Quantified Stiffness

New Home Forum Mostly Printed CNC – MPCNC Advice – MPCNC Quantified Stiffness

This topic contains 6 replies, has 3 voices, and was last updated by  Ryan 3 months, 4 weeks ago.

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    I am contemplating some mods to improve stiffness, in particular for the case of taller-than-recommended Z axis.

    I have made some measurements using a known load and a dial indicator, although it was a while ago and I lost them, so I will measure again.  The idea is that by measuring the deflection at different locations, I should be able to estimate the stiffness of the individual modes of flexing.  I’ve drawn some cartoons showing four modes that seem most significant:

    • “Twist” is deflection of the z-axis away from vertical
    • “Bend” is horizontal deflection of the gantry rail
    • “Belt” is stretching of the belts or zip ties
    • “Rack” is parallelogram deflection of the legs

    The method I’m using to measure stiffness is to use cords and pulleys to hang weights to pull horizontally at the bottom end of the Z axis.  I fashioned a pretty simple pulley which I’ve posted here: https://www.thingiverse.com/thing:3696218

    I was a reluctant to post numbers before because I am afraid my assembly might be poor, and low stiffness might reflect poorly on my machine and possibly on MPCNC.  But it’s essential to have numbers if I’m serious about making improvements.

    What I am wondering is what the target should be for stiffness in terms of mm per kg.  I am just starting to search online and am nowhere near a sense of what stiffness would be considered “decent” for milling aluminum or steel.  A starting point would be stiffness of a well-built MPCNC that is capable of milling steel.

    I’ll post my numbers later tonight and I’m hoping others might take measurements and share, or point me in the direction of some good information on stiffness, or advise me if my measurement-centric approach is not the right way to think about this.



    To measure deflection both ways I hang one weight 1.9 kg in weight, which pulls in the positive X direction.  Then I have a second weight of 3.8 kg arranged to pull in exactly the opposite direction for a net pull of 1.9 kg in the negative X direction.  By lifting the heavier weight I can shift from -1.9 to +1.9, back and forth and see how the machine moves.

    I attached the cords to the Z axis at a point 110 mm below the bottom of the center assembly.  The outside dimensions of my machine are 895 in X and 577 in Y.  The legs are long: the distance from the table to the underside of the side rails is 235 mm.

    These are the measurements:

    • 1.65 mm deflection at point where force is applied
    • 0.48 mm X movement of roller rolling along y max rail
    • 0.58 mm X movement of roller rolling along y min rail (belts are evidently not equally tight)
    • 0.61 mm deflection of gantry rail near center
    • 0.61 mm movement of center assembly in x direction
    • 0.127 mm movement of corners

    From the differences between these movements I’m inferring:

    • 0.127 mm racking of legs
    • 0.41 mm belt stretch
    • 0.075 mm bending of gantry rail
    • 1.04 mm twist of Z axis

    The deflection per kg would be these numbers divided by 3.8.

    The twist of Z axis is the worst, which confirms what I’ve heard essentially everyone say.  The belt stretch is I think my fault, because my zip ties are not fully straightened and I can see the zip ties move.  I think this is also why the two X belts show substantially different deflection.

    Racking of the legs is fixable with added supports.  This context also shows that it is hardly worthwhile without attention to other modes of deflection.  These other deflections are not so easy to remedy.  Belt stretch can be improved with Leon’s (BraunsCNC) approach, and I’d be interested to see how much it improves.

    I am also expecting to find that 1.04 mm twist of Z axis (at height of 4 3/8 inch below the bottom of the center assembly) to be due to poor assembly or some other imperfection on my end.  I don’t know what is typical but I have a hunch this is not normal.




    I don’t have anything to add at this time but I’m commenting to commend you for your approach and also so I’m notified of any updates you post. Good work!



    This could get interesting.

    Make sure on zip tie on each side is pulling the belt completely tight against the corner, that should instantly halve any issue you have. Than you can either shorten or lasso the other end if you lasso it just warp another tie around and get rid of any bulge your tie might have. I wouldn’t call it stretch unless you test just the belt outside of the system as I doubt the belt is adding much actual stretch.

    As for actual required rigidity super tough. The calc linked on the basics page has a load number, no idea how good it it is but I know it came up with 1.2kg for, what I consider to be, a beefy aluminum cut I made. I made the cut then put in the specs in to the calc to see what it came up with.

