A system fatigue reliability prediction method for large aviation planetary mechanism

Abstract

This invention discloses a system fatigue reliability prediction method for large aerospace planetary mechanisms. The steps are as follows: The fatigue load history of gear teeth under the coupled action of the system's global elastic behavior is calculated using the hierarchical finite element method to obtain load information; the probabilistic fatigue strength curve of the gear teeth is fitted based on gear low-cycle fatigue testing and the minimum order statistic conversion method; the load information and the probabilistic fatigue strength of the gear teeth are input into a reliability prediction model to obtain a system fatigue reliability prediction model that can consider the influence of system structural elements, establishing a mapping path from key structural elements of large aerospace planetary mechanisms to system reliability indicators. This invention leverages the stiffness potential of core structural elements to balance the contradiction between reliability and lightweight requirements in large aerospace planetary equipment; detailed tooth root stress calculations are not required in the system-level model; and a gear tooth probabilistic fatigue strength conversion method is proposed, thereby saving significant simulation and testing costs.

Description

Technical Field

[0001] This invention relates to a system fatigue prediction technology for large aerospace planetary mechanisms, specifically a system fatigue reliability prediction method for large aerospace planetary mechanisms. Background Technology

[0002] Large transport helicopters are strategically important military and civilian equipment related to core national interests, and are a significant indicator of a nation's aviation technology level and overall strength. High-power transmission system technology is a key technological area for improving the performance of heavy helicopters, reducing their noise and vibration levels, and controlling their life-cycle costs. Technologically advanced countries in this field have included the reliability and economic affordability of high-power transmission systems as key technical indicators in their advanced heavy helicopter development programs, and have proposed specific low-maintenance design requirements for the transmission systems. In the most numerous heavy helicopters currently in service, the large aerospace planetary transmission mechanism, as the foundation and core of its transmission system, largely determines the technological level of the transmission system and is one of the bottlenecks restricting the development of heavy helicopter transmission system technology.

[0003] As a deceleration terminal directly connected to the main rotor, the large aerospace planetary mechanism is the power transmission link in the heavy helicopter transmission system with the worst load environment and the highest strength requirements. The transmission system is one of the three key dynamic systems of a helicopter (engine system, transmission system, and rotor system). Whether considering weight or space, the transmission system cannot be redundantly designed. Therefore, the reliability of its core components directly determines the helicopter's service safety and life cycle cost.

[0004] In the area of ​​reliability analysis and modeling of gear transmission systems, numerous studies have meticulously analyzed the unique characteristics of gear transmissions in terms of system configuration, load transmission, and failure correlation from the perspective of reliability analysis and modeling. However, current research has significantly simplified the structural form of gear systems during reliability analysis, making it difficult to reflect the way and extent to which the internal structural features of the system affect the system's reliability indicators.

[0005] In existing technologies, the calculation of tooth root bending stress utilizes general-purpose finite element tools. These tools offer flexibility in processing, are not limited by input conditions such as geometric features and material properties, and provide relatively comprehensive analysis results (depending on the software's post-processing capabilities). However, the general-purpose finite element method incurs high computational costs in model setup and solution calculations, typically only applicable to isolated solutions of gear parts or a few teeth, and struggles to perform global calculations at the system level. Furthermore, predicting tooth bending conditions is difficult, or it's challenging to add appropriate boundary conditions to the model, especially for thin-walled rim gears or gears directly mounted on bearings (such as planetary gears with rotation and revolution characteristics), where the situation becomes even more complex. Summary of the Invention

[0006] In view of the fact that existing technologies greatly simplify the structure of gear systems in the reliability analysis process, making it difficult to reflect the influence of the internal structural features of the system on the system reliability index, this invention provides a system fatigue reliability prediction method for large aerospace planetary mechanisms, revealing the coupling influence mechanism of its dimensional changes on the stiffness conditions and fatigue reliability level of planetary gear trains.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] This invention provides a method for predicting the fatigue reliability of systems in large aerospace planetary mechanisms, comprising the following steps:

[0009] 1) Tooth root stress calculation: The fatigue load history of the gear teeth under the coupling effect of the global elastic behavior of the system is calculated using the hierarchical finite element method to obtain load information and provide load input variables for the reliability prediction model;

[0010] 2) Gear probabilistic fatigue strength fitting: Based on gear low-cycle fatigue test and minimum order statistic conversion method, the gear tooth probabilistic fatigue strength curve is fitted, providing an economical and effective strength input variable for the system reliability prediction model;

[0011] 3) Establish a fatigue reliability calculation model for parts: Establish a mapping path from key structural elements of large aerospace planetary mechanisms to system reliability indicators, and propose a reliability-driven multi-objective optimization design method for the structural dimensions of planetary mechanisms.

[0012] 4) Input the load information and the probabilistic fatigue strength of the gear teeth into the reliability prediction model to obtain a system fatigue reliability prediction model that can take into account the influence of system structural elements.

