CN107862122B - Full-circle self-locking blade dynamic frequency calculation method - Google Patents
Full-circle self-locking blade dynamic frequency calculation method Download PDFInfo
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- CN107862122B CN107862122B CN201711059167.5A CN201711059167A CN107862122B CN 107862122 B CN107862122 B CN 107862122B CN 201711059167 A CN201711059167 A CN 201711059167A CN 107862122 B CN107862122 B CN 107862122B
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Abstract
The invention relates to a method for calculating the dynamic frequency of a whole-circle self-locking blade, which adopts a three-dimensional finite element method to calculate the static strength and the modal frequency of the whole-circle self-locking blade under the concerned n different rotating speeds, and draws a Campbell diagram according to the modal frequency of each pitch diameter and each order obtained by calculation to obtain the resonance rotating speed of a triple point. In a certain contact positive pressure range, a rigidity unit is added in a shroud ring and lacing wire contact pair, and the complex nonlinear contact friction process is subjected to equivalent linearization treatment; considering the material and the processing mode of the blade, a relational expression of contact rigidity and contact positive pressure is provided; in the modal calculation, the influence of blade torsion recovery on the clearance between the contact surfaces is considered, and the influence of the contact state and the contact positive pressure on the contact rigidity is considered. Compared with the experimental test result, the deviation between the resonance rotating speed of the three-key point obtained by calculation and the measured value is small, the accuracy of the calculation result meets the engineering requirement, and a reliable basis is provided for the dynamic frequency check of the whole circle of self-locking blades.
Description
Technical Field
The invention belongs to the field of calculation of vibration frequency of a turbine blade, and particularly relates to a method for calculating the dynamic frequency of a full-circle self-locking blade.
Background
Full circle self locking blades are widely used in the design of long blades for steam turbines. The design of the long blade of the steam turbine adopts a friction damping structure of an integral shroud and a boss lacing wire (or only one of the two items). The blades with the friction damping structure are connected through contact surfaces at the shroud band and the lacing wire respectively, wherein the contact surfaces are in contact with each other (two opposite contact surfaces form a contact pair). In the installation state, two contact surfaces of the contact pair are parallel to each other, and a gap exists between the contact surfaces; under the rotating state, the blade body generates torsion recovery under the action of centrifugal force, so that the two contact surfaces are close to each other and are finally attached. Under the rotation state, when the blade vibrates, frictional damping is generated between the contact surfaces, so that vibration energy is dissipated, the aim of reducing the dynamic stress of the blade body is achieved, and meanwhile, the blade group has the characteristic of full-circle vibration and is also favorable for improving the vibration characteristic of the blade group.
Due to the highly nonlinear characteristic of the contact friction process, great challenges are brought to the calculation of the vibration frequency (namely the dynamic frequency) of the full-circle self-locking blade in the rotating state. A simplified method for calculating the dynamic frequency of a full-circle self-locking blade comprises the following steps: and determining the range of the node pairs needing to be coupled on the contact pairs according to the contact state after the static strength calculation by adopting three-dimensional finite element calculation, and mutually coupling the corresponding nodes on the two contact surfaces in the range, thereby simplifying the nonlinear problem into a linear problem and obtaining the dynamic frequency through modal calculation. But this method ignores the change in contact surface contact stiffness and the damping characteristics of relative slip. When the rotating speed is not high, the blade body torsion recovery is small, and the contact pressure is small, the dynamic frequency value obtained by calculation by the method is often much higher than the actual value, so that a large error is caused for checking the dynamic frequency of the whole circle of self-locking blades, and the requirement of engineering application cannot be met. Other models and methods for researching the vibration characteristics of the full-circle self-locking blade with the friction damping structure comprise the following steps: macro slip models, micro-motion slip models, contact kinematics models, and methods of solving blade responses, as represented by Harmonic Balance Method (HBM). The models and the methods are complex, the solving efficiency is not high, and certain limitations exist in engineering application.
Disclosure of Invention
The invention aims to solve the defects of the technology and provide a method for calculating the dynamic frequency of the whole-circle self-locking blade, which is simple and convenient to operate, high in calculation efficiency and accurate in result.
In order to achieve the above purpose, the present invention adopts the following technical scheme.
