imbalance (imbalance) rotating parts is one of the factors limiting the reliability of vehicles in operation. imbalance- a condition characterized by such a distribution of masses that causes variable loads on the supports, increased wear and vibration, contributes to the rapid fatigue of the driver.
Product imbalance is a vector quantity equal to the product of the local unbalanced mass m and the distance to the product axis r or the product of the product weight G and the distance from the product axis to the center of mass e, i.e. D = mr = Ge.
Types of imbalance
a - static, b - dynamic, mixed.
It is carried out when parts, assembly of components and assemblies occur during the manufacturing (recovery) process and changes its quantitative value during operation and maintenance.
Depending on the relative position of the axis of the product and its main central axis of inertia, there are three types of imbalance: static, moment and dynamic.
With static imbalance the axis of rotation OB of the part is displaced by eccentricity e and is parallel to the main central axis of inertia. This imbalance is inherent in disc-shaped parts (flywheels, clutch discs, pulleys, impellers, clutch assemblies, etc.) and manifests itself both in a static and dynamic state. Static imbalance is determined by the main vector of imbalances (static imbalance).
With momentary imbalance the product axis and its main central axis of inertia intersect at the center of mass. This imbalance is determined by the main moment of imbalances M or by two antiparallel vectors of imbalances equal in value in two arbitrary planes.
Momentary unbalance is a special case of a more general one - dynamic imbalance, in which the axis of the product and its main central axis do not intersect at the center of mass or intersect. It is inherent in parts and assemblies of the shaft type, consists of static and moment imbalances and is determined by the main imbalance vector and the main imbalance moment or by two reduced imbalance vectors (generally different in value and non-parallel) lying in two selected planes.
Imbalance products characterized by a numerical value (in g - mm, g cm, kg-cm) and an unbalance angle (in degrees) in the coordinate system associated with the axis of the product.
The main imbalance vector Bn can be decomposed into two parallel DCTl and Dm2 applied in the selected planes, and the main imbalance moment M can be replaced by the moment of a pair of equal antiparallel imbalances C,1 and DM2 in the same planes. Geometric sums Dt! + Ai = D and Dt2 + A2 = A form two reduced imbalances A and A in the selected planes, which completely determine the dynamic imbalance of the product.
When an unbalanced product rotates, a centrifugal force of inertia that is variable in magnitude and direction arises. Bringing products with imbalance into a balanced state is carried out by their balancing, i.e., determining the imbalance of the product and eliminating (reducing) it by removing or adding corrective masses at certain points. Depending on the type of imbalance of the body, two types of balancing are distinguished: static and dynamic.
Static balancing.
Static balancing is carried out on stands with prisms or rollers or on special machines for static balancing in dynamic mode (when the body rotates). Such balancing improves the balancing accuracy and opens up the possibility of process automation.
Dynamic balancing of rotating parts
With such balancing, two reduced imbalances A and A in the selected correction planes are determined and eliminated (reduced) by removing or adding two reduced corrective masses, generally different in value and located at different correction angles, in the coordinate system associated with the axis of the part. Dynamic balancing eliminates (reduces) both static and momentary imbalance, and the product becomes fully balanced.
Permissible imbalance of parts: crankshaft, cardan shaft, etc.
Static balancing called the alignment of the center of gravity of the part with its geometric axis of rotation. This is achieved by removing metal from the heavy part of the part, or by adding it by surfacing on its light part.
Flywheels, impellers of pumps, gear wheels and gears of gear drives of diesel plants, etc. are subjected to static balancing.
The rotation of parts with an unbalanced mass leads to the appearance of a centrifugal force or a pair of forces, which cause the mechanism to vibrate during its operation. Centrifugal force occurs when the center of gravity of the part does not coincide with its axis of rotation.
The scheme of action of centrifugal force when the center of gravity is shifted:
The unbalanced centrifugal force creates additional loads on the bearings, the magnitude of which can be determined by the formulas:
Where P1, P2— additional loads on bearings;
a, in- distance from the plane of action of the force WITH respectively to the left and right bearings, mm;
l— distance between bearing axes, mm.
The magnitude of the centrifugal force can be determined through the mass of the part and the amount of displacement of the center of gravity of the part relative to the axis of its rotation by the formula:
Where G- mass of the part, kg;
q— acceleration of gravity (9.81 m/s2);
w is the angular velocity (w = P on n/ 30, where n- rotation frequency, min - 1);
r- distance from the center of gravity to the axis of rotation of the part, m.
