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Stress Concentration in D-Profile Shaft
3

Stress Concentration in D-Profile Shaft

Stress Concentration in D-Profile Shaft

(OP)
Hello,
I'm having trouble determining how to account for stress concentrations at the root of the flat on a motor shaft due to overhung radial loading. I inherited a motor/pulley assembly that has an propensity for the shaft to snap off right at where it transitions from a D-shape to circular cross section. The pulley pictured below has a belt on it that applies the loading.


There is not a fillet where the shaft changes profile


I've looked through most of the resources I have here and I can't seem to find anything that addresses this particular situation. It' probably because it's not a great design...

So, I was just wondering how to properly calculate the fatigue life or at least how to account for the huge stress concentrations at that transition point due to bending.
Thank you!
-Shea

RE: Stress Concentration in D-Profile Shaft

If it is sharp enough corner it's likely to be 10X to 100X the nominal stress for a shaft that diameter. Most applications avoid the situation rather than accounting for it. You may be able to determine how many cycles the shaft is getting based on time in service and utilization.

If you have to use that motor, rework the shaft to smooth the transition.

RE: Stress Concentration in D-Profile Shaft

Flipping the pulley to reduce the overhang and being sure the belt is not over- tensioned can help too.

If the belt pull from transmitted torque looks to be a problem, increasing both pulley sizes to maintain the ratio reduces the working belt tension

Like others said, a sharp corner by itself is a big problem.

Got pictures of some failed shafts?
Stuff like the fracture initiation point, the fracture surfaces, setscrew bitemarks, and fretting from pulley micromotions can be valuable forensic clues.

RE: Stress Concentration in D-Profile Shaft

Who is the motor manufacturer - does their literature list allowable overhung load? That shaft may be intended for direct-coupled use where the shaft slips into a quill on a reducer, thus transmitting only a torsional moment, no bending moment. Even if you reduce the load enough to stop breaking shafts, you may still be overloading the shaft bearing and just move down the line of failure points. You really need to stick with rated loads.

RE: Stress Concentration in D-Profile Shaft

Thinking out loud here. Crankshafts on engines often have undercut fillets. Perhaps you could use a small file to undercut the sharp edge a bit. The loss in cross section area may be offset by the reduction in stress concentration. I don't know if this thought is true, the undercut fillets on crankshafts are rolled, not cut, so they contributed to the strength and reduce stress concentration.

https://www.researchgate.net/publication/317260473...

RE: Stress Concentration in D-Profile Shaft

Quote (Shea)

So, I was just wondering how to properly calculate the fatigue life or at least how to account for the huge stress concentrations at that transition point due to bending.

Why? What's the point?

It seems like you already have a history of in-service failures, so you must already know the fatigue life, right?

What value does a calculation add at this point?

Doesn't your goal need to be a new design?

Timing belt pulleys with QD or Taper-loc hubs are cheap and easy to find.

RE: Stress Concentration in D-Profile Shaft

Your belt is too tight. Or the orientation of the pulley creates too much overhung load. But I would go with excessive belt tightness. Some technicians believe a synchronous belt has to sing a high-C or its not tight enough. Wrong!!

Yes, the sharp corner of the flat is a contributing factor, but the manufacturer designed and built that motor to run with the correct range of belt tightness without failing. Loosen that belt, or flip the pulley around.

RE: Stress Concentration in D-Profile Shaft

I'd combine your service experience with a fatigue test program ... to identify if belt tension is critical (which it likely is)

Loading as well as geometry is critical for fatigue. I'll assume you're the motor manufacturer or that the motor design is fixed.

What service experience do you have ? time to failure (since purchase) ? running time (with known speed) ? non-failures ??

A test program would allow you to determine if the motor fails with the specified belt tension, and so failures are due to improper installation (an important point to mgmt).

What testing did you do with the initial design ? what fatigue analysis ?? or did you expect it'll work ok ??

How easy is it to replace the shaft ? Offer a rebuild service, save the customer from unscheduled downtime ? make a little money on the side ??

Would this feature be much different to a shoulder ? Thinking about, yes, maybe it is ... or consider as many different shoulders, due to different positions along the flat (you have a deep shoulder on the CL and almost no shoulder at the face of the shaft, all with the same fillet rad ... different geometries, different Kt)

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

RE: Stress Concentration in D-Profile Shaft

Hi sheafromme

If the motor complete with shaft is a bought out part then the manufacturer of the complete unit should be able to provide what maximum overhung loads can be applied when the motor is running. I suggest that you try to obtain that information and then compare that with your predictive overhung load plus whatever the belt tension is, obtaining that info could save you a lot of time.
Do you have any photos of the failed shafts? Some pictures would help us to help you further.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: Stress Concentration in D-Profile Shaft

(OP)
@3DDave Thank you for the response! That's what I feared...definitely makes sense about just avoiding the situation altogether but unfortunately I'm a bit backed into a corner in that I have a relatively narrow scope of allowable action on this. I could definitely see if the supplier could smooth that shaft transition then, thank you for the suggestion!

