A model correction-oriented gas turbine casing modal test method

Abstract

The application discloses a kind of model correction-oriented gas turbine casing modal test methods, belong to structural dynamics test and analysis technical field, including: radial free modal test is carried out to gas turbine casing, and the real number of test modal parameters is obtained;Establish the initial finite element model of gas turbine casing, obtain the calculation modal parameters by modal analysis, and the calculation modal vibration mode vector is projected to the test modal vibration mode vector direction;According to the frequency relative error FRE, modal confidence factor MAC and the rotation of tour group MAC, the correlation matching of calculation modal and test modal is completed.The application standardizes the process of radial free modal test of gas turbine casing, clearly gives the suspension mode of casing, the arrangement principle of test knocking point and vibration sensor, the matters needing attention of traversal knocking and the implementation method of complex modal real number, to ensure the accurate acquisition of test modal parameters.

Description

Technical Field

[0001] This invention belongs to the field of structural dynamics testing and analysis technology. Specifically, it relates to a modal testing method for gas turbine casings for model correction, which is used to correct the finite element model of gas turbine casing structure dynamics. Background Technology

[0002] Finite element analysis (FEM) can significantly reduce testing costs, avoid safety hazards, and shorten development cycles, playing an increasingly important role throughout the entire life cycle of gas turbines, including design, production, use, and maintenance. Due to the complexity of gas turbine structures and vibration responses, especially multi-layered thin-walled casing systems with several complex support plates and bearing housings, coupled with the presence of many simplified, equivalent, and uncertain parameters during modeling, it is virtually impossible to establish an accurate finite element model in one step. Therefore, model correction techniques, which improve the calculation accuracy of finite element models based on measured data by selecting appropriate correction parameters, have emerged.

[0003] Taking into account the structural characteristics of the gas turbine casing, selecting an appropriate suspension method, rationally arranging test impact points and sensor installation positions, and establishing a test model that balances accuracy and feasibility, are the cornerstones for conducting structural dynamic testing, analysis, and model correction of the gas turbine casing. Through appropriate simplification and reasonable equivalence, an initial finite element model of the gas turbine casing is established, and modal analysis is used to obtain the calculated modal parameters for each order within the frequency range of interest.

[0004] However, due to the limited number of test impact points and the non-proportional damping characteristics of the casing structure itself, the experimental modal results are incomplete complex modes, while the calculated modes are often real modes with a larger number of nodes. How to effectively conduct correlation matching between calculated and experimental modes, and thus reasonably determine the modal order for subsequent model correction, needs to be prepared during the modal testing and modal analysis stages. Therefore, this paper proposes a modal testing method for gas turbine casings oriented towards model correction, comprehensively considering the process and technical points of modal testing and modal analysis of gas turbine casings, effectively solving the problem of mode shape identification and correlation matching between calculated and experimental modes of complex casing structures, and efficiently carrying out finite element model correction. Summary of the Invention

[0005] To address the problems of existing technologies, this invention provides a modal testing method for gas turbine casings oriented towards model correction. The technical solution is as follows:

[0006] On the one hand, a modal testing method for gas turbine casings oriented towards model correction is provided, including the following steps:

[0007] Step 1: Conduct radial free modal tests on the gas turbine casing to obtain real-valued test modal parameters;

[0008] Step 2: Establish an initial finite element model of the gas turbine casing, obtain the calculated modal parameters through modal analysis, and project the calculated modal shape vectors onto the direction of the experimental modal shape vectors;

[0009] Step 3: Based on the frequency relative error (FRE), modal confidence factor (MAC), and toroidal group rotation (MAC), complete the correlation matching between the calculated mode and the experimental mode.

[0010] Furthermore, the specific steps of step one are as follows:

[0011] Select the mounting edge, the rotating surface of the casing, and the cross-section of the support plate that can be struck by the hammer as the test section, and mark the circumference number of the test section.

[0012] Using the bolt holes on the outermost side of the casing, three to four sets of steel wire ropes are evenly arranged to suspend the casing horizontally along the axial direction towards the suspension side, simulating radial free constraint.

