good point about the rotational velocity and not seeing the motion, that seems obvious now you've pointed it out! Unfortunately the result is still not as expected earlier in time unless the rotational velocity (via the joint load) is very small. Thank you for your help so far.
thank you for your help! Since I posted my first message I did something very similar to what you suggested but used a force with the translational joints instead of a displacement to represent the clamping force applied by the braking system. The joint is applied to the back faces of the pads and they are set to rigid and I have a frictional contact between each pad and the disc.
As before, with low velocities (about 1 rad/s) it is fine but with the ones I actually need to use (around 130 rad/s) I get an unconverged solution and crazy deformation like shown below, do you have any idea why? The screenshot shows the constraints too but I am happy to provide more detail. With either velocity I get a warning that there does not appear to be enough constraints to prevent rigid body motion but I am not sure what is the most suitable way to add those right now.