A full-circle self-locking blade dynamic frequency calculation method is characterized by comprising the following steps:
1) establishing a blade geometric model to ensure that the shroud ring and the lacing wires have circularly symmetric geometric characteristics;
2) dividing a finite element grid into the geometric model, wherein grid nodes of the shroud ring and the lacing wire contact pairs are in one-to-one correspondence;
3) calculating static strength at different rotating speeds, wherein the boundary conditions are as follows: applying a fixed constraint to the blade root; applying a circularly symmetric boundary condition to the circular symmetric cross section of the shroud ring and the lacing wire; arranging a contact unit on the contact surface of the shroud ring and the lacing wire; taking different rotating speeds as load steps, wherein the different rotating speeds are all larger than the lowest contact rotating speed, so that the shroud ring and the lacing wires can reach a contact state;
4) respectively calculating the contact positive pressure of the shroud band and the lacing wire at different rotating speeds
In the formula, F is the normal counter force on the contact surface of the shroud ring and the lacing wire at different rotating speeds obtained by calculating the static strength in the step 3), and the unit is as follows: n; a is the nominal contact area, which is defined as the area of the geometrical mutual overlapping area of the shroud band and the lacing wire contact pair, and the unit is: mm is2(considering that errors may exist in the actual processing and assembling processes of the blade, so that the contact state of the shroud ring and the lacing wire in actual contact may not be completely consistent with the contact state obtained by finite element calculation, and in order to reduce the influence of the errors and facilitate the statistics of the contact area, the nominal contact area is adopted);
5) respectively calculating equivalent contact stiffness of the shroud band and the lacing wire contact pair at different rotating speeds:
the problem of two machined rough surfaces coming into contact with each other can be equated with the problem of one surface having an equivalent roughness and another rigid plane coming into contact with each other. If the surface profile with equivalent roughness has fractal characteristics, the surface profile can be simulated by a specific fractal function. On the surface profile, the smaller asperities "parasitize" on the larger asperities, nesting one layer at a time. According to a fractal theory, a bump is simulated by a sphere, so that physical quantities such as elastic contact force, plastic contact force, actual contact area and the like of the bump and the plane in contact can be calculated by utilizing a classical theory of the contact of the sphere and the plane in a Hertz (Hertz) contact theory, the number of the bumps in a certain range is calculated by combining a distribution density function in the fractal theory, and finally, the total contact force, the total actual contact area, the normal stiffness and the tangential stiffness in the range are obtained through integration.
Considering the blade as steel, the contact surface is finished by milling or grinding, and the contact surface has fractal characteristics on the micro scale. Through the theoretical derivation and experimental correction, a relational expression of the contact rigidity and the contact positive pressure is obtained, and when the contact positive pressure is not more than 100MPa, the following formula is met:
kn＝1.05p0.7626 (2)
kτ＝0.7019p0.7696 (3)
in the formula, knNormal contact stiffness, unit: x 105MPa；kτTangential contact stiffness, unit: x 105MPa; p is the contact positive pressure of the contact surfaces of the shroud band and the lacing wire obtained in the step 4) at different rotating speeds, and the unit is as follows: MPa;
6) calculating the modal frequency of the blade at different rotating speeds, wherein the boundary conditions are as follows: applying a fixed constraint to the blade root; applying a circularly symmetric boundary condition to the circular symmetric cross section of the shroud ring and the lacing wire; contact units are arranged on contact surfaces of the shroud band and the lacing wires, meanwhile, rigidity units are added between node pairs with nonzero positive pressure in the shroud band and the lacing wires, the z axis of a unit coordinate system of the rigidity units is set as the normal direction of the contact surfaces, and a rigidity matrix corresponding to each rigidity unit is
In the formula (I), the compound is shown in the specification,
wherein N is the number of node pairs with nonzero positive pressure on the contact surfaces of the shroud ring and the lacing wires; k is a radical ofn、kτThe contact-to-normal contact stiffness and the tangential contact stiffness obtained in step 5) are respectively obtained; and 6.1) activating a contact unit and killing a rigidity unit by adopting a life-death unit method, and calculating static strength. The purpose is to make the contact pair in the contact state under the calculated rotating speed, the blade body generates torsion recovery under the action of centrifugal force, the contact surfaces are mutually attached, and the gap between the contact surfaces is eliminated. 6.2) on the basis of the static strength calculation in the step 6.1), killing a contact unit and activating a rigidity unit by adopting a life-death unit method to perform modal calculation. And 7) calculating modal frequencies of each pitch diameter and each order of the whole circle of self-locking blades at the concerned n different rotating speeds, and then drawing a vibration campbell diagram of the whole circle of self-locking blades according to the modal frequencies to obtain the three-key-point resonance rotating speed of the whole circle of self-locking blades.