[0013] Step 1) The calculation of tooth root stress includes:

[0014] 101) System-level Elasticity Simulation Modeling: Using semi-analytical finite element technology, a system-level elasticity simulation model of a large aerospace planetary mechanism is constructed to evaluate the elastic deformation of large thin-walled components and the meshing misalignment between gear teeth in the system, providing detailed load and displacement boundary conditions for the secondary sub-model of tooth root stress analysis.

[0015] 102) Constructing a secondary sub-model for tooth root stress analysis: A high-fidelity secondary sub-model for tooth root stress analysis is established based on the general finite element method. In the system-level model, the time-varying load lines on the tooth surface are obtained through quasi-static static analysis and applied to the tooth surface of the secondary sub-model for tooth root stress analysis as load boundary conditions. At the same time, the elastic deformation results of the system are extracted and applied to the tooth root stress analysis sub-model as displacement boundary conditions.

[0016] Step 101) Evaluate the elastic deformation of the large thin-walled component and the meshing misalignment between the gear teeth in the system as follows:

[0017] The tolerance search technology of the RotationMaster software platform was used to screen out the component connection node group, and the control parameters such as search criteria and selection method were adjusted in combination to establish the node rigid connection of the finite element component.

[0018] The finite element model in the system is condensed to extract the corresponding mass and stiffness matrices. Meanwhile, the deformation smoothness is used as an evaluation index, and the performance of each stiffness matrix is ​​tested by using the load transfer behavior between the condensed nodes.

[0019] Load boundary conditions are applied to the system model, and a global calculation of the quasi-static elastic mechanical behavior is performed on it to obtain the nodal displacement response and time-varying load line results of each elastic component.

[0020] In step 102), the secondary sub-model for tooth root stress analysis uses first-order hexahedral elements and an adaptive mesh density recommended by the RM software platform to accurately capture the steep stress gradient at the tooth root, so that the calculation of the secondary sub-model for tooth root stress analysis converges within a valid predetermined number of iterations.

[0021] Step 2) Gear probabilistic fatigue strength fitting includes the following methods:

[0022] 201) Gear bending fatigue test: Gear bending fatigue accelerated life test was conducted using a power flow closed gear rotation tester to provide strength information for fatigue reliability prediction model of large aerospace planetary systems;

[0023] 202) Gear tooth probabilistic strength fitting: The peak stress at the tooth root is used as the evaluation index of the stress level. The tooth root bending fatigue performance test is carried out under multiple stress levels using the group method. The direct data obtained is the gear life. The direct strength input variable of the reliability prediction model is obtained by using the probabilistic statistical transformation method to fit the gear tooth PSN curve based on the gear life data.

[0024] Step 3) Component fatigue reliability analysis includes:

[0025] 301) Establish a conditional probability expectation value algorithm for calculating the fatigue reliability of parts: Extend the traditional load-strength interference analysis method and establish a conditional probability expectation value algorithm for calculating the fatigue reliability of parts based on the probability distribution of stress level and the life distribution under a specified stress level.

[0026] 302) Fatigue reliability assessment model for series system considering failure correlation: Under deterministic load, the failures of each component in the system are independent of each other, and the conditional reliability of the series system is equal to the product of the conditional reliability of each component; considering the uncertainty effect of the load at the system level, a fatigue reliability assessment model for the series system is established. It is assumed that the load of the model follows a normal distribution, and the load of each component is normalized by transforming the mathematical relationship between the normal distribution and the standard normal distribution, thus considering the influence of the load uncertainty effect at the system level.

[0027] 303) Reliability model structure optimization considering the temporal characteristics of planetary systems: The kinematic equations of planetary transmission are derived based on the periodic operation law of planetary gear trains. At the same time, the number of single-tooth meshing times of various gears in the system within the same time interval is obtained to match the temporal characteristic attributes for the fatigue reliability assessment model of the system.

[0028] In step 302), for the static strength failure problem of the part under a single load, the reliability is regarded as a function of stress, and a conditional reliability model under a specified stress is established; for the fatigue reliability problem, a mathematical expression for calculating the fatigue reliability of the part based on the life distribution is constructed, and the fatigue reliability index of the part under random constant amplitude cyclic load is directly calculated.

[0029] The present invention has the following beneficial effects and advantages:

[0030] 1. This invention aims to ensure and improve the bending fatigue reliability of planetary gear trains. It utilizes the hierarchical finite element method to calculate the fatigue load history of gear teeth under the coupled global elastic behavior of the system. Based on low-cycle fatigue testing and the minimum order statistic transformation method, it fits the probabilistic fatigue strength of the gear teeth, providing economical and effective load and strength input variables for the system reliability prediction model. With significant simulation and testing cost advantages, it effectively constructs a mapping path from key structural elements of large aerospace planetary mechanisms to fatigue reliability indicators of planetary gear trains. Furthermore, it uses the rim thickness of the internal gear ring and the thickness of the planetary carrier base plate as key structural elements for system reliability and lightweight design, revealing the coupling influence mechanism of their dimensional changes on the stiffness conditions and fatigue reliability level of the planetary gear train. This forms a new method for reliability-driven structural optimization design of large aerospace planetary mechanisms, maximizing the stiffness potential of core structural elements to balance the contradiction between reliability and lightweight requirements in large aerospace planetary equipment.

