Saw-tooth worm gearing combines asymmetric tooth flanks with a worm that narrows toward its middle. Hiscox figure 910 shows this concave worm beside its wheel. The animation illustrates that arrangement; the calculator separately compares ideal forward and reverse friction relationships for selected angles and friction.
Ideal Asymmetric Worm-Friction Calculator
Explore a selected ideal asymmetric worm-friction model beside a normalized contact schematic.
Equation Used
- Lead, working-flank and back-flank angles are selected ideal angles.
- The selected friction coefficient is constant and is adjusted by cos α in the retained model.
- A zero reverse-efficiency result represents the model's static self-locking condition only.
- Exact tooth geometry, lubrication, speed, temperature, strength, wear, vibration and ratings are excluded.
The calculator does not define tooth count, center distance or conjugate tooth geometry; the 40-tooth animation is illustrative.
Normalized worm-and-wheel contact schematic
The animation shows a concave worm beneath an asymmetric-tooth wheel. The worm rotates about its horizontal shaft, advancing the 40-tooth wheel by one tooth per worm revolution. The shafts are perpendicular. Separate lower sketches show the selected lead angle and flank angles.
The tooth count, center distance, modules and conjugate tooth surfaces are not inputs, so the drawing establishes topology and directional contact only—not a manufacturable tooth form.
What the calculator determines
Select lead angle, an assumed friction coefficient, working-flank angle and back-flank angle. The calculator returns ideal forward efficiency, ideal reverse efficiency, the selected reverse-lock margin and the effective back-flank friction angle.
It does not calculate ratio, torque capacity, contact stress, temperature, lubrication behavior, wear, backlash, shaft or bearing loads, strength, service life or safe holding capacity.
Selected dry sliding-friction model
φw = atan(μ/cos αw) and φb = atan(μ/cos αb). Ideal drive efficiency is tan γ/tan(γ + φw). Ideal reverse efficiency is max[0, tan(γ − φb)/tan γ]. The selected lock margin is φb − γ.
The zero clamp denotes no reverse motion predicted by this static model; it is not an equipment holding rating.
Selected-input arithmetic
At γ = 5°, μ = 0.13, αw = 14.5° and αb = 35°, the model gives φb ≈ 9.02° and a lock margin of about 4.02°. Reverse efficiency is therefore clamped to zero in the selected model.
Ideal friction and actual gear behavior
These equations provide a simplified dry sliding-friction comparison. Real worm gearing depends on tooth geometry, ratio, materials, surface finish, lubrication, speed, temperature, deflection, manufacturing error and vibration; static and dynamic friction may differ.
The selected friction coefficient and angles do not define a complete gearset. Detailed tooth contact, shaft and bearing loads, materials, lubrication and operating conditions require a separate gear design. A positive calculated lock margin does not establish safe holding.
Questions
Does a positive lock margin guarantee holding?
No. It is only the result of the selected ideal friction model.
Why can reverse efficiency be zero?
When γ ≤ φb, this static model predicts no spontaneous reverse motion and the displayed reverse efficiency is clamped to zero.
Does the animation define a gear ratio?
The illustrated single-start worm advances a 40-tooth wheel, giving 1:40 motion. That example is fixed; the friction calculator does not select a gear ratio.
Can this size a hoist or safety device?
No. It contains no load, torque, strength, brake, redundancy or regulatory model.
Technical references
- OpenStax University Physics, Friction — static and kinetic friction concepts.
- NIST Special Publication 811 — SI units and quantity notation.
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