CN112329279A - Method for mode sorting of Campbell diagram - Google Patents

Method for mode sorting of Campbell diagram Download PDF

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CN112329279A
CN112329279A CN201910694410.3A CN201910694410A CN112329279A CN 112329279 A CN112329279 A CN 112329279A CN 201910694410 A CN201910694410 A CN 201910694410A CN 112329279 A CN112329279 A CN 112329279A
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宋会英
翁依柳
龚煦
龙丹
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AECC Commercial Aircraft Engine Co Ltd
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Abstract

The invention provides a Campbell diagram mode sequencing method, which comprises the steps of calculating MAC values among modal shape vectors of each order formed by central nodes of adjacent rotating speeds, and then carrying out mode sequencing on the modes of the adjacent rotating speeds according to the size of the MAC values, wherein the two-order modes with the largest MAC values have the largest correlation and are matched into the same mode pair; and finally, drawing a relation graph of each mode, frequency and rotating speed under different rotating speeds to obtain a Campbell diagram. The method for modal sequencing of the Campbell diagram provides a method for solving modal sequencing errors in the calculation of the Campbell diagram, is used for analyzing the Campbell diagram of a three-dimensional finite element model, and is high in precision and not easy to generate modal sequencing errors; the method overcomes subjectivity, uncertainty and difficulty in manually comparing the vibration modes to perform mode matching.

Description

Method for mode sorting of Campbell diagram
Technical Field
The invention relates to a campbell diagram modal sequencing method.
Background
Campbell diagram analysis is an important part of rotodynamic analysis. Common numerical calculation methods include a transfer matrix method and a finite element method, wherein the finite element model can be further divided into a shell model and a three-dimensional finite element model according to a simplification of the structure and a modeling method. The transfer matrix method and the beam-shell model are adopted for analysis, the operation speed is high, modal sequencing errors are not easy to occur, and the precision is low. The three-dimensional finite element model is adopted for analysis, the calculation precision is high, but the calculation speed is low, and modal sequencing errors are easy to occur.
With the improvement of the computer level and the development of commercial finite element software, the Campbell diagram analysis of the rotor by adopting a three-dimensional finite element model becomes a trend, the model modeling is convenient, excessive structure simplification is not needed, and meanwhile, the calculation precision is high. However, since the three-dimensional finite element model has a large scale, a large number of degrees of freedom, a large number of modal frequencies and a complex mode shape, a modal sequencing error often occurs in the campbell diagram analysis, and an erroneous campbell diagram is generated, as shown in fig. 1. For the problem of wrong modal sequencing, no effective solution exists at present, modal matching is usually performed by manually comparing modal shape, but because the model is complex and has more degrees of freedom, and the campbell diagram analysis is complex modal analysis, the manual comparison of the modal shape has great subjectivity and uncertainty, and is difficult.
Disclosure of Invention
The invention aims to provide a Campbell graph modal sorting method to solve the problem that a Campbell graph is easy to generate modal sorting errors in rotor dynamics analysis.
