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I. Static balance: Static balance is achieved by performing balancing on one side of the rotor; the residual unbalance after this process ensures that the rotor remains within the permitted limits for unbalance when at rest. This type of balance is also known as one-sided balance. II. Dynamic Balancing: Dynamic balancing involves performing balance corrections on two or more correction surfaces of the rotor simultaneously. The residual imbalance after these corrections is reduced to ensure that the rotor remains within the specified limits for allowable imbalance during operation. This type of balancing is also known as double-sided or multi-sided balancing. III. Selection and determination of rotor balancing. How to choose the method of rotor balancing is a key issue. There is a principle guiding this choice: as long as the requirements of the application after rotor balancing are met, static balancing should be used instead of dynamic balancing; and if dynamic balancing is possible, then static and dynamic balancing together should not be employed. The reason is simple: static balance is easier to achieve than dynamic balance, saving effort, labor, and costs. So how is the rotor balancing type determined? It is necessary to determine this based on the following factors and criteria: 1. The geometry and structural dimensions of the rotor; in particular, the ratio between the rotor diameter D and the distance b between its two end faces, as well as the spacing between the rotor supports, etc. 2. Operating speed of the rotor: Technical standards for rotor balancing requirements, such as GB3215, API610, GB9239, and ISO1940, etc. 3. Conditions for static balance of the rotor: In the GB9239 balancing standards, the conditions for static balance of a rigid rotor are defined as follows: If the spacing between the supports of a disc-shaped rotor is large enough and the axial runout of the disc-like portion during rotation is very small, so that couple imbalances (dynamic balance) can be ignored, then the imbalance can be corrected using a single correction surface, achieving single-sided (static) balance. It is necessary to verify whether these conditions are met for a specific rotor. After balancing a large number of rotors of a certain type on a plane, the maximum residual couple imbalance can be determined and then divided by the support distance. If, under the most unfavorable conditions, this value is not greater than half of the allowable remaining unbalance, then single-sided (static) balancing is sufficient. From this definition, it is easy to see that there are mainly three conditions under which a rotor requires only single-plane (static) balancing: (1) One is that the rotor has a disc-like geometric shape ； (2) One is that the support spacing when the rotor is balanced on a balancing machine should be large ； (3) Another requirement is that the end-face runout of the correction surface must be very small when the rotor is rotating. The above three conditions are explained as follows: (1) What is meant by a disc-shaped rotor is primarily determined by the ratio of the rotor’s diameter D to the distance b between its two opposite surfaces. According to the API610 standard, when D/b < 6, it is sufficient to perform single-sided balancing of the rotor ； When D/b≥6, it can be used as a criterion to determine whether the rotor is disc-shaped, but this cannot be taken as an absolute rule, as the type of balancing required for the rotor also depends on its operating speed. (2) There is no specific parameter specified for the support spacing; however, a ratio of this spacing to the rotor alignment distance b of ≥5 is considered to indicate that the support spacing is sufficiently large. (3) The axial runout of the rotor refers mainly to the end-face runout of the reference surface as the rotor rotates; since any rotor undergoing balancing tests is finely machined, the manufacturing process ensures that the tolerance between the rotor’s holes and the reference surface is very small, resulting in minimal end-face runout. Based on the conditions for single-sided (static) balancing of the rotor mentioned above, and in conjunction with the technical standards related to pumps (such as GB3215 and API610), the requirements for rotors that are to be balanced only statically are as follows: (1) For the rotors of single-stage and two-stage pumps, when the operating speed is < 1800 revolutions per minute, static balancing alone is sufficient, regardless of whether D/b < 6 or D/b ≥ 6. However, if dynamic balancing is required, it is necessary to ensure that D/b < 6; otherwise, only static balancing can be performed. (2) For the rotors of single-stage and two-stage pumps, when the operating speed is ≥ 1800 revolutions per minute, static balancing is sufficient if D/b ≥ 6. However, the remaining unbalance after balancing must be equal to or less than 1/2 of the allowable unbalance. If dynamic balancing is required, it is necessary to check whether the balance of the two correction surfaces can be achieved separately on a balancing machine; if not, only static balancing can be performed. (3) For some rotors such as open impellers, if end support cannot be achieved, only static balancing is sufficient. Since neither end can be supported, cantilevering is inevitable. This makes dynamic balancing on a balancing machine very dangerous; therefore, single-sided (static) balancing can only be performed on a balancing stand. 4. The conditions for achieving dynamic balance of a rotor are specified in standard GB9239: For any rigid rotor that does not meet the conditions required for static balance as a disc-shaped rotor, it is necessary to achieve balance in two planes, that is, through dynamic balance. The conditions for rotors that require only static balance are as follows (a balance accuracy of G0.4 represents the highest precision; generally, for pump impellers, a dynamic balance accuracy of G6.3 or G2.5 is chosen): (1) For single-stage and two-stage pumps, when the operating speed is ≥ 1800 revolutions per minute, dynamic balance should be performed as long as D/b < 6. (2) For multi-stage pumps and combined rotors (3 stages or more), dynamic balancing of the combined rotor shall be performed regardless of the operating speed. IV. Dynamic Balance Test The dynamic balance test is the process of conducting dynamic balance checks and corrections on the rotor to meet the requirements for its use. When parts are components that move in a rotational motion, such as various drive shafts, spindles, fan impellers, water pump impellers, cutting tools, and the rotors of electric motors and steam turbines, they are collectively referred to as rotating bodies. Under ideal conditions, the pressure exerted on the bearings is the same whether the rotating body is rotating or not; such a rotating body is a balanced rotating body. However, various