November 17, 2020

Intro to Rough Motor Sizing


Posted on November 17, 2020 by admin

How to vaguely guess the approximate ballpark size of moter required for your application. These are all ballpark numbers, but generally a good starting point for your average motor. Two important parameters: torque and speed.

Lets start with speed. This is the easy one:

  • For small inrunners (4″ OD or less), max speed is somewhere around 12k-16k RPM. For Hobbyking inrunners it depends on the quality of construction. For some motors, the magnets will fly off the rotor at high speeds, so probably no not exceed 15k rpm. If the rotor has a carbon or kevlar overwrap (or is an IPM), you can push the upper limit here, but hysteresis losses and eddy current losses will start to become very large. If the motor has both low pole count and very, very fine laminations, you can really rip- apparently some people push 25-50k RPM.
  • For big inrunners (8″ or more), max speed is probs 8k-10k RPM, but it depends a lot on how thin the laminations are, what the tooth shape is, etc. If you really want to know, test one til it ‘splodes. Apparently Tesla pushes their big inrunners pretty hard, up to 18k RPM. Again, these numbers can vary fairly wildly depending on a lot of factors: lamination thickness, mechanical integrity of rotor, etc.
  • For small outrunners (melon size, 100mm or less), max speed is 8000 RPM. Experimentally Mason has verified that pushing an SK3 to 10k for extended periods of time will cause it to ‘splode.
  • For big outrunners (6″ or more), 5k seems to be a good upper limit, as after this the eddy current and hysteresis losses become large.
  • For linear motors or axial flux, it depends a lot. Axial flux motors come in all different shapes and sizes, but generally are not used at high speeds for whatever reason. Linear motors generally run out of track before they hit high speeds, so it is a non-issue.

Next up: Torque. This is a little harder, so we turn to mathematics. Basically, what is conserved across motors is magnetic shear stress produced in the airgap. Just multiply the surface area of the rotor by the radius and magnetic shear stress and you can get the torque.

T = S*A*R

where: T = shaft torque [N*m], S = magnetic shear stress [N/m^2], A = active airgap area, also equal to: (stator stack height) * (rotor rad) * 2 * PI [m^2], R = argap radius [m].

For linear motors, the equation is similar, just without the radius:

F = S*A

where: F = mover force [N], S = magnetic shear stress [N/m^2], A = active airgap area [m^2].

Rule of thumb values for what S is, depending upon the moter in question:

  • For inrunners:
    • S = 25000 N/m^2 for air-cooled, continuous operation.
    • S = 45000 N/m^2 for peak torque of air cooled motor, as in 30 seconds at this torque smells like hot windings and after 1 min moter is on fire.
    • The MIT Cheetah robot which has specially designed inrunning motors rumored to go up to 190,000 N/m^2. However, this is obviously a pulse-torque application.
    • S varies wildly for water-cooled setups, depending on the thermal resistance to the water and the water flow rate. However, 40000 N/m^2 for continuous and possibly 60000 N/m^2 peak is probably a good place to start.
  • For outrunners:
    • S = 11000 N/m^2 for continuous, air-cooled operation. Outrunners do not cool very well, and generally have significantly less copper than a comparably sized inrunner because there is just less stator area.
    • S = 36000 N/m^2 for peak operation (about 5 seconds).
    • Outrunners also vary significantly based on what they are mounted to and the stator stack height.
  • For linear motors, use the same numbers as the inrunners. Linear motors are often water cooled and mounted to something big and heavy which can take the heat out very well, but often operate at low efficiency because of the end-effects. The inrunner numbers are a good place to start.

Happy motoring!! 🙂


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