Hmmm... I am not sure if this is entirely relevant but it may help so I offer it in that spirit. I have a Shapeoko S3 CNC machine that uses belt drive for each of the stepper motors (NEMA 23) and I first got the machine 3 years ago from new. I was unable to keep the belts tensioned correctly because they went through a right angled connector that was difficult to use well. Some symptoms were uneven tensions, size inaccuracies and the inability to find the best tension for the belts.They kept slackening at varying frequency but every few days. I wanted to mill metal and there was no way that I could even predict the result with my poor set-up.

The belts were 9mm wide GT2 timing belts supplied by Gates. I thought the belts were good quality so I set about looking for a better adjustment solution. I found a 3D printed item that kept the whole belt absolutely flat rather than doubled back on itself after following the right angled bracket and it looked to be a much better solution. I modified the end supporting plates of my CNC machine and attached the 3D printed revised adjustment mechanism. Gates provided an application to tune their belts by sound but it was very fussy to use and difficult to get an accurate reading. I tried a simple guitar tuner which worked on vibration to detect the frequency. This worked really well and I discovered that the tension of the 9mm wide GT2 belts, using the Gates data, could be anywhere from 100 to 150 Hz. I tuned my belts to C3 on the guitar tuner (130.81Hz) and they have stayed at that tension for 14 months!

You may also find this article by Liam Newcombe to be informative. It has a lot to say about belt deflection and backlash.

https://community.carbide3d.com/t/ba...ibration/28669