ISO 1940-1 is an international standard that defines balance quality requirements for rigid rotors using a system of G-grades. It provides the formula U_per = (9549 x G x M) / n to calculate permissible residual unbalance, and a table mapping G-grades to rotor types. It has been superseded by ISO 21940-11, but the G-grade values and methodology remain identical.

How do you calculate permissible residual unbalance from a G-grade?

Use the formula: U_per (g-mm) = (9549 x G x M) / n, where G is the grade number in mm/s, M is rotor mass in kg, and n is maximum service speed in RPM. For example, a 50 kg rotor at 3000 RPM with G 6.3: U_per = (9549 x 6.3 x 50) / 3000 = 1003 g-mm.

What G-grade should I use for a pump, fan, or motor?

G 6.3 for most industrial fans, pumps, and general electric motors. G 2.5 for high-speed or critical-service pumps (API 610), gas turbines, and turbo-compressors. G 1.0 for precision grinding spindles. G 16 for non-critical agricultural or crushing equipment.

How do you allocate tolerance between two correction planes?

For symmetric rotors: split 50/50. For asymmetric between-bearing rotors: U_left = U_per x (b/L), U_right = U_per x (a/L), where a and b are distances from centre of mass to left and right bearings, L = a + b. For overhung rotors, moment-based recalculation with tighter tolerances is required.

What types of unbalance does ISO 1940-1 define?

Three types: Static unbalance (mass axis parallel but displaced, corrected in one plane), Couple unbalance (mass axis through centre of mass but tilted, corrected in two planes), and Dynamic unbalance (general case combining both, corrected in two planes).

Can I verify ISO 1940-1 compliance with a portable balancer?

Yes. The Balanset-1A includes a built-in ISO 1940 tolerance calculator. It calculates U_per, allocates between planes, compares measured residual against the limit, and generates a formal balance report documenting compliance with the specified G-grade.

ISO 1940-1 — Balance Quality Requirements for Rigid Rotors — Vibromera

ISO 1940-1 — Balance Quality Requirements for Rigid Rotors

Q: What is the difference between ISO 1940-1 and ISO 21940-11?

ISO 21940-11:2016 supersedes ISO 1940-1:2003 as part of the comprehensive ISO 21940 series. The G-grade system, tolerance values, and application recommendations are identical. ISO 21940-11 incorporates minor editorial improvements but no technical changes.

Q: What is a rigid rotor?

A rigid rotor is one whose elastic deformations under centrifugal forces are negligibly small compared to the specified unbalance tolerances across its entire operating speed range. A rotor balanced at low speed remains balanced at operating speed. Rotors above their first bending critical speed are flexible.

Devices

Portable balancer & Vibration analyzer Balanset-1A

Parts

Vibration sensor

Parts

Optical Sensor (Laser Tachometer)

Complete vibration diagnostics and balancing kit from Vibromera, including four vibration sensors with cables, a signal interface module, laser tachometer with magnetic stand, digital scale, USB cable, and a carrying case. The system is designed for field rotor balancing and condition monitoring on industrial equipment.

Devices

Balanset-4

Parts

Magnetic Stand Insize-60-kgf

Parts

Reflective tape

Balanset-1A. Portable balancer , vibration analyzer

Devices

Dynamic balancer “Balanset-1A” OEM

📌 Canonical Reference Article — vibromera.eu

The foundational international standard defining the G-grade balance quality system — from G 0.4 (gyroscopes) to G 4000 (marine diesels). Now incorporated into ISO 21940-11, with identical G-grade values and methodology.

Permissible Residual Unbalance

ISO 1940-1 / ISO 21940-11 — enter rotor data, get U_per

G-Grade (Balance Quality)

Rotor Mass (kg)

Max Speed (RPM)

Correction Planes

Correction Radius (mm, optional)

Results — ISO 1940-1

Permissible residual unbalance

⚖️Enter rotor parameters
to calculate tolerance

G-Grade Balance Quality Grades

Logarithmic scale with factor 2.5 between adjacent grades — from ultra-precision G 0.4 to marine G 4000