The further improvement lies in that: in order to obtain a blade vibration Campbell diagram, n different rotating speed vibration data need to be tested, in the step 3), n different rotating speeds are set at equal intervals or unequal intervals as load steps, and the static strength at different rotating speeds n is calculated; in the step 4), respectively calculating the contact positive pressures of the shroud ring and the lacing wires at n different rotating speeds; in the step 5), calculating equivalent contact stiffness of the shroud band and the lacing wire contact pair under n different rotating speeds respectively; in step 6), calculating the modal frequency of the blade at n different rotating speeds; and further comprising:
the further improvement lies in that: the method is not only suitable for the whole circle of self-locking blades of the friction damping structure with the integral shroud band and the boss lacing wires, but also suitable for the whole circle of self-locking blades of the friction damping structure with the integral shroud band or the boss lacing wires.
The further improvement lies in that: in step 6), not only the z-axis of the unit coordinate system of the stiffness unit but also the x-axis or y-axis of the unit coordinate system of the stiffness unit may be set to the normal direction of the contact surface, in which case k is set to the normal direction of the contact surfacex、ky、kzAnd k isn、kτThe corresponding relationship of (a) needs to be adjusted accordingly.
Compared with the prior art, the invention has the beneficial effects that:
1. within a certain contact positive pressure range, the complex nonlinear contact friction process between two contact surfaces is subjected to equivalent linearization treatment, so that modal calculation can be performed by using a three-dimensional finite element method, and the calculation efficiency is high.
2. The material and the processing mode of the blade are considered, and a relational expression of the contact rigidity and the contact positive pressure is obtained through theoretical derivation and experimental correction. In the three-dimensional finite element modal calculation, the influence of blade torsion recovery on the clearance between the contact surfaces is considered, and the influence of the contact state and the contact positive pressure on the contact rigidity is considered. Compared with the contact surface node coupling method, the method of the invention is closer to the actual approximation of the contact surface friction damping phenomenon.
3. The dynamic frequency of the whole circle of self-locking blades is calculated by the method, the triple point resonance rotating speed is obtained, the triple point resonance rotating speed obtained by calculation is smaller in deviation with an actual measurement value by comparing with an experimental test result, the accuracy degree of the calculation result meets the engineering requirement, and a reliable basis is provided for checking the dynamic frequency of the whole circle of self-locking blades.
Drawings
FIG. 1 is a flow chart of a method for calculating the dynamic frequency of a full-circle self-locking blade.
FIG. 2 is a schematic view of a boss lacing wire and an integral shroud.
FIG. 3 is a schematic diagram of a finite element mesh and boundary conditions for a blade.
Fig. 4 is a schematic diagram of the stiffness elements of a tab tendon contact pair.
FIG. 5 is a graph of contact stiffness versus contact positive pressure.
FIG. 6 is a campbell diagram of a full-circle self-locking blade vibration of certain type.
Detailed Description
The present invention is described in further detail below with reference to the attached drawings.
According to the flow chart shown in the figure 1, calculating the dynamic frequency of a certain type of full-circle self-locking blade, drawing a blade vibration campbell diagram, and comparing the blade vibration campbell diagram with an experimental test result. The blade is made of high-strength stainless steel, and the contact surfaces of the shroud ring and the lacing wire are both ground. To adjust the blade frequency, the shroud thickness was reduced from 25mm before adjustment to 18mm after adjustment. And respectively calculating modal frequencies of the two blades with different shroud thicknesses at 7 rotating speeds of 2000-5000 rpm at an interval of 500 rpm.
1) As shown in fig. 2, in the installation state, a gap 201 is formed between the contact surfaces of two adjacent boss lacing wires 2 of the blade, the nominal gap value is 0.1mm, and a gap 101 is formed between the contact surfaces of two adjacent integral shroud rings 1, and the nominal gap value is 0.2 mm. The size of the two gap values is given according to the design. And establishing a blade geometric model, and constructing the shroud band 1 and the lacing wires 2 into structures which are convenient for applying circularly symmetric boundary conditions.
