A typical main propeller hub central piece topology optimization design method considering fatigue performance

Abstract

The present application belongs to the field of helicopter hub structure and structural optimization design, and particularly relates to a typical main hub central part topology optimization design method considering fatigue performance. The present application considers the stiffness, fatigue and mass of the main hub central part into the structural optimization design, proposes an equivalent fatigue dynamic stress which can equivalently represent the fatigue performance of the hub central part based on the helicopter fatigue design theory and the typical cumulative damage theory, takes the equivalent fatigue dynamic stress as the constraint of the topology optimization design, and realizes the forward optimization design of the main hub central part through the result topology optimization method.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of helicopter hub structure and structural optimization design, and particularly relates to a typical main hub central part topology optimization design method considering fatigue performance. BACKGROUND

[0002] The hub central part is a key moving part of the helicopter rotor system and bears complex load conditions during the helicopter task execution. In order to meet the upper-level requirements such as helicopter survival and combat, the performance indicators such as the service life, reliability and survivability of the hub structure are required to be extremely high. The traditional hub structure design adopts the reverse design idea, and the final main hub central part is obtained through repeated manual iteration of structure sample design and strength checking. The traditional design process is slow and needs manual iteration, and the structural stiffness and strength performance are not considered in the design. SUMMARY

[0003] The application aims to provide a typical main hub central part topology optimization design method considering fatigue performance.

[0004] TECHNICAL SCHEME

[0005] A typical main hub central part topology optimization design method considering fatigue performance comprises the following steps.

[0006] Step 1: obtaining the structure interface connected with the main hub central part, determining the design load and use condition of the main hub central part;

[0007] Step 2: based on the structure interface connected with the main hub central part, establishing an initial optimization design region,

[0008] Step 3: dividing the initial optimization design region into a designable region and a non-designable region and respectively performing mesh division on the designable region and the non-designable region to obtain a finite element model and a finite element mesh density matrix ρ;

[0009] Step 4: according to the use condition of the helicopter hub central part, applying boundary conditions to the established finite element model and completing the loading of multiple load conditions according to the design load of the hub central part; after the finite element calculation is completed, the structure displacement matrix U, the structure stress matrix σ, the structure stiffness matrix K, the structure strain matrix B and the structure mass M are obtained;

[0010] Step 5: determining the equivalent replacement relationship between the "hub central part equivalent fatigue dynamic stress" and the "fatigue life": wherein, S a is the equivalent fatigue dynamic stress of the hub central part, N is the fatigue life, A and α are material constants, S 0.2 is the yield limit, S -1 is the safety fatigue limit of symmetric cyclic loading, Sm the structural stress corresponding to the structural average load;

[0011] Step six: according to the finite element grid density matrix ρ, the structural displacement matrix U, the structural stress matrix σ, the structural stiffness matrix K, the structural strain matrix B and the structural mass M, a main shaft hub central piece topology optimization formula considering fatigue performance is established:

[0012] find ρ e (e = 1, …, Num)

[0013] min

[0014] s.t. K r (ρ e )U r = F r

[0015] σ d,r ≤ S a,r

[0016]

[0017] Wherein, Num is the number of structural units, e is the unit number, nu is the number of load cases, the structural stiffness (compliance) C r of the rth case, ρ e is the relative density of the unit e, U r represents the displacement column vector of the rth case, K r represents the stiffness matrix of the rth case, F r represents the load of the rth case, σ d,r represents the first principal stress of the rth case, S a,r represents the equivalent fatigue dynamic stress calculated corresponding to the rth case, M max represents the mass of the structure, is the maximum mass allowed in the design of the structure;

[0018] Step seven: the derivative of the objective function with respect to the design variable, the derivative of the constraint function with respect to the design variable in the main shaft hub central piece topology optimization formula in step six are calculated;

[0019] Step eight: the numerical value of the design variable ρ e is updated according to the derivative of the design variable and the derivative of the constraint function with respect to the design variable;

