A method for optimizing design parameters of a device with dry friction damping

Abstract

This invention discloses a method for optimizing the design parameters of a dry friction damping device. The steps are as follows: First, based on the substructure method and the RFFB method, and combined with finite element analysis software, a finite element model of two blades and a damping plate is established to determine the main degrees of freedom of the analysis object and reduce the dimension of the parameter matrix of each component. Second, based on the multi-degree-of-freedom Iwan friction model and the harmonic balance method, and combined with a general programming language, a degree-of-freedom reduction program and a harmonic response calculation program are developed. Finally, the calculation program is integrated, and different design parameters are changed multiple times to complete the parameter optimization analysis with the goal of achieving the best vibration reduction effect of the damping device. The advantage of this design method is that it can efficiently and accurately predict the vibration response of a dry friction damping blade assembly under harmonic excitation, and it is generally applicable to general dry friction damping systems, which is of great significance for the structural design and parameter optimization of damping devices.

Description

Technical Field

[0001] This invention belongs to the field of blade vibration control technology, specifically relating to a method for optimizing design parameters of a dry friction damping device. Background Technology

[0002] Damping on aero-engine blades can be broadly categorized into four types: material damping, friction damping, aerodynamic damping, and impact damping. Among these, friction damping and impact damping are two promising blade damping structures. Currently, research on impact damping is relatively limited, and it is believed that its contribution to vibration reduction is minimal during normal engine operation. Friction damping is currently the most effective vibration reduction technology. It does not require altering the blade's mass or stiffness; simply adding appropriate friction pairs at suitable locations can achieve the effect of dissipating energy and suppressing vibration. Its adjustment is also relatively simple; the degree of energy dissipation can be adjusted by changing conditions such as the normal pressure on the friction pair. Due to its numerous advantages and strong adaptability to various environments, it has broad development prospects.

[0003] However, as the structure of gas turbine rotor blades becomes increasingly complex, the finite element model mesh for vibration response prediction becomes denser and has a greater number of degrees of freedom. In addition, the vibration process of dry friction damping systems has complex nonlinearity, and solving the dynamic equations of the system's vibration characteristics often consumes a lot of time and resources. On this basis, reducing the dimensionality of the system before solving it can shorten the originally lengthy iterative calculation cycle to several hours or even tens of minutes, greatly improving computational efficiency. Summary of the Invention

[0004] The purpose of this invention is to ensure the accuracy of system vibration response calculation while shortening the calculation time of single harmonic response calculation, so as to calculate a sufficient amount of sample data within a certain time, obtain a sufficient sample space and design parameter set, and use it to design and optimize the key parameters of the damping device, thus providing a method for optimizing the design parameters of a dry friction damping device.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for optimizing the design parameters of a dry friction damping device, comprising:

[0006] Step S1: Using the finite element substructure method and the modal synthesis method based on the residual compliance matrix theory, establish the finite element model of the blade / damper system. Combined with general finite element analysis software, determine the master degree of freedom information of each substructure in the finite element model of the blade / damper system and complete the dimension reduction of the parameter matrix of each substructure.

[0007] Step S2: Based on the nonlinear friction model theory, establish several contact elements on the contact interface between the blade and the damper, and obtain the nodal load matrix and stiffness matrix of the contact elements, which are used as the main degree of freedom parameter matrices to participate in the matrix recombination process in step S3.

[0008] Step S3: Use a general programming language to compile a model reduction program. The model reduction program sorts and assembles the parameter matrices of each substructure obtained in Step S1, the nodal load matrix of the contact element obtained in Step 2, and the stiffness matrix of the contact element obtained in Step 2 according to the master degree of freedom node information of each substructure obtained in Step S1 into the overall parameter matrix of the analysis system.

[0009] Step S4: Define the structural design parameters of the damping device, and use a general programming language to develop a harmonic response calculation program, combining the model condensation program in Step 3.

