Dynamic parameter optimization method for multi-modal multi-objective elastic support dry friction damper

Abstract

The present application relates to the technical field of aero-engine design, and particularly relates to a multi-modal multi-target elastic support dry friction damper dynamics parameter optimization method, comprising: determining a controlled mode and a matched elastic support dry friction damper; single-mode elastic support dry friction damper dynamics parameter optimization; and multi-modal elastic support dry friction damper dynamics parameter optimization. The present application combines a particle swarm algorithm to automatically optimize the dynamics parameters of the elastic support dry friction damper in the single-mode elastic support dry friction damper dynamics parameter optimization and multi-modal elastic support dry friction damper dynamics parameter optimization stages, so as to determine the final dynamics parameters, thereby improving the design efficiency and accuracy of the dynamics parameters.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of aero-engine design, and particularly relates to a dynamic parameter optimization method for a spring-supported dry friction damper under multi-modal and multi-target conditions. BACKGROUND

[0002] In order to meet the requirements of high efficiency and high thrust-to-weight ratio of modern aero-engines, a double-rotor configuration is usually adopted for the rotor system of the aero-engine, and the high-pressure rotor system and the low-pressure rotor system are coupled through an intermediate bearing, so that there are multiple modes in the working speed range of the aero-engine, and the vibration characteristics are relatively complex. It is difficult to ensure that the best damping effect is obtained under each mode by using a conventional passive damping mechanism. Compared with the passive damping mechanism, the spring-supported dry friction damper can adjust and control the parameters of the damper in real time according to the working conditions and vibration levels of the aero-engine, so as to realize active control of the vibration of the rotor system, and therefore the spring-supported dry friction damper has broad prospects in the vibration suppression of the aero-engine.

[0003] In the prior art, a document entitled "Dynamic design method of spring-supported dry friction damper matched with rotor" determines the key design parameters of the spring-supported dry friction damper based on the analysis results of the vibration damping characteristics of the rotor system with respect to the parameters of the spring-supported dry friction damper, and establishes a dynamic design method and process of the spring-supported dry friction damper matched with the rotor. The effectiveness of the proposed design method is verified by taking a double-disc rotor with a spring-supported dry friction damper as an example. However, in the design process, the determination of the design parameters of the spring-supported dry friction damper and the correction of the structural parameters of the rotor system need simulation iteration, and the design is time-consuming and low in accuracy. In the prior art, a document entitled "Integrated configuration design and vibration suppression experiment of master-controlled spring-supported dry friction damper" gives the design requirement of the installation stiffness of the static friction sheet, that is, the installation stiffness of the static friction sheet , according to the condition that the dynamic parameters of the spring-supported dry friction damper need to meet the stiffness coefficient and the damping coefficient

[0004] , and establishes a dynamic parameter design method and process of the spring-supported dry friction damper in combination with the controllability of the rotor system (that is, the design position of the spring-supported dry friction damper should not be at the node of the controlled mode). The design method realizes accurate design of the installation stiffness of the static friction sheet and ensures the controllability of the rotor system. However, the accurate design of the dynamic parameters of the spring-supported dry friction damper in the design method cannot guarantee the best damping effect. The prior art also discloses that the design parameters of the spring-supported dry friction damper are optimized by taking the critical speed and the vibration displacement of the rotor system as the target and by using a particle swarm algorithm. The use of the intelligent optimization algorithm greatly improves the design efficiency and determines the optimal design parameters of the spring-supported dry friction damper. However, the optimization target established in the prior art only considers the dynamic characteristics of the rotor system and does not consider the damping characteristics of the spring-supported dry friction damper, so the spring-supported dry friction damper cannot achieve the best damping performance.In summary, the existing elastic support dry friction damper design method is mostly applied to simple rotor systems, while the double-rotor system widely used in actual aero-engines has a complex structure, and due to the coupling of the intermediate bearing, there are multiple modes in the working speed range, which is difficult to control, and the vibration reduction characteristics of the elastic support dry friction damper are not considered, so that the dynamic parameters cannot be accurately designed.

[0005] Therefore, it is necessary to provide a multi-modal multi-objective elastic support dry friction damper dynamic parameter optimization method to solve the above problems. SUMMARY

[0006] In order to overcome the problems in the prior art that the elastic support dry friction damper control rotor system structure is relatively simple, does not conform to the actual situation, and the vibration reduction characteristics of the elastic support dry friction damper are not considered, so that the dynamic parameters cannot be accurately designed, the present application provides a multi-modal multi-objective elastic support dry friction damper dynamic parameter optimization method.

[0007] The multi-modal multi-objective elastic support dry friction damper dynamic parameter optimization method of the present application adopts the following technical scheme, comprising:

[0008] Determine the controlled mode and the matching elastic support dry friction damper;

[0009] According to the design requirements, determine the first dynamic parameter variation range of the elastic support dry friction damper; take the critical displacement variation of the rotor system under the action of different normal pressures as the controllability of the elastic support dry friction damper; based on the critical speed constraint condition of the rotor system with the elastic support dry friction damper, and according to the critical displacement of the rotor system and the controllability of the elastic support dry friction damper, establish a multi-objective optimization function of the elastic support dry friction damper;

[0010] According to the first dynamic parameter variation range, generate a population, and use the particle swarm algorithm to minimize the multi-objective optimization function as the optimization target, and obtain the optimal dynamic parameters and sub-optimal dynamic parameters of the elastic support dry friction damper matched with the controlled mode through parameter optimization;

[0011] According to the optimal dynamic parameters and sub-optimal dynamic parameters of the elastic support dry friction damper, generate the second dynamic parameter variation range of the elastic support dry friction damper in the multi-modal optimization design; construct a multi-modal optimization function of the controlled mode according to the multi-objective optimization function value corresponding to the optimal dynamic parameters and sub-optimal dynamic parameters of the elastic support dry friction damper;

[0012] According to the second dynamic parameter variation range, generate a population, and use the particle swarm algorithm to minimize the multi-modal optimization function as the optimization target, and obtain the final dynamic parameters of the elastic support dry friction damper matched with the controlled mode through parameter optimization.

