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Dynamic balance and static balance I. Static balance Static balance is achieved by performing adjustments on one side of the rotor; the remaining imbalance after these adjustments ensures that the rotor is within the permitted limits for imbalance when at rest. Static balance is also known as one-sided balance. II. Dynamic Balancing: Dynamic balancing involves carrying out balancing operations on two or more correction surfaces of the rotor simultaneously. The remaining unbalance after these adjustments is reduced to ensure that the rotor’s unbalance remains within the specified allowable limits 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 cost. So how is the rotor balancing pattern determined? It needs to be determined based on the following factors and criteria: 1. The geometric shape and structural dimensions of the rotor, in particular the ratio of the rotor’s diameter D to the distance b between its two parallel surfaces, as well as the spacing between the supports of the rotor. 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 imbalance (dynamic balance) can be ignored, then the imbalance can be corrected using a single correction surface, achieving unilateral (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 pair imbalance can be determined and 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 mainly 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 alignment surface during rotation, as any rotor that is subjected to balancing tests has been finely processed; as a result, the tolerance between the rotor’s holes and the alignment surface is ensured, resulting in very low 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 provided that D/b ≥ 6. However, the remaining imbalance after balancing must be equal to or less than half of the allowable imbalance. 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 balance is sufficient. Since the ends cannot provide support, a cantilever structure is necessary; as a result, performing dynamic balancing on a balancing machine is very dangerous, and it is only possible to carry out single-sided (static) balancing 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 of disc-shaped rotors, it is necessary to achieve balance in two planes, that is, through dynamic balance. The conditions for rotors that require only static balancing are as follows (a balance accuracy of G0.4 represents the highest precision; generally, for pump impellers, a dynamic balancing accuracy of G6.3 or G2.5 is chosen): (1) For single-stage and two-stage pumps, whenever the operating speed is ≥ 1800 revolutions per minute, dynamic balancing should be performed if D/b < 6. (2) For multi-stage pumps and combined rotors (3 stages or more), dynamic balancing of the combined rotor should be performed regardless of the operating speed. IV. Dynamic Balancing Test The dynamic balancing test is the process of conducting dynamic balance checks and corrections on the rotor to meet its operational requirements. When components undergo 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 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 flexible rotors with a second-order critical speed. Due to the limited speed of balancing 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) The balance accuracy of a rotor that has been balanced on a dynamic balancer is difficult to maintain after it is installed in the machine. 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 shaft, even a rotor that has achieved high-precision balance on a dynamic balancer before leaving the factory may see a decrease in its balance accuracy as a result of transportation, reassembly, and other processes. As a result, unwanted vibrations may still occur when the rotor is operating at its rated 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 lack 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 utilizes a machine as a dynamic balancing stand. Vibration data from relevant parts of the rotor, measured by sensors, is processed to determine the magnitude and orientation of the imbalance on each balancing plane of the rotor. The imbalance is then eliminated through material removal or addition, 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. Accuracy class: G; unit: g·mm/kg. Examples of rotor types: G4000 – 4000: Crankshaft drive components for low-speed marine diesel engines with an odd number of cylinders and rigid mounting. G1600 – 1600: Crankshaft drive components for large two-stroke engines with rigid mounting. G630 – 630: Crankshaft drive components for marine diesel engines with rigid mounting ； Crankshaft drive components for rigidly mounted large four-stroke engines, G250; 250 crankshaft drive components for rigidly mounted high-speed four-cylinder diesel engines, G100; 100 crankshaft drive components for six-cylinder and multi-cylinder diesel engines. Complete (gasoline, diesel) engines for automobiles, trucks, and locomotives. G40 40 Automotive wheels, wheel rims, complete wheels ； Driving components for engines used in cars, trucks, and locomotives. G16 16 Crushers, parts for agricultural machinery ； Individual parts of (gasoline, diesel) engines for automobiles, trucks and locomotives. G6.3 6.3 Rotors of rigid turbine engines for gas and steam turbines, including main turbines for marine vessels (merchant ships) ； Turbocharger ； 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 aircraft gas turbines ； flywheel ； General parts of machine tools ； Ordinary motor rotor ； Individual parts of engines with special requirements. G1 1 Tape recorder and phonograph 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.