[0010] Step S5: Based on the harmonic response calculation program developed in Step S4, modify the structural design parameters of the damping device to obtain the peak amplitude of the blade / damper system at the observation point under different damping device structural design parameters. Find the damping device design parameter combination that minimizes the peak amplitude and the design parameter range that meets the damping device vibration reduction technical requirements, and complete the parameter optimization design with the goal of achieving the best vibration reduction effect of the damping device.

[0011] Further, step S1 specifically includes:

[0012] Step S11: In the finite element analysis software, the geometric model of all turbine blades and the matching damping device is modeled using the finite element substructure method to obtain the finite element model of the blades and the damper.

[0013] Step S12: In the finite element model of the blade and damper, define the material parameters, divide the finite element mesh and define the set of master degree of freedom nodes. Then, based on the modal synthesis method of residual compliance matrix theory, perform model reduction analysis on the finite element model of the blade and damper to obtain the master degree of freedom information of each substructure and complete the dimensionality reduction of the parameter matrix of each substructure.

[0014] Furthermore, the set of main degrees of freedom nodes includes: structural excitation points, structural monitoring points, contact endpoints, and other nodes of particular interest.

[0015] Furthermore, the substructure parameter matrix includes: the substructure mass matrix and the substructure stiffness matrix of the finite element model of the blade / damper system.

[0016] Furthermore, the master degree of freedom information includes: excitation point information, monitoring point information, and contact interface node information of the finite element model of the blade / damper system.

[0017] Further, step S2 specifically includes:

[0018] Based on the time-frequency interaction method and the contact friction model on the blade-damper contact interface, the tangential and normal contact loads of the unit are calculated, the state transition time is calculated, the friction motion period is calculated, and the nodal load matrix and contact stiffness matrix are calculated to obtain several contact elements on the blade-damper contact interface.

[0019] Furthermore, the harmonic response calculation process in step S4 includes:

[0020] Step S41: Define the structural design parameters of the damping device, and define the starting frequency, ending frequency, and initial frequency increment for harmonic response calculation;

[0021] Step S42: Obtain the overall parameter matrix through model condensation procedure;

[0022] Step S43: Based on the damping device structural design parameters, the overall parameter matrix, and the nonlinear equation iterative algorithm, solve the dynamic equation of the blade / damper system to obtain the frequency-displacement amplitude result, plot the frequency response function curve, and obtain the peak amplitude of the blade / damper system at the observation point under the input damping device structural design parameters according to the frequency-displacement amplitude result.

[0023] Furthermore, the structural design parameters of the damping device include: tangential contact stiffness, normal contact stiffness, friction coefficient, left and right edge plate angles, and damping plate design mass.

[0024] Beneficial effects:

[0025] 1. This invention is practical and versatile, and can meet the tasks of model condensation processing and optimization design for different blade models and different numbers of blade groups.

[0026] 2. By using a model condensation program, the parameter matrices of each substructure, the nodal load matrix of the contact element, and the stiffness matrix of the contact element are sorted according to the master degree of freedom node information of each substructure and assembled into the overall parameter matrix of the analysis system. This condenses the matrix that needs to be calculated and processed, thereby greatly reducing the calculation time of single harmonic response compared with existing technologies. The calculation time of single harmonic response is estimated to be between 5 and 15 minutes, and the average time for calculating the optimization experimental design of 200 sets of samples is about 20 hours.

[0027] 3. The relevant functions of this invention adopt a modular design. Each part can independently complete the corresponding task. When combined, they can solve most of the dynamic response problems of dry friction contact interface structures. Attached Figure Description

[0028] Figure 1This is a flowchart of the present invention.

[0029] Figure 2 This is a schematic diagram of the master degree of freedom nodes in the finite element model of the substructure.

[0030] Figure 3 This is a schematic diagram of the processing of master degree-of-freedom node information for the finite element model of the blade / damper system.

