> ## Content Index > Fetch the complete content index at: https://www.machinerymatters.com/llms.txt > Use this file to discover other available public pages before exploring further. # The Complete Balancing Series - URL: https://www.machinerymatters.com/balancing-series/ - Published: 2026-09-18T01:36:24.000Z - Updated: 2026-09-18T13:43:07.000Z - Description: Series guide. The balancing series in reading order: six articles from single-plane fundamentals to at-speed balancing of flexible rotors, seven calculators, and the knowledge check, each with a summary and a figure. - Author: Editor - Tags: Balancing, Series, #series-balancing Balancing is the correction of a rotor’s mass distribution so that it turns about its axis of rotation with minimal rotating force at its bearings. This series begins with single-plane, low-speed balancing of rigid rotors and finishes with multi-plane, at-speed balancing of flexible rotors. Calculators are provided along the way to assist understanding and help practitioners with real balancing work. A knowledge check is available at the end for those who want to confirm what they learned. The articles are free to read. The fundamentals calculators are available to free subscribers, and the advanced calculators and the knowledge check to premium members. ## Articles 1. [Single-Plane Balancing: The Fundamentals](https://www.machinerymatters.com/single-plane-balancing-the-fundamentals/)Article What unbalance is physically, how it is quantified in gram-millimeters and ounce-inches, when a single correction plane is enough, and how the API and ISO tolerance criteria set the residual a rotor may keep. The starting point for every article that follows. ω 0° reference + α β φ High spot (peak rotor displacement) e F = W·e·ω² Axis of rotation Heavy spot (center of mass, G) 2. [Two-Plane Balancing: The Fundamentals](https://www.machinerymatters.com/two-plane-balancing-the-fundamentals/)Article The taxonomy of static, couple, dynamic, and quasi-static unbalance, why a couple is invisible to one correction plane, and why two planes are sufficient for any rigid rotor. Introduces the per-plane and static-and-couple forms that the converters use. Side view Top view Static G G e Couple G G Quasi-static G G Dynamic G G Central principal axis of inertia Axis of rotation 3. [Low Speed Balancing Machines](https://www.machinerymatters.com/low-speed-balancing-machines/)Article The hard-bearing and soft-bearing architectures and the support resonance that divides them; the arbors, drives, transducers, and phase reference between the rotor and the reading; and the metrics that state what a machine can achieve. Read this before the procedure. Pedestal 1 Pedestal 2 force transducer F1 F2 A B UA UB ω zA zB s 4. [Low Speed Balancing Procedure](https://www.machinerymatters.com/low-speed-balancing-procedure/)Article Setting up the rotor and the machine, the measure-and-correct cycle, the correction methods and how a correction is split between available positions, and the residual unbalance verification test that proves the result independently of the machine’s calibration. The shop-floor article of the series. 1 2 3 4 5 6 7 8 rt test mass (mt) test positions, equally spaced 5. [At-Speed Balancing: The Fundamentals](https://www.machinerymatters.com/at-speed-balancing-the-fundamentals/)Article Critical speeds and mode shapes, what amplitude and phase do through a critical, and why a two-plane low-speed balance can leave a flexible rotor vibrating heavily at speed. Explains what at-speed balancing accomplishes and why it supplements rather than replaces the low-speed balance. Bearing Bearing First bending mode Second bending mode Node Node Node Anti-node 6. [At-Speed Balancing: Machines and Procedure](https://www.machinerymatters.com/at-speed-balancing-machines-and-procedure/)Article The vacuum-chamber facilities, the choice of correction planes for flexible rotors, the sequence of an at-speed job, the plane-by-plane influence coefficient method, modal balancing with plane sets, and how an at-speed balance is specified and accepted. The most advanced article in the series. Vacuum chamber Vacuum pump Drive Shaft seal Coupling Bearing Bearing Rotor Pedestal Pedestal Proximity probes