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Questions on Spline Design 5

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PearlRock

Aerospace
Apr 22, 2010
25
Dear all,

I am designing a flexible spline for an experimental application. I'm looking at ANSI B92.2M in the machinery guide. My root stresses appear to be too high. I am using the maximum effective length and my maximum diameter is restricted. If I could choose a larger diameter, this wouldn't be a problem. Unfortunately, I cannot. Beyond spline length and diameter, the root stress calculations are mostly stress factors, so proper spline design dictates I understand my stress factors quite well.


I've been looking at the spline application factor (Ka) table. My application is technically an electric motor connected to a dynamometer; however, this particular motor has horrible torque ripple. 400Nm peak; 250Nm avg at low speed. That makes my application factor very selection difficult, because is this application like a "normal" electric motor, or a "normal" internal combustion engine? Does torque ripple even matter for the selection of this stress factor? The difference in the application factor is quite significant....1.2 vs 2+. If I can use the lower value, my spline design is fine. If I cannot use a lower application factor, well....I'm not sure what I can do.

Is there any value in using a spline length longer than the maximum effective length?

Best regards
 
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PearlRock-

Yes those 400Nm torque impulses must be taken into account with your spline design. However, are you sure you need a flexible type spline joint? You can reduce root stresses by increasing the spline length as long as there is good load distribution along the spline face length at max torque conditions. In order to achieve this you will need to apply some lead compensation when producing your spline teeth. The typical recommendation for L/D of flexible splines is <1.0, but with proper lead compensation you might be able to use an L/D of 1.5 or more.

If root stress is a problem, the first thing I would suggest is to look at adjusting things like pressure angle and DP. The root fillets of external spline teeth will usually have higher stresses than the root fillets of the mating internal spline teeth, and I'm assuming this is the case with your spline. Using a slightly higher pressure angle on your spline teeth should reduce root fillet stress, but you need to make sure there is sufficient rim thickness for the higher radial forces. As a last resort you could also use a non-standard DP to maximize the spline PD within the available space.

Lastly, besides using lead compensation in the spline teeth, you can also modify the section thickness of the material behind the splines to produce a similar effect.

Good luck to you.
Terry
 
Hi Terry, thanks for the response!

[sad] Lead variation looks complicated. [sad] I'll have to look more into that. The Machinery Handbook doesn't seem to mention too much about that. If you know of any design references for that, I'd appreciate them.

Do I need a flexible type joint? You mean, opposed to a fixed/interference spline? I think it would be quite difficult to get this motor onto an interference spline, but I'm open to other options. I'm reading Dudley's original paper, and I see he mentions that a fixed spline has considerably better stress management characteristics.


As I'm reading through dudley's paper, I see that the application factor does appear to be based on the torque experienced. He mentions generator torque in a design and fault/overload case. Bad news for me. [sad]

"Lastly, besides using lead compensation in the spline teeth, you can also modify the section thickness of the material behind the splines to produce a similar effect."
It's not clear to me what you mean by this.

My pressure angle is currently 30deg. I'll investigate 37.5 & 45deg per your recommendation. Indeed, I agree a higher pressure angle may reduce tooth stresses.
 
tbuelna raises some excellent points.
Another one to add - use a full fillet profile, most spline standards show a flat root profile.
Also, when increasing the pressure angle; keep an eye on the hoop stresses of the component that has the female spline.
One thing to keep in mind; the vast majority of failed spline connections haven't done so because of tooth bending fatigue. Splined connections more often than not fail due to surface fatigue, or wear.


Ron Volmershausen
Brunkerville Engineering
Newcastle Australia
 
PearlRock-

Your Machinery's Handbook does discuss the effect of lead compensation on effective length, except they refer to it as "helix modification". See the attached graph comparing max effective length vs PD for different types of splines, and it has a curve for "fixed splines with helix modification".