[0013] Preferably, the steps for determining the controlled mode and its matched elastic dry friction damper are as follows:

[0014] The critical speed, mode shapes, and vibration displacement of the rotor system are determined using the finite element method.

[0015] Based on the critical speed of the rotor system, determine the various modes within the operating speed range of the rotor system;

[0016] The modes in which the critical displacement of the rotor system under each mode is greater than the preset critical displacement threshold are taken as the controlled modes.

[0017] Based on the mode shape of the controlled mode, select the spring-supported dry friction damper with the maximum relative displacement (i.e., the ratio of the vibration displacement of the spring-supported dry friction damper to the maximum displacement of the rotor system) as the spring-supported dry friction damper for matching the controlled mode.

[0018] Preferably, the expression for the controllability of the spring-loaded dry friction damper is:

[0019]

[0020] In the formula, No. The controlled mode matching is the controllability of the elastic-supported dry friction damper. F 1,i For the first The first normal force of the spring-supported dry friction damper with controlled mode matching. F 2,i For the first The second normal force of the spring-supported dry friction damper with controlled mode matching; For the first A controlled-mode matched elastic-supported dry friction damper applies a normal force. F 1,i The critical displacement of the rotor system; For the first A controlled-mode matched elastic-supported dry friction damper applies a normal force. F 2,i The critical displacement of the rotor system.

[0021] Preferably, the critical speed constraint condition is:

[0022]

[0023] In the formula, For the first i The expression for the critical speed constraint condition of the controlled mode; For the first i Critical rotational speed of the controlled mode; When there is no damper, the first iCritical rotational speed of the controlled mode; When the damper is in action, the first i Critical rotational speed of the controlled mode; This refers to the operating speed of the rotor system.

[0024] Preferably, the expression for the multi-objective optimization function is:

[0025]

[0026] In the formula, For the first The multi-objective optimization function corresponding to the spring-supported dry friction damper with controlled mode matching; For the first A vector consisting of the dynamic parameters of a spring-supported dry friction damper with controlled mode matching; In the first Critical displacement of a rotor system under the action of a spring-supported dry friction damper with controlled mode matching; For the first The controllability of the spring-supported dry friction damper with controlled mode matching; For the first The penalty function corresponding to the controlled mode is used to transform the constrained optimization problem into an unconstrained optimization problem using the penalty function method, where R is the penalty factor. For the first The expression for the critical speed constraint condition of the controlled mode; For the first The lower limit of the dynamic parameter composition vector of the spring-supported dry friction damper with controlled mode matching; For the first The upper limit of the dynamic parameter composition vector of the spring-supported dry friction damper with controlled mode matching; For the first i Critical rotational speed of the controlled mode; When there is no damper, the first i Critical rotational speed of the controlled mode; When the damper is in action, the first i Critical speed of the controlled mode.

[0027] Preferably, the expression for the multimodal optimization function is:

[0028]

[0029] In the formula, It is a multimodal optimization function; For the first Optimization weights for the first mode; Let be the order of the controlled mode; For the first iThe multi-objective optimization function value corresponding to the optimal dynamic parameters of the spring-supported dry friction damper with first-order mode matching; For the first i The multi-objective optimization function value corresponding to the suboptimal dynamic parameters of the spring-supported dry friction damper with first-order mode matching; For the first A multi-objective optimization function for a spring-supported dry friction damper with first-order mode matching.

[0030] Preferably, the range of variation of the first dynamic parameter is:

[0031]

[0032] In the formula, i For the first i The vector formed by the first dynamic parameters of the spring-loaded dry friction damper with first-order mode matching; k i For the first i The stiffness range of the squirrel cage spring in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching. s i For the first i The range of support stiffness values ​​for the static friction plate mounting ring in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching. m i For the first i The mass range of the static friction plate in the first dynamic parameter of the spring-supported dry friction damper with first-order mode matching; For the first i The lower limit of the stiffness of the squirrel cage spring in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The upper limit of the stiffness of the squirrel cage spring in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The lower limit of the static friction plate mounting ring support stiffness in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The upper limit of the static friction plate mounting ring support stiffness in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The lower limit of the static friction plate mass in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The upper limit of the static friction plate mass in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching.

[0033] Preferably, the range of variation of the second dynamic parameter is:

[0034]

[0035] wherein, is a vector of second dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n; is a vector of second dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n; is a range of stiffness values of the squirrel cage elastic support in the second dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n; is a range of stiffness values of the squirrel cage elastic support in the second dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n; is a range of stiffness values of the squirrel cage elastic support in the second dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n; is a range of stiffness values of the squirrel cage elastic support in the second dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n; is a range of stiffness values of the squirrel cage elastic support in the second dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n; is a range of stiffness values of the squirrel cage elastic support in the second dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization; is an optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order n after multi-objective optimization.

[0036] Preferably, the dynamic parameters of the elastic support dry friction damper include: the stiffness of the squirrel cage elastic support, the supporting stiffness of the static friction sheet mounting ring, and the mass of the static friction sheet.

[0037] The present application has the following advantages:

[0038] 1. This invention is mainly carried out in two stages. In the first stage of optimization design, multi-objective optimization design of the spring-supported dry friction damper under single-mode conditions is performed. That is, multi-objective optimization design is carried out for each controlled mode and its matched spring-supported dry friction damper to achieve the best vibration reduction effect of a single spring-supported dry friction damper. In the second stage of optimization design, comprehensive optimization design of the spring-supported dry friction damper under multi-mode conditions is performed. That is, comprehensive optimization design of multiple controlled modes and multiple dampers is carried out to achieve the best comprehensive vibration reduction effect of the spring-supported dry friction damper within the operating speed range. At the same time, in both optimization stages, particle swarm optimization algorithm is combined to automatically optimize the dynamic parameters of the spring-supported dry friction damper to improve the design efficiency and accuracy of the dynamic parameters.

