Rover Steering Torque

Question

I would like to calculate the required motor torque to turn a rover wheel whilst the rover is stationary. I have modelled the friction force as a distributed force acting equally along the width of the wheels, working against the turning direction (shown as clockwise).

From here I took an equivalent force of the weight multiplied by the coefficient of friction, divided by 6 as the weight will be distributed among 6 wheels. This equivalent force is acting at a distance of W/4 from the pivoting point (the black circle), and there are two of these forces acting in opposite directions to produce a counter moment to the desired wheel turning direction.

This results in required torque of: $\frac{m g \mu W}{12}$

However I am really not sure about my working. Wouldn't the steering torque increase by the contact length from the wheel squishing the ground and therefore would I need to include this?

Also if the rover wheel is a conventional tyre made of rubber and it would be operating on quite fine sand. Is there any way of working out a rough estimate of the coefficient of static friction? Or would I have to purchase some motors and do some testing?

I have included a top down view of my working and also a front view of the rover wheel and motor.

Thank you!

Answer 1

Apart from the problem highlighted by the comment of SolarMike (i.e. that the forces on the wheel are not always equally distributed and you need to take into account inclination or roll of contact) the biggest problem is the nature of the fine grained sand, which makes the problem far from trivial.

Although there is research carried out on e.g. rolling resistance on granular media or this, there are a lot factors that need to be considered about the specific problem, e.g.:

• angle of internal friction of the medium,

• velocity of movement,

• weight of the material,

• thickness of the granular media,

• tire grooves : i.e. all the ones below are sold as sand dune tires but their behaviour would be different

• deformability of the wheel tire itself,

• environmental factors like moisture,

• ...,

and even then the results might not entirely reproducible.

To avoid having to perform a lot of difficult to prepare and perform experiments, probably the best solution might be to overengineer the first prototype. I.e. select a good compromise, on size that fits, power that it delivers and cost.

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Interlude

At this point I realized that it was not entirely clear to me which of the below is more closer to your project. From the number of wheels I suspect that it is something similar to the latter.

Use	Picture
Toy for sand
self driving space exploration vehicles

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