Through vs Case Hardening to Fix Root Fatigue Failure 4

[thetank8]

A spur gear exhibited a broken tooth during a vibration test. The vibration of the overall assembly translated to an unknown input torque on the shaft of this gear which resulted in it impacting its mating gear in both directions. The rotation of the mating gear is ultimately constrained by a non-backdrivable worm.

Material: S45C through-hardened to HRC 40
Module: 0.35mm
# Teeth: 38
Pressure Angle: 20 deg
Profile Shift: None
Mating Gear Material: S45C through-hardned to HRC 55

First, from the photos of the broken tooth below, is it a correct assumption that the failure mode was fatigue breakage at the root of the tooth?

Second, would changing the material to something like a low-carbon alloy steel and carburizing so it is hard on the surface but still ductile at its core improve its performance? Or should I simply try to increase the through-hardness of the S45C gear as much as possible?

Photo:

Cross Section:

Please let me know if there is more information needed. Thanks!

 

[dinjin]

The basic tooth thickness for a module is
1.5708 x the module which would give
a rough value of .5498mm or .0216 inches.
This is a little module of .35mm.
Somehow, I think debree entered the system
and caused jamming and a bad mesh problem.
Did tips of the pinion break off and then
bottom out in the root of the pinion?
The photos are great!

 

[tbuelna]

I am still sticking with my diagnosis of meshing interference due to profile geometry issues. First of all it takes quite a bit of fine-tuning of both gears to get a 9T pinion/38T gear to smoothly mesh.

thetank8 stated in one of his posts that the pinion had a profile shift of 1.1 which is much more than is typically recommended for 9T. The effect of excessive profile shift is evident in photos 4 & 5 (above) of the pinion where you can see knife-edging of the tooth top lands. AGMA recommends limiting profile shift such that the minimum tooth top land width is no less than 30% of the module.

In the OP, both pinion and gear materials are listed as S45C (1045 carbon steel), with the gear thru hardened (q&t)to Rc40 and the pinion thru hardened (q&t) to Rc55. Rc40 is equivalent to a TS of around 185ksi and Rc55 is equivalent to a TS of around 287ksi, so if these numbers are correct neither the pinion or gear would seem to be lacking in root tensile or flank surface bearing capability. Even given the higher strength in the pinion material, I would have expected the pinion to experience a root failure before the 38t gear did, due to the fact that the pinion was accumulating fatigue load cycles at over 4 times the rate the gear was.

Interesting discussion. Maybe thetank8 can provide more details such as gear face widths, operating loads/speeds, and how long the parts were operated prior to failure. With this information we can run a quick analysis to determine if there is a bending or contact issue.

Regards,
Terry

 

[thetank8]

I really appreciate all the advice from everyone. Sorry for the delayed response. To answer some questions:

Speed and load: During normal operation, the max loading for the gear occurs at stall (0 RPM) where bending stress can reach ~250MPa according to Lewis formula. The gear can go as fast as 26 RPM but that is at the no-load condition. However, this failure occurred during an 8-hour vibration test (ISO 16750-3) where the gear was stationary but experienced ~500 N*mm of peak torque in the 10-500Hz range. In our limited field testing, we have not experienced such a failure.

Low backlash was a high design priority so we set center to center distance to 8.57mm, giving us a nominal linear backlash of only 0.006mm. This most likely explains the hard meshing issues some people have suggested. Is increasing the backlash recommended?

Heat Treatment: Quench and temper (don't know exact parameters, left that up to gear manufacturer). Yes, hardness and material was verified to be correct.

Yes, we performed material analysis of the original gear which showed that it was AISI 1020 carburized to around HRC 55 and a 0.04mm effective case depth. We reversed engineered the gear based on geometry measurements but did not have its AGMA quality measured.

Our gear’s quality was specified to JIS 1702 Grade 4. Inspection reports from the vendor show that this accuracy was met.

The gear is hobbed. The grease used is a synthetic hydrocarbon in a lithium soap thickener.

