Is a carbon fork strong enough for a hub motor?
My e-bike has a carbon front fork at which the hub motor will be mounted. At first sight, a carbon front fork appears too weak to handle the forces of a hub motor. To examine this, we have to be able to calculate the front fork stress due to hub motor. Here I try a method to solve the problem mathematically. We shall see that it is possible to mount a hub motor safely without hurting the carbon front fork.
Performing accurate 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.
Brake force compared with hub motor force
The maximum possible braking deceleration using the front brake, before pitch over occurs, is for typical bicycles about 0.5g. This means that at a speed of 18km/h it is possible to make an abrupt stop in 1s. Try it, it is possible. The brake distance is 2.5m, s = v2/(2*a). Every front fork is designed, and strong enough, to withstand at least these emergency stops.
We can see that the braking forces at the front fork are far stronger than the forces generated by a hub motor. No hub motor has the power to accelerate to 18kmh in 1s. Theoretically, the power required to achieve this is 1250W net.
Fork dropout failure
Fork dropouts can certainly not handle the rotational forces of a hub motor, especially when the dropouts are made from aluminium. A hub motor has a flat axle and creates a huge leverage that pushes the U-shaped slots apart. See here a cracked fork dropout:
Hub motor torque arms
Torque arms are commonly used to relieve the fork dropout and to spread the hub motor force:
Maximum hub motor torque
De graph of the used hub motor shows a maximum torque of 20Nm at 12.5A, see here:
But the motor can deliver more than 20Nm. The maximum motor torque depends on the motor controller maximum current. With a current limit of 25A the maximum motor torque is about 40Nm, the magnetic saturation of the motor not taken into account.
Hub motor torque arm length calculation
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.
At a certain small distance from the axis, the motor torque is larger than the brake torque. This means that here the fork might be too weak to handle the motor torque. With a torque arm, the point of application of the motor torque is shifted to a greater (safer) distance from the axis. I want to calculate at which distance the motor torque is as large as the maximum brake torque. This distance we call L. If the torque arm has at least the length L, the motor will not overstress the fork. If the fork withstands the brake torque, the same applies to the motor torque, assuming that everything is symmetrical.
To keep it simple, instead of a real fork, the fork angle is 90 degrees. The front wheel acts as a kind of rigid lever arm to the bike where on one side the brake force is applied.
- (a) The maximum brake force at the road is about 0.5g * 100kg = 500N.
- (b) At the front wheel axis the brake force is about 1000N because the lever arm is halved.
- (c) The substituted brake torque at the fork bottom is 1000N * L.
Suppose the motor has a maximum torque of 20Nm and k = 1.6. If the motor controller delivers up to 25A then the maximum motor torque is 40Nm when no magnetic saturation occurs.
- Hub motor torque = equivalent brake torque
- 40Nm = 1000N * L
- L = 0.04m
E-bike hub motor torque arm
For the carbon front fork, I made a special torque arm. The torque arm is screwed to an aluminium plate which is glued to the carbon front fork.
The torque arm strength was tested at an old carbon front fork with a weight on a long lever. One torque arm, glued to the front fork, can withstand at least 50Nm. For a 20Nm hub motor, the construction is 2.5 times overdimensioned if one torque arm is used.
At 4cm distance to the axis, the torque exposure to the fork from the hub motor is equal to the maximum (substituted) brake torque. For such a small distance it is likely that the fork is strong enough anyway, so a torque arm is not required to spread the motor force over the fork. A torque arm is only required to relieve the aluminum fork dropout from the motor torque. For stronger motors the safe length for a torque arm must be correspondingly larger. Moreover, to be sure, it never hurts to use a longer torque arm than strictly necessary.
Note that we assume that the fork is just strong enough to withstand the maximum brake force. In practice, a safety factor is built in. Moreover, I have treated here only a aspect. The effects of dynamic forces have not been studied.