Similar to @luc.onthego’s guidance, the rule of thumb we have used in medical instrument manufacturing is a minimum 4-to-1 ratio for resolution of your measuring equipment vs. the accuracy of the measurement you are trying to make. Maybe not as extreme as luc’s order-of-magnitude rule, but it still means your measuring equipment needs to have accuracy significantly better than the measurement.
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I’ve started working on a project to map the motion of the carriage using a mouse attached to the spindle and a RPI. Not very far along. My intention is to use it to “automagically calibrate” the machine for belt stretch in a gross sense the way we typically do it by hand - move along an axis a known amount and compare what the machine thinks it did vs what we measure with the mouse. I think I can also detect out of square x vs y with a little math. One of the things that will come out of that is a map of uneven belt stretch, which could potentially be used to adjust a project in X and Y like you would for an uneven bed in Z (not so common in CNC circles, but pretty common for 3d print and circuit board work). Not sure it’s worth it to do that, just saying you potentially could. @Julien did something very similar: DRO-based X/Y calibration jig (wannabee)
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IMO, other than non-cutting positioning accuracy, that’s really the only thing that makes sense since the deflection forces originate there. 
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Resonance analysis is feeling more like a stretch goal at this point, but here’s what I got so far…
Preface: I’m a very out-of-practice electrical engineer by training, and resonance analysis in the mechanical world isn’t quite as painless as doing frequency response plots for circuits… so someone please put me in my place if I’m getting off-track…
That said, I think this accelerometer might be the cheapest sorta-workable solution I’ve come across. The downside is that a max 400Hz sample rate constrains our highest detectable frequency to 200Hz (Nyquist–Shannon sampling theorem! I remembered something!). This is problematic, because a spindle spinning at 30krpm is generating a 500Hz signal all by itself. Multiflute cutters might multiply this?
I’m kinda ok with this, because most of my work is at 10-15krpm (166-250Hz) and people say single flutes are fantastic. Also, the frequency of the vibration that maybe portents doom in my rig seems to be below 200Hz. In my hope-it-works best-case, the generated signal barely peeks out of the sampling capability. But. Someone out there’s running 30krpm with a 4-flute, so maybe it’d be nice to get to 4kHz sampling… if that’s not a pipe dream…
So then once I have that figured out… Thinking to run FFT analysis after I hook up an unbalanced motor and do frequency sweeps, or just whack-a-router (with hammer), or let 'er rip with a standard cut and see what shows up.
Aside: I think some thinking needs done, too. Everyone seems to think lowering the resonant frequency of a machine is desirable, but I’m not so sure. I think amplitude reduction is the bigger issue. A fish whacking me in the face with its tail is lower frequency than a butterfly fluttering its wings at my nose, but I know which I’d prefer. It is probably a combination. I don’t remember enough of my EE stuff to guess.
Anyway, instrumentation shoppers unite?
Edit: This looks like a better choice. Also cheaper. Anyone know a better choice?
Edit: This looks like a good example workflow for FFT analysis with the previous device
Edit: Cheaper than the polish choice above.
Edit: Maybe a better choice if things are getting crazy. The ADXL345 device only does 16g. This does 200g, but is limited to 1.3KHz in X and Y, and 1kHz in Z.
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My question wasn’t worded clearly. Have you seen any figures around the magnitude of the force at the cutter? Maximum/typical stepper exertion, x/y/z? The spindle I’m sure also has some torque/torsion effect that translates to cutter force, but let’s maybe keep things manageable.
I mean, ultimately, I’m trying to do a comparative study of before-and-after mods figures, so I can arbitrarily pick, but I’ve seen dudes do 5 lbs, and then this guy does 10 lbs and got some scary looking deflection figures (0.040" in the y direction at full extension! vs 0.015" in the X at any Z height… legit 1.7-2.7x flexier in the Y than the X… maybe I need to get a move on with those linear rails)
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The stepper motors slip at around 18 lbf, so that’s what limits the maximum cutting force the machine can counteract. You might want to check those limits on your machine. When cutting properly, virtually all of the force on the machine is produced by the cutter’s interaction with the workpiece, so those forces are dependent on the cutting parameters. This calculator will estimate cutting forces for you, or you can use the formulas provided there to do it yourself. You can also estimate force by measuring router/spindle power input while cutting as described here.