For example, the center of gravity "0" of a rotating disk weighing 30 kg with a rotation speed of 3000 min - 1 is displaced from the center of the axis by r= 1 mm. Then the unbalanced centrifugal force is obtained:
that is, the axle load is 10 times the mass of the part itself. It follows that even a slight shift in the center of gravity can cause large additional loads on the bearings.
Static balancing is carried out on special stands. The main parts of the stand are knives (prisms), rollers or rolling bearings, on which the balanced part is mounted on the mandrel. Knives, rollers or bearings are placed in the same horizontal plane.
Static balancing of parts operating at a speed of up to 1000 min - 1 is carried out in one stage, and parts operating at a higher speed - in two stages.
At the first stage, the part is balanced to its indifferent state, that is, such a state in which the part stops in any position. This is achieved by determining the position of the heavy point, and then, from the opposite side, a balancing weight is selected and fixed. A piece of plasticine, putty, mastics, etc. is used as a balancing weight.
After balancing the part on its light side, instead of a temporary load, a permanent load is attached, or an appropriate amount of metal is removed from the heavy side, the scheme for installing temporary and permanent loads is shown in the figure:
Scheme of installation of temporary (P1) and permanent (P2) cargo:
B is a hard point.
Sometimes the place of installation of the balancing temporary weight is changed, which is accompanied by a change in the radius of its installation and, as a result, a change in its mass. The value of the mass of the constant balancing weight is determined from the balancing of the moments:
Where P1- mass of temporary cargo;
R2- mass of permanent cargo;
R, r are the installation radii of temporary and permanent loads, respectively.
For parts with a speed of up to 1000 min - 1 balancing is completed here.
The second stage of balancing is to eliminate the residual imbalance (imbalance) remaining due to the inertia of the part and the presence of friction between the mandrel and the supports. To do this, the end surface of the part is divided into six to eight equal parts, numbering them.
Part static balancing diagram:
a - marking the circumference of the end face of the part and the place of installation of the goods; b - development of the circle and the balancing curve.
Then the part with temporary load is installed so that point 1 is in the horizontal plane. At this point, the load is fixed, increasing its mass until the part leaves the state of equilibrium (rest) and begins to slowly rotate. The cargo is removed and weighed on the scales.
In the same sequence, work is performed for the remaining points of the part. The obtained values of the mass of goods are entered in the table:
Mass values of weights at the points of their installation on the part ( r):
According to the table, a curve is built, which, if balancing is performed accurately, should have the shape of a sinusoid. On this curve, the points of maximum (A max) and minimum (A min) are found.
The maximum point of the curve corresponds to the light part of the part, and the minimum point corresponds to the hard part of the part.
The mass of the balancing weight (imbalance) is determined by the formula:
Static balancing is considered satisfactory if:
Where TO is the mass of the unbalance of the part, g;
R- radius of installation of temporary cargo, mm;
G— weight of the part to be balanced, kg;
l st— the maximum allowable displacement of the center of gravity of the part from the axis of its rotation, microns.
The maximum allowable displacement of the center of gravity of the part is found from the diagram of the maximum allowable displacement of the center of gravity of the parts during static balancing.
Diagram of maximum allowable displacements of the center of gravity of parts during static balancing:
1 - for gear wheels, hydraulic clutch disks, propellers with a turbo drive; 2 - propellers of diesel installations, flywheels, impellers of centrifugal pumps and fans.
If the condition of the equation is met, then the balancing process ends here and the unbalance load on the part is not set. If the condition of the equation is not met, then the resulting mass of the weight "K" is set at point A max (radius 2) or removed at point A min (radius 6).
The quality of balancing parts is checked during operation of the diesel engine by its vibration.
The main source of machine vibration isrotor imbalance , which always takes place, due to the fact that the axis of rotation and the axis of inertia, passing through the center of mass, do not coincide. The unbalance of the rotors is divided into the following three types.
Static imbalance is an imbalance in which the rotor axis and its main central axis of inertia are parallel (see Fig. 1).
Fig.1
Momental imbalance is an imbalance in which the rotor axis and its main central axis of inertia intersect at the center of mass of the rotor (see Fig. 2).
Fig.2
Dynamic imbalance is an imbalance in which the rotor axis and its main central axis of inertia do not intersect at the center of mass or cross (see Fig. 3). It consists of static and momentary unbalance.
Note:Here and below, italicized terms and definitions established by GOST 19534 - 74. Balancing of rotating bodies. Terms.
Fig.3
A particular case of dynamic imbalance is quasi-static imbalance, in which the rotor axis and its main central axis intersect not at the center of mass of the rotor.
