Design method of strain balance force measuring system based on component coupling optimization

Abstract

The invention relates to the technical field of force measurement system design, and discloses a strain balance force measurement system design method based on component coupling optimization, which comprises the following steps: establishing a three-degree-of-freedom spring mass model, carrying out kinetic analysis, and establishing a characteristic equation of a strain balance force measurement system; establishing an expression containing a mass distribution parameter and a rigidity distribution parameter, combining the characteristic equation to obtain a characteristic equation containing the mass distribution parameter and the rigidity distribution parameter, introducing parameter variables to simplify and solve the characteristic equation, and finally obtaining the third-order inherent frequency of the strain balance force measuring system; selecting the maximization of the inherent frequency of the first-order mode as an optimization target, setting constraint conditions by taking the mass and rigidity distribution parameters as independent variables, then solving to obtain the optimal mass and rigidity distribution parameters, and using the optimal mass and rigidity distribution parameters to design the overall structure of the strain balance force measurement system; according to the method, the overall inherent frequency of the strain balance force measurement system is improved, and the force measurement performance is improved from the structural design level.

Description

Technical Field

[0001] The present invention relates to the technical field of force measurement system design, and in particular to a strain gauge balance force measurement system design method based on component coupling optimization. Background Art

[0002] The design criteria for the three core components of the traditional strain balance force measurement system, namely the aircraft model, the force balance and the bracket, are relatively independent. The stiffness and geometric dimension design of the components rely more on empirical criteria, which to a certain extent limits the room for improvement in the force measurement performance of the strain balance force measurement system from the structural design level. Summary of the Invention

[0003] In response to the above-mentioned deficiencies in the prior art, the present invention provides a design method for a strain balance force measurement system based on component coupling optimization, which is used to solve the problem that the design criteria of traditional strain balance force measurement systems are relatively independent and the design of component stiffness and geometric dimensions relies on empirical criteria, resulting in low force measurement performance of the strain balance force measurement system at the structural design level.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A design method for a strain gauge balance force measurement system based on component coupling optimization includes the following steps: S1. Simplify the analysis of the strain gauge balance force measurement system including the aircraft model, the force balance, and the bracket, and equate each force measurement channel of the strain gauge balance force measurement system to a three-degree-of-freedom spring-mass system, thereby establishing a three-degree-of-freedom spring-mass model. S2. Perform dynamic analysis on the three-degree-of-freedom spring-mass model and establish the characteristic equation of the strain balance force measurement system; S3. Based on the three-degree-of-freedom spring-mass model, establish an expression containing the mass distribution parameter and the stiffness distribution parameter, and combine it with the characteristic equation of the strain balance force measurement system to obtain the characteristic equation containing the mass distribution parameter and the stiffness distribution parameter; S4. Introduce parameter variables, simplify and solve the characteristic equation containing mass distribution parameters and stiffness distribution parameters, obtain the solution set of parameter variables, and then perform variable substitution to obtain the third-order natural frequency of the strain balance force measurement system; S5. Based on the third-order natural frequency of the strain gauge balance force measurement system, with maximizing the first-order modal natural frequency as the optimization goal, and with mass distribution parameters and stiffness distribution parameters as independent variables, and based on the aerodynamic shape of the aircraft model, the balance space limitations, and the service environment of the strain gauge balance force measurement system, set constraints such as geometric dimensions and installation position requirements for the independent variables, and solve the optimization goal under the constraints to obtain the optimal mass distribution parameters and stiffness distribution parameters; S6. Based on the optimal stiffness distribution parameters and the stiffness distribution parameters, the overall structure of the strain balance force measurement system is designed to obtain the designed optimal overall structure of the strain balance force measurement system.

[0005] The present invention has the following beneficial effects: 1. This invention proposes a design method for a strain gauge force measurement system based on component coupling optimization. This method, based on the strain gauge force measurement system as a whole, optimizes the stiffness and mass coupling of the aircraft model, measuring balance, and bracket. Specifically, a three-degree-of-freedom spring-mass model is established and the stiffness and mass distribution parameters are optimized. These parameters are then used as design criteria for the strain gauge force measurement system, replacing some traditional empirical formulas. This method improves the natural frequency of the strain gauge force measurement system as a whole, enhancing force measurement performance from a structural design perspective. 2. Optimize the stiffness distribution parameters and mass distribution parameters. By fully considering the stiffness distribution and mass relationship between each component, it is ensured that the overall performance of the strain balance force measurement system meets the use requirements. At the same time, by considering the reasonable stiffness distribution of each component that constitutes the strain balance force measurement system, it can also ensure that the system produces appropriate deformation when subjected to force, thereby improving measurement accuracy and stability. Considering a reasonable mass relationship can optimize the system's dynamic performance, natural frequency and response speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Figure 1 This is a flow chart of a design method for a strain gauge balance force measurement system based on component coupling optimization proposed in the present invention; Figure 2 This is a simplified structural diagram of a strain gauge balance force measurement system in an embodiment; Figure 3 Schematic diagram of the structure of a three-degree-of-freedom spring-mass model of an equivalent system of a strain balance force measurement system in an embodiment. DETAILED DESCRIPTION

