Modal analysis method of fan driving gearbox system

Abstract

The invention provides a modal analysis method for a fan driving gearbox system, which comprises the following steps of: S1, establishing a three-dimensional model of the fan driving gearbox system, and simplifying a gear pair wheel body in the fan driving gearbox system; s2, carrying out free modal analysis on the wheel body before and after simplification; s3, calculating the meshing stiffness of each single gear pair; s4, establishing connection on the gear pair based on the meshing stiffness matrix; s5, calculating the support stiffness of the bearing mounting surfaces of the input shaft and the output shaft, and applying the support stiffness to the bearing mounting surfaces of the input shaft and the output shaft; and S6, setting a boundary condition and a frequency analysis range of modal analysis, performing calculation, and performing modal identification on a modal calculation result to obtain a resonance rotating speed. According to the method, a more accurate calculation result can be provided.

Description

Technical Field

[0001] The present invention relates to the field of aero engines, and in particular to the field of fan drive gear boxes. Background Art

[0002] With the continuous improvement of the research and development and design level of aircraft engines, the gear-driven turbofan engine came into being. Its design concept is to install a set of gear reducers between the low-pressure rotor and the fan rotor composed of the boost stage and the low-pressure turbine, so that the fan rotor works at a low speed and the low-pressure rotor works at a high speed. The gear reducer is the fan drive gearbox, which adopts a star-type gear train herringbone gear transmission structure. In order to ensure the normal operation of the gear-driven turbofan engine, it is necessary to ensure that the vibration of the fan drive gearbox within the working speed range meets the airworthiness requirements.

[0003] The direct cause of abnormal vibration of the fan drive gearbox is generally that the excitation frequency hits the natural frequency of the system, the system resonates, and the vibration exceeds the limit, and even damages the components. The excitation frequency includes internal excitation and external excitation. The internal excitation is mainly the meshing frequency excitation of the gear system, which is the inherent characteristic of the involute gear; the external excitation includes the excitation caused by various errors and the excitation transmitted by other connecting parts. From the perspective of probability, external excitation is accidental and internal excitation is inevitable, so the modal analysis of the fan gear system needs to be combined with internal excitation.

[0004] At present, there are three main problems with the modal analysis methods of fan drive gearbox systems: (1) Existing system-level modal analysis mostly uses a discrete multi-degree-of-freedom mass-spring model, which greatly simplifies the structure and ignores many details of the three-dimensional model. There are problems of loss and non-intuitiveness in modal analysis; (2) The meshing excitation of the gear system is not considered reasonable. Common three-dimensional model modal analysis mostly uses constant meshing force loading to perform single gear shaft modal analysis or uses binding constraints to constrain gear pairs, ignoring the coupling of the gear system, resulting in a large difference between the calculated mode and the experiment; (3) The contact algorithm is used to calculate the contact of the gear pair and then calculate the prestressed mode. This method has a huge amount of calculation and takes a long time to calculate. Few hardware configurations can meet the requirements and is not applicable in engineering. Summary of the invention

[0005] An object of the present invention is to provide a modal analysis method for a fan drive gearbox system, which can provide more accurate calculation results.

[0006] To achieve the above-mentioned purpose, the modal analysis method of the fan drive gearbox system includes the following steps: S1 establishes a three-dimensional model of the fan drive gearbox system and simplifies the gear pair wheel body in the fan drive gearbox system; S2 performs free modal analysis on the wheel body before and after simplification; S3 calculates the meshing stiffness of each single pair of gear pairs; S4 establishes a connection on the gear pair based on the meshing stiffness matrix; S5 calculates the support stiffness of the bearing mounting surfaces of the input shaft and the output shaft, and applies it to the bearing mounting surfaces of the input shaft and the output shaft; S6 sets the boundary conditions and frequency analysis range of the modal analysis, performs calculations, performs modal identification on the modal calculation results, and obtains the resonant speed.

[0007] In one or more embodiments, in step S1, the simplification step of the gear pair wheel body is: cutting off the gear teeth part and part of the wheel rim, and applying the mass of the cut part to the center of mass of the wheel body in the form of a mass point.

[0008] In one or more embodiments, in step S3, the meshing stiffness is calculated by using a meshing stiffness formula or a contact algorithm.

