# Filament Thickness Sensors, What Are They And What Are They Good For?

I keep up with the trends in 3D printing reasonably well. The other day my friend mentioned that filament thickness sensing had been added to the latest version of the Marlin firmware. I had no idea what it was, but it certainly sounded cool. I had to find out more.

In industrial settings, filament is made by pulling extruding molten plastic at a certain speed into a cooling bath. The nozzle for 2.85mm filament and 1.75 mm filament is actually the same size, but the filament is stretched more or less as it leaves the nozzle. By balancing these three variables the extrusion machine can produce any size filament desired. Like any mechanical system, it needs constant adjustment to maintain that balance. This is usually done by measuring the filament with a laser after it has cooled, and then feeding this information back into the system. The better filament manufacturers have multiple lasers and very fast feedback loops. Some of the best offer +-0.04mm or less variation in thickness between any two points on the filament. Some of the worst have larger errors such as +-.10mm. Because the plastic is fed into the extruder at a fixed linear speed, this makes a variation in the volume of the plastic coming out of the nozzle per second. With the best we see a 4.41% variation in the volume of plastic extruded. With the worst we start to see 10.51% or more.

A printer is dumb. It works under the assumption that it is getting absolutely perfect filament. So when it gets 10.51% more plastic, it simply pushes it out and continues with its life. However, if the filament is off enough, this can actually show up as a visible defect on the print. Or in worse cases, cause the print to fail by over or under extrusion of plastic.

So, what does a filament thickness sensor do to correct this issue? To start to understand, we need to look at how the filament is dealt with by the software. When the slicer is compiling the G-code for a 3D print, it calculates the volume of plastic it needs in order to deposit a bead of plastic of a certain width and of a certain height per mm of movement. That was a mouthful. For example, when a printer printing 0.2mm layers moves 1mm it wants to put down a volume that’s 1.0mm long x 0.4mm wide x 0.2mm high. The filament being pushed into the nozzle has a volume per mm determined by the diameter of the filament.

$(\pi (radius_{filament})^{2}*length_{filament extruded})=volume$

The volume out per mm of filament in.

$(layer_{height}*layer_{width}*length_{move}) = volume$

The equation we are trying to balance.

Our goal is to integrate the thickness sensor into these functions to see what the thickness sensor is doing. This is a linear equation, so there’s nothing fancy here. Now, the layer height, layer width, and length of the move are determined by settings and model geometry respectively. These are fixed numbers so we don’t care about them. That leaves us the diameter of the filament and the length of filament extruded. As we mentioned before, typically the filament is assumed to be a fixed diameter. So all the software has to calculate is the length of filament that needs to be extruded per mm of combined movement in the x and y so that our volumes match.

But, we know that one of these variables is actually changing per millimeter as well. The filament diameter! So now we have a problem. If the filament diameter is changing all the time, our equation will never balance! In order to fix this we can add a multiplier to our equation. Since we have no control over the width of the filament we can’t modify that value. However, if we know the width of the filament, and we know the value its supposed to be, we can change the length of the filament extruded. This is because unlike the filament, we have control over the stepper motor that drives the extruder. This value is called the extrusion multiplier, and its determination is what the thickness sensor is all about.

So all the filament sensor does is measure the filament’s current diameter. It takes expected diameter and divides it by the value it just measured to get a simple percentage. It feeds that number back into our system as the extruder multiplier and slows or speeds up the stepper motor as needed. Pretty simple.

There are a few thickness sensors being toyed with right now. The first, as far as I can tell; let me know if I am wrong in the comments, was by [flipper] on thingiverse. He is in his third version now. The sensor works by casting a shadow of the filament as it passes by onto an optical sensor. The firmware then counts the pixels and works backwards to get the diameter. This value is sent to the Marlin firmware on the printer which does the rest. As is usual and wonderful in the open source community, it wasn’t long before others started working on the problem too. [inoranate] improved on the idea by casting more shadows on the sensor. The technique is still brand new, but it will be interesting to see what benefits it reaps.

Now comes the next question,”Is it worth upgrading my printer with a thickness sensor?” If you typically run poor filament, or if you extrude your own, yes. The current sensors can only measure +- .02mm. So for the best filament, you won’t really see a difference, but for worse stuff, you might. The latest firmware of the Lyman filament extruder, for making your own filament, also supports these sensors, letting you feed back into your production system like the industrial machines. All in all a very interesting development in the world of 3D printers.