# Electric motor for low speed, high torque application?

Background

For my mechanical engineering senior design project, we are designing a cargo transporter electric vehicle for off-road conditions. The vehicle needs to transport loads weighing up to about 22,000 N or about 5000 lbf.

The transporter will have a very slow speed (about 6 in/s). Using a coefficient of rolling resistance of 0.35, I calculated that the total power requirements would be about 5 hp. To calculate this, I took the rolling resistance force times the target speed of 6 in/s (P=FV).

Assuming that we use four electric motors, one for each wheel, I found a per-motor horsepower requirement of about 1.25 hp. For large wheels of about 3 ft diameter at the speed of 6 in/s, the wheel rotation rate is about 2.5 RPM. This yields a large torque requirement of around 3700 N-m or 2700 ft-lb.

I'm having trouble finding the right combination of DC motor and gearbox to fit this application.

Question

How can I size a DC motor for a high torque, low speed application? The torque load per motor is about 3700 N-m and the nominal rotation speed is about 2.5 RPM, yielding a power requirement of about 1.25 hp per motor.

I can find DC motors rated for this power, but definitely not for this torque requirement or rotational speed. Would I need a special gearbox? How do industry people normally solve this problem?

• You forgot to account for your required acceleration. Maintaining speed is one thing but you need to get up to speed first (preferably before the motor stalls and burns out). engineering.stackexchange.com/questions/31501/… Nov 18, 2022 at 0:38
• And yes you need a gearbox, a special gearbox if need be. If you cannot acquire one then you are going to have to reduce the output of the best gearbox using belts or chains. For your application, since motor mass and volume doesn't really matter you could go with hugely oversized motors since larger motors rotate more slowly, but you will take an efficiency hit. Nov 18, 2022 at 0:44
• @DKNguyen Thanks for your comment. I wasn't sure how to analyze the "acceleration" part of the motor selection. How do I analyze whether a motor can build up the necessary speed? Nov 18, 2022 at 1:35
• See that link. But if you're a MecE all I should need to say is it's as simple as deciding how long you're willing to wait. Nov 18, 2022 at 1:36
• Yes, it is. A combustion engine will stall and shut down but a motor spinning too slowly below it's no-load RPM will draw increasing amounts of current and overheat and burn out. So you need your motor to be large enough to be able to produce enough torque to be able to turn on startup and to accelerate through that overheating stall phase fast enough before the motor mass heats up too much (both of which are helped by a motor with more mass). And a larger motor tends to have a lower no-load RPM which pushes down what the minimum comfortable speed which in turn decreases the stall RPM window. Nov 18, 2022 at 2:09

First, make sure you know all load cases. You need to know which torque at which RPM you need to have. Then, find a motor + gearbox combination, check their rated torque, RPM and power. Consideration here are: cost, efficiency, type of controlling/driving and in this case especially, power supply. I can imagine that on a lunar base you might not have your 60 Hz 120 V AC?

Just a quick example of a process you'll need to iteratively go through. If start-up torque is not huge compared to steady state power/torque requirements, and let's make the wild guess you'll have DC system on the lunar base, and the application requires frequent starting, stopping, positioning, you could have a look at servo systems with bolt on planetary gearbox. Let's say a 5000 rpm motor and a 2.5 RPM load, requires a 1:2000 gear. Let's divide that by a worm 1:40 and a planetary gear box in the motor 1:50. Check torques, check other assumptions. Rinse and repeat.

By the way, are you sure about the 0.35 rolling friction coefficient? Seems high for rolling.

• 0.35 would not surprise me on regolith, which I presume is similar to a sandy beach or soft soil where even moving horizontally is technically rolling up hill since you sink in. Nov 18, 2022 at 18:32
• Yes, that sounds reasonable
– RJDB
Nov 18, 2022 at 18:43