CN111898238B - Constraint high-speed dynamic balance mechanics resolving method - Google Patents
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Abstract
A constrained high-speed dynamic balance mechanics solution method, comprising: calculating an influence coefficient through driving, trial weight and measurement, and establishing an influence coefficient matrix; according to the constraint condition of the dynamic balance standard, establishing a Lagrangian function: solving the optimal value of the counterweight by using a KKT condition; and performing weight addition and subtraction operation, and driving to correct the dynamic balance result. According to the invention, by adding the constraint to the intensity value under the key rotating speed, the intensity value of the key rotating speed is further reduced on the premise of ensuring the whole vibration reduction, and the stable operation of the rotor is ensured. The method is suitable for dynamic balance mechanical calculation of the turbomachinery rotor with high requirement on residual unbalance and working rotating speed at least exceeding first-order critical rotating speed. Low-cost operability of constrained high-speed dynamic balance solution can be achieved. The operator only needs to input the magnitude of the constraint severity value on a program panel, and the magnitude and the phase of the balance weight and the estimated value of the residual unbalance can be obtained through full-automatic calculation and analysis of the program.
Description
Technical Field
The invention relates to a dynamic balance mechanics calculating method. In particular to a constrained high-speed dynamic balance mechanical resolving method suitable for a turbomachine rotor.
Background
Dynamic balance is an important link for testing and correcting before delivery of turbine machinery, and fundamental frequency vibration caused by unbalance due to factors such as manufacturing tolerance is reduced by performing dynamic balance (weight adding and reducing) correction on a rotor. Dynamic balance before leaving a factory is usually developed based on a dynamic balance testing machine, and a rotor can be continuously in service after being remanufactured and also through dynamic balance correction. The traditional dynamic balance theory is quite mature, an ABC method is generally used for low-speed dynamic balance (rigid dynamic balance), and an influence coefficient method is generally used for high-speed dynamic balance, and the unbalance characteristic of the system is obtained through least square calculation to correct.
At present, with the technical transition of turbomachinery rotors from slow turbines to fast turbines, the traditional dynamic balance method has certain defects, and the ABC method is based on the rigid assumption of rotors, namely the working rotating speed is far from reaching the critical rotating speed, and the rigid assumption cannot be realized necessarily with the increase of the working rotating speed; although the influence coefficient method is suitable for the high-speed dynamic balance working condition, the influence coefficient method takes the mean square sum of the measured amplitudes as an objective function, the implementation process is heavy, the overall energy of the system is required to be reduced, and whether the intensity value under the key rotating speed meets the requirement or not cannot be effectively ensured.
The objective function of the existing unbalance method is to reduce the vibration amplitude of the whole system, and whether the intensity value under the key rotating speed meets the requirement or not cannot be effectively ensured.
Therefore, a high-speed dynamic balance technology needs to be developed, which can effectively perform high-speed dynamic balance correction on a system and can meet special requirements of different types of rotors. The high-speed dynamic balance detection process technology developed by the method can break through the blockade of the technology and equipment in western developed countries, expand the application products of the existing dynamic balance technology from sliding bearing series to rolling bearing series electromechanical equipment including aero-engines, and expand the service field and range of the electromechanical equipment.
Disclosure of Invention
The invention aims to solve the technical problem of providing a constrained high-speed dynamic balance mechanical calculation method which can give consideration to both the precision and the operability of high-speed dynamic balance.
The technical scheme adopted by the invention is as follows: a constrained high-speed dynamic balance mechanical resolving method comprises the following steps:
1) calculating an influence coefficient through driving, trial weight and measurement, and establishing an influence coefficient matrix;
2) according to the constraint condition of the dynamic balance standard, establishing a Lagrangian function:
wherein V is V 0 + A.p is the residual unbalance of the rotor, where V 0 The measured value is an initial vibration measured value and is an M multiplied by N order column vector, wherein M is the number of measuring points, N is the number of rotating speeds to be balanced, A is an influence coefficient matrix and is an (M multiplied by N) multiplied by K order matrix, K is the number of balancing surfaces, and p is a counterweight mass and is a K order column vector; m represents the number of rotating speeds to be added with constraint, subscript i is an integer less than or equal to m and represents the ith parameter, alpha i For a correspondingly constrained non-positive coefficient, V i For corresponding vibration measurements, V ti The intensity is the corresponding intensity standard;
3) solving the optimal value of the counterweight by using a KKT condition;
4) and performing weight addition and subtraction operation, and driving to correct the dynamic balance result.
