Balancing parts and assembly units. Balancing of rotating parts and assembly units Static and dynamic balancing of parts and assemblies
Unbalance of any rotating part of a diesel locomotive can occur both during operation due to uneven wear, bending, accumulation of contaminants in one place, when the balancing weight is lost, and during repair due to improper processing of the part (shift of the axis of rotation) or inaccurate alignment of the shafts. To balance the parts, they are subjected to balancing. There are two types of balancing: static and dynamic.
Rice. 1. Scheme of static balancing of parts:
T1 is the mass of the unbalanced part; T2 is the mass of the balancing load;
L1, L2 are their distances from the axis of rotation.
Static balancing. In an unbalanced part, its mass is located asymmetrically relative to the axis of rotation. Therefore, in the static position of such a part, i.e. when it is at rest, the center of gravity will tend to take a lower position (Fig. 1). To balance the part, a load of mass T2 is added from the diametrically opposite side so that its moment T2L2 is equal to the moment of the unbalanced mass T1L1. Under this condition, the part will be in balance in any position, since its center of gravity will lie on the axis of rotation. Equilibrium can also be achieved by removing part of the metal part by drilling, sawing or milling from the side of the unbalanced mass T1. On the drawings of parts and in the Repair Rules, a tolerance is given for balancing parts, which is called unbalance (g/cm).
Flat parts with a small ratio of length to diameter are subjected to static balancing: a gear wheel of a traction gearbox, a refrigerator fan impeller, etc. Static balancing is carried out on horizontally parallel prisms, cylindrical rods or on roller bearings. The surfaces of prisms, rods and rollers must be carefully processed. The accuracy of static balancing largely depends on the condition of the surfaces of these parts.
Dynamic balancing. Dynamic balancing is usually performed on parts whose length is equal to or greater than their diameter. On fig. 2 shows a statically balanced rotor, in which the mass T is balanced by a load of mass M. This rotor, when rotating slowly, will be in equilibrium in any position. However, with its rapid rotation, two equal, but oppositely directed centrifugal forces F1 and F2 will arise. In this case, a moment FJU is formed, which tends to rotate the rotor axis at a certain angle around its center of gravity, i.e. there is a dynamic imbalance of the rotor with all the ensuing consequences (vibration, uneven wear, etc.). The moment of this pair of forces can only be balanced by another pair of forces acting in the same plane and creating an equal counteracting moment.
To do this, in our example, it is necessary to attach to the rotor in the same plane (vertical) two loads with masses Wx = m2 at an equal distance from the axis of rotation. The weights and their distances from the axis of rotation are selected so that the centrifugal forces from these weights create a moment /y counteracting the moment FJi and balancing it. Most often, balancing weights are attached to the end planes of the parts or a part of the metal is removed from these planes.
Rice. 2. Scheme of dynamic balancing of parts:
T is the mass of the rotor; M is the mass of the balancing load; F1,F2 - unbalanced, reduced to the planes of the mass of the rotor; m1,m2 are balanced rotor masses reduced to planes; P1 P 2 - balancing centrifugal forces;
During the repair of diesel locomotives, such fast-rotating parts as the rotor of a turbocharger, the armature of a traction motor or other electric machine, the impeller of the blower assembly with the drive gear, the shaft of the water pump assembly with the impeller and gear wheel, cardan shafts of the drive of power mechanisms are subjected to dynamic balancing.
Rice. 3. Scheme of a cantilever type balancing machine:
1 - spring; 2 - indicator; 3 anchor; 4 - frame; 5 - machine support; 6 - bed support;
I, II - planes
Dynamic balancing is underway on balancing machines. A schematic diagram of such a cantilever type machine is shown in fig. 3. Balancing, for example, the armature of the traction motor is carried out in this order. Anchor 3 is placed on the supports of the swinging frame 4. The frame rests at one point on the support of the machine 5, and the other on the spring 1. When the anchor rotates, the unbalanced mass of any of its sections (except for the masses lying in the plane II - II) causes the frame to swing. The frame oscillation amplitude is fixed by indicator 2.