G 1.0

e·ω = 1.0 mm/s

Precision grinding spindles, tape recorders, small high-speed armatures

G 2.5

e·ω = 2.5 mm/s

Gas/steam turbines, turbo-generators, turbo-compressors, high-speed motors

G 6.3

e·ω = 6.3 mm/s

Standard — fans, pumps, flywheels, motors, machine-tool drives

G 16

e·ω = 16 mm/s

Agricultural machinery, crushers, cardan shafts, drive components

📋 Complete G-Grade Table — ISO 1940-1 / ISO 21940-11

G-Grade	e·ω (mm/s)	Typical Rotor Types	Notes
G 0.4	0.4	Gyroscopes, precision spindles, optical disc drives	Near limit of conventional balancing
G 1.0	1.0	Grinding spindle drives, tape recorders, small precision armatures	Requires ultra-clean conditions
G 2.5	2.5	Gas & steam turbines, turbo-generators, turbo-compressors, high-speed motors	Prevents premature bearing damage
G 6.3	6.3	Fans, pumps, flywheels, electric motors, machine tools, paper rolls	Most common — default grade
G 16	16	Cardan shafts (special), agricultural machinery, crushers, mine fans	Heavy-duty, severe conditions
G 40	40	Car wheels and rims, cardan shafts (standard), slow fans	Tyre variation dominates
G 100	100	Complete engines of cars, trucks, locomotives	IC engines as assemblies
G 250	250	Crankshafts of high-speed diesel engines	Component-level
G 630	630	Crankshafts of large 4-stroke engines, marine diesels on elastic mounts	Large low-speed reciprocating
G 1600	1600	Crankshafts of large 2-stroke engines	Very slow, massive foundations
G 4000	4000	Crankshafts of low-speed marine diesels on rigid foundations	Loosest requirements

📊 Pre-Calculated Tolerances for Common Industrial Rotors

Rotor Type	Mass (kg)	RPM	G	U_per (g·mm)	Per Plane	e_per (µm)
Small motor	8	2 900	G 6.3	166	83	20.7
HVAC fan	45	1 480	G 6.3	1 835	918	40.8
Pump impeller	25	2 950	G 6.3	510	255	20.4
Turbo-compressor	120	8 000	G 2.5	358	179	3.0
Paper roll	2 000	300	G 6.3	401 000	200 500	200.5
Power-plant fan	350	990	G 2.5	8 468	4 234	24.2
Grinding spindle	2	24 000	G 1.0	0.80	0.40	0.40
Car wheel	12	800	G 40	5 729	2 865	477

📐 Tolerance Allocation Methods — ISO 1940-1 Chapter 7

Rotor Type	Allocation	Formula	Notes
Symmetric	Equal split	U_L=U_R=U_per/2	Simplest case. Motors, some fans.
Asymmetric between-bearing	Proportional	U_L=U_per·(b/L)	Most common method.
Overhung (cantilever)	Moment-based	Statics eqns	Tighter tolerances on overhung plane.
Narrow (planes close)	Separate static+couple	Per ISO 21940-12	Different vibration effects.

What is ISO 1940-1?

Quick Answer

ISO 1940-1 (Mechanical vibration — Balance quality requirements of rotors in a constant (rigid) state) defines the G-grade balance quality system for rigid rotors. The formula U_per = (9 549 × G × M) / n calculates permissible residual unbalance. Superseded by ISO 21940-11:2016 with identical values. Default grade for industrial machinery: G 6.3.

ISO 1940-1 is the foundational document for rotor balancing worldwide. Its G-grade system is the de facto language of balancing: "balance to G 6.3" is understood by every specialist globally. The standard covers rigid rotors from tiny precision spindles to massive crankshafts, providing a universal framework for specifying, calculating, and verifying balance quality.

The standard applies only to rigid rotors — those whose elastic deformations under centrifugal forces are negligible across the operating speed range. Flexible rotors (operating above the first bending critical speed) are covered by ISO 21940-12.

The Rigid Rotor Concept

A rotor is classified as rigid if its mass distribution does not change significantly as speed varies from zero to maximum operating speed. The key consequence: a rotor balanced at low speed on a balancing machine remains balanced at its operating speed. This allows balancing at 300–600 RPM on a workshop machine while meeting tolerances at 3 000+ RPM in service.

If a rotor operates in the supercritical region (above the first bending critical speed) or near resonance, deflections change the effective mass distribution, and low-speed balancing may be ineffective at high speed. Such rotors are classified as flexible.

What ISO 1940-1 Does NOT Cover

Rotors with changing geometry (articulated shafts, helicopter blades). Resonance in rotor–support–foundation systems. Aerodynamic and hydrodynamic forces not related to mass distribution. For fans specifically, see ISO 14694 (BV/FV categories).

