Finding the diameter of a Triple Thread Worm Gear

Question

For a Board Exam Review:

A triple thread worm has a diameter of 3 inches. The wheel has 25 teeth and a pitch diameter of 5 inches. Material for both the worm and the wheel is of phosphor Bronze. Compute the Helix Angle

Answer is 0.2

Helix Angle can be obtained by trigonometry:

$${ \tan(H) = \frac{\pi \times D_{worm}}{L} }$$ $${ L = N_t * P_a }$$

Where L is the lead, N is the number of threads and P is the Axial Pitch.

$${ L = 3threads * 3in }$$

Well thats where I stopped. I don't know how to find the diameter of the worm gear without it being explicitly given to me. I tried other formulas but they were more of the diameter of the wheel instead of the gear. Is there a formula for solving the diameter of the gear?

Answer 1

If I get your descriptions right you have everything you need given. You can use the pitch diameter.

$$tan(H) = \frac{\pi \cdot d_p}{N_t \cdot P_a}$$

$$tan(H) = \frac{\pi \cdot 5\:\mathrm{in}}{25 \cdot 3\:\mathrm{in}}$$

$$tan(H) = \frac{5\pi}{75}$$

$$tan(H) = \frac{\pi}{15}$$

$$H = arctan \left( \frac{\pi}{15}\right)$$

$$H = ~ 0.20 \:\mathrm{rad}$$

There you go. Please remember to include the units if you post an answer. An angle of 0.2 could have been degree, too. At least I wasn't sure until after I calculated it.