[0007] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0008] like Figure 1 As shown, a design method for a strain balance force measurement system based on component coupling optimization includes the following steps S1-S6: S1. Simplify the analysis of the strain gauge balance force measurement system including the aircraft model, force balance, and bracket. Equivalently treat each force measurement channel of the strain gauge balance force measurement system as a three-degree-of-freedom spring-mass system, and establish a three-degree-of-freedom spring-mass model.

[0009] Specifically, the three-degree-of-freedom spring mass model includes a bracket-fixed frame, a floating frame, an aircraft model, and a balance force measuring unit; the bracket-fixed frame and the foundation are connected through the equivalent stiffness of the bracket-fixed frame, the bracket-fixed frame and the floating frame are connected through the equivalent stiffness of the balance force measuring unit, and the floating frame and the aircraft model are connected through the equivalent stiffness of the aircraft model.

[0010] In this embodiment, in order to simplify the overall process of the strain balance force measurement system, the specific steps are as follows: The strain balance force measurement system consists of three parts: an aircraft model, a force balance, and a bracket. The aircraft model is fixed to the floating frame of the balance, and the bracket is fixed to the fixed frame of the balance. Force measuring units of various force measurement channels are arranged between the floating frame and the fixed frame. The aerodynamic force measurement of the system is achieved by detecting the strain of each force measuring unit through sensors. The simplified structure of the strain balance force measurement system is as follows: Figure 2 As shown; Taking the strain balance force measurement system as the object, each force measurement channel of the strain balance force measurement system can be equivalent to a three-degree-of-freedom spring-mass system. According to the vibration dynamics theory, the system has a third-order natural frequency, and the natural frequency is independent of damping and external excitation. Therefore, the theoretical model system considering the natural frequency can be simplified to a three-degree-of-freedom spring-mass model, as shown in the following example: Figure 3 As shown, it includes a bracket-fixed frame, a floating frame, an aircraft model, and a balance force measuring unit. The bracket-fixed frame and the base are connected via the equivalent stiffness of the bracket-fixed frame, the bracket-fixed frame and the floating frame are connected via the equivalent stiffness of the balance force measuring unit, and the floating frame and the aircraft model are connected via the equivalent stiffness of the aircraft model.

[0011] S2. Perform dynamic analysis on the three-degree-of-freedom spring-mass model and establish the characteristic equation of the strain balance force measurement system.

[0012] Specifically, step S2 includes S21-S23: S21. Establish the free vibration equation of the three-degree-of-freedom spring-mass model, namely:

[0013]

[0014]

[0015] in, represents the mass matrix, represents the stiffness matrix, represents the vibration amplitude, represents the second derivative of the vibration amplitude, represents the equivalent mass of the bracket-fixed frame, represents the equivalent mass of the floating box, represents the equivalent mass of the aircraft model, represents the equivalent stiffness of the bracket-fixed frame, represents the equivalent stiffness of the balance force measuring unit, Represents the equivalent stiffness of the aircraft model.

[0016] In this embodiment, the free vibration equation of the three-degree-of-freedom spring-mass model is obtained according to the vibration dynamics theory.

[0017] S22. Establish the characteristic equation expression of the strain balance force measurement system, namely:

[0018] in, Indicates the natural frequency of the equivalent system of the force measurement system.

[0019] S23. Substitute the characteristic equation of the strain balance force measurement system into the free vibration equation of the three-degree-of-freedom spring-mass model to obtain the characteristic equation of the strain balance force measurement system, namely: .

[0020] S3. Based on the three-degree-of-freedom spring-mass model, an expression containing mass distribution parameters and stiffness distribution parameters is established, and combined with the characteristic equation of the strain balance force measurement system, the characteristic equation containing mass distribution parameters and stiffness distribution parameters is obtained.