Types of Unbalance

Unbalance = rotor's inertia axis ≠ rotation axis. In vector form: U = m × r (g·mm). ISO 1940-1 classifies three types:

Static unbalance: Inertia axis parallel to rotation axis but displaced. Single unbalanced mass equivalent. Correctable in one plane. Typical: pulleys, narrow gears, fan impellers (L/D < 0.5).
Couple unbalance: Inertia axis through centre of mass but tilted. Net force zero, but a couple (pair) rocks the rotor. Requires two planes.
Dynamic unbalance: General case — static + couple combined. Inertia axis neither parallel nor intersecting rotation axis. Requires two planes. Most real rotors have dynamic unbalance.

Specific Unbalance (Eccentricity)

Specific Unbalance

e = U / M

e in µm (g·mm/kg) | U = unbalance (g·mm) | M = rotor mass (kg) — displacement of centre of mass from rotation axis

The G-grade is defined as the product e × ω (mm/s) — the linear velocity of the rotor's centre of mass orbiting the rotation axis. This single number characterises balance quality independently of rotor size and speed.

The G-Grade System — Physical Basis

Mass Similarity

For geometrically similar rotors: U_per ∝ M → specific unbalance e_per should be constant. One standard applies across all sizes.

Speed Similarity

Centrifugal force F = M·e·ω². To maintain acceptable bearing loads at different speeds, e_per must decrease as ω increases:

G-Grade Definition

G = e_per × ω = constant (mm/s)

G 6.3 = centre of mass orbits at ≤ 6.3 mm/s | Adjacent grades differ by factor 2.5

Calculating Permissible Residual Unbalance

ISO 1940-1 / ISO 21940-11 Tolerance Formula

U_per = (9 549 × G × M) / n

U_per in g·mm | G = grade (mm/s) | M = rotor mass (kg) | n = max service RPM | 9 549 = 60 000/(2π)

Worked Example: Fan Rotor, G 6.3

Given: Centrifugal fan impeller, M = 200 kg, n = 1 500 RPM, G 6.3.

Total: U_per = 9 549 × 6.3 × 200 / 1 500 = 8 021 g·mm

Eccentricity: e_per = 8 021 / 200 = 40.1 µm

Per plane (symmetric, 2): 8 021 / 2 = 4 011 g·mm

At R = 400 mm: 4 011 / 400 = 10.0 g per plane

Always Use Maximum Service Speed

The speed in the formula must be the highest RPM in service — not balancing machine speed. Many rotors are balanced at 300–600 RPM but tolerance must use actual service speed (e.g. 1 480 RPM). Using balancing machine speed produces dangerously loose tolerances.

Allocation to Correction Planes

U_per applies to the rotor's centre of mass. In practice, balance in two planes (near bearings). Chapter 7 rules:

Symmetric Rotors

CoM at midpoint → equal: U_L = U_R = U_per / 2.

Asymmetric Between-Bearing

Asymmetric Allocation

U_left = U_per × (b / L) | U_right = U_per × (a / L)

a = CoM to left bearing | b = CoM to right bearing | L = a + b

Overhung Rotors

Overhung mass creates bending moment loading both bearings. Moment-based recalculation needed → typically much tighter tolerance on overhung plane. Common for pumps, single-stage compressors, cantilevered fan impellers.

Errors and Verification

Error Sources

Systematic: Machine calibration drift, eccentric mandrels, keyway effects (ISO 8821), thermal distortion.
Random: Sensor noise, support play, rotor seating variation.

Total error must not exceed 10–15% of tolerance. If larger, tighten working tolerance accordingly.

Assembly Effects

Component balancing ≠ assembly balance. Coupling eccentricity, radial runout, loose fits can negate component work. Trim balance the assembled rotor.

Verification Methods

Index test: Rotate rotor 180° on mandrel, remeasure. Change = fixture error.
Trial weight test: Add known mass, verify measured vector change matches expectation.
Field check: Measure vibration on bearings per ISO 10816.

Balanset-1A: Built-In ISO 1940-1 Compliance

The Balanset-1A automates ISO 1940-1: enter mass, speed, G-grade → instant U_per with automatic plane allocation. After balancing, compares residual vs. limit. The F6 Reports function generates a formal protocol documenting the achieved G-grade. Accuracy ±5% velocity, ±1° phase — sufficient for G 16 through G 2.5. The Balanset-4 extends to four channels for complex multi-bearing rotors.

Worked Examples

Case 1: Electric Motor — G 6.3

Rotor: 15 kW, 1 460 RPM, 35 kg, between-bearing symmetric.

