Method for predicting probability wear life of aeronautical self-lubricating plain bearing

Abstract

This invention discloses a method for predicting the probabilistic wear life of self-lubricating spherical bearings in aerospace applications. The method includes: constructing a piecewise linear wear accumulation model with revolutions per revolution (RPM) as the time variable; calculating the short-term wear depth under a single load cycle through numerical simulation; correcting the wear constant using experimental wear data to obtain the corrected wear rate for each stage; substituting the corrected wear rate into the piecewise wear accumulation model to calculate the RPM at which the accumulated wear depth reaches the allowable threshold; quantifying the uncertainty of key parameters in the piecewise wear accumulation model and obtaining the probability distribution of wear life using an uncertainty propagation method. This invention integrates mechanistic models and experimental data, enabling extrapolation from accurate short-term simulation to full-cycle wear accumulation, and providing confident probabilistic life prediction results, thus providing technical support for reliability analysis and maintenance decisions for aircraft transmission mechanisms.

Description

Technical Field

[0001] This invention belongs to the field of structural / mechanical life prediction technology, and specifically relates to a method for predicting the probabilistic wear life of aerospace self-lubricating joint bearings. Background Technology

[0002] Self-lubricating spherical plain bearings are high-performance bearings that require no additional lubricant. Their outer ring inner surface is bonded with a self-lubricating gasket, ensuring stable, low-friction motion between the inner and outer ring contact surfaces. As a key transmission component in aircraft flap mechanisms, aerospace self-lubricating bearings provide low-resistance, high-precision rotational support for the smooth extension and retraction of flaps. During flap extension and retraction, the spherical plain bearing undergoes intermittent reciprocating motion under low-speed, high-load conditions, leading to accelerated wear on the contact surfaces and affecting the motion accuracy and reliability of the flap system.

[0003] Existing methods for predicting the wear life of self-lubricating spherical plain bearings mainly fall into three categories: empirical modeling, data-driven methods, and mechanism-driven methods. Empirical modeling methods establish mathematical models based on classical wear theory, but they struggle to accurately characterize the nonlinear damage evolution behavior under complex service conditions. Data-driven methods rely heavily on bearing life tests, resulting in high data acquisition costs, and the life assessment results are difficult to extrapolate to other operating conditions. Mechanism-driven methods simulate the wear evolution process through the construction of physical models and numerical simulations, but existing methods lack a tight connection between short-term simulations and long-term predictions, and fail to adequately quantify the uncertainties of wear parameters.

[0004] Therefore, there is an urgent need for a method to predict the probabilistic wear life of self-lubricating spherical bearings that can integrate finite element simulation and experimental data, take into account both short-term accurate calculations and long-term trend extrapolation, and quantify parameter uncertainties. Summary of the Invention

[0005] To address the aforementioned issues, this invention discloses a method for predicting the probabilistic wear life of self-lubricating spherical bearings in aviation. Based on segmented wear theory, the method obtains short-term wear depth through finite element simulation, corrects the wear constant using experimental data, and extrapolates from accurate short-term simulation to full-cycle wear accumulation. Furthermore, the method transmits the uncertainty of key parameters through a wear accumulation model, thereby achieving probabilistic life prediction.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for predicting the probabilistic wear life of aerospace self-lubricating spherical bearings includes the following steps:

[0008] Step 1, establish a segmented wear accumulation model: Based on the wear evolution characteristics, the entire cycle wear process of the spherical bearing is divided into at least two continuous stages with different wear rates, and a segmented wear accumulation model with revolutions as the time variable is constructed; wherein, the model includes wear constant, contact pressure and stage transition inflection point as key parameters to be determined;

[0009] Step 2, Obtain short-term wear depth: Calculate the short-term wear depth under a single load cycle through numerical simulation. ;

[0010] Step 3, Correct the wear rate: Use experimental wear data to adjust the short-term wear depth. Error analysis and calibration are performed to inversely determine the true wear constants for each wear stage in the model described in step 1. and wear rate ;

[0011] Step 4, Predict deterministic lifespan: The corrected wear rate... Substitute the segmented wear accumulation model into the calculation of the cumulative wear depth at different revolutions. ,when When the allowable threshold is reached, the corresponding number of revolutions N is the predicted service life.

