# DC Motor, Torque vs RPM

I am making a pulley system (for an electric bike) that requires about 300rpm and 40lb-inch torque. The motor that I am looking at is a 24V DC Permanent Magnet Electric Motor Generator 250W 2750RPM from amazon (35$). (There is a geared version available, but it's 80$ more expensive). My question is:

If the motor is near full power and is under load, would the torque increase? For example, if it's under a load, such that the RPM is 300, does it impact the torque?

• A motor is just like you pedalling a bike. Under no load, you pedal at a certain speed. If you need to pedal harder for more torque, you pedal slower. But only up until a certain point where you can pedal no harder or until you hurt yourself, whichever comes first. Chances are extremely high that you will want to pay an extra \$80 for the geared version unless you can deal with the additional reduction in your pulley system (larger or multiple pulleys). If you try and put the 2750RPM motor under so much load torque that it only spins at 300RPM, it is going to burn out. Apr 14, 2021 at 6:52
• I see, thank you so much! Apr 14, 2021 at 6:55
• Ideally your motor would have the torque/speed/power curves in the datasheet; otherwise look for one with similar specs and design conservatively. Also, add protections, thermal and overcurrent as minimum Apr 14, 2021 at 7:03
• What do you mean by 'near full power'? In a PM motor, torque is proportional to armature current, and armature current reduces as angular velocity increases. So the maximum torque available is the stall torque.
– Chu
Apr 14, 2021 at 7:10
• @Chu we are all getting different scenarios mixed up. Torque is pretty much always proportional to armature current. But you say that "armature current reduces as angular velocity increases." This is true but only given the assumption of constant voltage (not variably controlled voltage). Apr 14, 2021 at 7:42

Usually motors are capable of putting out constant torque over a wide speed range. But power increases with RPM. That is because of the mathematical relationship between power and speed and torque.

Power = torque * speed * k. But if we convert torque to newton-meters and speed to radians/sec then k will be equal to 1.

This means that we can easily calculate the torque of your motor. Let's convert the speed to rad/sec first.

2750 RPM / 60 * 2 * Pi = 288 rad/sec

250 W / 288 rad/sec = 0.868 Nm

0.868 Nm = 7.68 in-lb

You can reduce the speed of your fast motor to 300 RPM by feeding it a low voltage or PWMing it. But if you try to get more than 7.68 in-lb from it you will overheat it either quickly or slowly, depending on how far over you go.

Therefore, I strongly advise you to use the one that is geared down. Ideally you would want a gear down of 7 to 1 or so to produce enough torque.

• Perfect, thank you so much. You explained it very well. I appreciate it Apr 14, 2021 at 7:18
1. A motor comparsion chart like below would give you a rough idea of the torque vs speed characteristic. 1. The above chart is from the following Q&A where you can find more useful info:

How to control DC motor speed by motor driver with PWM input? Asked 9 months ago Active 3 days ago Viewed 915 times

1. You might also find the above post's Appendix B - PWM Controlling Speed of JB37 Geared Motor particularly useful.

1. BTW, geared motor is usually much slower, but much more powerful, which I think is what your need for your bike. In other words, the gears are worth your extra bucks. :)

• Thank you, I will have a look into it! Apr 14, 2021 at 7:18
• #YesPlease, you are welcome. Have a great project. Cheers. Apr 14, 2021 at 7:28