In order to solve the above problems, the present invention provides the following technical solutions:
the invention provides a campbell diagram modality sequencing method, which comprises the following steps:
s1) establishing a three-dimensional finite element model of the rotor according to the rotor real object;
s2) establishing a central node on the rotor axis of the finite element model;
s3) carrying out rotor complex modal analysis under different rotating speeds, extracting the displacement corresponding to each order modal under different rotating speeds in the concerned freedom degree direction of the central node, forming the mode shape vector of each order modal under different rotating speeds, and recording the vector as
Figure BDA0002148913250000021
Wherein m represents the rotation speed ωmI represents the i-order mode;
s4) calculating the adjacent rotation speed ωa、ωbCentral joint ofMAC value between modal shape vectors of orders of point composition
Figure BDA0002148913250000022
Wherein phi isaiIs the rotational speed omegaaThe i-th order mode shape of the vibration mode,
Figure BDA0002148913250000023
is the rotational speed omegaaThe complex conjugate of the i-th order mode shape,
Figure BDA0002148913250000024
is the rotational speed omegaaThe transposition of the mode shape of the ith order mode,
Figure BDA0002148913250000025
is the rotational speed omegaaComplex conjugate transposition of the ith order mode shape; phi is abjIs the rotational speed omegabThe mode shape of the j-th order mode,
Figure BDA0002148913250000026
is the rotational speed omegabThe complex conjugate of the j-th order mode shape,
Figure BDA0002148913250000027
is the rotational speed omegabThe transposition of the mode shape of the j-th order mode,
Figure BDA0002148913250000028
is the rotational speed omegabComplex conjugate transposition of j order mode shape;
s5) carrying out mode sequencing on modes of adjacent rotating speeds according to the size of the MAC value, wherein the correlation of the two-order mode with the maximum MAC value is maximum and the two-order mode is matched as a same mode pair;
s6) drawing a relation graph of each mode, frequency and rotating speed under different rotating speeds to obtain a Campbell diagram.
In the technical scheme, frequency calculation at each rotating speed is based on a three-dimensional finite element model, frequency calculation precision is high, but modal sequencing is based on a vibration mode vector formed by key nodes determined by the positions of sites required to be set by a transmission matrix method, and modal sequencing errors are not easy to occur.
Preferably, step 2) comprises the steps of:
setting a station at the sudden change positions of a wheel disc, a support, a coupler, a shaft section bifurcation point, a shaft section inner diameter and a shaft section outer diameter of the three-dimensional finite element model;
dividing the equal-section shaft section with L/D <1 into a plurality of sections, wherein L is the length of the shaft section, and D is the outer diameter of the shaft section;
the stations are marked as S1 and S2 … … Sn, nodes closest to the axial positions of the stations are selected as key node sets SN1 and SN2 … … SNn, and the SNn corresponds to Sn;
for each key node set SNn, a central node CNn is established on the axis, and the central node CNn is connected with the corresponding key node set SNn.
In the technical scheme, through the steps, the central node can be established on the rotor axis of the finite element model, so that the mode vector based on the transfer matrix method is obtained, and effective data are provided for subsequent mode sequencing.
Preferably, a constraint equation is established between the central node CNn and the corresponding key node set SNn.
In the present technical solution, RBE3 is connected as a better connection mode between the central node and the corresponding key node set.
Preferably, in step 3), the directions of the degrees of freedom of the central node are x direction and y direction, the x direction and the y direction are perpendicular to the axial direction of the rotor, and the x direction and the y direction are perpendicular to each other, and the rotation speed ω is equal to or higher than the rotation speed ωmMode shape vector of lower i-order mode
Figure BDA0002148913250000031
As indicated by the general representation of the,
φmi＝(x1 y1 x2 y2 … xn yn)T
wherein x isnRepresenting the x-displacement, y, of the nth center nodenRepresents the y-displacement of the nth center node, and T represents the transposing of the matrix.
In the technical scheme, through screening the degree of freedom of the central node, data with larger degree of correlation can be obtained, and the degree of correlation between the vibration mode vector and the transverse vibration of the rotor is increased.
On the basis of the common knowledge in the field, the above preferred conditions can be combined randomly to obtain the preferred embodiments of the invention.
The positive progress effects of the invention are as follows:
the method for modal sequencing of the Campbell diagram provides a method for solving modal sequencing errors in the calculation of the Campbell diagram, is used for analyzing the Campbell diagram of a three-dimensional finite element model, and is high in precision and not easy to generate modal sequencing errors; the method overcomes subjectivity, uncertainty and difficulty in manually comparing the vibration modes to perform mode matching.
Drawings
Fig. 1 is a campbell diagram for generating modality sorting errors obtained by a conventional campbell diagram modality sorting method.
FIG. 2 is a schematic diagram of the steps of a method for modal sorting in a Campbell diagram of the present invention.