[0021] Specifically, step S3 includes S31-S32: S31. The ratios of the equivalent stiffness of the bracket-fixed frame and the aircraft model to the equivalent stiffness of the balance force measuring unit, and the ratios of the equivalent mass of the bracket-fixed frame and the aircraft model to the equivalent mass of the floating frame are used as stiffness distribution parameters and mass distribution parameters, and an expression containing the mass distribution parameters and the stiffness distribution parameters is established, namely:

[0022] in, It represents the ratio of the equivalent stiffness of the bracket-fixed frame to the equivalent stiffness of the balance force measuring unit. It represents the ratio of the equivalent stiffness of the aircraft model to the equivalent stiffness of the balance force measuring unit. represents the ratio of the equivalent mass of the bracket-fixed frame to the equivalent mass of the floating frame, Indicates the ratio of the equivalent mass of the aircraft model to the equivalent mass of the floating box.

[0023] In this embodiment, a simplified model is used to establish the relationship between mass distribution and stiffness distribution on the strain balance force measurement system model. In the force measurement system design process, the stiffness and mass of the balance are directly affected by the design range of the force measurement system, and are more closely and directly related to the design requirements. The parameter design margin is relatively small and easier to determine. In addition, the stiffness distribution of the balance affects the complexity of the entire system design, and its structural determination priority is higher than other core components. In order to more intuitively reflect the role of mass distribution and stiffness distribution in the optimal design of the strain balance force measurement system model, and taking into account the simplification of the model, this method selects the stiffness and mass ratio based on the equivalent stiffness and equivalent mass of the balance force measurement unit as the distribution parameters of the two.

[0024] S32. Substitute the expression containing the mass distribution parameter and the stiffness distribution parameter into the characteristic equation of the strain balance force measurement system to obtain the characteristic equation containing the mass distribution parameter and the stiffness distribution parameter, namely: .

[0025] S4. Introduce parameter variables, simplify and solve the characteristic equation containing mass distribution parameters, obtain the solution set of parameter variables, and then perform variable substitution to obtain the third-order natural frequency of the strain balance force measurement system.

[0026] Specifically, step S4 includes S41-S44: S41, introduce parameter variables as , the variable substitution formula is: .

[0027] S42. Based on the variable substitution formula, the characteristic equation containing the mass distribution parameter is simplified using the parameter variable to obtain a simplified characteristic equation, namely:

[0028] .

[0029] S43. Solve the simplified characteristic equation to obtain the solution set of parameter variables, namely:

[0030] in, 、 、 Represent three different parameter variable solutions respectively.

[0031] S44. The solution set of the parameter variables is again substituted using the variable substitution formula to obtain the third-order natural frequency of the strain balance force measurement system, namely:

[0032] in, 、 、 They represent the first-order mode, second-order mode, and third-order mode natural frequencies of the strain balance force measurement system respectively.

[0033] S5. Based on the third-order natural frequency of the strain balance force measurement system, with maximizing the first-order modal natural frequency as the optimization goal, and mass distribution parameters and stiffness distribution parameters as independent variables, and based on the aerodynamic shape of the aircraft model, the balance space limitations and the service environment of the strain balance force measurement system, set the constraints of the independent variables including geometric dimensions and installation position index requirements, and solve the optimization goal under the constraints to obtain the optimal mass distribution parameters and stiffness distribution parameters.

[0034] Specifically, based on the aerodynamic shape of the aircraft model, the balance space limitations, and the service environment of the strain gauge balance force measurement system, the specific process for setting the constraints of the independent variables, including geometric dimensions and installation position index requirements, is as follows: The geometric dimensions of the balance and the installation position index requirements between the balance and the aircraft model are set based on the aerodynamic shape of the aircraft model and the space limitations of the balance installation. The geometric dimensions of the aircraft model and the bracket and the bracket installation position index requirements are set based on the service environment of the strain balance force measurement system. At the same time, based on the theoretical basis of material mechanics, the design mass range and design stiffness range of each component of the strain balance force measurement system are obtained. Finally, the constraint conditions of the independent variables are obtained.

[0035] In this embodiment, the optimization goal is to maximize the first-order modal natural frequency among the three-order natural frequencies of the strain balance force measurement system, that is: , and then select Assign parameters by stiffness ( , ) and mass distribution parameter ( , ) as the independent variable, according to the set constraints of the independent variable, the genetic optimization method can be used to obtain the optimal values ​​of the stiffness distribution parameters and the mass distribution parameters under the optimal objective function, and then it is substituted into the expression containing the mass distribution parameters and the stiffness distribution parameters to determine the stiffness and mass of the aircraft model, the force measuring units of each channel of the balance, and the bracket.

