One thing that is slightly counter-intuitive with
regen is that applying more
regen braking force does not necessarily increase the
regen current going back into the battery pack. This is easy to understand when you realize that the maximum
regen braking torque occurs when all the motor phases are simply shorted together. In this situation, the
regen current simply circulates through the windings
of the hub motor generating heat, and none
of that energy ever flows back into the battery pack. At the other end, when the duty cycle (D)
of the motor controller is such that the effective voltage going to the hub motor (Vbatt * D) exactly matches the back emf voltage
of the motor, then there is also no current flowing into or out
of the battery as well, though in this case there is no braking torque either.
- Regen Amperage.gif (15.81 KiB) Viewed 5083 times
In between these two points the current flowing into the battery follows a parabolic shape, with the maximum
regen battery current occurring exactly in the middle. This is the point
of maximum power transfer
of energy back into the battery pack, and the hub is generating exactly half the braking torque that it would produce if all the windings were shorted. That's where you would want to be to get maximum amperage into the battery pack, but the efficiency
of turning kinetic energy into useable battery energy is only 50% at this point.
In general, the less the
regen braking current the higher the efficiency, since you have less I^2 R copper losses in the windings. However, if you are trying to slow to a stop, then applying a meager amount
of regen torque won't increase the total amount
of regen energy captured because even though the hub motor/controller may be converting a small amount
of kinetic energy into battery energy with very high efficiency, you'll meanwhile be loosing much more energy to air drag and rolling friction while you come to a prolonged stop. Likewise, if you come to a very abrupt
regen stop, you won't loose much
of your kinetic energy to air and rolling friction, but the efficiency
of converting that kinetic energy into battery energy via
regen will be quite poor. Somewhere in between these two points is some optimum
regen braking torque which would get a maximum amount
of energy back into the pack.
To get
an idea
of where it was at I did a series
of tests where I rode the
ebike up to 40 kph
on flat ground, then I engaged the proportional
regen in a tucked position and let the
ebike decellerate to a stop, this time recording the data at 5 Hz. The results from a typical test are shown below. Here at distance = 0 is where I first engaged the
regen. The yellow line is the kinetic energy
of me and the bike (1/2 mv^2, where m = 98.7 kg) while the purple line is the cumulative amount
of regen energy put in the battery pack. You can see that over the course
of coming to a stop from 40kph, I spanned a distance
of over 160 meters, starting off with 1.6 Wh
of kinetic energy, and ending with about 0.55 Wh
of electrical energy back in the battery.
- Decelleration with Minimal Regen.gif (4.98 KiB) Viewed 5068 times
A test with significantly more
regen is shown below, here coming to a stop from 40 kph in just 65 meters:
- Decelleration with Significant Regen.gif (5.04 KiB) Viewed 5067 times
This experiment was repeated a total
of 5 times in each case with the
regen throttle held steady at a different position. The net results are summarized in the graph below, where I have plotted the percentage
of the intial kinetic energy that was returned to the battery as a function
of the peak
regen current for that particular
regen throttle position.
- Kinetic Recapture Efficiency.gif (5.7 KiB) Viewed 5057 times
You can see that there is a pretty wide range from about 6 amps to 12 amps
of regen current where half
of the original kinetic energy was recovered. I was rather surprised that the result was this high and over such a broad range, and 6-12 amps is a good figure since it is within the scope
of what most modern rechargeable battery chemistries can take for maximum charge current (~0.5-1C, with
ebike packs averaging about 10 Ah).
Justin
.
(for misleading the public re 
A good solution maybe a custom rear axel for electric hub motors...larger locking nut with a cotter pin with more surface area, similar to 
