Root stress and contact stress determine the size of the gears, and they are discussed in another notebook.

Spur gears only generate forces in the gear plane, however helical gears generate an axial force component therefore need to be supported axially as well.

Tangential and radial forces in the gear plane cause bending moments on the supporing shafts.

This normal force, FN, can be decomposed into axial force Fa, radial force Fr, and tangential force Ft.

Figure 1 illustrates the tangential and radial forces in spur gears.

Figure 2 illustrates the normal force and its decomposition in the axial and transverse planes in helical gears.

Because of static equilibrium, the sum of this distributed force must equal the torque applied to the gear.

The moment generated by the tangential force at pitch circle equals the applied torque.

Ft frac2Tdp Considering the projection of the normal force in the transverse plane, the tangential force is one component; the other component is the radial force.

Fr Ft tanalphatw Considering the axial plane, the axial force is one component of the force.

Fa Ft tanbeta Lastly, the normal force is the vector summation of these three components, with its magnitude calculated as.

Geometry and operating conditions are as follows: - Number of pinion teeth is zp 15 - Number of wheel teeth is zw 45 - Normal module is mn 2.5 textmm - Normal pressure angle is alpha 20circ - Helix angle is beta 20circ - Center distance is a 80 textmm - Applied torque on the pinion is T 100 textNm.

The total normal force is then calculated from equation FN sqrtFa2 Fr2 Ft2.

Also, it should that the pinion and wheel will need to be supported, e.g.

Helical Gear Force Analysis