Most of stock Shapeoko deflection is likely caused by the Delrin V-Wheels and how they’re adjusted. Good linear rails should have much less deflection. 
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I’d be inclined to use (and have used) microphones and piezo-electric transducers with TrueRTA Audio Spectrum Analyzer software for real time analysis and/or Audacity for recording and post analysis.
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I was thinking about this, too. Maybe a later round idea. It’s hard to do better than the better grades of Delrin in the land of unreinforced plastics, when it comes to Young’s modulus (between 1-3GPa at room temp), and we’re worried about rail wear when it comes to aluminum or steel v-wheels. But… crazy idea… how about Lead (16 GPa), Bismuth (32 GPa), Paper Micarta (6ish GPa) or, shit-crazy, how about Lignum Vitae (14GPa)?
I have access to a CNC lathe…
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I suspect that all V-Wheels are fundamentally inferior to good linear rails because they have much less contact area with the guide rails.
Yep, I read this guys blog and ran some tests myself.
Based on this feeds and speeds calculator (http://brturn.github.io/feeds-and-speeds/beta.html
) that I found I enjoy using and get pretty accurate results with, I get the best results when I limit my radial loads to ~3lbs and axial loads to ~5lbs. I don’t have a stock Shapeoko but that frames cutting forces to that realm generally without too much deflection.
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I’ve been meaning to add an accelerometer to my HDZero for a while, but still haven’t got around to it. I keep alternating between doing something with an ADXL345 and looking at more expensive options that need less implementation work and can handle higher frequencies.
One paper on the topic: https://pdfs.semanticscholar.org/45dd/92afee1154e5329549eb73db255df392800d.pdf
I’ve had people suggest trying accelerometer apps on Androids or iPhones to see if they produce useful results, since pretty much every modern phone has a 3-axis accelerometer in it, along with more than enough CPU power to analyze the results in real time. It sounds like most phones do a lot of filtering on the data, so it may not produce useful results, but it’s basically free to try. Failing that, doing audio analysis (probably also on the phone) will be able to identify some types of vibration, but it’s hard to see how it’d notice a whole lot when it’s running next to a 25k RPM router.
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Be aware that resolution goes way down with the higher g rating. Be sure you actually need a higher rating before you use it that way.
Another way to do this is with a strain guage and a known mass (which is pretty much how the accelerometers work…but at a lot smaller scale/micromachined in the silicon)
What do you have then?
"Based on this feeds and speeds calculator (http://brturn.github.io/feeds-and-speeds/beta.html
) that I found I enjoy using and get pretty accurate results with,"
How do you know your accuracy results? For what materials and cutting conditions?
Good paper! It says: “Instead (in addition) of accelerometer, also [inexpensive] piezoelectric sensor could be used for detecting vibration values. Piezoelectric sensors can measure with higher frequency, but only in one direction. Measuring with higher frequency can bring out more distinct value structure and help in analysing section.” Even “sound cards” in modern computers can provide 24 bit floating point A-D conversions on at least 2 audio “microphone” channels at sample rates of 48 kHz (22 kHz bandwidth) for free! Or, you could just feel the vibrations with your hand.
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I have a:
Shapeoko 3 standard
- CNC4Newbie z-axis
- Steel GT2 belts
- X-axis linear rail brace
- @wmoy sticker on it (+3% extra rigidity)
I tested milling parameters with multiple materials (e.g aluminum, maple, HDPE), asked that feeds and speeds calculator what I should do given assumed constraints about radial and axial max forces and it gave me calculated parameters similar to what I found testing empirically. I have since tested new endmills on new materials with the previously assumed constraints with successful results. Perhaps I am not using your spreadsheet properly (most likely) but I enjoyed with this guys that it computes my parameters for me instead of with a guess-and-check approach.