Lead compensation is not really too complicated in theory. The way lead compensation (or helix modification) works is by manufacturing the external spline teeth with a controlled amount of lead in the opposite direction of input torque such that contact along the face becomes normalized at some desired torsional load condition. While simple in theory, in practice establishing the optimum amount of lead compensation can take some work. The reason splines with long engaged lengths do not load share along the face width is because the splined section of the shafts experience some small amount of torsional "wind-up". Basically the spline teeth become slightly twisted under load. But due to the relatively high local structural stiffness of the mating parts, even very tiny changes in the shape of the contacting surfaces can produce significant changes in stress distribution. So establishing the optimum amount of lead correction for your spline will likely require some detailed analysis work.

One important thing to consider with lead compensation is that it only works when the spline connection is loaded in one direction. I don't know if this is the case with your dynamometer drivetrain.

Regarding your question about modifying the section properties of the area backing the spline teeth, the goal is similar to applying lead compensation. By varying the radial thickness of the shaft material behind the teeth along the length of the spline you may be able to improve the face load distribution. Reducing the thickness of the material behind the spline teeth will reduce the local tooth bending stiffness. But as gearcutter pointed out, when doing this you need to keep an eye on the impact to overall stress levels in the shafts.

Hope that helps.
Terry
 
 http://files.engineering.com/getfile.aspx?folder=12b0c772-7fdd-4b8b-a50a-f7b5cfe23ec9&file=max_effective_spline_length.png
Yes, this is a bi-directional motor, so that will have to be considered. Machinery guide also makes note of a parallelism variation. Would that not give enhanced load capacity bi-directionally?

"Regarding your question about modifying the section properties of the area backing the spline teeth, the goal is similar to applying lead compensation. By varying the radial thickness of the shaft material behind the teeth along the length of the spline you may be able to improve the face load distribution. Reducing the thickness of the material behind the spline teeth will reduce the local tooth bending stiffness. But as gearcutter pointed out, when doing this you need to keep an eye on the impact to overall stress levels in the shafts."

So let me make sure I understand this, you are effectively suggesting an axial variation on the root fillet?


I should have been more clear in the original post as well. My tooth compressive stress is too high. Not the tooth root stress. My mistake.

Unless the parallelism variation is fruitful, I suspect I'm out of options. Changing the pressure angle didn't seem to improve the compressive stress much. I'll probably have to start searching for larger bearings to accommodate the shaft, which is unfortunate. This is a high speed application. KOYO only had 1 option at 35mm.
 
Quote"should have been more clear in the original post as well. My tooth compressive stress is too high. Not the tooth root stress. My mistake." Unquote

let me ask a question here if I may.and forgive me if I am way out in left field.
you state teeth compressive stress, and not tooth bending stress.
are we talking apples and orages or ?

since this is a spline would not be advisable to change the DP for more number of teeth? for more teeth to distribute the stress on the teeth.

Mfgenggear
 
PearlRock said:
So let me make sure I understand this, you are effectively suggesting an axial variation on the root fillet?

No, what I was suggesting is an axial variation/taper in thickness of the material backing up the internal spline teeth (ie. between the internal spline major dia and the OD of the shaft). This would allow you to "fine tune" the bend and twist of the loaded internal spline teeth along their axial length.

Since you now state that tooth flank contact stress is the problem, can you provide details about the spline configuration, installation details like shaft size/length/misalignment, materials/heat treatments used, and the loading conditions? All of these factors can have a big influence. The design approach given in Machinery's is very conservative, so if you provide as much detail as possible about your particular application we can tell you whether the recommendations in Machinery's are appropriate or not.

Regards,
Terry
 
@mfgenggear, I'm new to this topic. Machinery guide describes the stresses as different, so I can only assume there may be different solutions to each stress problem. This is a demanding application, so it's critical that I be as precise as possible.


@tbuelna
Here's the material being used on the connecting shaft: hardened 35NiCrMo16 tensile strength: 1800 – 1900MPa. 375MPa "alternating torque" I assume that's shear stress. They didn't mention the Hardness value, but I can ask the supplier for it if you wish.