[0031] 2. To address the trade-off between computational accuracy and cost in the general finite element method (FEM) for mechanical simulation analysis of large and complex gear systems, this invention proposes an advanced hierarchical finite element method (HEM) for tooth root stress analysis of large aerospace planetary mechanisms. This method directly bases its tooth root stress calculations on a detailed secondary sub-model of tooth root stress analysis. In the system-level model, time-varying load lines on the tooth surface are obtained through quasi-static analysis and then applied to the tooth surface of the secondary sub-model as load boundary conditions. Simultaneously, the system's elastic deformation results are extracted and applied to the secondary sub-model as displacement boundary conditions. Thus, the tooth root stress calculation results in the secondary sub-model naturally incorporate the effects of elastic deformation and meshing misalignment of the entire system. Furthermore, detailed tooth root stress calculations are not required in the system-level model, significantly reducing the computational cost of system-level analysis.

[0032] 3. The method of this invention has already considered the physical effects of rotation and offset of transmission components in the quasi-static analysis results of the system-level model. Therefore, the boundary conditions applied to the secondary sub-model of tooth root stress analysis are also much simpler. When facing the tooth root stress analysis task of large aerospace planetary systems, considering only the convenience of modeling and boundary condition setting, the analysis efficiency of the hierarchical finite element method will be much higher than that of the general finite element method.

[0033] 4. The method of the present invention aims to make the stress state at the root of the tooth of the sample the same as that of the service gear, make the tooth geometry parameters of the sample as consistent as possible with those of the service gear, and make the overall parameters of the sample equal to or similar to those of the service gear in terms of material properties, machining and heat treatment. Effectively ensuring these approximations helps to improve the prediction accuracy of the fatigue reliability index of the planetary system. Attached Figure Description

[0034] Figure 1A This is a schematic diagram of the overall structure of the planetary mechanism system in this invention;

[0035] Figure 1B This is an equivalent diagram of the input and output of the planetary mechanism system in this invention;

[0036] Figure 2 This diagram illustrates the degree of freedom settings of the planetary mechanism system in this invention.

[0037] Figure 3 This is a diagram illustrating the tooth root stress analysis process in this invention;

[0038] Figure 4 Images of gear samples involved in this invention;

[0039] Figure 5 The image shows a crack at the root of a gear, as described in this invention.

[0040] Figure 6 The image shows the morphology of the gear root crack as described in this invention.

[0041] Figure 7 This is a graph showing the probability life conversion curve of gear teeth in this invention;

[0042] Figure 8 This is a PSN fitting curve diagram of the gear teeth in this invention;

[0043] Figure 9 This is a diagram illustrating the edge thickness of the internal gear ring in this invention.

[0044] Figure 10 This is a diagram illustrating the thickness of the base plate of the planetary carrier in this invention;

[0045] Figure 11A This is a graph showing the elastic deformation of the ring gear involved in the method of the present invention.

[0046] Figure 11B This is a graph showing the increase in system reliability related to the method of this invention.

[0047] Among them, 1 is the internal gear, 2 is the planetary gear, 3 is the planet carrier, and 4 is the sun gear. Detailed Implementation

[0048] The present invention will now be further described with reference to the accompanying drawings.

[0049] This invention provides a method for predicting the fatigue reliability of systems in large aerospace planetary mechanisms, comprising the following steps:

[0050] 1) Tooth root stress calculation: The fatigue load history of the gear teeth under the coupling effect of the global elastic behavior of the system is calculated using the hierarchical finite element method to obtain load information and provide load input variables for the reliability prediction model;

[0051] 2) Gear probabilistic fatigue strength fitting: Based on gear low-cycle fatigue test and minimum order statistic conversion method, the gear tooth probabilistic fatigue strength curve is fitted, providing an economical and effective strength input variable for the system reliability prediction model;

[0052] 3) Establish a fatigue reliability calculation model for parts: Establish a mapping path from key structural elements of large aerospace planetary mechanisms to system reliability indicators, and propose a reliability-driven multi-objective optimization design method for planetary mechanism structural dimensions; based on this, analyze the influence of the thickness of the internal gear ring rim and the thickness of the planetary carrier base plate on the fatigue reliability of the planetary gear train.

[0053] 4) Input the load information and the probabilistic fatigue strength of the gear teeth into the reliability prediction model to obtain a system fatigue reliability prediction model that can take into account the influence of system structural elements.

[0054] The method of this invention constructs a mapping path from key structural elements of large aerospace planetary mechanisms to system reliability indicators, and incorporates the stiffness requirements of key structural features into the reliability indicators of planetary gear trains, forming a multi-objective optimization design of planetary mechanism structural dimensions driven by reliability.

