Torque calculations for a small electric vehicle

[domnu_filip]

Hello guys,

I'm trying to calculate the torque for a 3 wheeler electric (small vehicle).
2 driving wheels and one driven wheel. At the driving wheels we have a BLDC motor for each wheel.
We want to calculate the torque for resting( not going down hill) on inclined plane (angle={5,10,15 degrees}) and then to calculate the torque for move it up hill.

Also, I want to make sure that the wheels will not slip, how could I do this?

Witch is the max angle I can raise de vehicle before slipping?

How should I divide the torque between the 2 wheels?

The m=30 kg; wheel_radius=0.2 m; friction_coeficient=0.4 (I guess).

We want to calculate this torque in order to convert it and send it to the microcontroler as Iabc.

Please help me! :(
Best regards

 

[russ_watters]

Welcome to PF!

This is all pretty straightforward; do you know how to do a friction on an inclined plane problem? That's how you should start.

 

[domnu_filip]

Welcome to PF!

This is all pretty straightforward; do you know how to do a friction on an inclined plane problem? That's how you should start.

Well I have an ideea but I will listen to you, to check my knowledge after.
The friction force has to be calculated for each wheel?
If you can give me the steps I will be very gratefull.

 

[russ_watters]

Well I have an ideea but I will listen to you, to check my knowledge after.

That isn't how we do things on PF. You'll learn more effectively if you think through the problem yourself, rather than just take an answer from us. So please try.

Is this a school project, and at what level of education is it for/do you have?

The friction force has to be calculated for each wheel?

Each wheel you are trying to analyze the torque for!

 

[domnu_filip]

That isn't how we do things on PF. You'll learn more effectively if you think through the problem yourself, rather than just take an answer from us. So please try.

Is this a school project, and at what level of education is it for/do you have?

Each wheel you are trying to analyze the torque for!

Ok, I tried to calculate friction force with this formula : Ff= (coef_friction * m*g*cos(angle))/3*wheel_radius.

I used 3 because we have 3 wheels and I asume that the mass distribution on each wheel is even (is this correct?)

I am first year in college , computer science, and it is my personal project.

 

[russ_watters]

Ok, I tried to calculate friction force with this formula : Ff= (coef_friction * m*g*cos(angle))/3*wheel_radius.

I used 3 because we have 3 wheels and I asume that the mass distribution on each wheel is even (is this correct?)

Good start; that's the correct equation.

You defined two wheels as "driving wheels" and one as "driven wheel". What does it mean to be a "driven wheel"? Is there something applying torque to it to propel the cart? If so, what? If not, it shouldn't be part of an applied torque calculation.

 

[domnu_filip]

Good start; that's the correct equation.

You defined two wheels as "driving wheels" and one as "driven wheel". What does it mean to be a "driven wheel"? Is there something applying torque to it to propel the cart? If so, what? If not, it shouldn't be part of an applied torque calculation.

The "driven wheel" is a free wheel, like the back wheels on a fwd car, it is used to stable the cart.
Yes, the "driving wheels" are the one conected to the to the motors, for propeling the cart up hill.
What should I do next? What to look for?
How do I use this Ff?

 

[russ_watters]

The "driven wheel" is a free wheel, like the back wheels on a fwd car, it is used to stable the cart.

So if it's free, it has no torque applied and shouldn't be part of the calculation.

What should I do next? What to look for?

...so, the equation is actually a little mixed together (too complete?) and you'll have to take it apart a little to use it. 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.

Using the cosine tells you the maximum friction force available. Using it without the friction coefficient and with a sine function tells using the force due to gravity parallel to the surface. Set the two equations equal to find the maximum slope.

 

[domnu_filip]

So if it's free, it has no torque applied and shouldn't be part of the calculation.

...so, the equation is actually a little mixed together (too complete?) and you'll have to take it apart a little to use it. 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.

Using the cosine tells you the maximum friction force available. Using it without the friction coefficient and with a sine function tells using the force due to gravity parallel to the surface. Set the two equations equal to find the maximum slope.

Ok.
I set equal this equations:
m*g*sin_angle=coef_friction*m*g*cos_angle => angle_max=atan(coef_friction) ?

It is correct, it depends just on that coeficient?
Now, if we have the F force that pulls the cart down on the slope, the Ff_max (just on the driving wheels?) how do I find the force needed for resting on the slope(without rolling back?).
Thanks a lot!

 

[jack action]

http://hpwizard.com/hill-climbing.html

 

[berkeman]

@domnu_filip -- I don't think I've seen your free body diagrams (FBDs) yet, apologies if I've missed them. It's important to get into the habit of drawing your FBDs early in a problem, to help you organize your thoughts and to start applying the equations correctly.

