Controlled grade · rigid-rotor relation · no automatic acceptance

Residual-Unbalance Grade Relation Worksheet

Apply a balance-quality grade that has already been selected and approved for a documented rotor or assembly. The worksheet converts that controlled input into specific and total residual-unbalance magnitudes.

Exact 2π relationPoint or commaNo grade presets

Not an ISO acceptance calculator. This page does not select a balance-quality grade, decide whether a spindle/tool assembly behaves as a rigid rotor, allocate tolerance between correction planes, or determine an actual correction mass and angle. Those decisions require the current licensed standard, the machine/tool manufacturer specification and a controlled balancing procedure.

Approved inputs and traceability

Documented rotor / assembly mass m (kg) positive; use the same mass boundary as the approved criterion

Maximum service speed n (r/min) positive; as defined by the controlled criterion

Approved balance-quality grade G (mm/s) positive value copied from the cited requirement; no preset is inferred

Calculation / acceptance record ID

Rotor or assembly ID and configuration

Mass boundary and included components

Mass source, method and revision

Maximum-service-speed source and operating configuration

Grade-selection source, edition and exact clause / drawing

Rigid-rotor behaviour assessment and evidence

Correction-plane allocation document

Measurement / balancing procedure and instrument

Uncertainty, error allowance and reporting precision

Responsible engineer / reviewer

Review date

Notes and exclusions Optional: temperature, tooling state, clamping, balancing speed, runout controls, manufacturer limitations

G was selected outside this worksheet from a controlled current requirement applicable to this exact rotor / assembly configuration; the worksheet must not choose G from a generic machine-type table.
The rotor-behaviour assessment supports use of a rigid-rotor relation at the documented maximum service speed. Flexible-rotor procedures are outside this worksheet.
The displayed total magnitude has not been allocated to correction planes and is not an actual measured unbalance, correction weight, runout, bearing force or spindle deflection.
Acceptance will use the controlled plane allocation, measurement uncertainty, balancing-error allowance and manufacturer limits—not the displayed arithmetic alone.

Derived magnitudes

Angular speed ω

—

Specific residual-unbalance magnitude e

—

Specific magnitude in millimetres

—

Total residual-unbalance magnitude U

—

Total magnitude in kg·mm

—

Controlled input grade

—

Formula, units and classification

ω = 2πn / 60 [rad/s]
e = G / ω [mm]
e_µm = 1000G / ω = (30000/π)G/n [µm = g·mm/kg]
U = m · e [kg·mm] = 1000m · e [g·mm]

Simbolo	Quantity and unit	Confine
G	approved balance-quality grade in mm/s	controlled input; this worksheet does not select it
n	documented maximum service speed in r/min	not automatically the balancing-machine speed
ω	angular speed in rad/s	radian is dimensionless in this product
e	specific residual-unbalance magnitude, mm; numerically e in µm equals U/m in g·mm/kg	equivalent mass-eccentricity quantity, not geometric runout
m	documented rotor / assembly mass in kg	must match the criterion’s component boundary
Tu	total residual-unbalance magnitude in kg·mm or g·mm	not allocated between tolerance or correction planes

The arithmetic is a dimensional relation derived from the stated definition of grade G; it is not presented as a verified verbatim ISO equation. The exact π expression is retained rather than replacing 30000/π by the rounded constants 9549 or 9550.

Model boundary and removed unsupported outputs

No automatic spindle grade. The former page prescribed G0.4, G1 and G2.5 from generic speed bands and machine labels. Grade selection depends on the controlled rotor/assembly requirement; no universal spindle/toolholder preset is defensible.
No unsupported ISO-compliance verdict. ISO 21940-11 covers rigid-rotor procedures, tolerances, correction planes, allocation and balancing errors. Three numeric inputs cannot establish all of those conditions.
No fictitious deflection. The former code divided a derived force by a fixed 20 N/µm stiffness. Spindle/tool dynamic compliance depends on frequency, bearings, joints, clamping, tool overhang and measurement location.
No bearing-load claim. A grade-derived limit is not an actual measured unbalance; bearing reactions additionally depend on unbalance distribution, correction planes, rotor/support dynamics and speed.
No runout or surface-finish prediction. Equivalent specific residual unbalance is not spindle runout. Surface finish also depends on tool geometry, process forces, dynamics, material and control conditions.
No unused tool diameter or hidden state. Diameter presets, default values, auto-calculation, URL/local storage, calculation history, clipboard output and dynamic HTML were removed.

Source traceability

Claim	Classificazione	Evidence
ISO 21940-11:2016 Edition 1 establishes procedures and unbalance tolerances for rotors with rigid behaviour, including magnitude, correction planes, allocation and balancing-process errors; it excludes flexible-behaviour rotors.	Official ISO status and public scope; exact clauses licensed	ISO 21940-11:2016
Amendment 1:2022 applies to ISO 21940-11:2016 and is published.	Official ISO amendment status	ISO 21940-11:2016/Amd 1:2022
ISO 21940-2:2017 Edition 1 defines balancing vocabulary and remains current after confirmation in 2022.	Official ISO status and public scope	ISO 21940-2:2017
Published relation G = e_perΩ for permissible specific residual eccentricity and operating angular speed.	Peer-reviewed engineering paper; independent public statement of the relation	Li et al., Advances in Mechanical Engineering 13(1), 2021, Eq. 32
Permissible residual unbalance per kg (numerically µm) varies inversely with maximum service speed along constant G lines; typical rotor categories are illustrative.	Official balancing-machine manufacturer chart; visually inspected	Hofmann, Permissible residual unbalance chart (2018)

Accessed: 15 July 2026. ISO 21940-11:2016 is published and currently under systematic review, was last confirmed in 2021 and has Amendment 1:2022. Exact grade-selection tables, plane-allocation rules, error allowances and clauses remain NEEDS_LICENSED_SOURCE; none is reconstructed here.

Reference checks

For G = 2.5 mm/s and n = 10,000 r/min, the exact relation gives e = 2.387324146… µm, consistent with the G2.5 line near 2.4 µm on the published Hofmann logarithmic chart. With m = 1 kg the same case gives U = 2.387324146… g·mm. At G = 2.5 mm/s, m = 2 kg and n = 24,000 r/min, e = 0.994718394… µm and total U = 1.989436789… g·mm.

Questions

Which G grade should a machine-tool spindle use?

This worksheet deliberately does not answer that. Use the applicable current licensed requirement, the spindle and toolholder manufacturer specifications, the exact assembly configuration and an engineer-approved acceptance plan.

Is e the spindle runout?

No. Here e is an equivalent specific residual-unbalance magnitude. Geometric or dynamic runout is a different measured quantity.

Can total U be divided equally between two planes?

Not automatically. The permissible total and its allocation to tolerance/correction planes depend on the controlled rotor geometry, support and procedure. Use the applicable standard and balancing plan.