Comparing Accuracy and Resolution.

Why Compare?

Okay, why compare the two as some will say they have little to do with each other and other say they are functionally the same. Before we go on any further I am going to go for definitions so that we can get on the same page:

Accuracy: technical the degree to which the result of a measurement, calculation, or specification conforms to the correct value or a standard.

Resolution: technical The amount of detail which can be shown or created by an object or tool

Okay so now we have those, how does it apply to either CNC or 3D printing and can or do they affect each other? Yes and No is the answer and let's look at that.

Accuracy in a CNC and 3D printer is dictated by the type of drive system used. These are chosen for many different reasons to include cost, ease of construction, accuracy, and Load bearing to name some of the points that come into the process of choice.

Coupled to this is either a stepper motor (which we will be using in this discussion as base) or servos. Servos bring a whole new level to accuracy and an associated cost in equipment and complexity. They the superior choice in the area of both accuracy and repeatability.

The other areas of accuracy that is often over looked (and can affect both repeatability and resolution) are what type of support system are you using and what is the accuracy/tolerances of that. How true and ridged is the frame the frame and mounting points on the machine to insure that you don't have flex or induced misalignment.
You will hear many arguments over types of drives and why. Each have their function, I would strongly suggest NOT falling into the one is always better or superior than another. That debate is for another blog and they why and how of it applying to DIY or small business machines is for another day. back to the discussion on hand.

So Accuracy and repeatability directly affect resolution. Some would say that is the only direction that the effect goes. Not exactly. A stepper motor set at whole steps only will have a direct effect on accuracy and repeatability by the fact of the limits of what it can move. So no micro stepping becomes important as that allows for smaller segments and more use of the accuracy that a given drive system has within it. In turn that allows for higher resolution of a model, fine forming of arches (Which are broken into straight lines in most CAM and Slicing software.

So following that logic microsteps of great than 1/64 are great as they allow you to create extremely fine points of movement. IF only it worked that way. As you increase microstepping you decrease available torque. Unless you are running rather advanced logarithms in your firmware and drives that will be a full time loss (which means you don't get it back as you are slowing down to change direction of a cut or extrusion). So the knife cuts both ways. There is a medium point though.

A industry standard distance for measuring accuracy is 300mm (which is rather close to a foot some might take note). If you have a drive train that has a given accuracy (Accuracy trumps repeatability in that you have to get the wanted position before you can repeat it). Okay we have let's say 0.185mm/300mm (.007in/FT) accuracy and a repeatability of 0.0529/300mm (.002in/ft). This coupled with how much error we induce via either under powering the motors (most often with to little Voltage) or by trying to use too many microsteps and exceeding the usable torque curve, and lastly try to use to much acceleration with a motor and causing issues that way. Let's be kind to ourselves and say that we did the math and are powering our steppers at 75% of maximum voltage (That maximum is without cooling of the motors and can go higher with cooling or if the motors are not run for long periods of time under that full load). We are using 1/16 microsteps which with a TR1205 screw we get a per step resolution of 1.5625 um/step. You might notice that our per step resolution is well beyond what the machine tolerances will give us. The science that will give us the exact accuracy and resolution is why FEA programs exist unless you like doing large equation math problems (I don't).

The crux of the issue is that often we exceed the structural limits in an attempt to improve via software or other means. When designing and using your CNC or 3D printer take the time to learn what the capabilities really are and what the accuracy truly is this will help you in not only knowing what you need to do to improve product out come (professional/client/personal) but also to better understand where you can fudge and where you really can't. While technology is moving forward much of what it written here is still directly applicable and most likely will be for years to come.
So in closing on this article as I have rambled a bit. Insure you have the resolution to make the accuracy something more than a hoping that you can over come the physical limits of a machine.

With that best Luck in your business or hobby and for designers, good luck and yes I have set you a challenge.