Vibration analysis method of planetary gear train

Abstract

The invention provides a vibration analysis method of a planetary gear train, which is used for a planetary gear train with a misaligned flexible input shaft, and comprises the following steps: S1, establishing a three-dimensional finite element model of a planetary gear, carrying out modal analysis, and determining the danger frequency of a misalignment problem; s2, reserving a main node at a key position; s3, carrying out super-unit polycondensation on the planetary gear train; s4, dividing the input shaft according to a whole machine deformation result, and determining a connection section; s5, establishing a mechanical model of misalignment of the input shaft; s6, according to the modal shape and frequency of the three-dimensional model, selecting frequencies f1 and f2 corresponding to the bending shape as misalignment excitation frequencies, and adding an excitation load into the super-unit model to form a planetary gear train misalignment kinetic equation; and S7, performing time domain solution on the kinetic equation, and performing post-processing on a solution result. According to the method, the vibration amplitude generated by misalignment caused by complete machine deformation can be predicted, the design criterion of the flexible input shaft is perfected, and the process of repeated verification through multiple tests is shortened.

Description

Technical Field

[0001] This invention relates to the field of vibration analysis methods, and in particular to a vibration analysis method for planetary gear trains. Background Technology

[0002] In the existing technology, for GTF (Geared Turbofan) aircraft engines, the gearbox is an extremely important transmission device. In order to meet the requirements of large transmission ratio and high power transmission, the design size of the planetary gear train components of the gearbox will be larger, and the design of the planetary gear train will be more complex.

[0003] To reduce vibration and effectively alleviate the eccentricity problem between the fan shaft and the low-pressure turbine shaft, the input shaft usually adopts a flexible structure, which can simultaneously achieve decoupling of the vibration modes between the two.

[0004] Currently, most vibration simulation analysis methods for gearboxes in GTF aero engines focus on gear meshing and unbalanced vibration analysis. For misalignment issues, most methods involve collecting vibration data during experiments to identify misalignment faults.

[0005] Under the influence of aircraft maneuvering loads, the entire aircraft will deform, leading to parallel and angular misalignment issues between the fan shaft and the low-pressure turbine shaft of the GTF aero-engine gearbox. To mitigate the vibration caused by this problem, the input shaft is designed as a flexible shaft.

[0006] In order to quantitatively understand the magnitude of vibration caused by misalignment and to provide feedback guidance for the structural design of the input shaft, it is necessary to establish a simulation method for planetary gear trains that includes input shaft misalignment, and gradually improve the basis for input shaft design, thereby accelerating the design iteration of GTF aero engines.

[0007] However, there is currently no detailed simulation analysis method for the eccentricity problem caused by overall machine deformation in the flexible input shaft. Therefore, it is impossible to predict in advance the magnitude of the impact of misalignment between the fan shaft and the low-pressure turbine shaft.

[0008] In view of this, in order to address the misalignment problem caused by overall deformation of the flexible input shaft, the inventors of this application have designed a vibration analysis method for planetary gear trains in order to overcome the above-mentioned technical problems. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to overcome the misalignment defect caused by the overall deformation of the flexible input shaft of the planetary gear train in the prior art, and to provide a vibration analysis method for the planetary gear train.

[0010] The present invention solves the above-mentioned technical problems through the following technical solution:

[0011] A vibration analysis method for planetary gear trains, characterized in that the vibration analysis method is applied to planetary gear trains with misaligned flexible input shafts, and includes the following steps:

[0012] S1. Establish a three-dimensional finite element model of the planetary gear, perform modal analysis, and determine the critical frequency of misalignment problems;

[0013] S2, retain the master nodes in key positions;

[0014] S3. Perform super-unit condensation on the planetary gear train;

[0015] S4. Divide the input shaft according to the deformation results of the whole machine and determine the connection section;

[0016] S5. Establish a mechanical model for input axis misalignment;

[0017] S6. Based on the mode shapes and frequencies of the three-dimensional model, select the frequencies f1 and f2 corresponding to the bending mode shape as the excitation frequencies for misalignment, add the excitation load to the super-element model, and form the dynamic equations for the planetary gear train misalignment problem.

