I'm assuming your problem is a bit more complicated that what you ask
below, otherwise you can solve on the back of a beer coaster:
Vertical load on rails = mass * g
Assuming rolling instead of slipping tells us we can use static
friction coefficient between wheels and rails
Braking force = vertical load * friction coefficient
So your maximum deceleration is
deceleration = braking force / mass
Rewriting this gives:
max deceleration = static friction coefficient * g
If you speak of braking torque, you could add somewhere that
braking torque = braking force * wheel radius
So please tell us what more you need to know, otherwise this is solved
🙂
Of course all this is subject to many *assumptions*, such as: all
wheels bear the load equally. If that is not the case, you need 2 beer
coasters. If you wich to account for the effect that the rear wheels
will be unloaded due to the deceleration, you may need a calculator or
Mathcad. If you want to do that more accurately, accounting for springs
and dampers on the train wheels, you probably should start to use MDO or
some multibody dynamics software. If you want to model the wheel on
rails contact more accurately you probably need some more software that
can do contact simulations.
How accurate do you want it?
Best regards,
Patrick Asselman