In order to balance the anchor in the I-I plane, test weights of various masses are attached to its end face from the side of the collector (to the pressure cone) in turn and the frame oscillations are stopped or reduced to an acceptable value. Then the anchor is turned over so that the plane I-I passes through the fixed support of the bed 6, and the same operations are repeated for the plane II-II. In this case, the balance weight is attached to the rear thrust washer of the anchor.
After completion of all work on the acquisition, the parts of the selected kits are marked (letters or numbers) according to the requirements of the drawings.
Kausov M.A - editorial staff
Reliable and serviceable operation of rotating mechanisms depends on a large number of factors, such as: the alignment of the shafts of the unit; condition of bearings, their lubrication, fit on the shaft and in the housing; wear of housings and seals; gaps in the flow path; production of gland bushings; radial battle and shaft deflection; imbalance of the impeller and rotor; pipeline suspension; serviceability of check valves; condition of frames, foundations, anchor bolts and much more. Very often, a small defect is missed, like a snowball pulling others along, and as a result, equipment failure. Only taking into account all the factors, accurately diagnosing them in a timely manner, and observing the requirements of the specifications for the repair of rotating mechanisms, it is possible to achieve trouble-free operation of the units, ensure the specified operating parameters, increase the overhaul life, and reduce the level of vibration and noise. It is planned to devote a number of articles to the topic of repair of rotating mechanisms, which will address issues of diagnostics, repair technology, design modernization, requirements for repaired equipment and rationalization proposals to improve the quality and reduce the complexity of repairs.
In the repair of pumps, smoke exhausters and fans, it is difficult to overestimate the importance of precise balancing of the mechanism. How amazing and joyful to see the once rumbling and shaking machine, which was pacified and calmed by a few grams of counterweight, carefully installed in the “right place” by skillful hands and a bright head. You involuntarily think about what grams of metal mean on a fan wheel radius and thousands of revolutions per minute.
So what is the reason for such a sharp change in the behavior of the unit?
Let's try to imagine that the entire mass of the rotor together with the impeller is concentrated at one point - the center of mass (center of gravity), but due to manufacturing inaccuracies and uneven material density (especially for cast iron castings), this point is shifted some distance from the axis of rotation ( Figure No. 1). During the operation of the unit, inertial forces arise - F, acting on the displaced center of mass, proportional to the mass of the rotor, the displacement and the square of the angular velocity. It is they who create variable loads on the supports R, rotor deflection and vibrations, leading to premature failure of the unit. The value equal to the product of the distance from the axis to the center of mass by the mass of the rotor itself is called static imbalance and has the dimension [G x cm].
Static balancing
The task of static balancing is to bring the center of mass of the rotor to the axis of rotation by changing the mass distribution.
The science of rotor balancing is vast and varied. There are methods of static balancing, dynamic balancing of rotors on machine tools and in their own bearings. They balance a variety of rotors from gyroscopes and grinding wheels to turbine rotors and ship crankshafts. A lot of fixtures, machine tools and devices have been created using the latest developments in the field of instrumentation and electronics for balancing various units. As for the units operating in the thermal power industry, the regulatory documentation for pumps, smoke exhausters and fans imposes requirements for static balancing of impellers and dynamic balancing of rotors. For impellers, static balancing is applicable, because when the wheel diameter exceeds its width by more than five times, the remaining components (torque and dynamic) are small and can be neglected.
To balance the wheel, you need to solve three problems:
1) find the very "right place" - the direction in which the center of gravity is located;
2) determine how many “cherished grams” of the counterweight are needed and at what radius they should be placed;
3) balance the imbalance by adjusting the mass of the impeller.
Devices for static balancing
Static balancing devices help to find the place of imbalance. You can make them yourself, they are simple and inexpensive. Let's look at some constructions.