[0012] Step 5, predict probabilistic lifetime: Quantify the uncertainty of key parameters in the segmented wear accumulation model, and obtain the probability distribution of wear lifetime based on the segmented wear accumulation model using the uncertainty propagation method, which serves as the reliable lifetime range with a specific confidence level.

[0013] Furthermore, in step 1, the continuous stage includes a break-in wear stage, a stable wear stage, and a rapid wear stage, and the wear rate within each stage is constant; the segmented wear accumulation model is expressed as:

[0014] ,

[0015] In the formula, , , These represent the wear rates during the break-in period, the stable period, and the rapid wear period, respectively. To achieve a stable transition speed during the break-in period, For a stable-rapid transition speed, This refers to the number of revolutions required to prevent wear and failure.

[0016] Furthermore, in step 2, the numerical simulation employs the Arcard wear algorithm, which couples adaptive mesh technology with user subroutines, to simulate wear evolution within a single load cycle by iteratively executing mechanical analysis, wear calculation, and mesh updates.

[0017] Furthermore, in step 2, the short-term wear depth The calculation method is as follows:

[0018] Step 2.1: Establish an assembly model including the bearing inner ring, outer ring, self-lubricating liner, and spindle; define a contact pair between the inner surface of the self-lubricating liner and the outer surface of the bearing inner ring; and define a binding constraint between the outer surface of the self-lubricating liner and the inner surface of the outer ring.

[0019] Step 2.2, apply a dynamic load spectrum including swing angle, radial load and axial load, where a swing cycle completed in one loading is defined as a load cycle;

[0020] Step 2.3: In each incremental step, calculate the node wear based on the Archard wear model. In the formula, The wear constant is To contact pressure, For material hardness, The sliding distance increment is used, and the wear node is driven to move along the normal direction through the UMESHMOTION user subroutine; at the same time, ALE adaptive meshing technology is used to re-mesh the distorted mesh in real time, and the values ​​calculated for all increment steps within a load cycle are used. Accumulate the values ​​to obtain the short-term wear depth. .

[0021] Furthermore, step 3 specifically involves:

[0022] Step 3.1: Establish wear constants for each stage. Maximum contact pressure at median The functional relationship between them:

[0023] ,

[0024] In the formula, The median maximum contact pressure on the self-lubricating gasket is extracted from the finite element simulation. , , These correspond to the wear constants during the break-in period, the stable period, and the rapid wear period, respectively. It is the inverse function of the cubic relationship between the logarithmic wear constant during break-in and the median maximum pressure. , , , , , , , The coefficients are to be fitted.

[0025] Step 3.2, Establish short-term wear depth Wear constants at each stage Wear rate The proportional relationship between them: , In the formula, This is the simulated wear constant;

[0026] Step 3.3: Define the objective function as the root mean square error between the simulated wear rate and the experimentally measured wear rate. Use the particle swarm optimization algorithm to solve for the coefficients to be fitted, and substitute them into steps 3.1 and 3.2 to obtain the corrected wear rate for each stage.

[0027] Furthermore, the objective function is:

[0028] ,

[0029] In the formula, θ is the vector set composed of all the coefficients to be fitted in step 3.1; Let be the wear rate in the i-th wear stage; is the test wear rate for the corresponding stage; N is the number of wear stages involved in the correction.

[0030] The particle swarm optimization algorithm is used to solve for the minimum value of the objective function, thus obtaining the optimal undetermined coefficients θ. * , θ * Substituting the values ​​from steps 3.1 and 3.2, the corrected wear rates for each stage are calculated. , , .

[0031] Furthermore, in step 4, the cumulative wear depth is established based on the segmented wear rate. The definite integral expression for the number of revolutions n is as follows:

[0032] ,

[0033] In the formula, , , The revolutions interval;

[0034] Wherein, the integration constant , Through the boundary condition equations:

[0035] The solution is obtained;

[0036] when When the allowable wear depth threshold is reached, the corresponding revolutions n is the predicted service life.

[0037] Furthermore, in step 5, the uncertainty propagation method is as follows: based on the statistical distribution characteristics of each key parameter, Latin hypercube sampling is used to generate random parameter samples. Each sample group is substituted into the expression for cumulative wear depth described in step 4 to calculate the failure rotations, and the probability density distribution of wear life is obtained using the kernel density estimation method. .

[0038] Furthermore, step 5 also includes: based on the probability density distribution of the wear life. Calculate the confidence interval for the end of the lifetime and determine the safe service life under a given reliability.

[0039] Furthermore, the kernel density function is expressed as: In the formula, Let x be the estimated probability density function value at position x, and M be the total number of random samples generated by the Monte Carlo simulation. For bandwidth, Let x be the kernel function, representing the wear life of the bearing. The observed value of the j-th sample, i.e., the j-th group of random sampling parameters, is substituted into the cumulative wear depth. Then, the single-cycle wear life result was calculated.

[0040] Beneficial effects:

[0041] (1) Based on the segmented wear theory, this invention constructs a three-stage wear accumulation framework with clear physical meaning, which organically connects short-term simulation with long-term prediction, and overcomes the shortcomings of traditional empirical models in being unable to characterize nonlinear wear evolution and the poor physical interpretability of data-driven models.

[0042] (2) The present invention uses the ALE adaptive mesh technology coupled with the UMESHMOTION subroutine to couple the Archard wear algorithm, which realizes high-precision dynamic evolution simulation of bearing liner wear morphology. The wear constant is corrected by experimental data through particle swarm optimization algorithm, effectively integrating simulation and experimental data sources and improving prediction accuracy.

[0043] (3) The present invention systematically quantifies the uncertainties of key parameters such as simulated wear constant, contact pressure, and stage transition inflection point, and uses the uncertainty propagation method to achieve probabilistic prediction of wear life. It is applicable to probabilistic wear life prediction of self-lubricating spherical bearings in aircraft, and can also be extended to wear analysis of self-lubricating bearings under other similar working conditions, and has good engineering applicability. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the overall implementation of an embodiment of the present invention;

[0045] Figure 2This is a schematic diagram of a three-dimensional solid model of an aerospace self-lubricating bearing according to an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram of the reciprocating oscillating load spectrum according to an embodiment of the present invention;

[0047] Figure 4 This is a three-dimensional stress distribution map of the self-lubricating gasket in an embodiment of the present invention during the load cycle;

[0048] Figure 5 These are test wear depth measurement data from an embodiment of the present invention;

[0049] Figure 6 This is a wear accumulation and life prediction graph according to an embodiment of the present invention;

[0050] Figure 7 This is the wear failure lifetime probability distribution of an embodiment of the present invention. Detailed Implementation

[0051] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0052] This embodiment uses a self-lubricating bearing of a certain type of aircraft as an example to evaluate its wear life under a typical flight mission profile. Figure 1 As shown, the overall implementation process of the present invention includes: establishing a full-cycle segmented wear framework, constructing a finite element simulation model to calculate short-term wear depth, using experimental data to correct the wear constant, establishing a long-term wear accumulation model, quantifying the uncertainty of key parameters, and assessing the wear failure life probability based on uncertainty propagation.

[0053] Step 1: Establish a full-cycle segmented wear accumulation framework.

[0054] According to the theory of friction and wear, self-lubricating spherical bearings exhibit three typical stages in the full-cycle wear process: the running-in wear stage, the stable wear stage, and the rapid wear stage. In the running-in wear stage, due to the surface micromorphology, local contact stress exceeds the nominal stress, resulting in a high wear rate that decreases over time. In the stable wear stage, the contact surface tends to become smooth, and the wear rate remains constant. In the rapid wear stage, the shim thickness is below the critical value, and the friction coefficient and wear rate increase exponentially. The wear rates differ significantly in each stage; one revolution (i.e., the loading period of a single load spectrum) is defined as the smallest time unit for wear evolution. In this embodiment, the Arcard wear theory is used to describe the wear phenomenon between the contact surfaces of solid materials, and its calculation formula is:

[0055]

[0056] In the formula, This refers to the wear volume; The wear coefficient is a dimensionless coefficient. To contact pressure, This refers to the relative sliding distance; These are material parameters.

[0057] During the friction and wear process, the contact surface can be divided into multiple tiny contact units. Within each contact unit, the contact surface can be approximated as having an area of... The plane, and the contact pressure Uniform distribution; wear volume Approximate contact area With wear depth The product of , then:

[0058]

[0059] Therefore, the Arcard wear calculation formula can be used with wear depth. Represented as:

[0060]

[0061] Wear constants at different wear stages It remains approximately constant, and its magnitude is similar to the median maximum contact pressure. The relationship between the wear constant at each stage and the median maximum contact pressure is as follows:

[0062]

[0063] In the formula, , , Wear constants corresponding to the break-in period, stable period, and rapid break-in period, respectively; logarithmic break-in wear constant. and The relationship between them can be expressed using a cubic polynomial function:

[0064]

[0065] In the formula, for The inverse function; , , The model parameters were obtained using data fitting methods.

[0066] The finite element model can be used to obtain accurate simulations of short-term wear depth. Based on this, the unit wear rate for each wear stage is determined through proportional relationships. :

[0067]

[0068] In the formula, The wear constant is set to a constant value according to the reference. Determines the depth of short-term wear. Determines long-term wear and tear.

[0069] One short-term wear cycle is defined as one revolution. Taking one revolution as the time discrete unit, the unit wear rate after n revolutions satisfies the following:

[0070]

[0071] In the formula, , , These represent the wear rates during the break-in period, the stable period, and the rapid wear period, respectively. To achieve a stable transition speed during the break-in period, For a stable-rapid transition speed, The wear rate is the number of revolutions required to fail due to wear. The above unit wear rate model can accommodate changes in wear rate and integrate short-term wear prediction with long-term wear estimation.

[0072] Step 2: Construct a simulation model of bearing wear mechanism and perform numerical calculation of short-term wear depth.

[0073] Step 2.1: Taking a typical self-lubricating spherical plain bearing as the object, a four-component multi-body contact dynamics finite element simulation model including an inner ring, outer ring, self-lubricating gasket, and spindle is constructed using simulation software, such as... Figure 2 As shown in Table 1, the inner ring, typically made of stainless steel, is the component that directly contacts the self-lubricating gasket and undergoes relative motion. The outer ring, typically made of precipitation-hardened steel, has a self-lubricating gasket bonded to its inner surface. The self-lubricating gasket is bonded to a thin layer of PTFE (polytetrafluoroethylene) fabric composite material on the inner surface of the outer ring, with a nominal thickness of approximately 0.1 mm. This is the key functional layer providing low-friction characteristics and is also the primary site of wear. The spindle is a shaft-like component that passes through the inner ring and transmits motion and load. The critical contact interface of this bearing friction pair is the combination of the stainless steel inner ring and the PTFE fabric gasket. The material parameters of each component are shown in Table 1.

[0074] Table 1 Material parameters of self-lubricating bearings

[0075]

[0076] A surface-to-surface contact relationship was established between the inner surface of the self-lubricating gasket and the outer surface of the inner ring. Tangential behavior employed a penalty function algorithm, and the slip mode was finite slip. Coupling constraints were applied to the outer ring side, restricting six degrees of freedom. A binding constraint was set between the gasket and the outer ring (i.e., no relative motion was allowed between the two surfaces) to simulate ideal adhesion. The mesh used eight-node hexahedral linear non-coordinated mode elements (C3D8I). Multiple mesh schemes, from coarse to fine, were used, with maximum contact pressure and wear depth as the key response quantities to verify mesh independence. The mesh was considered convergent when the relative changes in each response quantity under two adjacent mesh schemes were both less than 5%. Considering both computational accuracy and solution efficiency, the final computational mesh size was selected to be no longer than 0.8 mm and no shorter than 0.1 mm.

[0077] Step 2.2, apply a reciprocating oscillating load spectrum representing a typical flight mission profile, such as... Figure 3 As shown, the load spectrum is divided into two continuous stages: In the first stage, the oscillation period is 10 s, the oscillation angle amplitude is 17.5°, the radial load is dynamically applied in a triangular wave pattern within the range of 3500-5000 N, and the axial load increases linearly from 100 N to 220 N; in the second stage, the oscillation period is 10 s, the oscillation angle is increased to 35°, the radial load expands to 3500-8000 N, and the axial load increases to 350 N. One loading cycle represents one revolution.

[0078] Step 2.3: Based on the multibody contact dynamics finite element simulation model constructed above, and combined with the UMESHMOTION subroutine, the wear amount is adaptively re-meshed and the wear profile is dynamically evolved.

[0079] In each incremental step, the node wear is calculated based on the Archard wear model. In the formula, The wear constant is To contact pressure, For material hardness, The sliding distance increment is used, and the wear node is driven to move along the normal direction through the UMESHMOTION user subroutine; at the same time, ALE adaptive meshing technology is used to re-mesh the distorted mesh in real time, and the values ​​calculated for all increment steps within a load cycle are used. Accumulate the values ​​to obtain the short-term wear depth. The UMESHMOTION subroutine can control and update mesh node positions within any Lagrange-Eulerian (ALE) method framework, ensuring stable mesh quality in large deformation analyses and avoiding computational problems caused by mesh distortion. ALE technology effectively analyzes friction and wear problems by redrawing the mesh and maintaining its topology. To simulate the wear process, the modified Archard wear model is integrated into the FORTRAN-written UMESHMOTION subroutine to achieve adaptive mesh constraint updates. Further optimization of model analysis and result interpretation is achieved by calling GETVRN, GETNODETOELEMCONN, and GETVRMAVGATNODE.

[0080] The wear simulation process is as follows:

[0081] 1) Initial mechanical analysis: Apply the oscillation-load spectrum to the multibody contact mechanical model and perform pure mechanical analysis to obtain the initial contact pressure and slip distance;

[0082] 2) Subroutine integration: The modified Archard wear model is embedded through the UMESHMOTION subroutine, and GETVRMAVGATNODE and GETVRN are called to obtain the node contact pressure and slip distance;

[0083] 3) Wear calculation and mesh update: The wear depth increment of the node is calculated based on pressure and cumulative slip distance, which drives the node to move along the normal and triggers ALE adaptive mesh remapping;

[0084] 4) Incremental step loop: Iteratively execute mechanical analysis → wear calculation → mesh update, dynamically evolving the wear morphology of the liner;

[0085] 5) Result extraction: Extract the contact force distribution, slip distance distribution and wear depth distribution of a single loading.

[0086] Based on the above process, a simulation analysis of flap bearing wear was conducted. The entire process included 104 analysis steps and 7364 wear nodes, with the stress distribution at each node as shown in the figure. Figure 4 As shown. The node with the largest cumulative wear depth is extracted to obtain the simulated wear amount per revolution. .

[0087] Step 3, correction of wear constant parameters.

[0088] Based on the wear constant calculation formula of equation (4), the wear constant is described. Maximum contact pressure at median The relationship between them, which includes multiple undetermined parameters, such as , , , , , , , Let θ be a vector. The essence of this correction step is to find a set of θ that minimizes the error between the "simulated wear prediction based on this parameter" and the "experimental measured wear." By combining experimentally measured wear data with simulated single-rotation wear data to construct an objective function, and using an optimization algorithm to iteratively optimize the undetermined coefficients in the wear constant calculation formula, the model parameters are accurately corrected to reflect the actual wear characteristics. Experimental measured wear data is as follows: Figure 5 As shown.

