Calculate worm gear torque from tangential load and pitch radius, or determine output torque and speed from power, ratio, and efficiency.

Use the tangential tooth-force component and pitch radius of the same gear.

Worm Gear Torque Formula

The following formula is used to calculate the Worm Gear Torque. 

Twg = L × r
  • Where Twg is the Worm Gear Torque (N-m)
  • L is the tangential tooth-load component (N), not the total contact force 
  • r is the radius of the pitch circle (m) 

Choose Torque from tooth force, Tangential tooth force or Pitch radius. Use the tangential component and pitch radius of the same gear: T = F × r. In Output torque from input power, n_out = n_in ÷ i, P_out = P_in × efficiency/100 and T_out = P_out ÷ (2πn_out/60). The reduction ratio i = input speed/output speed is at least 1. Efficiency examples are not predictions; this is a forward steady-state estimate, not a strength, thermal, starting-torque or self-locking check.

How to Calculate Worm Gear Torque?

The following two example problems outline how to calculate the Worm Gear Torque.

Example Problem #1:

  1. First, determine the tangential tooth load (N). In this example, it is 50 N.
  2. Next, determine the radius of the pitch circle (m). For this problem, the radius of the pitch circle (m) is calculated to be .23.
  3. Finally, calculate the Worm Gear Torque using the formula above: 

Twg = L * r

Inserting the values from above and solving the equation with the imputed values gives: 

Twg = 50 * .23 = 11.5 (N-m)

Example Problem #2: 

Using the same process as example problem 1, we first define the variables outlined by the formula. In this case, the values are:

tangential tooth load (N) = 1000

radius of the pitch circle (m) = .10

Entering these values yields:

Twg =1000 * .10 = 100 (N-m)