[0020] Step nine: it is judged whether the difference between the updated design variable and the design variable of the last step meets the convergence criterion, if the design variable does not converge, the updated design variable is brought into the third step to update the finite element model; if the design variable converges, step ten is continued;

[0021] Step ten: output the design variable matrix in the form of slice as an STL file;

[0022] Step eleven: import the STL file into a three-dimensional geometric modeling software to obtain a contour of the main hub central part of the helicopter, and establish a numerical model of the main hub central part according to the contour of the main hub central part of the helicopter;

[0023] Step twelve: perform finite element modeling on the numerical model of the main hub central part, apply the same boundary conditions as the optimization to perform finite element analysis, and further check whether the constraint conditions of the main hub central part topology optimization are met according to the analysis results;

[0024] Step thirteen: according to the finite element analysis results in step twelve, the main hub central part is locally optimized and adjusted to realize the final detailed design of the main hub central part of the helicopter.

[0025] Further, in step two, the selection principle of the initial optimization design region is: 1) the initial optimization design region meets the interface requirements of the main hub central part and other structures; 2) the initial optimization design region cannot interfere with other structures, neither static spatial interference nor motion interference.

[0026] Further, in step three, the designable region is used to carry out the topology optimization design of the main hub central part, the finite element mesh of this region is defined as the design variable of the topology optimization design, each mesh is considered as a separate design variable, and the number of mesh division in this region is the number of design variables defined in this topology optimization problem; the non-designable region is the part of the model that is not allowed to change, which is used to mechanically connect with other structural parts, to ensure the interface matching of the optimized structure and other connected structures.

[0027] Further, in step seven, the derivative of the objective function with respect to the design variable is:

[0028]

[0029] Where D is the material matrix, and p is the penalty value.

[0030] Further, in step seven, it also includes:

[0031] The stress constraints of all mesh elements are condensed into a global stress constraint by using P-norm norm, as follows:

[0032]

[0033] The derivative of the condensed stress constraint is obtained as follows:

[0034]

[0035] Where σ 11σ is the first principal stress term in the structural stress matrix. d For σ 11 The interpolation function.

[0036] Further, step eight specifically involves:

[0037] If the weighted sum of the derivatives of the objective function and constraint functions with respect to the design variables is negative, decrease the design variable ρ. e The value;

[0038] If the weighted sum of the derivatives of the objective function and constraint functions with respect to the design variables is positive, then increase the design variable ρ. e The value of ρ e The value ranges from 0 to 1.

[0039] Furthermore, the convergence criterion in step nine is: convergence is considered to be achieved when the difference between the updated design variable and the previous design variable is less than or equal to 1e-6.

[0040] Furthermore, the value of p is 3.

[0041] Beneficial effects:

[0042] To address the design requirements of metal structural components in helicopter rotor systems, and considering the characteristics of multi-load conditions and large-scale models, a topology optimization design method for typical rotor hub central components, taking into account fatigue performance, was studied. An optimization design model for a typical titanium alloy central component was established, with the structural compliance of the central component as the optimization objective. Constraints included structural mass and the equivalent fatigue dynamic stress level (characterized by fatigue performance under multi-load conditions). A topology optimization mathematical formula was constructed, and the sensitivity analysis of stress constraints with respect to design variables was studied in detail to achieve precise control of stress levels within the structure. By controlling the stress level of the optimized design structure, the fatigue life of the structure can be controlled, laying a key technological foundation for the development of next-generation high-reliability, high-survivability rotor structures. Attached Figure Description

[0043] Figure 1 Flowchart of optimized design for propeller hub central component;

[0044] Figure 2 Initial design structure of the propeller hub central component;

[0045] Figure 3 Final optimized design structure of propeller hub central component Detailed Implementation

