1. #1
    Hi all

    Finally I made my first CNC skeleton model in Autodesk Inventor.
    - The structure is composed of square hollow sections of size 100x100x6 mm
    - Structure weights about 555 kg
    - Dimensions: 2500x1500x500 mm (LxWxH)

    I analyzed it to find its natural frequencies. I found the following data:
    - 1st Mode: modal frequency: 60.69 Hz - maximum displacement: 151.2 mm (too high! I think if I use ANSYS more precise results could be found)
    - 2nd Mode: modal frequency: 66.76 - maximum displacement: 151.2 mm.

    I don't know any thing about acceptable ranges for frequencies and their corresponding displacements in CNC machines.

    Here you can see the model and modal analysis results:

    Thanks for any suggestions


  2. #2
    I analyzed the structure in ANSYS. Results are better and more hopeful but the question remains: What is the preferred (acceptable) range for frequencies and relevant deformation in CNC machines like the one that i am going to build? Any suggestions? Thanks.

  3. #3
    This thesis should help you. The sources which excite resonance in the system are the tool and motor, so you can consider the spindle speed and number of flutes for the former. The latter is less predictable, but potentially significant if you use stepper motors.

    You might find that avoiding symmetry helps reduce the magnitude of the deflection.
    Last edited by Jonathan; 10-05-2014 at 07:54 PM.
    Old router build log here. New router build log here. Lathe build log here.
    Electric motorbike project here.

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  5. #4
    I think you are worrying about the wrong part.

    You can always add dead weight to the bed if you have a vibration problem.

    Suggest you worry about connecting the bed to the tool tip. That is where you cannot add dead weight without needing more powerful motors or accepting slower rapid transits.

    It can be quite depressing with a large machine when you discover it will take 2 minutes for the head to move corner to corner without risk of losing position.

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  7. #5
    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).
    Building a CNC machine to make a better one since 2010 . . .
    MK1 (1st photo), MK2, MK3, MK4

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  9. Also, on a purely pragmatic observation, some diagonal bracing would significantly increase stiffness. That's one reason your analysis shows high levels of deflection.

  10. #7
    Is this for your laser cutter you're wanting to make? If so I can't see resonance being that much of an issue?

    Build log...here

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