[0009] In one or more embodiments, in S4, the gear pair includes a sun gear-planet gear pair and a planet gear-internal gear ring gear pair, and the steps of establishing a connection are: setting the planetary gear to two independent gear pair objects, namely, planetary gear-sun gear and planetary gear-internal gear ring, and establishing meshing boundary conditions respectively; establishing a distal end point with its base circle surface as a mapping surface at each tooth of the sun gear and the planetary gear, and connecting the distal end point at the sun gear with the distal end point at each planetary gear with a spring unit; dividing the inner ring surface of the internal gear ring into multiple parts, establishing multiple distal end points located on the base circle surface of the internal gear ring and with the inner ring surface of the internal gear ring as a mapping surface, and establishing a central distal end point with the multiple distal end points as a reference; connecting the distal end point at each planetary gear with the central distal end point with a spring unit; and assigning a meshing stiffness diagonal matrix to each of the spring units.

[0010] In one or more embodiments, the meshing stiffness diagonal matrix is ​​a 12x12 meshing stiffness diagonal matrix:

[0011]

[0012] Where C is a constant.

[0013] In one or more embodiments, in step S5, the stiffness of the bearing and the casing after the joint action is used as the support stiffness of the bearing mounting surfaces of the input shaft and the output shaft, and is applied to the bearing mounting surfaces of the input shaft and the output shaft in the form of a bushing unit.

[0014] In one or more embodiments, in step S6, a displacement constraint is set on the fixed surface as a boundary condition, and a modal analysis frequency range covering at least one times of the meshing frequency is set according to the speed range of the fan drive gearbox.

[0015] In one or more embodiments, the three-dimensional model of the fan drive gearbox system includes an input shaft, an output shaft, a sun gear, planetary gears, a torque transmission bracket, and a planet carrier.

[0016] In one or more embodiments, in step S6, a Campbell diagram is drawn in combination with the modal analysis results, and the resonant speed is obtained by analyzing the intersection of the meshing frequency line and the natural frequency.

[0017] The above method is based on the gear meshing stiffness matrix. It does not adopt the traditional method of massive structural simplification. Instead, it uses ANSYS software to establish a full three-dimensional finite element model, such as establishing a detailed connection relationship between multiple pairs of gear pairs in a full three-dimensional fan drive gearbox, and then applying the support stiffness of the transmission system bearing-casing, etc., applying the gear meshing stiffness matrix between the surfaces, and analyzing the modal characteristics of the system, thereby effectively improving the calculation accuracy and avoiding the problem of neglecting details and reducing accuracy due to simplification, thereby providing a valuable reference method for the resonance prediction and resonance cause analysis of the fan drive gearbox system, and the analysis results are highly accurate and intuitive. In addition, the method also comprehensively considers the calculation time cost and computer hardware configuration, and fully considers the operability of engineers, providing a set of analysis methods with short calculation time, low hardware configuration requirements, and strong operability. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The above and other features, properties and advantages of the present invention will become more apparent through the following description in conjunction with the accompanying drawings and embodiments, in which:

[0019] Figure 1 is a schematic structural diagram of an embodiment of a fan drive gearbox system;

[0020] Figure 2 It is a simplified schematic diagram of a gear pair;

[0021] Figure 3 is a flow chart of the modal analysis method for the fan drive gearbox system;

[0022] Figure 4 It is a schematic diagram of the meshing stiffness curve of helical gears;

[0023] Figure 5 It is a schematic diagram of the sun gear-planet gear pair connection;

[0024] Figure 6 It is a schematic diagram of the connection between the planetary gear and the internal ring gear pair;

[0025] Figure 7 It is a specific implementation flow chart of the modal analysis method of the fan drive gearbox system. DETAILED DESCRIPTION

[0026] The present invention is further described below in conjunction with specific embodiments and drawings. More details are elaborated in the following description to facilitate a full understanding of the present invention. However, the present invention can obviously be implemented in a variety of other ways different from the description herein. Those skilled in the art can make similar generalizations and deductions based on actual application situations without violating the connotation of the present invention. Therefore, the protection scope of the present invention should not be limited by the content of this specific embodiment.

[0027] It should be noted that these and other subsequent drawings are only examples and are not drawn to scale, and should not be used to limit the actual scope of protection required by the present invention.

[0028] The fan drive gearbox is a reduction gearbox installed between the low-pressure compressor and the fan. It is generally a star-shaped gear train, which allows the fan to work at a low speed and the compressor to work at a high speed, thereby improving the efficiency of the engine. Figure 1 As shown, the fan drive gearbox generally includes a sun gear 1, a planetary gear 2, an inner gear ring 3, an input shaft 4, an output shaft 5, a planet carrier 6, and a torque transmission bracket 7, and also includes a fixed bracket 8 and a casing fixed position 11. Among them, the input shaft 4 and the sun gear 1 form a gear pair, the output shaft 4 and the inner gear ring 3 form a gear pair, the sun gear and the planetary gear form a gear pair, and the planetary gear and the inner gear ring 3 form a gear pair.