[0039] 2. Based on the vibration reduction characteristics of the spring-supported dry friction damper, an evaluation index for the controllability of the damper is proposed. The controllability index can effectively measure the vibration reduction performance of the damper and has low sensitivity to low normal pressure. Therefore, in the process of optimizing the dynamic parameters of the spring-supported dry friction damper, it can effectively solve the problem that the influence of dynamic parameters on the damper's vibration reduction effect cannot be accurately analyzed due to changes in normal pressure. For the design of the dynamic parameters of the spring-supported dry friction damper, the dynamic characteristics of the rotor system and the vibration reduction characteristics of the spring-supported dry friction damper are comprehensively considered. Based on this, this invention constructs a multi-objective optimization function according to controllability and critical displacement. Then, based on the structure optimized by the multi-objective optimization function, a multi-modal optimization function is constructed. The multi-objective optimization function and the multi-modal optimization function have important reference value for evaluating the vibration reduction characteristics of the multi-damper under multiple modes, providing a basis for judgment for the optimization design of the damper's dynamic parameters, thereby obtaining the final dynamic parameters of the spring-supported dry friction damper, and ensuring that the spring-supported dry friction damper at each support point can play the best vibration reduction role under multiple modes within the operating speed range. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the 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.

[0041] Figure 1 This is a flowchart of a method for optimizing the dynamic parameters of a multimodal, multi-objective, lower-mounted spring-loaded dry friction damper according to the present invention;

[0042] Figure 2 This is a detailed flowchart of a method for optimizing the dynamic parameters of a multimodal, multi-objective, spring-loaded dry friction damper according to the present invention.

[0043] Figure 3Structure diagram of the elastic support dry friction damper of the present application;

[0044] Figure 4 Structure diagram of a double-rotor system with the elastic support dry friction damper of the present application;

[0045] Figure 5 Vibration displacement diagram of the double-rotor system without the elastic support dry friction damper;

[0046] Figure 6 Mode shape of the controlled mode of the double-rotor system;

[0047] Figure 7 Controllability curve of the elastic support dry friction damper with respect to the normal pressure;

[0048] Figure 8 Vibration displacement diagram of each order of the controlled mode after multi-objective optimization of the S2 step of the present application;

[0049] Figure 9 Vibration displacement diagram of each order of the controlled mode after multi-mode optimization of the S3 step of the present application.

[0050] Figure: 1, dynamic friction plate; 2, static friction plate; 3, static friction plate mounting ring; 4, piezoelectric ceramic actuator; 5, squirrel-cage elastic support; 6, rotor; 7, low-pressure rotor shaft; 8, fan first-stage disk; 9, fan second-stage disk; 10, high-pressure rotor shaft; 11, compressor first-stage disk; 12, compressor second-stage disk; 13, compressor third-stage disk; 14, compressor fourth-stage disk; 15, high-pressure turbine disk; 16, low-pressure turbine disk; 17, fifth elastic support point; 18, intermediate bearing; 19, third elastic support point; 20, second elastic support point; 21, first elastic support point; 22, rotor vibration displacement under the first-order mode of low-pressure excitation without the action of the elastic support dry friction damper; 23, rotor vibration displacement under the second-order mode of low-pressure excitation without the action of the elastic support dry friction damper; 24, rotor vibration displacement under the third-order mode of low-pressure excitation without the action of the elastic support dry friction damper; 25, rotor vibration displacement under the first-order mode of high-pressure excitation without the action of the elastic support dry friction damper; 26, rotor vibration displacement under the second-order mode of high-pressure excitation without the action of the elastic support dry friction damper; 27, rotor vibration displacement under the third-order mode of high-pressure excitation without the action of the elastic support dry friction damper; 28, rotor vibration displacement under the fourth-order mode of high-pressure excitation without the action of the elastic support dry friction damper; 29, low-pressure turbine disk vibration displacement under the first-order mode of low-pressure excitation after multi-objective optimization without the action of the elastic support dry friction damper; 30, low-pressure turbine disk vibration displacement under the first-order mode of low-pressure excitation after multi-objective optimization with the action of the elastic support dry friction damper; 31, 20% speed interval of the low-pressure rotor slow-speed rotating speed; 32, fan first-stage disk vibration displacement under the third-order mode of low-pressure excitation after multi-objective optimization without the action of the elastic support dry friction damper; 33, fan first-stage disk vibration displacement under the third-order mode of low-pressure excitation after multi-objective optimization with the action of the elastic support dry friction damper; 34, 20% speed interval of the low-pressure rotor cruising rotating speed; 35, low-pressure turbine disk vibration displacement under the first-order mode of high-pressure excitation after multi-objective optimization without the action of the elastic support dry friction damper; 36, low-pressure turbine disk vibration displacement under the first-order mode of high-pressure excitation after multi-objective optimization with the action of the elastic support dry friction damper; 37, compressor first-stage disk vibration displacement under the fourth-order mode of high-pressure excitation after multi-objective optimization without the action of the elastic support dry friction damper; 38, compressor first-stage disk vibration displacement under the fourth-order mode of high-pressure excitation after multi-objective optimization with the action of the elastic support dry friction damper; 39, 20% speed interval of the high-pressure rotor slow-speed rotating speed; 40, rotor vibration displacement under the first-order mode of low-pressure excitation after multi-modal optimization; 41, rotor vibration displacement under the third-order mode of low-pressure excitation after multi-modal optimization; 42, rotor vibration displacement under the first-order mode of high-pressure excitation after multi-modal optimization; 43, rotor vibration displacement under the fourth-order mode of high-pressure excitation after multi-modal optimization. DETAILED DESCRIPTION

[0051] With reference to the accompanying drawings, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of the present application.