[0013] Using the available bolt holes on the test section, the sensor bracket is fixed by bolt connection, and the vibration acceleration sensor is installed in the radial plane of the casing. The number of the measuring point where each sensor is located and the measurement response direction vector are recorded.

[0014] The accelerometers were connected to the data acquisition unit. The moving hammer method with fixed sensor positions was used to perform five coherent tapping excitations on each measuring point in the test model, and the responses of each sensor were recorded at the same time.

[0015] By using the multi-reference point least squares complex exponential method and combining it with the modal indicator function, the radial modes of each order within the test frequency range are picked from the steady-state diagram, and the natural frequencies and damping ratios of each order radial mode are obtained. The corresponding complex mode shapes are then calculated by combining them with the established test model.

[0016] Calculate the amplitude and phase of each test mode shape, and use the product of the amplitude and the sign function value of the phase cosine as the realized test mode shape.

[0017] Furthermore, the step of selecting the cross-sections of the mounting edge, the rotating surface of the casing, and the support plate that are strikeable by the hammer as test sections, and marking the circumference number of the test sections, also includes...

[0018] The points corresponding to the symmetry line of the support plate and the bisector of the included angle on the mounting edge and the rotating surface of the casing are used as test impact points. The points at the inner and outer connections and the middle position on the cross-section of the support plate are also used as test impact points. The number, coordinate position and unit vector of the impact direction of each impact point are determined in the cylindrical coordinate system, and a wireframe test model is established by connecting points, lines and surfaces.

[0019] Furthermore, the method of evenly arranging three to four sets of steel wire ropes using the bolt holes on the outermost mounting edge of the casing to suspend the casing horizontally along the axial direction towards the suspension side, simulating radial free constraint, also includes:

[0020] Each set of wire ropes uses a winding method where the rope passes through a single hole from top to bottom and exits through an adjacent hole from bottom to top. The free end is fixed to the suspension device directly above, and the length of the free end rope is not less than the diameter of the installation side.

[0021] Furthermore, the method of fixing the sensor bracket by bolts through the available bolt holes on the test section, installing the vibration acceleration sensor in the radial plane of the casing, and recording the number of each sensor's measuring point and the measurement response direction vector, also includes:

[0022] When two or more sensors are arranged on the same test cross section circumference, adjacent sensors are distributed at approximately 90°.

[0023] Furthermore, the specific steps of step two are as follows:

[0024] Establish the initial finite element model of the casing;

[0025] By matching the coordinates of the nodes in the simulation model with the impact points in the test model, the nodes corresponding to the impact points are selected.

[0026] Free modal analysis yields the natural frequencies of the calculated modes and the mode shape vectors of the corresponding nodes;

[0027] The amplitude and phase of the calculated modal shape vector are synthesized in the radial plane to obtain the angle between the calculated modal shape vector and the impact direction. The amplitude of the calculated modal shape vector is projected onto the impact direction. Combined with the projection of the unit vector of the impact direction in the radial and circumferential directions at the impact point, the calculated modal shape in the same direction as the experimental modal shape vector is obtained.

[0028] Furthermore, the specific steps of step three are as follows:

[0029] Based on the experimental modal results, calculate the FRE and MAC between each calculated mode and the experimental mode;

[0030] According to the test circumference, the calculated mode shape vector is subjected to a toroidal group transformation, so that the calculated mode shape vector is rotated one by one to the position of the adjacent support plate, and the MAC after rotation is calculated. A total of several toroidal group rotation MACs of the support plate are obtained.

[0031] Based on the correlation matching between the calculated mode shape and the test mode shape in the rotating MAC matrix of the touring group, the vibration type of each mode is determined. Taking into account the complexity of the casing structure, the number of measurement points of the test model and the accuracy of the test results, the FRE and MAC thresholds for correlation matching are given.

[0032] Given the FRE and MAC thresholds, the correlation matching between the calculated modes and the experimental modes considering the frequency and mode shape is completed, and subsequent finite element model correction is carried out.

