Sizing the components for a friction drive?

I want to make a friction drive for tracking a telescope for astrophotography work but lack the mechanical engineering knowledge to size the components appropriately. The drive is simply one smooth disc of material pressed against another - basically like two cogs, but without the teeth.

Coefficients of static friction for steel appear to vary, but a figure of 0.5 seems like a reasonable starting point.

I understand that the friction between the wheels is purely proportional to the force pushing the two surfaces together (not the contact area); so if two steel wheels were pushed together with 5N of force then the drive should handle 5N x 0.5=2.5N of force at the contact point, before losing traction.

That's the theory, but how would you go about actually choosing the diameter and thickness of the discs in your friction drive? Clearly below a certain thickness there's a risk the discs may bend/warp/deform as a result of the force applied to push them together, but there's also no point in making the discs too large.

There are commercial friction drive telescope mounts - such as the Mesu. One of their models (claimed to carry ~130kg) achieves a 3000:1 reduction with the use of three stages:

2mm diameter input to 40mm diameter output (20:1)
2mm diameter input to 50mm diameter output (25:1)
50mm diameter input to 300mm diameter output ( 6:1)

There's a diagram on the second page of this review: http://www.astro-imaging.com/Equipme...unt_Engels.pdf

For my application, I already have a 100:1 harmonic drive, and I'm looking to add a 10:1 friction drive stage, for a mount capable of carrying a telescope around 30kg.

The telescopes are usually balanced; such that you just need enough torque to get the scope moving. A previous test of my scope indicated something around 5Nm would be required. I put together a really hacky friction drive using MDF discs which slipped at around 2.7Nm, so it gives me hope this is feasible.

I'm limited to a diameter of around 160mm with my little metal lathe; which would point to a 16mm input driving a 160mm output - but would that be suitable? How thick should I make the discs? How do I calculate what would be suitable in mild steel?

I'm a bit of a beginner at this but if you want to model this, I think you want to use contact mechanics... in particular, https://en.wikipedia.org/wiki/Contac..._parallel_axes. You want to press the two cylinders together hard enough that they generate sufficient friction to not slip, but not so much that they indent. It's a bit tricky here since if there's not perfect alignment, the contact patch will be a point. This will also generate an increasing axial load until the two cylinders slip to relieve the force... but these equations may help you ballpark. You'll get the maximum force, the contact patch area for a force, and once you have the force and the static friction and patch area, you can get the force to slip. Make sure to design all the shafts to be properly supported, or your motor will be pretty unhappy.

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I should note that this may be one of those situations where you can do some simple calculations to ballpark, and then you should use FEM if you have it and then build a few iterations or build one and hope for the best by overdesigning a bit.

Many thanks - that wiki link will allow me to get an idea of the force between two discs. I assume then that the only requirement is to ensure that force required to not have the drive slip (for the planned load) must not be so great that it causes indentation/deformation of the discs. Not sure how I'd calculate that part, but I'll keep looking!