[0018] S7. Solve the dynamic equations in the time domain and perform post-processing on the solution results.

[0019] According to an embodiment of the present invention, step S1 includes: setting internal connection relationships, boundary constraints and support stiffness damping for the planetary gear train.

[0020] According to one embodiment of the present invention, the master node of the key location in step S2 includes the load application location, the boundary, and the required monitoring location.

[0021] According to an embodiment of the present invention, step S3 includes: considering the rotational speed characteristics and gyroscopic effect of the planetary gear train, it is divided into three super units: the input shaft rotor super unit, the output shaft rotor super unit, and the stator super unit.

[0022] According to one embodiment of the present invention, in step S4, the input shaft is divided into a driven rotor, a connecting section and a driving rotor, and the connecting section is misaligned.

[0023] According to an embodiment of the present invention, step S5 includes: equating the connecting segment to a coupling, including parallel misalignment, angular misalignment and mixed misalignment.

[0024] According to one embodiment of the present invention, the parallel misalignment is equivalent to applying a misalignment excitation force at the connection between the rotor and the coupling, with misalignment fault excitation force F in both the x and y directions. x and F y The expression is:

[0025]

[0026] Where M represents the equivalent mass of the coupling, and Δe represents the amount of parallel misalignment. ω represents the initial phase, ω represents the rotor speed, and t represents time.

[0027] According to one embodiment of the present invention, the angular misalignment is equivalent to the bending moment at the connection between the rotor and the coupling, the misalignment angle between the driving rotor and the driven rotor is α, and the angle between the projection axis and the x-axis after the driving rotor is projected onto the xy plane is β.

[0028] The torque T of the driving rotor, after being transmitted to the driven rotor via the coupling, can be decomposed into two parts T. z and T s ;

[0029] Among them, T z =Tcosα;T s =Tsinα;

[0030] T s Further decomposed into bending moments in the x and y directions:

[0031] T x =Tsinαcosβ;T y =Tsinαcosβ.

[0032] According to an embodiment of the present invention, the dynamic equation for the planetary gear train misalignment problem in step S6 is:

[0033]

[0034] Where M represents the equivalent mass of the coupling, F represents the excitation force generated by the parallel misalignment of the input shaft coupling, and T x T y This indicates the bending moment caused by angular misalignment.

[0035] According to an embodiment of the present invention, the post-processing in step S7 includes: observing the spectral characteristics and comparing the radial displacement and acceleration of the bearing position under undamped and damped conditions at two excitation frequencies f1 and f2.

[0036] The positive and progressive effects of this invention are as follows:

[0037] The vibration analysis method for planetary gear trains of this invention can predict the vibration amplitude caused by misalignment due to deformation of the whole machine, thereby providing a quantitative basis for the design of the input shaft.

[0038] The vibration analysis method improves the design criteria for flexible input shafts, accelerates the iterative design of structures, and shortens the process of repeated verification through multiple experiments. Attached Figure Description

[0039] The above and other features, properties and advantages of the present invention will become more apparent from the following description taken in conjunction with the accompanying drawings and embodiments, in which the same reference numerals always denote the same features, wherein:

[0040] Figure 1 This is a schematic diagram of a planetary gear train with a GTF configuration.

[0041] Figure 2 This is a flowchart of the vibration analysis method for planetary gear trains according to the present invention.

[0042] Figure 3 This is a schematic diagram of the equivalent partitioning of the input shaft in the vibration analysis method of the planetary gear train of the present invention.

[0043] Figure 4 This is a schematic diagram of the vibration results at excitation frequency f1 in the vibration analysis method of the planetary gear train of the present invention.

