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Force Analysis in Helical Gears

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The resultant force Fn acting on the tooth of a helical gear can be resolved into the following components. **PSG 8.56**

Ft = tangential component,

Fr = radial component,

Fa= axial component or thrust load

From the Geometry of the Helical Gear shown in the figure,

$\mathrm{F}_{\mathrm{r}}=\mathrm{F}_{\mathrm{n}} \sin \emptyset_{\mathrm{n}}$

$\mathrm{F}_{\mathrm{a}}=\mathrm{F}_{\mathrm{n}} \cos \emptyset_{\mathrm{n}} \sin \Psi=\mathrm{F}_{\mathrm{t}} \tan \Psi$

$\mathrm{F}_{\mathrm{t}}=\mathrm{F}_{\mathrm{n}} \cos \emptyset_{\mathrm{n}} \cos \Psi$

The tangential component is calculated from the applied torque, $M_{t}$ and radius of pitch circle, r as $F_{t}=\frac{M_{t}}{r}$

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