[0036] In addition, since different types of strain gauge balance force measurement system structures require different functional settings for their constraints, design criteria are provided for setting constraints with independent variables including geometric dimensions and installation location requirements, based on the aerodynamic shape of the aircraft model, the space limitations of the balance, and the service environment of the strain gauge balance force measurement system. In this embodiment, a functional relationship for the constraints of a multi-component box-type strain gauge balance is provided based on the above-mentioned design criteria for the constraints, specifically: First, select the I-type beam force measuring unit and determine the length of the force measuring unit according to the balance range and sensitivity requirements. ,width ,thickness , and obtain the stiffness of each force measuring unit for:

[0037] in, is the Young's modulus of the balance material. The box balance is a parallel model. According to the material mechanics formula, the effective stiffness of the balance can be obtained. for:

[0038] in, is the number of force measuring unit groups. × Width ×Height ) limit, reserve a certain space for the deformation space of the force measuring unit, the lead slot and the strain gauge pasting operation space, and set the floating frame quality coefficient , then the equivalent mass of the floating frame It can be obtained as follows:

[0039] in, is the density of the balance material, Reserve space volume.

[0040] Therefore, based on the above conditions, the stiffness constraint function is set as follows: According to the parameters of the spatial geometry of the wind tunnel test section where the strain gauge force measurement system is used, the geometric dimensions and installation positions of the bracket and the aircraft model are set. The equivalent cantilever length is set to According to the experimental requirements, the equivalent cantilever length of the bracket is set to , determine the length of the aircraft model to be , floating frame length To ensure that the wind tunnel test flow field is not affected by the overall deformation of the strain balance force measurement system, the deflection angle at the maximum deformation position of the aircraft model and the bracket should be less than 0.1°. Then the bending stiffness constraint function of the bracket and aircraft model is:

[0041] in, 、 are the Young's modulus of the material of the bracket and the aircraft model, 、 are the cross-sectional inertia moments of the bracket and the aircraft model, is the tangent function, The maximum range of the force measurement channel (usually the normal force range); So the formula and formula Substitute into the formula The constraint function (constraint condition) of the stiffness distribution parameter can be obtained as follows: .

[0042] Similarly, the quality constraint function is set as follows: is the density of the bracket material. Considering the stability requirements, in order to reduce the vibration coupling of the system model, is the allowable equivalent cross-sectional area of ​​the bracket, then the bracket mass The relationship is:

[0043] Considering that the inertial force is the interference term of the balance strain balance force measurement system, and the main source of the inertial force is the mass of the aircraft model, the inertial force proportional coefficient is set to , then the model quality constraint relationship is:

[0044] in, is the acceleration due to gravity.

[0045] So the formula and formula Substitute into the formula The constraint function (constraint condition) of the mass distribution parameter can be obtained as follows: .

[0046] S6. Based on the optimal stiffness distribution parameters and the stiffness distribution parameters, the overall structure of the strain balance force measurement system is designed to obtain the designed optimal overall structure of the strain balance force measurement system.

[0047] Specifically, step S6 includes S61-S63: S61. Using the optimal stiffness distribution parameters as the design criteria, design the force measuring unit form and spatial distribution, and obtain the structural form of the strain balance force measuring system.

[0048] In this embodiment, the optimal stiffness distribution parameter ( , ) as the design criterion, the force cell form and spatial distribution are designed to meet the stiffness distribution requirements. Furthermore, after selecting the balance, the spatial layout and structural form are relatively fixed, while after optimization, the changes are primarily to the size and position parameters. Because stiffness directly affects the cross-sectional dimensions and positions of the force cells, once the stiffness distribution is fixed, the balance structure can be considered fixed. Therefore, once the optimal stiffness distribution parameters are obtained, the structural form of the strain gauge balance force measurement system is determined.

[0049] S62. Using the optimal mass distribution parameters as the design criteria and the geometric dimension index requirements as the spatial design domain, the lightweight structure design of the aircraft model and bracket is carried out through topological optimization.

[0050] In this embodiment, the optimal mass distribution parameter ( , ) as the design criterion, the geometric dimension index requirements in the constraints in step S5 are used as the spatial design domain, and then the topology optimization method is used to perform lightweight structural design of the aircraft model and bracket, which can meet the mass distribution requirements.