[0055] This invention proposes an advanced hierarchical finite element method for tooth root stress analysis of large aerospace planetary mechanisms. It directly calculates tooth root stress based on a detailed 3D finite element sub-model of the gear teeth. In the system-level model, time-varying load lines on the tooth surface are obtained through quasi-static analysis and then applied to the tooth surface of the secondary sub-model for tooth root stress analysis as load boundary conditions. Simultaneously, the elastic deformation results of the system are extracted and applied to the secondary sub-model for tooth root stress analysis as displacement boundary conditions. Thus, the tooth root stress calculation results in the secondary sub-model naturally include the influence of elastic deformation and meshing misalignment of the entire system. Detailed tooth root stress calculations are not required in the system-level model, significantly reducing the computational cost of system-level analysis. The quasi-static analysis results of the system-level model already consider the physical effects of rotation and offset of transmission components, therefore the boundary conditions applied to the secondary sub-model for tooth root stress analysis are relatively simple. For tooth root stress analysis tasks of large aerospace planetary systems, considering only the convenience of modeling and boundary condition setting, the analysis efficiency of the hierarchical finite element method will be far superior to that of the general finite element method. Furthermore, unlike commercial finite element software that uses nonlinear equation solvers, this hierarchical finite element method employs an improved simplex solver to ensure convergence within a set number of effective iterations. Although the total number of degrees of freedom in a two-level finite element model can be very large, this hierarchical analysis approach still keeps the CPU time and memory required for computation within the capabilities of ordinary computers. This paper will use the structural details and material properties of a certain type of large aerospace planetary mechanism as a reference to construct its high-fidelity mechanical simulation model using the hierarchical finite element method. Based on this, the critical stress history at the tooth root under quasi-static elastic mechanical behavior is calculated, providing effective load input variables for the system fatigue reliability assessment model.

[0056] Step 1) The calculation of tooth root stress includes:

[0057] 101) System-level Elasticity Simulation Modeling: Using semi-analytical finite element technology, a system-level elasticity simulation model of a large aerospace planetary mechanism is constructed to evaluate the elastic deformation of large thin-walled components and the meshing misalignment between gear teeth in the system, and to provide detailed load and displacement boundary conditions for the secondary sub-model of tooth root stress analysis.

[0058] 102) Constructing a secondary sub-model for tooth root stress analysis: A high-fidelity secondary sub-model for tooth root stress analysis is established based on the general finite element method. In the system-level model, the time-varying load lines on the tooth surface are obtained through quasi-static analysis and applied to the tooth surface of the secondary sub-model for tooth root stress analysis as load boundary conditions. At the same time, the elastic deformation results of the system are extracted and applied to the tooth root stress analysis sub-model as displacement boundary conditions.

[0059] Step 101) System-level elastic mechanical behavior simulation modeling

[0060] First, a system-level elasticity simulation model of a large aerospace planetary mechanism is constructed using semi-analytical finite element technology. This model accurately assesses the elastic deformation of large thin-walled components and the meshing misalignment between gear teeth, providing detailed load and displacement boundary conditions for the secondary sub-model of tooth root stress analysis. The overall configuration of the planetary mechanism system model is as follows: Figures 1A-1B As shown, all planetary gears are evenly distributed along the circumference on the planet carrier, and the specific structural parameters of the planetary gear system are shown in Table 1. The power flow path inside the mechanism starts from the input shaft, passes through the sun gear and planetary gears, and then to the planet carrier. After reduction, the planet carrier finally transmits the motion and power to the main rotor shaft. The input shaft is mechanically described in the form of a Timoshenko beam, realistically reproducing its mass and stiffness distribution, and considering necessary degrees of freedom such as torsion, axial, and bending. Finite element modeling is used for large thin-walled components such as the planet carrier and internal gear ring, and their degrees of freedom are expressed using a fully flexible design. In addition, the elastic deformation of the reducer housing is not considered, and the inner and outer rings of each bearing are assumed to be rigid bodies, that is, they will not deform under load, but can only move or tilt as a whole. The input shaft is supported by two tapered roller bearings (TRB) in an O-type layout, and their outer rings are rigidly connected to the housing. X-type double-row tapered roller bearings (DRTRB) are installed inside each planetary gear, and the inner rings of the bearings are rigidly connected to the planet carrier. Radial ball bearings (RBBs) fix the planetary carrier and allow it a small amount of floating, which to some extent offsets the unequal load distribution between the planetary gears. Their outer rings are rigidly connected to the housing. The structural parameters of various bearing types are shown in Table 2. In the system model, the meshing stiffness of the gears and the support stiffness of the bearings are characterized by spring properties. The system degrees of freedom are set as follows: Figure 2 As shown.

[0061] Table 1 Geometric parameters of planetary gear train

[0062]

[0063] Table 2 Bearing structural parameters

[0064]

[0065] In step 101), the elastic deformation of the large thin-walled component in the system and the meshing misalignment between the gear teeth are estimated as follows:

[0066] The tolerance search technology of the RotationMaster software platform was used to screen out the component connection node group, and the control parameters such as search criteria and selection method were adjusted in combination to establish the node rigid connection of the finite element component.

[0067] The finite element model in the system is condensed to extract the corresponding mass and stiffness matrices. Meanwhile, the deformation smoothness is used as an evaluation index, and the performance of each stiffness matrix is ​​tested by using the load transfer behavior between the condensed nodes.

