Calculation
ηZ = tan γm/tan(γm+ρ′)
Small lead angles favour high ratios but reduce efficiency.
Roloff/Matek Gl. (23.18)
Worm-drive efficiency
Small lead angles favour high ratios but reduce efficiency.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Mesh efficiency ηZ — Mesh efficiency as a decimal, e.g. 0.8 for 80%.
- Lead angle γm — Mean worm lead angle.
- Equivalent friction angle ρ′ — Friction angle derived from friction coefficient and flank angle.
Example
γm=10° and ρ′=5° give ηZ≈0.658 or 65.8%.
Assumptions and limits
Driving worm in steady operation; bearing, seal and churning losses excluded.
Understand Worm-drive efficiency
Worm-drive mesh efficiency is a focused preliminary calculation based on Roloff/Matek. The calculator rearranges the closed-form relationship for every included quantity and deliberately separates this result from a complete component verification.
What does this quantity describe?
With the worm driving, mesh efficiency follows from mean lead angle and equivalent friction angle: ηZ=tanγm/tan(γm+ρ′).
Formula and variables
ηZ = tan γm/tan(γm+ρ′)
ηZ = tan γm / tan(γm + ρ′)
| Symbol / input | Meaning |
|---|---|
| Mesh efficiency ηZ | Mesh efficiency as a decimal, e.g. 0.8 for 80%. |
| Lead angle γm | Mean worm lead angle. |
| Equivalent friction angle ρ′ | Friction angle derived from friction coefficient and flank angle. |
Choose the inputs correctly
γm is mean lead angle. ρ′ represents flank friction including profile-angle influence; ηZ is returned as a decimal.
How to use the calculator
Select the target, enter all remaining quantities for the actual component, and verify the units. Then compare the result with the stated model limits and with the required strength, safety and operating checks.
Worked example
10° and 5° give ηZ=0.658 or 65.8%.
Understand the result and units
As γm approaches ρ′, efficiency falls sharply; the self-locking discussion in the book still does not justify release from an ideal value alone.
The calculator converts internally to coherent SI units. Length, force, torque, stress and angle may therefore use the offered units; dimensionless factors are entered as decimals.
What is taken from Roloff/Matek
Only the closed-form relationship from Kapitel 23.2.3, Zahnwirkungsgrad is used. Tabulated data, material limits and detailed design checks are not silently added; they remain explicit inputs or are expressly outside the model.
Typical applications
Worm-drive mesh efficiency supports option comparison, plausibility checks and early sizing within its machine-element cluster. Releasing a design requires the additional checks described in the cited chapter.
Assumptions, limits and common mistakes
Driving worm and mesh loss only; bearing, seal, churning, temperature and running-in effects are excluded. A driving wheel uses a different relationship.
Common mistake: Typical errors are misreading the effective length or force, entering percentages instead of decimals, and treating a preliminary result as a complete verification. In particular: Driving worm and mesh loss only; bearing, seal, churning, temperature and running-in effects are excluded. A driving wheel uses a different relationship.
Frequently asked questions
Is Worm-drive mesh efficiency a complete strength verification?
No. Driving worm and mesh loss only; bearing, seal, churning, temperature and running-in effects are excluded. A driving wheel uses a different relationship.
Where do the equation and validity limits come from?
Roloff/Matek, Machine Elements, Kapitel 23.2.3, Zahnwirkungsgrad; the local 21st edition was cross-checked against the available 24th edition.
Can I order the calculated value directly as a nominal size?
Only after matching it to available standard or manufacturer series and completing the additional safety, material and operating checks.