[0033] The beneficial effects of the technical solution provided by the embodiments of the present invention are as follows:

[0034] (1) This invention standardizes the process of radial free modal test of gas turbine casing, and clearly gives the suspension method of casing, the test impact point and the arrangement principle of vibration sensor, the precautions for traversing impact and the implementation method of complex modal realization, so as to ensure the accurate acquisition of test modal parameters;

[0035] (2) The correspondence between the nodes of the simulation model and the impact points of the test model is realized by coordinate matching, and the calculated modal shape vector is projected onto the direction of the test modal shape vector;

[0036] (3) Based on the relative frequency error, modal confidence factor (MAC) and toroidal group rotation (MAC), the problem of identifying complex mode shapes and matching correlations of the casing is solved, ensuring the efficient and smooth implementation of finite element model correction. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of a model-correction-oriented modal testing method for gas turbine casing according to an embodiment of the present invention;

[0039] Figure 2 A schematic diagram of the test model in an embodiment of the present invention;

[0040] Figure 3 A schematic diagram of the calculation model in an embodiment of the present invention;

[0041] Figure 4(a) is a radial schematic diagram of the projection of the calculated mode shape onto the test mode shape in an embodiment of the present invention;

[0042] Figure 4(b) is a circumferential schematic diagram of the projection of the calculated mode shape onto the test mode shape in an embodiment of the present invention;

[0043] Figure 5(a) Heatmap of the rotating MAC matrix of the touring group when α=0 in the embodiment of the present invention;

[0044] Figure 5(b) Heatmap of the rotating MAC matrix of the touring group when α=1 in the embodiment of the present invention;

[0045] Figure 5(c) Heatmap of the rotating MAC matrix of the touring group when α=2 in the embodiment of the present invention;

[0046] Figure 5(d) Heatmap of the rotating MAC matrix of the touring group when α=3 in the embodiment of the present invention;

[0047] Figure 5(e) Heatmap of the rotating MAC matrix of the touring group when α = 4 in the embodiment of the present invention;

[0048] Figure 5(f) Heatmap of the rotating MAC matrix of the touring group when α=5 in the embodiment of the present invention;

[0049] Figure 5(g) Heatmap of the rotating MAC matrix of the touring group when α=6 in the embodiment of the present invention;

[0050] Figure 5(h) Heatmap of the rotating MAC matrix of the circuit group when α=7 in the embodiment of the present invention;

[0051] Figure 5(i) Heatmap of the rotating MAC matrix of the touring group when α = 8 in the embodiment of the present invention;

[0052] Figure 5(j) Heatmap of the rotating MAC matrix of the circuit group when α=9 in the embodiment of the present invention;

[0053] Figure 5(k) Heatmap of the rotating MAC matrix of the circuit group when α = 10 in the embodiment of the present invention;

[0054] Figure 5(l) Heatmap of the rotating MAC matrix of the touring group when α=11 in the embodiment of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0056] This invention is a model-correction-oriented modal testing method for gas turbine casings, such as... Figure 1 As shown, it includes the following steps:

[0057] Step 1: Conduct radial free modal tests on the gas turbine casing to obtain real-valued test modal parameters;

[0058] Step 2: Establish an initial finite element model of the gas turbine casing, obtain the calculated modal parameters through modal analysis, and project the calculated modal shape vectors onto the direction of the experimental modal shape vectors;

[0059] Step 3: Determine the modal order for subsequent finite element model correction based on the relative frequency error, modal confidence factor (MAC), and tour group rotation (MAC).