[0051] S63. Based on the structural form of the strain balance force measurement system, the aircraft model and the bracket structure, and in combination with the installation position index requirements, three-dimensional modeling of the strain balance force measurement system is performed, and the modeled strain balance force measurement system is analyzed to determine whether the strain balance force measurement system meets the force measurement performance requirements. If so, the overall structure of the optimal strain balance force measurement system is obtained. Otherwise, the independent variables including the constraints of the geometric dimensions and the installation position index requirements are adjusted, and step S5 is continued.

[0052] In this embodiment, the structure of the strain gauge balance force measurement system is combined with the structure of the aircraft model and bracket, and the assembly model is completed using 3D modeling software with reference to the installation position index requirements in the constraint conditions in step S5. The modal natural frequency of the resulting model is then analyzed and verified using simulation analysis software. If the force measurement performance requirements are not met, the process returns to step S5, adjusts the constraint relationship between the various physical quantities, resets the index requirements, corrects the constraint conditions, and continues to optimize the strain gauge balance force measurement system. If the force measurement performance requirements are met, the optimization is stopped, and the optimal strain gauge balance force measurement system overall structure is ultimately output, completing the strain gauge balance force measurement system design task.

[0053] In summary, the present invention proposes a design method for a strain gauge force measurement system based on component coupling optimization. First, the design method formulates constraint design criteria for the entire strain gauge force measurement system. This method combines genetic optimization with topology optimization to find the optimal structure, thus breaking away from the limitations of empirical formulas and improving the design accuracy of the strain gauge force measurement system. Secondly, the three components—the aircraft model, the strain gauge, and the bracket—are coupled according to the design criteria. This ensures that the components that make up the strain gauge force measurement system have a reasonable stiffness distribution and a reasonable mass relationship, resulting in a final solution that achieves optimal force measurement performance under specified service conditions.

[0054] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0055] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A design method for a strain gauge force measurement system based on component coupling optimization, characterized in that: The following steps are involved: S1. Simplify the analysis of the strain gauge balance force measurement system including the aircraft model, the force balance, and the bracket, and equate each force measurement channel of the strain gauge balance force measurement system to a three-degree-of-freedom spring-mass system, thereby establishing a three-degree-of-freedom spring-mass model. S2. Perform dynamic analysis on the three-degree-of-freedom spring-mass model and establish the characteristic equation of the strain balance force measurement system; S3. Based on the three-degree-of-freedom spring-mass model, establish an expression containing the mass distribution parameter and the stiffness distribution parameter, and combine it with the characteristic equation of the strain balance force measurement system to obtain the characteristic equation containing the mass distribution parameter and the stiffness distribution parameter; S4. Introduce parameter variables, simplify and solve the characteristic equation containing mass distribution parameters and stiffness distribution parameters, obtain the solution set of parameter variables, and then perform variable substitution to obtain the third-order natural frequency of the strain balance force measurement system; S5. Based on the third-order natural frequency of the strain gauge balance force measurement system, with maximizing the first-order modal natural frequency as the optimization goal, and with mass distribution parameters and stiffness distribution parameters as independent variables, and based on the aerodynamic shape of the aircraft model, the balance space limitations, and the service environment of the strain gauge balance force measurement system, set constraints such as the independent variables' geometric dimensions and installation position index requirements, and solve the optimization goal under the constraints to obtain the optimal mass distribution parameters and stiffness distribution parameters; S6. Based on the optimal stiffness distribution parameters and the stiffness distribution parameters, the overall structure of the strain balance force measurement system is designed to obtain the designed optimal overall structure of the strain balance force measurement system.

2. The design method of a strain balance force measurement system based on component coupling optimization according to claim 1, characterized in that: The three-DOF spring-mass model includes a bracket-fixed frame, a floating frame, an aircraft model, and a balance force measuring unit; The bracket-fixed frame and the foundation are connected through the equivalent stiffness of the bracket-fixed frame, the bracket-fixed frame and the floating frame are connected through the equivalent stiffness of the balance force measuring unit, and the floating frame and the aircraft model are connected through the equivalent stiffness of the aircraft model.

