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Z axis drive issues - a couple (no replies)

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My printer is generally running good, but I noticed today in trying to set my Z0 position that there is some backlash in my Z positioning and maybe an inconsistency in the way Marlin handles the Z offset. The Z mechanism is 3 lead screws driven with one stepper with one idler for tensioning. The belt was loose when I started this but is now tight. The results did not change. BTW, my Z endstop is a nozzle activated piezo with an M48 std dev of 0.0229.

question #1: How much deflection should I get on a span of 47mm GT2 6mm belt?

I have set my Z offset to 0.05 in Marlin. When I home Z, Repetier shows Z = -0.05. When I step Z by 0.01, Repetier shows it going from -0.05 to 0.00. The next step goes to 0.01 etc. If I step Z by 0.1 initially, Repetier shows Z = 0.05
This seems like an inconsistency with Marlin. I would expect it to either take 5x 0.01 steps to get to 0.00, or any single step to go to that position. IE, a 0.01 step goes to 0.01, a 0.1 step goes to 0.1, a 1.0 step goes to 1.0, etc.

question #2: Does anyone else see this inconsistency or is there a reasonable explanation?

If I use a 0.08mm "shim" (paper), 9x 0.01 steps from home yields Z = 0.08. The same actual height as 1x 0.1 step + 3x 0.01 steps (Z = 0.08) based on the shim test. Does anyone else see this result, or do I have something set wrong?

In playing with this I notice that my shim tests were inconsistent. What I found was that if I go to Z = 0.08 then do -0.01 steps it takes 4 steps to get the screws to move. The stepper appears to move and the belt on one side of the stepper feels like it is moving, but the screws do not move until step 4 or 5. Therefore Z doesn't change and the shim gets confused.

question #3: Is this to be expected or do I have a bad pulley, belt, or idler and if so how do I figure out which is the problem?

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