I'm following ANSI B92.2M.
Here's the design I have right now:

effective engagement length is 32mm

EXTERNAL Involute/Straight/Fillet Root
Flexible Spline
Solid Shaft
Class 5 Tolerance
H/h Fit Class
32 tooth
Module 1
Pressure angle: 30deg
Pitch Diameter: 32mm REF
Base Diameter: 27.71281mm REF
Major Diameter: 33.000mm MAX
Form Diameter: 30.791mm
Minor Diameter: 30.102/30.200mm

Circular Tooth Thickness
Min Actual: 1.514mm
Max Effective: 1.571


INTERNAL Involute/Straight/Fillet Root
Flexible Spline
Class 5 Tolerance
H/h Fit Class
32 tooth
module 1
Pressure angle: 30deg
Pitch Diameter: 32mm REF
Base Diameter: 27.71281mm REF
Major Diameter: 33.800/33.898mm
Form Diameter: 33.200mm
Minor Diameter: 30.991mm MIN

Circular Space Width
Max Actual: 1.627mm
Min Effective: 1.571mm

Peak torque to be transmitted: 400Nm
Here are the stresses I calculated:
Max Tooth Root Shear Stress: 24Ksi (Machinery guide recommends less than 50ksi for hardened steel)
Pitch Diameter Shear Stress: 10Ksi (Machinery guide recommends less than 50ksi for hardened steel)
Max Tooth Compressive Stress @ 3540inlbs/3000RPM: 11Ksi (Machinery handbook says maximum should be 5Ksi for case hardened steel. I'm not sure what to do about this.)
Burst/Tensile Stress: 19Ksi (with 32mm spline engagement) (Machinery guide recommends less than 55ksi for hardened steel)


Misalignment has a big impact on the compressive stress according to the equation. I don't know what the misalignment of the test stand is, but I assume it's going to be extremely low. The mounting fixture is very robust; machined and assembled precise enough for high speed & torque transmission. I wonder if they can give me this information??

So the loading condition is why I posted this thread. This motor has very bad torque quality, and the application factor has a big impact on the compressive stress. I'm looking at at graph right now, where the torque goes roughly from ~0 to 400Nm (with additional torque pulses/harmonics) at 300Hz+ at constant speed!

I believe that is all the information you requested. Let me know if you need any more details. Any recommendations are welcome. Thanks for your time.
 
PearlRock-

Perfect. I wish everyone would provide this kind of detailed information when asking a question.

First, the material and HT cond. you described for the external spline is extremely high strength and has a high surface hardness (almost Rc53). So as gearcutter noted your spline is probably limited by surface contact stress. Using a simple P/A contact stress of around 5ksi is extremely conservative and will easily result in unlimited life for your spline. However, the torque value you should use for calculating the lifecycle contact stress value is far less than 400N-m. You should use a torque value based on a cubic mean value of the load cycles and torques the spline is subject to over its operating life. In your case, this torque value will likely be much closer to the 250N-m number you noted.

Also remember that the 5ksi contact stress recommendation is extremely conservative. Since your dyno driveshaft spline application is not flight critical and can be inspected on a regular basis, I would see no problem with designing it for a simple P/A contact stress of 11ksi with the materials described. However, you might want to take a closer look at the 54ksi torsional shear stress in the shaft with reversing, high-cycle load conditions.

Good luck to you.
Terry
 
Looks like I'm ok now. I spoke with the dyno manufacturer yesterday. Using the average torque instead of peak torque, the stress goes down considerably. There's still some uncertainty with the factors, but we think with the material selected, we should be in good shape.

Thanks for taking the time to discuss this with me
 
Looking back at one of your last posts you noted the torque loading the shaft is subject to is 0-400Nm at a frequency of 300Hz. That's 1.08x10^6 load cycles per hour, which is quite high. Have you checked to make sure your shaft has adequate fatigue capability for the loads/lifecycle you plan to subject it to?
 
Terry,

It is indeed quite high. For the spline calculations I went with 1million start-stop cycles and 1billion revolutions. The result was about 5ksi compressive stress. If this was for a long lifetime production environment, I'd want more, but the dyno manufacturer and I agreed we believe it should be acceptable for experimental application. What I have in the back of my mind is that the torque numbers I presented exist during low speed/transient. We're really more interested in high speed, where the torque is roughly 25-50% lower and the torque quality improves to an extent. In addition to that, the next phase of this project investigates new technology which should enhance the torque quality. I'm hoping all these factors will result in a spline with nearly unlimited life, but I'll be instructing the test engineers to be vigilant and use the highest safety protocols when going after peak loads.