[0060] The specific steps for Step One are as follows:

[0061] (1) Select the mounting edge, the rotating surface of the casing, and the cross-section of the support plate that can be struck by the hammer as test sections, and mark the circumference number of the test sections. In this embodiment, the form of letter C plus the circumference number is used for recording, such as C1 being the mounting edge on the front side of the outer ring; among them, the points corresponding to the symmetry line of the support plate and the bisector of its included angle on the rotating section are taken as test striking points, and the points at the inner and outer connection and the middle position on the cross-section of the support plate are taken as test striking points; determine the number and coordinate position (ρ) of 372 striking points in the cylindrical coordinate system O-PΘZ. E ,θ E ,z E ) and the unit vector γ of the striking direction E The subscript E represents the test mode; to facilitate coordinate matching with the simulation model nodes, the coordinates of the test impact points are transformed to a Cartesian coordinate system O-XYZ with the same origin; without loss of generality, the coordinate transformation method for a certain test impact point M is as follows:

[0062]

[0063] In the formula, Δx is the axial offset between the test model and the simulation model, and M is the unit vector of the impact direction. The superscripts X, Y, and Z represent the components of the three coordinate axes. By connecting 372 points into lines or surfaces, a wireframe-like test model is created, such as... Figure 2 As shown;

[0064] (2) Using the bolt holes on the outermost side of the casing, three sets of steel wire ropes are evenly arranged to suspend the casing horizontally along the axial direction towards the suspension side to simulate radial free constraint; each set of steel wire ropes adopts a winding method of passing through a single hole from top to bottom and passing through the adjacent hole from bottom to top, and the free end is fixed on the suspension device directly above, and the length of the free end rope is not less than the diameter of the installation side;

[0065] (3) Using the available bolt holes on the test section, fix the sensor bracket by bolt connection, install 12 unidirectional vibration acceleration sensors in the radial plane YOZ of the casing, record the number of the measuring point where each sensor is located and the measurement response direction vector; when two or more sensors are arranged on the circumference of the same test section, the two adjacent sensors are approximately 90° apart.

[0066] (4) Connect the arranged acceleration sensors to the data acquisition unit, and use the moving force hammer method with fixed sensor positions to perform five coherent tapping excitations on each measuring point in the test model, while recording the response of each sensor.

[0067] (5) By using the multi-reference point least squares complex exponential method and combining it with the modal indicator function, the first 10 modes are picked from the steady-state diagram to obtain the natural frequencies f of each radial mode. E Damping ratio λ E The corresponding complex mode shape vectors of each order are calculated based on the established test model.

[0068]

[0069] In the formula, the superscript T represents transpose, and the superscript C represents complex mode;

[0070] Among them, the k-th order mode shape The components of point M are expressed as follows j is the imaginary unit;

[0071] (6) Calculate the amplitude and phase of each test mode shape. For the k-th mode shape... There is point M in the middle.

[0072]

[0073] Amplitude With phase θ E,k The product of the sign function values ​​of the cosines is used as the experimental mode shape at point M after realization. Components, i.e.

[0074]

[0075] In the formula, the symbolic function is defined as follows:

[0076]

[0077] Similarly, the realized modal shape vectors of each order can be obtained.

[0078] The specific steps for step two are as follows:

[0079] (1) Ignoring local details such as openings, chamfers, and accessories, establish an initial finite element model of the casing, such as... Figure 3 As shown;

[0080] (2) By matching the coordinates of the simulation model nodes with the impact points of the test model, the nodes corresponding to the impact points are selected; without loss of generality, let the simulation model node N have coordinates (x... A ,y A ,z A If a point M in the test model can be matched, then we have

[0081] min((x A -x E ) 2 +(y A -y E ) 2 +(z A -z E ) 2 )

[0082] (3) The natural frequencies f of the first 14 calculated modes are obtained through free modal analysis. A and the modal shape vectors of the 372 nodes corresponding to the 372 test impact points.

[0083]

[0084] Among them, the i-th order mode shape The components of point N are expressed as follows

[0085] (4) Calculate the amplitude and phase of the mode shape vectors in the radial plane YOZ. For the first... i Calculation of mode shapes There are N points in the middle.

[0086]

[0087] Calculate the phase angle θ of the modal shape vector A,i The tapping direction at the matched test tapping point M The included angle is

[0088]

[0089] As shown in Figures 4(a) and 4(b), the amplitude of the modal shape vector will be calculated. Projected onto the direction of impact, combined with the unit vector of the impact direction at point M. By projecting the modal components in the radial and circumferential directions, we can obtain the calculated modal components that are in the same direction as the experimental modal vector.

