A V-toothed Gear is a cylindrical gear with teeth cut in two opposing helical rows that meet at the centre to form a V-shape across the face width. Unlike a single helical gear that pushes a constant axial thrust into the bearings, V-toothed Gearing cancels that thrust internally because the two helices pull in opposite directions. This lets engineers run high helix angles for quiet, high-overlap meshing without paying for big thrust bearings. Marine reduction gearboxes, steel rolling mill drives, and large turbine sets use them to transmit megawatts at low vibration.
V-toothed Gear Interactive Calculator
Vary tangential tooth load, opposing helix angles, and load split to see axial thrust cancellation in a V-toothed gear.
Equation Used
The calculator resolves the tangential tooth force into opposite axial components on the two helical halves. When betaR equals betaL and load share is 50 percent, the opposing axial forces are equal, so the net thrust into the shaft bearings is zero.
FIRGELLI Automations - Interactive Mechanism Calculators.
- Tangential load is split between the two helical halves by the load-share input.
- Right and left axial forces act in opposite shaft directions.
- Pressure angle, radial force, friction, and bearing compliance are ignored.
- Equal helix angles and equal load sharing should give zero net thrust.
Operating Principle of the V-toothed Gear
A V-toothed Gear, also called V-toothed Gearing or — when the two helices meet without a centre groove — a herringbone gear, works by splitting the tooth face into two mirror-image helical halves. When torque enters the pinion, each half generates an axial force component along the shaft. Because the helix angles are equal and opposite, those two forces sum to zero at the gear body. The radial and tangential force components stay, but the shaft sees no net thrust. That is the whole point of the geometry — you get the smooth, high-contact-ratio meshing of a steep helical gear without forcing the bearings to react thousands of newtons of axial load.
The geometry only works if both halves are cut to matching helix angles within tight limits. Typical helix angles run 25° to 35°. If the two halves drift out of symmetry by more than about 0.05° you start seeing residual axial thrust, uneven load sharing between the halves, and a characteristic howl at mesh frequency. The face width on each helix is usually 1.5 to 2.5 times the normal module, and the centre relief groove on a true double-helical (as opposed to herringbone) is wide enough for the cutter to run out cleanly — usually 8 to 15 mm on industrial sizes.
Failure modes are predictable. If the bull gear shifts axially because a thrust collar wears, one helix carries more load than the other and pitting starts on the overloaded flank within a few hundred hours. If lubrication oil film breaks down at the V apex (where chip evacuation is hardest in herringbone designs), micropitting shows up first at the centre of the face. And if the two halves were ever cut on separate setups without indexing properly, you'll measure a phase mismatch — the teeth on one side lead or lag the other side by a tooth thickness fraction, and the gear will never run quiet no matter how good the bearings are.
Key Components
- Right-hand helix half: Carries half the tangential load and produces an axial thrust component pointing one way along the shaft. Helix angle typically 25°–35°, ground to within ±0.005 mm lead variation over the face width on industrial gears.
- Left-hand helix half: Mirror of the right-hand half, producing equal and opposite axial thrust. Helix angle must match the right-hand side to better than 0.05°, otherwise residual thrust loads the shaft bearings and the mesh runs uneven.
- Centre relief groove (double-helical only): Machined gap between the two helices, 8–15 mm wide, to give the hob or shaper cutter clearance at runout. Herringbone variants skip this groove and require a special slotter such as the Sykes generator.
- Shaft and journal bearings: Carry only radial load because axial thrust cancels internally. This is the design payoff — bearings can be sized for radial duty alone, often plain white-metal journals on large marine sets rather than thrust bearings.
- Lubrication jets: Direct oil into the mesh and into the centre groove. Flow rates of 5–15 L/min per mesh are typical on a 2 MW marine reduction unit. Too little flow and micropitting starts at the V apex within 500 operating hours.
Where the V-toothed Gear Is Used
V-toothed Gearing turns up wherever high power, low vibration, and zero net thrust matter at the same time. Marine propulsion, heavy industry, and large prime movers all lean on this geometry because the alternatives — straight spur gears or single helicals with massive thrust bearings — either run too noisy or cost too much to support. Citroën built its early reputation on this gear shape, which is why the company logo is two stacked chevrons.
- Marine Propulsion: The main reduction gearbox between a MAN B&W two-stroke diesel and the propeller shaft on container ships such as the Maersk Triple-E class uses double helical bull gears to transmit upward of 60 MW without thrust loading the slow-speed shaft.
- Steel Rolling Mills: Pinion stands at SSAB's Oxelösund plate mill in Sweden run V-toothed gear sets to split torque between upper and lower work rolls, where reversing loads would tear single-helical bearings apart within months.
