GB/T 9239.1-2026 Mechanical vibration - Rotor balancing - Part 1: Introduction
1 Scope
This document provides a general background to balancing technology, as used in the ISO 21940 series, and directs the reader to the appropriate parts of the series that include vocabulary, balancing procedures and tolerances, balancing machines and machine design for balancing.
Individual procedures are not included here as these can be found in the appropriate parts of ISO 21940.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 2041 Mechanical vibration, shock and condition monitoring - Vocabulary
Note: GB/T 2298-2010, Mechanical vibration, shock and condition monitoring - Vocabulary ( ISO 2041:2009, IDT)
ISO 21940-2 Mechanical vibration - Rotor balancing - Part 2: Vocabulary
Note: GB/T 9239.2-2025, Mechanical vibration - Rotor balancing - Part 2: Vocabulary ( ISO 21940-2:2017, IDT）
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 2041 and ISO 21940-2 apply.
4 Fundamentals of balancing
4.1 General
Balancing is a procedure by which the mass distribution of a rotor (or part of a rotor or module) is measured and adjusted to ensure that unbalance tolerances are met.
Many factors can cause rotor unbalance, e.g. non-homogenous material, manufacture, assembly, wear during operation, debris or an operational event. It is important to understand that every rotor, even in series production, has a unique individual unbalance distribution.
New rotors are commonly balanced by the manufacturer in balancing machines before installation into their operational environment. Following rework or repair, rotors can be rebalanced in a balancing machine or, if appropriate facilities are not available, the rotor can be balanced in situ (for details, see ISO 21940-13). For in-situ balancing, the rotor is held in its service bearings and support structure and rotated within its operational drive train.
When rotated, unbalance generates forces that can be directly measured by force gauges mounted on the structures supporting the bearings or indirectly by measuring either the motion of the bearing or the shaft. The unbalance vector can be calculated from these measurements and balancing achieved by adding, removing or moving correction masses on the rotor. Depending on the balancing task, the mass corrections are performed in one, two or more correction planes.
Inertia forces due to unbalances or correction masses added during the balancing process induce an excitation of the rotor and support system, which is observed as once-per-revolution vibration. Once-per-revolution vibration and vibration at other frequencies can also be excited by other effects, e.g. asymmetric stiffness, magnetic or fluid forces, but it is only the once-per-revolution effects that can be compensated for by balancing. Non-linear systems can also cause frequencies other than at once per revolution to be generated but these are usually a second order effect.
The theory of balancing is widely described in the literature (see e.g. References [11], [12]), and therefore only the basics are presented here to aid the understanding of the terms used in balancing standards and to direct the user towards the appropriate parts of ISO 21940.
4.2 Unbalance of a single disc
The simplest mechanical model of a rotor consists of a single disc supported on two bearings by a massless shaft as shown in Figure 1. An unbalance mass, mU , on the disc with a radial distance from the shaft axis, r, generates the unbalance vector, U, whereby U = mUr. The unbalance vector U is expressed in the unit of mass times length, usually kg • m, but for practical reasons, smaller units are generally used, e.g. kg • mm, g • mm or, for very small unbalances, mg • mm.
Note: Bold font indicates vector quantities.
At a rotational speed n (angular velocity Ω), the unbalance causes a centrifugal force F = UΩ2 . When expressing the unbalance, U, in kg • m, and the angular velocity, Ω, in rad/s, F is expressed in newtons, N.
a) Unbalance of a disc as unbalance mass mU at radius r
b) Unbalance of a disc as unbalance vector U
Figure 1 Unbalance of a disc
The unbalance, U, can be expressed as the eccentricity, e, of the disc mass, M, from the shaft axis, given by the expression U = M • e. See Figure 2.
Figure 2 Unbalance of a disc, expressed as the eccentricity of the mass centre from the shaft axis
4.3 Unbalance distribution
For a general rotor, with a certain axial length, unbalance is made up of an infinite number of unbalance vectors, distributed along the shaft axis. If a lumped-mass model is used to simulate the rotor behaviour, the unbalance can be represented by a finite number of unbalance vectors of different amplitudes and angular directions, as illustrated in Figure 3.
Figure 3 Unbalance distribution in a rotor modelled as K disc elements perpendicular to the z axis
4.4 Unbalance representation
If all unbalance vectors were corrected in their respective planes, the rotor would be perfectly balanced but, in practice, it is neither possible nor necessary to measure and correct for all the individual unbalances. Throughout the ISO 21940 series, the following representations are used to specify rotor unbalance:
a) resultant unbalance Ur , vector sum of all unbalance vectors distributed along the rotor;
Note 1: The plane to state the resultant unbalance can be arbitrarily chosen.
