Calculation of front fork stress due to hub motor

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avandalen   100 W

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Calculation of front fork stress due to hub motor

Post by avandalen » May 11 2011 3:57pm

My bicycle has a carbon front fork, at which I will mount a hub motor. At first sight, a carbon front fork appears too weak to handle the forces of a hub motor.
I wanted to solve this problem mathematically. I have done calculations which show that it is in principle safe to mount a hub motor in every front fork.

http://www.avdweb.nl/solar-bike/mechani ... motor.html

The approach is:
Performing strength calculations on a bicycle's front fork is not possible because hereof no information is provided. But I suppose that a front fork is in principle strong enough for hub motor mounting if the motor forces at the fork are lower than the brake forces, which can handle a front fork easily. Since the fork design is basically symmetrical, whatever it can take in braking force should be more or less the same as the hub motor pulling force.

This is an e-bike with a hub motor mounted in a dedicated carbon front fork:

Image

Hub motor torque arm length calculation:

Image

For the distractions see my website.

The conclusion is: At 2cm distance to the axis, the torque exposure to the fork from a 20Nm hub motor is equal to the maximum substituted brake torque. For a hub motor of 40Nm the torque arm should be at least 4cm long if we assume that the fork is just strong enough to withstand the maximum brake force.

If the calculations are not correct please reply!

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Re: Calculation of front fork stress due to hub motor

Post by neptronix » May 11 2011 4:14pm

I have heard many discussions where everyone has said that this is a really bad idea. A front fork breakage will send you flying over the handlebars, and that happens on aluminum and steel forks.

Have you taken that into consideration?

I can't help you with the calculations but i wanted to pitch in because i am concerned about your safety.
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Re: Calculation of front fork stress due to hub motor

Post by Joe Perez » May 11 2011 4:34pm

I'm not a ME, nor did I study any of the ME-style stuff in college, so please feel free to contradict me here. My world is currents and voltages, not stresses and strains.

It seems to me that, under braking, some (most? all?) of the force which is being applied between the universe and the fork is happening relatively high up on the fork, at the point where the brake caliper is attached to it.

In the case of a hub motor, the force is being applied much lower down, at or near the dropouts, which gives it a much longer arm to act upon.
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Re: Calculation of front fork stress due to hub motor

Post by FMB42 » May 11 2011 4:38pm

Another "problem" with carbon fiber forks (and carbon fiber tubing in general) is that their strength characteristics are dependent on the type of weave (the thickness of the strands) and the lay-up pattern (the angles of intersection of the "fabric"). These design parameters give engineers the ability to create a carbon fork that is strong, yet stiff in one direction (i.e. under braking conditions) and more compliant in another (i.e. under "compression" and/or while being driven by a hub motor).

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Re: Calculation of front fork stress due to hub motor

Post by Xrain » May 11 2011 4:45pm

I haven't worked through your calculations, but one think you are forgetting to consider is road stresses.

While the fork might be able to handle the stresses on a perfectly smooth road with no indentations. If you combine the shock of hitting a road bump at speed with the added stress of the motor, there is a higher probability it can fail.It's certainly possible for the bike to survive just fine for an extended period of time, but it only take a sufficiently bad bump for it to fail. And generally when something like this fails it happens at a rather poor time, sending you over the handle bars at a pretty good speed.


Another thing to consider with carbon fiber, is it's flexibility. CF is significantly more flexible than steel or aluminum, the fork might not even break but its possible the dropout could get spread enough for the motor to come out of the dropouts.


If I were you I'd not risk an extremely expensive carbon fiber fork, and just mount the motor on the rear with torque arms.

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Re: Calculation of front fork stress due to hub motor

Post by neptronix » May 11 2011 4:50pm

^-- what he said.

Regardless of the frame material, i'd be running the motor in the rear anyway.
Not that i would run a hub motor on a carbon fiber bike though, regardless of the front or rear config..
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Re: Calculation of front fork stress due to hub motor

Post by dogman dan » May 11 2011 4:59pm

It's not the "strength" that's the problem. It's the way carbon, and alloy fail. All at once.

Having said that, I am running a front motor on alloy forks. The use of a properly fitted pair of torque arms helps prevent the load that will crack my dropouts.

So why not use two torque arms and put it on a carbon fork? One reason is that the carbon fork may not be capable of taking the side load on the fork, in the spot where the torque arm is attached. You could break the whole fork off, instead of cracking just the dropouts.

But the real reason it would be dumb, is a motor is going to simply ruin a sweet riding carbon bike. Motorize a steel fork road bike that weighs twice as much, and rides just as good once motorized.