[0031] Figure 4 This is a schematic diagram of the substructure parameter matrix and master degree of freedom node information file.

[0032] Figure 5 The main program of this invention is designed with a variable module.

[0033] Figure 6 Flowchart for calculating the harmonic response of a single blade

[0034] Figure 7 The result is the frequency response function calculated for the single-stage blade harmonic response.

[0035] Figure 8 This is a sample space diagram for the optimized experimental design of an embodiment of the present invention.

[0036] Figure 9 This is a graph showing the variation of the peak amplitude of an embodiment of the present invention with a single design variable. Detailed Implementation

[0037] The invention will now be further explained with reference to the accompanying drawings.

[0038] like Figure 1 As shown, the present invention provides a method for optimizing the design parameters of a device with dry friction damping, comprising:

[0039] Step S1: Using the finite element substructure method and the modal synthesis method based on the residual compliance matrix theory, establish the finite element model of the blade / damper system. Combined with general finite element analysis software, determine the master degree of freedom information of each substructure in the finite element model of the blade / damper system and complete the dimension reduction of the parameter matrix of each substructure.

[0040] Step S2: Based on the nonlinear friction model theory, establish several contact elements on the contact interface between the blade and the damper, and obtain the nodal load matrix and stiffness matrix of the contact elements, which are used as the main degree of freedom parameter matrices to participate in the matrix recombination process in step S3.

[0041] Step S3: Use a general programming language to compile a model reduction program. The model reduction program sorts and assembles the parameter matrices of each substructure obtained in Step S1, the nodal load matrix of the contact element obtained in Step 2, and the stiffness matrix of the contact element obtained in Step 2 into the overall parameter matrix of the analysis system according to the master degree of freedom node information of each substructure obtained in Step S1.

[0042] Step S4: Define the structural design parameters of the damping device, and use a general programming language to develop a harmonic response calculation program, combining the model condensation program in Step 3.

[0043] Step S5: Based on the harmonic response calculation program developed in Step S4, modify the structural design parameters of the damping device to obtain the peak amplitude of the blade / damper system at the observation point under different damping device structural design parameters. Find the damping device design parameter combination that minimizes the peak amplitude and the design parameter range that meets the damping device vibration reduction technical requirements, and complete the parameter optimization design with the goal of achieving the best vibration reduction effect of the damping device.

[0044] In step S1, the geometric model of all turbine blades and their supporting damping devices is modeled using the finite element substructure method in the finite element analysis software to obtain the finite element models of the blades and dampers. The finite element analysis software is opened, the geometric model of the blade / damper system is imported, the element type and material parameters of the model are defined, and the finite element mesh is generated. After the mesh is generated, the set of master degree of freedom nodes is defined. Then, the model reduction analysis is performed on the finite element model of the blades and dampers based on the modal synthesis method of residual compliance matrix theory to obtain the master degree of freedom information of each substructure and complete the dimensionality reduction of the parameter matrix of each substructure. The finite element model of the blade / damper system consists of multiple finite element models of blades and dampers. Therefore, the above process is repeated for multiple finite element models of blades and dampers to obtain the master degree of freedom information of each substructure in the finite element model of the blade / damper system and complete the dimensionality reduction of the parameter matrix of each substructure. The set of master degree of freedom nodes includes: structural excitation points, structural monitoring points, contact pair endpoints, and other nodes of special interest.

[0045] In this embodiment, the schematic diagram of the master degree of freedom nodes of the substructure of the finite element model of the blade / damper system is shown below. Figure 2 As shown, after defining the set of master degree-of-freedom nodes, all elements in the master degree-of-freedom node set are selected to form a group. Then, the contact surface nodes, excitation force loading nodes, and amplitude monitoring nodes are selected to form another group. The finite element model of the blade / damper system is divided into multiple substructures. Then, based on the modal synthesis method of residual compliance matrix theory, the substructures are reduced and analyzed and calculated to obtain the master degree-of-freedom information of each substructure and the parameter matrix of each substructure after dimension reduction. The schematic diagram of the node information processing of the finite element model of the blade / damper system is shown below. Figure 3 As shown, other nodes of special interest can be any node, determined according to the actual situation.