rotating bodies used in engineering, due to factors such as uneven material composition or defects in the blanks, errors that occur during processing and assembly, and even asymmetric geometric shapes from the design stage, result in the centrifugal inertial forces generated by each tiny particle on these rotating bodies not being able to cancel each other out. These centrifugal inertial forces act through the bearings on the machinery and its foundation, causing vibrations and noise, accelerating bearing wear, and shortening the lifespan of the machinery; in severe cases, this can lead to destructive accidents. To this end, the rotor must be balanced to achieve the permitted balance accuracy level, or the amplitude of the resulting mechanical vibrations must be reduced to an acceptable range. V. Balancing Methods 1. Process balancing method The testing system used in the process balancing method is less susceptible to interference, offers high balancing accuracy and efficiency; it is particularly suitable for performing individual balancing of rotating mechanical components in the production process. It plays a significant role in the field of dynamic balancing, and this balancing method is widely used in steam turbines and aero engines. However, the process balancing method still has the following problems: (1) The speed at balance is different from the operating speed, resulting in a decrease in balancing accuracy. For example, many rotors are unstable rotors with a second-order critical speed. Due to the limited speed of balance machines, using conventional balancing methods cannot effectively prevent deformation of these rotors at high speeds, which in turn leads to imbalance. (2) Balancing machines (especially high-speed vertical balancing machines) are expensive. (3) For rotors that have been balanced on a dynamic balancer, it is difficult to ensure their balance accuracy after installation. Since the supporting conditions during dynamic balancing are different from those under the actual operating conditions of the rotor, and the fit between the rotor and the balancing device is also different from the fit between the rotor and its own axis, even a rotor that has achieved high-precision balance on a dynamic balancer before leaving the factory may see a decline in its balance accuracy after processes such as transportation and reassembly. As a result, unwanted vibrations can still occur when it operates at its working speed. (4) Some rotors, due to size and weight constraints, are difficult or even impossible to balance on a balancing machine. For example, in the case of very large rotors such as those found in large generators and turbines, the absence of appropriate large-scale balancing devices often results in an inability to achieve balance ； For large high-temperature steam turbine rotors, elastic thermal warping often occurs, and it disappears automatically after the machine is shut down. Such rotors require thermal dynamic balancing, and it is clearly impossible to achieve this balance using a balancer. (5) The rotor must be removed in order to perform dynamic balancing, which results in long downtime, slow balancing speeds, and significant economic losses. 2. On-site dynamic balancing of the entire machine: To overcome the shortcomings of the aforementioned process balancing method, the on-site dynamic balancing of the entire machine was proposed. The balancing operation of the assembled rotating machinery in its installed condition on-site is called overall on-site balancing. This method uses a machine as the balance machine base; vibration data from relevant parts of the rotor is measured by sensors, and this data is processed to determine the imbalance amounts and their positions on each balance plane of the rotor. The imbalance is then eliminated by removing mass or adding mass, thereby achieving high-precision balancing. Since on-site dynamic balancing of the entire machine is carried out directly on the machine itself, no dynamic balancing machine is required; only a low-cost testing system is needed, making it more economical. Furthermore, since the rotor is balanced under actual operating conditions, there is no need for additional processes such as assembly, allowing the entire machine to achieve a high level of balance accuracy while in operation. As an important branch of on-site dynamic balancing technology for complete machines, online dynamic balancing technology is also experiencing rapid development and holds great promise. Since the process balance method is one of the earliest classic dynamic balancing methods. The on-site dynamic balancing technology for the entire machine was developed to address the problems existing in process balancing technology. VI. Balance accuracy Precision class G, in g.mm/kg. Examples of rotor types: G4000 – 4000; crankshaft drives for low-speed marine diesel engines with a single number of cylinders and rigid installation. G1600 – 1600; crankshaft drives for large two-stroke engines with rigid installation. G630 – 630; crankshaft drives for marine diesel engines with rigid installation ； Crankshaft drives for rigidly mounted large four-stroke engines, G250; 250 crankshaft drives for rigidly mounted high-speed four-cylinder diesel engines, G100; 100 crankshaft drives for six-cylinder and multi-cylinder diesel engines. Complete (gasoline, diesel) engines for cars, trucks, and locomotives. G40 40 automobile wheels, wheel rims, complete wheels ； Driving components for engines used in cars, trucks, and locomotives. G16 16 crusher, parts for agricultural machinery ； Individual parts for (gasoline, diesel) engines used in cars, trucks, and locomotives. G6.3 6.3 Gas and steam turbine engines, including the rigid turbine engine rotors of marine (commercial) vessel main turbines ； Turboscharger ； Machine tool drive components ； Rotors for medium and large motors with special requirements ； Small motor rotor ； Turbopump. G2.5 2.5 Gear for the main turbine of seagoing vessels (merchant ships) ； Centrifuges, pump impellers ； fan ； Rotor components of aero gas turbines ； flywheel ； General parts of machine tools ； Ordinary motor rotor ； Individual parts of engines with special requirements. G1 1 Tape recorder and record player drive components ； Grinding machine drive component ； Small armatures with special requirements. G0.4 0.4 Spindle, grinding wheel, armature, and gyroscope of precision grinders. Considering technological advancement and economic feasibility, the International Organization for Standardization (ISO) established the globally recognized ISO 1940 balance grade in 1940. This standard classifies rotor balance grades into 11 levels, with increments of 2.5 times between each level; balance machines range from the highest requirement of G0.4 to the lowest of G4000. The unit is grams per millimeter per kilogram (gmm/kg), and it represents the eccentric distance of the imbalance from the rotor’s axis.