to a controlled pre-load.
- Pinion Bearing Housing: Heavy spherical-roller-bearing housing on a fabricated baseplate. Adjustable on shims in three axes — radial centre distance, axial position, and tilt — so installers can dial in tooth contact pattern during commissioning.
- Open-Gear Lubrication System: Spray manifold delivering high-viscosity adhesive lubricant on a timed cycle, typically 5-15 minute intervals. Includes a heated reservoir, metering pumps, and proximity-monitored nozzles that alarm if a spray header blocks.
- Inching Drive: Auxiliary gearbox engaged through a clutch to creep the ring at 0.05-0.2 RPM for inspection, maintenance, and controlled cool-down on hot kilns. Skipping the inching cycle on a hot kiln warps the shell within hours.
Where the Spiral Hoop Gear Is Used
Spiral hoop gears appear anywhere you need to rotate a very large, very heavy cylinder slowly and continuously. The combination of split-ring construction, helical tooth load sharing, and open-gear lubrication scales to drum diameters that would be impossible to drive through a central shaft. Cement, mining, and pulp-and-paper account for most installations, but you also find them on dredge trommels, sugar mill rolls, and large machine-tool turntables.
- Cement Production: Girth gear on the FLSmidth ROTAX-2 rotary cement kiln, typically 4.5-6 m kiln diameter rotating at 0.5-5 RPM under a 4 MW dual-pinion drive.
- Mining: Ring gear on Metso Outotec Premier ball and SAG mills, with hoop diameters up to 12 m driving mills loaded to 400+ tonnes of steel ball charge.
- Pulp & Paper: Drive ring on Andritz rotary lime kilns at kraft pulp mills, where the hoop turns the kiln shell at 0.5-2 RPM during lime mud calcining.
- Heavy Machine Tools: Table-drive ring on Pittler PV SL and Schiess vertical turret lathes, where a precision-ground spiral hoop indexes a 4-8 m chuck table for turning wind-turbine bearing races.
- Mineral Processing: Trommel screen drive at iron ore handling facilities such as the Rio Tinto Cape Lambert ports, where a spiral hoop turns oversized scrubber drums at 8-15 RPM.
- Sugar Refining: Mill roll turning gear on tandem cane mills at facilities like the Tongaat Hulett Felixton mill in South Africa, where the hoop drives the top roll at 4-6 RPM under crushing load.
The Formula Behind the Spiral Hoop Gear
The tangential force at the pitch line is what sizes the pinion teeth, the bearings, and the motor. You need to know it across the full operating range — at the low end where the mill or kiln is starting up against breakaway friction, at nominal running torque, and at the upper end where a charge lock-up or feed surge spikes the load. The sweet spot for tooth life and lubrication film stability sits between roughly 40% and 70% of rated tangential load. Below that you under-utilise the gear and risk micro-pitting from poor film generation. Above it you climb into Hertzian stress territory where flank pitting accelerates non-linearly.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Ft | Tangential tooth force at the pitch circle | N | lbf |
| T | Torque transmitted by the ring gear | N·m | lbf·ft |
| Dp | Pitch diameter of the spiral hoop | m | ft |
| P | Drive power at the gear | W | hp |
| n | Rotational speed of the hoop | RPM | RPM |
Worked Example: Spiral Hoop Gear in a copper concentrator SAG mill girth gear
You are sizing the spiral hoop gear and pinion drive on a 36 ft × 19 ft SAG mill at a copper concentrator in northern Chile, similar in scale to the units running at the Codelco Chuquicamata operation. The mill turns at 9.0 RPM nominal under a 13 MW twin-pinion drive, with a girth gear pitch diameter of 11.0 m. You need to know the tangential force per pinion across startup, nominal, and surge conditions to specify pinion face width and bearing capacity.
Given
- Ptotal = 13,000,000 W
- Dp = 11.0 m
- nnom = 9.0 RPM
- Pinions = 2 —
- Helix angle β = 8 °
Solution
Step 1 — split the total power between the two pinions, since this is a twin-pinion drive:
Step 2 — compute pitch line velocity at nominal 9.0 RPM:
Step 3 — tangential force per pinion at nominal running:
That is the steady-state load each pinion tooth set carries. At the low end of operation — controlled mill startup at roughly 40% of nominal speed under breakaway friction — the drive sees about 60% of rated torque applied at 3.6 RPM, giving Ft,low ≈ 0.60 × 1,254 = 750 kN per pinion. The lubricant film here is thin because hydrodynamic generation needs sliding speed, which is why most installations dose extra lubricant on a startup-priming cycle.
Step 4 — high-end surge condition. A SAG mill charge lock-up or sudden feed slug routinely spikes torque to 1.6× nominal for 1-3 seconds before the controller catches up:
That is the load you size pinion-tooth bending stress and pinion-shaft bearing dynamic capacity against. Push the design margin below 1.6× and you will see tooth-root cracking on the pinion within the first year — the classic symptom is a ferrous-debris alarm on the gear-spray return filter long before any visible damage on the flanks.