The centrifugal force caused by unbalance is determined by the formula:
Ftsn = P/g w 2 r = P/g (?n/30) 2 r, (1)
where w = 2?f = ?n/30 is the angular velocity,
f is the number of revolutions of the rotor per second,
n is the number of revolutions per minute,
P is the weight of the rotor, q = 9.81m/sec2 is the free fall acceleration,
r is the radius of the unbalanced mass or the eccentricity modulus.
At high speeds, unbalanced masses can develop centrifugal forces to unacceptable values, which will lead to the destruction of the machine. For most machines, achieving an unbalanced centrifugal force of approx. 30% of the rotor weight is the limit.
The product of an unbalanced mass and its eccentricity is called unbalance. The imbalance is a vector quantity. The term "imbalance value" is more commonly used, which is equal to the product of the unbalanced mass and the modulus of its eccentricity.
Imbalances of the rotors during operation can be caused by wear of the working parts, changes in the fit of the disks, loosening of the fastening of the elements included in the rotors, deformation and other factors leading to displacement of the masses relative to the axis of rotation.
The unbalance value is usually indicated in gmm, gcm. 1gcm = 10gmm.
Sometimes the ratio of the unbalance value to the mass of the rotor is used to set the tolerance, calledspecific imbalance
. The specific unbalance corresponds to the eccentricity of the center of mass of the rotor.
e st \u003d D / m (2)
Imbalances are eliminated by balancing.Balancing is the process of determining the values and angles of rotor imbalances, and reducing them by adjusting the masses. In practice, two types of balancing have become widespread: static and dynamic.
2. Balancing. General information
Static balancing is usually carried out in one plane of correction and is applied mainly to disc rotors. It can be used if the ratio of the length of the rotor to its diameter does not exceed 0.25.The plane of correction is the plane perpendicular to the axis of the rotor, in which the center of the corrective mass is located. (mass used to reduce rotor imbalances).
During static balancing, the main rotor imbalance vector is determined and reduced, which characterizes its static imbalance. The main imbalance vector is equal to the sum of all imbalance vectors located in different planes perpendicular to the rotor axis (see Fig. 4).
For rotors whose lengths are commensurate with the diameters or exceed them, static balancing is ineffective, and in some cases can be harmful. For example, if the correction plane is at a considerable distance from the main imbalance vector, then by reducing the static imbalance, you can increase the moment imbalance.
Dynamic balancing -this is such a balancing, in which the imbalances of the rotor are determined and reduced, characterizing its dynamic imbalance (see Fig. 4). With dynamic balancing, both torque and static unbalance of the rotor are reduced simultaneously.
There are many balancing methods. All of them are based on the assumption of the linearity of the system, that is, the oscillation amplitudes are considered proportional to the imbalance value, and the phases are independent of its magnitude. There is single-plane and multi-plane balancing. With single-plane balancing, the calculation of corrective masses is performed sequentially for each correction plane, with multi-plane balancing - simultaneously.
Multi-plane balancing using the method of simultaneous measurement of the amplitudes and phases of vibrations is most common when balancing the rotors of units of the GTK 10-4 type. More precisely, the most common is two-plane balancing, which is a special case of multi-plane balancing. To calculate the corrective masses with this balancing method, it is necessary to perform at least three starts: one initial (zero) and two trial with unit (trial) masses m p1 , m p2 , set at distances r n1 , r n2 from the axis of rotation (see Fig. 5). The order and combinations of installations of test weights may be different.
Fig.5.
When using this balancing method, it is believed that the system allows the use of the superposition principle. The calculation of the corrective masses and their installation locations in such a system can be done in various ways: graphical, analytical or graphic-analytical.
Graphical and graphic-analytical calculations with the construction of fairly complex vector diagrams were widely used before the advent of balancing tools with microprocessors. Methods for performing such calculations can be found in the literature. At present, they are practically not used, since modern technology makes it easier, more accurate and faster to solve such problems.
Modern microprocessor technology with the help of software solves the calculation problem most often analytically. Let's consider what is the essence of solving this problem.
Oscillations of the rotor - support structure system can be described by a system of equations (at each start, two equations with six unknowns).
A0 = ? a1 D I +? a2 DII
B0 = ? c1 D I + ? c2 D II
A1 =? a1 (D I +r p1 m p1) + ? a2 DII
B1 = ? v1 (D I +r p1 m p1) + ? c2 D II (5)
A2 = ? a1 D I + ? a2 (D II + r p2 m p2 )
B2 = ? c1 D I + ? v2 (D II + r p2 m p2)
Where, A 0, A 1, A 2, B 0, B 1, B 2 - amplitudes of oscillations of supports "a", "b" at zero and trial starts, made at the same frequency.