RE: Stress Concentration in D-Profile Shaft

(OP)
@Tmoose
I actually think I may go with the flipped pulley suggestion you had, it would allow the flat transition to be within the pulley instead. I already developed a tensioning procedure that prevents over-tensioning (ostensibly) but there are hundreds in the field already...
I'm thinking it's the overhung load not torque; as far as I can calculate from my tension recommendations there are many with the load over the mfg recs.
Here's a picture of the shaft, it's right at the transition point:

RE: Stress Concentration in D-Profile Shaft

(OP)
@dvd Thanks for the response! My spec for the tension is now below the mfg allowable overhung load dazed unfortunately there are a lot in the field that already got delivered apparently.
I think you may be onto something with the motor use-case; the literature seems to reflect that at least from what I've seen.

RE: Stress Concentration in D-Profile Shaft

(OP)
@TugboatEng Thank you for the input and resource, I think the manufacturer could do something to help out with the undercut; I'll reach out to them about it!

RE: Stress Concentration in D-Profile Shaft

(OP)
@MintJulep It's partially my own interest to see if I can make theoretical converge with the field results and also to fulfill a requirement for the report haha!

RE: Stress Concentration in D-Profile Shaft

(OP)
@Jboggs Thanks for your response, I have since updated the tensioning procedure for exactly the reasons you laid out hourglass I think I may end up flipping the pulley around because otherwise it has to rest right at that flat transition due to other assembly constraints.

RE: Stress Concentration in D-Profile Shaft

(OP)
@rb1957 Definitely makes sense, I'm almost entirely certain that the belt tension is the culprit but not entirely sure in what way it causes failure besides excessive stress concentration at the flat to shaft transition.
Motor design and some other parameters are fixed unfortunately. This is also not my design so I'm sort of trying to piece together the process as I go but it's a bit opaque. I'm sort of retroactively doing the analysis to at least piece together what happened and perhaps to inform future design of related systems. Thanks for the food for thought!

RE: Stress Concentration in D-Profile Shaft

(OP)
@desertfox Thank you for the response! I did find that the overhung load was over mfg specs and have already implemented a better tensioning procedure. Unfortunately, some failed units were below the overhung load spec and there are also a lot of these in the field already. I inherited this issue/design so it's been a bit of detective work to figure out exactly what assumptions were made. Here's a picture if you want to see more closely.

RE: Stress Concentration in D-Profile Shaft

Hi sheafromme

Thanks for the response and photographs and it certainly looks like a fatigue failure, have a look at this site giving photos of failed shaft and their causes.

https://www.efficientplantmag.com/2012/07/failure-...

I appreciate that the shaft isn’t completely round and that there will be a stress concentration where the flat is, however if you ignore the flat on the shaft for the sake of a calculation and assume that shaft is completely round you can then calculate the maximum principle stresses using the mohr circle. The shaft is failing under fatigue however the maximum principle tensile stress causing the failure is a combination of the overhung load and the motor torsion and not one or the other.
Google mohr stress circle for shafts under torsion and bending loads.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: Stress Concentration in D-Profile Shaft

I have a suggestion for a fix:

I can see the inner race of the motor bearing in your picture. Manufacture a spacer that slides over the shaft and rear against the bearing inner race.

The spacer should be long enough to extend beyond the step transition between D and round sections. A few thousand of an inch should be sufficient without negatively impacting belt alignment.

Butt the pulley firmly against the spacer prior to tightening the set screw.

Ideally, some of the bending forces will be transfered by the spacer so less will be seen by the shaft.

Your success will depend greatly on how firmly you can butt the two together. Perhaps a Belleville spring arrangement will make assembly more forgiving?

RE: Stress Concentration in D-Profile Shaft

won't belt tension create bending at the section ? so flipping the pulley makes the off-set less, yes?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

RE: Stress Concentration in D-Profile Shaft

Hi

Go to page 40 on this link, it shows how to calculate the torsional stiffness and hence the stress on a shaft with a single flat.

https://apps.dtic.mil/sti/tr/pdf/ADA064109.pdf

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: Stress Concentration in D-Profile Shaft

Though a very useful document worth keeping around, this is a bending failure, not a torsion failure.

