- #1

- 13

- 3

Hi everyone,

I'm working on designing a vehicle that uses electric motors, but I'm having a little trouble finding the load and acceleration torques in order to select the right motors to use.

m = total mass of vehicle

a = acceleration

μ_r = rolling friction coefficient

r = wheel radius

N = normal force (vehicle weight)

J = moment of inertia

F_r = rolling friction

T_L = load torque

T_a = acceleration torque

α = angular acceleration

Here's what I've calculated so far. If I've made any mistakes or left anything out, please correct me.

I tried calculating this in two ways and got two different answers.

1. First I used a free body diagram, attached below.

2. Here's where I'm getting confused.

Any help is appreciated. Thanks :)

I'm working on designing a vehicle that uses electric motors, but I'm having a little trouble finding the load and acceleration torques in order to select the right motors to use.

**Variables:**m = total mass of vehicle

a = acceleration

μ_r = rolling friction coefficient

r = wheel radius

N = normal force (vehicle weight)

J = moment of inertia

F_r = rolling friction

T_L = load torque

T_a = acceleration torque

α = angular acceleration

**Assumptions:**- m = 50 kg (distributed evenly across 4 wheels)
- a = 2 m/s^2
- μ_r = 0.02
- r = 0.1 m
- Vehicle driven by two back wheels using two separate electric motors (direct drive)
- Driving on a flat surface

**Calculations:**Here's what I've calculated so far. If I've made any mistakes or left anything out, please correct me.

**Load torque:**- F_r = μ_r * N
- N = 50 kg * 9.81 m/s^2 = 490.5 N
- F_r = 0.02 * 490.5 N = 9.81 N
- T_L = F_r * r
- T_L = 9.81 N * 0.1 m = 0.981 Nm

**Acceleration torque:**I tried calculating this in two ways and got two different answers.

1. First I used a free body diagram, attached below.

- F = ma = 50 kg * 2 m/s^2 = 100 N
- 2 Driving wheels --> 2T = Fd = 100 N*0.1 m = 10 Nm
- T = 5 Nm (per driving wheel)

2. Here's where I'm getting confused.

- T_a = J*α ------- for one wheel
- α = a/r = 2/0.1 = 20 rad/s
- J = 0.5*m*r^2 = 0.5*25*0.1^2 = 0.125 kg*m^2--------------- I used 25 kg here since there are two driving wheels --> each one will accelerate half of the mass, if that makes sense. Is this assumption correct?
- T_a = J*α = 0.125*20 = 2.5 = 1/2 the T_a I previously calculated. What am I doing wrong here?

Any help is appreciated. Thanks :)

#### Attachments

Last edited: