Spatial gear transmission system reliability evaluation method fusing failure physics and degradation data

Abstract

The invention discloses a spatial gear transmission system reliability evaluation method fusing failure physics and degradation data, and belongs to the technical field of mechanical reliability engineering and fault prediction. The method aims to solve the problem of reliability evaluation of the spatial gear transmission system under the conditions of extreme environment, small sample, multi-failure mode coupling and significant individual difference. The method comprises the following steps: firstly, establishing a gear dynamics model considering nonlinear excitation to obtain dynamic meshing force; then, respectively constructing wear and fatigue degradation models based on failure physics; then, introducing an inverse Gaussian random process considering individual differences to carry out single failure mode reliability modeling; and finally, a Copula function is utilized to construct a binary correlation competition failure model, and system-level reliability comprehensive evaluation is realized. Through the technical route of physical mechanism driving, uncertainty quantification and data statistics fusion, a complete evaluation system is formed, and key technical support is provided for on-orbit health management and life prediction of the space gear transmission system.

Description

Technical Field

[0001] This invention relates to the field of mechanical reliability engineering and fault prediction technology, and in particular to a reliability assessment method for spacecraft space gear transmission systems. Background Technology

[0002] Space gear transmission systems (such as satellite solar array drive mechanisms) are the core power transmission units of spacecraft, and their reliability directly determines the mission lifespan and success or failure of the spacecraft. However, existing reliability assessment methods face serious challenges: 1. Extreme scarcity of full life cycle data: The long life cycle, high reliability, and high cost of full life cycle testing result in a severe shortage of failure samples.

[0003] 2. The failure mechanisms are complex and interconnected: multiple failure modes such as tooth surface wear and contact fatigue coexist and influence and promote each other in terms of physical mechanisms.

[0004] 3. Significant individual product differences: Minor differences in manufacturing, assembly, and environment lead to dispersed degradation trajectories among products.

[0005] 4. Uncertainty originates from a wide range of sources: design parameters, material properties, external loads, and the internal state of the system all contain uncertainties.

[0006] Existing statistical methods, accelerated life tests, deterministic failure physics models, or single stochastic process models based on large sample failure data are all insufficient to simultaneously address the issues of multi-failure mode coupling and individual variability under conditions of data scarcity. Therefore, developing a comprehensive reliability assessment method that can deeply integrate physical mechanisms and degradation data, and effectively quantify uncertainty, individual variability, and multi-mode correlations, has become an urgent need to improve the design level and on-orbit management capabilities of space gear transmission systems. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a high-precision and highly applicable method for evaluating the reliability of a spatial gear transmission system.

[0008] The technical solution of the present invention is as follows:

[0009] A lumped-parameter torsional vibration dynamic model of a space planetary gear system is established. This model comprehensively considers time-varying meshing stiffness and tooth flank clearance. b And tooth surface friction effect. The system dynamic differential equations were established by Newton-Euler method, and numerical integration was performed by dimensionless treatment and Runge-Kutta method to output the dynamic meshing force time history curves of each meshing pair.

[0010] Based on the dynamic meshing force obtained in step S1, construct the following respectively: Tooth surface wear degradation model: Based on Archard's adhesive wear theory, a discrete model is constructed with wear depth as the degradation factor, and the wear coefficient is considered. K The time-varying and impact wear effects.

[0011] Gear fatigue degradation model: Based on Miner's linear cumulative damage theory, dynamic meshing force is converted into stress, load spectrum is compiled by rainflow counting method, mean stress is corrected by Goodman criterion, and cumulative damage degree is calculated.

[0012] At the same time, the uncertain parameters (design, material, load, state parameters) in the model are systematically identified and quantified, and a specific probability distribution is assigned to them.

[0013] The physical degradation obtained in step S2 is treated as a stochastic process and modeled using an inverse Gaussian process, with its increments. To characterize individual variability, the drift parameters are assumed to follow a Gamma distribution. The Bayesian Markov chain Monte Carlo method is used for parameter estimation, and the reliability function under a single failure mode is calculated.

[0014] For the two competing failure modes that are correlated: wear and fatigue: 1. Using the results of step S3, determine its marginal reliability function.

