Maximum torque without wheel slip

[GGplayz]

TL;DR

How to figure out maximum torque that a DC motor can apply in order to prevent wheel slip.

I am designing a mini sumo robot which should contain two DC motors. I made a design for some motors which output a stall torque of 4.6 kg-cm each. My wheel radius is 3.4 cm and a depth of 2.2 cm and I plan to make it out of silicone. Wanting as little slip as possible while stalling what could the maximum torque of one motor be. The robot also weighs 0.5kg. I think that the coefficient of friction should be at around 1 and I also read that adhesion increases CoF but the wheels shouldn't be able to pick up a standard A4 paper (80g/m2).

 

[jack action]

Answer these questions to find the answer:

1. Knowing the CoF and vehicle weight, what is the maximum force the wheels can handle?
2. Knowing the maximum force the wheels can handle and the wheel radius, what is the equivalent wheel torque?
3. Assuming the motor is connected to the wheel through a gearbox with a known gear ratio, how would the motor torque relate to the wheel torque?

 

[Baluncore]

Welcome to PF.

The maximum torque produced by a PM DC brush motor is proportional to the current flowing through the motor. At zero speed, the current is determined simply by the internal resistance of the motor, and the supply voltage.

How will you control the motor?
Can you limit the current through the motor?

 

[GGplayz]

Welcome to PF.

The maximum torque produced by a PM DC brush motor is proportional to the current flowing through the motor. At zero speed, the current is determined simply by the internal resistance of the motor, and the supply voltage.

How will you control the motor?
Can you limit the current through the motor?

I know, this scenario is when two sumo robots are face to face and they push each other, the motor is controlled through a motor driver and a microcontroller, I could reduce current and maybe somehow detect this scenario and slow down the motors but it would rather be a waste to buy a motor with higher torque abilities. Also does lowering power also decrease rpm? not that it would matter much when stalling. But actually what causes wheel slip exactly?

 

[Baluncore]

But actually what causes wheel slip exactly?

The transition from static to dynamic or sliding friction.

If you can switch the motor current on/off quickly, it will build up torque until the wheel slips and CoF falls, then each time the current ceases it will regain traction, with the higher static CoF. That "switching friction" mode averages out for better traction than if you avoid slip altogether. Traction control is a winning combination.

You probably control the motor with PWM from a microcontroller. That regulates average voltage, which sets the average speed, which is not what you want for maximum torque. PWM is usually too fast, to get better "unslip" control, use a lower frequency PWM to control the current.

 

[GGplayz]

The transition from static to dynamic or sliding friction.

If you can switch the motor current on/off quickly, it will build up torque until the wheel slips and CoF falls, then each time the current ceases it will regain traction, with the higher static CoF. That "switching friction" mode averages out for better traction than if you avoid slip altogether. Traction control is a winning combination.

You probably control the motor with PWM from a microcontroller. That regulates average voltage, which sets the average speed, which is not what you want for maximum torque. PWM is usually too fast, to get better "unslip" control, use a lower frequency PWM to control the current.

Thank you for your answer it does help, also after I did some sketches I realized that the torque drawn will be enough to push the load, and maybe + opposing force from other robot. While in stall there might be decent slippage and I'll look into it and when load isn't being opposed wheel slip can be 0 or minimal.

 

[sophiecentaur]

I could reduce current and maybe somehow detect this scenario

How would that relate to a realistic model of actual wrestlers? Wouldn't look like one of them was just giving up pushing? What do real wrestlers do about slippage? Sounds a bit like ABS type requirement.

 

[GGplayz]

How would that relate to a realistic model of actual wrestlers? Wouldn't look like one of them was just giving up pushing? What do real wrestlers do about slippage? Sounds a bit like ABS type requirement.

Hmmm, any idea on how to calculate if the wheel would slip or not in such situation, in theory after the motor reached its maximum velocity which is almost instantly, acceleration would be 0 meaning forward force of motor is also 0, also it would mean that idk if there is such thing but angular force of wheel would be zero thus making tire slippage while moving at max also be zero. But when accelerating wouldn't it make a hell of a lot of slippage? Also when in stall it would mean that velocity is 0 and acceleration somewhat small making forward / backward force small which shouldn't cause slip. If you have any idea of how to better calculate forces acting on robot please tell me because I really don't know this stuff well.

 

[jack action]

But when accelerating wouldn't it make a hell of a lot of slippage?

Slippage only appears when the force coming from the wheel torque exceeds the available friction force. If the available friction force is high, the acceleration can be high (without slippage).

Also when in stall it would mean that velocity is 0 and acceleration somewhat small making forward / backward force small which shouldn't cause slip.

Velocity and acceleration are independent of each other. Acceleration can be very large, even if the velocity is 0. If the friction force is large enough to support the wheel torque, the entire vehicle will accelerate, together with the wheel. If not, slippage occurs and the wheel's angular velocity alone will accelerate.

 

[sophiecentaur]

any idea on how to calculate if the wheel would slip or not in such situation,

The basic laws of friction work here. Slip will occur when the tangential force from the wheel equals the weight force (on the wheel) times the coefficient of friction.

But this is a model and the two robots are the same (?) so the main aim is to make the motion 'look right'. Clearly it's down to the tyre material and the surface it works on. You would have to base design on lots of experiments with different materials.