# Finding the diameter of a Triple Thread Worm Gear

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

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?

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.

• Thanks but I notice you used L = number of teeth * Axial Pitch; My definition of L = number of threads * Axial Pitch. Is this possible? Aug 3, 2015 at 1:25
• I could be wrong here however from my understanding the number of teeth on the wheel has an influence on the angle whilst I don't really see why the 'lenght' of the worm should factor in here, thus why you would use the number of threads instead of the number of teeth. Aug 3, 2015 at 9:04