One more point. I'm too dumb to follow your calculations. But this I know. I've never had braking forces screw up a dropout on a bike, not even on 50 mph descents. We used to decend some hairy rocky mountian passes for grins, and used our brakes plenty. But I've seen even moderately powered hubmotors walk right out of dropouts, bending the hell out of em. Don't ask me why it's so harsh, I just have seen that it is. It simply doesn't compare to braking loads. I speculate that the reason is that you don't have flat axles on a regular wheel. It can't have the leverage a flat axle on a hubmotor has. It just pries dropouts apart.

Thinking a bit more, braking forces on the dropouts are going to be different. If rotational, any slip does no damage. On the flat axle, rotation is always going to cause damage. Got a fork you can destruct test? Put a 10 mm square bar in the dropouts. Then apply rotational force with 10 cm long wrench. You'll damage the dropouts. This is what happens if your axle nuts work loose one bit. The pulling force is no problem. It's rotating a square bar in your dropouts that destroys them. Got a good dentist? And orthopedist?

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Re: Calculation of front fork stress due to hub motor

Post by Joe Perez » May 11 2011 5:13pm

dogman wrote:(...)
But this I know. I've never had braking forces screw up a dropout on a bike, (...) But I've seen even moderately powered hubmotors walk right out of dropouts, bending the hell out of em.
That's kind of where my thinking was going.

Under braking, there is no rotational force at all being applied between the axle and the fork. The forces involved are all linear- between the road and the tyre, and then between the wheel and the brake caliper. (Well, I suppose you could claim that rotational force was being applied between the tyre and the wheel... Let's not go there.)

With a hubmotor, there is rotational force between the motor and the fork at the axle. Even if you have two very stout torque arms, the motor is still trying very hard to twist the fork.
Last edited by Joe Perez on May 11 2011 6:12pm, edited 1 time in total.
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Re: Calculation of front fork stress due to hub motor

Post by dogman dan » May 11 2011 5:26pm

Yup. once you do screw up and lose the compression from the tight nuts, the carnage is amazing. If it can shred a comoly dropout, imagine what happens with alloy or carbon.

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Re: Calculation of front fork stress due to hub motor

Post by avandalen » May 14 2011 5:33am

neptronix wrote:I have heard many discussions where everyone has said that this is a really bad idea. A front fork breakage will send you flying over the handlebars, and that happens on aluminum and steel forks.

Have you taken that into consideration?

I can't help you with the calculations but i wanted to pitch in because i am concerned about your safety.
Maybe it is not a good idea, I want know if it's safe. I will do destructive testing before on other carbon forks to check safety. I can also build the hub motor in the rear wheel.

Here in the Netherlands everybody has a full health insurance but I don't want to use it.

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Re: Calculation of front fork stress due to hub motor

Post by avandalen » May 15 2011 3:02am

Joe Perez wrote:
dogman wrote:(...)
With a hubmotor, there is rotational force between the motor and the fork at the axle. Even if you have two very stout torque arms, the motor is still trying very hard to twist the fork.
What do you think of this argument?

It is clear that a hub motor generates a torque at the front fork. During braking, the front fork will also be exposed to a force, which is linear. To compare the motor torque at the fork with the braking force, the latter must be converted into a torque. The brake force can be mathematically substituted by a torque which is dependent on the distance to the axis at which the torque is taken.

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Re: Calculation of front fork stress due to hub motor

Post by Hillhater » May 15 2011 3:31am

The hub motor torque will only ever damage the drop out area .
The braking force is much(x10) greater than the hub motor force but does not act in the same way, ..it is trying to break the fork off at the head tube.
If your torque arms are tough enough and long enough to withstand the motor torque (and secure the wheel to the fork) you need not worry.
BUT..if it were me, i would swap it out for a sus fork anyway ! :wink:
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Re: Calculation of front fork stress due to hub motor

Post by avandalen » Jun 19 2011 2:01pm

I made a prototype of a strong torque arm for the carbon front fork. The strength was tested on an old carbon front fork and with a weight on a long lever. I was not able to damage the torque arm or the front fork.
Image

Image
See here:
http://www.avdweb.nl/solar-bike/mechani ... motor.html

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Re: Calculation of front fork stress due to hub motor

Post by Hillhater » Jun 19 2011 7:31pm

I will never understand why people dont make torque arms as long as possible ?
Each time you double the length of the torque arm you halve the stress loading on the fixing point !
If you are going to make a torque arm...make a long one !
..and ...design it such that the fixing bolt is not taking the torque loading !
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Re: Calculation of front fork stress due to hub motor

Post by neptronix » Jun 19 2011 8:20pm

And at least use more than one bolt.