Note 2: If the plane for the resultant unbalance is the plane of the mass centre, the unbalance is called static unbalance.
b) resultant moment unbalance Pr, the vector sum of the moments of all the unbalance vectors distributed along the rotor with respect to an arbitrarily selected plane perpendicular to the shaft axis;
GB/T 9239.1-2026 Mechanical vibration - Rotor balancing - Part 1: Introduction
1 Scope
This document provides a general background to balancing technology, as used in the ISO 21940 series, and directs the reader to the appropriate parts of the series that include vocabulary, balancing procedures and tolerances, balancing machines and machine design for balancing.
Individual procedures are not included here as these can be found in the appropriate parts of ISO 21940.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 2041 Mechanical vibration, shock and condition monitoring - Vocabulary
Note: GB/T 2298-2010, Mechanical vibration, shock and condition monitoring - Vocabulary ( ISO 2041:2009, IDT)
ISO 21940-2 Mechanical vibration - Rotor balancing - Part 2: Vocabulary
Note: GB/T 9239.2-2025, Mechanical vibration - Rotor balancing - Part 2: Vocabulary ( ISO 21940-2:2017, IDT）
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 2041 and ISO 21940-2 apply.
4 Fundamentals of balancing
4.1 General
Balancing is a procedure by which the mass distribution of a rotor (or part of a rotor or module) is measured and adjusted to ensure that unbalance tolerances are met.
Many factors can cause rotor unbalance, e.g. non-homogenous material, manufacture, assembly, wear during operation, debris or an operational event. It is important to understand that every rotor, even in series production, has a unique individual unbalance distribution.
New rotors are commonly balanced by the manufacturer in balancing machines before installation into their operational environment. Following rework or repair, rotors can be rebalanced in a balancing machine or, if appropriate facilities are not available, the rotor can be balanced in situ (for details, see ISO 21940-13). For in-situ balancing, the rotor is held in its service bearings and support structure and rotated within its operational drive train.
When rotated, unbalance generates forces that can be directly measured by force gauges mounted on the structures supporting the bearings or indirectly by measuring either the motion of the bearing or the shaft. The unbalance vector can be calculated from these measurements and balancing achieved by adding, removing or moving correction masses on the rotor. Depending on the balancing task, the mass corrections are performed in one, two or more correction planes.
Inertia forces due to unbalances or correction masses added during the balancing process induce an excitation of the rotor and support system, which is observed as once-per-revolution vibration. Once-per-revolution vibration and vibration at other frequencies can also be excited by other effects, e.g. asymmetric stiffness, magnetic or fluid forces, but it is only the once-per-revolution effects that can be compensated for by balancing. Non-linear systems can also cause frequencies other than at once per revolution to be generated but these are usually a second order effect.
The theory of balancing is widely described in the literature (see e.g. References [11], [12]), and therefore only the basics are presented here to aid the understanding of the terms used in balancing standards and to direct the user towards the appropriate parts of ISO 21940.
4.2 Unbalance of a single disc
The simplest mechanical model of a rotor consists of a single disc supported on two bearings by a massless shaft as shown in Figure 1. An unbalance mass, mU , on the disc with a radial distance from the shaft axis, r, generates the unbalance vector, U, whereby U = mUr. The unbalance vector U is expressed in the unit of mass times length, usually kg • m, but for practical reasons, smaller units are generally used, e.g. kg • mm, g • mm or, for very small unbalances, mg • mm.
Note: Bold font indicates vector quantities.
At a rotational speed n (angular velocity Ω), the unbalance causes a centrifugal force F = UΩ2 . When expressing the unbalance, U, in kg • m, and the angular velocity, Ω, in rad/s, F is expressed in newtons, N.
a) Unbalance of a disc as unbalance mass mU at radius r
b) Unbalance of a disc as unbalance vector U
Figure 1 Unbalance of a disc
The unbalance, U, can be expressed as the eccentricity, e, of the disc mass, M, from the shaft axis, given by the expression U = M • e. See Figure 2.
Figure 2 Unbalance of a disc, expressed as the eccentricity of the mass centre from the shaft axis
4.3 Unbalance distribution
For a general rotor, with a certain axial length, unbalance is made up of an infinite number of unbalance vectors, distributed along the shaft axis. If a lumped-mass model is used to simulate the rotor behaviour, the unbalance can be represented by a finite number of unbalance vectors of different amplitudes and angular directions, as illustrated in Figure 3.
Figure 3 Unbalance distribution in a rotor modelled as K disc elements perpendicular to the z axis
4.4 Unbalance representation
If all unbalance vectors were corrected in their respective planes, the rotor would be perfectly balanced but, in practice, it is neither possible nor necessary to measure and correct for all the individual unbalances. Throughout the ISO 21940 series, the following representations are used to specify rotor unbalance:
a) resultant unbalance Ur , vector sum of all unbalance vectors distributed along the rotor;
Note 1: The plane to state the resultant unbalance can be arbitrarily chosen.
Note 2: If the plane for the resultant unbalance is the plane of the mass centre, the unbalance is called static unbalance.
b) resultant moment unbalance Pr, the vector sum of the moments of all the unbalance vectors distributed along the rotor with respect to an arbitrarily selected plane perpendicular to the shaft axis;
