How much power is needed to steer tires?

[qpham26]

Homework Statement

I am trying to design a car with simple front rack-and-pinion steering system.
Exactly like this one


I am having trouble find the right motor for the job, assuming typical tire of regular car and the car weight 1ton (included everything)
The shape will be simple rectangular
Assume everything is given like μ_s, R of wheel

Homework Equations

The Attempt at a Solution

I haven't deal with this subject for a very long time and especially this particular problem isn't similar to the things I have dealt with.
I was able to find out the drive power needed for the rear axle but for the steering I couldn't go very far and I have tried asking my professor but he said he hadn't teach this stuff for decade so he couldn't help me as well.

Please help me.
Thanks for your time.

 

[Simon Bridge]

Back of envelope:

taking power as work over time...
$P=\tau_{app}\theta/\Delta t$

$\Delta t$ is the amount of time you want the wheel to rotate in... you'd think of it as a steering response.

The minimum applied torque at the tires would be just that needed to overcome friction ... $\tau_{min}=\mu Mg$

If you are using BTC steering like the video - you'll need to account for the resistance of the return mechanism.

There will be some wrinkles depending on the exact setup - and I'm sure the engineers here will have some advise too - but you should be able to figure it from there.

 

[qpham26]

Back of envelope:

taking power as work over time...
$P=\tau_{app}\theta/\Delta t$

$\Delta t$ is the amount of time you want the wheel to rotate in... you'd think of it as a steering response.

The minimum applied torque at the tires would be just that needed to overcome friction ... $\tau_{min}=\mu Mg$

If you are using BTC steering like the video - you'll need to account for the resistance of the return mechanism.

There will be some wrinkles depending on the exact setup - and I'm sure the engineers here will have some advise too - but you should be able to figure it from there.

I just want it to turn, returning isn't necessary.
and I don't get the way you expressed power. since I don't have any idea about the amount of time i want it to rotate. I just want it to be able to turn and stay turned is fine to me.

would it be possible to find the force to over come the static friction and use it to find out the torque or power from the motor?
and how would I do something like that?

thanks.

 

[haruspex]

Are you trying to turn the wheels while stationary or only when moving?

 

[CWatters]

If you are actually building it then I'd measure the torque required, then knowing the speed at which you want the wheels to move you can calculate the power.

If not then you would need to calculate/estimate the frictional forces. Will be tricky but not impossible. You could probably work out the frictional forces properly but I would cheat...

Basically you have a contact patch under type. Let's say it's a rectangular patch of length L. I would calculate the force required to drag the whole wheel sideways (that's independent of contact area) then assume the force acts at say L/2 from the pivot when the wheels are turned. That should give a conservative answer for the torque at the wheel.

Then use whatever gearing you have to work out the torque and speed required at the motor. Perhaps assume lock to lock neds to be a few seconds?

Once you have the rpm at the motor convert it to angular velocity (radians/second).

Then multiple torque & angular velocity to give the power required.

Perhaps apply a safety factor of say 2?

 

[Simon Bridge]

and I don't get the way you expressed power. since I don't have any idea about the amount of time i want it to rotate. I just want it to be able to turn and stay turned is fine to me.

The wheel won't turn instantly - it takes some time to change angles. You need to know how fast you want this to be.

If you choose a slow time, then you save power, but the steering will feel sluggish.
Of course - you could see how auto manufacturers do power steering.

The others have covered the rest so I won't repeat it here.

 

[CWatters]

PS. If the professor can't help he won't know if the answer is wrong :-)

 

[qpham26]

would the power needed to turn the wheels while stationary be greater than while moving?
of so than using the motor with that much power would be fine.

 

[qpham26]

PS. If the professor can't help he won't know if the answer is wrong :-)

that is what I was thinking. That is why I am trying to do this as simple as possible xD

 

[CWatters]

would the power needed to turn the wheels while stationary be greater than while moving?
of so than using the motor with that much power would be fine.

Yes. It's much easier to steer when moving. This was very obvious before full size cars had power steering.