[0089] The specific correction process is as follows:

[0090] Step 3.1, define the deviation measure (objective function) between the "simulation value" and the "error value":

[0091] The objective function is defined as the root mean square error between the simulated wear rate and the experimentally measured wear rate:

[0092]

[0093] In the formula: θ is the vector set consisting of all undetermined coefficients at each stage. ; Let be the wear rate in the i-th wear stage. It is derived from equation (4) and the current parameter θ; The wear rate corresponding to the i-th stage is calculated from the experimentally measured data; N is the number of wear stages involved in the correction.

[0094] Step 3.2, Construct the parameter space:

[0095] The parameters in the wear constant calculation formula are not arbitrary; the search range needs to be set based on physical meaning or preliminary research experience. In this embodiment, the particle swarm optimization (PSO) algorithm is used, setting the particle swarm size, the maximum number of iterations, and randomly initializing the position of each particle (i.e., a set of parameters θ to be corrected), ensuring that they are within a reasonable range.

[0096] Step 3.3, iterative optimization, minimizing error:

[0097] The parameters θ are continuously adjusted through optimization algorithms (such as particle swarm optimization, PSO) until the objective function is achieved. Minimum.

[0098] In this embodiment, the particle swarm optimization algorithm is used for optimization, and the process is as follows:

[0099] 1) Parameter initialization: Set the particle swarm size to 50, the maximum number of iterations to 200, and randomly initialize the search range of θ;

[0100] 2) Simulation wear rate calculation: For each set of undetermined coefficients, calculate the wear constant for each stage according to equations (4) to (5). Then substitute into equation (6) to calculate the wear rate at each stage. ;

[0101] 3) Objective function evaluation: Calculate the objective function value for each individual particle in the current particle swarm. ;

[0102] 4) Update individual and global optimum: Update the historical best position of individual particles and the global optimum position of the population;

[0103] 5) Convergence criterion: If the global optimum changes by less than 10 in 20 consecutive iterations. −6 If the maximum number of iterations is reached, the iteration will terminate.

[0104] 6) Output the result: Output the optimal undetermined coefficient θ * The corrected wear constants and wear rates for each stage are obtained by substituting them into the model.

[0105] The fitting parameters of the wear constants for each stage obtained through the above optimization process are shown in Table 2.

[0106] Table 2 Fitting parameters of wear constants at each stage

[0107]

[0108] The corrected wear rates for each stage are: break-in period 1.00 × 10⁻⁶ -6 mm / revolution, stabilization period 3.57 × 10 -7 mm / revolution, 2.35 × 10⁻⁶ during the acute phase -6 mm / revolution.

[0109] Step 4: Long-term wear accumulation model and life prediction.

[0110] Based on the three-stage wear framework established in step 1, the wear rate remains constant within each stage, but jumps occur between stages. Therefore, the cumulative wear depth... It is the number of revolutions. The piecewise linear function. Integrating the piecewise wear rate shown in equation (7) along the rotational domain, we obtain the result after... Long-term wear accumulation depth model after conversion for:

[0111]

[0112] By integrating piecewise equation (9) and rearranging, the explicit expression for the bearing wear accumulation model is obtained as follows:

[0113]

[0114] In the formula, and The constant is the integral constant, which ensures the continuity of the wear depth function at the connection points of each stage. These two continuity conditions constitute the boundary condition equations:

[0115]

[0116] In this embodiment, based on the settings in step 1, the cumulative wear depth at the break-in to stable transition inflection point is taken as 23% of the allowable wear depth, and at the stable to abrupt transition inflection point as 35%, with the allowable wear depth threshold set to 100 μm. The wear rates obtained in step 3 are substituted into the bearing wear accumulation model (10) to solve for the cumulative wear depth. The revolutions corresponding to reaching the allowable wear depth threshold. In this embodiment, the first inflection point occurs after 23,084 revolutions, when the cumulative wear reaches 23 μm, marking the end of the break-in phase and the transition to the stable wear phase; the second inflection point occurs when the revolutions increase to 122,278, when the cumulative wear crosses the critical value of 58 μm, triggering the transition from the stable phase to the rapid wear phase; the service life end is 130,632 revolutions, when the cumulative wear reaches the service life threshold of 100 μm, and the bearing fails.

