2018 Torque Arm Tests, Splined Interface Design and Tabbed Washers

justin_le

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In some sense this is a decades old follow up to our initial torque arm experiments from this thread
https://endless-sphere.com/forums/viewtopic.php?p=211356#p211356

The standard for imported ebike hubs back then was M12 or M14 axles that were ground flat to 10mm in order to use the dropout slots for anti-rotation torque. This wasn't always adequate to stop axles from spinning and a whole industry of after-market torque arms sprung up to address this intrinsic design deficiency. The use of an M12 or M14 axles with flats also meant that the motor axle would sit lower in a dropout slot than a standard bicycle hub, enough that in many cases the disk brake caliper pads are only half engaged with the rotor.

Axles_Diams_In_Dropouts.jpg

It's possible to file the top of the dropout slot square and deeper, but that's a level of frame modification that most people would prefer to avoid.

Meanwhile, all of the non-import hub motors from that era (Wavecrest Tidalforce, Heinzmann, BionX) had an integrated torque arm which either directly clamped to the frame, or in the case of BionX had a serrated mate to the dropout face, ie proper design engineering.

Almost 10 years later and it's like nothing has changed. All the common imported motors are still using axle flats as the primary means of anti torque rotation, and we're were constantly dealing with afterthought torque arms to address that.

For us we're definitely ready to move on! Not that torque arm production hasn't been an OK little side business but it's really not the way that the industry should continue heading.

In this thread I'm going to go over our current development and testing cycle of a splined axle interface for internal torque arms that we're hoping could provide substantial benefit to hub motors.
 
Our basic goal was to try and modify a MAC rear cassette motor axle with the following objectives:
  • Side cable exit
  • Actual 10mm Axle diameter in dropout for proper bike frame fit
  • Torque arm that fits inside the dropout face
  • Splined interface for very high spinout strength
  • Tight fit so that there is no rocking with regen
  • Ability to withstand at least 200 Nm without failing

Making splines on the axle was the easy bit, the trickier detail is getting the cable to exit on the diagonal. The MAC motor has a 17mm diameter shaft on the disk side and that doesn't leave much room to squeeze a cable exit and still have a solid 10mm axle. It seems like it just fit.

Splined Axle CAD.jpg
Axle Section View.jpg

With the wire coming out this way, there isn't room for it to stay entirely inside the dropout. Instead the cable will have to enter into the dropout slot under the axle and then loop down, effectively coming out of the bike frame as though it emerged from the dropout slot.

Assuming that this strategy works, then it should be something we could easily get other motor manufacturers like Crystalyte and eZee to use as well, since they also all tend to have a 17mm axle diameter inside the dropout.

MAC motors was kind enough to make us a prototype axle like this for us to validate the design and let us do initial torque arm experiments. I wanted us to be analytic in the testing and so last month we built a nice little axle spinout testing jig. It's got a long steel arm with strain gauges and a potentiometer on the axle to measure the amount of axle rotation. Both the Torque and Potentiometer signals go into a CA3 which was hacked a bit to provide a live data output that we could log while applying torque on the axle until failure.

Torque Arm Test Jig.jpg
 
Holy cow! This is such a great idea! I am very interested in seeing what the results of the tests will be. If I was a betting man, I'd put money on the axle breaking at the wire exit before that torque arm strips.
 
electricwheels.de said:
Excellent Jig - I'm looking forward to see the graphs.

I was realllyy looking forwards to seeing proper graphs of torque arms failing too from this test jig, and I can tell you that they don't disappoint!

We only had the one sample splined axle to work with so we decided to do all of the prototyping and testing using aluminum torque arm plates. That way the torque arm would fail but the axle splines should stay in tact for additional tests.

One other constraint we had in the design is that the torque arm plate had to install over the axle with a connectorized cable already coming out of the motor, which means that the splined interface piece has to be 'U' shaped. A complete circle wouldn't work as then there would be no way to pass through a large overmolded motor connector plug through the splined opening of the torque arm.

