2018 Torque Arm Tests, Splined Interface Design and Tabbed Washers

justin_le said:
Even if the machining (not lasering, fwiw) was off and one tooth initially had most of the contact, that contact patch would almost immediately deform until other teeth or splines are making contact and things get distributed. And it does this well before actual shear failure of any tooth.

Okay. I did this calculation last night, but it was nearly 3.00am my time, which is never a good time for math and given my previous attempts, I decided to leave till today and check it.

I have, I believe it is correct, but check it, and do with it what you will. Below is the inevitable image showing most of the salient data. (I've always drawn sketches for this stuff.)

What I set out to do was see how far the face of one of the Al splines would compress before the widening area of that face -- compress a curve, the contact area widens as it compresses -- would be sufficient for the shear strength of 6061-T6 to arrest the compression.

The formula I started with is that for the Shear modulus: G = Fl / AΔx
G = Shear modulus (26Gpa for 6061-T6)
F = Force acting (100Nm @8.5mm = 11764N (2.644ksi))
l = Initial length (perpendicular to force for shear) = 8.5mm
A = Cross-sectional area. (I start with the contact area taken from the image: 0.34mm * 5mm(~3/16") = 1.7e-6m^2)
Δx = the compression distance I sought.

Plugging those numbers into the formula I get Δx = 0.00226230m. 2.26mm give or take.

The model of the fluted shaft and torque plate is drawn from one of your close-up photos above, and should be more or less correct. The arc of short wiggly lines through the section of the TP flute are tangents to the force arc every 0.5° (where the shear planes go as the axle rotates), and the arc length is 3.73410mm.

That means the axle would compress the Al by 60.5% of the section of the tooth before stopping!.

Ah,but the area would increase as it progresses, and as it compresses, other teeth will come into contact and the load will start to be distributed.

So then I started looking at how the width of the section of a 2mm radius tooth increases as the axle cut across its diameter; and trying to make some assumptions for the depth the first tooth would need to penetrate before the second tooth came into contact, assuming some reasonable manufacturing tolerance.

I started with 50microns (a gnat's under 2thou") which is as good as most people can achieve (on steel) with a surface grinder and way better than I've ever seen achieved with a wiggle (rotary) broach; and they tend to 'wander' in aluminium.

The best case scenario I calculated was with ±0.000 tolerance on both parts -- impossible -- and I got a little under 0.5mm of compression before things equalised and the axle stopped compressing the TP teeth. 0.5/3.7341*100 = 13.4%

The problem is, the 'Elongation at break' figure given for 6061-T6 is 10%. It would never stop cutting! Which is pretty much exactly what your tests showed.

You could try using 7075-T6, but it's shear modulus is exactly the same at 26GPa, and it elongation at break is only 7.9%. It's ultimate, tensile and fatigue strength are all about double that of 6061, but it achieves it by being over 50% harder (150 brinell vs 96 for 6061).

Harder means less ductile, hence less elongation before failure.And that's before you start considering the bogeymen of cyclic fatigue, shock loads, et. al.

Double the thickness of the TPs and use very expensive Al, or move to steel (flutes work for gearbox shafts at the clutch, and sliding joints in drive shafts), but I think persuading manufacturers to start cutting flutes rather than flats on their axles -- given the price pressure -- is asking a lot.

Once again. Good luck.

9FluteShearPlane.jpg
 
justin_le said:
And it does this well before actual shear failure of any tooth.

And finally, a graph of axle rotation against contact arc length and penetration depth:ContactArc.vs.PenetrationDepth.vs.AxleRotation.jpg
 
Buk___ said:
......... but I think persuading manufacturers to start cutting flutes rather than flats on their axles -- given the price pressure -- is asking a lot........

Well, I guess that puts us back to square one.....

Square 1 Axle and Torque  Arm 2.JPG
Square 1 Axle and Torque arm.JPG

:D
 
What fantastic testing! As always, great thought process and testing process.



And I see that the heavy analysis is still part and partial for many members here. I find it quite refreshing to see tests showing the torque arms doing what the final goal is, and yet there is still heavy discussion on why it won't work :lol: Love you guys!!
 
johnrobholmes said:
........ I find it quite refreshing to see tests showing the torque arms doing what the final goal is, and yet there is still heavy discussion on why it won't work :lol: Love you guys!!