The simplest device for static balancing are knives or prisms (Figure No. 2), installed strictly horizontally and in parallel. Deviation from the horizon in the planes parallel and perpendicular to the axis of the wheel should not exceed 0.1 mm per 1 m. The level of "Geological exploration 0.01" or the level of the corresponding accuracy can serve as a means of verification. The wheel is put on a mandrel with polished support necks (you can use a shaft as a mandrel, after checking its accuracy in advance). The parameters of the prisms from the conditions of strength and rigidity for a wheel weighing 100 kg and a mandrel neck diameter d = 80 mm will be: working length L = p X d = 250 mm; width about 5 mm; height 50 - 70 mm.
Mandrel necks and working surfaces of prisms should be ground to reduce friction. Prisms must be fixed on a rigid base.
If the wheel is allowed to freely roll over the knives, then after stopping the center of mass of the wheel will take a position that does not coincide with the bottom point, due to rolling friction. When the wheel rotates in the opposite direction, after stopping it will take a different position. The average position of the lower point corresponds to the true position of the center of mass of the device (Figure #3) for static balancing. They do not require precise horizontal installation like knives and rotors with different pin diameters can be mounted on discs (rollers). The accuracy of determining the center of mass is less due to additional friction in the roller bearings.
Devices are used for static balancing of rotors in their own bearings. To reduce friction in them, which determines the accuracy of balancing, vibration of the base or rotation of the outer rings of the support bearings in different directions is used. 
Balancing scales.
The most accurate and at the same time complex static balancing device is a balancing scale (Figure No. 4). The design of weights for impellers is shown in the figure. The wheel is mounted on a mandrel along the axis of the hinge, which can swing in one plane. When the wheel rotates around the axis, in various positions it is balanced with a counterweight, by the value of which the place and imbalance of the wheel are found. 
Balancing Methods
The amount of imbalance or the number of grams of corrective mass is determined in the following ways:
-selection method, when by installing a counterweight at a point opposite to the center of mass, the wheels are balanced in any position;
-trial mass method - Mp, which is set at a right angle to the "heavy point", while the rotor will turn through an angle j. The corrective mass is calculated by the formula Mk \u003d Mn ctg j or 
will be determined by the nomogram (Figure No. 5): through the point corresponding to the test mass on the Mn scale, and the point corresponding to the angle of deviation from the vertical j, a straight line is drawn, the intersection of which with the Mk axis gives the value of the corrective mass.
As a test mass, you can use magnets or plasticine.
Round trip method
The most detailed and most accurate, but also the most laborious, is the round trip method. It is also applicable to heavy wheels, where a lot of friction makes it difficult to accurately determine the location of the imbalance. The surface of the rotor is divided into twelve or more equal parts, and a test mass Mn is sequentially selected at each point, which sets the rotor in motion. Based on the data obtained, a diagram is built (Figure No. 6) of the dependence of Mp on the position of the rotor. The maximum of the curve corresponds to the “easy” place, where it is necessary to set the corrective mass Мк = (Мп max + Мп min)/2. 
Ways to eliminate imbalance
After determining the location and magnitude of the imbalance, it must be eliminated. For fans and smoke exhausters, the imbalance is compensated by a counterweight, which is installed on the outer side of the impeller disk. Most often, electric welding is used to secure the load. The same effect is achieved by removing metal in a “heavy” place on the impellers of pumps (according to the requirements of technical specifications, metal removal to a depth of no more than 1 mm in a sector of no more than 1800 is allowed). At the same time, they try to correct the imbalance at the maximum radius, since with an increase in the distance from the axle, the influence of the mass of the corrected metal on the balance of the wheel increases.
Residual imbalance
After balancing the impeller, due to measurement errors and inaccuracies of the devices, a shift in the center of mass remains, which is called residual static unbalance. For impellers of rotating mechanisms, the regulatory documentation specifies the permissible residual imbalance. For example, for the wheel of the network pump 1D1250 - 125, a residual imbalance of 175 g x cm is set (TU 34 - 38 - 20289 - 85).
Comparison of balancing methods on different devices
The specific residual imbalance can serve as a criterion for comparing the balancing accuracy. It is equal to the ratio of the residual imbalance to the mass of the rotor (wheel) and is measured in [µm]. Specific residual imbalances for various methods of static and dynamic balancing are summarized in Table No. 1.