[0052] An embodiment of the multi-modal multi-objective underpinning dry friction damper dynamics parameter optimization method of the present application needs to be explained. In the embodiment, the structure of a double-rotor system with an underpinning dry friction damper is taken as an example for illustration, as shown in Figure 3 and Figure 4 The double-rotor system with the underpinning dry friction damper includes a low-pressure rotor system, a high-pressure rotor system, an intermediate bearing, and an underpinning dry friction damper. The low-pressure rotor system includes a low-pressure rotating shaft 7, a fan first-stage disk 8, a fan second-stage disk 9, a low-pressure turbine disk 16, and a first elastic support point 21, a second rigid support point 20, and a fifth elastic support point 17. The high-pressure rotor system includes a high-pressure rotating shaft 10, a compressor first-stage disk 11, a compressor second-stage disk 12, a compressor third-stage disk 13, a compressor fourth-stage disk 14, a high-pressure turbine disk 15, and a third elastic support point 19. The high-pressure rotor system and the low-pressure rotor system are coupled through the intermediate bearing 18. The first elastic support point, the third elastic support point, and the fifth elastic support point in the double-rotor system composed of the high-pressure rotor system and the low-pressure rotor system are respectively provided with a one-support underpinning dry friction damper, a three-support underpinning dry friction damper, and a five-support underpinning dry friction damper.

[0053] Specifically, the steps of the multi-modal multi-objective underpinning dry friction damper dynamics parameter optimization method of the embodiment are as shown in Figure 1 and Figure 2 The steps include:

[0054] S1, determining a controlled mode and a matched underpinning dry friction damper of the controlled mode;

[0055] Specifically, the critical speed, the modal shape and the vibration displacement of the rotor system are solved based on the finite element method; the critical speed of the rotor system is determined, and each mode in the working speed range of the rotor system is determined, wherein the dynamic characteristics of the rotor system are analyzed in advance to obtain the critical speed of the rotor system; the mode in which the vibration displacement of the rotor system is greater than the preset vibration displacement threshold is taken as the controlled mode; according to the modal shape of the controlled mode, the elastic support dry friction damper with the maximum relative displacement is selected as the elastic support dry friction damper matched with the controlled mode. It should be noted that each mode is a plurality of critical speeds existing in the working speed range of the rotor system. The controlled mode refers to the mode in which the vibration displacement of the rotor system at the critical speed exceeds the design requirement in the plurality of modes of the rotor system without the action of the elastic support dry friction damper, wherein the maximum relative displacement is the maximum ratio of the vibration displacement of the elastic support dry friction damper to the displacement of the rotor system.

[0056] In the embodiment, the dynamic characteristics of the rotor system are analyzed based on the finite element method widely used in the literature. The finite element calculation method proposed in “Rotor Dynamics of Aeroengines” is used to obtain that there are 7 modes existing in the working speed range of the double-rotor system, and the vibration displacement of the rotor system without the action of the damper is as shown in Figure 5 , and the modal shape of the controlled mode is as shown in Figure 6 . The 7 modes are the low-pressure excited first mode, the low-pressure excited second mode, the low-pressure excited third mode as shown in Figure 5 a, and the high-pressure excited first mode, the high-pressure excited second mode, the high-pressure excited third mode, and the high-pressure excited fourth mode as shown in Figure 5 b. Among them, the critical displacements in the rotor vibration displacements 22 and 24 of the first mode and the third mode excited by the low pressure and the rotor vibration displacements 25 and 28 of the first mode and the fourth mode excited by the high pressure all exceed 150 um (i.e. the critical displacement threshold preset in the embodiment is 150 um), which are the controlled modes of the elastic support dry friction damper in the embodiment. Among them, as shown in Figure 6 a, the low-pressure excited first mode in the controlled mode is a pitch modal shape in which the turbine end vibration is dominant, and the relative displacement of the five support point elastic support dry friction damper 17 is the largest; as shown in Figure 6 b, the low-pressure excited third mode is a first-order bending modal shape in which the fan end vibration is dominant, and the relative displacement of the one support point elastic support dry friction damper 21 is the largest; as shown in Figure 6 c, the high-pressure excited first mode is a pitch mode in which the turbine end vibration is dominant, and the relative displacement of the five support point elastic support dry friction damper 17 is the largest. The modal shape of this mode is similar to the modal shape of the low-pressure excited first mode; as shown in Figure 6As shown in FIG. 2, the high-pressure excitation fourth-order mode is a dominant pitch mode of the compressor end vibration, in which the relative displacement of the three-fulcrum elastic support dry friction damper 19 is the largest. According to the characteristics that the elastic support dry friction damper at the position of the largest relative displacement in the mode shape of the controlled mode has a better damping effect on the order mode, the elastic support dry friction damper matched with the controlled mode is determined, and the vibration displacement of each order controlled mode is determined to determine the monitoring position, which is specifically shown in Table 1.

[0057] Table 1

[0058]

[0059] S2, optimization of the kinetic parameters of the elastic support dry friction damper under single mode;

[0060] Specifically, the first kinetic parameter variation range of the elastic support dry friction damper is determined according to the design requirements; the variation amount of the critical displacement of the rotor system under different positive pressures is taken as the controllability of the elastic support dry friction damper; under the constraint of the critical speed, and according to the critical displacement of the rotor system and the controllability of the elastic support dry friction damper, a multi-objective optimization function of the elastic support dry friction damper is established; a population is generated according to the first kinetic parameter variation range, and a particle swarm algorithm is adopted to take the minimum of the multi-objective optimization function as the optimization target, so as to obtain the optimal kinetic parameters and suboptimal kinetic parameters of the elastic support dry friction damper matched with the controlled mode through parameter optimization. It should be noted that the multi-objective is an optimization target established according to the dynamic characteristics of the rotor system and the design requirements, and the damping characteristics of the elastic support dry friction damper.

