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PM motor scaling laws

Hubmotors, such as used for bicycles, belongs to the category small PM motors (permanent magnetic). These motors have by nature a lower efficiency than large ones. These are the relationships with the motor diameter d. The distraction of the formulas is rather complicated, see "Aandrijfsystemen" J.H.J. Boekema.

  • Maximum power Pmax ~ d4
  • Efficiency η ~ d2 

So the efficiency of an electromotor is proportional to the square of the diameter. If we use the motor only at a certain speed and torque, the efficiency can be optimized.

Hub motor weight

Hub motors are too heavy and too large for the little power they deliver. The cause is that manufacturer takes no unnecessary risks to avoid repairs during the guarantee period. Some 250W hub motors have a weight of more than 3kg. To illustrate, here is an example of a high efficiency axial gap dc motor from Lynch Motor Company. The LEM 130 95s model as a weight of 3kg and an output of 3kW. The peak efficiency is 87%.

Lynch axial gap motors
Lynch axial gap motors

Here is another example, the "LRP 50920 Vector 8 Brushless Modified" RC car motor: 1.360W, 275g, efficiency 91%.

LRP 50920 Vector 8 Brushless 1.360W 275g Efficiency 91%
LRP 50920 Vector 8 Brushless 1.360W 275g Efficiency 91%

It should be noted that all these motors are high speed. After considering these motors, I wonder whether it is possible to build ebike hub motors with a higher efficiency and with a lower weight. But often there is no effort to save weight. This is an ebike hub motor with a weight of 3.9kg and a power of just 250-500W.

Common heavy ebike hub motor 250-500W 3.9kg
Common heavy ebike hub motor 250-500W 3.9kg

I made a list of PM motors with their weight. There is a line that indicates the lightweight motors. Motors above the line are unnecessary too heavy.

BLDC hub motor weight versus power

Manufacturer Type Power [W] Weight [kg]
Tongxin-Cute Q75 200 1.20
Tongxin-Keyde 98SWXR36 180 1.40
Tongxin-Cute Cute-85 250 1.76*
Tongxin-Cute Cute-100 350 2.09*
Tongxin-Cute Cute-128 500 3.00
Tongxin-Cute Cute-12 1000 4.45
Bafang SWXK 250 2.80
Bafang 350W 350 4.60
Crystalyte 209 250 3.90
Crystalyte 404 1120 5.50
Goldenmotor MBG36F 250 2.60
Goldenmotor MBG36R 250 3.00
Goldenmotor HBS36R 1000 5.00
Bionx PL-250 Light 250 4.10
Bionx PL-500 HS 500 4.70
Conhismotor 48V 1000W 1000 6.20
Conhismotor 48V 350W 350 4.50
Conhismotor 24V 250W 250 4.70
Tongxin 36V moto 160 2.30
Bafang SWXU 250 1.90
       
Lynch Motor Company 95S 4000 3.00
Lynch Motor Company D127 21000 8.50
Lynch Motor Company D135 29000 11.00
Perm motor PGM 132 7200 11.00
Mars motors ET-M 12500 10.90

* the motor weight (without cables) is measured by myself.

Tongxin Keyde Cute Goldant

Note that Keyde, Cute and Goldant hub motors all are made by Tongxin.

Hub motors without specifications are suspect

It is noticeable that for many hub motors, the supplier has no data or graphs. They are suspected in advance:

  • There are charts, but because insufficient motor performance, these are not published.
  • The engine has more power than allowed by law to obtain more power during acceleration and therefore obtain a higher ranking in consumer tests.

The motor data that always must be known are k, Ri and Tf. It is possible to extract the data from the motor chart. See here.

Hub motor history

Wheel hub motors are nothing new. Here is an example of hub motors at the Semper Vivus from 1900:

Porsche Semper Vivus from 1900 (Porsche Media Central)
Porsche Semper Vivus from 1900 (Porsche Media Central)

Using RC aircraft motors for e-bikes

These motors are lightweight, powerful and they have a high efficiency.
See more here: The New and Improved Brushless Electric Scooter Power System Guide

Do you have any comments? Please let me know.
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