    My quick and dirty test. Which is crazy, we have nearly the same numbers on different sized builds, with very different loads. I think that means overall rigidity is good but maybe the builds need to be preloaded a bit to get rid of that fist 1mm deflection. I had always thought about forcing a tiny bend in the 6 main rails…or the center need to get reworked again.


    1 user thanked author for this post.


    Agreed the “belt stretch” is mostly not really belt stretching. I just realized I could probably print out the dual-endstop pieces and measure how much the belt is actually stretching vs. how much the ends are moving. Just to prove it and put numbers to it.

    I’ll check that link and see if I can digest the measurements that have been done before. Thank you.



    I don’t generally like to post my plans in advance, because I don’t want to jinx it and I don’t want to feel obligated, but this I need to share.

    I am considering a stacked version with basically two MPCNC machines stacked on top of each other, with the Z axis traveling through both.  Only the lower gantry would have a motor and lead screw to drive the Z axis vertically.


    The upper gantry would constrain the Z axis from twisting.  Both sets of gantry rails would have motors and belts like the MPCNC, and each motor driver would drive four stepper motors in series instead of two.  I can get a 24V power supply to make sure I’m not running out of voltage with so many motors in series.

    To maximize stiffness, I was considering extra stiff rails for the lower gantry and the Z axis, shown in yellow.  The upper gantry need not be quite as stiff.  This depends on the height, which I’ll get to in a bit.  It’s fairly easy to find 1″ (25.4 mm OD) tube with thick or thin walls, so I was thinking the yellow rails can be thick-walled, while the blue rails are cheaper.  The green outer frame has lower stiffness requirement, and I was considering using 3/4″ EMT to minimize cost.

    I will need to design corner pieces that allow the legs to pass through, which should be straightforward enough.  If I go with mix-and-match tubing sizes I will need to make a roller piece that rolls on 3/4″ EMT but accepts a 25.4mm gantry rail, which I was thinking I would just take the “C” design and bore out a 25.4mm cylinder digitally on the STL file.  The center assemblies would be unmodified “J” design since all rails are the same size.

    Side panels of wood or diagonal braces would support the machine from racking.  Mid-span supports on the lower rails would minimize sagging, but one interesting possibility is using the upper assembly to support the weight of the tool and Z axis, either though a counter-weight or some elastic.  It seems to me the upper rails could sag a lot before it has a negative effect on the system, so why not have the upper rails bear all the weight.  Apart from speed, I would have much less penalty for heavy tools or rails.


    The height of the upper portion presents an interesting choice.  Let’s say the lower rails are 1 foot from the deck, and the upper rails are x feet above the lower rails.  Then one kg of horizontal force on the tool at maximum extension (minimum Z) produces 1/x kg of force on the upper gantry (in the opposite direction), and 1+1/x kg of force on the lower gantry.  (This neglects the center assembly’s stiffness against twisting.)  The mathematically “ideal” height is perhaps very tall, resulting in the Mostly Printed Telephone Booth :).  But there are diminishing returns, so for practical reasons I will probably choose an overall height of perhaps 4 feet.  Horizontal dimensions are not yet decided but won’t be more than 4 feet.  With some thought into the corner design, it should be possible to make the height adjustable without disassembling the machine.

    Cost wise, this build is definitely a higher expense.  Most parts you have to pay for twice, but the tool, the z-motor and leadscrew, and the electronics are paid for only once.  I’m estimating about $160 for motors, belts, bearings, PLA, and conduit.  I don’t have a good number for thick-walled tube or the 5/16″ hardware but my rough estimates are about $600 all-in.


    I have mentioned before that I don’t have any “real work” to put this machine to use.  This is entirely academic/entertainment.  A certain minimum Z height does matter for a tool changer, and the tool change capability also demands more x/y area because it gets consumed by the tools.  I have not yet looked seriously into a 4th axis (or 5th, ha), but I am expecting that it could require a decent Z height to fit under the tool.  Also MPCNC as 3D printer would require some Z height, although it is a pretty silly waste of stiffness.

    I know this “just in case” for everything is not the smart way to achieve any one purpose for real work, but since my purpose is experimentation I think it will serve me well.





    I can’t wait to see it moving!

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