[0046] The patent adopts the idea of forward design, applies the topology optimization design technology to the main hub central part design, and carries out the safety life topology optimization design research of the hub central part considering the fatigue performance in combination with the helicopter fatigue strength design theory for the helicopter rotor hub central part design requirements of multiple load conditions and complex load modes. The method proposed by the patent starts from the helicopter hub moving part S-N curve and cumulative damage theory, combines the structure safety fatigue limit of the equal life curve correction, establishes the mathematical equation suitable for the safety life topology optimization design of the main hub central part, carries out the sensitivity analysis of the design variable, and establishes the optimization design model of the typical main hub central part. By controlling the equivalent stress of the safety life of the main hub central part, the purpose of controlling the fatigue life of the structure is achieved, a new idea is provided for the design of the main hub central part with long service life and high reliability, and a key technical foundation is laid for the research and development of the next generation of high reliability and high survivability rotor structure.

[0047] The patent proposes a typical main hub central part topology optimization design method considering fatigue performance. The method proposed by the patent is a numerical calculation method for the optimization design of the main hub central part of the helicopter. The method mainly considers the stiffness, fatigue, mass and other performance indicators of the main hub central part in the structure optimization design. Based on the helicopter fatigue design theory, the equivalent fatigue dynamic stress equivalent to the fatigue performance of the hub central part is proposed considering the typical cumulative damage theory, and the equivalent fatigue dynamic stress is taken as the constraint of the topology optimization design. The forward optimization design of the main hub central part is realized through the result topology optimization method, such as Figure 1 The specific implementation path of the patent is as follows:

[0048] Firstly, the main hub central part design needs to meet the interface with other structures to ensure that the optimized design structure can match the interface with other structures and can be installed with other structures. The structure interface connected with the main hub central part, the design load of the main hub central part and the use condition are obtained, which are necessary for the design of the main hub central part.

[0049] Secondly, based on the interface of the main hub central part, an initial optimization design area is established. The initial optimization design area is a larger space, in which the main hub central part will be designed subsequently. The initial optimization design area can completely wrap the central part to be optimized, that is, the structure optimization design is only allowed in the initial optimization design area defined by us, so the selection of the initial optimization design area is very important. The selection of the initial optimization design area needs to follow the following rules: 1) the initial optimization design area meets the interface requirements of the main hub central part and other structures; 2) the initial optimization design area cannot interfere with other structures, neither static space interference nor motion interference.

[0050] The third step involves dividing the initial optimization design region into a designable region and an undesignable region, and then meshing the designable and undesignable regions to obtain the finite element model and the finite element mesh density matrix. The designable region is used for topology optimization design of the main propeller hub central component. The finite element mesh in this region is defined as the design variable of the topology optimization design, and each mesh is considered a separate design variable. The number of meshes in this region is the number of design variables defined for this topology optimization problem. The undesignable region is the part of the model that cannot be changed and is used for mechanical connection with other structural components to ensure the interface compatibility of the optimized structure with other connection structures.

[0051] The fourth step involves applying appropriate boundary conditions to the established finite element model based on the actual operating conditions of the helicopter rotor hub central component. Multiple load conditions are applied according to the design loads of the rotor hub central component, ensuring the established finite element model accurately describes the operating conditions of the helicopter rotor hub central component and laying the foundation for subsequent structural topology optimization. After the finite element calculations are completed, the structural displacement matrix U, structural stress matrix σ, structural stiffness matrix K, structural strain matrix B, and structural mass M are obtained and can be used for subsequent topology optimization design of the main rotor hub central component.

[0052] Fifth, this patent proposes an equivalent fatigue dynamic stress index for the propeller hub central component, corresponding to the fatigue life index of the central component. The fatigue constraint is transformed from a life constraint to a stress constraint, and an equivalent substitution relationship is proposed between "equivalent fatigue dynamic stress of the propeller hub central component" and "fatigue life".

[0053] Considering the characteristics of the helicopter rotor hub central component during flight operations and the influence of average load on alternating load damage, an equivalent fatigue dynamic stress formula for the rotor hub central component is proposed, utilizing the structural average load on the alternating load:

[0054]

[0055] Among them, S a The equivalent fatigue dynamic stress of the central component of the propeller hub is given by N, where N is the fatigue life, A and α are material constants, and S is the stress at stress α. 0.2 For the yield limit, S -1 For the safe fatigue limit of symmetrical cyclic loading, S m This represents the structural stress corresponding to the average load on the structure.

