Load Calculations For Dry Running Gears

[gearcutter]

Does anyone know of standards available for load calculations of non lubricated steel gears?

Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

 

[Matt51]

Nope. What stresses are you planning to run?

 

[gearcutter]

Hi Matt,

Once again, thanks for the response.
I propose to use case hardened 4317 or En36a, 58-62Rc, with a ground tooth profile of around AGMA 12.
S/N curves for these materials suggests a surface pressure of around 1400N/mm2 at 1e +10 cycles.
At 4.2e +06 cycles (required life) S/N curves show around 1928N/mm2
Maximum calculated single tooth surface stress on the pinion @ the operating PCD is around 715.61 N/mm2 .
Circumferential speed at PCD is around 0.70 m/sec.
Maximum calculated flash temperature is around 62oC.
This is with an application factor of 1.25.


Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

 

[israelkk]

The problem of dry gears is not just surface stresses. A serious issue is wear and scoring to to the sliding friction between the mated teeth.

 

[dimjim]

I took a coarse with Ray Drago and he mentioned a customer that use no lubrication with very accurate gears with no problem. Since the application is so unusual, I doubt you will see and standard created or published. I assume you will be running these in at slower speeds until you are certain that you are having minimum wear, scuffing, or pitting. I assume the pinion is the driver and you have a long addendum design for the pinion. I guess you can tell I favor recess action gearing.

 

[tbuelna]

israelkk is correct. Gears without lubrication will have high friction, causing heating, which in turn will cause de-tempering of the gear case and core material, and ultimately resulting in structural failure. Even with a very well designed, full recess action gear mesh, the dry-metal-on-dry-metal friction will be very high. And it will be very difficult to adequately cool those teeth, even at pitch line velocities below 130 ft/min.

And by the way, how do you come by a flash temperature without any lubricant. Flash temperature is only relevant when there is some lube film present.

Have you considered dry-film lubricants (MoS2) for the gear teeth. They are suitable for contact stresses below 20ksi, but unfortunately won't work at the contact stress you have noted- 1400N/mm2 (203 ksi). I'm also not clear on the number of load cycles. Is it 10 or 1x10^10 (10 billion)? If it's more than 1x10^7 load cycles, then your contact stress is too high for your material/heat treat, even for an oil lubed gear mesh operating with a lamda above 1.0.

 

[israelkk]

gearcutter

Can you give more information on the gear and what it is for?

Is it a standard industrial speed reducing gearbox working continuously or for an intermittent small angle actuator?

 

[gearcutter]

I don’t have the relevant qualifications in these fields so please pardon my ignorance; after all I’m just a gear cutter.

tbuelna & israelkk; Thank you for the valid and important concerns you both mention. I’m not sure but it almost sounds to me that both of you are saying that perhaps it can’t be done. I admit that the problem is not a common one but none the less, non lubricated steel gears are widely used in industry. It appears that there are no standards for this type of application and this surprises me due to fact there are so many sets out there working quite satisfactorily.

dimjim: One day I hope to get to the US and take part in one of Ray’s workshops. You touch on the point of accuracy; this is one area I feel that requires careful consideration in this application.

tbuelna; In answer to your questions:
From what I understand of the subject; Flash Temperature can be derived from one of Blok’s equations (in this case taken from Dudley’s Gear Handbook, edited by Dennis Townsend) where lubricant film has no relevance to the instantaneous surface temperature under hertzian contact. Blok’s “Classical” equation for Flash Temperature assumes hertzian pressure distribution, equal surface temperature on both surfaces and no oil film. My understanding of Tribology is that Flash Temperature does not necessarily have to include heat generation & heat conduction within the oil film and heat transfer to the contacting bodies. As far as I can see…..Blok’s equation seems to show that this is in fact the case. In fact none of the flash temperature equations I’ve been able to find use oil film data. Am I missing something?

I’m yet to fully understand the theory but would it be correct to theorise that, when the lubrication regime is in an E.P. boundary condition and lambda less than 0.40 and sliding speed is less than 1.5m/sec, the convection of heat generated from within the oil film to the surrounding sliding bodies would approach a point where it would have less relevance on Flash Temperature? After all……..boundary lubrication suggests that, due to a higher number of asperity contacts and those asperities either deforming or shearing off and also reduced sliding or rolling between the members less oil is available for developing an E.H.D. film. Wouldn’t this then suggest that, because of the reduced amount of lubrication present, the heat developed within the oil due to shearing and pressure is going to have less of an effect on the surrounding bodies?
The 1400N/mm^2 contact stress you claim I mention as being the actual contact stresses involved is incorrect. Please re-read my posting and you will see that this figure is taken from the S/N Curve for the material I propose to use. As my post states, the calculated stress is around 715N/mm^2.