[0044] Figure 5 This is a schematic diagram of the vibration results at excitation frequency f2 in the vibration analysis method of the planetary gear train of the present invention. Detailed Implementation

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0046] Embodiments of the invention will now be described in detail with reference to the accompanying drawings. Preferred embodiments of the invention will now be described in detail, examples of which are shown in the drawings. Wherever possible, the same reference numerals will be used in all the drawings to denote the same or similar parts.

[0047] Furthermore, although the terminology used in this invention is selected from commonly known and used terms, some terms mentioned in this specification may have been selected by the applicant in his or her judgment, and their detailed meanings are explained in the relevant sections of the description herein.

[0048] Furthermore, the invention should be understood not only through the actual terminology used, but also through the meaning implied by each term.

[0049] like Figure 1As shown, the GTF planetary gear train includes an input shaft 10, a sun gear 20, planet gears 30, a ring gear 40, a fan output shaft 50, a planet carrier 60, a support structure 70, and a first bearing 80, a second bearing 81, and a third bearing 82. The sun gear 20 and the third bearing 82 are mounted on the input shaft 10, while the first bearing 80 and the second bearing 81 are sequentially mounted on the fan output shaft 50. The planet carrier 60 is mounted on the support structure 70, the planet gears 30 are mounted on the planet carrier 60, and the ring gear 40 is connected to the fan output shaft 50 and located outside the planet gears 30.

[0050] like Figures 2 to 5 As shown, this invention discloses a vibration analysis method for planetary gear trains, specifically for planetary gear trains with misaligned flexible input shafts. The flexible input shaft refers to the input shaft in the planetary gear train, which has low stiffness and serves to reduce the effects of eccentricity and system vibration. Misalignment typically refers to the degree of inclination or offset between the centerlines of two adjacent rotors. A planetary gear train is a gear train with only one degree of freedom; it is a coaxial transmission device (i.e., the output axis coincides with the input axis) and uses several identical planetary gears evenly distributed around the central gear. Vibration analysis refers to analyzing a series of characteristics exhibited by an object during vibration, mainly including natural frequency, resonant frequency, and amplitude.

[0051] The vibration analysis method includes the following steps:

[0052] Step S1: Establish a three-dimensional finite element model of the planetary gear, perform modal analysis, and determine the critical frequency of misalignment problems.

[0053] Preferably, step S1 includes: setting internal connection relationships, boundary constraints, and support stiffness damping for the planetary gear train.

[0054] Step S2: Retain the master nodes at key locations.

[0055] Preferably, the key nodes in step S2 include the load application location, the boundary, and the required monitoring location.

[0056] Step S3: Perform super-unit condensation on the planetary gear train.

[0057] Preferably, step S3 includes: considering the rotational speed characteristics and gyroscopic effect of the planetary gear train, it is divided into three super units: the input shaft rotor super unit, the output shaft rotor super unit, and the stator super unit.

[0058] In step S3, the mass matrix M, stiffness matrix K, and damping matrix C are derived.

[0059] Step S4: Divide the input shaft according to the deformation results of the whole machine and determine the connection section.

[0060] Preferably, such as Figure 3 As shown, in step S4, the input shaft is divided into a driven rotor (e.g., the sun gear end section 100 in this embodiment), a connecting section (e.g., the drum-shaped section 200 in this embodiment), and a driving rotor (e.g., the low-pressure turbine shaft end section 300 in this embodiment). The connecting section is misaligned, which involves a misalignment problem.

[0061] Step S5: Establish a mechanical model for input axis misalignment.

[0062] Preferably, step S5 includes: equating the connecting segment to a coupling, including parallel misalignment, angular misalignment, and mixed misalignment.

[0063] The mechanical modeling methods for input shaft misalignment include, but are not limited to, methods that equate the drum-shaped section 200 (connecting section) to a coupling, including parallel misalignment, angular misalignment, and mixed misalignment problems.