Our very first test piece actually looked a bit like a U, with the matching splines, and it the open end of the arm was held captive between two metal plates. This failed with relatively little torque, and not with any of the teeth actually shearing off. Instead, the entire thing rotated like a cog and a chain.

First Failure.jpg

Clearly we needed a larger outer diameter of the aluminum plate, and something to hold the end captive so that they couldn't slide past one another so easily. That lead to this design here, with a pinching bolt (not shown) that clamps the two ends of the arm tight.

2nd Torque Arm Attempt.jpg

This tested better, but was still fundamentally flawed. Unfortunately we had the CA's data averaging set to like 1.2 sec so the torque data just goes in a few discrete steps. You can see that for the first 30 Nm of force, there is almost no deflection at all on the axle, and then after that it yields quite a bit, ultimately failing at 80 Nm with over 15 degrees of axle twist

Graph of R2.jpg

When we look at the arm itself, we see that only one tooth actually sheared off, which we presumed is what happened at the 30 Nm point. After that, the rotating axle effectively spread the torque arm plate open, smearing the aluminum in the process but not actually breaking it further.

Torque Arm Walkout.jpg
 
We tried then doing a test after that with 4 bolts rather than just 4 holding the open arm to the back plate, hoping that this would prevent the kind of spreading open and enlargening of the splined hole.

The results are better. The full spinout torque reached 110 Nm, and happened at just 4-5 degrees rather than 15 degrees. However, we could still see that there was almost no deflection at all until ~30 Nm, and then after that something gives the the material has a much shallower degree vs applied torque yields curve.

Graph of R3.jpg

When we looked at the torque arm plate, once again there was only ONE tooth that was sheared off. The rest were all deformed to various degrees but not actually broken.

Aluminum Single Tooth Shear.jpg


At this point we thought it would be good to make up an sample torque arm that was a closed full circle rather than being an open 'U" just to establish a benchmark for what the torque / angle curve would look like if all the teeth were stressed the same way and failed simultaneously. So it was off to machine this on the mill last week:

Full Circle Arm.jpg

The results though were not all that much better than our two part arm with the open 'U' piece, peaking now at 120 Nm rather than 110 Nm. We see once again a very stiff response up to 30 Nm, then something gives as we start to have measurable axle rotation.

Test Data, Full Circle Spline, 6061.jpg

When we looked at the failed torque arm, it was apparent that the issue here isn't so much that the splined axle is "spreading open" the torque arm plate. Rather, what was happening is that once the first tooth broke off on the plate, the entire axle was then able to 'walk down' as it was being rotated and into the cavity of the torque arm plate where the wire exit would normally be located.

Some Walking Down.jpg
 
justin_le said:
...what was happening is that once the first tooth broke off on the plate, the entire axle was then able to 'walk down' as it was being rotated and into the cavity of the torque arm plate where the wire exit would normally be located.
...a squashing the cable in the process = back to the drawing board. :(
Instead od using rounded teeth, try using trapeziod teeth with a slightly negative angle. The rounded section at the top of each tooth acts as a ramp aiding the downwards movement. A negative angled flat does the opposite, the shaft wants to go towards the closed end.
 
I agree that just using the axle flats is a lame way to prevent the axle from spinning. The spline would be much better in many respects. Ideally, the motor should have a larger ID on the bearing to allow a larger axle diameter so you don't need a hollow axle and you have a larger diameter shoulder to grab onto. I liked the old Hienzmann motor style where the arm is integrated into the motor.

Heinzmann.jpg

Another fail in most of the current systems is slack in arm. If you are using regen, the axle goes from drive to brake and if there is any free play in that, the nuts are doomed to coming loose. Having the arm clamp onto the axle so there is no free play is vital.

If aluminum is too soft, maybe go to hardened steel?
 