Of all the static balancing devices, the balance gives the most accurate result, however, this device is the most complex. The roller device, although more difficult to manufacture than parallel prisms, is easier to operate and gives a result not much worse.
The main disadvantage of static balancing is the need to obtain a low coefficient of friction at high loads from the weight of the impellers. Increasing the accuracy and efficiency of balancing pumps, smoke exhausters and fans can be achieved by dynamic balancing of rotors on 
machine tools and in our own bearings.
Applying static balancing
Static balancing of impellers is an effective means of reducing vibration, bearing stress and increasing machine life. But it is not a panacea for all ills. In “K” type pumps, one can limit oneself to static balancing, and for the rotors of “KM” monoblock pumps, dynamic balancing is required, since there is a mutual influence of imbalances between the wheel and the rotor of the electric motor. Dynamic balancing is also necessary for the rotors of electric motors, where the mass is distributed along the length of the rotor. For rotors with two or more wheels, having a massive connecting half-coupling (for example, SE 1250 - 140), the wheels and the clutch are balanced separately, and then the rotor assembly is dynamically balanced. In some cases, to ensure the normal operation of the mechanism, it is necessary to dynamically balance the entire unit in its own bearings.
Precise static balancing is necessary, but sometimes not enough the basis for reliable and durable operation of the unit.
At high speeds of rotation, even a slight unbalanced mass of the part relative to the axis of rotation can cause a significant unbalanced centrifugal force, causing an additional dynamic load on the bearings, which leads to premature wear of the parts. Unbalanced centrifugal forces are one of the main causes of hydraulic transmission vibration, which is a very harmful phenomenon.
Static balancing. An indicator of the static balance of a part is its ability to maintain a state of rest in any position on horizontal guides. The part to be balanced is installed in such a way that the unbalanced mass R (Fig. 41) is located in a horizontal plane passing through the axis of the part to be balanced. On the opposite side of the part, a load n is attached, at which the unbalanced mass R could tell the balanced part to rotate through a small angle. Then the part to be balanced is rotated in the same direction by 180°, i.e., in such a position that the load n and the mass R would again be in the horizontal plane. In this case, the mass R will outweigh and the product will tend to turn in the opposite direction. Next, an additional load P is selected to the load so that the item to be balanced remains in the position in which it is placed.
If static balancing is performed on rolling prisms, then the resulting friction forces at the support points
Rice. 41. The static balancing scheme of the part prevents the part from rolling. The balancing accuracy depends on the ratio of the torque generated by the unbalanced mass and the torque of the friction forces at the support points.
dynamic balancing. The rotating parts of a hydraulic transmission, in the form of rotors, although statically balanced, can be unbalanced, which contributes to the wear of the shaft journals and bearings, as well as the appearance of vibrations that can lead to the destruction of parts. Unbalanced masses create centrifugal forces. Regardless of the location in the rotor (for example, a shaft assembled with pump wheels) of unbalanced masses, their size and quantity, the total action is reduced to two forces acting on the supports, different in magnitude and direction. These forces cause the bearings to vibrate, and through them the hydraulic transmission housings.
For dynamic balancing, machines of the Minsk Machine Tool Plant are used. The imbalance is eliminated by drilling or removing metal in technologically provided places (correction planes).
The tasks of dynamic balancing are to choose a plane for correcting unbalanced masses and to determine the magnitude and position of the reduced unbalanced masses in these planes.
The simplest device for dynamic balancing consists of two elastic bearing supports (Fig. 42, a). One of the supports is locked with the help of appropriate devices during balancing, and the other is allowed to freely oscillate in the vertical plane, and when the resonance passes, the amplitude of oscillations of this support is measured. Dividing the circumference of one of the wheels into eight equal parts and numbering them (Fig. 42, b), install a test load in turn in each of the numbered places (at the same radius) and measure the range of resonant vibrations with each installation of the test load.
The measurement results are recorded and applied in a rectangular coordinate system (Fig. 42, c), which is used to judge the position and size of the balancing load. The lowest point of the obtained curve (point K) determines the location of the equation
Rice. 42, Scheme of dynamic balancing of a weighing load. By several attempts to change the load at a given point, the mass of the balancing load is determined.
