Belt Tension - BainbridgeArtisanResourceNetwork/Mark4_printer GitHub Wiki

Setting the tension of the belt is one of the more challenging aspects of getting a CoreXY printer working properly. Proper belt tension is needed to maintain the accuracy of the print head.

Concepts behind proper belt tension

Setting the best belt tension is a balance between these factors.

1. Higher belt tension means higher stress is put on the bearings, leading to earlier wearout and higher rolling friction.
2. Higher belt tension means more bending stresses put on the standoffs holding the pulleys, which can lead to bending/tilting of the standoffs and warping of the top plate. If the axes of the pulleys get tilted, the belt will run towards one side of the pulley, and may even run off the pulley. If the top plate warps, the print nozzle will no longer operation in a plane - the top of parts will not be flat.
3. Lower belt tension can lead to belt "flapping" during print head acceleration. This is because when the print head accelerates or decelerates, it's mass will increase the tension in one end of the belt, while decreasing it in the other end. If the tension in the end with decreased tension goes to zero, the belt will sag and may come off a pulley, or shift on the motor's drive pulley.
4. acceleration and deceleration of the print head can lead the various segments of the belt to vibrate (like a guitar string) and this vibration can translate into slight movements of the print head and visible artifacts in the part being printed.

So, what's the right tension? My opinion is that higher is better, as long as the top plate stays flat, the standoffs stay straight, and the bearings have a reasonably long life.

The importance of equal belt tension

There are two separate belts in our system and if the tension in them is not equal, there is be a constant torque on the bridge, which will try to pull it out of square with the Y-rails. This can lead to un-square parts and early failure of the bearings in the Y-Rails.

Quantifying belt tension

There are tools that can directly measure the tension in a belt, but we don't have one. An alternate, but effective method is to measure the vibration frequency of the belt and using the properties of the belt to calculate the tension in the belt. Acoustic frequency measurement tools apps are widely available (for instrument tuning), and we can use one of these to measure the vibration frequency of the belt.

The equation for the frequency of vibration of a string is well-described in this wiki page: (wikipedia - string vibration), and shown just below, where fn = the frequency of the nth harmonic n = the harmonic (we are only interested in n=1) L = the length of the belt segment vibrating T = the tension in the belt mu = the mass per unit length of the belt

Setting N=1 and solving for T, yields the following equation:

T = 4 * mu * (l * f) ^2

The belt we bought to use on used on our wood proto is 5M long and has a mass of 65gm, which means the belt has a weight per length of has a mass of 13gm/M.

Out belt tension equation is now

T = 52gm/M * (l*f)^2

The graph below shows Belt tension as a function of frequency for a few belt lengths. The longest (0.587M) is the length of the belt on the side of the plate (parallel to the Y-axis) and the next (0.438M) is the length of the belt across the back of the top plate.