[0061] Step 21, the first kinetic parameter variation range of the elastic support dry friction damper is determined according to the design requirements. Specifically, the kinetic parameters and the first kinetic parameter variation range of the one-fulcrum elastic support dry friction damper, the three-fulcrum elastic support dry friction damper and the five-fulcrum elastic support dry friction damper in the embodiment are shown in Table 2.

[0062] Table 2

[0063]

[0064] Step 22, a multi-objective optimization function of the elastic support dry friction damper is established:

[0065] The critical speed of the fourth-order controlled mode without the action of the damper is shown in Table 3:

[0066] Table 3

[0067]

[0068] The working speeds of the high-pressure rotor system and the low-pressure rotor system are shown in Table 4:

[0069] Table 4

[0070]

[0071] From Table 3 and Table 4, it can be seen that the critical speed of the first order mode excited by the low pressure is 1750.7 r / min, which is close to the slow speed of the low pressure rotor 2940 r / min; the critical speed of the third order mode excited by the low pressure is 4761.5 r / min, which is between the slow speed 2940 r / min and the cruise speed 7070 r / min of the low pressure rotor; the critical speed of the first order mode excited by the high pressure is 1866 r / min, which is close to the slow speed 7175 r / min of the high pressure rotor; the critical speed of the fourth order mode excited by the high pressure is 4670.6 r / min, which is close to the slow speed 7175 r / min of the high pressure rotor. In addition, under the action of the damper, the critical speed of the controlled mode will increase, and the critical speed of the controlled mode under the action of the damper also needs to meet the critical speed constraint condition. Therefore, according to the critical speed constraint condition, the critical speed of the rotor system should avoid 20% of the working speed, and the critical speed constraint condition of the first order mode excited by the low pressure, the critical speed constraint condition of the third order mode excited by the low pressure, the critical speed constraint condition of the first order mode excited by the high pressure and the critical speed constraint condition of the fourth order mode excited by the high pressure are constructed respectively. The specific expression is:

[0072] (1)

[0073] In the formula, ωL1 is the critical speed constraint condition of the first order mode excited by the low pressure; ωL3 is the critical speed constraint condition of the third order mode excited by the low pressure; ωH1 is the critical speed constraint condition of the first order mode excited by the high pressure; ωH4 is the critical speed constraint condition of the fourth order mode excited by the high pressure; ωL1 is the critical speed of the first order mode excited by the low pressure; ωL3 is the critical speed of the third order mode excited by the low pressure; ωH1 is the critical speed of the first order mode excited by the high pressure; ωH4 is the critical speed of the fourth order mode excited by the high pressure; ωL1 is the critical speed value of the first order mode excited by the low pressure under the action of the elastic support dry friction damper; ωL3 is the critical speed value of the third order mode excited by the low pressure under the action of the elastic support dry friction damper; ωH1 is the critical speed value of the first order mode excited by the high pressure under the action of the elastic support dry friction damper; This refers to the critical speed value of the first-order mode of high-pressure excitation under the action of the spring-supported dry friction damper. The critical speed constraint means that the critical speed of the rotor system under the action of the spring-supported dry friction damper should be avoided by 20% of the operating speed.

[0074] By changing the normal pressure of the spring-supported dry friction damper, the controllability of the spring-supported dry friction damper as a function of the normal pressure is obtained, such as... Figure 7 As shown, when the normal pressure varies within a certain low range, the controllability of the spring-supported dry friction damper is less sensitive to the normal pressure. Furthermore, when the normal pressure exceeds a certain value, the controllability gradually decreases with increasing normal pressure. Therefore, in the optimization design of the dynamic parameters of the spring-supported dry friction damper, the controllability of the damper under a relatively small normal pressure can be solved. In this embodiment, the first and second normal pressures are respectively set as... =0N, =10N, meaning that in this embodiment, the controllability of the spring-loaded dry friction damper is:

[0075] (2)

[0076] In the formula, For the first Controllability of a spring-supported dry friction damper with controlled mode matching. For the first The first normal force of the spring-supported dry friction damper with controlled mode matching; For the first The second normal force of the spring-supported dry friction damper with controlled mode matching; For the first The controlled mode matching spring-supported dry friction damper is applied The critical displacement of the rotor system; For the first The controlled mode matching spring-supported dry friction damper is applied The critical displacement of the rotor system; it should be noted that the controllability of the spring-supported dry friction damper refers to the change in the critical displacement of the rotor system under different normal pressures, which is the evaluation index of the vibration reduction performance of the spring-supported dry friction damper. The critical displacement of the rotor system refers to the vibration displacement at the critical speed of the rotor system under the control of the spring-supported dry friction damper, which is used as the evaluation index of the vibration reduction effect of the spring-supported dry friction damper. For the vibration displacement of the rotor system, the monitoring positions corresponding to each controlled mode are selected, as shown in Table 1. Since the spring-supported dry friction damper can be actively controlled, there are multiple control methods to choose from. The control algorithm used in this embodiment is shown in Equation (3). Based on this control strategy, the optimal design of the dynamic parameters of the spring-supported dry friction damper is achieved. The specific control algorithm is as follows:

[0077] (3)