3. The design method of a strain balance force measurement system based on component coupling optimization according to claim 2, characterized in that: Step S2 specifically includes: S21. Establish the free vibration equation of the three-degree-of-freedom spring-mass model, namely: in, represents the mass matrix, represents the stiffness matrix, represents the vibration amplitude, represents the second derivative of the vibration amplitude, represents the equivalent mass of the bracket-fixed frame, represents the equivalent mass of the floating box, represents the equivalent mass of the aircraft model, represents the equivalent stiffness of the bracket-fixed frame, represents the equivalent stiffness of the balance force measuring unit, represents the equivalent stiffness of the aircraft model; S22. Establish the characteristic equation expression of the strain balance force measurement system, namely: in, Indicates the natural frequency of the equivalent system of the force measurement system; S23. Substitute the characteristic equation of the strain balance force measurement system into the free vibration equation of the three-degree-of-freedom spring-mass model to obtain the characteristic equation of the strain balance force measurement system, namely: 。 4. The design method of a strain balance force measurement system based on component coupling optimization according to claim 3, characterized in that: Step S3 specifically includes: S31. The ratios of the equivalent stiffness of the bracket-fixed frame and the aircraft model to the equivalent stiffness of the balance force measuring unit, and the ratios of the equivalent mass of the bracket-fixed frame and the aircraft model to the equivalent mass of the floating frame are used as stiffness distribution parameters and mass distribution parameters, and an expression containing the mass distribution parameters and the stiffness distribution parameters is established, namely: in, It represents the ratio of the equivalent stiffness of the bracket-fixed frame to the equivalent stiffness of the balance force measuring unit. It represents the ratio of the equivalent stiffness of the aircraft model to the equivalent stiffness of the balance force measuring unit. represents the ratio of the equivalent mass of the bracket-fixed frame to the equivalent mass of the floating frame, Indicates the ratio of the equivalent mass of the aircraft model to the equivalent mass of the floating frame; S32. Substitute the expression containing the mass distribution parameter and the stiffness distribution parameter into the characteristic equation of the strain balance force measurement system to obtain the characteristic equation containing the mass distribution parameter and the stiffness distribution parameter, namely: 。 5. The design method of a strain balance force measurement system based on component coupling optimization according to claim 4, characterized in that: Step S4 specifically includes: S41, introduce parameter variables as , the variable substitution formula is: ； S42. Based on the variable substitution formula, the characteristic equation containing the mass distribution parameter is simplified using the parameter variable to obtain a simplified characteristic equation, namely: ； S43. Solve the simplified characteristic equation to obtain the solution set of parameter variables, namely: in, 、 、 Represent three different parameter variable solutions respectively; S44. The solution set of the parameter variables is again substituted using the variable substitution formula to obtain the third-order natural frequency of the strain balance force measurement system, namely: in, 、 、 They represent the first-order mode, second-order mode, and third-order mode natural frequencies of the strain balance force measurement system respectively.

6. The design method of a strain balance force measurement system based on component coupling optimization according to claim 5, characterized in that: Based on the aerodynamic shape of the aircraft model, the balance space limitations, and the service environment of the strain gauge balance force measurement system, the specific process for setting the constraints of the independent variables, including geometric dimensions and installation position requirements, is as follows: The geometric dimensions of the balance and the installation position index requirements between the balance and the aircraft model are set based on the aerodynamic shape of the aircraft model and the space limitations of the balance installation. The geometric dimensions of the aircraft model and the bracket and the bracket installation position index requirements are set based on the service environment of the strain balance force measurement system. At the same time, based on the theoretical basis of material mechanics, the design mass range and design stiffness range of each component of the strain balance force measurement system are obtained. Finally, the constraint conditions of the independent variables are obtained.

7. The design method of a strain balance force measurement system based on component coupling optimization according to claim 6, characterized in that: Step S6 specifically includes: S61. Using the optimal stiffness distribution parameters as the design criteria, design the force measuring unit form and spatial distribution, and obtain the structure of the strain balance force measuring system; S62. Using the optimal mass distribution parameters as the design criteria and the geometric dimension requirements as the spatial design domain, a lightweight structural design of the aircraft model and bracket is performed through topological optimization. S63. Based on the structural form of the strain balance force measurement system, the aircraft model and the bracket structure, and in combination with the installation position index requirements, three-dimensional modeling of the strain balance force measurement system is performed, and the modeled strain balance force measurement system is analyzed to determine whether the strain balance force measurement system meets the force measurement performance requirements. If so, the overall structure of the optimal strain balance force measurement system is obtained. Otherwise, the independent variables including the constraints of the geometric dimensions and the installation position index requirements are adjusted, and step S5 is continued.

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