Aaahhhh, but the goal was 200Nm. Justin is not there yet. He's got it close though.

:D
 
e-beach said:
johnrobholmes said:
........ I find it quite refreshing to see tests showing the torque arms doing what the final goal is, and yet there is still heavy discussion on why it won't work :lol: Love you guys!!



Aaahhhh, but the goal was 200Nm. Justin is not there yet. He's got it close though.

:D


The mild steel failed at 280Nm, page one.
 
I appreciate the benefits of using aluminum, even 7000-series, but...I am just as certain the final product will be some type of steel that can be cycled tens of thousands of times without developing cracks that propagate. In a multi-spline design, its almost impossible to precisely get two parts to mate perfectly using cost-effective methods. If you agree, then only a few splines will be immediately loaded at a normal cruise speed.

Once hard acceleration is applied, those engaged splines will flex ever so slightly, which will then engage most of the remaining splines to some degree, spreading the peak load over many splines (I like splines). Then, on heavy regen (worst-case scenario), the assembly will flex in the other direction. There are affordable steels that have the hardness to not deform under the anticipated loads, the toughness to not develop cracks, and the springiness to flex a very slight amount....tens of thousands of times without failure.

edit: I was a hydraulic mechanic at McDonnel Douglas, and we used hydraulics to cycle parts for peak failure analysis, and also life-cycle stress analysis. I am not an engineer, just a wrench-head.
 
It is my understanding that steel will always spring back as long as it is not pushed past the yield point. The splines should yield in the contact patches until enough contact area is made to distribute the force along multiple teeth, and from there on out it will always have the same contact area.

If the clamping bolt gives enough preload, the two parts will bed into each other without any slop developing between the parts. This is why I believe Justin has chosen the splined interface to begin with. There might be a single retightening of the clamp bolt at the 100km point, much like how wheels need to be retightened once after the spoke heads bed into the hub shell and nipples bed into the rim. Of course on a wheel build, it is possible to pre-stress the wheel and prevent the break-in period. On a splined torque arm, this isn't really possible. It would stand to reason that the bedding in of the splined torque arm will be such a small amount that the clamping bolt takes care of it completely.

At this point there is not much left but to cycle test them on the bench or in real life and see how it goes. I would gladly run them on a bike after the data that Justin has shown. Even if the clamping bolt needs one retightening, it is still worlds better than current options!
 
johnrobholmes said:
.......The mild steel failed at 280Nm, page one.

First yield 150 Nm..... Page 1
It's only at 150 Nm that we noticed the arm not returning to the same zero point.


:D
 
Put torque arms on both sides :mrgreen: 300nm should be enough for most motors.

I think Buk is on to something with the modulus though. A harder material that elongates less at the fail point should greatly improve things. I'd go for heat treated 4140 chromoly.
 
fechter said:
I think Buk is on to something with the modulus though. A harder material that elongates less at the fail point should greatly improve things. I'd go for heat treated 4140 chromoly.

Modulus and hardness (in the engineering sense) are not closely related. For instance, 7075-T6 aluminum has higher hardness than mild steel, but is three times less stiff.

In this situation, I'm not sure how important modulus is. It seems to me that it almost wouldn't matter.
 
I love the work, any progression in this area is a benifit no doubt, making an oval torque arm more operational with big power and regen does make sense but it's not a high demand area and that's why we have had such a nominal design, because the money to develop what Justin is doing will see very little return on the torque arm front.

But if hub motors in general can be redesigned to use this as a standard then it best be patented because the Chinese will be all over this making inferior versions.

At 2kw my 8mm high grade stainless torque arms spilt into a 4mm plate each side hold my mxus 3k in place just fine, but I know if I power the hub on 96v and 80mps then I'll be replacing them quiet often along with an axle that will be deforming no doubt.

I'd like to see the axle of a hub motor with a splined outer and a threaded inner , Use ever increasing sizes of spines with bigger hub units to stay away from the hub itself yielding the axle under full load.