[0046] In step S2, based on the time-frequency interaction method and the contact friction model at the blade-damper interface, the tangential and normal contact loads of the elements are calculated, the state transition time is calculated, the friction motion period is calculated, and the nodal load matrix and contact stiffness matrix are calculated. This yields several contact elements at the blade-damper interface, and the nodal load matrix and stiffness matrix of each contact element are obtained. The contact friction model at the damper interface is obtained using actual experimental data and finite element analysis software.

[0047] In this embodiment, the finite element analysis software used is ANSYS 19.2.

[0048] In step S3, a model reduction program is developed using a general-purpose programming language. This program sorts and assembles the substructure parameter matrices obtained in step S1, the nodal load matrices of the contact elements obtained in step 2, and the stiffness matrices of the contact elements obtained in step 2, according to the master degrees of freedom node information of each substructure obtained in step S1, into the overall parameter matrix of the analysis system. The reduced-dimensional substructure parameter matrices and the master degrees of freedom information of each substructure will be presented as files in the finite element analysis software, such as... Figure 4 As shown.

[0049] In step S4, the structural design parameters of the damping device are defined. Combining the model condensation procedure from step 3, a harmonic response calculation program is developed in the finite element analysis software, such as... Figure 5 As shown, the harmonic response calculation program operates as follows: First, the structural design parameters of the damping device, the starting frequency, the ending frequency, and the initial frequency increment for the harmonic response calculation are defined. Then, the overall parameter matrix is ​​obtained through a model reduction program. Next, based on the overall parameter matrix and a nonlinear equation iterative algorithm, the dynamic equations of the blade / damper system are solved to obtain the frequency-displacement amplitude results. The frequency response function curve is then plotted, and the peak amplitude of the blade / damper system at the observation point under the input damping device structural design parameters is obtained based on the frequency-displacement amplitude results. The calculation process for a single blade group harmonic response is as follows: Figure 6 As shown, the frequency response function calculated for a single blade harmonic response is as follows: Figure 7 As shown.

[0050] In step S5, the structural design parameters of the damping device are continuously changed, and sample data of the blade tip resonance amplitude are obtained by combining the harmonic response calculation program. Based on a large number of experimental samples, the curve of resonance amplitude versus design parameters is plotted to obtain the optimized design scheme that maximizes the vibration reduction effect of the damping device, as well as the design parameter range that ensures the vibration reduction effect of the damping device meets the technical specifications. The optimized experimental design sample space is as follows: Figure 8 As shown, the curve of peak amplitude variation with a single design variable is as follows: Figure 9 As shown.

[0051] This invention uses a model condensation program to sort and assemble the parameter matrices of each substructure, the nodal load matrix of the contact element, and the stiffness matrix of the contact element according to the master degree of freedom node information of each substructure into the overall parameter matrix of the analysis system. This condenses the matrix that needs to be calculated and processed, thereby greatly reducing the calculation time of single harmonic response compared with the prior art. The calculation time of single harmonic response is estimated to be 5 to 15 minutes. The average time for calculating the optimization experimental design of 200 sets of samples is about 20 hours. It can efficiently and accurately predict the vibration response of blade groups with dry friction damping under simple harmonic excitation, and is generally applicable to general dry friction damping systems. It is of great significance for the structural design and parameter optimization of damping devices.