Tolerance: U_per = 9 549 × 6.3 × 35 / 1 460 = 1 442 g·mm → 721/plane.

At R = 80 mm: 721 / 80 = 9.0 g/plane. Shop balanced: 180 g·mm residual. ✅

Case 2: Pump — Overhung Impeller, G 6.3

Rotor: Shaft + impeller 18 kg, 2 950 RPM. Impeller 6 kg overhung 120 mm. Bearing span 250 mm.

Total: U_per = 367 g·mm. Moment allocation: front ≈ 202, rear ≈ 165 g·mm.

Field balanced with Balanset-1A single-plane: 8.5 g at 230°. Final: 95 g·mm. ✅

Case 3: Turbo-Compressor — G 2.5

Rotor: 3-stage, 65 kg, 12 000 RPM. Slightly asymmetric.

Tolerance: U_per = 129 g·mm → 65/plane → at R = 95 mm: 0.68 g/plane.

Sub-gram precision → shop high-speed machine only. Index test: mandrel error < 5 g·mm. Final: 28 g·mm/plane. ✅

ISO 1940-1 → ISO 21940-11

G-grade values, formulas, application tables — identical. No technical changes.
ISO 21940 series: Part 11 (quality), Part 12 (flexible), Part 14 (procedures), Part 21 (descriptions), Part 31 (susceptibility), Part 32 (keys).
Both designations used interchangeably in practice.
ISO 14694 BV categories reference G-grades directly.

ISO 21940-11: This standard — G-grade system.
ISO 21940-12: Flexible rotor balancing.
ISO 10816 / ISO 20816: Vibration evaluation — operational result of balance quality.
ISO 14694: Fan-specific BV/FV categories → G-grades.
ISO 8821: Keyway influence (half-key convention).
API 610 / API 617: Petroleum pumps/compressors referencing ISO 1940.

Official standard: ISO 1940-1 on ISO Store →

← Back to Glossary Index

Frequently Asked Questions — ISO 1940-1

G-grade balance quality system for rigid rotors

▸ What is the difference between ISO 1940-1 and ISO 21940-11?

ISO 21940-11:2016 supersedes ISO 1940-1:2003. The G-grade system, tolerance values, and application tables are identical. ISO 21940-11 includes minor editorial improvements but no technical changes. Both designations are used interchangeably.

▸ How do I calculate permissible residual unbalance?

U_per = (9 549 × G × M) / n — G = grade (mm/s), M = mass (kg), n = max RPM. Example: 50 kg at 3 000 RPM, G 6.3 → 9 549 × 6.3 × 50 / 3 000 = 1 003 g·mm. Divide by planes for per-plane value.

▸ What is a rigid rotor?

A rotor whose elastic deformations under centrifugal forces are negligibly small across its operating speed range. Balanced at low speed → stays balanced at operating speed. Rotors above first bending critical speed are flexible and require ISO 21940-12.

▸ What G-grade for pumps, fans, or motors?

G 6.3 — most fans, pumps, general motors. G 2.5 — turbines, turbo-compressors, critical pumps (API 610). G 1.0 — grinding spindles. G 16 — agricultural/crushers. For fans: ISO 14694 BV categories map to G-grades.

▸ How to allocate tolerance between planes?

Symmetric: 50/50. Asymmetric: proportional to bearing reactions — U_left = U_per×(b/L). Overhung: moment-based with tighter overhung-plane tolerance. The Balanset-1A handles allocation automatically.

▸ What are the three types of unbalance?

Static — displaced but parallel, one-plane fix. Couple — tilted through CoM, two-plane fix. Dynamic — general (static+couple), two-plane fix. Most real rotors: dynamic unbalance.

▸ Why are G-grades on a logarithmic scale?

Factor 2.5 between grades covers the full range from gyroscopes (G 0.4) to marine diesels (G 4000). Logarithmic scaling is appropriate because perceived vibration severity and bearing life follow logarithmic relationships. Each step ≈ same relative change in quality.

▸ Can I verify compliance with a portable balancer?

Yes. Balanset-1A: built-in ISO 1940 calculator, automatic plane allocation, real-time comparison of residual vs. limit, formal balance report. ±5% accuracy sufficient for G 16–G 2.5. For G 1.0, careful preparation needed.

Balance to ISO 1940-1 — In the Field

Vibromera portable balancers include built-in ISO 1940 tolerance calculators, automatic plane allocation, and formal balance reports documenting the achieved G-grade.

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