Worm gearing terminology 1

[sboyce]

Forgive my ignorance, I'm a bit of an engineering newbie, just started working and all.
I'm trying to design a non-backdriving worm and worm gear mate. I've read that this condition is satisfied when the worm lead angle is less than the inverse tangent of the coefficient of friction between the worm and worm gear. I think I've got a good pair picked out, but the catalog also lists something called the pressure angle. What is this and how(if at all) does it relate to the worm lead angle?
Also, I'm using a coefficient of friction of 0.18 (bewteen bronze and steel). Is this realistic? Are there other factors I need to consider about the interaction between bronze and steel in such an application?

-Sam Boyce
Asst. Mechanical Engineer

http://www.AppleAid.com

 

[eromlignod]

There is no real relationship between pressure angle and lead angle, though for some multiple-start worms it is sometimes advantageous to use larger pressure angles for the larger lead.

The pressure angle is the angle at which force is transmitted at the point of contact between the gear teeth and is usually standard for a given group of gears, just like spur gears. The two common P.A.'s are 20 and 14-1/2 deg. (and sometimes 25 deg.) This angle is a parameter of the tooth profile and remains the same regardless of the pitch or diameter.

The lead angle of the worm depends on several things.

The diametral pitch of the wormgear is basically a measure of the size of the teeth: a larger pitch number means smaller teeth. It also is indicative of the circular pitch (arc distance between teeth along the pitch circle), and obviously larger teeth will have greater distances between them. This determines how far apart (lead) and how deep the worm threads are, since they have to mate up with the gear.

The diameter of the worm also affects the angle. The wormgear must be cut to fit up with this diameter. The lead angle is basically the angle that the threads are inclining if you opened the thread helix out flat. So in one turn of the worm, you have travelled one circumference of the worm along the helix and one lead of thread upward along the worm axis. A larger diameter worm means a smaller angle and a larger thread lead means a larger angle.

Simple, right? Well, now we add "starts". Starts are individual, independent threads on the worm. An ordinary machine screw has only one start since the same thread traces all the way up the screw. But a worm can have multiple starts. So if you traced a thread on a two-start worm with a red marker, you would find that only every other thread would appear red. That's because there is another separate thread. So with each single turn of the worm, a given thread actually advances two pitches. So such a worm would have a greater lead angle than a single-start worm.

If your wormgear has a relatively large number of teeth (more than 15 or so) and your application isn't a super-high-precision one, then the pressure angle doesn't matter much...pick the cheaper one.

The lead angle affects the irreversibility of the mechanism though. Bear in mind that even if the angle and friction coefficient say that the pair is irreversible, vibration might prove this wrong. If you can stand a little back-driving over time, then don't worry about it, but for a critical applicaion, you may want to add a brake.

Hope this helps without being too verbose

Don
Kansas City