[0056] Based on this formula, this paper proposes the equivalent fatigue dynamic stress S corresponding to any lifespan N. a The relationship between stress and life is characterized by a formula. Furthermore, the fatigue equivalent dynamic stress constraint condition for subsequent topology optimization is given, which controls the dynamic stress level σ for each working condition. d ≤S a .

[0057] Step 6, according to the various data obtained in step 4, the hub central piece topology optimization formula considering fatigue performance is established. The design variables, objective function and constraint function of the topology optimization formula are determined.

[0058] 1) Design variables: the structure is meshed by finite elements, and each element is assigned a relative density p e (0≤p e ≤1), i.e. the topology optimization design variable, p e =0 represents that no material is arranged at the element, and p e =1 represents that the element is arranged with material;

[0059] 2) The objective function of topology optimization is defined as the minimum flexibility of the hub structure. The flexibility of the structure is a global variable, which is essentially the concept of internal deformation energy of the structure under load;

[0060] 3) The constraint of topology optimization is defined as the first principal stress of the structure being less than the equivalent fatigue dynamic stress proposed in step 5 above, and the mass of the structure being less than the upper limit of the mass, and the topology optimization design problem of the hub central piece is established.

[0061] find p e (e=1,……,Num)

[0062] min

[0063] s.t.K r (ρ e )U r =F r

[0064] σ d,r ≤S a,r

[0065]

[0066] Where Num is the number of structure elements, e is the element number, nu is the number of load cases, the structure stiffness (flexibility) C r of the rth case, p e is the relative density of element e, U r represents the displacement column vector of the rth case, K r represents the stiffness matrix of the rth case, F r represents the load of the rth case, s d,r represents the first principal stress of the rth case, S a,r represents the equivalent fatigue dynamic stress calculated corresponding to the rth case, M max represents the mass of the structure, is the maximum mass allowed for structure design.

[0067] Step 7, the objective function and the constraint function presented in this patent are actually the functions of the performance indicators of the structure with respect to the design variables. In order to clarify the influence of the design variables on the performances, the derivatives of the objective function with respect to the design variables, the derivatives of the constraint function with respect to the design variables need to be calculated. The derivatives are also called sensitivities. Since the design variables of the topology optimization are vectors, the calculation of the derivatives of the objective function and the constraint function with respect to the design variables is also called sensitivity vector.

[0068] The derivative of the objective function with respect to the design variables is:

[0069]

[0070] where D is the material matrix, p is the penalty value, generally taking the value of 3.

[0071] Since stress is a local physical quantity, for such a large-scale structure as the hub central part, the number of constraints caused by the stress constraint of each element is huge, which will inevitably lead to huge calculation amount. In order to avoid this problem, P-norm norm is used to condense the stress constraints of all elements into one global stress constraint, as follows:

[0072] The derivative of the constraint function with respect to the design variables is:

[0073]

[0074] Step 8, based on the sensitivity vector, the update iteration of the design variables is realized. The numerical value of the sensitivity vector of the objective function with respect to the design variables mainly represents the influence of the increase of each design variable by a small amount on the objective function; the numerical value of the sensitivity vector of the constraint function with respect to the design variables mainly represents the influence of the increase of each design variable by a small amount on the constraint function, according to the sensitivity of the objective function and the constraint function with respect to the design variables, the numerical value of the design variable ρ e is updated.

[0075] If the weighted value of the sensitivity of the objective function and the constraint function with respect to the design variables is negative, the numerical value of the design variable ρ e is reduced;

[0076] If the weighted value of the sensitivity of the objective function and the constraint function with respect to the design variables is positive, the numerical value of the design variable ρ e is increased; ρ e takes the value of 0-1.