Phase reference ## Calculators 1. [Balance Tolerance Calculator](https://www.machinerymatters.com/balance-tolerance-calculator/)CalcSubs Companion tool to [Single-Plane Balancing: The Fundamentals](https://www.machinerymatters.com/single-plane-balancing-the-fundamentals/). Enter the rotor weight, the maximum continuous speed, and the correction radius, and select the API criterion or an ISO grade; the tool reports the allowable residual unbalance, the allowable unbalance mass at your radius, and the rotating force at speed, in US or SI units. G 0.4 G 1 G 2.5 G 6.3 G 16 G 40 300 1,000 3,000 10,000 30,000 0.1 1 10 100 1,000 10,000 Maximum continuous speed, N (RPM) Permissible specific unbalance, U/W (g·mm/kg) ≈ e (µm) 2. [Two-Plane Unbalance Converter](https://www.machinerymatters.com/two-plane-unbalance-converter/)CalcSubs Companion tool to [Two-Plane Balancing: The Fundamentals](https://www.machinerymatters.com/two-plane-balancing-the-fundamentals/). Converts between the per-plane form and the static-and-couple form of a rigid rotor’s unbalance, in either direction, and names the condition the result describes. Per-plane form Static-and-couple form A B UA UB L \= A B Ueq Ceq 3. [Pedestal Force Converter](https://www.machinerymatters.com/pedestal-force-converter/)CalcSubs Companion tool to [Low Speed Balancing Machines](https://www.machinerymatters.com/low-speed-balancing-machines/). Converts the forces measured at a hard-bearing machine’s two pedestals into the unbalance in two correction planes, and back, from the balancing speed, the pedestal span, and the plane positions. Pedestal 1 Pedestal 2 force transducer F1 F2 A B UA UB ω zA zB s 4. [Correction Splitting Calculator](https://www.machinerymatters.com/correction-splitting-calculator/)CalcPremium Companion tool to [Low Speed Balancing Procedure](https://www.machinerymatters.com/low-speed-balancing-procedure/). Splits a required correction between two available angular positions and reports the two component masses together with the total the split costs. 0° θ1 θ θ2 r m m1 m2 5. [Residual Unbalance Verification Calculator](https://www.machinerymatters.com/verification-calculator/)CalcPremium Companion tool to [Low Speed Balancing Procedure](https://www.machinerymatters.com/low-speed-balancing-procedure/). Fits the circle through six, eight, or twelve verification readings; reports the verified residual with its calibration scale check and reading scatter; compares it against the tolerance and the machine’s reported residual; and prints a record. 50 100 150 200 250 g·mm 0° 90° 180° 270° R1 R2 R3 R4 R5 R6 R7 R8 Rr Rc 6. [At-Speed Balancing Calculator](https://www.machinerymatters.com/at-speed-balancing-calculator/)CalcPremium Companion tool to [At-Speed Balancing: Machines and Procedure](https://www.machinerymatters.com/at-speed-balancing-machines-and-procedure/). Runs an at-speed balancing job from baseline and trial readings: influence coefficients for up to five planes across probes and speeds, least-squares corrections against the acceptance limits, and trim runs, with autosave and a saved-file record. 25 50 75 µm 0° 90° 180° 270° Rotation X0 XT ΔX H · Ucor 7. [Plane Set Calculator](https://www.machinerymatters.com/plane-set-calculator/)CalcPremium Companion tool to [At-Speed Balancing: Machines and Procedure](https://www.machinerymatters.com/at-speed-balancing-machines-and-procedure/). Determines the proportions of a plane set for a target mode from the plane positions, so that the set moves that mode while adding no net force or moment, and hands the set to the At-Speed Balancing Calculator. End plane Quarter-span plane Midspan plane Quarter-span plane End plane Bearing Bearing First-mode set Second-mode set ## Knowledge check 1. [Balancing Knowledge Check](https://www.machinerymatters.com/balancing-knowledge-check/)TestPremium Twenty-two auto-scored questions on application, calculation, and judgment across the six articles and seven calculators, open-book with lookup links, with a per-article score breakdown, save and resume, and a printable certificate at 80 percent or better. Click any figure to enlarge it. The [Library](https://www.machinerymatters.com/library/) lists every article and tool on the site by topic. ×