? a1, ? a2, ? in 1 , ? at 2 – coefficients of influence, representing the vectors of oscillations of supports "a" and "b", caused by unit masses mp1, mp2.
D I , D II – initial imbalances in the selected correction planes I and II.
r p1 m p1 , r p2 m p2 - introduced imbalances due to the installation of single (trial) masses, in correction planes I and II.
Six vector quantities are unknown in these equations: D I , D II , ? a1, ? a2, ? at 2 , ? at 2 . To find them, it is necessary to solve the system of these equations. Determining the influence coefficients and corrective masses to compensate for the initial imbalances is a rather difficult task. However, the solution of such a problem with the help of modern means is carried out automatically in the process of launches. The influence coefficients determined from equations (5) can be used to calculate the corrective masses when balancing subsequent rotors of the same type without performing two test runs.
In cases where the number of correction planes is greater than 2 (for example, if one rotor with more than 2 supports is being balanced or coupled rotors are balanced), the number of test runs is determined by the number of correction planes, in each of which test masses are sequentially installed . The equations describing the oscillations of the system are formed in the same way as in two-plane balancing. The system of these equations and its solution become more complicated, since the number of influence coefficients increases due to the increase in the number of correction planes and the number of equations increases due to the increase in the number of starts.
Most often, dynamic balancing is carried out on balancing machines. Usually balancing on machines is carried out at a lower speed than the operating speed of the rotors. This is due to the technical capabilities of balancing machines. High-speed balancing machines are not widely used due to their high cost and high energy consumption. Balancing on low-speed machines is quite effective and provides high accuracy in cases where the rotors belong to the classrigid rotors. For flexible rotorsbalancing on low-speed machines is not always effective.
A rigid rotor is defined as a rotor that is balanced at a rotational speed less than the first critical one in two arbitrary correction planes and whose residual unbalance values will not exceed the allowable ones at all rotational speeds up to the highest operational one. Dynamic balancing of a rigid rotor is carried out, as a rule, in two planes.
A flexible rotor is defined as a rotor that is balanced at a speed less than the first critical speed in two arbitrary correction planes and whose residual unbalance values may exceed those allowed at other speeds up to the highest operating speed. . When balancing flexible rotors, as a rule, more than two correction planes are used.
3. Choice of tolerance and balancing accuracy
It is known from practice that vibration velocity is the most objective criterion for assessing vibration. Proceeding from this, most often the assessment and normalization of the vibration state is carried out according to the vibration velocity. Therefore, it is customary to set the balancing tolerance in such a way as to have an acceptable vibration velocity in the operating speed range. Based on these conditions, the allowable unbalance should change inversely with the rotor speed. That is, the higher the operating speed, the smaller the allowable unbalance should be. Therefore, the following dependency must be provided:
eating w = Const. , where e is the specific imbalance, w is the angular frequency.
It is assumed that the rotor and supports are rigid. The value of estw was taken as the determining factor in the classification of the balancing accuracy.
Rigid rotor balancing accuracy classes are established by GOST 22061-76 in accordance with the international standard ISO 1949.
According to this classification, each class is characterized by a constant value e st w. Each subsequent class differs from the previous one by 2.5 times. GOST 22061-76 establishes 13 accuracy classes; from zero to twelfth, for different groups of rigid rotors. Rotor gas pumping units belong to the 3rd class of accuracy. The values of permissible imbalances are calculated and set by the machine developer in accordance with GOST 22061-76.
4. Features of balancing large rotors
Balancing of large-sized OK TVD GTK 10-4 rotors has its own characteristics, although there are no regulatory documents establishing any separation of rotors depending on their dimensions. With large lengths (more than 4 meters) and large masses of rotors (weighing several tons), it is necessary to take into account the effect of thermal deformations on imbalances. With such dimensions, the temperature of the rotors is not the same at different points. This is due to the fact that there are always sources of thermal radiation and convection currents in production facilities. Yes, and the balancing machines themselves are such. Long rotors are especially sensitive to the slightest temperature difference in the radial direction. The conducted studies of the influence of thermal deformations of the rotors (OK HPT of the GTK 10-4 unit) on imbalances show that a temperature drop in the radial direction by 1ºС (with a rotor length of 4 meters or more) leads to thermal imbalances that are 5-10 times higher than the tolerance. To avoid balancing errors due to thermal deformations, it is necessary to provide preliminary thermal stabilization of the balanced rotors. In practice, this is done in the following way. The rotors supplied for balancing are kept in the room until its temperature equalizes with the ambient temperature. Then the rotor is mounted on the machine and set into rotation. The rotor weighing more than 5 tons must be kept in the continuous rotation mode (or in the start-stop-start mode) for at least 2 hours and only after that it should be balanced. During rotation, the temperature is equalized in the radial direction. If balancing was interrupted for some reason (stopping rotation for about 1 hour or more), then its completion should be preceded by a rotor rotation operation to equalize the temperature in the radial direction. For breaks of less than 2 hours, the rotation time to equalize the temperature requires no more than the break time.
