Gear Design criteria for Momentary Overload 9

[morris9791]

Dear Experts,

I have to size a gear that is sufficient for momentary overload, for example a max stall torque.

According to AGMA, the gear material yield stress (Say) should be used to determine the max allowable stress instead of the fatigue bending strength (Sat).

1) By how much is one allowed to exceed the yield stress of the gear material when sizing for stall torque?

2)Is it an absolute must the applied stress is less that the yield stress in gears or is there some leeway?

3)Is there a way of calculating the number of cycles we may get out of a gear that is exposed to greater stresses than yield (Plasticity)? I haven’t found anything in AGMA.
Surely since the applied stress is much localised at the root fillet that it may not cause global deformation.

Application is off-road military vehicles.
Please bear with me as I am a newbie in gear design and learning all the time. Its great getting opinions off very experienced guys in this forum. Thanks


Any information is appreciated.

Best Regards
Eddie

 

[BobM3]

If you exceed the yield stress, the teeth will permanently deform rendering the gear useless.

 

[plasgears]

If you can justify plastic gears and the gearbox size resulting, you will find that Nylon 6 is very forgiving. High hardness metal gears and filled plastic gears are not forgiving. The key is to look at elongation; high elong. tells of elastic-plastic toughness, which will forgive overloads. Repeated load testing will be important to justify the design for production release.

 

[dinjin]

I would think that life of gears would be similar to the design life of roller bearings. Life would be an inverse cubic function of the loads. Since the static running loads are generally 1/2 of the Stall loads, the life would be 1/2 to the third power meaning the life of the stall loads would be 1/8 of the life of the running loads.
Actually roller bearing are to the 3.1 power but it should give you a rough estimate. Do not exceed the yield values
for max stall conditions.

 

[MikeHalloran]

If the teeth are stressed past yield, _even_momentarily_, the contact geometry changes, and any correlation to the fatigue life of roller bearings is lost.

Didn't someone mention shock loading, too?





Mike Halloran
Pembroke Pines, FL, USA

 

[tbuelna]

morris9791,

A gear tooth that suffers permanent deformation, whether due to surface contact (brinnelling) or bending, is a damaged tooth. And that gear should be removed from service as soon as possible. While it may continue to provide some functionality for a limited period of time, it will eventually fail. And this loading condition is not something that gears are usually designed for.

What may be confusing you is how you have interpreted one of the basic design requirements that most military mechanical systems usually must meet. Military mechanical systems all typically have a basic design requirement that states something to the effect that all components must be capable of accepting a full stall torque load applied to the system (ie. a jammed mechanism) without experiencing structural failure. But a permanent plastic deformation of the parts is still considered acceptable.

dinjin almost got it right in his post about varying cyclic loads. To establish a load value for assessing fatigue life of components like bearings and gears, that undergo cyclic loads of varying magnitude and frequency throughout their life, a root-mean-cubed (RMC) function is normally employed which summarizes the total conditions of loads and cycles into one simplified set of values. But this RMC derived value is only suitable for normal operating conditions, and not failure modes like stalls or jams.

Best of luck.
Terry

 

[israelkk]

morris9791

Are you referring to the vehicle transmission or another gear based actuation system?

To my experience local yielding at the root of the tooth will be unnoticeable in terms of gear accuracy and meshing when the gear torque is the issue. To affect the output torque condition you need to go into deep plasticity and not just reach local yield point. Again it depends on the type of use. If this gear has to be very accurate in terms of angular accuracy such as for an optical system then you should avoid yielding. However if it is a gear system just to produce torque and angular accuracy is not crucial then such yielding will not affect the performance of the system.

However, life will be limited and gear efficiency will decrease a little. You also have to take into account that load condition where there is a local yielding at the root of the tooth will have very high local bearing load (Hertz stresses) between the mating teeth which will affect the smoothness of operation. Therefore, if you are referring to the vehicle transmission which need to continue normal driving then yielding after the overload you should avoid yielding

To summarize, if you are referring to a "torque system" and some loss of efficiency is taken into account, then you can use the system beyond yield. You will need to increase backlash to allow some bending to the teeth. As long as the teeth will not break, the torque, the factor of safety and life cycle are met, you can overload the gear. However, you have to verify such design by tests.