[0090]

[0091] Similarly, the calculated modal shape is obtained in the same direction as the experimental modal shape vector.

[0092]

[0093] The specific steps for step three are as follows:

[0094] (1) Based on the experimental modal results, calculate the frequency relative error matrix FRE and MAC matrix MAC between each calculated mode and the experimental mode, as shown in Figure 5(a).

[0095]

[0096] The i-th computational mode and the k-th experimental mode can be expressed as follows:

[0097]

[0098] (2) Perform a circuit group transformation on the calculated modal shape vectors according to the test circumference, so that the calculated modal shape vectors The system rotates sequentially to the position adjacent to the support plate, with a rotation interval of 30°, and calculates the MAC after rotation, resulting in a total of 12 rotation MAC matrices MAC(α) for the cycle group; where, for the i-th order calculation mode and the k-th order test mode, the MAC is calculated. ik After rotating α times, we have

[0099]

[0100] In the formula, matrix T is the fundamental transformation matrix of the touring group.

[0101] Taking 24 test tapping points on circumference C1 as an example, each rotation changes 2 test tapping points. After α changes, there is...

[0102]

[0103] Where O is the zero matrix and E is the identity diagonal matrix;

[0104] (3) Based on the correlation matching between the calculated mode shape and the test mode shape in the rotating MAC matrix MAC(α) of the touring group, the vibration type of each mode is determined. As shown in Figure 5, the first 4 calculated modes are repeated once with the corresponding test modes after rotating 90°. See Figures 5(a), 5(d), 5(g) and 5(j) for details. That is, the first 4 modes are generally characterized by 2-nodal-diameter vibration. Considering the complexity of the casing structure, the number of measurement points of the test model and the accuracy of the test results, the FRE and MAC thresholds for correlation matching in this embodiment are given as 10% and 0.6, respectively.

[0105] (4) Under the given FRE and MAC thresholds, complete the correlation matching of the calculated mode and the test mode considering the frequency and mode shape. The correlation matching of the i-th calculated mode and the k-th test mode is denoted as (Ai,Ek), then there are (A1,E1), (A2,E2), (A3,E3), (A4,E4), (A6,E6), (A7,E7) and (A8,E10), and the subsequent finite element model correction is carried out accordingly.

[0106] The beneficial effects of the technical solution provided by the embodiments of the present invention are as follows:

[0107] This method can comprehensively address the process and key technical points of modal testing and analysis of gas turbine casings. It clearly defines the suspension method of the casing, the principles for the arrangement of test impact points and vibration sensors, the precautions for traversing impact points, and the implementation method for realizing complex modes, ensuring the accurate acquisition of test modal parameters. By projecting the calculated modal shape vectors onto the test modal shape vectors and combining the frequencies and modal shape indices, it solves the problem of identifying complex modal shapes of the casing and matching their correlations, ensuring the efficient and smooth implementation of finite element model correction.

[0108] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A modal testing method for gas turbine casings oriented towards model correction, characterized in that, Includes the following steps: Step 1: Conduct radial free modal tests on the gas turbine casing to obtain real-valued test modal parameters; Step 2: Establish an initial finite element model of the gas turbine casing, obtain the calculated modal parameters through modal analysis, and project the calculated modal shape vectors onto the direction of the experimental modal shape vectors; Step 3: Based on the frequency relative error (FRE), modal confidence factor (MAC), and circuit group rotation (MAC), complete the correlation matching between the calculated mode and the experimental mode; The specific steps of step one are as follows: Select the mounting edge, the rotating surface of the casing, and the cross-section of the support plate that can be struck by the hammer as the test section, and mark the circumference number of the test section. Using the bolt holes on the outermost side of the casing, three to four sets of steel wire ropes are evenly arranged to suspend the casing horizontally along the axial direction towards the suspension side, simulating radial free constraint. Using the available bolt holes on the test section, the sensor bracket is fixed by bolt connection, and the vibration acceleration sensor is installed in the radial plane of the casing. The number of the measuring point where each sensor is located and the measurement response direction vector are recorded. The accelerometers were connected to the data acquisition unit. The moving hammer method with fixed sensor positions was used to perform five coherent tapping excitations on each measuring point in the test model, and the responses of each sensor were recorded at the same time. By using the multi-reference point least squares complex exponential method and combining it with the modal indicator function, the radial modes of each order within the test frequency range are picked from the steady-state diagram, and the natural frequencies and damping ratios of each order radial mode are obtained. The corresponding complex mode shapes are then calculated by combining them with the established test model. Calculate the amplitude and phase of each test mode shape, and use the product of the amplitude and the sign function value of the phase cosine as the realized test mode shape.