Fig. 3 is a schematic step diagram of step 2) of the method of campbell diagram modality ordering shown in fig. 2.
Fig. 4 is a schematic view of the finite element rotor model of step 2) of the method of campbell diagram mode ordering shown in fig. 2.
Fig. 5 is a schematic positional diagram of a station of the finite element rotor model of step 2) of the method of campbell diagram modal ordering shown in fig. 2.
Fig. 6 is a schematic location diagram of the site and the central node in step 2) of the campbell diagram modality ordering method shown in fig. 2.
Fig. 7 is a schematic position diagram of the site, the center node, and the key node set in step 2) of the campbell diagram modality ordering method shown in fig. 2.
Fig. 8 is a campbell diagram obtained by the method of modal ordering of campbell diagrams shown in fig. 2.
Detailed Description
The present invention is further described in the following description with reference to specific embodiments and the accompanying drawings, wherein the details are set forth in order to provide a thorough understanding of the present invention, but it is apparent that the present invention can be embodied in many other forms different from those described herein, and it will be readily appreciated by those skilled in the art that the present invention can be implemented in many different forms without departing from the spirit and scope of the invention.
As shown in fig. 1, the present invention provides a campbell diagram modality sorting method, which comprises the following steps:
s1) establishing a three-dimensional finite element model of the rotor according to the rotor real object;
s2) establishing a central node on the rotor axis of the finite element model;
s3) carrying out rotor complex modal analysis under different rotating speeds, such as k-order modal; extracting the displacement corresponding to each order of mode in the concerned freedom degree direction of the central node under different rotating speeds to form the mode shape vector of each order of mode under different rotating speeds, and recording the vector as
Figure BDA0002148913250000041
Wherein m represents the rotation speed ωmI represents the i-order mode;
s4) calculating the adjacent rotation speed ωa、ωbMAC value between modal shape vectors of each order composed of central nodes
Figure BDA0002148913250000051
Wherein phi isaiIs the rotational speed omegaaThe i-th order mode shape of the vibration mode,
Figure BDA0002148913250000052
is the rotational speed omegaaThe complex conjugate of the i-th order mode shape,
Figure BDA0002148913250000053
is the rotational speed omegaaThe transposition of the mode shape of the ith order mode,
Figure BDA0002148913250000054
is the rotational speed omegaaComplex conjugate transposition of the ith order mode shape; phi is abjIs the rotational speed omegabThe mode shape of the j-th order mode,
Figure BDA0002148913250000055
is the rotational speed omegabThe complex conjugate of the j-th order mode shape,
Figure BDA0002148913250000056
is the rotational speed omegabThe transposition of the mode shape of the j-th order mode,
Figure BDA0002148913250000057
is the rotational speed omegabComplex conjugate transposition of j order mode shape;
s5) carrying out mode sequencing on modes of adjacent rotating speeds according to the size of the MAC value, wherein the correlation of the two-order mode with the maximum MAC value is maximum and the two-order mode is matched as a same mode pair;
for example, at a rotational speed ωaThe 10 th order mode is calculated at the rotation speed omegabWhen 10 orders of mode are calculated, matching the 10 orders of mode at the rotating speed can obtain a 10 × 10 MAC matrix which represents the correlation. For example, the rotation speed ω a2 nd order mode in 10 order modes and rotation speed omegabThe MAC value of the 1 st mode is the largest, that is, the correlation between the two modes is the largest, and the two modes are the same mode pair.
S6) drawing the relationship graph of each mode with frequency and rotation speed under different rotation speeds to obtain a campbell diagram, as shown in fig. 8.