Aerospace and military system are usually designed to break beyond a factor of 1.5 on the maximum expected load at all conditions.
At a factor of 1.25 some permanent yielding (tooth bending, local deformation at tooth contact) is allowed as long as it doesn't affect total performance.
At a factor of 1.15 no measurable permanent bending and deformation is allowed.
Note: to prove life cycle you need a factor of safety of 4 to 10 on the expected life.

dinjin

Aerospace bearing for actuation systems can have momentary loads twice the static load listed in the roller bearing catalog and there are systems that uses even much higher loads as long as the bearing will not break.

 

[ExRanger]

If you are talking about carburized steel gears, then you can, depending on how the gears are processed, get some significant residual compressive stress in the gear teeth. For that reason they probably won't locally yield at the same stress as a typical stress strain test specimen. If you take the tenisle yield stress for 9310, for example, of 130 ksi - a carburized and hardened steel gear may not yield until the local stress in the root is well above that.

Having said that, if you do yield the root of the tooth locally without causing a significant permanent deformation in the tooth as a whole, then I would think you have strain-hardened the root and the fatigue life after that point should still be good.

However if you cause the tooth to move, then the stresses on that tooth will be greatly altered and you need to do a new analysis or test to determine them. You should also check what your static overload does in terms of the surface contact stress. I think you could brinell the tooth like tbuelna mentioned and cause early surface failure as a result.

One other thing to keep in mind is that if you overload one side of a tooth in tension, you could be overloading the opposite side in compression especially if the tooth has compressive residual stress locked into it. If you yield in compression, then you lose some of your residual stress on that side. This is important in teeth that have reversed loading, such as certain planet gears or idlers.

 

[morris9791]

Thanks Guys,
Some interesting comments there that I will note. I am specifically referring to the differential gears in a standard open diff. I currently need to size these for a stall torque. I will aim to stay below yield since I believe I have some design scope.
Can anyone source the RMC approach? Is this mentioned in AGMA? I don’t think I want to use this unless I can reference it against some source etc.

Also as a side note, I was trying to ‘physically’ see how a standard open differential ‘splits’ the torque to each half shaft. Does anyone understand this or is it counter intuitive and perhaps math is required to see why it splits?
I mean it appears that all standard open diff’s still splits the torque 50:50 regardless of the pinion / gear ratio / geometry inside the diff. ?


Best Regards
Ed

 

[MikeHalloran]

The symmetry typical of bevel gear diffs means the torque is split 50/50, because the pin gear works like a lever, pressing on the flanks of the side gears, while the pin in its center transfers the torque.

Planetary diffs, more commonly found in interaxle applications, can have an asymmetrical torque split.



Mike Halloran
Pembroke Pines, FL, USA

 

[mfgenggear]

would you need to oversize your gears to prevent yielding.

 

[tbuelna]

morris9791,

If you want to design for an acceptable stall torque load with your (straight bevel?) diff gearset, then you should use a simple static Hertzian contact approach, since there will be no EHL oil film effects to consider.

Roark's will give you the necessary equations to establish the brinnell (elastic) limits of your gear tooth contacts, as long as you know the relative gear tooth profile's radius of curvature, face widths, contact ratio, and the metallurgical properties of the gear tooth contact surfaces.

A brinnell failure is generally considered a loading condition that produces a permanent strain of .0001 inch or more in the contact surface.

Hope that helps.
Terry

 

[israelkk]

tbuelna

I think you meant 0.0001 of the minimum mating diameter/radius of curvature (a non dimensional ratio). In rolling bearings it is 0.0001 of the ball/roller diameter.

 

[morris9791]

Hi Guys,

Tbuelna: I understand the Hertzian contact you suggested would be for compressive stresses on the bearing surface of the mating pair.
So, I need to examine both this bearing compressive stress AND the tensile stress developed at the tooth root fillet. Whichever stress is the higher needs to be considered against the selected material yield.
Is this a reasonable approach?

Also which equations are you referring to in Roark's? I am looking at table 33 case number 4 'general case of 2 bodies in contact'
It requires radius of curvature alright but it doesn’t ask for contact ratio or metallurgic properties of gears. Can you clarify?

Appreciating peoples help. Thanks
Ed

 

[morris9791]

Guys,

I have located the contact yield analysis for static / low cycle loading in Drago's fundamentals in gear design. Good book.

Thanks again for your input.

Cheers

 

[tbuelna]

israelkk,

Thank you for the correction. Should have read ">0.0001D" not .0001 inch.

Regards,
Terry