[0078] In the formula, F i The positive pressure of the elastic support dry friction damper of the controlled modal matching of the first i order; r d,i The displacement of the elastic support dry friction damper of the controlled modal matching of the first i order; The support stiffness of the mounting ring of the static friction sheet of the elastic support dry friction damper of the controlled modal matching of the first i order; m i The mass of the static friction sheet of the elastic support dry friction damper of the controlled modal matching of the first i order; The operating frequency of the elastic support dry friction damper of the controlled modal matching of the first i order; The tangential contact stiffness between the dynamic friction sheet and the static friction sheet; The friction coefficient between the dynamic friction sheet and the static friction sheet, which is related to the materials selected for the dynamic friction sheet and the static friction sheet of the elastic support dry friction damper, and in the embodiment, , Based on the critical speed constraint condition of the rotor system with the elastic support dry friction damper, and according to the critical displacement of the rotor system and the controllability of the elastic support dry friction damper, a multi-objective optimization function of the elastic support dry friction damper is established, and the expression of the multi-objective optimization function is:

[0079] (4)

[0080] In the formula, L represents the number of the controlled modal, and in the embodiment, L_1, L_3, H_1 and H_4 correspond; The multi-objective optimization function corresponding to the first order controlled modal; The vector composed of the dynamic parameters of the elastic support dry friction damper of the first order controlled modal matching; The critical displacement of the rotor system under the action of the elastic support dry friction damper of the first order controlled modal matching; The controllability of the elastic support dry friction damper of the first order controlled modal matching; The penalty function corresponding to the first order controlled modal, the penalty function method is used to convert the constraint optimization problem into an unconstrained optimization problem, R is a penalty factor, The expression of the critical speed constraint condition of the first order controlled modal; The critical speed constraint condition of the first Lower limit value of dynamic parameter composition vector of the elastic support dry friction damper of the controlled modal matching; For the first Upper limit value of dynamic parameter composition vector of the elastic support dry friction damper of the controlled modal matching; For the first i Critical speed of the controlled modal; Critical speed of the first i Critical speed of the controlled modal; Critical speed of the first i Critical speed of the controlled modal.

[0081] Step 23, the step of obtaining the optimal dynamic parameters and the suboptimal dynamic parameters of the elastic support dry friction damper matched with the controlled modal is: adopting the improved particle swarm algorithm proposed in the article “Helicopter power turbine rotor system optimization method based on improved particle swarm algorithm[J]. Acta Aeronautica Et Astronautica, 2023, 45(01): 242-258.” (DOI:10.7527 / S1000-6893.2023.28608), setting the total group number as 30 and the iteration number as 20 times. The optimization direction of the improved particle swarm algorithm is to adjust the dynamic parameters of the elastic support dry friction damper in the first dynamic parameter change range, so as to realize the minimum of the multi-objective optimization function value of the elastic support dry friction damper under each controlled modal. The optimal dynamic parameters and the suboptimal dynamic parameters of the elastic support dry friction damper under each controlled modal obtained after optimization are shown in Table 5.

[0082] Table 5

[0083]

[0084] In Table 5, Optimal; Suboptimal, then Indicates that the first modal of high pressure excitation is taken as the controlled modal, and the five support point elastic support dry friction damper matched with the controlled modal, that is, the optimal dynamic parameters of the five support point elastic support dry friction damper matched with the first modal of high pressure excitation correspond to the multi-objective optimization function value; Indicates the multi-objective optimization function value corresponding to the suboptimal dynamic parameters of the five support point elastic support dry friction damper matched with the first modal of high pressure excitation. It should be noted that the particle swarm algorithm is prior art, which has the advantages of parallel computing and good robustness, has strong global search ability for nonlinear and multi-peak problems, and can ensure high efficiency and accuracy in the optimization design of the dynamic parameters of the elastic support dry friction damper.

[0085] Step 24, the optimal dynamic parameters of each support point elastic support dry friction damper are obtained, and the finite element method is used to calculate the vibration displacement of each controlled modal, asFigure 8 a is the vibration displacement of the rotor system under the first order mode excited by low pressure, Figure 8 a is the vibration displacement of the rotor system under the first order mode excited by low pressure, Figure 8 b is the vibration displacement of the rotor system under the third order mode excited by low pressure, Figure 8 c is the vibration displacement of the rotor system under the first order mode excited by high pressure, Figure 8 d is the vibration displacement of the rotor system under the fourth order mode excited by high pressure. After optimization, the critical displacement in the vibration displacement 30 of the low pressure turbine disk under the first order mode excited by low pressure with the action of the elastic support dry friction damper, the vibration displacement 33 of the fan 1st stage disk under the third order mode excited by low pressure with the action of the elastic support dry friction damper, the vibration displacement 36 of the low pressure turbine disk under the first order mode excited by high pressure with the action of the elastic support dry friction damper, and the vibration displacement 38 of the compressor 1st stage disk under the fourth order mode excited by high pressure with the action of the elastic support dry friction damper are all lower than . And the critical speed of each order controlled mode with and without the action of the damper does not appear in the gray area of each figure, that is, the critical speed avoids 20% of the working point, which meets the design requirements. Thus, the dynamic parameter optimization design of the elastic support dry friction damper under single mode is completed.

[0086] S3, dynamic parameter optimization of the elastic support dry friction damper under multiple modes;

[0087] Specifically, according to the optimal dynamic parameters and the suboptimal dynamic parameters of the elastic support dry friction damper, a second dynamic parameter variation range of the elastic support dry friction damper in the multi-mode optimization design is generated; a multi-mode optimization function of the controlled mode is constructed according to the multi-objective optimization function values corresponding to the optimal dynamic parameters and the suboptimal dynamic parameters of the elastic support dry friction damper. A population is generated according to the second dynamic parameter variation range, and a particle swarm algorithm is adopted to take the minimum of the multi-mode optimization function as the optimization target, so as to obtain the final dynamic parameters of the elastic support dry friction damper matched with the controlled mode through parameter optimization.

