AGMA surface endurance strength and AGMA bending strength 6

[noobita]

Does anyone knows how to calculate the AGMA surface endurance strength and the AGMA bending strength?

I'm looking for a general formula (if there is, the ones i know are for steel), if there is? If not, does anyone knows these values for aluminum 2024-t4 and 303 stainless steel ( i need these values to calculate the safety factors).

For example, Sf(safety factor for bending) = (St x Yn/ Kt x Kr)/sigma (at this moment i have all values less the St).
Best regards

 

[israelkk]

Each gear width is necessary in order to estimate their ability to live the stall torque and the maximum torque for the expected life cycle.
Are those gears use rack/profile shift or are as is?

 

[tbuelna]

Is your fatigue life of 10^8 load cycles based on the 13T input pinion?

The knock down factor of 0.70 for fully reverse tooth bending fatigue stress is fine for vacuum melt quality steel alloys.

The allowable fatigue stress limit for a given material will vary based on the reliability rate used. For example, a material at L2 (98% reliability) will have a lower fatigue stress limit than it does at L10 (90% reliability). The statistical reliability rate required in your gear drive is something you must consider when calculating fatigue life. And it will depend on how critical your application is.

 

[noobita]

First of all, thanks again. DO you know if eng-tips has private message? Since would do this proccess much easier.

@israelkk, modifying what i posted about the gears:

(13/54) -> 80dp, face width(F) 2.5mm (0.1inches), x1=0.34 (pinion), x2=-0.34 (gear)
(15/53) -> 80dp, F 3mm (0.12inches), x1=0.34 (pinion), x2=-0.34 (gear)
(15/35) -> 64dp, F 3.5mm (0.16inches), x1=0.34 (pinion), x2=-0.34 (gear)
(13/27) -> 48dp, F 5mm (0.2inches), x1=0.3 (pinion), x2=-0.14 (gear)
(14/39) -> 48dp, F 8mm (0.32inches), x1=0.34 (pinion), x2=-0.34 (gear)

PS: I'm not sure about the profile shift, so these values are only estimates

I'm really trying to find a suitable material (this gears that i have posted are for the dynamixel mx-64, so the design works and material will last).

@tbuelna, the 10^8 cycles are only for the first pinion. The objective is that the entire system lasts at least 20000 hours (if not possible, 10000 hours) in the max continuous torque (so, first pinion should last something like 3x10^8cyles and last stage gear only approximately 3x10^6 cycles (again, this for maximum continuous operation, not operation at stall torque).

 

[israelkk]

As far as I know the SDP, PIC, BERG gears are not corrected (profile/rack shifted) therefore, they will last much less than corrected gears.

10000 hours at 7000 rpm at 8W is 4.2 x 10^9, it is more than 10^8.
You need to specify the gearbox output load at continuous torque and at pick torque and the number of gearbox output RPM in both cases. From this data you go back and calculate the RPM and torque at each gearbox stage and check if the gears can live for the desired cycles 10000/20000 hours definition is not clear unless it continuously rotate at a specific rpm and torque for the whole 10000/20000 hours).

I did a quick check for the pinion made of material at 120 Brinnel hardness (2024 T4) therefore, the gears from SDP, PIC and BERG will not live more than 3000 rotations for the pinion and 22000 for the gear in bending loads. For surface loads they will fail instantly (I used 8W, 7000 rpm).

No matter what material you choose all gears must be custom designed and manufactured. You may get away with 2024-T4 for the pinion but it must have profile shift/rack shift to avoid undercut and excessive sliding velocity. From by experience the pinion is usually not the most loaded gear, generally a middle stage and/or the output stage are the most critical.

 

[israelkk]

Sorry for my previous calculations I used incorrect HP (10 times larger 0.11HP instead of 0.011HP). The pinion and gear from SDP (120 Brinnel hardness (2024 T4)) may be OK for the 8W, 7000 rpm case. The program I used didn't allow the 13 tooth pinion without correction to avoid undercut and with the correction it's OK. However, the gears from the catalog have undercut to my best knowledge. Therefore, they need to be carefully checked.

 

[noobita]

Hi israelkk, once again thanks for your help. The sdp can make the profile shift of the gears by request (from what i read from their website), but at this stage the gears would be custom made. Could you tell me what program did you used (this because i searched online for a lot of programs and couldn't find a suitable one, kissoft seemed the best, but with the tutorial version you can't do much)? I made the calculations in a self made excel worksheet, and according to my calculations i would be needing a material with a hardness of at least 240 (this for last stage), for first stage the 120HB would be ok

Best regards

 

[israelkk]

I use an old program from Fairfield Mfg. They used to sell it 25 years ago and then made it free on their website. Lately they removed it and it is no longer available. Just to clarify, all gear calculation formulas for surface stresses in the literature and those used by AGMA, DIN, ISO etc., assumes proper lubrication between mating teeth where always an oil film exists between the mating gear teeth. If the oil film breaks from any reason and a metal to metal contact exists, the formulas are no longer valid and the gear considered ruined. Therefore, use the formulas with care if you use only grease.

 

[tbuelna]

noobita-

As israelkk noted above, each tooth of your 13T pinion operating at 7000rpm for 10k hours will be subject to 10^9 load cycles. This is quite a large number of load cycles, and the stress limits used when designing for this case basically means you'll end up with unlimited fatigue life.

