Tip Relief and Gear Design

I can answer part 2 and part 3 of the question.

When the mating gears go into operation, there will be a deflection taking place on both the mating teeth due to elastic deformation on the contact zone.

Due to this , the incoming gear of the drive will bite into the driven gear instead of rolling into contact (those are not still in contact hence not deformed)

To avoid this biting into (which will continue and will not be self corrected) the incoming zone (ie the tip) are corrected by giving a recess, usually curved. These are called tip modification. Also the wedge created by the undercut helps in the lubrication of the contact.

So these are required,

The amount will depend on the amount of deformation expected- the worst case scenarion. may be covered under gear design books/ standards. However as far as I know it is the gear designers prerogative and the shape of the relief also is decided by them.

I like your article, but still i am intrested in formuale that is used to calculate tip relief amount

Interesting question from the OP. It has been a long time since I last worked with tip-relieved gear and pinion sets, and this was in my days spent designing sections of printing presses.

Interestingly, we did this not so much to avoid tooth stress and the resulting "noise" of operation, but we did it to avoid the minute changes in peripheral speed as the teeth of each gear engaged and disengaged. This could cause fine lines and dot to slur and result in poor quality. The term for such evidence is "gear marks" and it is quite evident on the finer printing tasks.

The gears that caused the most issues were those of smaller tooth counts; specifically those for small circumference printing cylinders. In this case (14" circumference) the gears typically had fifty-six (56) teeth and this small quantity of teeth made the generation of a true involute curve more difficult.

As far as formulae are concerned-I cannot furnish one. Perhaps the OP needs to contact a shop who specializes in the production of smooth, precise gears of low tooth count. Perhaps it is done by trial and experience, but I doubt that in all cases.

Best Regards,

Ing. Robert Forbus

The gear softwares have the calculation but they are all dependent on the tooth-stress (which as I mantioned causes gear deflection).

The exact formula I don't know, and the basic designers may know/used to know and now is inbuilt in the softwares along with the modifications, crowning etc,

I have to unload this brain f... if you will. Because of the trouble that the point of contact creates in regards to gear/teeth/friction/meshing I pondered a remedial shape. Something like a 'ball & socket' set up might prove to be a more vigorous pairing. Mostly because there would be a wider contact surface between the drive & the driven gears. I see specially better lubrication dynamics too. (which is a component of the closer tolerances). No- I'm not a trained engineer. Thanks Carlos PS If there were two (or more) sets of engaging 'gears'. One set off set to engage when the other is disengaging.

"The choices you make might be mistakes but its never too late to turn around." Johnny Lang- musician

Just a few remarks, in no particular order:

1. Tip relief (also termed 'correction') is used to counter premature contact (as said before) caused by both elastic deflections and pitch/ profile errors, as well as to make the stiffness more uniform throughout the mesh cycle. Both interventions affect gear dynamics but in different ways. A popular -if slightly crude- formula (found in older texts, i.e in R. G Munro, Data item on profile and lead correction, BGA Technical Publications, 1988):

relief req'd=max elastic deflection + max pitch/profile error

(if you are looking for a fast formula, there you have it. a bit of FEA will tell you the deflection -alternatively Cornel's compliance formula, I forget source though- and measuring errors should be straight-forward if you have the right equipment)

However, gears not operating at constant load have different deflections, and over-relieving can be as bad as under-relieving. Fortunately, there seems to exist a 'flat region' in the parametric space where discrepancies between design and real-life do not matter as much, i.e. in Spitas:

http://www.geartech.net/html/dynamics.html

2. To further complicate things, 'long relief' vs. 'short relief' schemes have a significantly different effects on the resulting dynamics. I could give you the info, but only if you are very interested and generally knowledgeable in gears in order to follow through. For most practical purposes, you'll never need to know these details.

3. For low-speed applications no, it is not necessary. Gears will 'run-in' anyway. Or better, just apply a small tip chamfer, which is quite usual in such cases.

4. For high speeds, you need tip relief or suffer terrible dynamics.

5. As indicated by the sensitivity analysis in the link above, it only makes sense to relieve modestly/ highly accurate gears. With innacurate gears you are flying blind, may fall outside the 'flat region' and end up doing more harm than good.

6. Lest you didn't know, material removal for tip-relief is in the order of microns (well, depending on gear size). Anything done crudely will fall under the category 'chamfer' instead (see point 2)

7. To answer parts #2 and #3 of your question in a nutshell: #2: important in high-speed/ accuracy apps, #3: generally not unless high-speed

8. I may be forgetting a lot of other things right now.

By the way, in light of the above, those who need tip relief usually know it. Evidently you are purchasing (not manufacturing), so state your speed and load requirements to the manufacturer and they will advise on the best option (that they can offer)

I hope this helps

But please let me know how to calculate deflection in gear teeth?

You should really pay attention to the replies. As said before, either:

1. FEA

2. Google:Cornell+compliance->R.W. Cornell, Compliance and stress sensitivity of spur gear tooth, J. Mech. Des. Trans ASME 103 (1981)

I had a look at your few other posts. While trying to learn about gears from scratch is admirable, it's also hopeless. If you are a practicing engineer, learning like that is very dangerous.

My honest advice: You shouldn't go around calculating things with improper training (that includes internet queries). Gears, being one of the most difficult, ill-understood and dense subjects, are the worst possible subject you could pick.

you are right.

but FEA is also based on formulae.

Tip relief is calculated based on knowhow or specialised software. Tooth deflections and stiffnesses alter along the line of action, so a manual calculation might not be sufficient.

There is a lot of software available, albeit very expensive, that can calculate the most optimal flank topology (tip relief, crowning, helix correction...), based on shaft, bearing and tooth deflections.

My recommendation would be, don't try this at home, go to specialists.