Documented mass-moment bookkeeping — no balance verdict
Hammer-Set Mass-Moment Vector Ledger
Sum individual hammer mass × CG-radius vectors and their axial moments about a documented reference plane. The ledger exposes static and couple-type bookkeeping that a position-total check can miss.
Documented vector ledger
Implemented vector bookkeeping
|U| = √(Ux²+Uy²)
Cx = Σzimiricosθi ; Cy = Σzimirisinθi
U has units kg·m and represents the projected mass first moment. C has units kg·m² and is its axial moment about the stated z=0 plane. Changing the reference plane changes C when U is nonzero. These are general vector sums, not formulas that by themselves establish ISO conformance.
Why axial position matters
Two equal masses at 0° and 180° can give |U|≈0. If they lie on opposite sides of the reference plane, their axial moments can add rather than cancel, giving |C|≠0. The former page summed all disc columns into circumferential position totals, so it could report “balanced” while disc-to-disc couple information was absent.
Current ISO balancing context
As checked on 12 July 2026, ISO 21940-11:2016 edition 1 is published and under systematic review, with published Поправка 1:2022. It addresses procedures and tolerances for rotors with rigid behaviour, including permissible residual unbalance, correction planes, allocation and balancing errors; it excludes flexible behaviour. ISO 21940-12:2016 addresses flexible-behaviour rotors and was confirmed in 2025.
No invented percentage tolerance
The former script classified |ΣM∠θ|/ΣM below 1% as balanced and above 2% as unbalanced. That ratio omitted radius, axial plane, complete rotor mass, operating speed, rotor behaviour and any licensed tolerance route. The thresholds and automatic redistribution advice were removed. Permissible residual unbalance, correction-plane allocation and measurement uncertainty must come from the current project-adopted standard/OEM specification and field balancing evidence.
Not a balancing measurement: a hammer mass ledger does not include the shaft, discs, pins, wear, runout, assembly errors or operating deformation. Verify the assembled rotor with suitable balancing/vibration measurements and the applicable rigid/flexible-rotor procedure before release.