2 flats on an axle is OK, when the torque arm is used the correct way.
Here a torque arm fitted with a Crystalyte HS3540:
.
torque arm forward.JPG
.
The torque arm is made from 4 mm thick alloy 7075 T6 and is used with 4 additional torque washers:
.
torque washer.JPG
.
They are connected with 2 pieces dia 3 x 18 mm steel dowels, which go through all 5 layers and turning it into a solid block.
Similar principle on the reku torque arm on the opposite side:
.
torque arm reku.JPG
.
The arms are made from 2 parts, so that a preload can be applied. Using so-called RIPP screws, they won't loosen even under vibration.
The torque arm rests in a piece of POM against the frame tube, and is always parallel to the tube. The cable tie only makes sure that they don't get lost, but is not needed.
.
 
Thank you for taking the time to document this and make it publicly available, Justin! I've been somewhat involved in this project, but am continuously amazed by the time and care that you bring to the projects you take on.

Seems that the torque arm failures are from the arm's teeth progressively failing, one-at-a-time, allowing the axle to rotate. I trust that you'll be able to find a way to more evenly distribute the torque on the teeth to increase strength.

Playing with the motor simulator, it seems that a 12T Mac motor powered by a 52V battery and a 90A phase current limit controller can get to 120 N-m of stall torque. Ideally, the torque arm wouldn't show any signs of failure at that torque, and really higher to get a margin of safety. What do you think is a reasonable design goal of torque applied without any sign of failure? 200 N-m? More?

fechter said:
...Ideally, the motor should have a larger ID on the bearing to allow a larger axle diameter so you don't need a hollow axle and you have a larger diameter shoulder to grab onto. I liked the old Hienzmann motor style where the arm is integrated into the motor. ...

A larger ID on the bearing would be great, but this requires re-working the planetary gear system the motor might use, which is sized to fit over a 17mm axle. For any geared motor, this is prohibitively expensive - plus, you don't have much room on the non-drive side of a rear hub motor due to the disc rotor attachment. Also, a torque arm integrated into the motor (which would be awesome!) is very difficult to pull off with a modern rear hub motor due to the disc brake on one side, and gear cassette on the other.

electricwheels.de said:
...Here a torque arm fitted with a Crystalyte HS3540:

The torque arm is made from 4 mm thick alloy 7075 T6 and is used with 4 additional torque washers:

They are connected with 2 pieces dia 3 x 18 mm steel dowels, which go through all 5 layers and turning it into a solid block.

Similar principle on the reku torque arm on the opposite side...

The arms are made from 2 parts, so that a preload can be applied. Using so-called RIPP screws, they won't loosen even under vibration.
The torque arm rests in a piece of POM against the frame tube, and is always parallel to the tube...

Wow! That's a very secure torque arm assembly. How long did it take you to install? The goal with this project is to have an effective torque arm with a streamlined installation, and that doesn't run into the disc rotor spacing issues described in Justin's first post.
 
Based on my little experience with materials, I think part of the problem you're running into on these is the same problem you can get with toothed gears, with the teeth deforming and/or shearing off at the roots partly due to the sharp-edged transitions between arm and teeth.

Softening that with some radius would probably help.

Using a different material would also make a difference. I think the failure occuring at basically the same Nm each time means it's to do with the material failure point. Either a different aluminum, or a steel, would give you different failure points. (or possibly different failure modes).

Keep in mind that I'm an intuitive thinker, rather than a really educated one, so I could be completely wrong. ;)
 
electricwheels.de said:
...a squashing the cable in the process = back to the drawing board. :(

For sure, but the drawing board is not a sad face, that's a happy face place to be. This kind of challenge in product development and testing is fun and exciting!

Instead od using rounded teeth, try using trapeziod teeth with a slightly negative angle. The rounded section at the top of each tooth acts as a ramp aiding the downwards movement. A negative angled flat does the opposite, the shaft wants to go towards the closed end.