[0064] The drum-shaped section 200 (connecting section) is equivalent to a coupling. It is a flexible coupling with relatively small radial stiffness, torsional stiffness, and angular stiffness. When the whole machine is eccentric, the local deformation is large. Its flexible characteristics must be taken into account when making the equivalent mechanical model.

[0065] For example, in this embodiment, preferably, the parallel misalignment is equivalent to applying a misalignment excitation force at the connection between the rotor and the coupling, with misalignment fault excitation force F in both the x and y directions. x and F y The expression is:

[0066]

[0067] Where M represents the equivalent mass of the coupling, and Δe represents the amount of parallel misalignment. Let ω represent the initial phase, ω represent the rotor speed, and t represent time. According to the above formula, the excitation force for parallel misalignment is a harmonic of the rotor speed.

[0068] The angular misalignment is equivalent to the bending moment at the connection between the rotor and the coupling. After the torque of the driving rotor is transmitted to the driven rotor through the coupling, the existence of the tilt angle will generate a bending moment T that causes the rotor to bend and vibrate, in addition to the torque. This bending moment and the speed of the driving rotor also satisfy the 2nd harmonic relationship.

[0069] The misalignment angle between the active rotor and the driven rotor is α, and the angle between the projection axis and the x-axis after the active rotor is projected onto the xy plane is β.

[0070] The torque T of the driving rotor, after being transmitted to the driven rotor via the coupling, can be decomposed into two parts T. z and T s ;

[0071] Among them, T z =Tcosα;T s =Tsinα;

[0072] Next, T s Further decomposed into bending moments in the x and y directions:

[0073] T x =Tsinαcosβ;T y =Tsinαcosβ.

[0074] Step S6: Based on the mode shapes and frequencies of the three-dimensional model, select the frequencies f1 and f2 corresponding to the bending mode shape as the excitation frequencies for misalignment, add the excitation load to the super-element model, and form the dynamic equations for the planetary gear train misalignment problem.

[0075] Preferably, the dynamic equation for the planetary gear train misalignment problem in step S6 is:

[0076]

[0077] Where M represents the equivalent mass of the coupling, F represents the excitation force generated by the parallel misalignment of the input shaft coupling, and T x T y This indicates the bending moment caused by angular misalignment.

[0078] Step S7: Solve the dynamic equation in the time domain and post-process the solution.

[0079] Preferably, the post-processing in step S7 includes: observing spectral characteristics, and comparing the radial displacement and acceleration results of the bearing position under undamped and damped conditions at two excitation frequencies f1 and f2 (e.g., Figure 4 and Figure 5 (As shown).

[0080] As described above, this invention addresses the input shaft misalignment problem by proposing a modeling method for the input shaft misalignment and a vibration response analysis method for the planetary gear train. The drum-shaped section of the input shaft has relatively low stiffness and primarily bears the misalignment deformation it faces. Therefore, the input shaft is divided into three sections: the low-pressure turbine shaft end section (driving rotor), the drum-shaped section (connecting section), and the sun gear end section (driven rotor). The drum-shaped section is considered the connecting section, and a mechanical model of the input shaft misalignment is established, thereby applying the misalignment excitation load to the planetary gear train model.

[0081] The model of the planetary gear train is relatively complex. Considering the rotational speed characteristics and gyroscopic effect, the three-dimensional finite element model of the planetary gear train is condensed into super-elements to achieve a rapid solution of the dynamic equations of the planetary gear train.

[0082] In summary, the vibration analysis method for planetary gear trains of the present invention can predict the vibration amplitude caused by misalignment due to overall machine deformation, thereby providing a quantitative basis for the design of the input shaft.

[0083] The vibration analysis method improves the design criteria for flexible input shafts, accelerates the iterative design of structures, and shortens the process of repeated verification through multiple experiments.

[0084] For those skilled in the art, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application and therefore remain within the spirit and scope of the exemplary embodiments of this application.