In regards to my own shaft, I'm a bit worried about that. As far as I understand, I'll need a steel at least as strong as the dyno shaft for these calculations to be valid. I designed the motor and the drive, but I'm weak when it comes to steel selection. This material appears to be on par with some Inconel, aermet and titanium brands, which is unfortunate for obvious reasons. I've entered discussions with a few companies to see what I can get my hands on. If you have any recommendations on this subject, I'd be happy to hear what you (or anyone) has to say.

Best regards
 
PearlRock-

Based on the operating conditions and service environment you listed, I'd suggest making the shaft from a vacuum melt Nitralloy N material (AMS 6475) with a nitride case hardening. Follow the quench & temper recommendations on the data sheet, shape the spline teeth, round all sharp corners appropriately, nitride the shaft, remove the white layer, and then lightly finish grind or hone the spline flanks to improve their surface quality if you feel it's necessary. This will give a tough 180ksi core and a hard nitrided case surface that is very resistant to fretting. If you want an extra bit of insurance with fatigue life you can shot peen the shaft body and spline roots just prior to finish grind/hone operations.

For your reference I've attached an S-N curve for air-melt 4340 steel at 200ksi UTS, which should give you a rough idea of allowable stress levels at high numbers of load cycles. You mentioned looking at some exotic materials like Aermet, but personally I try to stay away from these except as a last resort. Do everything you can to make the design work using more conventional steel alloys, such as optimizing the spline geometry, shot peening, optimizing the shaft section properties, etc. If you can make the baseline shaft design work using conventional materials like 4340 or Nitralloy N, then you will have the option in the future of increasing the capability of the shaft simply by making a material substitution to something like 300M.

Good luck to you.
Terry
 
 http://files.engineering.com/getfile.aspx?folder=94cedd22-5f7a-461c-a76a-99a5262f47dc&file=4340_s-n_curve.pdf
Terry,


Thanks for your comments. Your knowledge and wisdom is vast. You're extremely helpful. I've been kind of (by kind of, I mean a lot) stressing out the last couple days trying to understand this material relationship to this spline. So I can make more informed decisions in the future, what does the case hardening actually mean in regards to the spline? If the tensile strength is lower than the quillshaft, that means my allowable shear stress is lower. I suppose in my case, that's irrelevant because my shear stress is already fairly low. It's my compressive stress that I need to be worried about. Does the case hardening and all those other processing methods improve the compressive stress? I don't understand why allowable compressive stress of the spline is so low according to machinery guide. Steels are not usually rated by compressive stress as far as I know, so the numbers seem very foreign to me. How does fatigue relate to the case hardening in this application, wouldn't a large hardening increase the potential for brittle fracture?


On a side note, I stumbled upon this thread:
You recommended this fellow a grease retaining o-ring and major diameter fit type. The o-ring is a logical suggestion. I think I should ask my Dyno manufacturer to add that? Is it more appropriate to put the o-ring on the male or female spline? Is my spline a Major Diameter fit????? ANSI B92.2M automatically assumes the major diameter fit requirement, right? Good lord why is this so difficult [sad] This is why I wanted to use a flexible shaft coupling. *shakes fist at dyno engineers*

Best regards,
PR
 
PearlRock-

First of all, you must remember that the tooth flank contact stress limits suggested in Machinery's and other references are very conservative, and they are intended to provide unlimited life for most applications. As mfgenggear noted, almost every spline connection will likely be life limited by contact fretting wear. But stop and think for a second just how low a 5ksi contact stress limit actually is in comparison to a material having a Fbru limit of over 250ksi.

With regards to your questions about lubrication of the spline joint, grease can work well if there are proper provisions for keeping the grease in place. With a rotating spline joint you must use a sealing arrangement that keeps the grease from being displaced from the spline interface by dynamic forces. The presence of a grease film at the spline contact interface inhibits the fretting wear process.
 
Ok, I'm starting to understand now. These surface measures are more about fatigue/fretting prevention, as opposed to stress/design. I think that clears up most of my confusion.

And thank you for the material recommendations. That will keep me going in the right direction.

Regards,
PR
 
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