[0077] The ninth step is to judge whether the updated design variable and the change of the design variable in the last step meet the convergence criteria (generally, when the difference between the updated design variable and the last design variable is less than or equal to 1e-6, it is considered to be converged). If the design variable does not converge, the updated design variable is brought into the finite element model in the third step to replace the finite element model in the last step, and the subsequent work is continued; if the design variable converges, the tenth step is carried out.

[0078] The tenth step is to obtain the design variable p e The output in the form of a slice is an STL file containing the node coordinate information of each unit of the final optimized structure. The file can describe the final result of the hub central piece topology optimization design. The result file is a slice file that can be used for 3D printing, and can also be used as a conceptual configuration for engineers to design structures.

[0079] The eleventh step is to import the hub central piece topology optimization result file (STL file) obtained in the last step into any three-dimensional geometric modeling software to obtain the outline of the main hub central piece of the helicopter, and the numerical model of the main hub central piece can be established according to the outline expressed by the optimization result. In this step, the main hub central piece is designed as a conceptual reference based on the topology optimization result configuration, and the structure is arranged according to the force transmission path obtained by topology optimization to obtain the final numerical model of the main hub central piece.

[0080] The twelfth step is to perform finite element modeling on the final numerical model of the main hub central piece obtained by the three-dimensional modeling software, and perform finite element analysis by applying the same boundary conditions as the optimization. According to the analysis result, it is further checked whether the constraint conditions of the main hub central piece topology optimization are met.

[0081] The thirteenth step is to perform local optimization adjustment on the main hub central piece according to the simulation result of the last step to realize the final detailed design of the main hub central piece of the helicopter.

[0082] The key points of the typical main hub central piece topology optimization design method considering fatigue performance of the application are as follows:

[0083] A modeling method of initial optimization design region for hub central piece topology optimization design is established; a method of dividing designable region and non-designable region in initial optimization design region is given; a method of fast finite element modeling and load case application for hub central piece is given; a relationship between structure fatigue performance and equivalent fatigue dynamic stress is established, and the equivalent fatigue dynamic stress is introduced into the topology optimization design of main hub central piece; a topology optimization mathematical equation is proposed, and a topology optimization mathematical equation with structure stiffness as optimization objective and structure equivalent fatigue dynamic stress and structure mass as constraints is defined; a topology optimization model output is a slice file, and geometry reconstruction is completed through a three-dimensional modeling software; a detailed design method of main hub central piece based on topology optimization result is given; a forward design method of main hub central piece considering structure fatigue performance is proposed, and the structure before and after design is shown in Figs. Figure 2 、 Figure 3 .