[0029] The current modal analysis method for fan drive gearbox system cannot provide more precise calculation data. The modal analysis method for fan drive gearbox system disclosed in the present invention can obtain more accurate analysis results and improve engineering practice efficiency.

[0030] Modal analysis methods for fan drive gearbox systems are as follows: Figure 3 As shown, the method includes the following steps: S1. Establish a three-dimensional model of the fan drive gearbox system and simplify the gear pair wheel body in the fan drive gearbox system; S2. Perform free modal analysis on the wheel body before and after simplification; S3 calculate the meshing stiffness of each single pair of gear pairs; S4 establish a connection on the gear pair based on the meshing stiffness matrix, such as the sun gear-planet gear pair and the planet gear-ring gear pair; S5 calculate the support stiffness of the input shaft and output shaft bearing mounting surface, and apply it to the input shaft and output shaft bearing mounting surface; S6 set the boundary conditions and frequency analysis range of the modal analysis, and perform calculations, perform modal identification on the modal calculation results, and obtain the resonant speed. After obtaining the resonant speed, the resonance prediction and resonance cause analysis of the fan drive gearbox transmission system can be realized.

[0031] For example, step S7 may also be included to check whether the resonant speed obtained in S6 meets the vibration requirements. If not, steps S1-S5 are adjusted until the resonant speed of the model meets the vibration requirements, indicating that the model meets the requirements and can guide subsequent actual assembly links.

[0032] Specifically, in S1, the three-dimensional model of the fan drive gearbox system is imported into the finite element software, and the corresponding material parameters are applied. The three-dimensional model mainly includes a sun gear 1-planet gear 2-internal gear ring 3 gear pair, an input gear shaft 4, an output gear shaft 5, a planetary carrier 6 and a torque transmission bracket 7, wherein the planetary gear, sun gear and internal gear ring are all herringbone gears. The step of simplifying the gear pair wheel body refers to cutting off the gear tooth part and part of the wheel rim, and applying the cut-off mass to the center of mass of the wheel body in the form of a mass point. To facilitate the application of the meshing matrix, the wheel body is cut along the gear base circle, and a common node constraint is set. The internal spline of the sun gear 1 is similar to the gear, and is also simplified in the above manner to obtain a simplified sun gear 8, a simplified planetary gear 9 and a simplified internal gear ring 10, as shown in FIG. Figure 5 and Figure 6 shown. Figure 5 In the figure, A represents the sun gear, B represents the mass of the gear teeth removed from the inner ring gear, and C represents the mass of the spline of the inner ring of the sun gear. The points A, B, and C coincide at Figure 5 Center, DH are the masses of the teeth deleted from the five planetary gears; Figure 6 It shows 10 connections between the inner ring gear and the planetary gear, connected by a spring connection model.

[0033] In step S2, the free modal analysis before and after simplification should ensure that the free modal frequency error of the sun gear 1 and the planetary gear 2 before and after removal does not exceed 3%, and the vibration mode is not affected, and the free modal frequency error of the inner ring gear 3 before and after simplification does not exceed 7%, and the vibration mode is not affected.

[0034] In step S3, two methods can be used to calculate the meshing stiffness of a single pair of sun gear-planet gear and planet gear-ring gear. One is to use the meshing stiffness formula to calculate when the gear parameters meet the ISO standard. The second is to use the contact algorithm for analysis, that is, to establish a quasi-static contact analysis model for gear meshing, extract the rotation angle of the master and driven gears over time, and calculate the time-varying meshing stiffness curve based on the applied load. The fluctuation of the meshing stiffness curve of the herringbone gear over time is small, and the average meshing stiffness is taken as the input of the meshing stiffness matrix.

[0035] The meshing stiffness matrix [K] is:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] Where c = cosα nn ,s=sinα nn ,c b =cosβ,s b = sinβ, α n refers to the gear pressure angle, β is the helix angle, r p,g K is the radius of the gear base circle. m is the average value of the calculated meshing stiffness. The meshing stiffness matrix above realizes the matrix calculation between surfaces, which can effectively improve the calculation simulation accuracy compared with the simplified single point method.