[0068] Load boundary conditions are applied to the system model, and a global calculation of the quasi-static elastic mechanical behavior is performed on it to obtain the nodal displacement response and time-varying load line results of each elastic component.

[0069] RotationMaster (RM) is an advanced simulation platform directly designed for the comprehensive analysis and calculation of complex transmission systems. It completes the positioning and assembly of various transmission components, utilizes RM's tolerance search technology to select component connection node groups, and jointly adjusts control parameters such as search criteria and selection methods to establish rigid connections between finite element components. Subsequently, the finite element model in the system is condensed to extract the corresponding mass and stiffness matrices. Simultaneously, deformation smoothness is used as an evaluation index, and the performance of each stiffness matrix is ​​verified by examining the load transfer behavior between condensed nodes. Finally, load boundary conditions are applied to the system model, and a global calculation of quasi-static elasticity is performed to obtain the nodal displacement response of each elastic component and the time-varying load line results on the tooth surface, providing displacement and load boundary conditions for the secondary sub-model of tooth root stress analysis.

[0070] Step 102) Construct a secondary sub-model for tooth root stress analysis

[0071] In the system-level model, time-varying load lines on the tooth surface are obtained through quasi-static static analysis and applied to the tooth surface of the tooth root stress analysis sub-model as load boundary conditions. Simultaneously, the system's elastic deformation results are extracted and applied to the tooth root stress analysis sub-model as displacement boundary conditions. Thus, the tooth root stress analysis results of the sub-model naturally include the effects of elastic deformation and meshing misalignment of the entire system. Furthermore, the system model also considers dynamic behaviors such as gear rotation and meshing. When these key factors are fully expressed in the system model, the overall structure of the tooth root stress analysis sub-model can be significantly simplified, potentially containing only a few teeth and corresponding rim features (overall configuration as shown). Figure 3 In As shown in the figure, its modeling and computation costs will be more focused on the geometric details of the tooth root. In terms of model quality, the sub-model of tooth root stress analysis has more comprehensive tooth root geometric elements than the system model, and its accuracy level, mesh quality and other quality indicators are also higher.

[0072] A high-fidelity sub-model for tooth root stress analysis was established based on the general finite element method (GEM). The detailed gear solid model, already parameterized and defined in the system-level model, was used as an auxiliary modeling element in the 3D finite element sub-model, thus addressing the modeling difficulties of the general finite element method to some extent. Furthermore, to further alleviate the conflict between computational accuracy and speed, first-order hexahedral elements were used in the sub-model for tooth root stress analysis. When the mesh size is relatively coarse, the tooth tip may appear "serrated" due to shear locking or hourglass effects caused by first-order elements, but this does not affect the stress analysis results at the tooth root. The RM software platform can recommend an economical adaptive mesh density to accurately capture the steep stress gradient at the tooth root and ensure that the sub-model converges within a predetermined number of iterations. In the system-level analysis, the meshing force on the teeth is applied through supercondensation nodes; however, in the sub-model for tooth root stress analysis, the meshing force is applied using the tooth surface load line obtained from the system-level analysis. This is a significant difference in the setting of load boundary conditions between the two methods.

[0073] Taking the sun gear as an example, the tooth root stress analysis program of the secondary sub-model of tooth root stress analysis is run. The maximum principal stress value at the tooth root is calculated based on the first strength theory. The calculation results of the system's elastic deformation and tooth surface load lines are applied to the secondary sub-model of tooth root stress analysis as input conditions, such as... Figure 3 As shown, the model is then solved according to the set number of rotation steps. During the engagement and disengagement of the gear teeth, the secondary sub-model for tooth root stress analysis performs a finite element solution once for each tooth rotation step, based on the overlap ratio of the gear pair in the system. Although this makes the stiffness decomposition and load vector inverse substitution process relatively complex (involving multiple recursive traversals at the substructure level), it is worthwhile to significantly reduce computational costs by appropriately increasing the complexity of the program. Figure 3 In The calculation results of the root stress of the sun gear teeth are presented. When the teeth are in single-tooth meshing, the corresponding root stress values ​​are relatively high. Under the assumption of complete system rigidity (i.e., without inputting the system's elastic deformation results into the secondary sub-model of the root stress analysis), the simulated root stress results are 11.9%–12.3% higher than the simulation results considering system deformation. This indicates that ignoring the flexible behavior characteristics of large aerospace planetary mechanisms may directly lead to overly conservative structural strength design schemes. Furthermore, the stress results obtained using the root bending stress calculation method in the international standard ISO 6336 are also indicated. Figure 3 of The corresponding calculation model is as follows. The simulation results without considering the elastic deformation of the system are in good agreement with this result (which also does not fully consider the deformation factors of the system), which to some extent proves the effectiveness of the load boundary conditions and other model parameter settings in the simulation analysis process. Figure 3 middle, The system's elastic deformation results are illustrated in the figure. The result of the load line on the tooth surface is illustrated. This is a secondary sub-model for tooth root stress analysis, used for calculating tooth root stress. This is a curve showing the maximum bending stress at the tooth root.

