Spur / helical force components
Gear mesh force
Inputs
User-entered torque at the stated gear pitch circle; transients are excluded.
User-entered operating pitch diameter; geometry is not derived.
User-entered transverse working pressure angle in degrees.
User-entered helix angle in degrees; use 0 for a spur mesh.
Results
Pitch-line tangential force
2,500
Declared-angle radial force
909.93
Declared-angle axial force
669.87
Resultant mesh force
2,743.5
Ft = 2T/dp; Fr = Ft·tan(αt); Fa = Ft·tan(β); FN = √(Ft² + Fr² + Fa²)
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Axial response · Beam deflection & reactions · Elastic stability · Solid-shaft torsion
Method
Formula, when it applies, and when it does not
Calculate pitch-line tangential, radial, axial, and resultant force components from torque, pitch diameter, transverse pressure angle, and helix angle.
Ft = 2T/dp; Fr = Ft·tan(αt); Fa = Ft·tan(β); FN = √(Ft² + Fr² + Fa²)
When
- Parallel-axis spur or helical mesh
- Declared pitch diameter
- Declared transverse pressure and helix angles
- Static pitch-circle force approximation
Don’t
- This is a static pitch-circle force decomposition for a user-defined parallel-axis spur or helical mesh. It excludes tooth geometry, mesh stiffness, shaft/bearing support, backlash, lubrication, vibration, tooth strength, durability, safety, and approval.
Shigley's Mechanical Engineering Design