[0042] In S4, the steps of establishing a connection on the gear pair are as follows: setting the planetary gears into two independent gear pair objects of planetary gear-sun gear and planetary gear-inner gear ring, respectively establishing meshing boundary conditions; establishing a distal end point with its base circle surface as the mapping surface at each tooth of the sun gear 8 and the planetary gear 9, and for the sun gear 8 and the planetary gear 9 of the herringbone gear structure, establishing a distal end point at half of each herringbone tooth (similar to the helical tooth), and connecting the distal end point of the sun gear 8 with the distal end point of each planetary gear 9 by a spring unit; dividing the inner annular surface of the inner gear ring into multiple parts according to the number of planetary gears, such as Figure 5 and Figure 6 In the five planetary gear system embodiments shown, the inner surface of the inner ring gear 10 is equally divided into 5 or multiples of 5, and a plurality of distal end points located on the base circle surface of the inner ring gear 10 and taking the inner surface of the inner ring gear 10 as the mapping surface are established, and the number of the distal end points is the number of equal divisions, and then a central distal end point is established based on the above distal end points; the distal end point at each planetary gear 9 is connected to the central distal end point by a spring unit; and a meshing stiffness diagonal matrix is ​​assigned to each spring unit.

[0043] At this point, the gear meshing characteristics of the sun gear 8, planetary gear 9 and ring gear 10 have been simplified to a spring connection model. The two sets of helical teeth are connected by 20 springs in total. Under each spring, a set of APDL commands is added to replace the original COMBIN14 unit with the MATRIX27 unit to give a 12x12 meshing stiffness diagonal matrix. The meshing stiffness diagonal matrix refers to:

[0044]

[0045] Where C is a constant calculated by the K matrix, such as K 11m c b 2 s 2 After calculation, it is C1 here. That is, the 12×12 matrix here. Since each pair of action points has 12 relationships, the meshing stiffness diagonal matrix here is a 12x12 meshing stiffness diagonal matrix.

[0046] In step S5, the stiffness of the bearing and the casing after the joint action is used as the support stiffness of the bearing mounting surfaces of the input shaft 4 and the output shaft 5, and is applied to the bearing mounting surfaces of the input shaft and the output shaft in the form of a bushing unit.

[0047] In step S6, setting the boundary conditions and frequency analysis range of the modal analysis refers to setting displacement constraints on the fixed surface, and setting a modal analysis frequency range that covers at least one times the meshing frequency according to the speed range of the fan drive gearbox. Modal identification refers to selecting the bending vibration mode of the shaft, the five-pitch vibration mode of the inner ring gear, and other five-pitch coupling vibration modes that are more dangerous to the fan drive gearbox. The resonant speed refers to drawing a Campbell diagram in combination with the modal analysis results. The intersection of the meshing frequency line and the natural frequency is the resonant speed obtained by analysis.

[0048] After the resonant speed is obtained, it is checked whether the vibration requirement is met. If not, it is necessary to return to step S1 to make further structural adjustments to the model until the resonant speed of the model meets the vibration requirement.

[0049] Combine the following Figure 7 A flowchart of a specific embodiment is shown to further illustrate what is described in the present application.

[0050] First, step S101 is performed to import the three-dimensional model of the fan drive gearbox system and apply material parameters; then steps S102 and S103 are performed to simplify the gear pair body and perform free modal analysis on the gears before and after simplification. A judgment step S104 is performed to determine whether the simplification requirements are met. The free modal analysis before and after simplification should ensure that the free modal frequency error of the sun gear 1 and the planetary gear 2 before and after the removal does not exceed 3%, and the free modal frequency error of the inner ring gear 3 before and after simplification does not exceed 7%.

[0051] Then, steps S105-109 are performed to establish a gear pair connection based on the meshing stiffness matrix, apply support stiffness at the bearing, set boundary adjustment and analysis range, perform modal identification, select the bending vibration mode of the shaft, the five-pitch diameter vibration mode of the inner gear ring, and other five-pitch diameter coupling vibration modes that are more dangerous to the fan drive gearbox, and obtain the intersection of the meshing frequency line and the natural frequency by drawing the Campbell diagram, that is, the resonant speed.

[0052] Finally, a judgment step S110 is performed to check whether the resonant speed obtained in S6 meets the vibration requirements. If not, the resonance prediction and resonance cause of the fan drive gearbox transmission system are analyzed, and the process returns to step S101 until the resonant speed of the model meets the vibration requirements, indicating that the model meets the requirements and can guide subsequent actual assembly steps.

