hy yeah, mathematics ?! is so ...
if ae = tool dia / 2 then chip thickness = fz else chip thickness < fz
in other words, the more ae is different from tool_radius, the more chip_thickness is smaller than fz
as an extreme case, if ae = 0, then chip_thickness will be zero
an analogy is that to a car wheel : for example, if you drive at 100km/h, then :
... wheel center speed is 100 kmh
... wheel point that is on the ground, has 0 kmh
... wheel point far away from the ground, thus located at top of the wheel, has 200 kmh
when it comes to circles, most stuff changes with radius haha
please check atached images :
... 01 simple cad construction, that delivers same values as the ones from your example; i didn't get 0.1040, but 0.1036 and 0.1044, so pretty close
... 02 zooming in the area of chip thikness, so to show how those lines are constructed in the direction of the radius; at this moment i can sugest 2 aproaches :
...... compute 2 segments, one above ae, and other below ae, then avergae their lengths
...... compute a single segment, that has his middle on the ae line ( the one sketched with blue )
... 03 your initial data fz 0.13 generated a thickness of 0.104, smaller than 0.13, so the software sugests increasing fz to 0.16, in order to get a thickness of 0.13, that is identical with your inital data; such a sugestion pops up only under a safety rule : ae < dia / 3
i hope is ok now please feel free to ask whatever you wish / kindly