Bevel and Worm Gear Force Analysis

Bevel and worm gear force analysis

Ref: Mechanical Engineering Design, Second Edition by Joseph Edward Shigley

Worm Gear

p. 543-550

As shown in figure 12-16 on page 544 the forces exerted on the worm gear are given by

Where is the pressure angle, is the lead angle and µ is the coefficient of friction. For our worm gear radians and radians. An unknown is the coefficient of friction between a nickel plated stainless steel worm and a molybdenum worm gear. We know it takes, as an upper limit 100 in.lbs to rotate the jaw with the tubes clamped. We also know it takes 6 in.lbs to rotate the jaw through the worm. Also, the gear reduction through the worm is 80. So the efficiency of the worm is

Using equation 12-26 and solving for the coefficient of friction we find

From the torque and the pitch radius of the worm we can find the tangential force on the worm:

From this we can find the total force and the other two force components:

And so

The thrust on the worm is 60 lbs and the transverse component is

Keep in mind that these forces are at the worm pitch diameter, not on the axel axis. So, to be thorough, the moment about the gear should be taken into consideration when computing the load on the bearings.

Bevel Gear

p. 555-558

The transmitted load through a bevel gear is given by

Where W_t is the transmitted load tangent to the gear radius, T is the torque and r_av is the pitch radius.

The torque transmitted through the worm gear is 6 in.lbs. This torque is transmitted through the Geneva Mechanism with a driven wheel minimum radius of 0.25 in and the driver having a radius of 0.75 in. The torque on the bevel is therefore,

The average pitch radius for the gear is 7/16 in. So,

The total force on the gear also has two other components, radial (W_r) and axial (W_a) as shown in figure 12.23 p. 557 in the above referenced book. They are determined by

being the pinion pitch angle and  being the gear pitch angle.

Where N_G and N_p are the gear and pinion teeth numbers.

The resultant forces are

The pinion is 90 degrees to the gear and so the radial and axial forces are swapped. So, the thrust force on the pinion axel is 9.1 lbs. The transverse force is