[0053] The above method is based on the gear meshing stiffness matrix. ANSYS software is used to establish the connection between multiple pairs of gear pairs in the fan drive gearbox system, and then the support stiffness of the transmission system bearing-casing, etc. is applied to establish a complete three-dimensional finite element modal analysis model. A systematic analysis and study of the system modal characteristics is carried out, and the stiffness matrix between surfaces is applied. The relationship between multiple pairs of gear pairs is comprehensively considered, thereby effectively improving the calculation accuracy. It provides a valuable reference method for the resonance prediction and resonance cause analysis of the fan drive gearbox system.

[0054] In addition, the above method fully considers the coupling effect of the gear system and the supporting effect of each connecting part, introduces the gear meshing stiffness matrix and the support stiffness of the transmission system bearing-casing, etc., establishes the coupling effect of the gear system and the supporting effect of each connecting part that need to be considered when establishing the analysis model, and also comprehensively considers the calculation time cost and computer hardware configuration, and fully considers the operability of engineers, with short calculation time, low hardware configuration requirements and strong operability.

[0055] Although the present invention is disclosed as above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, any modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope defined by the claims of the present invention.

Claims

1. A modal analysis method for a fan drive gearbox system, characterized in that: The steps include: S1 establishes a three-dimensional model of the fan drive gearbox system and simplifies the gear pair body in the fan drive gearbox system; S2 performs free modal analysis on the wheel body before and after simplification respectively; S3 calculates the meshing stiffness of each single pair of gears; S4 establishes connections on the gear pair based on the meshing stiffness matrix; S5 calculates the support stiffness of the bearing mounting surfaces of the input shaft and the output shaft, and applies it to the bearing mounting surfaces of the input shaft and the output shaft; S6 sets the boundary conditions and frequency analysis range of the modal analysis, performs calculations, performs modal identification on the modal calculation results, and obtains the resonant speed.

2. The modal analysis method of the fan drive gearbox system according to claim 1, characterized in that: In step S1, the steps for simplifying the wheel body of the gear pair are: cutting off the gear teeth part and part of the wheel rim, and applying the mass of the cut part to the center of mass of the wheel body in the form of a mass point.

3. The modal analysis method of the fan drive gearbox system according to claim 1, characterized in that: In step S3, the meshing stiffness is calculated by using a meshing stiffness formula or a contact algorithm.

4. The modal analysis method of a fan drive gearbox system according to claim 1, characterized in that: In S4, the gear pair includes a sun gear-planet gear pair and a planet gear-ring gear pair, and the steps of establishing the connection are: Set the planetary gears to two independent gear pairs: planetary gear-sun gear and planetary gear-ring gear, and establish meshing boundary conditions for each pair. A distal point with its base circle surface as the mapping surface is established at each tooth of the sun gear and the planet gear, and the distal point at the sun gear is connected with the distal point at each planet gear by a spring unit; The inner ring surface of the inner gear ring is divided into multiple parts, multiple distal end points located on the base circle surface of the inner gear ring are established, the inner ring surface of the inner gear ring is used as the mapping surface, and the central distal end point is established based on the multiple distal end points; Connect the distal end point of each planetary gear with the central distal end point using a spring unit; A meshing stiffness diagonal matrix is ​​assigned to each of the spring units.

5. The modal analysis method of the fan drive gearbox system according to claim 4, characterized in that: The meshing stiffness diagonal matrix is ​​a 12x12 meshing stiffness diagonal matrix: Where C is a constant.

6. The modal analysis method of a fan drive gearbox system according to claim 1, characterized in that: In step S5, the stiffness of the bearing and the casing after the joint action is used as the support stiffness of the bearing mounting surfaces of the input shaft and the output shaft, and is applied to the bearing mounting surfaces of the input shaft and the output shaft in the form of a bushing unit.

7. The modal analysis method of a fan drive gearbox system according to claim 1, characterized in that: In step S6, a displacement constraint is set on the fixed surface as a boundary condition, and a modal analysis frequency range covering at least one times of the meshing frequency is set according to the speed range of the fan drive gearbox.

8. The modal analysis method of a fan drive gearbox system according to claim 1, characterized in that: The three-dimensional model of the fan drive gearbox system includes an input shaft, an output shaft, a sun gear, a planetary gear, a torque transmission bracket and a planet carrier.

9. The modal analysis method of a fan drive gearbox system according to claim 1, characterized in that: In step S6, a Campbell diagram is drawn in combination with the modal analysis results, and the resonant speed is obtained by analyzing the intersection of the meshing frequency line and the natural frequency.

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