[0074] Step 2) Gear probabilistic fatigue strength fitting includes the following methods:

[0075] 201) Gear bending fatigue test: Gear bending fatigue accelerated life test was conducted using a power flow closed gear rotation tester to provide strength information for fatigue reliability prediction model of large aerospace planetary systems;

[0076] 202) Gear tooth probabilistic strength fitting: The peak stress at the tooth root is used as the evaluation index of the stress level. The tooth root bending fatigue performance test is carried out under multiple stress levels using the group method. The direct data obtained is the gear life. The direct strength input variable of the reliability prediction model is obtained by using the probabilistic statistical transformation method to fit the gear tooth PSN curve based on the gear life data.

[0077] 201) Gear bending fatigue test

[0078] The power flow input of the closed-loop gear rotation tester adopts a conical friction surface mechanical loading device to ensure that the power flow is maintained during high-cycle (>10) operation. 7 Reliable sealing is ensured under the following conditions. The gear pairs inside the test gearbox adopt a full-tooth-width contact assembly, and lubrication and cooling of the gear pairs are achieved through oil spraying during the test. Based on the gear specimen (e.g., Figure 4 The predetermined failure state adjustment of the vibration monitoring system and accelerometer thresholds (as shown) enables the testing machine to have an autonomous shutdown function under sudden fatigue tooth breakage, ensuring the consistency of failure states for all gear samples. Each tooth root crack, as shown... Figure 5 As shown, the final shape and size are basically the same; the fatigue fracture morphology of the tooth root is displayed in Figure 6 In the image, the macroscopic morphological features of the fatigue extension zone and the instantaneous failure zone can be clearly seen.

[0079] The structural details and parameters of the gear specimen are as follows: Figure 5As shown in Table 3, the bending fatigue strength of the test specimens is used to simulate the tooth strength of actual service gears, providing a direct strength input variable for the planetary system reliability model. To ensure the stress state at the tooth root of the test specimens is the same as that of the service gear, the tooth geometry parameters of the test specimens are made as consistent as possible with those of the service gear. Furthermore, the overall parameters of the test specimens are made equal to or similar to those of the service gear in terms of material properties, machining, and heat treatment. Effectively ensuring these approximations will help improve the prediction accuracy of the planetary system fatigue reliability index. In addition, it is assumed that the bending fatigue fracture at the tooth root begins at the maximum tooth root stress (mid-tooth width), thus ignoring the size effect in the tooth width direction of the spur gear. Based on this, the tooth width of the test specimens is reduced to lower the testing cost. All gear specimens come from the same production batch to minimize the dispersion of test data.

[0080] Table 3 Test Equipment Parameter Table

[0081]

[0082] 202) Gear tooth probability strength fitting

[0083] Peak tooth root stress was used as the evaluation index for stress level, and a group method was employed to conduct tooth root bending fatigue performance tests at four stress levels. In this embodiment, the selected stress levels and the number of test points at each stress level were 649 MPa (17 points), 618 MPa (22 points), 586 MPa (29 points), and 555 MPa (38 points), respectively. During the test, the testing machine automatically stopped when any tooth on the gear specimen failed first. The direct data obtained was the gear life, not the tooth life, which characterizes the ability of the individual gear to maintain good transmission function under the current stress level. From a probabilistic perspective, the more teeth a gear has, the more potential failure points it has. Therefore, under the same stress and rotational speed conditions, the failure risk of the gear increases with the number of teeth. In this test, one full rotation of the specimen was counted as one gear life. Under this conventional counting mode, the statistical characteristics of the number of teeth lead to differences in probabilistic life between gears and individual teeth. A probabilistic statistical transformation method based on gear life data to fit the PSN curve of gear teeth is used to obtain the direct strength input variables for the reliability prediction model.

[0084] In the statistical processing of the experimental data, the two-parameter Weibull distribution function was first used to fit the probability distribution of the gear life points under each stress level. Then, the probability life transformation between gears and teeth was performed by model (1):

[0085]

[0086] Where, β GearLet β be the shape parameter of the gear life distribution, and θ be the shape parameter of the tooth life distribution. Gear Let θ be the scale parameter of gear life distribution, θ be the scale parameter of tooth life distribution, and Z be the number of teeth;

[0087] Finally, the least squares method was used to linearly fit the same probability quantiles of the tooth life distribution under each stress level in a logarithmic coordinate system. The resulting tooth bending fatigue PSN curves are shown below. Figures 7-8 As shown. Under deterministic loads, the dispersion of fatigue life generally increases as the stress level decreases. Therefore, in a linear coordinate system, the PSN curve family will present an "umbrella-shaped" form with a small opening at the top and a large opening at the bottom. However, due to the use of a logarithmic coordinate system, the curve family presents a corresponding inverted form.

[0088] Step 3) Component fatigue reliability analysis includes:

[0089] 301) Establish a conditional probability expectation value algorithm for calculating the fatigue reliability of parts: Extend the traditional load-strength interference analysis method and establish a conditional probability expectation value algorithm for calculating the fatigue reliability of parts based on the probability distribution of stress level and the life distribution under a specified stress level.