At adjacent rotational speeds ω1、ω2For example, for a rotational speed ω1Ith order mode vector and rotation speed omega2The MAC value of the jth order mode vector is:
Figure BDA0002148913250000058
for rotational speed omega1The 10-order mode, the rotation speed omega is calculated2The 10-order mode is also calculated, MAC is a matrix of 10 x 10, and the mode is calculated at two rotating speeds according to the value of MACAnd (4) sequencing line modes. For example for rotational speed ω 11 st order mode and rotation speed omega2The 2 nd order mode MAC value is maximum, which means that the correlation of the two orders of modes is maximum, the matching is the same mode pair, and so on, and the mode matching under different rotating speeds is completed.
According to the method, when the Campbell diagram of the rotor is analyzed, a three-dimensional finite element model is firstly adopted for modal analysis at different rotating speeds, so that the analysis accuracy can be guaranteed, when modal sequencing is carried out, specific position nodes and the concerned degrees of freedom of the nodes are selected for modal correlation analysis at different rotating speeds, modal matching at different rotating speeds is completed, the modes of similar vibration modes at different rotating speeds are classified into a modal pair and matched into the same modal pair, and a relation graph of frequency and rotating speed of each modal pair at different rotating speeds is drawn to obtain the Campbell diagram.
According to the method, frequency calculation at each rotating speed is based on a three-dimensional finite element model, frequency calculation accuracy is high, however, modal sequencing is based on a vibration mode vector formed by key nodes determined by the positions of sites required to be set by a transmission matrix method, and modal sequencing errors are not prone to occurring. The method integrates the advantages of a three-dimensional finite element model and a transfer matrix method (or adopts a beam-shell model), and overcomes the disadvantages of the transfer matrix method (or adopts the beam-shell model) of the three-dimensional finite element model.
Therein, a finite element rotor model is shown in fig. 4. As shown in fig. 5 to 7, the specific method for establishing the central node on the rotor axis of the finite element rotor model in step 2) mainly comprises the following steps:
s21) arranging stations S1 and S2 … … Sn at the sudden change positions of a wheel disc, a support, a coupler, a shaft section bifurcation, a shaft section inner diameter and a shaft section outer diameter of the three-dimensional finite element model, as shown in FIG. 5;
s22) dividing the equal-section shaft section with L/D <1 into a plurality of sections, wherein L is the length of the shaft section, and D is the outer diameter of the shaft section;
s23) marking the stations as S1 and S2 … … Sn, selecting nodes which are closest to the axial positions of the stations as key node sets SN1 and SN2 … … SNn, wherein the SNn corresponds to Sn;
s24) for each key node set SNn, a center node CNn is established on the axis, the center node CNn being connected with the corresponding key node set SNn, as shown in fig. 6-7.
Constraint equations are established between the central nodes CNn and the corresponding key node sets SNn, for example, RBE3, multipoint constraint, and the like are adopted.
Through the steps, the central node can be established on the rotor axis of the finite element model, so that the vibration mode vector based on the transfer matrix method is obtained, and effective data are provided for subsequent mode sequencing.
Since the nth central node of the three-dimensional solid unit has 3 degrees of freedom, wherein the z direction is an axial direction, and the x direction and the y direction are perpendicular to the z direction. For an aircraft engine rotor, if only transverse vibration is concerned, only x-direction and y-direction displacement, namely displacement of translational freedom degree, is concerned.
Therefore, when only the displacement in the x-direction and the y-direction is concerned, the rotation speed ω is calculated in step 3)mMode shape vector of lower i-order mode
Figure BDA0002148913250000071
As indicated by the general representation of the,
φmi＝(x1 y1 x2 y2 … xn yn)T
wherein x isnRepresenting the x-displacement, y, of the nth center nodenRepresents the y-displacement of the nth center node, and T represents the transposing of the matrix.
Through screening the degree of freedom of the central node, data with larger degree of correlation can be obtained, and the degree of correlation between the vibration mode vector and the transverse vibration of the rotor is increased.
The method for modal sequencing of the Campbell chart provides a method for solving modal sequencing errors in the calculation of the Campbell chart, is used for analyzing the Campbell chart of a three-dimensional finite element model, and has high precision and is not easy to generate modal sequencing errors; the method overcomes subjectivity, uncertainty and difficulty in manually comparing the vibration modes to perform mode matching.