2. The method for modal testing of gas turbine casings oriented towards model correction as described in claim 1, characterized in that, The selection of the mounting edge, the rotating surface of the casing, and the cross-section of the support plate that can be struck by the hammer as the test section, and the marking of the circumference number of the test section, also includes... The points corresponding to the symmetry line of the support plate and the bisector of the included angle on the mounting edge and the rotating surface of the casing are used as test impact points. The points at the inner and outer connections and the middle position on the cross-section of the support plate are also used as test impact points. The number, coordinate position and unit vector of the impact direction of each impact point are determined in the cylindrical coordinate system, and a wireframe test model is established by connecting points, lines and surfaces.

3. The method for modal testing of gas turbine casings oriented towards model correction as described in claim 1, characterized in that, The method of evenly arranging three to four sets of steel wire ropes using the bolt holes on the outermost mounting edge of the casing to suspend the casing horizontally along the axial direction towards the suspension side, simulating radial free constraint, also includes: Each set of wire ropes uses a winding method where the rope passes through a single hole from top to bottom and exits through an adjacent hole from bottom to top. The free end is fixed to the suspension device directly above, and the length of the free end rope is not less than the diameter of the installation side.

4. The method for modal testing of gas turbine casings oriented towards model correction as described in claim 1, characterized in that, The method of fixing the sensor bracket by bolts through available bolt holes on the test section, installing the vibration acceleration sensor in the radial plane of the casing, and recording the number of each sensor's measuring point and the measurement response direction vector also includes: When two or more sensors are arranged on the same test cross section circumference, adjacent sensors are distributed at approximately 90°.

5. The method for modal testing of gas turbine casings oriented towards model correction as described in claim 1, characterized in that, The specific steps of step two are as follows: Establish the initial finite element model of the casing; By matching the coordinates of the nodes in the simulation model with the impact points in the test model, the nodes corresponding to the impact points are selected. Free modal analysis yields the natural frequencies of the calculated modes and the mode shape vectors of the corresponding nodes; The amplitude and phase of the calculated modal shape vector are synthesized in the radial plane to obtain the angle between the calculated modal shape vector and the impact direction. The amplitude of the calculated modal shape vector is projected onto the impact direction. Combined with the projection of the unit vector of the impact direction in the radial and circumferential directions at the impact point, the calculated modal shape in the same direction as the experimental modal shape vector is obtained.

6. The method for modal testing of gas turbine casings oriented towards model correction as described in claim 1, characterized in that, The specific steps of step three are as follows: Based on the experimental modal results, calculate the FRE and MAC between each calculated mode and the experimental mode; According to the test circumference, the calculated mode shape vector is subjected to a toroidal group transformation, so that the calculated mode shape vector is rotated one by one to the position of the adjacent support plate, and the MAC after rotation is calculated. A total of several toroidal group rotation MACs of the support plate are obtained. Based on the correlation matching between the calculated mode shape and the test mode shape in the rotating MAC matrix of the touring group, the vibration type of each mode is determined. Taking into account the complexity of the casing structure, the number of measurement points of the test model and the accuracy of the test results, the FRE and MAC thresholds for correlation matching are given. Given the FRE and MAC thresholds, the correlation matching between the calculated modes and the experimental modes considering the frequency and mode shape is completed, and subsequent finite element model correction is carried out.

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