This is true, but part of our design goal was also that the spline modifications be relatively easy for the hub motor companies (MAC motors, Crystalyte, eZee, MXUS etc.) to do with the same CNC equipment that produces the axles. We thought that a rounded spline like this allow for it to be machined either with live tooling coming in from the end of the axle, or with a ball-end mill on the side of the axle. To do trapezoidal teeth profile could require EDM or custom tooling.

Anyways, none of this would be an issue if the cable exit didn't consume a full 1/3rd or so of the splined arc. In order to prevent the axle from having some freedom to role down into this extra space after the failure of one or two teeth we needed something that would constrain the axle against moving here. One possibility we saw was having a plate that presses against the round portion of the axle shoulder where the diameter is larger and there is no cable exit.

Axle Shoulder for Support Plate.jpg

This was fairly easy to do by exending the backing plate of the arm long enough to press up and mate to this part of the axle. Here you can see that plate on a steel prototype.

Steel Backing Plate.jpg

We also decided to change the testing method slightly. Instead of gradually applying torque on the axle until it failed while logging the torque and angle, we did a pulsing motion. Each pulse of torque was 5 or 10 Nm stronger than the previous pulse, and this way we could see more definitively when the arm had had yielded somewhat and was no longer returning to the same zero point. So now, rather than an angle on the 'X' axis, we have time on the 'X' axis and plots of both the torque (blue) and deflection angle (red).

The results done this way are a lot more revealing. Here it is with a closed loop aluminum torque arm (ie not one that could support the side cable exit)

Test Results with Al plate, full circle.jpg

You can see that we don't have clearcut yielding going on until we've pushed it to 80 Nm, and the failure happens all the way up at 160 Nm. In this case there were multiple teeth that sheared off

Full Tooth Shearage.jpg

We thought that would be a handy benchmark reference for what we could aspire to with a well designed 'U' shaped arm that accommodated the cable exit slot.

And how did it? With an open 'U' shaped arm but with a steel backing plate that pressed against the axle shoulder, the results were actually even better than this:

Test Data, R5 arm with Steel back plate.jpg

We didn't get any plastic deformation until exerting more than 120 Nm on the lever. At 160 Nm, we were at 2 degrees of overall yield/deflection, the same as the closed circle test arm, but we were able to go over 190 Nm before failure. That's with an aluminum torque arm that's just 3/16" thick! I was pretty impressed. It's quite uncommon for anyone would have an ebike hub motor setup that is pushing 120 Nm of motor torque.that's an amount of phase current that would overheat and burn up most ebike hubs in very short order.
 
liontail said:
Playing with the motor simulator, it seems that a 12T Mac motor powered by a 52V battery and a 90A phase current limit controller can get to 120 N-m of stall torque.

Oops, I didn't see this post when I just submitted mine. It's true that the motor simulator shows 120 Nm, but I suspect that we're into non-linear and demagnetization realm of the MAC motor at that level of phase current, so the actual torque is likely to be less than this. We just today received a 150A 40V 6kW power supply from ebay that will let us repeat the tests here with more modern equipment.
https://endless-sphere.com/forums/viewtopic.php?p=216194#p216194
That is going to be a phase - two of this project, establishing the actual worst case motor torques.

Ideally, the torque arm wouldn't show any signs of failure at that torque, and really higher to get a margin of safety. What do you think is a reasonable design goal of torque applied without any sign of failure? 200 N-m? More?

At this stage that's exactly what we're shooting for, 200 Nm. The fact that we could just about hit this with a machined 6061 aluminum arm surprised me. And this is with a plate that is 3/16" thick, but our next sample of custom MAC axles will have the splines going to a depth of 1/4", which would mean even 33% more metal and torque.

Anyways, that brings us back to this:

fechter said:
If aluminum is too soft, maybe go to hardened steel?