Reducing the leverage to reduce the bending moment is good; reducing the tension in the belt to reduce the bending moment is also good.

Using a spring-loaded idler is a better long-term solution as it allows removing slots that can be used by techs to get the tension as high as they think it needs to be.

Blending out the flat to remove the sharp corner is still a useful change to make. The typical radiused undercut is usually to allow a more precise fit, but it does reduce the stress concentration.

RE: Stress Concentration in D-Profile Shaft

Hi

The failure is the result of the maximum principle tensile stress causing the fatigue and that tensile stress is the resultant of both the over hung load and the torsional stress due to the torque. So with the information about torsion the principle stresses can be calculated using a mohr circle. At least that’s what I think.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: Stress Concentration in D-Profile Shaft

Is there any indication that the set-screw - shaft joint has slipped? Set-screws have terrible durability so should be limited to alignment/clocking, not driving torque. I wouldnt be surprised if it slipped and overloaded the shaft.

RE: Stress Concentration in D-Profile Shaft

Torsional stress is typically not fully-reversed every revolution,usually just a variation, bending stress is fully-reversed each turn of the shaft. I like the calculation methodology of ASME B106.1, which is a withdrawn standard, but still in use in the material handling industry where infinite life is based on the bending moment, and not the torsional moment.



RE: Stress Concentration in D-Profile Shaft

Set screw on D shafts work fine. Set screws on round shafts not so much.

RE: Stress Concentration in D-Profile Shaft

This link explains what I have been saying, the combined bending stress and shear stress from torsion are vectorally added.

https://www.youtube.com/watch?v=Fp5-jjmaksM*!***pr...***!*

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: Stress Concentration in D-Profile Shaft

Handling stress concentrations in your motor shaft transition can be tricky. To tackle this, consider using the notch sensitivity factor ('q') and exploring the stress concentration factor (Kt) specific to your design. These factors provide insights into fatigue life and the severity of stress concentrations.

For fatigue life calculations, check out methods like the modified Goodman diagram or S-N curve. Yet, given the unique challenges, consulting with a mechanical engineer for a finite element analysis (FEA) is a smart move. They can simulate stress distributions and suggest modifications for enhanced resilience.

RE: Stress Concentration in D-Profile Shaft

The end of the flat is clearly causing a very intense stress concentration. You can attempt to calculate it but the stress concentration factor required to converge on reality is going to be on a very steep part of a curve somewhere. Maybe the value of the math is to back-calculate the stress concentration factor based on real life data. The failure is driven by the alternating stress, considering how far the crack propagated before finally snapping off.

I agree with flipping the pulley (possibly halving your bending moment) and reducing the belt tension. Adequate belt tension with synchronous belts is generally not as much as you'd expect if the job is pure torque transmission. Tugboat's idea for the shoulder spacer is good, but it does require a way to draw it down hard from the shaft end and the motor bearing inner race needs to be mounted against a shaft shoulder to support that. But above all I'd be hammering the motor vendor to blend out the end of that flat and not leave the sharp step. Or rework them yourself, and make sure that the rework operation leaves the machining lay marks in the axial direction of the shaft, not across the shaft. Ideally you'll be able to get that done with minimal undercut.

RE: Stress Concentration in D-Profile Shaft

This D shape has some similarities to a keyway

There are 2 traditional methods for machining the end of a keyway as shown at figure 1 page 2 here https://backend.orbit.dtu.dk/ws/portalfiles/portal...
(a) end-milled or profile keyway; (b) sledrunner keyway


I think each of these would have an analogous approach that could be applied towards transitioning from the D shape shaft profile to the circular profile.

I'm not sure which is the more favorable reduction in stress concentration.

Quote (geesaman.d)


Or rework them yourself, and make sure that the rework operation leaves the machining lay marks in the axial direction of the shaft, not across the shaft.

That sounds similar to the sledrunner approach to me

EDIT - I wonder if the end-milled might be doable without removing the rotor to save time? EDIT 2 - although I guess rotor needs to be held more stationary than bearings can accomplish and not sure how much load we want to put on the bearings. Maybe a chuck on end of shaft would help those things, or maybe it's just a bad idea to even attempt machining the shaft without removing the rotor (I leave that to others more mechanically inclined than me to decide).

RE: Stress Concentration in D-Profile Shaft

Somewhere I have information on Navsea etc design of LOW stress keyways/keyseats.
My recollection is complicated variable radiuses are required that blossom off the end of the keyseat where the sledrunner detail would be applied.