Although the present invention has been disclosed in terms of the preferred embodiment, it is not intended to limit the invention, and variations and modifications may be made by one skilled in the art without departing from the spirit and scope of the invention. Any modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the scope of protection defined by the claims of the present invention, unless departing from the content of the technical solution of the present invention.

Claims (4)

1. A method for mode sorting of Campbell diagrams is characterized by comprising the following steps:
s1) establishing a three-dimensional finite element model of the rotor according to the rotor real object;
s2) establishing a central node on the rotor axis of the finite element model;
s3) carrying out rotor complex modal analysis under different rotating speeds, extracting the displacement corresponding to each order modal under different rotating speeds in the concerned freedom degree direction of the central node, forming the mode shape vector of each order modal under different rotating speeds, and recording the vector as
Figure FDA0002148913240000011
Wherein m represents the rotation speed ωmI represents the i-order mode;
s4) calculating the adjacent rotation speed ωa、ωbMAC value between modal shape vectors of each order composed of central nodes
Figure FDA0002148913240000012
Wherein phi isaiIs the rotational speed omegaaThe i-th order mode shape of the vibration mode,
Figure FDA0002148913240000013
is the rotational speed omegaaThe complex conjugate of the i-th order mode shape,
Figure FDA0002148913240000014
is the rotational speed omegaaThe transposition of the mode shape of the ith order mode,
Figure FDA0002148913240000015
is the rotational speed omegaaComplex conjugate transposition of the ith order mode shape; phi is abjIs the rotational speed omegabThe mode shape of the j-th order mode,
Figure FDA0002148913240000016
is the rotational speed omegabThe complex conjugate of the j-th order mode shape,
Figure FDA0002148913240000017
is the rotational speed omegabThe transposition of the mode shape of the j-th order mode,
Figure FDA0002148913240000018
is the rotational speed omegabComplex conjugate transposition of j order mode shape;
s5) carrying out mode sequencing on modes of adjacent rotating speeds according to the size of the MAC value, wherein the correlation of the two-order mode with the maximum MAC value is maximum and the two-order mode is matched as a same mode pair;
s6) drawing a relation graph of each mode, frequency and rotating speed under different rotating speeds to obtain a Campbell diagram.
2. The method of campbell diagram modality ordering according to claim 1, characterized in that step 2) comprises the steps of:
setting a station at the sudden change positions of a wheel disc, a support, a coupler, a shaft section bifurcation point, a shaft section inner diameter and a shaft section outer diameter of the three-dimensional finite element model;
dividing the equal-section shaft section with L/D <1 into a plurality of sections, wherein each section is provided with a station, L is the length of the shaft section, and D is the outer diameter of the shaft section;
the stations are marked as S1 and S2 … … Sn, nodes closest to the axial positions of the stations are selected as key node sets SN1 and SN2 … … SNn, and the SNn corresponds to Sn;
for each key node set SNn, a central node CNn is established on the axis, and the central node CNn is connected with the corresponding key node set SNn.
3. The method of campbell diagram modality ordering according to claim 2, characterized in that constraint equations are established between the central nodes CNn and the corresponding set of key nodes SNn.
4. The method for mode ordering according to claim 1, wherein in step 3), the directions of the degrees of freedom of the central node are x-direction and y-direction, the x-direction and the y-direction are perpendicular to the axial direction of the rotor, the x-direction and the y-direction are perpendicular to each other, and the rotation speed ω is higher than the rotation speed ωmMode shape vector of lower i-order mode
Figure FDA0002148913240000021
As indicated by the general representation of the,
φmi＝(x1 y1 x2 y2 … xn yn)T
wherein x isnRepresenting the x-displacement, y, of the nth center nodenRepresents the y-displacement of the nth center node, and T represents the transposing of the matrix.
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