Advice about Acceptable range of viberation

[routercnc]

To add to Jonathan and Robin's comments, this is not the right type of analysis.

Resonances of the bed in that condition don't tell you much as they will completely change when the mass and stiffness of the gantry is added.

But even if you did model the complete cnc machine (bed, gantry, spindle, motors, rails etc.) and carry out a 'normal modes' analysis, you would just end up with a list of frequencies and associated modeshapes. This is of little help because it does not tell you how much the structure will displace at that frequency for a given force.

What you need to do instead is calculate the 'dynamic stiffness' of the system, and that requires you to apply a dynamic force (i.e. at force across a frequency range, or a sine sweep) at a selected point on the structure and in a selected direction. The boundary conditions for the analysis would be to ground the workpiece (say some 100mm x 100mm x 20mm arbitrary part), and calculate the dynamic stiffness at the cutting tool in some extended position. Do this in X, Y, and Z directions. You may need high end software to do this analysis.

This would give you dynamic stiffness of the tool in N/mm against frequency (Hz). You would see a gradually rising line (dynamic stiffness tends to increase with frequency), with drop outs where the resonances were.

There are 2 possible next steps:
Firstly if the dropouts were too severe (big resonances) then you can stiffen the machine, add mass, or for the higher frequency resonances add a damping material such as sand filling. Be aware that the lower modes would be less affected by damping if at all. With these improvement actions the machine will vibrate less during cutting and give a better finish.

Secondly there could be problems if the resonances occur near the spindle motor orders or the cutting tool orders during the rpm range used during cutting. These are the machine excitation frequencies and if they get close to any of the machine natural frequencies then the machine will vibrate more than when it is away from resonance.

Since the spindle can run at a large range of speeds, the excitation frequencies from the spindle motor or the tool is also fairly large so you are guaranteed to pass through the machine resonances as some point unless you always cut with the same tool at the same rpm.

To be honest unless you want to delve into this area for fun, then I would suggest you just carry out a 'static stiffness' analysis of the machine by applying a force at the tool tip, or collet, in each direction in turn (X,Y,Z) and calculate the deflection. This will give you the basic stiffness of the machine in N/mm. If this is low (say <1000N/mm) then you will also have lots of resonances and the resonances will also have low stiffness. If this is high, then you will have less resonances, and the resonances will be stiffer (deflect less).