As regards to the wires I'd like to see a sleeve with holes around it to bring the wires out of the hub this would have large outer bearing that mates it to the hub flange then a smaller inner bearing to support the axle shaft, the axle would no longer be hollow and the phase wires can get as meaty as you like so its sporting 3 bearings 2 on the phase side and one on the normal drive side but been a hub the axle will just pop out either end.
 
fechter said:
Put torque arms on both sides :mrgreen: 300nm should be enough for most motors.

I think Buk is on to something with the modulus though. A harder material that elongates less at the fail point should greatly improve things. I'd go for heat treated 4140 chromoly.

Hardness is the wrong property to look for; and I think you may have missed the point about elongation.

When you are relying on the material's ductility to allow multiple bearings surfaces -- that are slightly misaligned due to manufacturing tolerances -- to align, you need a material that allows greater elongation before breaking, not less.

And there is no purpose in making the torque plate harder than the axle, you'll just damage the axle.

Chromoly steel (unhardened) would be a good choice as its shear modulus at 73GPa, is nearly 3 times that of the strongest (in shear) Al, which are all around the 26GPa regardless of the variations in tensile strength and hardness. (Basically Al, in any of its guises, is lousy in shear!).

The fundamental limits of the system are defined by:
  • The mechanical properties of the steel used for the axle.
    Assuming that obtaining those specs is not possible -- determining them from sample would be destructive, and only indicative of the sample destroyed -- which makes asking for them to be changed difficult (to what?); then the best you can do is assume that they are 'adequate for purpose'.
    .
  • The diameter at which the forces act, and the derivable area in shear.
    This is pretty much defined by the 10mm 'standard' drop out used by the frame makers and the best the motor manufactures can do is the 14/10 arrangement we get now.

    One can safely assume that they increased this from the once common 12/10 arrangement for good reason.

Jason's design seeks to increase the torque moment by increasing the diameter to 17mm, dodging the problem of the dropout size by placing the torque plate behind the dropout.

That 's a good move in two ways:
  1. It reduces the leverage acting by a little over 17.5%.

    1 / 0.014 = 71.43 vs. 1 / 0.017 = 58.83.

    The material for the bearing surface has to contend with 17.5% lower forces.
    .
  2. It increases the space (area) available to resist the torque by the same factor.

    With the forces acting tangentially to the rotating axle, the radius through which the bearing points turn, defines both the amount of material that can be used to resist it, and thus the strength (shear strength) required to do so.
    .

    Reading that back it is about as clear as mud, so its 'demo time', (with apologies to SCD:ITT fans :) ):

    junk51.jpg

    If you look at the 14/10 flats arrangement on the left, you can see that the circumference is split almost exactly (184°/176°) between the axle and dropout/TP.

    On the right, Jason 9-flute design splits the increased circumference roughly 2 to 1 in favour of the TP. That's a good idea if you intend to make the TP from a less strong material like Al.

    Ie. The 14mm flats axle has 46mm of arc in the axle, where the 17mm still has 35mm of arc in the axle despite the 2:1 ratio.

    The problem comes from it splitting that 234°/ 35mm of TA material into 9 sections.

    Where the 14/10 arrangement has 23mm of arc * the TA thickness resisting each point of shear; the 17mm/9 flute design only has (26°/360°) * (17mm * π) = 3.85mm of material resisting each point of shear.

    If the materials were manufactured to exact sizes (no tolerances) then that wouldn't be a problem, as all the flutes would engage simultaneously and the forces would be split evenly and only 1/9th would be acting on that 3.85mm.

    But as initially, only 1 flute will engage, it takes the full force until it deforms sufficiently for the others to also engage. Whilst that deformation may still be within the elastic limits of the material, it still imposes a fatigue on it which would cause fatigue failure over time/cycles.

    But with only 3.85mm * 4.7mm and a 26Gpa shear modulus, resisting the full 2600ksi, it moves directly into plastic deformation and the shear plane reaches right through the material on the first loading, and it fails. The axle rotates on, engages the second flute, same thing happens again and you have a cascading failure.

    This is exactly what Jason's tests demonstrate.

If you reduced the number of flutes to 5, and kept the same 1:2 ratio of axle to TP, then the shear area of the TP increases to 7.12mm * 4.7mm and it might survive the first encounter; but who's going to bet on the life expectancy given Al's propensity to cyclic fatigue?

