Documentation/Modules/Worm Gear Drive

Worm Gear Drive

Worm efficiency and contact stress screening

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Worm efficiency and contact-stress screening

Assumptions

  • Linear elastic material behavior unless noted otherwise.
  • User is responsible for load combinations and load factors per the selected design code.
  • Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

  • Thermal rating and full AGMA worm worksheets are out of scope.

Engineering checks

CheckINDUSEUISO
Drive efficiencyimplemented———
Contact stress utilizationimplemented———

Worm Gear Drive (worm-gears)

Purpose

Screen worm and worm-wheel drives for efficiency, sliding velocity, contact stress, and thermal load. Worm drives provide high speed reduction in compact envelopes but generate significant sliding and heat.

Physics & theory

A worm is a helical gear with one or few teeth (threads); the worm wheel mates at 90° shaft angle. Lead angle and friction angle determine efficiency: for driving worm. Self-locking occurs when , preventing back-driving.

Sliding velocity along tooth flanks is high compared to spur gears, limiting efficiency and promoting wear. Contact stress uses Hertzian line contact with equivalent radii from worm and wheel geometry. Heat generation must be dissipated to avoid oil breakdown.

Governing equations

Numerical method

Closed-form geometry and efficiency calculations. Friction coefficient from material pair and lubrication. Contact stress screened against allowable; thermal power loss computed for oil bath sizing guidance.

Inputs

ParameterDescription
Worm threads, wheel teethTooth counts
module, faceWidthAxial module and face width
power, speedWorm speed and power
Friction coefficientFrom material/lubrication
Material allowablesContact stress limit

Outputs

  • Gear ratio, efficiency, self-locking flag, sliding velocity, contact stress utilization, heat loss (kW).

Design codes & checks

  • Indicative: Efficiency, contact stress utilization
  • DIN: DIN 3996 worm gear load capacity (reference)
  • ISO: ISO/TR 14521 worm gear rating (reference)

Assumptions & limitations

  • Cylindrical worm with throated wheel; no double-enveloping geometry.
  • Steady-state thermal balance not fully solved — heat loss is screening only.
  • Wear and pitting life not computed to ISO/TR 14521 full method.
  • Manufacturing tolerance effects on contact pattern omitted.

References

  1. ISO/TR 14521:2020. Gears — Calculation of load capacity of worm gears.
  2. DIN 3996:2016. Tragfähigkeitsberechnung von Zylinderschneckengetrieben.
  3. Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 13.
  4. Dudley, D. W. Handbook of Practical Gear Design, 2nd ed.
  5. PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
  6. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.
Maintainer note: Worm efficiency and contact stress.