Worm Gear Forces

Calculating Final Forces

Now that we've got the forces from the gear mesh, we can calculate tangential, radial, and axial forces which are necessary to determine shaft and bearing loads.  To start we either have to assume an input torque to the worm or an output torque from the gear.

Worm Tangential and Gear Axial Forces

We will assume we know the input torque, and the worm tangential force is determined by:

Ftw = Ti ÷ rpw

Where Ti is input torque, and rpw is the pitch radius of the worm.  NOTE: Appropriate unit conversion must also be incorporated.

From earlier, we know that Ftw = Fag.  Also Ftw = Fx + Ffx therefore:

Ftw = Fn [(cos Φn sin λ) + μ cos λ]     {Equation 1}

Worm Axial and Gear Tangential Forces

The worm axial force is given by:

Faw = Fz - Ffz = Fn [(cos Φn cos λ) - μ sin λ]     {Equation 2}

Solving equation 1 for Fn and substituting into equation 2:

Faw = [Ftw ((cos Φn cos λ) - μ sin λ)] ÷ [(cos Φn sin λ) + μ cos λ]

From earlier, Faw = Ftg.

The gear output torque is:

To = Ftg rpg

Where To is output torque, and rpg is the pitch radius of the gear.  NOTE: Appropriate unit conversion must also be incorporated.

Worm Radial and Gear Radial Forces

The worm radial force is given by:

Frw = Fy = Fn sin Φn     {Equation 3}

Solving equation 1 for Fn and substituting into equation 3:

Frw = [Ftw sin Φn] ÷ [(cos Φn sin λ) + μ cos λ]

From earlier, Frw = Frg.