Derivation of an admissible scratch-depth limit

Derive the admissible scratch-depth limit by combining the individual vibration metrics measured for scratched angle-grinder spindle shafts.

Background

The experiments indicated threshold-type behavior for axial scratches: scratches near 10 micrometres remained within system-level variability, whereas scratches near 20 micrometres produced clear increases in vibration metrics. Although this supports defining a maximum admissible depth, the paper leaves unresolved how the separate vibration measures should be combined to calculate that limit.