So can you show us your FBD for each of the driven wheels in the situation where the motor torques are balancing the force trying to roll the vehicle back down the slope? Assume that the friction forces are high enough so that the driven wheels are not slipping for this first FBD...

https://en.wikipedia.org/wiki/Free_body_diagram

 

[domnu_filip]

@domnu_filip -- I don't think I've seen your free body diagrams (FBDs) yet, apologies if I've missed them. It's important to get into the habit of drawing your FBDs early in a problem, to help you organize your thoughts and to start applying the equations correctly.

So can you show us your FBD for each of the driven wheels in the situation where the motor torques are balancing the force trying to roll the vehicle back down the slope? Assume that the friction forces are high enough so that the driven wheels are not slipping for this first FBD...

https://en.wikipedia.org/wiki/Free_body_diagram

 

[berkeman]

Good! The non-driven wheel will not have any frictional force along the surface of the incline, though, so take that out.

And can you now label the torques for the two driven wheels and use the FBD to solve for them?

 

[domnu_filip]

Good! The non-driven wheel will not have any frictional force along the surface of the incline, though, so take that out.

And can you now label the torques for the two driven wheels and use the FBD to solve for them?

Don't know how to label the torque :(

 

[Lnewqban]

Do not underestimate additional weight of batteries, chassis, brakes, controls, steering, etc.
Consider that the greater the hill slope, the less normal force and traction you will have on the driven wheels when the car is going up (total weight vector tilts towards the free wheel).

It is important to determine the maximum slope and minimum coefficient of friction (worst condition).
If a radio controlled car, or experimental one, the slope could be as high as the terrain demands.
If used on legal paved streets, consider that 20 degrees is the worse you could ever find and that rubber-dry pavement coefficient can be as high as 0.8.

Please, see:
https://en.wikipedia.org/wiki/Grade_(slope)

 

[domnu_filip]

Do not underestimate additional weight of batteries, chassis, brakes, controls, steering, etc.
Consider that the greater the hill slope, the less normal force and traction you will have on the driven wheels when the car is going up (total weight vector tilts towards the free wheel).

It is important to determine the maximum slope and minimum coefficient of friction (worst condition).
If a radio controlled car, or experimental one, the slope could be as high as the terrain demands.
If used on legal paved streets, consider that 20 degrees is the worse you could ever find and that rubber-dry pavement coefficient can be as high as 0.8.

Please, see:
https://en.wikipedia.org/wiki/Grade_(slope)

The vehicle main parts are these, the aprox. mass is 30 kg.

So.. are my equations correct? If yes, how do I go further?

 

[Lnewqban]

Those would be 15 Kg of batteries and 15 Kg the rest of the car.
Determine the angle of slope first, as well as normal reaction force on each contact patch of wheels.

Torque on each driven wheel will be determined by the resulting force pulling the car back in alignment with the road divided by 2, or less, if you wish to introduce a safety factor due to such things like uneven traction, sideways inclination of road, difference in motor output.
You know that torque is tangential force times radius of wheel.

The maximum torque that each wheel could develop within the traction limits should be the static friction force between that wheel and the surface, which depends on the normal force, which depends on the important angle of the slope.

These calculations seem to be pretty similar to yours:
https://mae.ufl.edu/designlab/motors/EML2322L Drive Wheel Motor Torque Calculations.pdf

 

[domnu_filip]

Torque on each driven wheel will be determined by the resulting force pulling the car back in alignment with the road divided by 2, or less, if you wish to introduce a safety factor due to such things like uneven traction, sideways inclination of road, difference in motor output.
You know that torque is tangential force times radius of wheel.

I don’t get that part when I have to divide by 2. In the document that you shared, it says that you should divede by 2 when you have horinzontaly road. So for a slope it is a different method?

 

[berkeman]

I don’t get that part when I have to divide by 2. In the document that you shared, it says that you should divede by 2 when you have horinzontaly road. So for a slope it is a different method?

Your two drive wheels are at the same height on the slope, right?

 

[jack action]

Don't know how to label the torque :(

It is still equal to 0 in the x-direction. The torque of the wheels will be $T_L = \frac{F_{fL}}{r_L}$ and $T_R = \frac{F_{fR}}{r_R}$ where $r$ is the wheel radius and $F_f$ is the wheel-road friction force for the front wheels. The maximum friction force is $F_{f \max} = \mu N_f$.

Although your equations are technically good, you should consider both front wheels together instead of separately ($N_f$ instead of $N_{fL} + N_{fR}$) when in the side view analysis. Then you can assume that each wheel provides half the torque (hence why you have to divide by 2).

 

[domnu_filip]

Your two drive wheels are at the same height on the slope, right?

Yes.

 

[domnu_filip]

Yes.

How do I get the distance between axles, I mean, I have a 3 wheeler, the distance between axles are the same to a 4 wheel car? I have to measure "a triangular mode" between the 3 wheels?