Claims

1. A topology optimization design method for a typical main propeller hub central component considering fatigue performance, characterized in that, include: Step 1: Obtain the structural interface that connects to the central component of the main propeller hub; Determine the design load and operating conditions of the central component of the main propeller hub; Step 2: Based on the structural interface of the main propeller hub central component connection, establish an initial optimization design region. Step 3: Divide the initial optimization design region into a designable region and an undesignable region, and perform mesh generation on the designable region and the undesignable region respectively to obtain the finite element model and the finite element mesh density matrix ρ; Step 4: Apply boundary conditions to the established finite element model according to the operating conditions of the helicopter rotor hub central component, and complete the loading of multiple load conditions according to the design load of the rotor hub central component. After the finite element calculation is completed, the structural displacement matrix U, structural stress matrix σ, structural stiffness matrix K, structural strain matrix B, and structural mass M are obtained. Step 5: Determine the equivalent substitution relationship between "equivalent fatigue dynamic stress of the propeller hub central component" and "fatigue life": ,in, The equivalent fatigue dynamic stress of the central component of the propeller hub. For fatigue life, and For material constants, For yield limit, The safe fatigue limit for symmetrical cyclic loading. The structural stress corresponding to the average load on the structure; Step Six: Based on the finite element mesh density matrix ρ, structural displacement matrix U, structural stress matrix σ, structural stiffness matrix K, structural strain matrix B, and structural mass M, establish the topology optimization formula for the main rotor hub central component considering fatigue performance: in, Here, 'e' represents the number of structural units, and 'e' represents the unit number. For the number of load conditions, the first Structural stiffness under various working conditions , Let e ​​be the relative density of element e. This represents the displacement column vector for the r-th working condition. Represents the stiffness matrix for the r-th working condition. This represents the load for the r-th operating condition. This represents the first principal stress in the r-th working condition. This represents the equivalent fatigue dynamic stress calculated for the r-th working condition. This is expressed as the mass of the structure. The maximum mass allowed by the structural design; Step 7: Calculate the derivatives of the objective function and the constraint functions with respect to the design variables in the topology optimization formula for the main propeller hub central component in Step 6; Step 8: Update the design variables based on the derivatives of the design variables and the derivatives of the constraint functions with respect to the design variables. The value; Step 9: Determine whether the difference between the updated design variables and the previous design variables meets the convergence criterion. If the design variables do not converge, then bring the updated design variables into the third step to update the finite element model; if the design variables converge, continue to step 10. Step 10: Output the design variable matrix as an STL file in slice form; Step 11: Import the STL file into the 3D geometric modeling software to obtain the outline of the helicopter main rotor hub central component, and establish the digital model of the main rotor hub central component according to the outline of the helicopter main rotor hub central component. Step 12: Perform finite element modeling on the digital model of the central component of the main propeller hub, apply the same boundary conditions as the optimization, and perform finite element analysis. Based on the analysis results, further verify whether the constraints of the topology optimization of the central component of the main propeller hub are met. Step Thirteen: Based on the finite element analysis results in Step Twelve, perform local optimization and adjustment on the central component of the main rotor hub to achieve the final detailed structural design of the helicopter rotor hub central component.

2. The topology optimization design method for a typical main propeller hub central component considering fatigue performance according to claim 1, characterized in that, In step two, the selection principles for the initial optimization design area are: 1) The initial optimization design area meets the interface requirements between the central component of the main propeller hub and other structures; 2) The initial optimization design area cannot interfere with other structures, and there can be neither static spatial interference nor motion interference.

3. The topology optimization design method for a typical main propeller hub central component considering fatigue performance as described in claim 1, characterized in that, In step three, the designable region is used to carry out the topology optimization design of the central component of the main propeller hub. The finite element mesh of this region is defined as the design variable of the topology optimization design. Each mesh is considered as a separate design variable. The number of mesh divisions in this region is the number of design variables defined in this topology optimization problem. The undesignable region is the part of the model that is not allowed to be changed. It is used for mechanical connection with other structural components to ensure the interface compatibility of the optimized structure with other connection structures.

4. The topology optimization design method for a typical main propeller hub central component considering fatigue performance as described in claim 1, characterized in that, In step seven, the derivative of the objective function with respect to the design variables is: Where D is the material matrix and p is the penalty value.

5. The topology optimization design method for a typical main propeller hub central component considering fatigue performance according to claim 4, characterized in that, Step seven also includes: The P-norm is used to consolidate the stress constraints of all mesh elements into a single global stress constraint, as follows: Differentiating the stress constraint after condensation, we obtain: Where, σ 11 σ is the first principal stress term in the structural stress matrix. d For σ 11 The interpolation function.

6. The topology optimization design method for a typical main propeller hub central component considering fatigue performance according to claim 1, characterized in that, Step eight, specifically: If the weighted sum of the derivatives of the objective function and constraint functions with respect to the design variables is negative, reduce the design variables. The value; If the weighted sum of the derivatives of the objective function and constraint functions with respect to the design variables is positive, then increase the design variables. The value, The value ranges from 0 to 1.

7. The topology optimization design method for a typical main propeller hub central component considering fatigue performance as described in claim 1, characterized in that, The convergence criterion in step nine is: convergence is considered to be achieved when the difference between the updated design variable and the design variable in the previous step is less than or equal to 1e-6.

8. The topology optimization design method for a typical main propeller hub central component considering fatigue performance according to claim 4, characterized in that, The value of p is 3.

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