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I bought ADXL345 and LIS3DH accelerometers this weekend. We’ll see what makes more sense. While I used plenty of Audacity in school, I never really liked having to shoehorn voltage ranges into acceptable mic voltage ranges, and mic/piezo only gets me 1D info as @gmack alluded to. The MEMS accelerometers offer simultaneous 3D acceleration, which, with a brain twice the size of mine, could yield higher insight.
I also have a stretch goal of trying to produce an arduino-based FFT analyzer that I could use to fine-tune my intuitions about chatter.
In deflection-land, doing some initial testing, it looks like I need a new stand for my dial indicator (well, the stand is ok - the arms/articulation are trash). Despite this, I’ve started playing around and found about 0.004" of deflection in the gantry alone in the -Y at 10 lbs (measuring at the beam, not the spindle! Like 8 inches right of the SHAPEOKO logo). I guess that’s the sum total of V-wheel compression, belt slack/elasticity, and beam deflection, which seems fair, but at the same time surprising to me - I would have expected less on what is intuitively the sturdiest axis. I’m going to resolve the stand arm situation and report back.
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I would stress the machine in a few different directions to seat all components into place.
Then make final adjustments on the wheels and belts and such to ensure there’s no play.
You could create a basic program to warm up the machine - common practice on larger CNCs.
Even a 10 minute cycle time moving the spindle all around the bed at RPM will help rather than cold.
Get the components up to temp and they will tighten up a bit in relation to each other.
Then proceed with testing
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I also picked up an ADXL345 this weekend, and I’m planning on wiring it into a Raspberry Pi 4, which should have more than enough CPU for doing FFTs. And, more importantly, is easier to grab data off of than an Arduino. It’ll probably take me a while to get around to anything useful, though.
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Revisiting deflection today with a slightly better setup (cleaned shipping oil from dial indicator arm)
Setup: Shapeoko 3 XXL, stock belts tightened to 10 in-lbs, 40 degrees F ambient, stock MDF baseboard with threaded inserts in 2" grid and 1/2" sacrificial MDF spoilboard on top.
Testing the center-of-beam movement with 10 lb deflections in the -Y (pulling towards me, standing in front)
Spindle at “NE” on Rapid position (back of machine): 0.005" deflection, return to zero each time (tested 5x)
Spindle at “E” on Rapid position (Middle of Y axis): 0.008" deflection, returned to 0.0015" (was able to push back to zero) for four runs, 0.0085" deflection, returning to 0.002" (able to push back to zero) once
Spindle at “SE” on Rapid position (Front of machine): 0.007" deflection, returning to 0.002" (able to push back to zero), tested 5x
So this is exciting. Just testing translational stress, we’re at 8 thou on the strongest/stiffest axis with a 10 lb deflection load. I had expected to see the deflections get worse at we approached the front of the machine (longer belt length being stretched?), but that wasn’t the case. Also surprised that the deflections would “stick” to some small extent (except at the back of the machine). To be continued with more datapoints, hopefully with warmer temperatures.
ALSO.
Horizontal deflections vs my wasteboard mounted indicator are surprisingly sensitive to pressures applied to the wasteboard. As a side test, a calibrated gallon of Great Value drinking water weighing 8.68 lbs placed ~center of wasteboard induced a -Z deflection in the wasteboard of 0.006" (measured relative to gantry)
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The topic of wasteboard sagging in the middle (under its own weight and when pushing on it when e.g. using the tape and glue method) comes up regularly, especially on XXLs, so I would not be surprised that in terms of bang for the buck, any kind of mechanical reinforcement under the middle area of the wasteboard will appear at the top of your list. Aluminium beds will be there too, but considering the price I expect they will show up much lower in the list.
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