Exactly. As I mentioned in the first post, the reason that we were using aluminum was so that we could be sure it was the torque arm that failed and the steel axle and axle splines would remain unscathed for additional tests. It wasn't because I thought that the final arms would necessarily be from aluminum, but if it turns out that they could then that would be awesome. Lighter, faster/cheaper to machine, minimal corrosion concerns.

Having done what I thought was sufficient design validation we then went ahead and made an identical but all steel torque arm to see at what point the motor splines would fail. Just mild steel mind you, not hardened.

Steel Arm.jpg

The test data that was interesting. You could push up to 120-130 Nm, the axle would rotate almost 2 degrees, but when you released the torque the axle would be bounce right back to 0 degrees. It's only at 150 Nm that we noticed the arm not returning to the same zero point. We kept going up 170Nm, 180 Nm,... 250 Nm, 260 Nm, then SNAP!

Steel Test Data.jpg

What failed wasn't the splines at all, but the hardened M6 bolt that we were using as a shear pin holding the torque applying lever arm to the axle. We should have use a 6mm keystock for this but didn't have a broaching tool.

Sheared Bolt.jpg

Here is how these two arms looked like after the test. On the aluminum arm almost all (5 of the 7) teeth sheared off right at the root. while only 2 teeth had their tops smeared over. On the mild steel arm, there is no damage to the teeth since we weren't able to torque it to failure. But you can see that there is still some skewing on top and bottom of the 'U' as a result of twisting force at the 180 degree bend.

AL vs Steel.jpg

This isn't too surprising given that a 280 Nm torque is producing over 7000 POUNDS of total force at a 17mm diameter. That's 1000 pounds per tooth.
 
justin_le said:
However, we could still see that there was almost no deflection at all until ~30 Nm, and then after that something gives the the material has a much shallower degree vs applied torque yields curve.

You went from elastic to plastic deformation. Remove the TP at that point and check the dimensions.

What type, temper and thickness of Al are you using?
 
justin_le said:
This isn't too surprising given that a 280 Nm torque is producing over 7000 POUNDS of total force at a 17mm diameter.

There's the leverage affect.

justin_le said:
That's 1000 pounds per tooth.

Probably not.

Unless both your components are exactly the same size and shape -- to within a few microns, then one spline face on the axle will contact one spline face on the TA first; then that becomes a fulcrum and the axle twists until another pair connect.

Until the deformation of those two teeth/spline pairs reaches a point to bring another into contact, those two teeth will be splitting the load between them.

If the material of one or the other (hopefully the TA) has exceeded its yield point before the third (and subsequent) splines are contacted, then they will fail, and the full load will transfer to the next two; and so on.

I have serious reservations about the benefits of splines over flats. The idea is sound -- spreading the load -- but it would require specifying such tight tolerances and a level of accuracy of machining for both parts that it would be hugely expensive to achieve if axles and TAs were manufactured as matched pairs (triples); and impossible if they are to be manufactured by different companies/countries.

If you have time for an experiment, lay your hands on a (cheap) double ended spanner that has the same size C-slot, and a ring on either end. (Same material for both tests.) The find yourself the highest quality bolts the same size head; and use an extension pipe to torque the bolt until the spanner fails.

Generally, the ring will fail first, especially the 12-point ring type; simply because only two contact areas are taking the load, and the ring doesn't have as much material for any two contact points as the C-slot type.
 
One question is how much is enough? With enough torque, either the wheel will spin or the bike will do a wheelie. Maximum possible torque will depend on wheel size, tire traction, bike weight and geometry. 200nm seems like a reasonable goal. That would equate to roughly 130 lbs of thrust on a 26" wheel.

With the systems I've used in the past, the free play between the TA and the axle always resulted in hammering and deformation of the edges and eventual loosening of the axle nuts. I thought one approach might be to use a tapered interface such that tightening the axle nut (or some other bolt) wedges the two parts together with a high clamping force. Something similar to a TaperLock bushing. One down side of this approach might be a tendency for it to be difficult to get apart once tightened. The right taper angle could solve this.

