Bearings & Power Transmission

Gear Cutting Cycle Time: Hobbing, Shaping, and Grinding Trade-offs

Gear ratio = driver teeth / driven teeth = output torque / input torque (inverted from speed ratio). Here is how to calculate gear ratios and use them for power transmission sizing.

Gear Ratio = Number of Teeth on Driven Gear / Number of Teeth on Driver Gear = Input Speed / Output Speed. For a driver gear with 20 teeth meshing with a driven gear with 80 teeth: gear ratio = 80/20 = 4:1. If input speed = 1,800 RPM, output speed = 1,800/4 = 450 RPM. Output torque = Input Torque x Gear Ratio x Efficiency. At 10 Nm input torque and 98% mesh efficiency: output torque = 10 x 4 x 0.98 = 39.2 Nm. Power is conserved (minus friction losses), so speed reduction multiplies torque by the same ratio.

Multi-stage gearbox total ratio = product of individual stage ratios. For a 3-stage gearbox with ratios of 3:1, 4:1, and 3:1: total ratio = 3 x 4 x 3 = 36:1. Total efficiency = product of individual stage efficiencies. At 98% per stage: total efficiency = 0.98^3 = 94.1%. Each additional gear stage adds complexity and reduces efficiency. Worm gear sets have lower efficiency (50-90% depending on lead angle) compared to helical gears (97-99%). For high-ratio, high-efficiency applications, planetary gearboxes achieve ratios up to 100:1 in a single stage at 95-98% efficiency.

Gear mesh frequency = shaft RPM x number of teeth. For a 40-tooth gear on a 1,200 RPM shaft: mesh frequency = 1,200 x 40 = 48,000 cycles/min = 800 Hz. Gear mesh frequency is the primary vibration signature for gear health monitoring. A vibration peak at mesh frequency that grows in amplitude over time indicates gear wear or damage. Sideband frequencies around mesh frequency indicate modulation from shaft eccentricity or gear manufacturing error.

Gear module (metric) or diametral pitch (inch) determines tooth size and load capacity. Module = pitch diameter (mm) / number of teeth. Common modules: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5. Larger module means larger teeth, higher load capacity, lower speed. For the same center distance, larger module reduces the number of teeth per gear, increasing gear ratio options. Gear strength increases approximately with the square of the module (contact fatigue) and linearly with face width.

Gear lubrication selection is critical for life and efficiency. For pitch line velocities below 3 m/s: grease or splash lubrication. For 3-15 m/s: circulating oil lubrication. Above 15 m/s: pressure-jet oil lubrication directly to the mesh. Viscosity selection depends on operating temperature and speed. ISO VG 220 is common for industrial gearboxes at moderate speeds and temperatures. At high temperatures or where efficiency is critical, synthetic oils (PAO, PAG) reduce losses by 0.5-1% per stage compared to mineral oils.

Published 2026-05-28.