[0090] 302) Fatigue reliability assessment model for series system considering failure correlation: Under deterministic load, the failures of each component in the system are independent of each other, and the conditional reliability of the series system is equal to the product of the conditional reliability of each component; considering the uncertainty effect of the load at the system level, a fatigue reliability assessment model for the series system is established. It is assumed that the load of the model follows a normal distribution, and the load of each component is normalized by transforming the mathematical relationship between the normal distribution and the standard normal distribution, thus considering the influence of the load uncertainty effect at the system level.

[0091] 303) Reliability model structure optimization considering the temporal characteristics of planetary systems: The kinematic equations of planetary transmission are derived based on the periodic operation law of planetary gear trains. At the same time, the number of single-tooth meshing times of various gears in the system within the same time interval is obtained to match the temporal characteristic attributes for the fatigue reliability assessment model of the system.

[0092] In step 302), for the static strength failure problem of the part under a single load, the reliability is regarded as a function of stress, and a conditional reliability model under a specified stress is established; for the fatigue reliability problem, a mathematical expression for calculating the fatigue reliability of the part based on the life distribution is constructed, and the fatigue reliability index of the part under random constant amplitude cyclic load is directly calculated.

[0093] This embodiment redesigns the key geometric features of a large aerospace planetary mechanism using a system fatigue reliability prediction method. It screens reliability-sensitive structural elements of large thin-walled components in the system and performs multi-objective dimensional optimization analysis. Simulation analysis shows that the internal gear ring rim and planet carrier play a major supporting role in the planetary gear train, and their core structural parameters largely determine the meshing quality of the entire planetary gear train. Insufficient stiffness of the internal gear ring rim leads to excessive tooth bending deformation, and insufficient stiffness of the planet carrier base plate causes severe planetary shaft misalignment. These design flaws increase the risk of fatigue tooth breakage in the planetary gear train. The corresponding dimensions are shown in the figure. Figures 9-10 As shown.

[0094] The results of elastic deformation of the internal gear ring and planetary carrier, and the reliability results of the planetary gear train are presented in... Figure 11A In the figure, a total of 30 data points were calculated. Six points were selected when the thickness of the internal gear ring rim was between 10 and 35 mm, with a point spacing of 5 mm; five points were selected when the thickness of the planetary carrier base plate was between 12 and 36 mm, with a point spacing of 6 mm. When the dimensions of the rim and base plate change, the finite element model generated by free mesh generation may have mesh quality differences, which will cause deviations in the calculation of tooth root stress. To better ensure the consistency of the finite element model mesh quality, adjusting the effective size and minimum angle of the finite elements is used as a model quality control method. As the thickness of the internal gear ring rim increases, its elastic deformation gradually decreases. Figure 11A It can be observed that when the rim thickness reaches 25.3 mm, the maximum nodal displacement almost stops decreasing, indicating that the increased internal gear stiffness reserve achieved by increasing the rim size at this limit cannot be effectively utilized. Meanwhile, the elastic deformation response of the internal gear is also affected to some extent by the size of the planetary carrier base plate. Under the same rim thickness, the deformation of the internal gear decreases slightly with the increase of the base plate thickness, indicating that the improved system stiffness conditions caused by the thickening of the planetary carrier base plate have a positive effect on the mechanical environment of the internal gear.

[0095] Figure 11BThis paper illustrates the variation of fatigue reliability indices of a planetary gear train under the combined influence of rim and base plate dimensions. As the rim thickness of the internal gear ring increases, system reliability continuously improves, but the increase stalls at a rim thickness of 22.5 mm. Simultaneously, system reliability also increases with increasing planetary carrier base plate thickness, but this improvement also stalls at a thickness of 30.5 mm. The reliability curves in this figure reflect the coupled influence mechanism of rim and base plate dimensions on system reliability. Within the rim thickness range of 10–22.5 mm, the growth rate of each reliability curve continuously increases with the increase of the planetary carrier base plate thickness, indicating that within a certain range, their dimensional growth has a mutually reinforcing effect on optimizing system reliability indices. The optimal design point is set at a reliability growth rate of less than 0.03%. Considering the static strength requirements of the internal gear ring and planetary carrier, the optimal matching values ​​for two key structural dimensions in this large aerospace planetary mechanism are finally determined: an internal gear ring rim thickness of 22.5 mm and a planetary carrier base plate thickness of 30.5 mm.

[0096] The method of this invention effectively constructs a mapping path from key structural elements of large aerospace planetary mechanisms to fatigue reliability indicators of planetary gear trains with significant advantages in simulation and testing costs. It takes the rim thickness of the internal gear ring and the thickness of the planetary carrier base plate as key structural elements for system reliability and lightweight design, and reveals the coupling influence mechanism of their size changes on the stiffness conditions and fatigue reliability level of the planetary gear train, thus forming a new method for reliability-driven structural optimization design of large aerospace planetary mechanisms.