[0015] 2. A two-stage parameter estimation method is used to estimate the parameters of various Copula functions (such as Gumbel, Frank, and Clayton), and the optimal model is selected based on the AIC / BIC criterion.

[0016] 3. Using the selected optimal Copula function, construct the joint reliability function of the system to achieve comprehensive system-level reliability assessment and lifetime prediction.

[0017] 1. Integration of mechanism and data-driven approaches: A closed loop of "physical mechanism-driven, uncertainty quantification-data statistical integration" is constructed, which combines mechanism accuracy and statistical robustness.

[0018] 2. Addressing the small sample problem: By utilizing performance degradation data instead of scarce fault data, the feasibility of evaluation in small sample scenarios is greatly improved.

[0019] 3. Accurate quantification of individual differences and pattern correlation: Through random effects and Copula functions, it truly reflects the complex dependencies between individual product differences and multiple failure modes, and the evaluation results are more in line with engineering practice.

[0020] 4. Provide full-process technical specifications: Provide a complete and operable technical route from dynamic analysis to system comprehensive evaluation. Attached Figure Description

[0021] Figure 1 : Overall implementation flowchart of the present invention; Figure 2 Nonlinear dynamic model of a space planetary gear system; Figure 3 Time-varying meshing stiffness and dynamic meshing force curves; Figure 4 Wear depth simulation and load spectrum statistical results; Figure 5 Comparison of reliability functions based on inverse Gaussian processes; Figure 6 Comparison chart of system reliability and single failure mode reliability based on Copula. Detailed Implementation

[0022] The invention will now be described in detail with reference to the accompanying drawings, using the sun gear in the fourth-stage planetary gear train of a certain type of satellite solar array drive mechanism as a specific embodiment. The sun gear is made of 0Cr17Ni4Cu4Nb precipitation-hardening stainless steel.

[0023] according to Figure 2 The lumped-parameter torsional vibration model shown is used to establish the dynamic model of the 2K-H planetary gear train. Input parameters such as the number of teeth on the sun gear, the number of teeth on the planet gears, the module, the pressure angle, the tooth width, the input torque, and the input speed. The Weber energy method is used to calculate the following results: Figure 3 (a) shows the time-varying meshing stiffness curve, with tooth flank clearance and friction coefficient set. A system of dynamic differential equations is established using the Newton-Euler method, and after dimensionless transformation, numerical integration is performed using the MATLAB ode45 solver to obtain the following results: Figure 3 (b) shows the dynamic meshing force time history of the sun gear-planet gear, with an amplitude of 1800. N ~2200 N Fluctuating within a certain range, this dynamic load serves as the precise input for all subsequent physical degradation analyses.

[0024] Tooth surface wear modeling: Taking the sun gear as the object, its tooth profile is discretized into 100 micro-elements. According to the Archard model, for each discrete point... j In each meshing cycle i In the simulation, the normal load, relative slip velocity, and time-varying wear coefficient are calculated. After running one meshing cycle (corresponding to 10 hours of task time), the simulation results are as follows: Figure 4 (a) shows the evolution of tooth surface wear depth, with the maximum wear depth occurring in the tooth tip region. An allowable wear threshold is set.

[0025] Gear fatigue modeling: Dynamic meshing forces are converted into tooth surface contact stresses according to ISO 6336 standard. Load spectra are compiled using the rainflow counting method, and the results are as follows: Figure 4 (b) The average stress was corrected using the Goodman criterion (material tensile strength) to obtain the equivalent symmetrical cyclic stress amplitude. The cumulative damage after 10 hours of operation was calculated using the corrected gear contact SN curve and Miner's rule. A failure threshold was then set.

[0026] Uncertainty quantification: Assigning probability distributions to key parameters, such as module, tooth width, and input torque.

[0027] Fatigue damage degradation data for six sun gear samples at ten task time points were generated through simulation. An inverse Gaussian process model considering individual differences was established, with a mean function and drift parameters. Parameter estimation was performed using the Bayesian MCMC method in OpenBUGS software, yielding the posterior distribution mean: , , . The estimated parameters and threshold values ​​were substituted into the reliability function formula to calculate the reliability function for the fatigue failure mode. Figure 5 The reliability function considering individual differences and that of the standard inverse Gaussian process are compared. At the hour, the reliability of the former is 0.72 lower than that of the latter, which verifies the necessity of considering individual differences.