[0117] Step 5: Predict probabilistic wear life based on the uncertainty propagation method.

[0118] The wear process of self-lubricating bearings is affected by many uncertainties, including material property fluctuations, load randomness, and manufacturing errors. To obtain probabilistic life prediction results, the uncertainties of key wear parameters need to be quantified, and a large number of parameter samples need to be generated using Monte Carlo simulation. Based on the uncertainty of wear transmission parameters accumulated through segmented wear, the probabilistic wear life prediction of the bearing can be achieved (rather than a single deterministic value). The key uncertainty parameters affecting the wear accumulation process include the following three categories:

[0119] 1) Simulated wear constant ( In finite element simulations, the wear constant in the Archard wear model is usually set to a constant value. However, the wear constant of real materials exhibits a certain degree of dispersion with changes in contact stress, temperature, and surface condition.

[0120] 2) Median maximum contact pressure ( This parameter directly affects the calculation of wear depth. Due to actual load fluctuations and assembly errors, the contact pressure on the gasket is not a fixed value. By finite element simulation of multiple load cycles, the contact pressure history of all wear nodes within a complete cycle is extracted, and the 95th percentile value is used as the representative value. The distribution characteristics are then statistically analyzed.

[0121] 3) Transition inflection point ( , The cumulative wear depth corresponding to the inflection point is affected by factors such as initial surface roughness, critical gasket thickness, and material compatibility, and thus exhibits a certain degree of variability. Its distribution is determined based on statistics of wear rate variation points in experimental data.

[0122] The statistical distribution characteristics of each parameter are shown in Table 3.

[0123] Table 3 Uncertainty Distribution of Key Wear Parameters

[0124]

[0125] The specific steps for uncertainty propagation and lifetime calculation are as follows:

[0126] Step 5.1, Sampling to generate parameter samples:

[0127] Based on the mean and coefficient of variation of each parameter in Table 3, Latin hypercube sampling was used to generate 10 5 Group of random parameter vectors ( , , , ).

[0128] Step 5.2, substitute the parameters into the model and calculate the lifetime corresponding to a single set of parameters:

[0129] For each set of parameters obtained from sampling, the number of revolutions N corresponding to the wear threshold (i.e., the lifespan under that set of parameters) is solved by simultaneously solving equations (4), (5), (6), (10), and (11). The specific process is as follows:

[0130] 1) Based on equation (4) Solve (in the formula) (obtained by inverting the polynomial in equation (5)).

[0131] 2) Based on equation (6) ( , , )and Solve for the unit wear rate ;

[0132] 3) Based on equation (10) , The cumulative wear depth is obtained by piecewise integration (in the formula). , Equation (11) determines the continuity condition.

[0133] 4) Solve for the lifetime N, where the allowable wear threshold is... We need to find a way to satisfy The number of revolutions N. Since equation (10) is a piecewise function, we discuss it in terms of intervals:

[0134] If N≤ The wear is in the break-in stage, solve the equation ;

[0135] like <N≤ The wear is in a stable phase, solve the equation ;

[0136] If N> The wear is in a rapid stage, solve the equation .

[0137] Step 5.3, from single-group lifetimes to probability distribution, statistical lifetime distribution:

[0138] 10 5 Group parameter samples, repeat step 2, to obtain 10 5 There are N1, N2, ... lifetime samples. The wear accumulation process and failure lifetime of all samples are collected, and a wear accumulation vs. lifetime prediction graph is plotted as follows: Figure 6 As shown. To statistically analyze the failure lifetime distribution, the probability density function of wear lifetime is obtained using the kernel density estimation method. The expression for kernel density estimation is:

[0139]

[0140] In the formula, For kernel function, For bandwidth.

