Worm and Worm-Wheel Geometry
Worm and worm-wheel geometry - the right-angle, high-ratio, often self-locking gear pair.
Example
You enter
- Worm axial pitch (in) 0.5
- Worm starts (threads, 1-4) 1
- Worm pitch diameter (in) 2
- Worm-wheel teeth N 40
You get
- Lead (in) 0.5
- Lead angle (deg) 4.55
- Gear ratio 40 : 1
- Wheel pitch dia (in) 6.366
- Center distance (in) 4.183
Details, formula, and sources
Lead L = axial pitch x starts, lead angle = atan(L/(pi x worm pitch dia)), ratio = wheel teeth / worm starts, wheel pitch dia = N x axial pitch / pi, center distance = (d_worm + d_wheel)/2. A 0.5 in single-start worm of 2 in pitch dia on a 40-tooth wheel: 0.5 in lead, 4.55 deg lead angle (self-locking), 40:1, 6.37 in wheel, 4.18 in center. A small lead angle (below ~5 deg) tends to self-lock -- why a single-start worm holds a hoist load; a multi-start worm back-drives. Geometry only; the material pair and lube govern load and efficiency. The gear drawing and Machinery's Handbook govern.
lead = axial_pitch x starts; lead_angle = atan(lead/(pi x d_worm)); ratio = wheel_teeth/starts; wheel_pitch_dia = N x axial_pitch/pi; center = (d_worm + d_wheel)/2.
Worm and worm-wheel geometry (Machinery's Handbook; AGMA worm-gearing), first-principles, by name.
The worm-gear lead, lead-angle, ratio, and center-distance relations are standard published gear geometry (Machinery's Handbook).
Estimate. AHJ and licensed professional govern.
Field names used by the API: axial_pitch_in, worm_starts, worm_pitch_dia_in, wheel_teeth, lead_in, lead_angle_deg, gear_ratio, wheel_pitch_dia_in, center_distance_in
- Lead and lead angle lead = axial pitch x starts; lambda = atan(lead/(pi x d_worm))Machinery's Handbook worm gearing
- Ratio and sizing ratio = wheel teeth/starts; wheel pitch dia = N x axial pitch/pi; center = (d_worm + d_wheel)/2gear geometry
- Self-locking a lead angle below ~5 deg tends to self-lock (friction dependent); geometry only, not load/efficiencyscope of this tile