2) As shown in fig. 3 and 4, finite element meshes are divided for the geometric model, wherein mesh nodes 203 of the shroud band and the tie bar contact pairs correspond one to one.
3) And (4) calculating static strength. The boundary conditions are as follows: the rotation speed is omega 2000rpm, and fixed constraint is applied to the blade root 4; applying a circularly symmetric boundary condition to the circular symmetric cross section (102, 202) of the shroud ring and the lacing wire; and contact units are arranged on the contact surfaces of the shroud ring and the lacing wires. The blade body 3 generates torsion recovery under the action of centrifugal force, and the contact rotating speed of the shroud band and the lacing wire of the blade is calculated to be lower than 1500 rpm.
4) According to the normal counter force on the contact surface of the shroud band and the lacing wire obtained in the step 3), the nominal contact area of the shroud band and the lacing wire is combined, and the relation (1)
And calculating the contact positive pressure of the shroud band and the lacing wire at omega of 2000 rpm.
5) According to the contact positive pressure of the shroud band and the lacing wire obtained in the step 4), combining the relation formula (2) k of contact rigidity and contact positive pressuren＝1.05p0.7626Relational expression (3) kτ＝0.7019p0.7696(as shown in fig. 5), the equivalent contact stiffness of the shroud band and the lacing wire at ω 2000rpm was calculated.
6) And (4) calculating the mode. The boundary conditions are as follows: the rotation speed is omega 2000rpm, and fixed constraint is applied to the blade root 4; applying a circularly symmetric boundary condition to the circular symmetric cross section (102, 202) of the shroud ring and the lacing wire; contact units are arranged on the contact surfaces of the shroud band and the lacing wires, meanwhile, as shown in figure 4, rigidity units are added between pairs of nodes with nonzero positive pressure in the shroud band and lacing wire contact pairs, and rigidity matrixes corresponding to the rigidity units are determined by formula 4. Fig. 4 illustrates tie contact pairs, where the gap between two contact surfaces is exaggerated and only 3 stiffness elements are added for clarity of demonstrating the stiffness elements added between pairs of nodes with non-zero positive pressure in a one-to-one correspondence. The z-axis of the unit coordinate system of the stiffness unit is perpendicular to the contact surface. And (4) activating a contact unit and killing a rigidity unit by adopting a life-death unit method, and calculating static strength. On the basis, a life-death unit method is adopted, a contact unit is killed, a rigidity unit is activated, and modal calculation is carried out.
7) And (5) repeating the steps 3) to 6), and respectively calculating modal frequencies of the rest 6 rotating speeds of 2500-5000 rpm at intervals of 500 rpm. And under all calculated rotating speeds, the contact positive pressure of the shroud ring and the lacing wires is less than 100 MPa.
8) And (3) respectively calculating the dynamic frequency of the blade with the shroud thickness of 25mm and 18mm by adopting the methods of the steps 1) to 7), and drawing a vibration campbell diagram of the whole circle of self-locking blades according to the calculated pitch diameters and modal frequencies of each order of the whole circle of self-locking blades to obtain the three-focal-point resonance rotating speed of the whole circle of self-locking blades, as shown in fig. 6. In the figure, a natural frequency line sequentially represents the natural frequency of 1-order vibration with 5-9 pitch diameters from bottom to top, and experimental test results are not drawn in the figure.
Compared with the experimental test results, the deviation between the calculated triple point resonance rotating speed and the measured value is less than 2%, as shown in tables 1 and 2.
