I was wondering how you calculate how much cutting force is being applied to the tool tip. Like is that say 20kg of weight up against the tool and the work.
Then from that how do you work out how big a linear rail you need?
Can someone give me a link to an example that has already been done?
My little site on MIG welding http://www.learn-how-to-weld.com/mig-welding/
Both your Y-axis (gantry) and Z-axis should experience a largely radial load when your Z-axis is fully retracted. With full extension, you have a simple vector addition from where the tool bit contacts the material to be cut. Take each connection in-turn (e.g., compute the Z-axis, then compute the Y-axis). What you will often find is that it is easier to figure out your maximum force that you can apply, since this is in reality a controllable variable.
All that being said, a few practical issues to bear in mind:
1) For linear rails/slides, the price difference is relatively small when going from smaller to larger. In fact, I found that the larger rails were often cheaper, though with more expensive shipping, than smaller rails since most people seem focused on buying the smaller rails (e.g., 30mm rail was cheaper for me than 15mm rail) when purchasing on eBay.
2) Even the small stuff, that's appropriate, should have more than sufficient load bearing capacity within the limits of a home-built CNC.
3) In so long as you aren't going for an industrial-grade machine (e.g., to machine tool steel), then you shouldn't be hitting force issues for your motion components. With aluminum and other soft metals, you will want a relatively shallow depth of cut at a relatively slow feed rate.
To plow through thick wood at speed, you will run into spindle, bit and chip removal issues long before you should run into mechanical force issues. Remember, this is just like a hand tool: you want the tool to do the work. High force delivered into an inappropriate tool leads to bad edges, broken bits and burnt out spindles.
All that being said, F=ma is your friend.
As an aside, for my own machine that is under construction, I have an order of magnitude of play between my designed use case and the limits of the SR30 slides/rails that I am using -- and that is with the SR30s being used on their side, rather than with the designed-for radial load.