# Torque calculations for a small electric vehicle

• domnu_filip
In summary: First off, you went all the way to torque, not force. It's fine, but for a start you need the force because you need to compare the friction force with the available friction (you wanted the maximum slope, among other things). Take away the wheel radius and number of wheels for now.So if it's free, it has no torque applied and shouldn't be part of the calculation.
Lnewqban said:
Then, from previous tests, you should have narrowed how much amps your motors will need to receive in oder to provide the precise torque needed to compensate for the pulling rearwards gravity component.
Your modulating control should match that level of precision.
Otherwise, your car may still slowly move up or down the slope after you place it on it.
And in up motion, I will use this for calculating the max angle.

And one more question, the calculation from that document, are valid for an angle smaller than maximum angle?
Thanks!

I am not sure about those equations.
Could you show us what the terms mean and a free body diagram of forces?

Right here, in my case FWD.

Last edited:
Thank you.
I do not see the ##F_r## that is shown in the equations in that diagram.

Do you want to find the torque of each wheel as a function of those variables for your work rather than calculating a value for a determined slope?

Lnewqban said:
Thank you.
I do not see the ##F_r## that is shown in the equations in that diagram.

Do you want to find the torque of each wheel as a function of those variables for your work rather than calculating a value for a determined slope?
Yes, I want to find the torque of each wheel as a function of those variables.
Hope it helps; Do you know to should I calculate the rolling resistance on a slope?

domnu_filip said:
Yes, I want to find the torque of each wheel as a function of those variables.
Hope it helps; Do you know to should I calculate the rolling resistance on a slope?
View attachment 259933
But we are calculating for steady condition first: no rolling resistance.

Lnewqban said:
But we are calculating for steady condition first: no rolling resistance.
Yeah I know, I was just curious how can I do that in future.

Yes, you could once you are ready to compute the dynamic condition of the car moving uphill.
For static conditions, the equation for finding the angle is correct, being ##f_r=0##

That would be the maximum angle for which your driven wheels will keep traction.

The torque that each of both driven wheels should deliver in order to keep the car from rolling backwards should be equal to half the total weight (0.5 mg) times the sin of the angle of the slope times the radius of the wheel.

domnu_filip
Lnewqban said:
The torque that each of both driven wheels should deliver in order to keep the car from rolling backwards should be equal to half the total weight (0.5 mg) times the sin of the angle of the slope times the radius of the wheel.
And for going uphill?

domnu_filip said:
And for going uphill?
For that, you will need to estimate a desired rate of acceleration.
That means an additional torque will be needed to overcome the inertia of the car.
The maximum slope will need to be a little less than for static condition, or wheels may slide under the increased torque, as tangential force may become bigger than the available friction on the contact points.
Unless you are rolling on deflated tires, I believe that rolling resistance at constant speed could be dusregarded.

Lnewqban said:
For that, you will need to estimate a desired rate of acceleration.
That means an additional torque will be needed to overcome the inertia of the car.
The maximum slope will need to be a little less than for static condition, or wheels may slide under the increased torque, as tangential force may become bigger than the available friction on the contact points.
Unless you are rolling on deflated tires, I believe that rolling resistance at constant speed could be dusregarded.
So, I have too add this to my stationary torque? Torque= ( m*g*sin_angle+(m*g*cos_angle*Crr) +Fa)*wheel_radius*resistance_factor?

No need to add torques up.
The value of the torque for stationary condition is smaller than the one needed for acceleration.

Lnewqban said:
No need to add torques up.
The value of the torque for stationary condition is smaller than the one needed for acceleration.
Ok, what is the condition for acceleration?
I mean, how should I calculate the torque for starting from resting on the slope (previous case), to move uphill?

Last edited:
Lnewqban said:
I believe that we already have covered that.
Could you repeat please? I understand a little slow I guess :D

Last edited:
Lnewqban said:
If I have the wheels mounted directly on the BLDC motor axle, how should I calculate the wheel torque?
I ask this because, if I send the command to the motor, e.g. 5 Nm necessary to keep the vehicle steady on the incline, how do I get the feedback for the control loop?
So, if I calculated that the vehicle needs 5 Nm to rest on the slope, it is correct to measure the wheel torque and consider it as feedback to my torque control loop?
And how do I should I calculate the wheel torque in this case?

Wouldn't your feedback come from an accelerometer? You set a certain amount of torque, expecting a certain amount of acceleration. If the resulting acceleration is different from what is expected, you apply the necessary correction.

jack action said:
Wouldn't your feedback come from an accelerometer? You set a certain amount of torque, expecting a certain amount of acceleration. If the resulting acceleration is different from what is expected, you apply the necessary correction.
Yes, but how do I convert it? And btw I want it to rest...

If you want the acceleration to be zero (at rest), then you have calculated a constant value for your torque ##C##, say 5 N.m. If the vehicle accelerate (+ve or -ve), then you need to counterbalance your torque by the amount of acceleration ##a## that is measured (it should be zero).

So you get your new torque value ##T## to apply with ##T = C + rma## where ##r## is your wheel radius, ##m## is the vehicle mass and ##a## the measured acceleration.

If you can measure the velocity ##v##, that is even better, because your trying to reach for ##v = 0##, which is your true objective. then the desired acceleration might be to reach for ##\frac{dv}{dt}## where ##dv## will be some fraction of ##v## and ##dt## will be based on your feedback loop time interval.

jack action said:
If you want the acceleration to be zero (at rest), then you have calculated a constant value for your torque ##C##, say 5 N.m. If the vehicle accelerate (+ve or -ve), then you need to counterbalance your torque by the amount of acceleration ##a## that is measured (it should be zero).

So you get your new torque value ##T## to apply with ##T = C + rma## where ##r## is your wheel radius, ##m## is the vehicle mass and ##a## the measured acceleration.

If you can measure the velocity ##v##, that is even better, because your trying to reach for ##v = 0##, which is your true objective. then the desired acceleration might be to reach for ##\frac{dv}{dt}## where ##dv## will be some fraction of ##v## and ##dt## will be based on your feedback loop time interval.
I have the speed of the motor axle is spining, in rad/s, if I have the wheel directly on that axle, or a hub-motor (segway), can I use that value?

Yes

Hello guys, I'm working for a home project and I want to made a simulation on a BLDC motor, which have a wheel attached to it's axle. (It is a part of small cart, 2 BLDC motors with 2 wheels directly mounted on the axle). So can I control the torque this way? What regulator should I use? How to integrate the load torque in motor subsystem?

No one?..

domnu_filip said:
What regulator should I use?
When I shop for BLDC motors online, I see that many of the include the manufacturer's regulator as part of the package.

• Mechanical Engineering
Replies
8
Views
4K
• Mechanical Engineering
Replies
10
Views
1K
• Mechanical Engineering
Replies
15
Views
2K
• Mechanical Engineering
Replies
3
Views
1K
• Mechanical Engineering
Replies
7
Views
1K
• Mechanical Engineering
Replies
3
Views
3K
• Engineering and Comp Sci Homework Help
Replies
102
Views
5K
• Mechanical Engineering
Replies
4
Views
1K
• Mechanical Engineering
Replies
10
Views
6K
• Mechanical Engineering
Replies
5
Views
3K