[0088] Step 31, the step of generating the second dynamic parameter variation range of the elastic support dry friction damper in the multi-mode optimization design according to the optimal dynamic parameters and the suboptimal dynamic parameters of the elastic support dry friction damper is:

[0089] Wherein, the second dynamic parameter variation range is shown in Table 6.

[0090] Table 6

[0091]

[0092] Step 32, the step of constructing the multi-mode optimization function of the controlled mode is:

[0093] The multi-modal optimization function of the controlled mode is constructed according to the multi-objective optimization function values corresponding to the optimal and suboptimal kinetic parameters of the elastic support dry friction damper, wherein the optimization weight of each mode is 1, and the optimization weight can also be defined according to the importance of the optimized mode in the specific implementation. The expression of the multi-modal optimization function is

[0094] (5)

[0095] In the formula, is the multi-modal optimization function. is the multi-objective optimization function of the five-support-point elastic support dry friction damper matched with the first mode under low pressure excitation. is the multi-objective optimization function of the one-support-point elastic support dry friction damper matched with the third mode under low pressure excitation. is the multi-objective optimization function of the five-support-point elastic support dry friction damper matched with the first mode under high pressure excitation. is the multi-objective optimization function of the three-support-point elastic support dry friction damper matched with the fourth mode under high pressure excitation. is the multi-objective optimization function value corresponding to the optimal kinetic parameters of the five-support-point elastic support dry friction damper matched with the first mode under low pressure excitation. is the multi-objective optimization function value corresponding to the suboptimal kinetic parameters of the five-support-point elastic support dry friction damper matched with the first mode under low pressure excitation. is the multi-objective optimization function value corresponding to the optimal kinetic parameters of the one-support-point elastic support dry friction damper matched with the third mode under low pressure excitation. is the multi-objective optimization function value corresponding to the suboptimal kinetic parameters of the one-support-point elastic support dry friction damper matched with the third mode under low pressure excitation. is the multi-objective optimization function value corresponding to the optimal kinetic parameters of the five-support-point elastic support dry friction damper matched with the first mode under high pressure excitation. is the multi-objective optimization function value corresponding to the suboptimal kinetic parameters of the five-support-point elastic support dry friction damper matched with the first mode under high pressure excitation. is the multi-objective optimization function value corresponding to the optimal kinetic parameters of the three-support-point elastic support dry friction damper matched with the fourth mode under high pressure excitation. is the multi-objective optimization function value corresponding to the suboptimal kinetic parameters of the three-support-point elastic support dry friction damper matched with the fourth mode under high pressure excitation.

[0096] The step 33 is the step of obtaining the final kinetic parameters of the elastic support dry friction damper matched with the controlled mode, and the step is as follows:

[0097] The improved particle swarm algorithm proposed by Wang Siqi in the article "Helicopter power turbine rotor system optimization method based on improved particle swarm algorithm[J]. Acta Aeronautica et Astronautica, 2023, 45(01): 242-258." (DOI:10.7527 / S1000-6893.2023.28608) is used, and the total number of groups is set to 30 and the iteration number is 20 times. The optimization direction of the improved particle swarm algorithm is realized by adjusting the dynamic parameters of the elastic support dry friction damper in the second dynamic parameter change range to realize the minimum value of the multi-modal optimization function. The final dynamic parameters of the elastic support dry friction damper of each support point are shown in Table 7.

[0098] Table 7

[0099]

[0100] Step 34, verifying the optimization design result

[0101] The final dynamic parameters of the elastic support dry friction damper of each support point are obtained, and the finite element method is used to calculate the vibration displacement of each order controlled mode, as shown in Table 8. Figure 9 Figure 9 a is the third order mode of low pressure excitation, Figure 9 b is the fourth order mode of high pressure excitation, after optimization, the critical displacement in the low pressure turbine disc vibration displacement 40 under the action of the elastic support dry friction damper under the first order mode of low pressure excitation, the fan 1 stage disc vibration displacement 41 under the action of the elastic support dry friction damper under the third order mode of low pressure excitation, the low pressure turbine disc vibration displacement 42 under the action of the elastic support dry friction damper under the first order mode of high pressure excitation, and the compressor 1 stage disc vibration displacement 43 under the action of the elastic support dry friction damper under the fourth order mode of high pressure excitation are all lower than , which meets the design requirements. Thus, the dynamic parameter optimization design of the elastic support dry friction damper under multi-modal and multi-target is completed.

[0102] The above only describes the preferred embodiments of the present application and does not limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.​

Claims

1. A method for optimizing the dynamic parameters of a multi-modal multi-target under-pinned branch dry friction damper, characterized in that, The application relates to a method for optimizing a rotor system with a matched elastic support dry friction damper. The method comprises the following steps: determining a controlled mode and a matched elastic support dry friction damper; determining a first dynamic parameter variation range of the elastic support dry friction damper according to design requirements; taking a critical displacement variation amount of the rotor system under different normal pressures as controllability of the elastic support dry friction damper; establishing a multi-objective optimization function of the elastic support dry friction damper based on a critical speed constraint condition of the rotor system with the elastic support dry friction damper and according to the critical displacement of the rotor system and the controllability of the elastic support dry friction damper; generating a population according to the first dynamic parameter variation range, and adopting a particle swarm algorithm to take a minimum of the multi-objective optimization function as an optimization target, so as to obtain optimal dynamic parameters and suboptimal dynamic parameters of the elastic support dry friction damper matched with the controlled mode through parameter optimization; generating a second dynamic parameter variation range of the elastic support dry friction damper in multi-mode optimization design according to the optimal dynamic parameters and the suboptimal dynamic parameters of the elastic support dry friction damper; constructing a multi-mode optimization function of the controlled mode according to multi-objective optimization function values corresponding to the optimal dynamic parameters and the suboptimal dynamic parameters of the elastic support dry friction damper; 2. The method of claim 1, wherein generating a population according to the second dynamic parameter variation range, and adopting a particle swarm algorithm to take a minimum of the multi-mode optimization function as an optimization target, so as to obtain final dynamic parameters of the elastic support dry friction damper matched with the controlled mode through parameter optimization. The steps for determining the controlled mode and the matched elastic support dry friction damper are as follows: solving the critical speed, the mode vibration mode and the vibration displacement of the rotor system based on the finite element method; determining each mode in the working speed range of the rotor system according to the number of the critical speed of the rotor system; taking a mode with a vibration displacement of the rotor system greater than a preset vibration displacement threshold value as the controlled mode; 3. The method of claim 1, wherein selecting an elastic support dry friction damper with the largest relative displacement as the elastic support dry friction damper matched with the controlled mode according to the mode vibration mode of the controlled mode.