- Power Generation: Steam turbine reduction gearboxes on geared turbo-generator sets, like those built by MAAG Gear in Switzerland, use double helical first reductions to step down 6,000 RPM turbine speed to 1,500 RPM generator speed.
- Cement Plants: Central drives on FLSmidth ball mills use herringbone gear sets between the motor and the mill shell to handle the 5–10 MW of grinding power without axial loads on the trunnion bearings.
- Automotive History: André Citroën's first business, before founding the car company, was manufacturing herringbone-cut steel gears in Paris from 1900 onwards — the chevron logo on every Citroën vehicle today is a stylised V-toothed gear tooth.
- Heavy Mining: Bucket-wheel excavator slew drives at lignite mines such as Garzweiler in Germany run V-toothed reducers in the final stage to transmit hundreds of kilowatts at very low RPM with no axial reaction into the slew ring.
The Formula Behind the V-toothed Gear
The key sizing equation for a V-toothed Gear is the axial force component on each helix half. You compute it because the whole reason for choosing this geometry is to make sure the two halves cancel cleanly. At the low end of the typical helix-angle range — around 20° — the axial component is modest and a single helical with a thrust bearing might do the job cheaper. At the high end, 35° and above, you get exceptional mesh overlap and quiet running, but the per-half axial force gets large enough that any helix-angle mismatch produces serious residual thrust. The sweet spot for industrial drives sits at 28°–32°, where you get most of the smoothness benefit without the geometry becoming hypersensitive to manufacturing error.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Fa | Axial force on one helix half (cancelled by the opposite half in a V-toothed gear) | N | lbf |
| Ft | Tangential force at the pitch circle, computed from torque and pitch radius | N | lbf |
| β | Helix angle of one half (the V is symmetric, so each half has angle β) | degrees | degrees |
| T | Input torque on the pinion shaft | N·m | lbf·ft |
| rp | Pitch radius of the pinion | m | in |
Worked Example: V-toothed Gear in a paper machine main drive gearbox
Sizing the first-reduction V-toothed gear set on a Voith paper machine main drive at the Stora Enso Skoghall mill in Värmland Sweden, where a 2.4 MW four-pole motor at 1,485 RPM drives into a pinion that needs to step down to 380 RPM at the dryer-section line shaft. The pinion has a pitch radius of 90 mm and the design team is choosing the helix angle for each half of the V.
Given
- P = 2400 kW
- Nin = 1485 RPM
- rp = 0.090 m
- βnominal = 30 degrees
Solution
Step 1 — compute the input torque from power and speed:
Step 2 — compute tangential force at the pinion pitch radius:
Step 3 — compute axial force per helix half at nominal 30° helix angle:
At the low end of the typical range, β = 20°, the axial force per half drops to Fa,low = 171,470 × tan(20°) ≈ 62,400 N. That is small enough that a single-helical with a properly sized tapered roller thrust bearing could carry it — the V-tooth geometry isn't earning its keep at this angle.
At the high end, β = 35°, Fa,high = 171,470 × tan(35°) ≈ 120,000 N per half. This is where V-toothed Gearing pays off: 120 kN is far beyond what you'd want a thrust bearing to carry continuously on a 24/7 paper-machine duty, but with two helices in opposition the shaft sees zero net axial load. Quiet running and high contact ratio come almost for free.
Step 4 — confirm the sweet spot. At 30° you get tan(30°) = 0.577, meaning each half generates 99 kN. A 0.05° helix angle mismatch between the two halves leaves a residual thrust of about 170 N — small, manageable, and well within what the journal bearing's locating collar can handle.
Result
Each helix half generates 99,000 N of axial force at the nominal 30° helix angle, and the V-toothed geometry cancels both halves to roughly zero net thrust on the shaft. At 20° the per-half force is only 62 kN — modest enough that the V-tooth complexity isn't justified — while at 35° each half pushes 120 kN, which is exactly where the cancelling geometry becomes essential rather than optional. The 28°–32° band is where most industrial paper-mill and marine designs settle. If you measure residual axial movement on the pinion shaft above 0.1 mm under load, the most likely causes are: (1) helix angle mismatch between the two halves exceeding 0.05° because the cutter setup drifted between the two passes, (2) thermal growth offsetting one helix relative to the other if the gear body wasn't symmetric about the centre groove, or (3) a worn axial locating collar letting the shaft float far enough that one helix begins carrying disproportionate tangential load and amplifying the asymmetry.
