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.

Let's Look at terms, as words ARE important

Terms (words we use to define)

In going back over my writing and having folks ask questions I have come across the problem of terms being used for things other than what they actually mean. This can cause all sorts of headache and fray the patience of many well meaning souls who are really trying to help others but due to mis-communication  you end up with the wrong idea getting across or not understanding what an issue is for some one. So below I will be listing terms and what they mean and a bit of how they apply to different process'. Hopefully folks will find this useful and will help reduce headaches for everyone.

Rigidity:  The ability to resist flexing or forces that cause distortion. This helps in the world of CNC and 3D printing in a couple of ways. increased ease in forces going into motion and not being absorbed by the machine. Decrease in some forms of resonance. it can also aid in calibrating a machine due to both of the above proprieties.  Too rigid, or too much rigidity can cause issues of binding, and stress points that will fail. Though too much rigidity is a had point to get to in many types of machines.

Microstepping: Is a process in CNC and 3D printing where by either software or circuitry you intentionally split the full step of a stepper motor down into fractions of a step. Common is 1/2, 1/4, 1/8, and beyond. Use has multiple benefits and some down sides and requirements. It is not positioning though it can affect positioning (increasing microstepping to where you are exceeding the maximum steps/sec will induce error that will be cumulative).

Drive: When dealing in the CNC & 3D printing world this refers to how you are moving the tool module along an axis (not all machines use the same drive on all axis, an Prusa i3 uses 2 belt drives and 1 dual screw drive. What a drive runs on can be many different items from linear rails, rollers, and assorted options.

Steps per: This is an area that can have more than one use. Steps per unit of measurement or unit of measurement per step tells you the resolution of an axis. Steps per revolution tell you how many steps a motor makes in order to move 360°. That number also affects resolution as it is used to arrive at the measured distance per step. It is also the starting point for how much microsteps can be reasonably used

Drivers:  The hardware that controls the electrical movement of a motor whether that is a Servo (closed loop) or a Stepper (Open and closed loops) that depending on type will limit current and possibly voltage. They come in digital and analog types and are mostly voltage rated with controls to limit current. They can be found in either on board, pull up or stand alone designs. They also can have safety measures against stalling, back EMF, and other features.

Commissioning: When dealing with machines industrial or light industrial, commissioning refers to the process where set up, intial run checks and first servicing is done to the machine to insure proper functioning. This can also be applied to the hobbyist/small shop environment as it is a good practice and helps to insure proper functioning.

To Be Continued......