The step 1) comprises the following steps:
let the unbalance amount on the two correction surfaces be
And
the value of the vibration detected at the bearing is
And
obtaining an influence coefficient matrix according to a superposition principle:
wherein [ a ]]For determining the coefficients, for the deflection matrix of a linear system, a first trial weight is applied to a first correction surface by means of a trial weight method
Measuring the vibration value to obtain
Then there are
The first trial weight is removed, and a second trial weight U is added on the second correcting surface 2 In the same way, obtain
The step 3) comprises the following steps:
optimizing said Lagrangian function according to KKT conditions:
α i ≤0
α i (V i -V ti )＝0
wherein p is k Represents the kth component of the weight vector p, which represents the conjugate variable of the original complex variable;
substituting partial derivative as zero condition into Lagrange function to obtain corresponding alpha i A value of (d);
finding the optimal counterweight mass p optimal And is brought into V＝V 0 In the + A · p formula, the magnitude of the residual unbalance amount is estimated.
According to the constrained high-speed dynamic balance mechanics calculating method, constraints are added to the intensity value under the key rotating speed, the intensity value of the key rotating speed is further reduced on the premise of ensuring the whole vibration reduction, and the stable operation of a rotor is ensured. The programming can be further carried out, and the operability and the usability are considered under the condition of effectively improving the dynamic balance precision. The method is suitable for dynamic balance mechanical calculation of the turbomachinery rotor with high requirement on residual unbalance and working rotating speed at least exceeding first-order critical rotating speed. Low-cost operability of constrained high-speed dynamic balance solution can be achieved. The operator only needs to input the magnitude of the constraint severity value on a program panel, and the magnitude and the phase of the balance weight and the estimated value of the residual unbalance can be obtained through full-automatic calculation and analysis of the program.
Drawings
FIG. 1 is a block diagram of an exemplary embodiment of an axial flow compressor rotor of the present invention, model number AV 50;
FIG. 2 is a graph of operating speed severity values (Nyquist plot and Bode plot) before equilibrium;
fig. 3 is a value of the operating speed intensity after balancing.
Detailed Description
The following describes a constrained high-speed dynamic equilibrium mechanical solution method according to the present invention in detail with reference to the following embodiments and accompanying drawings.
The invention relates to a constrained high-speed dynamic balance mechanics resolving method, which comprises the following steps:
1) calculating an influence coefficient through driving, trial weight and measurement, and establishing an influence coefficient matrix; the method comprises the following steps:
let the unbalance amount on the two correction surfaces be
And
the value of the vibration detected at the bearing is
And
wherein [ a ]]For determining the coefficients, for the deflection matrix of a linear system, a first trial weight is applied to a first correction surface by means of a trial weight method
Measuring the vibration value to obtain
Then there are
The first trial weight is removed, and a second trial weight U is added on the second correcting surface 2 In the same way, obtain
2) According to the constraint condition according to the dynamic balance standard, establishing a Lagrangian function:
wherein V is V 0 + A.p is the residual unbalance of the rotor, where V 0 Is an M × N order series of initial vibration (no test weight) measurementsVector, wherein M is the number of measuring points, N is the number of rotating speeds to be balanced, A is an influence coefficient matrix which is an (M multiplied by N) multiplied by K order matrix, K is the number of balancing surfaces, p is counterweight mass, a K order column vector M represents the number of rotating speeds to be added with constraint, subscript i is an integer less than or equal to M and represents the ith parameter, alpha is the number of the measuring points, and the number of the rotating speeds to be balanced is the number of the rotating speeds to be added with the constraint i As a non-positive coefficient of the corresponding constraint, V i For corresponding vibration measurements, V ti The intensity is the corresponding intensity standard;
the dynamic balance standard can adopt an ISO 1940-1:2003(E) standard or a GB/T9239.2-2006 standard.
3) Solving the optimal value of the counterweight by using a KKT condition; the method comprises the following steps:
optimizing said Lagrangian function according to KKT conditions:
α i ≤0
α i (V i -V ti )＝0
wherein p is k Represents the kth component of the weight vector p, which represents the conjugate variable of the original complex variable;
substituting partial derivative as zero condition into Lagrange function to obtain corresponding alpha i A value of (d); it is possible to find most of a i The value is zero, which is a characteristic of convex function optimization, i.e. constraints that are 'far away' from the objective function have no effect on the objective function.
