Each pass gets a little closer to the spindle.

[kotovasia5120]

Each passageway is slightly closer to the spindle on the z axis. This is most likely not a correctly specified backlash, as I understand it?

[kotovasia5120]

Also, if you enter a number and press the arrow for z, the numbers change, but there is no movement. For x, movement occurs without problems

[duebelpapst]

Each passageway is slightly closer to the spindle on the z axis. This is most likely not a correctly specified backlash, as I understand it?

I had the same problem with H4 and also with H5.
After days of trial and error, I realized that the error only occurs when the X-axis stepper motor is connected.
I was able to solve the problem by installing a ULN2803 in the output line for Z-Step. I tapped the 5V voltage for the ULN directly from the power plug of the H5.

[kachurovskiy]

Each passageway is slightly closer to the spindle on the z axis. This is most likely not a correctly specified backlash, as I understand it?

No, wrong backlash would not have this effect. In repeated movements e.g. left 1mm, right 1mm, left 1mm, right 1mm, ..., the carriage would move between the same 2 points on the lathe. I.e. the error is not accumulating.

Unless you've materially modified the motion control code, the problem you have indicates that some of the STEP impulses to the driver are ignored by the driver - due to loose terminal screw, long wire, voltage loss on the way, driver damage or interference.

Also, if you enter a number and press the arrow for z, the numbers change, but there is no movement.

This also hints at the problems with the step signal. This can only happen in 1 direction on a driver because when you set DIR high, it lowers the voltage of your STEP high signal and may bring it below the detection threshold of your particular driver (see datasheet of your driver).

Note that you'd measure different voltages on the output of your ELS controller and on the input of the driver since wires do have an effect on this.

For x, movement occurs without problems

This can help you debug - swap terminals for X and Z on the ELS controller and see if the problem moves to the new axis. If it does, problem is on the ELS side. If the problem stays on the same axis, the problem is on the driver side.

[kotovasia5120]

I added logic level converters by replacing the control signals from 3.3V to 5v and ran 999 passes. The error accumulates along both axes.