Documentation/Modules/Internal Gears & Rack

Internal Gears & Rack

Internal spur and rack-and-pinion strength screening

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Indicative closed-form or numerical model

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

  • Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
  • Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

CheckINDUSEUISO
Bending strength safety factorimplementedimplementedimplementedimplemented
Contact (pitting) strength safety factorimplementedimplementedimplementedimplemented
Scuffing safety factorplannedplannedplannedplanned
Bending fatigue safety factorimplementedimplementedimplementedimplemented
Contact fatigue safety factorimplementedimplementedimplementedimplemented
Micropitting safety factorplannedplannedplannedplanned

Internal Gears & Rack (internal-gears-rack)

Purpose

Screen internal spur gear pairs and rack-and-pinion drives for Lewis bending and simplified Hertzian contact stress.

Physics & theory

Internal gearing uses a pinion meshing inside a ring gear; rack drives convert rotation to linear motion. Tangential force at the pitch line is . Lewis bending uses a higher form factor for internal pinions than external gears. Contact stress uses Hertzian line-contact screening between pitch cylinders.

Governing equations

Numerical method

Closed-form Lewis and Hertz screening via solveInternalGearsRackEngine with type-specific form factors.

Inputs

ParameterDescription
gearTypeinternal or rack
power, speedTransmitted power and pinion rpm
module, faceWidth, tooth countsGeometry
materialYield and elastic properties

Outputs

  • Bending and contact safety factors, pitch diameters, pitch-line velocity.

Design codes & checks

  • Indicative: Lewis + Hertz screening
  • ISO: ISO 6336 reference context (screening)

Assumptions & limitations

  • No microgeometry, scuffing or planetary kinematics. Rack uses representative mating radius for contact only.

References

  1. Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, Ch. 13–14.
  2. ISO 6336-1:2019 — gear rating principles.
Maintainer note: Internal spur and rack Lewis/Hertz screening.