 

[domnu_filip]

Those would be 15 Kg of batteries and 15 Kg the rest of the car.
Determine the angle of slope first, as well as normal reaction force on each contact patch of wheels.

Torque on each driven wheel will be determined by the resulting force pulling the car back in alignment with the road divided by 2, or less, if you wish to introduce a safety factor due to such things like uneven traction, sideways inclination of road, difference in motor output.
You know that torque is tangential force times radius of wheel.

The maximum torque that each wheel could develop within the traction limits should be the static friction force between that wheel and the surface, which depends on the normal force, which depends on the important angle of the slope.

These calculations seem to be pretty similar to yours:
https://mae.ufl.edu/designlab/motors/EML2322L Drive Wheel Motor Torque Calculations.pdf

I have a question, in the calculation process of maximum slope I need the distance between the axles( for a 4 wheel car).
In my case, I have a 3 wheeler, how should I consider the lengths?
http://hpwizard.com/hill-climbing.html

 

[Lnewqban]

I have a question, in the calculation process of maximum slope I need the distance between the axles( for a 4 wheel car).
In my case, I have a 3 wheeler, how should I consider the lengths?
http://hpwizard.com/hill-climbing.html

Same thing.
Distance between axles is the same.

 

[domnu_filip]

Same thing.
Distance between axles is the same.

So I could consider the rear wheel like"an axle", right?
Like I did earlier in the photo with side view.

 

[Lnewqban]

So I could consider the rear wheel like"an axle", right?
Like I did earlier in the photo with side view.

Yes.
The main thing is to determine the reaction forces on those three point of contacts in your free body diagram of forces.
You will need to assume a location of the center of mass of the loaded car using your best judgement.

 

[domnu_filip]

Those would be 15 Kg of batteries and 15 Kg the rest of the car.
Determine the angle of slope first, as well as normal reaction force on each contact patch of wheels.

Torque on each driven wheel will be determined by the resulting force pulling the car back in alignment with the road divided by 2, or less, if you wish to introduce a safety factor due to such things like uneven traction, sideways inclination of road, difference in motor output.
You know that torque is tangential force times radius of wheel.

The maximum torque that each wheel could develop within the traction limits should be the static friction force between that wheel and the surface, which depends on the normal force, which depends on the important angle of the slope.

These calculations seem to be pretty similar to yours:
https://mae.ufl.edu/designlab/motors/EML2322L Drive Wheel Motor Torque Calculations.pdf

And what are the conditions that vehicle is resting on the slope, acording to the document you shared here?

 

[Lnewqban]

And what are the conditions that vehicle is resting on the slope, acording to the document you shared here?

The document shows only calculations for maximum traction force of a robot with plastic wheels climbing a max slope of 2 degrees.
That case seems to be far from yours, but it may have some validity as a general example.

For you vehicle resting on a slope, your motors and controls (and brakes, for power off condition) should be able to precisely provide enough torque to compensate for the natural tendency of rolling back down the slope, which again, depends on the maximum slope your car will be dealing with.

 

[domnu_filip]

The document shows only calculations for maximum traction force of a robot with plastic wheels climbing a max slope of 2 degrees.
That case seems to be far from yours, but it may have some validity as a general example.

For you vehicle resting on a slope, your motors and controls (and brakes, for power off condition) should be able to precisely provide enough torque to compensate for the natural tendency of rolling back down the slope, which again, depends on the maximum slope your car will be dealing with.

Ok, but I want that my vehicle is resting on the slope using the engines power, not the brakes, I want to calculate the torque needed for that. That's why I asked you about that document, because in the "resting case" I think I don't need the : Fa = force required to accelerate to final velocity , and RR = force necessary to overcome rolling resistance [lb] .

Should I consider them 0 ?

 

[domnu_filip]

For you vehicle resting on a slope, your motors and controls (and brakes, for power off condition) should be able to precisely provide enough torque to compensate for the natural tendency of rolling back down the slope, which again, depends on the maximum slope your car will be dealing with.

For beginning I will put the vehicle manually on the slope, and I expect to not roll down the slope.

 

[Lnewqban]

Should I consider them 0 ?

Yes.
No rolling resistance.
Pushing forward forces of two wheels balance rearward gravity force component, assuming your contact patches have enough traction, which depend on normal gravity force component acting on each of them.

 

[Lnewqban]

For beginning I will put the vehicle manually on the slope, and I expect to not roll down the slope.

Your wheels would be rotating while in the air, just to be precisely stopped when contacting the surface of the slope?

 

[domnu_filip]

Your wheels would be rotating while in the air, just to be precisely stopped when contacting the surface of the slope?

Yes, kind of.

 

[Lnewqban]

Yes, kind of.

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.

 

[domnu_filip]

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.

Ok, I used the steps described in that document, without Fa and RR, because there is no rolling, and no speed?
Is this correct?