[0028] Using the method in step S3, the reliability function of the wear failure mode is obtained, and at hourly values, the reliability is calculated. A two-stage maximum likelihood estimation method is employed to estimate the parameters of the Frank, Gumbel, and Clayton Copula functions, and the AIC values ​​are calculated (-181.78, -201.08, and -87.64, respectively). Based on the minimum AIC criterion, the Gumbel Copula is selected as the optimal model, and its estimated parameters are [value missing]. The joint reliability function of the system is constructed using the selected Copula function. The system reliability at hourly values ​​is calculated. Figure 6 The data clearly shows that the system reliability curve consistently lies below the reliability curves of both single-failure-mode failures, demonstrating that the assessment results are more conservative and reasonable after considering competing failures and correlations. Based on the curves, the average lifespan of the sun gear can be predicted to be approximately 25.5 hours, providing a crucial basis for on-orbit maintenance decisions.

Claims

1. A reliability assessment method for a spatial gear transmission system that integrates failure physics and degradation data, characterized in that, Includes the following steps: S1. Establish a nonlinear dynamic model of the gear transmission system and solve for the dynamic meshing force. S2. Based on the dynamic meshing force, construct the wear physical degradation model and fatigue physical degradation model of the gear respectively; S3. Based on the output of the physical degradation model, establish an inverse Gaussian stochastic process model that considers individual differences to achieve reliability assessment of single performance degradation index; S4. Based on the Copula function connecting the wear and fatigue degradation modes, a binary correlation competing failure model is constructed to achieve a comprehensive system-level reliability assessment.

2. The method according to claim 1, characterized in that, In step S1, the nonlinear dynamic model is a lumped-parameter torsional vibration model of a space planetary gear system. The modeling process specifically includes: calculating the time-varying meshing stiffness using the Weber energy method and performing Fourier series fitting; comprehensively considering the nonlinear effects of tooth flank clearance and tooth surface friction; establishing a system of dynamic differential equations using the Newton-Euler method, and performing numerical solutions using dimensionless processing and the Runge-Kutta method.

3. The method according to claim 1, characterized in that, In step S2, the wear physical degradation model is based on Archard's adhesive wear theory, and its core calculation formula is a discrete form of the cumulative wear depth model. Furthermore, the time-varying nature of the wear coefficient K with the number of cycles and the impact wear effect described by the Poisson process were considered; The fatigue physical degradation model is based on Miner's linear cumulative damage theory. Its core process includes: converting dynamic meshing force into tooth surface stress according to ISO standards; compiling a load spectrum using the rainflow counting method; correcting the mean stress using the Goodman criterion; and finally calculating the cumulative damage degree based on the corrected SN curve. .

4. The method according to claim 1 or 3, characterized in that, Step S2 also includes a systematic quantification process for the uncertainty parameters in the model, which include design parameters, material parameters, load parameters and state parameters, and assigns specific probability distributions to these parameters, wherein the friction coefficient in the state parameters is defined as a variable that degrades over time.

5. The method according to claim 1, characterized in that, In step S3, considering individual differences is achieved by adjusting the drift parameter of the inverse Gaussian process. Follows Gamma distribution This is achieved by employing Bayesian inference methods combined with Markov chain Monte Carlo simulation to estimate model parameters, and then using the estimated parameters to calculate the reliability function under single failure modes. .

6. The method according to claim 1, characterized in that, Step S4 specifically includes: S4.1 Using the results of step S3, determine the edge reliability function for the lifetime of each failure mode. ; S4.

2. A two-stage parameter estimation method is adopted. First, the marginal distribution parameters are estimated independently. Then, the marginal distribution parameters are fixed, and the parameters of various Copula functions are estimated by the maximum likelihood estimation method. S4.

3. Select the optimal model from the Copula function family based on the Akaike information criterion or the Bayesian information criterion. S4.4 Utilizing the selected optimal Copula function Construct the joint reliability function of the system And under the competing failure assumption, complete the system-level reliability assessment and lifetime prediction.

7. The method according to claim 6, characterized in that, The Copula family of functions includes at least GumbelCopula, Frank Copula, and Clayton Copula.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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