Having balanced the part in one plane, the same is done when it is balanced in another plane. Installing a balancing weight on the other side causes an imbalance on the first side. Therefore, a second check is made with the installation of the necessary additional corrective weight, which would compensate for the imbalance.
When rotating parts and assemblies operating at high speeds, unbalanced centrifugal forces arise, creating an additional load on parts and supports. The result is vibration that causes premature wear and failure. The imbalance (unbalance) of the part occurs due to the asymmetrical placement of the mass relative to the axis of rotation when its dimensions deviate from those specified according to the drawing, the different density of the metal in individual parts of the part and the complexity of the part shape. The unbalance of the part is estimated by the value of the moment of the unbalanced mass about the axis of rotation.
The magnitude of the centrifugal force causing vibration is determined as follows:
where m- unbalanced mass; ω - angular speed of rotation of the part, rad/sec; Q- weight of the rotating part, N; q- acceleration of gravity, cm/sec2 (m/sec2); r- the value of the displacement of the center of gravity of the part, cm (m); n- frequency of rotation of the part per second, rev / sec.
Static balancing. Static balancing of parts is carried out on prisms or rollers. If the unbalanced part is installed on prisms or rollers, then under the influence of the weight of the unbalanced mass, a torque M k \u003d Q 1 r 1 is created, tending to rotate the part until its weighted side with the weight of the unbalanced mass Q 1 takes the lower position. The value of the weight of the balancing load Q 2 and its distance r 2 from the axis of rotation are selected in such a way that the equality is observed:
Q 1 r 1 = Q 2 r 2 where: Q 2 \u003d Q 1 r 1 / r 2,(68)
The practical elimination of the imbalance is done by removing an equivalent amount of metal from the weighted side by drilling, milling, scraping, filing, or attaching a corrective weight, which, however, is rare.
The accuracy of balancing parts on prisms depends on the friction force that occurs between the prisms and the necks of the shafts or mandrels on which the tested parts are mounted. Therefore, to improve the balancing accuracy, it is necessary to harden the working surfaces of the prisms and the neck of the mandrels to a high hardness HRC 50-56 and finish grinding. The working length of the prisms is taken within (2-2.5) πD, where D is the diameter of the neck of the mandrel in cm.
In static balancing on rollers, the roller devices used are equipped with ball or roller bearings. The process of static balancing on rotating rollers is carried out in the same way as on prisms. The balancing accuracy on the rollers depends on the dID ratio (Fig. 42). The smaller this ratio, the more accurate the balancing.
Depending on the mass of the parts to be balanced, the following roller sizes are used: with a mass of up to 250 kg D = 100 mm l = up to 40 mm;
with a mass of up to 1,500 kg D = 150 mm l = up to 70 mm.
Static balancing is applied to parts that have a small length and a relatively large diameter: pulleys, flywheels, clutch discs.
Fig.42. Scheme of static balancing on rollers 
Fig.43. Dynamic imbalance
dynamic balancing. For parts whose length significantly exceeds the diameter (crankshafts and cardan shafts), dynamic balancing is used. If the part, statically balanced by weights Q 1 and Q 2 (Fig. 43), located diametrically opposite, is rotated around the axis, then two oppositely directed centrifugal forces I 1 and I 2 will appear at its ends, forming a pair of forces. These centrifugal forces tend to push the part out of its supports, loading them and causing vibrations to occur. The magnitude of the dynamic imbalance will be the greater, the greater the length of the arm of the perturbing pair of forces.
For the dynamic balance of the part, it is necessary to install equal weights Q 1 ’ and Q 2 ’ at the points opposite to the areas of placement of goods Q 1 and Q 2 . The part can be balanced with weights G 1 and G 2 installed in any plane perpendicular to the axis of the shaft, provided that the moments of centrifugal forces arising from these weights during the rotation of the part will be equal to the moments of centrifugal forces J 1 and J 2 formed from loads Q 1 and Q 2 .