Claims

1. A system fatigue reliability prediction method for large aviation planetary mechanisms, characterized in that The method comprises the following steps: 1) tooth root stress calculation: the tooth fatigue load history under the coupling of system global elastic behavior is calculated by using hierarchical finite element method, and load information is obtained to provide load input variables for the reliability prediction model; 2) gear probability fatigue strength fitting: the gear low-cycle fatigue test and the minimum order statistic transformation method are used to fit the gear probability fatigue strength curve, and economic and effective strength input variables are provided for the system reliability prediction model; 3) establishment of part fatigue reliability calculation model: a mapping path from key structural elements of large aviation planetary mechanism to system reliability index is established, and a reliability-driven planetary mechanism structure size multi-objective optimization design method is proposed; 4) the load information and the gear probability fatigue strength are input into the reliability prediction model to obtain a system fatigue reliability prediction model which can consider the influence of system structural elements; The tooth root stress calculation in step 1) comprises: 101) system-level elastic mechanics behavior simulation modeling: a system-level elastic mechanics simulation model of the large aviation planetary mechanism is constructed by using semi-analytical finite element technology, and the elastic deformation of the large thin-walled part in the system and the meshing misalignment between the gears are evaluated to provide detailed load and displacement boundary conditions for the tooth root stress analysis secondary submodel; 102) construction of tooth root stress analysis secondary submodel: a high-fidelity tooth root stress analysis secondary submodel is established based on the general finite element method; in the system-level model, the time-varying load line on the gear surface is obtained through quasi-static statics analysis, and is loaded on the gear surface of the tooth root stress analysis secondary submodel as the load boundary condition; at the same time, the system elastic deformation result is extracted and loaded into the tooth root stress analysis submodel as the displacement boundary condition; Step 3) establishment of part fatigue reliability calculation model comprises: 301) establishment of conditional probability expectation value algorithm for part fatigue reliability calculation: the traditional load-strength interference analysis method is expanded, and a conditional probability expectation value algorithm for calculating the fatigue reliability of parts based on the probability distribution of stress level and the life distribution under a specified stress level is established; 302) series system fatigue reliability evaluation model considering failure correlation: under the action of the deterministic load, the failures of the parts in the system are independent of each other, and the conditional reliability of the series system is equal to the product of the conditional reliabilities of the parts; the load uncertainty effect is considered on the system level, and a series system fatigue reliability evaluation model is established; it is assumed that the load obeys the normal distribution, and the load normalization of each part is realized through the mathematical relationship transformation between the normal distribution and the standard normal distribution, so that the influence of the load uncertainty effect is considered on the system level; 303) reliability model structure optimization considering the time sequence characteristics of the planetary system: the kinematics equation of the planetary transmission is derived according to the periodic operation law of the planetary gear train, and the single-tooth meshing times of various gears in the system within the same time interval are obtained to match the time sequence characteristic attribute of the system fatigue reliability evaluation model.

2. The system fatigue reliability prediction method for a large aircraft-oriented planetary mechanism according to claim 1, characterized by In step 101), the elastic deformation of the large thin-walled part in the system and the meshing misalignment between the gears are evaluated as follows: The tolerance search technology of the Rotation Master software platform is used to screen out the component connection node group, and the search criteria and selection mode control parameters are jointly adjusted to establish the node rigid connection of the finite element component. The finite element model in the system is condensed to extract the corresponding mass and stiffness matrix, and the deformation smoothness is used as an evaluation index to test the performance of each stiffness matrix by means of the load transfer behavior between the condensed nodes. The load boundary conditions are applied to the system model, and the global operation of the quasi-static elastic mechanics behavior is performed to obtain the node displacement response of each elastic component and the time-varying load line results of the tooth surface.

3. The system fatigue reliability prediction method for a large aircraft-oriented planetary mechanism according to claim 1, characterized by The tooth root stress analysis secondary sub-model in step 102) adopts a first-order hexahedral element, and the adaptive grid density recommended by the RM software platform is used to accurately capture the steep stress gradient at the tooth root position, so that the tooth root stress analysis secondary sub-model calculation converges within the effective predetermined number of iterations.

4. The system fatigue reliability prediction method for a large aircraft-oriented planetary mechanism according to claim 1, characterized by Step 2) Gear probability fatigue strength fitting includes the following methods: 201) Gear bending fatigue test: using a power flow closed gear rotating test machine to carry out gear bending fatigue accelerated life test, providing strength information for large aviation planetary system fatigue reliability prediction model; 202) Tooth probability strength fitting: taking the tooth root stress peak value as the evaluation index of stress level, using the grouping method to test the tooth root bending fatigue performance at multiple stress levels, obtaining the direct data of gear life, and obtaining the direct strength input variable of the reliability prediction model by the probability statistical transformation method based on the gear life data to fit the tooth P-S-N curve.

5. The system fatigue reliability prediction method for large aircraft-oriented planetary mechanisms according to claim 1, characterized in that In step 302), for the static strength failure problem of the part under the action of a load, the reliability is regarded as a function of stress, and a conditional reliability model under a specified stress is established; for the fatigue reliability problem, a mathematical expression form for calculating the fatigue reliability of the part based on the life distribution is constructed, and the fatigue reliability index of the part under the action of random constant amplitude cyclic load is directly calculated.

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