The CoreXY Belt "Tuning" Myth

I have seen uncountable forum posts, comments, emails, etc., about the need to "tune" belts in a corexy mechanism. The comments usually involve something about phone apps that read the frequency of a plucked belt and how you have to precisely match the tensions of the belts. The concept seems to scare off many would be corexy DIYers, thinking that there is some sort of voodoo required to get corexy machines to work properly. 

It's all nonsense.

There is one primary goal in setting the belt tension. It is to set the tension so that the X and Y axes are square. If they aren't square your prints won't be square- i.e. they will be distorted. What is more important to you, getting perfect middle C from the belts, or getting undistorted prints out of your machine?

It is apparently not obvious why tensioning the belts can affect the squareness of the axes so I have prepared some diagrams, below, that illustrate the concept. They are based on a diagram I have used a lot in the past so they may look familiar. I used UMMD's stacked belt layout, but the same concepts apply to any other belt layout you may use.

Fundamental assumption- you built the machine so that the X and Y axes are square when there are no belts on the mechanism. Don't assume you can use belt tension to correct for sloppy construction! If your axes aren't square without the belts, no ifs, ands, or buts, it's wrong. Fix it.

There are different ways to tension the belts, but adjustment must always be done on each belt, independently. If you move P3 or P4 in the Y direction, you tension both belts. That's not what we want to do. I illustrate tensioning by moving the motors. You could tension this belt by adjusting the attachments at the extruder carriage, or by having pulleys pressed against the belt between P3 and P4 or between the A motor and P4. 

Note: In the examples I use moving the motors to tension the belts because that's how I do it in my printer. It doesn't matter how you tension each belt- screw adjustments at the extruder carriage, moving motor, etc., the effect of the increased tension on the belt will be the same on the X axis.

When you move the A motor, P1 and P2 will experience forces created by the tension in the belt. There will be X and Y components of the forces at those pulleys, but we can ignore the X components because they don't affect the position of the X axis. The Y components of the force, illustrated by the green arrows are equal and in opposite directions. That is what causes the X axis to tilt out of square with the Y axis.

If everything is made of metal and bolted together tightly, how can the X axis possibly rotate out of square with the Y axis? Let's see... the Y axis bearing blocks to which the X axis rail is attached are not perfectly rigid and will deform slightly. The Y axis rails and whatever they are mounted on will also flex a little (especially if they are end-supported round rails). The X axis itself will also flex a little. All those little imperfections add up and will allow the X axis to tilt relative to the Y axis. Don't believe it? Try this experiment before you put belts on the mechanism:

Hold one end of the X axis against one of the mechanical stops at one end of the Y axis. Now grab the opposite end of the X axis and try to move it along the Y axis. Of course it moves. The X axis acts as a long lever arm against the opposite, fixed end of the axis. A little force applied at the free end turns into a big force at the opposite end of the axis, causing all those little flexures to occur. Notice that it doesn't take a lot of force to move the free end of the X axis. 

Also note, if you stood any of the pulleys up on their axles like fence posts, the mounts will flex, especially if they are anchored in printed plastic brackets. The printer's frame, if it's made out of thin materials such as plywood or 20mm square t-slot, will also distort, so you want to build your printer to minimize these problems- design pulley supports to hold the axles at the top and bottom, and build a rigid frame for the printer or at least its XY stage. The diagrams below ignore these problems.

Now imagine what adding the second belt is going to do:

2nd belt in place before it is tensioned...

Now tension the 2nd belt by moving the B motor.

Notice the forces created (red) are opposite those created when the first belt was tensioned (green). Also notice that the arrows representing all the forces are longer because tensioning the second belt (red) increases tension on the first belt (green).

The X axis rotates back into square with the Y axis and your printer will now be able to make undistorted prints.

 If your printer's mechanism were built with absolutely perfect mechanical symmetry, the belts would be equal in tension when the axes are square. No one builds printer mechanisms with perfect symmetry, therefore when the axes are square, the belts tensions will not be exactly equal. It doesn't matter. Belt driven linear positioning mechanisms work well over a wide range of belt tensions. 

I've put the above illustrations together into an animated .gif file:

Some manufacturers, such as Gates, have phone apps to set the belt tension based on the type and size of belt, the length of span, etc., so you can use it to set the tension to the manufacturer's specified optimal tension value (assuming you know what that value is, and can convert it to frequency). I wouldn't assume that all belts have the same optimal tension, so if you're using no-name Chinese belts and adjusting them to Gates specs, you may or may not be getting what you are expecting. OTOH, it's nice to have some objective indication of belt tension, even if it isn't optimal. The good news is that belt tension isn't critical al long as you set it high enough that the belts don't flop around but not so high that they cause excessive wear on the bearings in the motors or binding of the mechanism. "Tight, but not too tight" applies.

I hope this clears up some of the silliness that the internet always seems to provide a home for..