4. The method of claim 1, wherein The relative displacement is a ratio of the vibration displacement of the elastic support dry friction damper to the displacement of the rotor system. In the formula, The Controllability of the elastic support dry friction damper matched with the controlled modal, F 1,i The First positive pressure of the elastic support dry friction damper matched with the controlled modal of the n-th order, F 2,i The Second positive pressure of the elastic support dry friction damper matched with the controlled modal of the n-th order; The Positive pressure applied by the elastic support dry friction damper matched with the controlled modal of the n-th order F 1,i Critical displacement of the rotor system; The Positive pressure applied by the elastic support dry friction damper matched with the controlled modal of the n-th order F 2,i Critical displacement of the rotor system.

5. The method of claim 1, wherein The controllability of the elastic support dry friction damper is expressed as: wherein is the critical speed constraint expression for the m-th controlled mode; i is the critical speed constraint expression for the m-th controlled mode; is the critical speed constraint expression for the m-th controlled mode; i is the critical speed constraint expression for the m-th controlled mode; is the critical speed constraint expression for the m-th controlled mode; i is the critical speed constraint expression for the m-th controlled mode; is the critical speed constraint expression for the m-th controlled mode; i is the critical speed constraint expression for the m-th controlled mode; is the operating speed of the rotor system.

6. The method of claim 1, wherein The critical speed constraint condition of the rotor system with the elastic support dry friction damper is: In the formula, is the multi-objective optimization function corresponding to the elastic support dry friction damper of the controlled modal matching of the order is the vector composed of the dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order is the critical displacement of the rotor system under the action of the elastic support dry friction damper of the controlled modal matching of the order is the controllability of the elastic support dry friction damper of the controlled modal matching of the order is the penalty function corresponding to the controlled modal of the order , the penalty function method is used to convert the constraint optimization problem into an unconstrained optimization problem, and R is a penalty factor, is the expression of the critical speed constraint condition of the controlled modal of the order is the lower limit value of the vector composed of the dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order is the upper limit value of the vector composed of the dynamic parameters of the elastic support dry friction damper of the controlled modal matching of the order i is the critical speed of the controlled modal of the order i is the critical speed of the controlled modal of the order without the action of the damper i is the critical speed of the controlled modal of the order with the action of the damper​​​​​​​​​​ 7. The method of claim 1, wherein The multi-objective optimization function is expressed as: wherein, is a multi-modal optimization function; is the optimization weight of the th modal; is the order of the controlled modal; is the optimization weight of the i th modal; is the multi-objective optimization function value corresponding to the optimal kinetic parameters of the elastic support dry friction damper matched with the i th modal; is the multi-objective optimization function value corresponding to the suboptimal kinetic parameters of the elastic support dry friction damper matched with the i th modal; is the multi-objective optimization function corresponding to the controlled modal of the elastic support dry friction damper matched with the th modal.

8. The method of claim 1, wherein The multi-mode optimization function is expressed as: In the formula, x i For the first i The vector formed by the first dynamic parameters of the spring-loaded dry friction damper with first-order mode matching; k i For the first i The stiffness range of the squirrel cage spring in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching. s i For the first i The range of support stiffness values ​​for the static friction plate mounting ring in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching. m i For the first i The mass range of the static friction plate in the first dynamic parameter of the spring-supported dry friction damper with first-order mode matching; For the first i The lower limit of the stiffness of the squirrel cage spring in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The upper limit of the stiffness of the squirrel cage spring in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The lower limit of the static friction plate mounting ring support stiffness in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The upper limit of the static friction plate mounting ring support stiffness in the first dynamic parameter of the modally matched spring-loaded dry friction damper; the second... i The lower limit of the static friction plate mass in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching; For the first i The upper limit of the static friction plate mass in the first dynamic parameter of the spring-loaded dry friction damper with first-order mode matching.

9. The method of claim 1, wherein The first dynamic parameter variation range is: In the formula, the second dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order; the stiffness range value of the squirrel cage elastic support in the second dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order; the supporting stiffness range value of the static friction sheet mounting ring in the second dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order; the mass range value of the static friction sheet in the second dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order; the optimal stiffness of the squirrel cage elastic support in the optimal dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order after multi-objective optimization; the suboptimal stiffness of the squirrel cage elastic support in the suboptimal dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order after multi-objective optimization; the optimal supporting stiffness of the static friction sheet mounting ring in the optimal dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order after multi-objective optimization; the suboptimal supporting stiffness of the static friction sheet mounting ring in the suboptimal dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order after multi-objective optimization; the optimal mass of the static friction sheet in the optimal dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order after multi-objective optimization; the suboptimal mass of the static friction sheet in the suboptimal dynamic parameter of the elastic support dry friction damper of the controlled modal matching of the first order after multi-objective optimization.

10. The method of claim 1, wherein The second dynamic parameter variation range is: The dynamic parameters of the elastic support dry friction damper include the stiffness of a squirrel-cage elastic support, the supporting stiffness of a static friction piece mounting ring and the mass of the static friction piece.

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