In the destructive test with the spline, the skewing is a bad thing. Some tab/slot feature that prevents skewing independent of the bolts might be good. Re aligning the slot in the TA so the pinch bolt is parallel to the TA axis and not 90 deg. might be helpful in preventing the skew also. Think about how a pipe wrench or strap wrench works. As the torque increases, the jaws tighten. Of course this would be much stronger in one direction than the other, but that might be OK.
 
justin_le said:
But you can see that there is still some skewing on top and bottom of the 'U' as a result of twisting force at the 180 degree bend.
Thinking back to AmpedBikes TAs - perhaps the skewing could be reduced if the inner edges of the U were shaped to engage a matching filler plate. Unlike the shaft, the TA parts are laser cut, so there are many shaping options for the serrations to minimize redirecting forces in undesirable directions.


AmpedBikesTA.pngfillerPlate2.jpg

Just a thought...
 
Buk___ said:
...........

I have serious reservations about the benefits of splines over flats. The idea is sound -- spreading the load -- but it would require specifying such tight tolerances and a level of accuracy of machining for both parts that it would be hugely expensive to achieve if axles and TAs were manufactured as matched pairs (triples); and impossible if they are to be manufactured by different companies/countries.

........

I agree with Buk 100% on this one. The splines are cute and if I were a splined lever I might even ask yours out on a "splined-date." :lol:

However, flats with rounded corners would be more robust and easier to make. Something similar to a bottom bracket axle and crank.

Or have a big robust steel ring welded to the axle, before the dropouts and bolt to that. (Think Dr. Bass ultimate torque arm welded to the axle.) You would have to press out the axle for some types of repairs but it would be a much more robust torque arm.

:D
 
As long as the final arm is one piece with a channel machined in it, rather than a plate bolted to an elongated C, I suspect the deformation wouldn't be an issue up to the point something else fails instead.
 
teklektik said:
Thinking back to AmpedBikes TAs - perhaps the skewing could be reduced if the inner edges of the U were shaped to engage a matching filler plate. Unlike the shaft, the TA parts are laser cut, so there are many shaping options for the serrations to minimize redirecting forces in undesirable directions.

The primary benefit of the splines on that design is it allows it to used at any of 24 different position -- every 15°-- and the same part can be used on both sides, so an effective way to have one part that will fit both sides of many bikes.

It's still the flats of the insert that take the load first.
 
I'm still thinking that an axle like this one would be easier to make and more solid. And if 4 points of orientation aren't enough, then a pentagon, hexagon, heptagon or octagon could be used. Anyway something like this....

LikeThisAxle.JPG

:D
 
If there's an adequate torque arm, it seems to me that you don't need orientation control. A regular round 10mm axle stud or bolt will do to fix the hub to the frame.

I really like the loosely fitted hexagonal interface torque arm used on the Copenhagen Wheel, and I think more manufacturers should do it that way. A pentagonal or square interface might be even better.
 
Buk___ said:
teklektik said:
Thinking back to AmpedBikes TAs - perhaps the skewing could be reduced if the inner edges of the U were shaped to engage a matching filler plate. Unlike the shaft, the TA parts are laser cut, so there are many shaping options for the serrations to minimize redirecting forces in undesirable directions.

The primary benefit of the splines on that design is it allows it to used at any of 24 different position -- every 15°-- and the same part can be used on both sides, so an effective way to have one part that will fit both sides of many bikes.

It's still the flats of the insert that take the load first.
The reference is about using the laser cut serration concept in flat stock to create parts that interlock to resist movement. It has nothing to do with the specific use of that idea in the the AmpedBike TA and has nothing to do with resisting rotation - it is about pressing that idea into service for linear rather than rotary motion to address the skew problem.

  • FWIW - a cool enhancement to the toothed offset idea in the AmpedBikes TA is that the hole in the insert is aligned so the TA can actually be jogged a 1/2 tooth position simply by flipping over the insert.
 
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