Result
Each pinion carries 1,254 kN of tangential force at nominal 9. 0 RPM running. In practical terms that is the load a face width of roughly 750-900 mm at module 30-32 absorbs comfortably with a 280-320 HB ring and 58-62 HRC pinion. The low-end startup load of 750 kN is where lubricant film failures show up — micro-pitting from boundary-regime contact — and the 2,006 kN surge load is where tooth-root fatigue lives. If your measured tangential force runs 15-25% above the calculation, look at three things in this order: (1) a sticking trunnion bearing dragging up breakaway torque, often visible as elevated motor current at startup, (2) helix-angle mismatch between pinion and ring after a flank regrind, which crowds load onto one end of the tooth, or (3) a worn spring-plate mount letting the ring run eccentric, which produces a once-per-revolution torque ripple you can pick up on a drive-current trace.
When to Use a Spiral Hoop Gear and When Not To
Spiral hoop gears are not the only way to drive a large rotating drum. The two main alternatives are a straight-spur (non-helical) girth gear and a gearless ring-motor drive, where the mill shell itself becomes the rotor of a synchronous motor. Each option trades cost, load capacity, and complexity differently.
| Property | Spiral Hoop Gear | Straight-Spur Girth Gear | Gearless Ring-Motor Drive |
|---|---|---|---|
| Typical operating speed | 0.5-15 RPM | 0.5-15 RPM | 0.1-12 RPM, infinitely variable |
| Maximum power per drive | ~22 MW (twin pinion) | ~12 MW (twin pinion) | ~35 MW |
| Load sharing across teeth | 2-3 teeth in contact via helix angle | 1-2 teeth, higher peak stress | Magnetic — no mechanical teeth |
| Capital cost (relative) | 1.0× | 0.8× | 1.8-2.5× |
| Pinion bearing thrust load | Significant axial thrust from helix | Negligible axial load | None |
| Lubrication interval | Open-gear spray every 5-15 min | Open-gear spray every 5-15 min | None — no gear teeth |
| Typical service life | 25-30 years with regrinds | 20-25 years, more flank pitting | 30+ years |
| Best application fit | Cement kilns, SAG/ball mills 4-22 MW | Smaller mills, lime kilns under 6 MW | World-class mining mills above 18 MW |
Frequently Asked Questions About Spiral Hoop Gear
Almost always thermal growth you didn't account for. On a hot kiln or a mill with a bearing that runs warmer on one end, the ring grows radially more on the hot side, which tilts the pitch line relative to the pinion axis. You aligned cold and the geometry walks off as soon as the unit reaches operating temperature.
Check it by taking contact-pattern bluing prints both cold and after 4 hours at temperature. If the band shifts inboard when hot, shim the pinion housing to crown the cold pattern slightly outboard so it lands centred when warm. Most OEMs allow a 0.05-0.10 mm/m taper across the face width to compensate.
The crossover sits around 6-7 MW. Below that, a single pinion with a robust gearbox is simpler, cheaper, and easier to align. Above it, the tooth-root bending stress on a single pinion drives the module and face width into territory where the pinion itself becomes a forging headache — and the ring needs to be heavier to carry the unbalanced radial load.
Twin-pinion splits torque, halves the radial load on the ring, and gives you redundancy: you can run on one pinion at reduced load while servicing the other. The tradeoff is a load-sharing control system to keep the two pinions within roughly 5% of each other on torque, otherwise one chews while the other coasts.
Most likely the split-joint bolts have relaxed. A girth gear is two half-rings bolted together, and the joint passes each pinion twice per revolution. If joint clamp load drops, the rim flexes microscopically as the joint rolls through mesh, which excites a once- or twice-per-rev rumble in the 1-5 Hz range depending on mill speed.
Re-torque the split-joint bolts to spec — usually a controlled bolt-stretch measurement, not just torque wrench — and check for any visible witness mark or fretting at the joint faces. Fretting means the joint has been moving and the faces may need re-machining before re-bolting.
The formula gives steady-state tangential force. Startup adds three loads on top: breakaway friction in the trunnion or slipper bearings (often 2-3× running friction until the hydrodynamic film establishes), inertial torque to accelerate the rotating mass, and unbalanced charge torque on a mill where the ball charge sits at the bottom and has to be lifted to the toe angle.
For a SAG mill the combined startup torque commonly hits 150-180% of running torque for 10-30 seconds. That is why these drives use either a starting clutch, a wound-rotor motor, or a variable-frequency drive — to manage that current ramp without tripping protection.
Yes, and it's done routinely. Specialist contractors like CMD Gears or Artec Machine bring portable grinding rigs that mount on the pinion bearing baseplates and grind the ring while it slow-rotates on the inching drive. You can typically remove 1.5-3 mm of flank material per regrind and get 2-3 regrind cycles out of a girth gear before the tooth thickness drops below the bending-stress allowable.
Economical limit is roughly 8-10% loss of original tooth thickness at the pitch line. Beyond that you are gambling against a tooth-root crack, and replacement is cheaper than the unplanned failure that follows.
Higher helix angle increases axial thrust on the pinion shaft. If the pinion thrust bearing has any axial play — even 0.1-0.2 mm — the pinion oscillates axially under the alternating thrust component as each tooth engages and disengages. That axial chatter shows up as a high-frequency vibration component you didn't have at lower helix angle.
Above roughly 12° helix on a girth gear you are usually better off going to a double-helical (herringbone) configuration to cancel thrust, or accepting the lower helix angle and tightening tooth quality grade instead. Most cement and mining girth gears settle at 6-10° as the practical sweet spot.
References & Further Reading
- Wikipedia contributors. Gear. Wikipedia
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