As far as load cycles; as I understand it, the S/N charts I’m looking at show (1e +01) is equivalent to 10. So (1e+10) would be 10,000,000,000. I note that I made a mistake in my post; the required life is not 4.2e+06 rather it should have been 4.65e+07 or 46,500,000 cycles or 10,000 hours @ around 77.50 rpm. Once again, I have no qualifications in regards to maths or engineering so please correct me if I’m wrong.

israelkk: below is the current gear data and also the data of the set I propose to use.

Based on ISO6336 this is the best I can come up with remembering that this standard requires lubrication. I figured that if I can come up with a design that has the highest flank safety while trying to reduce the amount of sliding by using 25 deg PA, I might have a chance or at least have a point to start off with. I can get higher flank safeties by reducing the PA but this increases sliding.

The current configuration uses a type of nylon called Ertalon, which is extruded bar stock, for the pinion and flame hardened K1045 carbon steel for the gear. Estimated AGMA 2000 grade is around 6-7. This is mainly due to the estimated amount of distortion of the ring type gear as a result of flame hardening.

Service life of the nylon pinion varies between different machines but an average life expectancy is around 50 – 100 hours. The machines are being run at greater capacity than what they were originally designed for.

The machines are called Take Up Units and are part of a wire galvanising line. The machines are at the end of the line and pull the wire from the start of the line and then coil the wire into bundles. So load is steady and even.
Drive is provided by VFD controlled 9kw motors and transmitted to the gear sets via V belts and pulleys.

Current Gear Data, Plastics To Niemann:
Module = 5.08
Pressure angle = 20deg
Helix angle = 12.50deg
Zp = 34
Zg = 55
F.W. p = 40mm
F.W.g = 40mm
Xp = -0.4544
Xg = -0.5346
Centre distance = 226.00mm
Application factor = 1.25
Required Service life = 10,000hrs
Safety root Pinion = 0.1537
Safety flank Pinion = 0.1472

Proposed Gear Data to ISO6336:
Material: Case Hardened 4317, 58-62 Rc
AGMA 12
Module = 3.75
Pressure angle = 25deg
Helix angle = 12.25deg
Zp = 45
Zg = 73
F.W. p = 68mm (max. due space constraints)
F.W.g = 56mm (max. due space constraints)
Xp = 0.0194
Xg = -0.1269
Centre distance = 226.00mm
Application factor = 1.25
Required Service life = 10,000hrs
Safety root Pinion = 3.795
Safety flank Pinion = 2.253

Any thoughts would be much appreciated.





Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

 

[israelkk]

gearcutter

This is a whole different ball game. Using one gear of plastic in a pair is not as sever as using two metal gears. As for formulas for life I do not familiar with any standard in the subject. I would use Lewis formulas for bending and will make sure that the bending stresses on the plastic gear will be less than 0.3*Ultimate tensile strength.

You can adopt the maximum PV values and theory used for plastic bushings and apply them for the sliding speed and pressure between the mated teeth.

One more note is that usually the pinion is the weak link in any pair of gears, therefore, I would use a metal pinion and plastic gear.

I do not understand why the designers selected dry gearbox for a wire drawing machine which can be maintained and use a well lubricated industrial gearbox.

If it was a food processor, blender, a home and office printer, etc., I could understand using dry or dry and lightly greased lubricated plastic gears in a gearbox but I fail to understand this selection of materials for an industrial machine.

 

[dimjim]

Ron,

I still think I would go with a long addendum
design on these. You might try to use a 33 tooth pinion
replacement for the 34 tooth pinion cut on the same gear
blank so you can use the same center distance. See if that gives you longer life. You would not have to change the gear design this way. Carburizing the gear may
create less distortion than flame hardening.
The gear ratio goes from about 1.62 to 1.67. I do not
know if that would be a problem or not in this design.
I seldom see plastic paired with steel. Great to learn and hear of something different. I also wonder if they make a plastic with graphite added and if it would give you longer life. We used plastic and canvas with graphite added. I forget what they called this material. It was used in a cage design and did reduce wear. I know plastic is affected by different states of humidity and do not know
how that affects your design.