When to Use a V-toothed Gear and When Not To
V-toothed Gearing competes mainly with single-helical and straight spur designs. The decision usually comes down to power level, noise budget, and how much you want to spend on bearings. Below roughly 500 kW the case for V-tooth is weak — a single helical with a decent thrust bearing wins on cost. Above 2 MW the V-tooth becomes the default in serious industrial duty.
| Property | V-toothed Gear (double helical / herringbone) | Single helical gear | Straight spur gear |
|---|---|---|---|
| Net axial thrust on shaft | Zero (cancels internally) | High — proportional to tan(β) | Zero |
| Typical helix angle range | 25°–35° | 10°–20° (limited by thrust) | 0° |
| Power capacity per stage | Up to 70 MW (large marine sets) | Up to ~5 MW practical | Up to ~2 MW practical |
| Manufacturing cost (relative) | 3×–5× spur cost | 1.5×–2× spur cost | Baseline |
| Noise at full load | Lowest — high contact ratio | Low | Highest — pure radial impacts |
| Bearing requirement | Radial only — journal or roller | Radial + heavy thrust bearing | Radial only |
| Sensitivity to helix mismatch | High — 0.05° causes residual thrust | N/A | N/A |
| Typical service life (industrial) | 100,000+ hours | 60,000–100,000 hours | 30,000–60,000 hours |
Frequently Asked Questions About V-toothed Gear
If your gear is being cut on a hob or shaper, you need the centre groove because the cutter needs runout space — that's a double-helical. If you have access to a Sykes-type generator that can cut both helices simultaneously without a groove, you get a herringbone, which has the advantage of slightly higher load capacity per face width because the full face is cutting teeth.
Practically, anything above 500 mm pitch diameter is almost always cut as a grooved double-helical because the equipment to cut a true continuous herringbone at that scale is rare and slow. Below 200 mm the herringbone is often preferred because the centre groove eats too much percentage of the face width.
Twice-mesh-frequency excitation almost always points to a phase error between the two helices — the teeth on one side are angularly offset from the teeth on the other side by a small fraction of the circular pitch. Visual inspection won't catch it; you need a coordinate measuring machine or a tooth-trace recording.
The common cause is indexing the gear blank between the two cutting passes without using a registered fixture. Even 0.1° of indexing error puts the two halves out of phase enough that each tooth pair on one side meshes slightly before its counterpart on the other side, producing the doubled excitation. Fix is regrinding the second helix using the first as the angular reference.
Usually yes, and it's a common upgrade path on older industrial gearboxes that have started shedding thrust bearings. The radial loads stay almost identical because tangential and radial force components don't change with the V-tooth geometry — only the axial component cancels. So your existing radial bearings are fine.
What you do need to check is the housing axial length. A V-toothed equivalent of a single-helical face-width gear is typically 10–20% wider because each helix needs its own face plus the centre groove. If your housing doesn't have that much axial room you'll need to drop face width and recheck Hertzian contact stress.
Drift under load with cancelling geometry means the cancellation isn't perfect. The three culprits in order of likelihood: (1) thermal expansion is asymmetric because the oil is cooler on one side of the mesh than the other, producing a slight helix-angle differential under operating temperature; (2) the two halves were ground at slightly different lead values, so under deflection the contact patch on one helix walks faster than the other; (3) the load is itself asymmetric because the input shaft has a bending mode that loads one helix more than the other.
Quick diagnostic: measure shaft float at 25%, 50%, and 100% load. Linear growth with load points to lead mismatch. Float that appears suddenly above a temperature threshold points to thermal asymmetry.
Probably not. At 200 kW input power, the axial force on a single helical at 15° helix angle works out to a few thousand newtons — easily handled by a standard tapered roller thrust bearing that costs a fraction of the V-tooth machining premium. The cost crossover where V-tooth starts winning on total installed cost is usually around 800–1,500 kW depending on local labour rates.
The exception is acoustic-sensitive applications. If the mixer is in a food plant where noise regulations bite, the lower mesh excitation of a high-helix V-tooth can be worth the money even at low power. Otherwise pick single helical and put the savings into better bearings.
For a single helical, the optimum is usually 12°–15° because higher angles drive thrust bearing cost up faster than they reduce mesh-induced radial vibration on the radial bearings. For a V-toothed gear, that constraint disappears, so you push the helix angle up to where contact ratio plateaus — typically 30°–32°.
Going past 35° gains very little additional contact ratio (it's asymptotic) but starts making the gear more sensitive to manufacturing error, raising the cost of holding tolerance. So the practical answer is: aim for 30° and only go higher if you have strict noise targets and a top-tier gear grinder available.
References & Further Reading
- Wikipedia contributors. Helical gear. Wikipedia
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