teslanv
1 MW
This post is meant to inform those who struggle with the relationship of windings and power as they relate to direct drive hub motors.
I test a lot of MXUS direct drive Hub motors and a variety of controllers for compatibility.
And I think I have a good understanding of how the relationship of stator width, and winding (turn-count) affects the Kv (RPM per Volt) and Kt (Torque per Amp) of a given motor size and winding.
The KEY fact to remember about the relationship of Kv and Kt is that they are inversely proportional, and when you multiply the two values, you get a constant. THIS IS TRUE FOR EVERY ELECTRIC MOTOR DESIGN, REGARDLESS OF SIZE.
The formula for Kv and Kt is:
Kv x Kt = 9.549, where Kt is expressed in Newton-Meters of torque per Amp of phase current
It's easier to understand when you look at a standard "205" (9C Clone) motor design, and observe the KV as it relates to a common winding and different stator widths, and compare the results.
So let's start with a MXUS "3000W" 4T winding. - This motor has a stator and magnet width of 45mm, and the winding is made up of 16 strands of 0.5mm copper magnet wire (in parallel) wound around each stator tooth a total of 4 times. The phase resistance of this configuration is about 0.105 Ohms, and the KV of this configuration is about 8.9 RPM per volt, unloaded, which means the torque is equal to 9.549/8.9 or 1.07 NM per Amp.
Now let's compare the SAME winding but in a narrower stator width.
The MXUS "1000W" motor has a stator width of 28mm. The common winding option for this motor is a 9 x 7T (9 strands of copper in parallel x 7 turns around the stator tooth), and the resulting Kv is about 8.5 RPM per volt. However, I special ordered a "4T" winding in the 28mm motor, which has a much higher Kv. The "1000W" 4T winding, just like the "3000W" 4T winding has the same number of strands of copper in parallel (16 Strands of 0.5mm magnet wire) wound around each stator tooth, 4 times. This very fact, means that the 4T winding in EITHER MOTOR should be able to accept the same amount of phase current with near identical copper losses. And in fact, the narrower 28mm motor in theory should be able to accept slightly MORE phase current than the 45mm motor, since the total length of the winding copper is 136mm shorter than the 45mm motor [(45mm-28mm) x 8 = 136mm] - Since the copper losses are directly related to the resistance in the winding, it should be clear that both 4T windings should accept a similar amount of phase current before they overheat.
The Kv of a given motor design with the same winding and a different stator width is inversely proportional to the stator width.
The 45mm Motor, 4T winding has a Kv of 8.9 (45mm x 8.9Kv = 400.5)
The 28mm motor, 4T winding has a Kv of 14.3 (28mm x 14.3mm = 400.4)
The difference lies in how much torque the 28mm 4T motor can output. Since the Kv is higher (14.3 RPM per Volt), the torque is proportionally lower as compared to the 45mm motor. The Torque of the 28mm motor is only (9.549/14.3 = 0.667 Nm per Amp of phase current.
Now let's look at total torque output.
The 4T winding of the 45mm motor begins to overheat at 42.6A, so let's use 40A Phase current as the basis of our calculation
The 3000W (45mm) motor produces 1.07 Nm of torque per Amp, so at 40A, the total torque output would be 42.8 Nm of torque.
In comparison, the 1000W (28mm) motor produces 0.667 Nm of torque per amp, so at the same phase current as the 45mm motor, it's only outputting a total of 26.71 Nm of total torque.
Don't misinterpret my statements, however. The 28mm motor will require more phase current to run at the same speed as the 45mm motor. I am NOT saying that the motors are equal in terms of performance. They are only equal in terms of the phase current they can tolerate before they overheat.
The bottom line is this:
You can run roughly the same phase current to any stator width of a motor design, so long as the winding pattern is the same. But you will get a lower total torque output from the narrower stator motor at that same "safe" phase current.
I test a lot of MXUS direct drive Hub motors and a variety of controllers for compatibility.
And I think I have a good understanding of how the relationship of stator width, and winding (turn-count) affects the Kv (RPM per Volt) and Kt (Torque per Amp) of a given motor size and winding.
The KEY fact to remember about the relationship of Kv and Kt is that they are inversely proportional, and when you multiply the two values, you get a constant. THIS IS TRUE FOR EVERY ELECTRIC MOTOR DESIGN, REGARDLESS OF SIZE.
The formula for Kv and Kt is:
Kv x Kt = 9.549, where Kt is expressed in Newton-Meters of torque per Amp of phase current
It's easier to understand when you look at a standard "205" (9C Clone) motor design, and observe the KV as it relates to a common winding and different stator widths, and compare the results.
So let's start with a MXUS "3000W" 4T winding. - This motor has a stator and magnet width of 45mm, and the winding is made up of 16 strands of 0.5mm copper magnet wire (in parallel) wound around each stator tooth a total of 4 times. The phase resistance of this configuration is about 0.105 Ohms, and the KV of this configuration is about 8.9 RPM per volt, unloaded, which means the torque is equal to 9.549/8.9 or 1.07 NM per Amp.
Now let's compare the SAME winding but in a narrower stator width.
The MXUS "1000W" motor has a stator width of 28mm. The common winding option for this motor is a 9 x 7T (9 strands of copper in parallel x 7 turns around the stator tooth), and the resulting Kv is about 8.5 RPM per volt. However, I special ordered a "4T" winding in the 28mm motor, which has a much higher Kv. The "1000W" 4T winding, just like the "3000W" 4T winding has the same number of strands of copper in parallel (16 Strands of 0.5mm magnet wire) wound around each stator tooth, 4 times. This very fact, means that the 4T winding in EITHER MOTOR should be able to accept the same amount of phase current with near identical copper losses. And in fact, the narrower 28mm motor in theory should be able to accept slightly MORE phase current than the 45mm motor, since the total length of the winding copper is 136mm shorter than the 45mm motor [(45mm-28mm) x 8 = 136mm] - Since the copper losses are directly related to the resistance in the winding, it should be clear that both 4T windings should accept a similar amount of phase current before they overheat.
The Kv of a given motor design with the same winding and a different stator width is inversely proportional to the stator width.
The 45mm Motor, 4T winding has a Kv of 8.9 (45mm x 8.9Kv = 400.5)
The 28mm motor, 4T winding has a Kv of 14.3 (28mm x 14.3mm = 400.4)
The difference lies in how much torque the 28mm 4T motor can output. Since the Kv is higher (14.3 RPM per Volt), the torque is proportionally lower as compared to the 45mm motor. The Torque of the 28mm motor is only (9.549/14.3 = 0.667 Nm per Amp of phase current.
Now let's look at total torque output.
The 4T winding of the 45mm motor begins to overheat at 42.6A, so let's use 40A Phase current as the basis of our calculation
The 3000W (45mm) motor produces 1.07 Nm of torque per Amp, so at 40A, the total torque output would be 42.8 Nm of torque.
In comparison, the 1000W (28mm) motor produces 0.667 Nm of torque per amp, so at the same phase current as the 45mm motor, it's only outputting a total of 26.71 Nm of total torque.
Don't misinterpret my statements, however. The 28mm motor will require more phase current to run at the same speed as the 45mm motor. I am NOT saying that the motors are equal in terms of performance. They are only equal in terms of the phase current they can tolerate before they overheat.
The bottom line is this:
You can run roughly the same phase current to any stator width of a motor design, so long as the winding pattern is the same. But you will get a lower total torque output from the narrower stator motor at that same "safe" phase current.