 

[Matt51]

You might try the websites of companies that specialize in plastic gears, such as Ticona. Kleissgears.com has papers online on the subject.
Pitting and scoring will not be the issue. Wear or breakage of the composite pinion will be the issue. I am not sure case hardening of the gear is beneficial or desirable. Ticona or Kleiss could tell you a good material combination to go with. There is one company, I forget their name, but they make garage door openers with unlubricated gears, but one of the gears is a bronze made of something like oilite that has lubricant in it. You can find them with a Google search.
I designed a gear set for an application that was hot and dry, too hot for composites. We used steel. I used a "composite" tooth form, similar to the old AGMA standard of the 1920's. Involute gears wore out rapidly, these gears worked just fine. If you make a plot of specific sliding, the specific sliding was reduced with the composite tooth form, and was more uniform across the entire tooth. Involute gears when they wear, start to wear at the gear tip to pinion root, where specific sliding is greatest, and this non-uniform wear causes a fast wear out of the gear set. The composite tooth form had wear, but it was more uniform across the tooth profile, allowing the part to last the required life.
See if the engineers at Ticona or Kleiss are willing to recommend a good material combination for you. They also have guidelines published on what stresses you can design composite gears to. There are some fatigue curves published on the web for some of the better composites, like Dupont Zytel or PEEK. This would be good for bending stress. I will see if I can locate, you probably can with a Google search.

 

[dimjim]

The material that I was trying to remember was Ryertex
Grade CG.

 

[gearcutter]

Gents,

Once again, thanks for all your responses but I'm afraid you're not reading my posts properly or perhaps I'm not explaining myself in a clear enough manner.

The set the customer is currently using is nylon/steel with a service life of around 50-100 hours. This is obviously not satisfactory. This is where I'm proposing using steel on steel......as a replacement for the nylon/steel sets.

Remember, my original post posed the question; if anyone knew of load calculation standards that allowed for the design of steel/steel gears?


Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

 

[Matt51]

Ron,
I know of no such standards. I am telling you, the steel on steel will fail. You can consider making one out of oilite or similar bronze (google search spinodal bronze). Or, you will have to design non-involute gears, a combination of involute and cycloidal gear. Been there, done that.

Regards,
Matt

 

[Matt51]

I meant to add, you can consider steel on steel if you can add grease every few hours.

 

[gearcutter]

Matt,

Yes I agree; the dry running steel on steel will prematurely fail due to the lack of lube. But, would steel/steel unlubricated last longer than nylon/steel unlubricated considering the nylon/steel set have a safety factor of less than 0.15? This is all I'm trying to achieve, is giving the customer something better than what they have at present.

Unfortunately grease or dry lube is not an option due to accessibility & environmental constraints.

I’m working towards conducting a trial of a couple of different steel/steel combinations, so this will ultimately determine the possibilities suitable for this application.


Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

 

[Matt51]

Ron,

I am saying, from experience, that steel on steel unlubricated involute gears will probably wear out faster than nylon on steel unlubricated involute gears.

You could consider flame spraying one of the steel gears with tungsten carbide. Because this applies an uneven coating, you are limited to low pitch line velocities. However, the coating eventually wears away also.

The companies that design composite gears can give you the best material combination for wear. You might be able to improve life just by selecting the best composite to steel combination. Some of the composites like PEEK have good lubricating properties.

 

[Matt51]

I heard of someone make gears out of solid Stellite that ran without oil. I never tried it myself though.

 

[plasgears]

Consider running a nylon pinion against a mating acetal gear without lube. There is a synergy bet the two matls.

 

[Matt51]

I think Plasgears has the best answer, I have searched his posts in the past, for information regarding composite gears.

One last choice would be wood gears. Lignum Vitae. John Harrison, when he invented super accurate clocks to determine longitude for ships, originally designed all his clocks to operate without lubrication. Some ran for centuries, lignum vitae has a coefficient of friction about the same as teflon, and is the densest strongest wood known. Lignum later was used for ship propshaft bearings.

Anyway, I think Plasgears has the right answer.