A sufficiently strong machine

[JAZZCNC]

As I'm sure you're aware, you can improve the response of a resonant system in just two ways - either raise the stiffness to reduce the magnitude of the deflection, or increase the damping so the error dies away faster. Therefore comparing the stiffness of each option is very much related to comparing the overall response for resonant conditions.

The linear guides do have some damping effect, due to the oil layer between the bearings and rail. Adding rail with two bearings, as you suggest, would therefore increase the damping factor, as it increases the surface area in contact. Instead of adding an additional rail and two bearings, you could increase the stiffness and damping by adding one bearing to each of the existing rails which is likely more cost effective. This also has the added slight bonus of evening out errors in rail straightness and generally aligning two rails is a easier than three. Either way, this damping effect isn't that large as the surface area in contact is small, so you're probably better off improving damping in other areas such as joints in the frame. You can also add non-load bearing sliding contact bearings to further improve the damping effect, which will make a bigger difference as sliding bearings will have a much greater surface area in contact.

If you take the load ratings from the Hiwin datasheet and plot them versus rail size, it seems that the load rating is proportional to the rail size raised to the power 1.7. So if we assume the stiffness of the rail is proportional to the load rating and that the magnitude of the force on each linear bearing is similar, to increase the stiffness by the same factor as adding one additional rail (i.e. 50% as you're spreading the load between 6 bearings instead of 4), you only have to increase the rail size by 27%. So for example going from a 15mm rail to 20mm, or 20mm to 25mm would gain slightly more stiffness than adding the additional rail. Similarly if you want to double the stiffness, then instead of going from two rails to four, you could increase the rail size by 50% (e.g use 30mm rails instead of 20mm).

Looking at it a different way, if you plot the price of the linear rails and linear bearings versus their size, it's a pretty convincing linear relationship. So by increasing the rail size you have an exponential gain (x^1.7) in stiffness for a linear increase in price. If you add more rails you have a linear gain in stiffness for a linear gain in price.

Wow that's lot of waffle just to say you don't agree Jon (well think that's what your saying.?) so I'll keep it short and simply say don't agree with your Waffle.!!

I'm sure if you where to model accurately this full machine in Cad and add the rails like I suggest so load is spread across 3 areas then do a Stress analysis on it in all directions and compare deflection at the cutting tip you'll see a difference worth the effort compared to just adding another bearing on each rail or increasing rail/bearing size.?

All said and done thou Whether it's worth the effort is dependant on it's use and it's current design it isn't exactly flimsy is it so probably fine for 99.9% of any HD-DIY work.!!