[0085] Furthermore, this application uses specific terms to describe embodiments of the application. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of the application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different locations in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of the application can be appropriately combined.

[0086] Similarly, it should be noted that, in order to simplify the description of the embodiments disclosed in this application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of this application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this disclosure method does not imply that the subject matter of this application requires more features than those mentioned in the claims. In fact, the embodiments have fewer features than all the features of the single embodiments disclosed above.

[0087] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A vibration analysis method for planetary gear trains, characterized in that, The vibration analysis method is used for planetary gear trains with misaligned flexible input shafts, and includes the following steps: S1. Establish a three-dimensional finite element model of the planetary gear, perform modal analysis, and determine the critical frequency of misalignment problems; S2, retain the master nodes in key positions; S3. Perform super-unit condensation on the planetary gear train; S4. Divide the input shaft according to the deformation results of the whole machine and determine the connection section; S5. Establish a mechanical model for input axis misalignment; S6. Based on the mode shapes and frequencies of the three-dimensional model, select the frequencies f1 and f2 corresponding to the bending mode shape as the excitation frequencies for misalignment, add the excitation load to the super-element model, and form the dynamic equations for the planetary gear train misalignment problem. S7. Solve the dynamic equations in the time domain and perform post-processing on the solution results.

2. The vibration analysis method for planetary gear trains as described in claim 1, characterized in that, Step S1 includes: setting internal connection relationships, boundary constraints, and support stiffness damping for the planetary gear train.

3. The vibration analysis method for planetary gear trains as described in claim 1, characterized in that, The key nodes in step S2 include the load application location, the boundary, and the required monitoring location.

4. The vibration analysis method for planetary gear trains as described in claim 1, characterized in that, Step S3 includes: considering the rotational speed characteristics and gyroscopic effect of the planetary gear train, it is divided into three super units: input shaft rotor super unit, output shaft rotor super unit, and stator super unit.

5. The vibration analysis method for planetary gear trains as described in claim 1, characterized in that, In step S4, the input shaft is divided into a driven rotor, a connecting section, and a driving rotor, and the connecting section is not aligned.

6. The vibration analysis method for planetary gear trains as described in claim 5, characterized in that, Step S5 includes: equating the connecting segment to a coupling, including parallel misalignment, angular misalignment, and mixed misalignment.

7. The vibration analysis method for planetary gear trains as described in claim 6, characterized in that, The parallel misalignment equivalent is to apply a misalignment excitation force at the rotor and coupling connection, and the misalignment fault excitation force F in x, y two directions x and F y The expression is: Where M represents the equivalent mass of the coupling, and Δe represents the amount of parallel misalignment. ω represents the initial phase, ω represents the rotor speed, and t represents time.

8. The vibration analysis method for planetary gear trains as described in claim 6, characterized in that, The angular misalignment is equivalent to the bending moment at the connection between the rotor and the coupling. The misalignment angle between the driving rotor and the driven rotor is α. After the driving rotor is projected onto the xy plane, the angle between the projection axis and the x-axis is β. The torque T of the driving rotor, after being transmitted to the driven rotor via the coupling, can be decomposed into two parts T. z and T s ; Among them, T z =Tcosα;T s =Tsinα; T s Further decomposed into bending moments in the x and y directions: T x =Cynαcosβ;T y =Sinαcosβ。 9. The vibration analysis method for planetary gear trains as described in claim 1, characterized in that, The dynamic equation for the planetary gear system misalignment problem in step S6 is: Where M represents the equivalent mass of the coupling, F represents the excitation force generated by the parallel misalignment of the input shaft coupling, and T x T y This indicates the bending moment caused by angular misalignment.

10. The vibration analysis method for planetary gear trains as described in claim 1, characterized in that, The post-processing in step S7 includes: observing the spectral characteristics and comparing the radial displacement and acceleration of the bearing position under undamped and damped conditions at two excitation frequencies f1 and f2.

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