#002 E-Bike (V2,V3,V4)

last updated: 10/1/22

Version 5.5

The 12s 13AH battery pack was disassembled so I could use the cells elsewhere - so I had to shop around for a 13s (up from 12s) 14 AH battery for the bike.

Analysis of Batteries

As well as having a higher nominal resistance, this battery also proved to have a lower internal resistance.

Statistic	Old Custom	New Bought
Maximum Voltage	4.2*12 = 50.4V	4.2*13 = 54.6V
Nominal Voltage	3.7*12 = 44.4V	3.7*13 = 48.1V
Stated Maximum Current	5C or 68A	75A
Measured Internal Resistance	0.19 Ohms	0.12 Ohms
Voltage at 60A	44.4 - 0.19*60 = 33V	48.1 - 0.12*60 = 40.9V
Power at 60A	33*60 = 1980W	40.9*60 = 2454W
Power at 100A	2540W @ 25V	3610W @ 36V

Calculated with real data of voltage and current.

The bike still suffers from what I will call motor saturation - the point where the controller is powering each phase with 100% of the voltage but back EMF and winding resistance limits the current and power. To solve this problem I can increase the voltage which would require a new battery and controller or I could increase the KV of the motor.

If I double the KV of the motor, I get different performance statistics. Real world physics aside, a doubling in KV results in a doubling of RPM and a halving of torque at a given voltage and current.

However, a buck converter (aka my ESC) is a great way to trade voltage for current. MY ESC claims to output 200A per phase, so lets say 100A per phase, which is still double my phase current for the bike as it is. So, I would have the same torque but have higher RPMs... and be able to suck more power from the battery! Hopefully this is next change.

Version 5

The last issue with the bike was that the back belt consistently slipped, and the noise from the plastic pulleys was quite obnoxious. The solution was to go from a double reduction to a single reduction. Also, the metal pulley on the motor shaft would be the only other pulley besides the wheel pulley. The belt would now be tightened by rotating the metal bracket that the motor is attached to around the point where it is attached to the seat post. The lost 2:1 reduction was partially accounted for with a reduction in KV on a new BLDC motor, although speed did go down.

I did all those things in about two hours. Here's the result.

I have been riding the bike daily for the entirety of my sophomore year. It is powerful, has good range and is fun to ride. It saves me a 20 minute walk to class and back three times a day easily... I had one issue with the BMS lead wires disconnecting from one of the cells which led to that cell not being balanced, but luckily it was savable.

Analysis

Around February 2023, I installed a cheap power meter into the handlebars to measure the voltage and current of the bike. I noticed that the bike did not draw much current above 20 mph. Utilizing the VESC's logging ability, I recoreded a bunch of fun datapoints and got to analysis.

A typical acceleration run. Power is the light blue line and is in 100s of watts, so divide by 10 to get KW.

From what I can tell, the motor for the V5 version was not selected well. At 100% duty cycle and 20 mph, the motor already only draws 30 amps. 30 amps at 44 volts is only 1.3kW... not enough!

A 3D plot of motor current as a function of motor voltage and RPM

I found this super helpful article on motor selection from Benjamin Vedder, the creator of VESCs. It points out that for motors of equivalent size changing KV does not effect waste heat per unit of torque. My goal is higher power and higher speed with the same belt geometry. If I were to double the motor KV, I could operate at my same performance with double my current at half my voltage. The reality of speed controllers means that no additional load is required from battery. (200% amps at 50% voltage is 100% power). But, I can use 100% of my voltage, and keep higher currents during higher RPMs. This led to Version 6.

Version 4

The last upgrade upgraded the controller to be capable of up to 50 volts. The last battery was a 7s lipo, cobbled out of a 6s with one cell dead and a 2s. It had no BMS and had to be charged with a drone battery charger. It was 8000 mAh, and needed to be charged to go more than my usual ride to classes.

The new battery is much better. I fabricated it myself out of the same yellow cells (QB26800) I used in my car. I can go three times as far and get to speeds that are completely unreasonable for a bike. It has a BMS and is lithium ion.

	Old	New
Voltage	7s (25.9V)	12s (44.4V)
Capacity	8 Ah	13.6 Ah
Burst Current	240 A	68 A
Energy	207 Wh	603 Wh
Top Speed	22 mph	35 mph

The battery without the BMS on the front. It is 'waterproofed' with purple packing tape. It has 1/4 inch plywood on the sides and carboard on bottom and top.

Version 3

Version 2

The premise of V2 rests on one major issues with V1: It just wasn't strong enough. For the smaller upper timing belt, the forces were all conveyed into the single bracket that both the motor and hex bearing were bolted into. The larger belt, however, had a single aluminum plate that only balanced out forces from one axis on one side of the axle. Version two is based on the idea that two brackets, both secured in two places on the E-Bike, provides enough rigid force in order to be able to turn the motor up to full power, compared to the time-based spool-up I had previously.

Construction was fairly standard for aluminum: I shaped the parts with a sawzall and a large adjustable wrench. I put it all together, and took it out for a test ride. Surprisingly, nothing broke. It was in operation for several spring months. The cheap speed controller finally gave out after I attempted to go up a long hill at full speed on a hot day. As of now, I just need to put down 100 dollars for higher-quality speed controller.