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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!

enter image description here

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    $\begingroup$ Are you sure that the mass will be always equally shared between 6 wheels? What happens if one side is on a rock with 2 wheels in the air? $\endgroup$
    – Solar Mike
    Aug 22 at 5:59
  • $\begingroup$ When I was taught to drive, few vehicles had power steering so you learnt to turn the wheels as the vehicle moved forward or back. This reduces the forces on the mechanism and the power input needed. So write the code to do the same… $\endgroup$
    – Solar Mike
    Aug 22 at 6:57
  • $\begingroup$ Thanks for your comment, for the sake of stationary turning of the steering motors I made an assumption that the mass will be equally shared between the 6 wheels. I probably should have included this assumption in the post. Also I will be implementing steering whilst moving forwards and backwards, but for tight spaces that might require pivoting, I would like to be able to turn the front and back two wheels whilst stationary. $\endgroup$
    – Bailey
    Aug 22 at 7:26
  • $\begingroup$ Consider a hydraulic system - then the pump power could be used for many things apart from steering, such as suspension height adjustment. $\endgroup$
    – Solar Mike
    Aug 22 at 8:22
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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 enter image description here

  • 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.


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 enter image description here
self driving space exploration vehicles enter image description here

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  • $\begingroup$ Thanks for you comment, I understand how difficult it might be in picking the perfect motor for the steering joints as the friction coefficient will be quite hard to determine. The rover suspension and steering will be more like the perseverance rover. $\endgroup$
    – Bailey
    Aug 22 at 7:31

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