The teeth of the pinion did not break off. The only damage was at the sharp tip shown in Picture 5 of my previous post and the wear marks shown in Picture 4.

Gear face width = 3.5mm; Pinion face width = 4.2mm

Hope this info helps. I would still appreciate any recommendations for changes to fix this issue. Thanks again for your help.

 

[gearcutter]

It seems that this project is important to you and your organisation.
Therefore, I would highly recommend that you engage the services of a gear design & failure consultant. It will be money well spent.
The AGMA's website lists several on their website with many of those mentioned being amongst the world's best.

Here's the link -

http://www.agma.org/membership/consultant-list/

Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

http://www.aussieweb.com.au/email.aspx?id=1194181

 

[tbuelna]

thetank8,

Thanks for the additional input.

I ran a quick check on your gear mesh and I got a bending stress in the gear root of 20.2ksi with a torque of 500N-mm at the gear. But with 500N-mm applied at the pinion (2110N-mm at the gear due to the 4.22:1 gear ratio) I got a bending stress in the gear root of 84.9ksi. Based on what you posted about your stationary gear fatigue lifecycle test, I can assume that there is a unidirectional load applied to a single tooth for around 7x10^6 cycles (~250Hz for 8 hours). Based on the description of the materials/heat treatment you are using for your 38T gear, a bending stress in the root of 84.9ksi is far too high for 7x10^6 unidirectional load cycles. With air-melt quality steel and L10 reliability you probably want to keep the root bending stress levels below 30ksi for that number of load cycles, just as a rough guess.

Using the face widths you provided, for a torque of 500N-mm at the pinion I got a face contact stress of around 620ksi, and for a torque of 500N-mm at the gear the face contact stress was around 302ksi. Given a gear flank surface hardness of Rc40 even a contact stress of 302ksi is far too high for 7x10^6 load cycles. Thru hardened Rc40 steel will probably suffer permanent deformation (yield) at bearing stress levels somewhere around 250ksi.

You must also consider that my analysis assumes uniform contact along the gear faces, and even a small amount of misalignment/displacement/geometry error can significantly increase these calculated stress levels. And finally, I must offer a disclaimer on the accuracy of my calculations. I have not double checked them, so take them with a grain of salt. But from what I can tell your gear design may have some stress issues that need to be addressed.

Hope that helps.
Terry

 

[mfgenggear]

terry

nice post

Mfgenggear
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[dinjin]

thetank8,
Please confirm your outside diameter of the pinion.
If the profile shift is 1.1 you would have pointed
teeth. Do you mean a profile shift of .55 ?

(9 plus 2 plus 2.2) x .35 yields 4.62 mm.

Is the outside diameter 4.62 mm? My layout shows
the hob creating a 4.44 mm truncating the addendum.
If the pinion addendum is truncated by the hobbing
process, the contact ratio may be less than 1.00

 

[thetank8]

dinjin, the 1.1 profile shift is correct and it does have pointed teeth:

 

[dinjin]

What is the outside diameter???
Thanks for the drawing.
Is the od truncated like I suspect?
It appears to be about 25 percent which
is a lot if the od is 4.44 mm. This would
then give you a contact ratio of 1.107
assuming the center distance is 8.57 mm.

 

[gearcutter]

"The vibration of the overall assembly translated to an unknown input torque on the shaft of this gear which resulted in it impacting its mating gear in both directions." - thetank8

Thinking about the resonant frequency of the overall system and more specifically the natural resonant frequency of the gear/tooth that ultimately failed.

