Typical main propeller hub central part topological optimization design method considering fatigue performance

Abstract

The invention belongs to the field of helicopter propeller hub structures and structural optimization design, and particularly relates to a typical main propeller hub central part topological optimization design method considering fatigue performance. According to the method, the rigidity, fatigue and quality of the main propeller hub central part are considered in the structural optimization design, the equivalent fatigue dynamic stress capable of being equivalent to the fatigue performance of the propeller hub central part is proposed by considering the typical cumulative damage theory based on the helicopter fatigue design theory, and the equivalent fatigue dynamic stress serves as the constraint of the topological optimization design; and forward optimization design of the main propeller hub central part is realized through a result topological optimization method.

Description

Technical Field

[0001] The invention belongs to the field of helicopter hub structure and structural optimization design, and specifically relates to a topological optimization design method for a typical main hub central component taking fatigue performance into consideration. Background Art

[0002] As a key moving component of the helicopter rotor system, the hub centerpiece is subjected to complex load conditions during the helicopter's mission. In order to meet the upper-level requirements of helicopter survival and combat, extremely high requirements are placed on the performance indicators of the hub structure, such as life, reliability, and survivability. Traditional hub structure design mostly adopts the reverse design concept, and the final main hub centerpiece is obtained through multiple rounds of manual iterations of structural proofing design and strength verification. The traditional design process is slow to iterate and requires manual iterations one after another, and the structural stiffness and strength performance are not considered during the design. Summary of the invention

[0003] Purpose of the invention: To provide a topological optimization design method for a typical main hub central component taking fatigue performance into consideration.

[0004] Technical solution:

[0005] A typical main hub centerpiece topology optimization design method considering fatigue performance includes:

[0006] Step 1: Obtain the structural interface connected to the main hub center piece; determine the design load and operating conditions of the main hub center piece;

[0007] Step 2: Establish an initial optimization design area based on the structural interface of the main hub centerpiece connection.

[0008] Step 3: Divide the initial optimization design area into a designable area and an undesignable area and perform mesh division on the designable area and the undesignable area respectively to obtain a finite element model and a finite element mesh density matrix ρ;

[0009] Step 4: According to the working condition of the helicopter hub center component, the boundary conditions are applied to the established finite element model, and the loading of multiple load conditions is completed according to the design load of the hub center 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;

[0010] Step 5: Determine the equivalent replacement relationship between "equivalent fatigue dynamic stress of hub centerpiece" and "fatigue life": Among them, S a is the equivalent fatigue dynamic stress of the hub centerpiece, N is the fatigue life, A and α are material constants, S 0.2 is the yield limit, S -1 is the safe fatigue limit for symmetrical cyclic loading, Sm is the structural stress corresponding to the average load of the structure;

[0011] Step 6: According to the finite element mesh 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, the main hub central component topology optimization formula considering fatigue performance is established:

[0012] findρ e (e=1,……,Num)

[0013] min

[0014] ikB r (ρ e ) r =F r

[0015] σ d,r ≤S a,r

[0016]

[0017] Where Num is the number of structural units, e is the unit number, nu is the number of load conditions, and the structural stiffness (compliance) C under the rth condition is r , ρ e is the relative density of unit e, U r Represents the displacement column vector of the rth working condition, K r Represents the stiffness matrix F of the rth working condition r represents the load of the rth working condition, σ d,r represents the first principal stress of the rth working condition, S a,r represents the equivalent fatigue dynamic stress calculated for the rth working condition, M max Expressed as the mass of the structure, The maximum mass allowed for the structural design;

[0018] Step 7: Calculate the derivatives of the objective function with respect to the design variables and the derivatives of the constraint function with respect to the design variables in the main hub center component topology optimization column in step 6;

[0019] Step 8: Update the design variable ρ according to the derivative of the design variable and the derivative of the constraint function with respect to the design variable e The value of

[0020] Step 9: Determine whether the difference between the updated design variables and the previous design variables meets the convergence criteria. If the design variables do not converge, bring the updated design variables into the third step to update the finite element model; if the design variables converge, continue to step 10;

[0021] Step 10: Output the design variable matrix as an STL file in the form of slices;

[0022] Step 11: Import the STL file into the 3D geometric modeling software to obtain the outline of the helicopter main rotor hub center piece, and establish the main rotor hub center piece digital model according to the outline of the helicopter main rotor hub center piece;

[0023] Step 12: Perform finite element modeling on the digital model of the main hub central component, 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 component topology optimization are met based on the analysis results;

[0024] Step 13: According to the finite element analysis results in step 12, local optimization and adjustment are performed on the main rotor hub center piece to achieve the final structural detailed design of the helicopter rotor hub center piece.