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Sources of information taken into accountwhen compiling a methodological manual for balancing rotors.
GOST 19534 - 74. Balancing of rotating bodies. Terms.
GOST 22061 - 76 System of balancing accuracy classes and guidelines.
Guidelines for balancing rotors GTU on a balancing machine and in their own bearings. "Orgenergogaz" M., 1974.
Vibrations in technology. T.6. Vibration and shock protection. Ed. Corresponding Member USSR Academy of Sciences K.V. Frolova. M. "Engineering", 1981
Sidorenko M.K. Vibrometry of gas turbine engines.
Large parts such as pulleys, flywheels, rotors, and blowers rotating at high speeds must be well balanced to avoid wobble, vibration, misalignment, and increased stress on bearings. There are three types of imbalance:
Unbalance caused by the shift of the center of gravity of the part relative to the axis of rotation, in which the force of inertia is reduced to one resultant centrifugal force. Such an imbalance is typical for parts with a small axial length compared to the diameter (flywheels, pulleys, gear wheels) and is eliminated by static (single-plane) balancing;
Unbalance, in which the forces of inertia are reduced to a resultant pair of forces that creates a centrifugal moment of inertia about the axis of rotation;
Unbalance, in which the forces of inertia are reduced
To the resultant force and to the pair of forces.
The second and third types of unbalance are typical for parts that have a significant length compared to the diameter (rotors) and are eliminated by dynamic (two-plane) balancing.
It is believed that the permissible displacement of the center of gravity is equal to
The quotient of 2-10 divided by the square of the speed of the part.
static or force balancing is based on the use of a static unbalanced moment, under the action of which the part rotates until the heaviest part is vertically under the axis of rotation of the part and it becomes possible to balance by installing additional weights on the diametrically opposite side of the part or by lightening the heaviest part of the part. Static balancing is performed by mounting the part on prisms, rotating supports, scales or directly at the installation site of the part. Sometimes the part is pre-fixed on the mandrel. Balancing prisms, manufactured with high precision from hardened steel, are installed on the balancing device in parallel and horizontally with an accuracy of 0.02 mm / m. The balancing process consists of two operations.
First operation is to correct the underlying imbalance. To do this, the circumference of the end face of the part to be balanced is divided into 6-8 parts and, turning the part on prisms by 45 °, each time they find and mark the lower point, i.e. the heaviest part. If at the same time the same point occupies the lower position, then a diameter is drawn through it and, picking up a load at its opposite end, the imbalance is compensated, i.e., an indifferent equilibrium is reached. The load can be putty or small pieces of metal glued to the part. Then the temporary weights are replaced by permanent ones, firmly fixed to the part in the right place, and the correct balancing is controlled. Sometimes, on the contrary, the weighted parts of the part are lightened by drilling small recesses.
Second operation consists in determining the residual imbalance due to the presence of friction forces between the prisms and the mandrel or eliminating the so-called undetected imbalance. At the same time, on each of the marked divisions, the weights are fixed alternately in the horizontal plane at points equally distant from the center, until the part begins to rotate on the prisms. The masses of test weights are entered in the table, and on its basis a curve is built that fixes the extreme points that correspond to the largest difference in weights (Fig. 7.16). The lowest point of the curve corresponds to the heaviest part of the part. The final balancing weight must be installed in a diametrically opposite place. The value of the load is determined by the formula
Q(^max -
Where Q - the size of the cargo; Amax And Aiin - respectively, the maximum and minimum mass of loads located on the same diameter.
An additional weight is attached to the part at the point corresponding to the highest point of the curve, and a final check is made, determining the residual unbalance. The permissible value of static imbalance depends on the design of the machine and its mode of operation. The accuracy of static balancing on prisms makes it possible to detect a residual displacement of the center of gravity of the part from the axis of rotation by 0.03-0.05 mm, and on balancing scales up to 5 microns.
Dynamic bachelor are carried out at machine-building plants, since it is difficult to implement it under the conditions of installation and repair in the workshops of dairy industry enterprises.
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