Finding the optimal counterweight mass p optimal And carry over into V ═ V 0 In the + A · p formula, the magnitude of the residual unbalance amount is estimated.
4) And performing weight addition and subtraction operation, and driving to correct the dynamic balance result.
The calculation can be carried out according to the constrained high-speed dynamic balance mechanics calculation method, and the steps of the constrained high-speed dynamic balance mechanics calculation method can also be programmed, so that an operator only needs to input the magnitude of the constraint severity value on a program panel, and the magnitude and the phase of the balance weight and the estimated value of the residual unbalance can be obtained through full-automatic calculation and analysis of the program.
Examples
Fig. 1 shows an axial compressor rotor of type AV50, which is the object of an embodiment of the invention, the parameters required for dynamic balancing including:
number of correction surfaces: when the rotor of the model is produced and processed, a full-circle balancing groove is reserved on each of two sides of a shaft section, a screw hole is reserved in the middle of the shaft end, and balancing quality can be installed, so that the number of usable correction surfaces is three, and as #1, #2 and #3 in fig. 1 respectively represent 3 faces which can be corrected;
number of measurement points: the method comprises the following steps of performing dynamic balance by using a 50-ton high-speed balancing machine generated by a Shenke company, wherein at present, only two support swing frames are arranged at a measuring point, so that the number of the measuring points is two;
correcting the rotating speed: the dynamic balance process adopts speed increase and reduction, the working rotating speed is about 5200 revolutions, the measured value is recorded once every 30 revolutions, and about 150 rotating speed measured values are recorded (the former 300 revolutions reserve low-speed dynamic balance and are not used);
and (3) restricting the rotating speed: critical rotation speed (3800 revolutions) and working rotation speed (5200 revolutions)
FIG. 2 shows the operating speed status before the dynamic balance correction, which indicates that the measured value of the swing frame exceeds 1mm/s (exceeds the standard). After the dynamic balance correction is carried out by using the method of the invention, the intensity value is greatly reduced, and the intensity value after the dynamic balance correction is only about 0.4mm/s is shown in figure 3. The dynamic balance effect of the constrained high-speed dynamic balance mechanical calculation method is good.
Claims (2)
1. A constrained high-speed dynamic balance mechanical calculation method is characterized by comprising the following steps:
1) calculating an influence coefficient through driving, trial weight and measurement, and establishing an influence coefficient matrix;
2) according to the constraint condition of the dynamic balance standard, a Lagrangian function is established:
wherein V is V 0 + A.p is the residual unbalance of the rotor, where V 0 The measured value is an initial vibration measured value and is an M multiplied by N order column vector, wherein M is the number of measuring points, N is the number of rotating speeds to be balanced, A is an influence coefficient matrix and is an (M multiplied by N) multiplied by K order matrix, K is the number of balancing surfaces, and p is a counterweight mass and is a K order column vector; m represents the number of rotating speeds to be added with constraint, subscript i is an integer less than or equal to m and represents the ith parameter, alpha i For a correspondingly constrained non-positive coefficient, V i For corresponding vibration measurements, V ti The intensity is the corresponding intensity standard;
3) solving the optimal value of the counterweight by using a KKT condition; the method comprises the following steps:
optimizing said Lagrangian function according to KKT conditions:
α i ≤0
α i (V i -V ti )＝0
wherein p is k Represents the kth component of the weight vector p, which represents the conjugate variable of the original complex variable;
substituting partial derivative as zero condition into Lagrange function to obtain corresponding alpha i A value of (d);
finding the optimal counterweight mass p optimal And carry over into V ═ V 0 In the + A.p formula, the size of the residual unbalance is estimated;
4) and performing weight addition and subtraction operation, and driving to correct the dynamic balance result.
2. A constrained high speed dynamic equilibrium mechanics solution method according to claim 1 wherein step 1) comprises:
let the unbalance on the two correction surfaces be U 10 And U 20 The value of the vibration detected at the bearing is Y 10 And Y 20 And obtaining an influence coefficient matrix according to a superposition principle:
wherein [ a ]]For determining the coefficients, a first trial weight U is applied to the first correction surface by a trial weight method 1 Measuring the vibration value to obtain
Then is provided with
The first trial weight is removed, and a second trial weight U is added on the second correcting surface 2 In the same way, obtain
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