[0025] Furthermore, in step 2, the selection principles of the initial optimization design area are: 1) the initial optimization design area meets the interface requirements between 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.

[0026] Furthermore, in step three, the designable area is used to carry out the topology optimization design of the main hub central part. The finite element mesh of this area is defined as the design variable of the topology optimization design. Each mesh is considered to be a separate design variable. The number of mesh divisions in this area is the number of design variables defined in this topology optimization problem. The undesignable area is the part of the model that is not allowed to change. It is used for mechanical connection with other structural parts to ensure the interface matching between the optimized structure and other connecting structures.

[0027] Furthermore, in step 7, 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] Furthermore, step seven also includes:

[0031] The P-norm norm is used to condense the stress constraints of all grid cells into a global stress constraint as follows:

[0032]

[0033] And the stress constraint after condensation is derived to obtain:

[0034]

[0035] Among them, σ 11is the first principal stress term in the structural stress matrix, σ d is 11 The interpolation function of .

[0036] Furthermore, step eight is specifically as follows:

[0037] If the weighted values ​​of the derivatives of the objective function and constraint function with respect to the design variable are negative, reduce the design variable ρ e The value of

[0038] If the weights of the derivatives of the objective function and constraint function with respect to the design variable are positive, increase the design variable ρ e The value of ρ e The value is 0-1.

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

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

[0041] Beneficial effects:

[0042] Aiming at the design requirements of the metal structural parts of the helicopter rotor system hub, considering the characteristics of multiple load conditions and large-scale models, a study on the topological optimization design method of the typical hub center part considering fatigue performance was carried out. A typical titanium alloy center part optimization design model was established, with the flexibility of the center part structure as the optimization target, and the structural mass and the equivalent fatigue dynamic stress level of the structure under multiple load conditions as constraints. The mathematical formula for topological optimization was constructed, and the sensitivity analysis of the stress constraint on the design variables was studied in detail to achieve precise control of the stress level in the structure. By controlling the stress level of the optimized design structure, the fatigue life of the structure can be controlled, laying a key technical foundation for the research and development of the next generation of high-reliability and high-survivability rotor structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Hub centerpiece optimization design flow chart;

[0044] Figure 2 Initial design structure of hub centerpiece;

[0045] Figure 3 The final optimized design structure of the hub centerpiece DETAILED DESCRIPTION

[0046] This patent adopts the idea of ​​forward design and applies the topology optimization design technology to the design of the main hub centerpiece. Aiming at the design requirements of helicopter rotor hub centerpieces with multiple load conditions and complex load-bearing modes, combined with the helicopter fatigue strength design theory, a study on the topology optimization design of the safe life of the hub centerpiece considering fatigue performance is carried out. The method proposed in the patent starts with the SN curve and cumulative damage theory of the helicopter hub moving parts, combined with the structural safety fatigue limit corrected by the equal life curve, to establish a mathematical formula suitable for the topology optimization design of the safe life of the main hub centerpiece, carry out the sensitivity analysis of the design variables, and establish a typical main hub centerpiece optimization design model. By controlling the safe life equivalent stress of the main hub centerpiece, the purpose of controlling the fatigue life of the structure is achieved, providing new ideas for the design of long-life and high-reliability main hub centerpieces, and laying a key technical foundation for the research and development of the next generation of high-reliability and high-survivability rotor structures.

[0047] This patent proposes a typical main hub center component topology optimization design method considering fatigue performance. The patent proposes a numerical calculation method for the optimization design of helicopter main hub center components. The method is proposed mainly to take into account the stiffness, fatigue, mass and other performance indicators of the main hub center component in the structural optimization design. Based on the helicopter fatigue design theory, the typical cumulative damage theory is considered to propose an equivalent fatigue dynamic stress that can be equivalent to the fatigue performance of the hub center component, and the equivalent fatigue dynamic stress is used as a constraint for the topology optimization design. The forward optimization design of the main hub center component is achieved through the result topology optimization method, such as Figure 1 , the specific implementation path of this patent is as follows:

[0048] The first step is that the design of the main hub centerpiece needs to meet the interface with other structures, ensure that the optimized design structure can match the interface with other structures, and the optimized design structure can be installed with other structures. Obtaining the structural interface connected to the main hub centerpiece and clarifying the design load and operating conditions of the main hub centerpiece are necessary for the design of the main hub centerpiece.