Thus, dynamic balancing consists in creating an additional pair of forces with the help of balancing weights. From what has been said, it follows that in such details as pulleys, clutch discs, flywheels, there cannot be a large leverage of a pair of forces, therefore their dynamic imbalance is less than static. Due to the large diameter, the static imbalance of these parts can be significant, which is why they are subjected to this type of balancing. Conversely, for crankshafts and cardan shafts, dynamic imbalance is much more important. Dynamic balancing of parts is carried out on special machines manufactured by the industry.
To balance any rotating part, it is necessary that its center of gravity lies on the axis of rotation, and the centrifugal moments of inertia are equal to zero. The discrepancy between the center of gravity of the part and the axis of rotation is called static imbalance, and the inequality zero centrifugal moments of inertia - dynamic imbalance.
4.1 Static balancing of parts
Static imbalance is easily detected when the part is mounted with support journals on parallels or rollers. Usually, parts are subjected to static balancing, whose diametrical dimensions are much larger than the length along the axis of rotation (flywheels, disks, pulleys, impellers, etc.), since in this case the dynamic component can be neglected.
During static balancing, the installation of test weights determines the places and magnitude of the imbalance. Unbalance is eliminated by removing an equivalent amount of material from the part or by installing corrective weights. Excess material for massive parts (flywheels) is removed by drilling or milling, and for thin-walled parts (pulleys, disks, rotors) - by eccentric turning or grinding.
After the imbalance is eliminated, a second (control) balancing is performed. If the residual imbalance exceeds the value allowed by the technical requirements, the balancing is repeated
4.2 Dynamic balancing of parts
Dynamic balancing is applied to rotating parts or assemblies operating at high speeds, in which the length along the axis of rotation exceeds the diametrical dimensions (for example, beater drums of combine harvesters or to bent shafts of engines).
Even in a statically balanced part, there may be an uneven distribution of mass along the length relative to the axis, which, at a significant rotation frequency, creates a moment of centrifugal forces on the arm L (see Figure 1) and, consequently, additional loads on the supports and vibration.
Unbalance is detected on special balancing machines when the part rotates at operating speeds and is eliminated, as in static balancing, only in two or more correction planes, selected depending on the design of the part.
Dynamic balancing eliminates the need to perform static balancing.
To perform dynamic balancing, installations are required that ensure the rotation of the part, control of the centrifugal forces of unbalanced masses or the moments of these forces acting on the supports, as well as identifying the plane of location of the unbalanced masses.
Figure 1 Bringing the rotor acting on the rotor to two planes of force correction
This circumstance is precisely used in the dynamic balancing of parts. For balancing, two planes are chosen on the part, perpendicular to the axis of rotation and convenient for installing balancing weights or removing part of the part material - the so-called correction plane. The machine is set up so that it is possible to determine the location and size of the weights that should be added (or removed) in each of the planes to fully balance the part.
Dynamic imbalance is detected on balancing machines. In the repair industry, electric balancing machines with elastic supports are most widely used (see Figure 2).
The unbalanced masses of the part cause mechanical vibrations of the movable supports (1). With the help of sensors (2) these mechanical vibrations are converted into electrical ones. Moreover, the voltage of the electric current in the sensor is directly proportional to the magnitude of the mechanical oscillation of the support, i.e. imbalance. In the measuring device (3), the current is amplified and read on the milliammeter (4) as unbalance readings.
Figure 2 Diagram of a machine for dynamic balancing of crankshafts:
1 - movable supports (cradles); 2 - oscillation sensor; 3 amplification and measurement unit; 4 - milliammeter; 5 - strobe lamp; 6 - electric motor; 7 - strobe limb; 8 - dial reading the angle of rotation of the shaft.
The angular arrangement of unbalanced masses is determined by a stroboscopic device. The strobe lamp is controlled by the voltage of the vibration sensor, and each time the unbalanced mass vector passes the horizontal plane from the front side of the machine, the lamp (5) flashes and reflects a certain number on the strobe dial (8). Due to the stroboscopic effect, the numbers on the dial appear to be stationary.