Bevel Gears Force Analysis

Force Analysis

The forces in a straight bevel gear has the same components that a helicoidally gear or a spur gear have. This components are tangential force, axial force and radial force. Inthe case of a straight bevel gear, the forces are these:
Wa=Wttanϕsenα
Wr=Wttanϕcosα
W=Wtcosϕ
Wt, Tangential component: This force produces the torque.
Wa, Axial component: This force produces athrust along the shaft direction
Wr, Radial component
ϕ, Pressure angle
α, Pitch cone angle

Usually, we assume that the load is normally distributed along the tooth, but in reality we have avariation, because the tooth doesn’t have the same width.
Taken from http://www.frbb.utn.edu.ar/carreras/materias/elementosdemaquinas/cap09-02.pdf

Taken fromhttp://www.frbb.utn.edu.ar/carreras/materias/elementosdemaquinas/cap09-02.pdf

In the case of a spiral bevel gear
Wa=WtcosΨ(tanϕnsenα∓senψcosα)
Wr=WtcosΨ(tanϕncosα±senψsenα)

The upper signs of the two equations are employed whendealing with a pinion with a clockwise spiral, and the inferior signs of the two equations are used when dealing with a pinion with a counterclockwise spiral.

For best results calculating the forces inthe above equations, we must employ the appropriate α. αp, if we have a pinion, and αg if we have a gear.
Taken from http://nptel.iitm.ac.in/courses/IIT-MADRAS/Machine_Design_II/pdf/2_13.pdf

Takenfrom http://nptel.iitm.ac.in/courses/IIT-MADRAS/Machine_Design_II/pdf/2_13.pdf



For the tangential force, Wt, it can be determined by the torque applied with its mean radius.
Wt=2TdmNumeric Example
Two shafts with a 90º between both, are connected by a par of bevel gears. This gears have a ratio of 2.5:1. The module of 20º full depth involute teeth at outer radius is 5mm.The teeth number is 30. If the power transmitted is 10Kw at 400rpm on the pinion, determine the tangential force at the mean radius, and the axial thrust on the pinion and the gear. B=67mm...