[0049] The second step is to establish an initial optimization design area based on the interface of the main hub central part. The initial optimization design area is a larger space, and the main hub central part will be designed in this space later. The initial optimization design area can completely wrap the central part that will be optimized and designed next, which means that the structural optimization design is only allowed to be carried out in the initial optimization design area we defined, so the selection of the initial optimization design area is very critical. The selection of the initial optimization design area needs to comply with 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] In the third step, the initial optimization design area is divided into a designable area and an undesignable area, and the designable area and the undesignable area are meshed separately to obtain a finite element model and a finite element mesh density matrix. The designable area is used to carry out the topology optimization design of the main hub central part. The finite element mesh of this area is defined as the design variable of the topology optimization design. Each mesh is considered to be a separate design variable. The number of mesh divisions in this area is the number of design variables defined in this topology optimization problem. The undesignable area is the part of the model that is not allowed to change. It is used for mechanical connection with other structural parts to ensure the interface matching between the optimized structure and other connecting structures.

[0051] The fourth step is to apply correct boundary conditions to the established finite element model according to the actual working conditions of the helicopter hub centerpiece, and complete the loading of multiple load conditions according to the design load of the hub centerpiece, so that the established finite element model can accurately describe the working conditions of the helicopter hub centerpiece, laying the foundation for subsequent structural topology optimization. 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 can be used for the subsequent topology optimization design of the main hub centerpiece.

[0052] The fifth step is to propose an equivalent fatigue dynamic stress index of the hub center part corresponding to the fatigue life index of the main hub center part. The fatigue constraint condition is transformed from life constraint to stress constraint, and the equivalent replacement relationship between "equivalent fatigue dynamic stress of the hub center part" and "fatigue life" is proposed.

[0053] According to the characteristics of the helicopter hub centerpiece in flight use, considering the influence of average load on alternating load damage, it is proposed to use the structural average load to alternating load, and the equivalent fatigue dynamic stress formula of the hub centerpiece is given as follows:

[0054]

[0055] Among them, S a is the equivalent fatigue dynamic stress of the hub centerpiece, N is the fatigue life, A and α are material constants, S 0.2 is the yield limit, S -1 is the safe fatigue limit for symmetrical cyclic loading, S m is the structural stress corresponding to the average load of the structure.

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

[0057] Step 6: Based on the data obtained in step 4, establish the main hub centerpiece topology optimization formula considering fatigue performance. Clarify the design variables, objective function and constraint function of the topology optimization formula.

[0058] 1) Design variables: The structure is meshed by finite elements, and each unit is given a unit relative density ρ e (0≤ρ e ≤1), that is, topology optimization design variable, ρ e =0 means that no material is arranged at this unit, ρ e =1 means that the unit arranges materials;

[0059] 2) The objective function of topology optimization is defined as minimizing the compliance of the hub structure. The compliance of the structure is a global variable, which is essentially the concept of the internal deformation energy of the structure after being loaded.

[0060] 3) Define the constraints of topology optimization as the first principal stress of the structure is less than the equivalent fatigue dynamic stress proposed in the fifth step above, and the structural mass is less than the upper limit of the mass, and establish the topology optimization design problem of the hub centerpiece.

[0061] findρ e (e=1,……,Num)

[0062] min

[0063] ikB r (ρ e ) r =F r

[0064] σ d,r ≤S a,r

[0065]

[0066] Where Num is the number of structural units, e is the unit number, nu is the number of load conditions, and the structural stiffness (compliance) C under the rth condition is r , ρ e is the relative density of unit e, U r represents the displacement column vector of the rth working condition, K r The stiffness matrix F represents the rth working condition. r represents the load of the rth working condition, σ d,r represents the first principal stress of the rth working condition, S a,r represents the equivalent fatigue dynamic stress calculated for the rth working condition, M max Expressed as the mass of the structure, The maximum mass allowed by the structural design.