TABLE 1 resonant rotation speed of certain type of blade (shroud thickness 25 mm)' triple point
TABLE 2 resonant rotation speed of certain type of blade (shroud thickness 18 mm)' triple point
Claims (4)
1. A full-circle self-locking blade dynamic frequency calculation method is characterized by comprising the following steps:
1) establishing a blade geometric model, and aiming at a shroud ring and a lacing wire, enabling the shroud ring and the lacing wire to have circular symmetric geometric characteristics;
2) dividing a finite element grid into the geometric model, wherein grid nodes of the shroud ring and the lacing wire contact pairs are in one-to-one correspondence;
3) calculating static strength at different rotating speeds, wherein the different rotating speeds are all larger than the contact rotating speed, so that the shroud ring and the lacing wire can reach a contact state, and the boundary conditions are as follows: applying a fixed constraint to the blade root; applying a circularly symmetric boundary condition to the circular symmetric cross section of the shroud ring and the lacing wire; arranging a contact unit on the contact surface of the shroud ring and the lacing wire;
4) respectively calculating the contact positive pressure of the shroud band and the lacing wire at different rotating speeds
In the formula, F is the normal counter force on the contact surface of the shroud ring and the lacing wire at different rotating speeds obtained by calculating the static strength in the step 3), and the unit is as follows: n; a is the nominal contact area, which is defined as the area of the geometrical mutual overlapping area of the shroud band and the lacing wire contact pair, and the unit is: mm is2；
5) Respectively calculating equivalent contact stiffness of the shroud band and the lacing wire contact pair under different rotating speeds, wherein the calculating method comprises the following steps:
considering that the blade is made of steel, the contact surface is subjected to milling or grinding finish machining, the contact surface has fractal characteristics on the microcosmic aspect, the contact rigidity and the contact positive pressure have a power function relationship, and when the contact positive pressure is not more than 100MPa, the following formula is met:
kn＝1.05p0.7626 (2)
kτ＝0.7019p0.7696 (3)
in the formula, knNormal contact stiffness, unit: x 105MPa；kτTangential contact stiffness, unit: x 105MPa; p is the contact positive pressure of the contact surfaces of the shroud band and the lacing wire obtained in the step 4) at different rotating speeds, and the unit is as follows: MPa;
6) calculating the modal frequency of the blade at different rotating speeds, wherein the boundary conditions are as follows: applying a fixed constraint to the blade root; applying a circularly symmetric boundary condition to the circular symmetric cross section of the shroud ring and the lacing wire; contact units are arranged on contact surfaces of the shroud band and the lacing wires, meanwhile, rigidity units are added between node pairs with nonzero positive pressure in the shroud band and the lacing wires, the z axis of a unit coordinate system of the rigidity units is set as the normal direction of the contact surfaces, and a rigidity matrix corresponding to each rigidity unit is
In the formula (I), the compound is shown in the specification,
wherein N is the number of node pairs with nonzero positive pressure on the contact surfaces of the shroud ring and the lacing wires; k is a radical ofn、kτThe calculation method of the blade modal frequency at a certain rotating speed for the contact-to-normal contact stiffness and the tangential contact stiffness obtained in the step 5) is as follows:
6.1) activating a contact unit and a killing rigidity unit by adopting a life-death unit method, and calculating static strength;
6.2) killing a contact unit and activating a rigidity unit by adopting a life-death unit method on the basis of the static strength calculation in the step 6.1) to perform modal calculation;
7) and after calculating the modal frequencies of each pitch diameter and each order of the whole circle of self-locking blades at the concerned n different rotating speeds, drawing a vibration campbell diagram of the whole circle of self-locking blades according to the modal frequencies, and obtaining the 'triple point' resonance rotating speed of the whole circle of self-locking blades.
2. The method for calculating the dynamic frequency of the full-circle self-locking blade according to claim 1,
in the step 3), setting n different rotating speeds at equal intervals or unequal intervals as load steps, and calculating the static strength at different rotating speeds n;
in the step 4), respectively calculating the contact positive pressures of the shroud ring and the lacing wires at n different rotating speeds;
in the step 5), calculating equivalent contact stiffness of the shroud band and the lacing wire contact pair under n different rotating speeds respectively;
and 6), calculating the modal frequency of the blade at n different rotating speeds.
3. The method for calculating the dynamic frequency of the full-circle self-locking blade according to claim 1, wherein in the step 6), the x-axis or the y-axis of the unit coordinate system of the stiffness unit is set as the normal direction of the contact surface, kx、ky、kzAnd k isn、kτThe corresponding relationship of (a) is adjusted accordingly.
4. The method for calculating the dynamic frequency of the whole-circle self-locking blade is characterized by being suitable for the whole-circle self-locking blade with a friction damping structure of an integral shroud band and a boss lacing wire simultaneously and also suitable for the whole-circle self-locking blade with the friction damping structure of the integral shroud band or the boss lacing wire only.
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| CN114320479B (en) * | 2022-01-05 | 2024-04-02 | 杭州汽轮动力集团股份有限公司 | Rotor blade design method, rotor blade and steam turbine for driving air separation compressor |
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