From an article 'Tooth Tips' by William Crosher;

In 1963 serious tooth breakages in helicopter transmissions were attributed to gear resonance conditions with insufficient damping. In R.J. Drago and F.W. Brown’s paper 80-C2/DET-22, reference is given to a helicopter gear that exploded during operation because one of the resonant frequencies coincided with an excitation frequency. Crane traveling drives have been subject to the sudden fracture of one or more bevel gear teeth, normally the high-speed stage. Sometimes the fracture occurs long after it has been in service, and at other times this happens almost immediately. This failure pattern is associated with resonance. In these drives torsional vibrations arise from the pulsating torque of the gear/shaft/coupling. These vibrations are increased when the bevel gear’s mesh frequency approximates the shaft/coupling frequency. In automotive transmissions drive rattle is excited by the angular acceleration caused by the fluctuating torque output. Since the resonance cannot be avoided, it is only diminished by improvements in the gear layout. In a temper mill, after replacing gears the gear mesh frequency resulted in chatter marks. Data was gathered with the use of modern vibration analysis. It was learned that the vibration from the gear mesh is amplified as it goes through resonance between 200 to 300 rpm. And this energy was being transferred through the strip to the mill rolls. -

http://www.gearsolutions.com/article/detail/5870/william-crosher-tooth-tips

Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

http://www.aussieweb.com.au/email.aspx?id=1194181

 

[mfgenggear]

thetank

clearly there is good feedback from all
we may disagree or agree but use checklist and go through this list & do more testing & analysis.
remove what it is not.

it appears to me there is not one smoking gun but numerous issues.
It would behoove you to hire an expert to assist you but not replace you. so that you can benefit
from his or her experience.

use all of the above suggestions and do testing.
to me if the original gears where case harden then it must be for wear factor.
through harden gears may not be sufficient.

backlash may be an issue and there is a possibility hard meshing is part of the problem.
with no or to little backlash gears will self destruct. add more backlash.

you can not fool an old gear manufactures eye. quality is a definite issue. bad surface finish will attribute to early gear failure.

also as pointed out the gear geometry needs fine tuning. if the pinion is profile shifted up to prevent undercutting then the gear should be shift down to allow the correct backlash at the correct mounted center distance. master gear gears should be manufactured to the correct center distance.these should be made & used to test the parts. a total composite & tooth to tooth composite test will tell a lot about the quality & verify the correct maintained backlash.

do gear teeth bending test make sure the gear teeth will maintain the required stress & force values.
after all is done above re do the vibration test.

plus I wanted to add that a designer can calculate and make sure the tips of both gears clear the form diameters of it's mating parts.
thus making sure there is no interference. and repeating myself, a Total Composite check (TCE) will verify this.

the correct gear data block use should be specified on the engineering drawing. all applicable data should be specified & should be verified.
I would take your gears to an independent lab & have them inspect. and all data should be charted & recorded.


Mfgenggear
if it can be built it can be calculated.
if it can be calculated it can be built.

 

[tbuelna]

If the profile shift is 1.1 you would have pointed teeth.....

dinjin,

I've attached a chart that gives some examples of how a tooth profile changes with varying amounts of profile shift for various numbers of teeth. At the upper right there is an example of a 12T gear with +0.8 profile shift coefficient (which is a far less extreme case than a 9T gear with +1.1 profile shift coefficient) and it clearly shows a knife-edge tip. So your comment about the addendum being truncated on the pinion teeth and how it results in reduced contact ratio are excellent.

thetank8,

I would also agree with mfggeareng's recommendations above. When you experience a problem in testing, the smartest approach is to thoroughly inspect and document the condition of the test hardware, then present these findings to an expert in the field. And as noted, the failure may be the result of several issues, including both design and manufacturing problems. While it's fun for the participants on this forum to speculate on the causes of your gear problems, you really should hire a bonafide gear specialist to help resolve them. However, I must say that you have done a great job of providing documentation (photos, test conditions, material & HT, etc.) so that we all could have fun discussing the subject. So thanks for that!

Best regards,
Terry

 

[dinjin]

If the center distance is not fixed, I would recommend
a smaller profile change on the pinion to avoid not
only pointed teeth but assure than the addendum is not
truncated. Did these brittle pointed teeth break off
and create the debree that obviously was in the mesh?
This is a poor design. Enough said. Maybe nitrided
hardening would have been a better choice if core
strength was not a problem.