How much does stuff bend ? How much support does the router table need to stay effectively true ? How thick does my MDF support beam have to be ? Is Aluminium any better ?

Calculating deformation (strain) depends on how a supporting beam is held at its ends (fixed, supported, or free). EngineersEdge list a number of useful formulas. For example, if the support beam is supported on both ends and has a single weight at its centre, the formula is y = F L^3 / ( 48 E I ), where y is the displacement height, F is the force (weight), L is the length of the beam, E is the Modulus of Elasticity, and I is the Area Moment of Inertia.

*Bit Bender ©.*

*Use German beer for greater precision.*

*Das kommt vom Reinheitsgebot.*

Assume a weight of 20kg (a bit more than half the gantry weight as we use at least 2 support beams). Assume beam length L = 1m (approximate length of router table). Assume a support beam made from MDF, width 16mm and height 100mm.

As you undoubtedly know, MDF has a modulus of elasticity of E = 4 GPa = 4x10^9 N/m2 and Aluminum has E = 70GPa, ie, it bends 17.5 times less than MDF given the same volume and shape. Now the Area Moment of Inertia for a rectangular shape can be found on Wikipedia and is I = b h^3 / 12. So, for b=16mm and h=100mm, we get 1.33e-6 m4. Inserting all these values into the deflection formula, we easily find - naturally and without pen and paper: y = 0.77mm.

In layman's terms, an MDF support beam of 1 metre length, 16mm thick, and 100mm high, which is supported at both ends and holds a weight of 20kg at its centre will have a central displacement of 0.77mm.

A similar calculation can be carried out for a support beam made from a 50mm x 3mm aluminium beam. It will be displaced by 1.87mm. Things look better when both ends are fixed. MDF moves by 0.19mm and aluminium 0.47mm.

There is a difference in price: MDF = $2.92 (based on a 1200x900 board). Aluminium = $21.98 (based on a 1000mm Aluminium angle). And a difference in weight: MDF = 1.1kg. Aluminium = 0.79 kg.

An MDF board of 76mm height and 16mm thick will bend less than 50mm x 3mm aluminium. Kind of interesting.

Based on this, it would be fine to use 100mm MDF support beams for the table.

...and I hope it's all true.

## 2 comments:

I don't think that anyone building a hobby CNC machine has ever gorn into this much detail for selecting building materials!

Good work though!

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