What is a Worm Gear?

A worm gear set consists of a worm (a screw-like cylinder) that meshes with a worm wheel (a gear). Worm gears provide very high gear reduction ratios in a compact package, and many designs are self-locking — the wheel cannot drive the worm.

Key Parameters

• Worm Threads (Starts): The number of helical threads on the worm. Single-start gives highest ratio; multi-start increases efficiency.
• Wheel Teeth: The number of teeth on the worm wheel.
• Diameter Factor (q): Ratio of worm reference diameter to module: d₁ = q × m. Higher q gives a stiffer worm.
• Lead Angle: The helix angle of the worm thread. Larger angles increase efficiency but reduce self-locking.

Formulas

• Gear Ratio: i = N₂ / z₁ (wheel teeth / worm starts)
• Worm Pitch Diameter: d₁ = q × m
• Wheel Pitch Diameter: d₂ = N₂ × m
• Lead: L = z₁ × π × m
• Lead Angle: γ = arctan(L / (π × d₁))
• Center Distance: a = (d₁ + d₂) / 2

Applications

• Elevator and conveyor drives
• Steering mechanisms
• Guitar tuning pegs and instrument mechanisms
• Heavy machinery speed reduction