The most important thing to remember is to design all of your drive system components (gears, bearings, shafts, etc) so that they have balanced fatigue life. It usually does no good to have some components in the system that have much greater fatigue life than others.

 

[noobita]

Thanks again israelkk and tbuelna.

Responding first to israelkk, yeah, i know all the formulas are based in proper oiled systems.

tbuelna, that's why i'm asking here, don't know if it is asking too much, help on finding suitable materials. I already posted all the system design, i can post the calculations (need to find the proper material to resist the stall torque too, not only the maximum continuous ratings - those i already decipher - but for the stall torque i don't think the system can handle it). How do you normally choose the material for this?

Best regards

 

[tbuelna]

When analyzing your drivetrain components such as gears and bearings, you need to run a couple different cases. There is the 10K hour composite lifecycle fatigue case you describe above. There might also be a max torque case for a limited number of hours. And there is the stalled condition you describe.

The most difficult case to analyze accurately is the stalled condition. Since the stall torque is almost 4X the max operating torque, this is likely the case that will drive your design. You would need to go through each mesh and determine the precise point during a single tooth passing thru mesh where the surface contact stresses are highest. This would be affected by factors like contact ratio, pressure angle, profile shift, geometry errors, etc. The max static contact stress should be well below what would produce a permanent deformation in the tooth flank surface. What you'll find is that when you account for the combined worst case condition at each of your five gear meshes the result will be rather discouraging. But if this is a requirement which you must be able to demonstrate by analysis that your gear drive is capable of meeting, then that's what you must do. Also, remember to check your bearings are good at this stalled condition.

 

[israelkk]

To design for stall torque you must specify a number of loading to stall torque (7.3N-m) that the gear will/may see. Even if in real life this should not happen, during the development process it will surely happen and a lot, as a result of mistakes, improper behavior of unfinished control system, human errors etc,. To this you need to take a safety of factor of x4 as tbuelna stated. When you will have this number then you can make calculations and select gear sizes and materials. In aerospace many systems are designed to live the extensive testings during the development even though in real life they work only one time.

If the system is needed to be as accurate as in optical sight systems then not only a breakage of the gear teeth is an issue but deformation of the teeth surface will be an issue. For some systems even a permanent deformation of the teeth can be allowed as the torque is transmitted without a breakage of the teeth.

 

[tbuelna]

What is important is what you can show by analysis. Testing only serves to validate your analysis work. A permanent deformation of a gear tooth or bearing race surface would only be acceptable in a failure condition, where the device would subsequently be removed from service.

 

[noobita]

Let me see if i understood what you said. Imagine i do calculations for a specific diametral pitch, face width, profile shift, etc...it gives me an value of 20kpsi (this is only for the maximum continous torque). Then, i multiply by the cycles factor and the Safety factor, which you said i should use 4, and have to find a material that should withstand 80kpsi, for example. Is this correct?

Now in the design, for first stage pinion i have this value for bending force: 8698,649473 psi (maximum continuous), for 20000 hours, n = 3,57x10^8cycles, which gives yn pinion 0,955, temperature factor 1, reliability factor of 0,85. So, if you say safetic factor should be 4, material should be abble to withstand at least 31kpsi, is this?

Best regards

 

[israelkk]

When I said x4 safety factor it was on the "desired life cycle" at stall, maximum continuous, etc,. Not on the stress level. For example, if you expect the gearbox to see stall torque 100 times during development, testings, and application phases you need to show by calculations and tests that after 400 cycles to stall that the gearbox did the desired job. The reason for this factor is that fatigue is a wide spread statistical phenomena. Ultimate and yield stress of materials are more strict and controlled statistical phenomena than the fatigue life of same material. While the "stress level safety factor of safety" in aerospace can go from 1.25 to 4 depends how critical and risky is a failure to human life, in fatigue the safety factor on the life cycle to failure can go from x4 to x10. For example, even though in tests your gear box lived the 400 cycles to stall torque, you can guaranty only 100 cycles.

 

[gearcutter]

I would suggest that you assemble a cumulative damage model. Miner's Rule is the simplest to use, the Inverse Power Law-Weibull model is more complicated but the results are more accurate.

Remember that, no matter which technique you use, the more load stages that you can assemble into your model, the more accurate the results will be. Start with a minimum of 3.

Have a look at this page to get you started -

http://www.weibull.com/hotwire/issue116/hottopics116.htm

 

[noobita]

According to calculations, i would need a material with a bending strength of 50kpsi+, that is even possible? Exists any material like this (hardened of course - i know nitrided, like 4140 have 42kpsi - and this is for maximum continous, not even stall, at stall i would need 4x10^8, what seems impossible)?

 

[tbuelna]

gearcutter makes a very good point about how and when a few discrete elevated load cycles get applied can produce different results on fatigue life. If these elevated load cycles occur early in the component's life their effect on fatigue life is different than if they occur later in the component's operating life. For example, if your component is good for say 1000 load cycles at the stall condition when new, after operating for 90% of its design life (18K hours) at normal conditions, it would only be able to handle a tiny fraction of the number of stall condition load cycles as when new. Also consider the opposite case, where a large percentage of the stall condition load cycles occur within the initial 10% of design life (2K hours) at normal conditions. There might not be sufficient fatigue life remaining in the component to last 20K hours under normal conditions.