But the best you could do is return to flats. With 17mm axle and 12mm flats, it splits the 53mm circumference almost exactly 50/50 (as with the 14/10 combination). That gives 13.35mm of material to resist the shear, nearly 4 times as much as the 9-flute design.

And if you went to the square design (per e-beach's model above), you effectively split the load into 4, and give almost the entire 53mm of circumference over to resisting the torque:
junk52.jpg

If this has a weakness, it is the risk of 'knocking the corners off' the axle; but if the TP material is softer than the axle, that cannot happen.

Then you could look at history, and you realise that this is almost exactly what the bicycle engineers did in the early 80's when they got rid of cotter pins on the pedal cranks, and moved to the tapered square design that served so well until the marketeers got their hands on and decided that proprietary was good for profits (Octolink et. al.). Those guys (in the 80s) knew what they were at!

Of course, they went one step further; they added the taper. The benefit of the taper is that it, for the most part, eliminates the problem of manufacturing tolerances. The taper uses the 3rd dimension to take up any slack in the first two and 5 or 10 thou of tolerance ceases to be an issue.

The problem with using it on motor axles is the need for those axles to accommodate different thicknesses of dropout plates, and different widths of 7/8/9/10/11 sprocket sets. The motor manufacturers already have to contend with the latter issue -- using different axles. If Jason could persuade them to move the torque arrangement behind the dropout plate, it eliminates the former problem.

But in doing so, creates another; that of some mechanism to take up the slack in the axle direction.
 
Chalo said:
In this situation, I'm not sure how important modulus is. It seems to me that it almost wouldn't matter.

First, it depends which modulus you are talking about, that of elasticity or shear.

And given this situation is all about shear strength (or lack thereof) the latter is very important. Even primary.

However, the elasticity is also important as it defines the transition from elastic to plastic deformation; ie. the point of failure.

"Stiffness" on the other had is not a property of the material, but rather a property of the component's shape.

The real red-herring here is the need for "hardness"; there's no point in the TP being harder than the axle.
 
Hey wow, this turned a bit more lively than I had anticipated. Thanks everyone for pitching in and it's good to see the general interest in a solution beyond 'axle flats'.

johnrobholmes said:
If the clamping bolt gives enough preload, the two parts will bed into each other without any slop developing between the parts. This is why I believe Justin has chosen the splined interface to begin with.

Exactly exactly, thanks JRH for catching onto this. The primary appeal of splines to me was precisely this concept that it can be pinched with relative ease to have zero slop and full tooth engagement. And the pinching can even achieve the necessary preload to deform contact surface irregularities, compensating for tolerance issues, ensuring all teeth are engaged and that there is no play on torque reversal with regen. And as you mentioned, if it was to have an initial break-in when the metal surfaces seat against each other, then this can be snugged up with the pinch bolt once any play is noted. The analogy with seating spoke heads in a hub flange is spot on.

When you have a square style interface the ability to snug things up after the metal has deformed is not nearly as good. At least that's the sense that I get from all my firsthand experiences of squishing metal interfaces with flat axles. For instance rather than the idealized picture painted here where the entire circumference is resisting in shear

file.php

What actually happens is that the metal yiels significantly at each corner, as you can see in these earlier tests with flat axles. There is no shearing failure, just significant deformation around the point of high stress.

file.php

from https://endless-sphere.com/forums/viewtopic.php?p=211724#p211724

With a square interface, once that happens even a little bit it's hard to snug it up again, as the flat surfaces have become curved outwards.

All this said, I completely agree that if a square interface does demonstrate itself to be adequate, that would be a preferred option for the sake of being an easier interface for people to build to. Remember that we have a ~9mm diameter motor phase cable that needs to exit the the axle, so what we'd be looking it is this:

Square Interface Axle.jpg

as opposed to this:

Splined 3D Model with Arm.jpg


I have my doubts that the square will be nearly as stiff at resisting initial axle rotation, and my bet it that it will show deflection of a few degrees at much lower torque than the splined version, but that the final failure torques may be similar. However, I could easily be wrong and will let evidence speak for itself one way or another.

Off to the milling maching to go make a square axle prototype!
 