[0067] Step 7. The objective function and constraint function proposed in this patent are actually functions of various performance indicators of the structure with respect to the design variables. In order to clarify the impact of the design variables on various performances, it is necessary to calculate the derivative of the objective function with respect to the design variables and the derivative of the constraint function with respect to the design variables. The derivative is also called sensitivity. Since the design variables of topology optimization are vectors, the derivatives of the objective function and constraint function with respect to the design variables are also called sensitivity vectors.

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

[0069]

[0070] Among them, D is the material matrix, p is the penalty value, which is generally taken as 3.

[0071] Since stress is a local physical quantity, for large-scale structures such as the hub centerpiece, the number of constraints caused by each unit's individual stress constraint is huge, which will inevitably lead to a huge amount of calculation. In order to avoid this problem, the P-norm norm is used to condense the stress constraints of all units into a global stress constraint, as follows:

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

[0073]

[0074] Step 8: Update and iterate the design variables based on the sensitivity vector. The value of the sensitivity vector of the objective function with respect to the design variables mainly indicates the impact of increasing a small amount of each design variable on the objective function; the value of the sensitivity vector of the constraint function with respect to the design variables mainly indicates the impact of increasing a small amount of each design variable on the constraint function. The design variables ρ are updated according to the sensitivity of the objective function and the constraint function with respect to the design variables. e The numerical value of .

[0075] If the weighted values ​​of the objective function and constraint function with respect to the design variable are negative, reduce the design variable ρ e The value of

[0076] If the weighted values ​​of the objective function and constraint function with respect to the design variable are positive, increasing the design variable ρ e The value of ρ e The value is 0-1.

[0077] The ninth step is to determine whether the changes between the updated design variables and the previous design variables meet the convergence criteria (generally, when the difference between the updated design variables and the previous version of the design variables is less than or equal to 1e-6, it is considered converged). If the design variables do not converge, bring the updated design variables into the third step to replace the finite element model in the previous step, and continue with the subsequent work; if the design variables converge, proceed to the tenth step.

[0078] Step 10: The design variable ρ obtained by optimization in step 9 is e The STL file is output in slice form, which contains the coordinate information of each unit node of the final optimized structure. This file can describe the final result of the topological optimization design of the hub centerpiece. This result file is a slice file that can be used for 3D printing, and can also be used as a conceptual configuration for engineers' structural design.

[0079] In the eleventh step, for the helicopter main hub center part, the hub center part topology optimization result file (STL file) obtained in the previous step is imported into any 3D geometric modeling software to obtain the helicopter main hub center part contour, and the main hub center part digital model can be established according to the contour expressed by the optimization result. Among them, the main hub center part designed in this step uses the topology optimization result configuration as a conceptual reference, and the structure is arranged according to the force transmission path obtained by topology optimization to obtain the final main hub center part digital model.

[0080] In the twelfth step, the final digital model of the main hub central part obtained by the 3D modeling software is subjected to finite element modeling, and the same boundary conditions as the optimization are applied for finite element analysis. Based on the analysis results, it is further verified whether the constraint conditions of the main hub central part topology optimization are met.

[0081] In the thirteenth step, local optimization and adjustment are performed on the center piece of the main rotor hub according to the simulation results of the previous step to realize the final structural detailed design of the center piece of the helicopter rotor hub.

[0082] Key points of the topological optimization design method of a typical main hub central component considering fatigue performance of the present invention:

[0083] A modeling method for the initial optimization design area of ​​the hub center part topology optimization design was established; a method for dividing the designable area and the non-designable area in the initial optimization design area was given; a method for rapid finite element modeling of the hub center part and application of load conditions was given; the relationship between the fatigue performance of the structure and the equivalent fatigue dynamic stress of the structure was established, and the equivalent fatigue dynamic stress was introduced into the topology optimization design of the main hub center part; a topology optimization mathematical formula was proposed, which defined the topology optimization mathematical formula with structural stiffness as the optimization target and structural equivalent fatigue dynamic stress and structural mass as constraints; the topology optimization model was output as a slice file, and the geometric reconstruction was completed through 3D modeling software; a detailed design method for the main hub center part based on the topology optimization results was given; a forward design method for the main hub center part considering the structural fatigue performance was proposed, and the structural design before and after was as follows. Figure 2 , Figure 3 shown.

