Measurement-data worksheet · one radial trace

Documented Single-Trace Radial Indicator Worksheet

Reduce equally spaced radial indicator readings from one complete revolution to an observed sampled range and a first-harmonic diagnostic, while preserving the datum, setup and instrument record.

Max − min traceNIST single-trace fitNo ISO balance conversion

Not a conformance or balancing verdict. This worksheet does not establish a geometric runout tolerance, prove compliance with ISO 1101, replace an ASME B89 measurement procedure, or convert shaft-surface readings into ISO 21940 residual unbalance. The applicable drawing, datum simulation, measurement plan, uncertainty and decision rule remain controlled project inputs.

Documented trace and setup

Equally spaced indicator readings over exactly one revolution One signed plain decimal per line (or separated by semicolons); use a decimal point or decimal comma. Do not repeat the 0° reading at 360°.

Reading unit

Four to 720 readings are accepted. Scientific notation, units inside the reading list and comma-separated lists are intentionally rejected because decimal comma is supported.

Project / equipment

Feature / shaft identifier

Axial section / probe location

Drawing datum / reference axis

Mounting, support and rotation method

Instrument / probe / calibration ID

Resolution and uncertainty record

Sampling / angle-index method

Prepared / reviewed by

Record date

Uwagi Optional: temperature, surface condition, repeat number, rotation direction, drawing callout

The list contains one complete revolution at equal angular increments, from one axial section, with no duplicated endpoint. Probe position, sign convention, zero, unit, support and rotation method remained unchanged throughout the trace. The documented datum simulation, seating, surface condition, instrument status and sampling density are appropriate for the intended measurement record. I understand that sampled range can miss unsampled extrema and that the first harmonic does not by itself separate workpiece form, setup/spindle error, centre offset or rotor mass unbalance.

Reference results

Observed sampled indicator spread (max − min)

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Half of sampled range (not automatically eccentricity)

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First-harmonic amplitude

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First-harmonic peak-to-peak

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First-harmonic maximum phase

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Residual sampled range after mean + first harmonic

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Minimum / maximum reading

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Mean reading

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Samples / nominal angular increment

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Equations and meaning

For N equally spaced readings yᵢ at θᵢ = 2πi/N, the direct trace reduction is:

sampled spread = max(yᵢ) − min(yᵢ)
half-range = sampled spread / 2

Following the NIST single-trace least-squares construction:

mean = (1/N) Σyᵢ
a = (2/N) Σ[yᵢ cos(θᵢ)]
b = (2/N) Σ[yᵢ sin(θᵢ)]
first-harmonic amplitude = √(a² + b²)
Δᵢ = yᵢ − mean − a cos(θᵢ) − b sin(θᵢ)

The first-harmonic phase is reported relative to the first reading and the recorded rotation direction. The residual range is max(Δᵢ) − min(Δᵢ). All are descriptive results from the entered samples; no tolerance, uncertainty allowance or acceptance decision is generated.

Dimensional check

Trigonometric terms and N are dimensionless, so mean, a, b, harmonic amplitude, residuals and ranges retain the reading unit. Exact conversions used are 1 mm = 1000 µm and 1 mil = 25.4 µm.

Model boundary

Sampled trace, not continuous extrema. Unless the actual continuous maximum and minimum were captured, the discrete range can underestimate the one-revolution indicator movement. Increase angular density or use a validated continuous acquisition method.
One section, not total runout. Readings at one fixed axial section do not establish total runout of the complete surface. Exact drawing interpretation and conformance require the controlled ISO 1101 or applicable drawing standard.
Setup is part of the result. The datum/reference axis, mounting, support deformation, seating, probe direction, surface form, dirt/burrs, instrument error and spindle/error motion can affect the trace.
Half-range is not generally eccentricity. It equals centre offset only for the idealized case where a perfect circular feature has pure centre offset relative to the rotation/reference axis and other harmonics/errors are absent.
No residual-unbalance conversion. ISO 21940-11 concerns residual mass unbalance of rotors with rigid behaviour. A journal surface trace is not a measurement of the rotor mass-centre distribution; the former TIR = 2e_za G-grade screening path has been removed.
No acceptance decision. Drawing tolerance, measurement uncertainty, guard band and decision rule remain external. Exact clauses and tolerance values are NEEDS_LICENSED_SOURCE unless a controlled document is supplied.

Source traceability

Claim	Klasyfikacja	Evidence
Single-trace equally spaced least-squares mean, cosine/sine coefficients and residual	Published public metrology method; not an ISO formula	NIST/SEMATECH e-Handbook, 2.3.4.4.1 Single-trace roundness design
A single trace cannot separate spindle error from workpiece error	Published NIST limitation	Same NIST/SEMATECH section; weakness of the single-trace method
Dynamic radial surface displacement can contain spindle error motion, form, alignment and vibration contributions	Published NIST research summary	NIST, Anandan et al., 2011
Geometrical runout specification framework	Current standard identification only; no clause or tolerance copied	ISO 1101:2017, Edition 4, published and confirmed in 2022
Rigid-rotor residual-unbalance scope, not geometric shaft runout	Current standard scope/status only	ISO 21940-11:2016 z Amendment 1:2022; under systematic review in 2026
Axes-of-rotation measurement methods	Current ASME identification/scope only; exact procedure remains licensed	ASME B89.3.4-2010 (R2024), stabilized maintenance
1 in = 25.4 mm exactly	Exact SI conversion	NIST SP 811, Appendix B.8

Accessed: 15 July 2026. Public sources establish the numerical reduction and standard scopes. They do not establish the project datum simulation, sampling density, uncertainty, tolerance or decision rule. Worksheet URL: https://vibromera.eu/calculators/shaft-radial-runout/

Reference sample trace

For equally spaced readings [10, 0, −10, 0] µm starting at 0°, the exact analytic result is: sampled range 20 µm; mean 0; a = 10 µm; b = 0; first-harmonic amplitude 10 µm; phase 0°; residual range 0. This verifies the implementation algebra but is not a tolerance example.

Questions

Does TIR always equal twice eccentricity?

No. Twice-centre-offset is an ideal special case for a perfect circle with pure offset. An actual indicator trace can contain form, datum/setup, spindle/error-motion and sampling contributions. This worksheet therefore labels range/2 as half-range, not eccentricity.

Can this trace be compared with ISO 21940 balance grade G?

No direct conversion is made. ISO 21940-11 controls residual mass unbalance for rotors with rigid behaviour; a surface indicator trace does not locate the rotor mass centre. Balance must be measured and evaluated by the applicable controlled balancing procedure.

Is one axial trace enough for total runout?

No. This worksheet reduces one fixed-section trace only. The exact geometric specification, datum and verification procedure must come from the drawing and the applicable controlled standard.

What value is acceptable?

No universal value is generated. Use the controlled drawing or OEM tolerance together with a documented measurement uncertainty and decision rule. If the exact standard clause is unavailable, retain NEEDS_LICENSED_SOURCE.