How can we calculate the required torque to accelerate an electric sports wheelchair?

[Andres9292]

Hi everyone, Im trying to select an appropriate dc brushless motor to design a Power Soccer wheelchair. I already did my calculations, but I did it 2 ways and my answers are not the same. Please help. Here is the design problem:

I have the "cart" weighs 150 kg and has to be able to have 150 kg capacity, so it is a 300 kg body. It has to have 2 motors: each attatched to a gearbox and then to a 10" diameter wheel.

For now, the variables I chose for my design are:

The cart has to reach 14.36 km/h or 3.99 m/s and must reach its max speed after 1.6 seconds. The motor has a rated speed of 2400 and a gearbox of 1:8 ratio.

I tried finding the power and torque 2 different ways, but they dont match. The first calculation I did was:

Cart max speed

vcart= Pi*(D)*nwheel = 3.14*0.254(m)*300(rpm)/60(sec/min)= 3.99 m/s = 14.36 km/h

Transition speed

vcart= (3.99/1.6)t

vcart= 2.49 t

Acceleration

a=2.49 m/s^2

Force needed to reach 3.99 m/s in 1.6 sec

F=ma=300*2.49= 780.51 N

1st method
Up until this point there isnt any problem. But now i use 2 different methods to find power and torque. The first one I did using the procedure found in this website:

https://www.engineeringtoolbox.com/car-acceleration-d_1309.html

Distance traveled

d=d0+v0*t+a*(t^2)/2= 2.49*(1.6^2)/2= 3.19m

Power required

P=F*d/t= 780.51*3.19/1.6= 1557 W

Since there are 2 motors, each motor needs to be

Pm= P/2= 778 W = 1 HP

Wheel Torque
Tw=9.55*P/nwheel= 9.55*778/300= 24.78 Nm

Motor Torque
Tm= 9.55*P/nmotor= 9.55*778/2400= 3.1 Nm

2nd method

Force required by each wheel

Fw=F/2= 390.25N

Torque required for each wheel

Tw=F*r= 390.25(N)*0.127(m)= 49.56 Nm

Torque required for each motor

Tm= 49.56/8= 6.29 Nm

Power required for each motor

Pm= T*n/9.55= 6.29*2400/9.55= 1557 W = 2 HP

As you can see, 1 calculation says the motor needs 1 HP and 3.1 Nm of torque, but the other one says I need double the power and torque. I tried making sure that im not screwing up while considering that there are 2 motors but that doesnt appear to be the problem. Can you help me figure out what is the correct calculation? Is one of these methods flawed?

Thanks

 

[gruntguru]

The power calculation (method 1) assumes constant power. 1 hp at zero speed = infinite torque! Real motors are torque limited so you need to factor the torque or power curve of the motor you are considering.

je suis charlie

 

[Andres9292]

http://www.volcanomotor.com/products/24v_2400rpm_1hp_brushless_dc_motor-en.html

What I understand from your answer is that the first method is flawed and that what I have to do is since the torque calculated from the 2nd method is Tm=6.29Nm, I have to go to the motor chart and see if a certain motor can give me that torque at 0 speed. Is that right?

 

[gruntguru]

Pretty much. If the motor has a flat torque curve from zero (not unusual) the initial acceleration is easy to calculate. Most motors are power limited above a certain rpm so the torque starts dropping off above that point. If you really need constant torque all the way to max speed (unlikely) you have to choose a larger motor that makes the required torque at max speed and electrically limit the torque through the range. (The power requirement at max speed is easy - velocity times thrust.) 3.99 x 780.5 = 3.1 kW

je suis charlie

 

[LionelHutz]

You calculated average power. Power is 0 at 0 rpm and linearly ramps to rated power at rated rpm. So, since you ramped from 0 to rated rpm and the average power is 1HP, the rated power of the motor would be 2HP.

Your force answer is wrong by a bit.