Efficiency of Spiral Gears Calculator

Formula

The formula to calculate the Efficiency of Spiral Gears is:

$\eta = \frac{\cos(\alpha_2 + \Phi) \cdot \cos(\alpha_1)}{\cos(\alpha_1 - \Phi) \cdot \cos(\alpha_2)}$

Where:

$\eta$ is the Efficiency
$\alpha_2$ is the Spiral Angle of Gear Teeth for Gear 2 (rad)
$\alpha_1$ is the Spiral Angle of Gear Teeth for Gear 1 (rad)
$\Phi$ is the Angle of Friction (rad)

Definition

The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power.

Example Calculation

Let's assume the following values:

Spiral Angle of Gear Teeth for Gear 1 ( $\alpha_1$ ) = 0.785398163397301 rad
Spiral Angle of Gear Teeth for Gear 2 ( $\alpha_2$ ) = 0.524471440224197 rad
Angle of Friction ( $\Phi$ ) = 0.41887902047856 rad

Using the formula:

$\eta = \frac{\cos(0.524471440224197 + 0.41887902047856) \cdot \cos(0.785398163397301)}{\cos(0.785398163397301 - 0.41887902047856) \cdot \cos(0.524471440224197)}$

Evaluating:

$\eta = 0.513710250745906$

The Efficiency is 0.513710250745906.

Conversion Chart

Spiral Angle of Gear Teeth for Gear 1 (rad)	Spiral Angle of Gear Teeth for Gear 2 (rad)	Angle of Friction (rad)	Efficiency
0.7	0.524471440224197	0.41887902047856	0.539943911895
0.75	0.524471440224197	0.41887902047856	0.524768669741
0.8	0.524471440224197	0.41887902047856	0.509062161715