Claims

1. A typical main hub centerpiece topology optimization design method considering fatigue performance, characterized in that: include: Step 1: Obtain the structural interface connected to the main hub center piece; Determine the design load and operating conditions of the main hub centerpiece; Step 2: Establish an initial optimization design area based on the structural interface of the main hub centerpiece connection. Step 3: Divide the initial optimization design area into a designable area and an undesignable area and perform mesh division on the designable area and the undesignable area respectively to obtain a finite element model and a finite element mesh density matrix ρ; Step 4: According to the working condition of the helicopter hub centerpiece, the boundary conditions are applied to the established finite element model, and the loading of multiple load conditions is completed according to the design load of the hub centerpiece; 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 replacement relationship between "equivalent fatigue dynamic stress of hub centerpiece" and "fatigue life": , Among them, S a is the equivalent fatigue dynamic stress of the hub centerpiece, N is the fatigue life, A and α are material constants, S 0.2 is the yield limit, S -1 is the safe fatigue limit for symmetrical cyclic loading, S m is the structural stress corresponding to the average load of the structure; Step 6: According to the finite element mesh 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, the main hub central component topology optimization formula considering fatigue performance is established: find e (e=1,……,Num) s.t.K r (ρ e )U r =F r s d,r ≤S a,r M max ≤M max Among them, N um is the number of structural units, e is the unit number, nu is the number of load conditions, and the structural stiffness (compliance) C under the rth condition is r , ρ e is the relative density of unit e, U r represents the displacement column vector of the rth working condition, K r Represents the stiffness matrix F of the rth working condition r represents the load of the rth working condition, σ d,r represents the first principal stress of the rth working condition, S a,r represents the equivalent fatigue dynamic stress calculated for the rth working condition, M max Expressed as the mass of the structure, The maximum mass allowed for the structural design; Step 7: Calculate the derivatives of the objective function with respect to the design variables and the derivatives of the constraint function with respect to the design variables in the main hub center component topology optimization column in step 6; Step 8: Update the design variable ρ according to the derivative of the design variable and the derivative of the constraint function with respect to the design variable e The value of Step 9: Determine whether the difference between the updated design variables and the previous design variables meets the convergence criteria. If the design variables do not converge, 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 the form of slices; Step 11: Import the STL file into the 3D geometric modeling software to obtain the outline of the helicopter main rotor hub center piece, and establish the main rotor hub center piece digital model according to the outline of the helicopter main rotor hub center piece; Step 12: Perform finite element modeling on the digital model of the main hub central component, 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 component topology optimization are met based on the analysis results; Step 13: According to the finite element analysis results in step 12, local optimization and adjustment are performed on the main rotor hub center piece to achieve the final structural detailed design of the helicopter rotor hub center piece.

2. The typical main hub center component topology optimization design method considering fatigue performance according to claim 1 is characterized in that: In step 2, the selection principles of the initial optimization design area are: 1) the initial optimization design area meets the interface requirements between 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.

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

4. The typical main hub center component topology optimization design method considering fatigue performance according to claim 1 is characterized in that: In step 7, the derivative of the objective function with respect to the design variable is: Where D is the material matrix and p is the penalty value.

5. The typical main hub center component topology optimization design method considering fatigue performance according to claim 1 is characterized in that: Step seven also includes: The P-norm norm is used to condense the stress constraints of all grid cells into a global stress constraint as follows: And the stress constraint after condensation is derived to obtain: Among them, σ 11 is the first principal stress term in the structural stress matrix, σ d is 11 The interpolation function of .

6. The typical main hub center component topology optimization design method considering fatigue performance according to claim 1 is characterized in that: Step 8, specifically: If the weighted values ​​of the derivatives of the objective function and constraint function with respect to the design variable are negative, reduce the design variable ρ e The value of If the weights of the derivatives of the objective function and constraint function with respect to the design variable are positive, increase the design variable ρ e The value of ρ e The value is 0-1.

7. The typical main hub center component topology optimization design method considering fatigue performance according to claim 1 is characterized in that: The convergence criterion in step nine is: convergence is considered when the difference between the updated design variables and the design variables in the previous step is less than or equal to 1e-6.

8. The typical main hub center component topology optimization design method considering fatigue performance according to claim 4 is characterized in that: The value of p is 3.

Images