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

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

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

(OP)
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-acceleratio...

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

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

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

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

(OP)
http://www.volcanomotor.com/products/24v_2400rpm_1...

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?

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

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

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

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.

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