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Machine Design

Worm Gear Efficiency & Self-Locking Calculator

Compute forward efficiency, reverse efficiency, and self-locking threshold from lead angle and friction coefficient. Tooth forces, heat generation, and thermal limits in real time.

Parameters
Lead Angle λ 10.0 °
Friction Coefficient μ 0.050
Gear Ratio i 20
Input Power P 1.0 kW
Input Speed n 1450 rpm
Worm Pitch Diameter d_w 50 mm

Efficiency Formulas

$$\eta_{fwd} = \frac{\tan\lambda}{\tan(\lambda+\varphi)}$$ $$\varphi = \arctan(\mu)$$

Self-locking: $\lambda < \varphi$

$$\eta_{rev} = \frac{\tan(\lambda-\varphi)}{\tan\lambda} \; (\lambda > \varphi)$$
Forward Efficiency η (%)
Reverse Eff. / Lock
Output Torque (N·m)
Output Speed (rpm)
Heat Generated (W)
Tangential Force Wt (N)
Back-driving allowed