[0052] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing design parameters of a device with dry friction damping, characterized in that, include: Step S1: Using the finite element substructure method and the modal synthesis method based on the residual compliance matrix theory, establish the finite element model of the blade / damper system. Combined with general finite element analysis software, determine the master degree of freedom information of each substructure in the finite element model of the blade / damper system and complete the dimension reduction of the parameter matrix of each substructure. Step S2: Based on the nonlinear friction model theory, establish several contact elements on the contact interface between the blade and the damper, and obtain the nodal load matrix and stiffness matrix of the contact elements, which are used as the main degree of freedom parameter matrices to participate in the matrix recombination process in step S3. Step S3: Use a general programming language to compile a model reduction program. The model reduction program sorts and assembles the parameter matrices of each substructure obtained in Step S1, the nodal load matrix of the contact element obtained in Step 2, and the stiffness matrix of the contact element obtained in Step 2 according to the master degree of freedom node information of each substructure obtained in Step S1 into the overall parameter matrix of the analysis system. Step S4: Define the structural design parameters of the damping device, and use a general programming language to develop a harmonic response calculation program, combining the model condensation program in Step 3. Step S5: Based on the harmonic response calculation program developed in Step S4, modify the structural design parameters of the damping device to obtain the peak amplitude of the blade / damper system at the observation point under different damping device structural design parameters. Find the damping device design parameter combination that minimizes the peak amplitude and the design parameter range that meets the damping device vibration reduction technical requirements, and complete the parameter optimization design with the goal of achieving the best vibration reduction effect of the damping device.

2. The method for optimizing design parameters of a dry friction damping device according to claim 1, characterized in that, Step S1 specifically includes: Step S11: In the finite element analysis software, the geometric model of all turbine blades and the matching damping device is modeled using the finite element substructure method to obtain the finite element model of the blades and the damper. Step S12: In the finite element model of the blade and damper, define the material parameters, divide the finite element mesh and define the set of master degree of freedom nodes. Then, based on the modal synthesis method of residual compliance matrix theory, perform model reduction analysis on the finite element model of the blade and damper to obtain the master degree of freedom information of each substructure and complete the dimensionality reduction of the parameter matrix of each substructure.

3. The method for optimizing design parameters of a dry friction damping device according to claim 2, characterized in that, The set of main degrees of freedom nodes includes: structural excitation points, structural monitoring points, contact endpoints, and other nodes of particular interest.

4. The method for optimizing design parameters of a dry friction damping device according to claim 2, characterized in that, The substructure parameter matrix includes: the substructure mass matrix and the substructure stiffness matrix of the finite element model of the blade / damper system.

5. The method for optimizing design parameters of a dry friction damping device according to claim 2, characterized in that, The master degree of freedom information includes: excitation point information, monitoring point information, and contact interface node information of the finite element model of the blade / damper system.

6. The method for optimizing design parameters of a dry friction damping device according to claim 1, characterized in that, Step S2 specifically involves: Based on the time-frequency interaction method and the contact friction model on the blade-damper contact interface, the tangential and normal contact loads of the unit are calculated, the state transition time is calculated, the friction motion period is calculated, and the nodal load matrix and contact stiffness matrix are calculated to obtain several contact elements on the blade-damper contact interface.

7. The method for optimizing design parameters of a dry friction damping device according to claim 1, characterized in that, The harmonic response calculation process in step S4 includes: Step S41: Define the structural design parameters of the damping device, and define the starting frequency, ending frequency, and initial frequency increment for harmonic response calculation; Step S42: Obtain the overall parameter matrix through model condensation procedure; Step S43: Based on the damping device structural design parameters, the overall parameter matrix, and the nonlinear equation iterative algorithm, solve the dynamic equation of the blade / damper system to obtain the frequency-displacement amplitude result, plot the frequency response function curve, and obtain the peak amplitude of the blade / damper system at the observation point under the input damping device structural design parameters according to the frequency-displacement amplitude result.

8. The method for optimizing design parameters of a dry friction damping device according to claim 1, characterized in that, The structural design parameters of the damping device include: tangential contact stiffness, normal contact stiffness, friction coefficient, left and right edge plate angles, and damping plate design mass.

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