Kind of like how a dove's wings attach .
https://media.istockphoto.com/id/89282675/photo/wh...=

RE: Stress Concentration in D-Profile Shaft

Tmoose - I can't read your link. But I wonder if end milling using a radiused bit would give a favorable reduction in stress concentration.

RE: Stress Concentration in D-Profile Shaft

Just a dremel and a grinding bit and 30 seconds or less would ease that sharp stress riser. Not even a lot of skill - just erase the corner and stop.

RE: Stress Concentration in D-Profile Shaft

Dremel is suitable for the sledrunner. It would probably require disassembly of the motor to get enough working room for the wheel that close to the motor frame. But maybe disassembly is inevitable anyway? (I wondered about that in "edit 2" of my post timestamped 17:18)

RE: Stress Concentration in D-Profile Shaft

Using a radiused end mill to cut the flat would be a improvement but geeaaman brought up the direction of the surface finish. Utilizing the side of the mill would provide the correct orientation of finish.

However, these solutions would require manufacturing new motors with correctly specified shaft features. A little hand finishing can be done in the field and *may* solve the problem.

A third option is to make a new pulley that extends past the step with a close or interference fit. In the case of the close fit, utilize some retaining compound to make it like an interference fit.

RE: Stress Concentration in D-Profile Shaft

About the third option: The stiffness to cantilever from the tiny projection is unlikely to be enough to work. Essentially it would have to act as if the remainder of the shaft was cut off. It looks like a 1/3 diameter long engagement would be supporting a load about 5 diameters out.

RE: Stress Concentration in D-Profile Shaft

Quote (3DDave)

The stiffness to cantilever from the tiny projection is unlikely to be enough to work. Essentially it would have to act as if the remainder of the shaft was cut off. It looks like a 1/3 diameter long engagement would be supporting a load about 5 diameters out.
So I think you're saying it's not practical to support the shaft from the end during machining, and therefore not practical to work without motor disassembly. That was feedback I was looking for, thanks

RE: Stress Concentration in D-Profile Shaft

This is IMO a deceptively complicated fatigue problem.

The belt tension will cause what is effectively a static bending load on the shaft. Then of course, there is also the torsional shear stress on the shaft.

But because the shaft is not symmetrical, as it rotates around, the effect of the Kf and the stress state will change. And the variation of the peak torsional stress will not be in phase with the variation in peak bending stress, because the peak bending location will occur on the "opposite" side of the shaft every 180 degrees of rotation.

So what you have is a complex, multiaxial stress state with fluctuating (non-constant mean stress) level, and the fluctuation is mutually asynchronous.

Basically, one of the most complicated scenarios you could have.

Even if you could find a Kt for a stepped shaft in a handbook like Peterson, I doubt you could find a solution that covers all of the orientations of the shaft you need through the load cycle.

If I were set on predicting a fatigue life instead of redesigning the assembly, what I would do is develop a basic FEM for the shaft and get results from the loads in maybe 10-20 orientations.

Then I would pick a couple points on the shaft and develop a repeated duty cycle, mapping out the stress variation over time. Then I would apply the SEQA method or maybe even critical plane methodology to cover the complex fluctuating multiaxial damage accumulation.

They key thing here is that if you can correlate the predicted life to the life you've seen in service, you'll know your prediction methodology is decent.

So then you could repeat your analysis with different levels of mean and alternating stress to figure out what the load limits are in order to meet whatever service goal you have.


Then I would want to compare my predictions to the in-service data.

Keep em' Flying
//Fight Corrosion!

RE: Stress Concentration in D-Profile Shaft

Just looking at the photograph unless it’s a trick of the light the crack initiation point appears to be at shiny bit on the shaft of the motor going into the motor body which could well be on the top of the motor flat looking at the other half which is held in the OP’s hand. There are possibly some other crack initiation sites around about 200-270 degrees from the first one I mentioned. I would start with a Mohr circle based on the shaft on its maximum BM at the shaft flat.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: Stress Concentration in D-Profile Shaft

Quote (electricpete)

That sounds similar to the sledrunner approach to me

Yes, I'm advocating for a sledrunner type end finish here. And the machining/grinding lay marks be axial, which is normal for a sledrunner cut. I think that and reducing the bending moment will put this to bed.

RE: Stress Concentration in D-Profile Shaft

may be you can have a look to "Stress concentration factors - Pilkey - to the chapter related to -shoulder fillet on non-circular contour in a flat stepped bar-"

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