As for the carbon fiber, drilling a hole in it and constantly putting force on it could end up nasty.
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Re: Calculation of front fork stress due to hub motor

Post by amberwolf » Jun 19 2011 10:32pm

Actually, it looks like the screw only holds the arm to the small plate, and that plate appears to be glued (epoxied?) onto the fork.

In my limited experience, many epoxies do not act very well in shear like that, but I'm sure that some do. If that is indeed glued on there, I certainly hope that it is one of those that is ok with shear stresses. :)

If it were me, I'd have at the least a wide banding clamp of some type around that point, to prevent the back-and-forth rocking of the arm (minute as it might seem) from slowly fracturing the epoxy the same way it could that of the dropouts themselves.


Mostly because epoxies (like CF and fiberglass construction using them) tend to fail quite suddenly, without macroscopic warning signs you might otherwise notice during "preflight" visual inspections.

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Re: Calculation of front fork stress due to hub motor

Post by docnjoj » Jun 22 2011 12:24pm

What ever happened to Justins treatise on fork failure? That had some calculations in it and a lot of experimentation! Can someone find it? It really should be a sticky!
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Re: Calculation of front fork stress due to hub motor

Post by neptronix » Jun 23 2011 10:22pm

http://bustedcarbon.com

Gallery of carbon fiber failures.
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Re: Calculation of front fork stress due to hub motor

Post by docnjoj » Jun 24 2011 12:18pm

Yup! Thanks AW!
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E-bike stable at our house

Steintrike Mad Max full suspension trike rear Cute 100H going on: Whoops, Cute wheel broke but I fixed it.
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Re: Calculation of front fork stress due to hub motor

Post by dequinox » Aug 27 2015 4:50pm

I briefed the calculations avandalen made, and I'm not sure the model holds. The stress in the fork member caused by braking forces, and the stress caused by a motor/torque arm combination are two completely different problems. This is because the forces applied are in different locations, and with different magnitudes. See the diagrams below for an idea of what the free body diagrams would look like.

Braking:
Braking forces.png
Motor accelerating, w/ torque arm:
Acceleration forces.png
These two free body diagrams will generate very different shear/moment diagrams, and the problem gets even more complex when you consider that the second area moment of the "beam" (fork member) is changing since the fork is tapered.

Add to all of this that the weave/etc really affects the material properties (next to impossible to nail this down to a single figure for "most" carbon fiber... even a range is difficult to provide for "general calculations" like this fellow is trying to do) and that the fatigue loading on the fork will be different than what it was designed (and hopefully tested by the manufacturer) for... and this calculation basically has no meaning in the real world.

I'm really not saying that your efforts were worthless, however. I think your practical experiments are by far the better route to go. I think you verified that the fork will hold up in a static case, but the dynamic loading that it will go through is difficult to test. I think the best solution for this situation is to use a steel or chromoly fork, and the second best solution...if you must use a carbon fork... is to do what you did with the torque arm mounting plate glued to the CF. Making it large like that is a good idea... it reinforces the fork well and provides lots of surface area for the epoxy to hold.

Just a few thoughts from someone who is schooled in mechanical engineering... I really don't mean to rain on your idea or anything. I just think it's a little more complicated than you thought it was in your problem statement.
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Re: Calculation of front fork stress due to hub motor

Post by d8veh » Aug 27 2015 6:04pm

There's disk brake carbon forks now, which are designed to take a strong torque around the axle. I can't see a problem with them when using say a 250w motor. The torue arm can be anchored to the brake caliper mount.

Having said that, I would say, why put the motor in the front if you can put it in the rear, which has a lot of advantages?

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Re: Calculation of front fork stress due to hub motor

Post by Punx0r » Aug 28 2015 3:20am

Front fork failure at 100mph :D

https://www.youtube.com/watch?v=rTfu0hjVtzE

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Re: Calculation of front fork stress due to hub motor

Post by alfantastic » Aug 28 2015 11:35am

Punx0r wrote:Front fork failure at 100mph :D

https://www.youtube.com/watch?v=rTfu0hjVtzE
Ouch :D

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Re: Calculation of front fork stress due to hub motor

Post by dequinox » Aug 28 2015 12:51pm

d8veh wrote:There's disk brake carbon forks now, which are designed to take a strong torque around the axle. I can't see a problem with them when using say a 250w motor. The torue arm can be anchored to the brake caliper mount.

Having said that, I would say, why put the motor in the front if you can put it in the rear, which has a lot of advantages?
Now this would be a much better way to compare the stress between braking and motor torque. Avandalen, you may want to re-do your math portion using this instead of the rim-brakes as a comparison.
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