Nice CAD's...and I have been staring at them for far too long to see where I might make comment for improvements. I have some notions of how I would change things. And I might ad my 2¢ later, but then I got to thinking.......

Why fight the world of e-bike motor manufacturing just to sell a few more torque arms.

Why not just sell standardized frames with 10 x 14 mm dropouts. They might make more money then selling torque arms and offer a better product compared to having to customize an existing bike frame to solve a safety problem by modding a part for a frame that was not built to suit the propose.

Back to staring at the CAD's

Anyway my 2¢

:D
 
justin_le said:
What actually happens is that the metal yiels significantly at each corner, as you can see in these earlier tests with flat axles. There is no shearing failure, just significant deformation around the point of high stress.

With 1/8" material, predictable enough.

justin_le said:
I have my doubts that the square will be nearly as stiff at resisting initial axle rotation, and my bet it that it will show deflection of a few degrees at much lower torque than the splined version, but that the final failure torques may be similar. However, I could easily be wrong and will let evidence speak for itself one way or another.

Off to the milling maching to go make a square axle prototype!

I wasn't recommending it.

Only analysing it, and noting its precedence in history. And noting that it needs the taper to get around the problem of tolerances; and that creates its own problems.

I did start looking at a square taper design to fit behind the dropout, and worked out that a 7° axle taper would need to be 7mm wide to accommodate 5mm of torque plate allowing for a combined tolerance of 0.25mm/0.010".
junk52.jpg

But I couldn't see a way of providing space for your cable, whilst still ensuring that the taper didn't become a fulcrum, completely destroying any benefits.

With the CAD design you've posted, with no taper to take up those manufacturing tolerances, the square split through the diagonal, and the pinch bolt 50mm away from the action; and so much of the corners 'knocked off', you've almost turned the square into an octagon and thrown away all of the squares benefits over flats; reducing the circumferential length resisting torque by almost 40% from almost 53mm to 33.31mm; and created (I think) pre-loaded stress point opposite the cable opening that is destined, almost designed, to fail:junk53.jpg

I agree the top version is idealised, and there is probably no way around the need for the cable opening, but rather than moving the sides of the square (diamond) out to produce a ~2mm flat on the corners -- with the inevitable loss of resistance material -- you could leave the sides alone, and put a small (say 0.5mm) radius on the corners.

I'd also look at putting a small diameter hole (say 1mm dia.) where the red circle is in the second image to redistribute the pinch bolt, pre-load stresses; but that's off the top of my head without any analysis.

Depending which CAD you're using, many of them come with an FEA module that would be useful here.

Anyway, it'll be interesting to see what you make and how it fares in test. Without changes to the cad you posted, I suspect not very well.
 
justin_le said:
Off to the milling maching to go make a square axle prototype!

Okay. This is my quick attempt at checking the stresses in (my attempt to reproduce) your square design:junk54.jpg

The important bit is the bottom close-up. The vertical lines around the centre of rotation on the left are there to measure the compression and tension in the material. Kind of like virtual strain gauges.

What they show is that the material to the right of the CoR experiences a 1.5% (max) compression in length; whilst the material to the left of CoR stretches by 5% (max).

In steel, with ~23% elongation before break, that is no problem, and there would be no need to take extra measures to relieve the stresses.

In Al, with 10% or 7.9% elongation, that is a concern. It would probably survive the first test, and perhaps a second, but over cycles?

I estimate (not calculate*) that in mild steel, this design should be good for around 250Nm; and in annealed ChroMoly, probably 30% or so higher, so maybe 325Nm. This assumes that the torque arm is made of at least 5mm thick plate and the axle is made of a tougher material than the torque arm.

*Not calculated, because it would be a waste of time to perform calculations based upon my guess of the dimensions of your design. It is impossible to extract any accuracy from a 2D render of a 3D design -- especially if you don't know if perspective has be added -- which is why I prefer 2D.
 
I have also only 2 cents of an idea or it's more a question to the calculation professionals...

What's wrong with the(normal flat axle) clamping dropouts we are using on the "big bikes"?

... I mean we re pushing up to 20kw from a dead stop and if you're searching about sheared off axles you only find that historic crystalyte crap.

A single ta is nt that ideal at all.
Snapping an axle is more easy.
To be honest... Never saw a snapped axle when used 2 TA.

if I had a wish I would prefer an "update" about how the wires comes out of the motor. It's always shitty with the disc brake.
Always needing disc Spacers... Extend the brake bracket... Making it more flexing....
 
Merlin said:
I have also only 2 cents of an idea or it's more a question to the calculation professionals...

What's wrong with the(normal flat axle) clamping dropouts we are using on the "big bikes"?

... I mean we re pushing up to 20kw from a dead stop and if you're searching about sheared off axles you only find that historic crystalyte crap.

A single ta is nt that ideal at all.
Snapping an axle is more easy.
To be honest... Never saw a snapped axle when used 2 TA.

if I had a wish I would prefer an "update" about how the wires comes out of the motor. It's always shitty with the disc brake.
Always needing disc Spacers... Extend the brake bracket... Making it more flexing....

From my perspective, 14/10 flats are about the perfect solution for motors that are intended to be retro-fitted to ordinary bike frames with standard 10mm dropouts. And generally, that means 250w to say 2kw hubs.

For this class of motor, replacing the standard dropout plates with beefy, pinch-bolt style torque plates as most of you high performance guys do isn't an option that most bicycle-with-a-bit-of-assistance people (like myself) would consider. And using pinch-bolt style add-on torque plates makes remove/replacing the rear wheel for punctures and other road-side maintenance a pain.

I'm currently running my 800W geared hub at 36V/20A and seeing maximum peeks of just under 1000W of draw. I'm still relying on the supplied tabbed washers for torque control. I'm looking to upgrade the battery pack to 48V and my controller will go to 40A, if I felt the need and dared. Before then I need to find a better TP solution; hence my interest/involvement.

Jason is looking at having his manufacturer(s) modify their axles for him, but that's beyond my reach.

I'm currently considering this design for my use:

5layerSpringSteelTorquePlate.jpg

It's 5 layers of 1mm (unhardened & untempered) spring steel, riveted together, with 'kinks' in the tabs that engage the axle flats. By using 5 layers of thin, annealed spring steel, I'm hoping that I will be able to make these at home with simple hand tools. I might look at termpering them to some low value -- circa 50HRC -- to improve the longevity of the 'spring', without making them hard enough to damage the axle. (Not sure about that!)

The top view cross section shows how the axle nut will compress the kinks, causing them to close up the gap either side of the axle flats.

The dropout plates on my steel frame have room and are sufficiently thick, that I will be able to permanently bolt the torque plates to them and so removing/replacing the wheel at the roadside for punctures, will not require any extra tools or trouble than a normal wheel.

I'll probably reduce the number of rivets and bolts to two of each on opposite diagonals.

All of which is probably irrelevant to you hot-rodding guys, but the design might be adaptable for your needs if you see any benefits to it.
 
Buk___ said:
..........
With the CAD design you've posted, with no taper to take up those manufacturing tolerances, the square split through the diagonal, and the pinch bolt 50mm away from the action; and so much of the corners 'knocked off', you've almost turned the square into an octagon and thrown away all of the squares benefits over flats; reducing the circumferential length resisting torque by almost 40% from almost 53mm to 33.31mm; and created (I think) pre-loaded stress point opposite the cable opening that is destined, almost designed, to fail.......

I was thinking similar thoughts when I was staring at the cads last night. So here is a early morning thought....

Get that bolt as close to the square as possible while still having some materiel to act as a 4th wall. If the cable is exiting at an angle anyway, it should go around the bolt and into the TA slot.
Square 2.JPG
Square 2a.JPG

:D
 
e-beach said:
I was thinking similar thoughts when I was staring at the cads last night. So here is a early morning thought....

Get that bolt as close to the square as possible while still having some materiel to act as a 4th wall. If the cable is exiting at an angle anyway, it should go around the bolt and into the TA slot.

:D

Inspired by a pair of nutcrackers, this dodges the issue of getting around/over the cable:junk55.jpg

The hinge detail is a little complex (and entirely wrong in my attempt at a 3D representation) but both jaws/legs are identical, so there is only one part to manufacture.

I've shown a rivet, but it could equally be a press-fit pin, by slightly reaming the hole in one leg.

It'd need a bolt through the legs which I haven't shown.
 
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