[0141] By this probability density function Integrating, we obtain the cumulative distribution function of wear life. (i.e., a probability distribution where lifespan ≤ n) is used to determine the bearing's lifespan under a specific reliability. This is achieved through... You can query the "lifetime at a specific reliability (such as 95%)" (i.e., the n corresponding to F(n)=0.95).

[0142] After Monte Carlo simulation, the probability density distribution of wear life is obtained as follows: Figure 7As shown. It should be noted that the uncertainty quantification and Monte Carlo simulation in step 5 are based on the deterministic wear accumulation model in step 4, without changing the physical framework of the model itself. Step 4 predicts the theoretical lifespan under ideal conditions, assuming all input parameters are fixed and accurate, and calculates a definite number of revolutions. Step 5, however, predicts the lifespan in real-world engineering scenarios, acknowledging that input parameters such as wear constants and loads are uncertain, and calculates a distribution with a confidence level range, such as a 95% probability that the lifespan exceeds 80,000 revolutions. By introducing a parameter distribution, an extension from deterministic lifespan prediction to probabilistic lifespan prediction is achieved, making the prediction results more consistent with engineering realities.

[0143] The above embodiments verify the effectiveness of the probabilistic wear life prediction method proposed in this invention. This method integrates wear mechanism simulation and experimental data, realizing reliable extrapolation from short-term accurate simulation to full-cycle wear accumulation, and can provide a scientific basis for life prediction and maintenance decisions of aircraft transmission mechanisms.

[0144] The embodiments described above are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A method for predicting the probabilistic wear life of aerospace self-lubricating spherical bearings, characterized in that, Includes the following steps: Step 1: Based on the wear evolution characteristics of the spherical bearing throughout its entire life cycle, the wear process is divided into at least two continuous stages with different wear rates, and a segmented wear accumulation model with the number of revolutions n as the time variable is established; wherein, the model includes the wear constant, contact pressure and stage transition inflection point as key parameters to be determined; Step 2: Using simulation software, perform numerical simulation of the spherical plain bearing for a single load cycle to calculate the short-term wear depth within that cycle. ; Step 3: Introduce the wear data obtained from the experiment, and determine the short-term wear depth. Error analysis and calibration are performed to inversely determine the true wear constants of each stage in the model described in step 1. and wear rate ; Step 4, adjust the wear rate accordingly. Substitute the segmented wear accumulation model into the calculation of the cumulative wear depth at different revolutions. ,when When the allowable threshold is reached, the corresponding number of revolutions N is the predicted service life. Step 5: Quantify the uncertainty of the key parameters in the segmented wear accumulation model. Based on the segmented wear accumulation model, use the uncertainty propagation method to obtain the probability distribution of wear life as the reliable life range with a specific confidence level.

2. The method for predicting the probabilistic wear life of self-lubricating spherical bearings in aerospace according to claim 1, characterized in that, In step 1, the continuous stage includes a break-in wear stage, a stable wear stage, and a rapid wear stage, and the wear rate within each stage is constant; the segmented wear accumulation model is expressed as: ， In the formula, , , These represent the wear rates during the break-in period, the stable period, and the rapid wear period, respectively. To achieve a stable transition speed during the break-in period, For a stable-rapid transition speed, This refers to the number of revolutions required to prevent wear and failure.

3. The method for predicting the probabilistic wear life of self-lubricating spherical bearings in aerospace according to claim 1, characterized in that, In step 2, the numerical simulation uses the Arcard wear algorithm coupled with adaptive mesh technology and user subroutines to simulate the wear evolution within a single load cycle by iteratively executing mechanical analysis, wear calculation and mesh update.

4. The method for predicting the probabilistic wear life of aerospace self-lubricating spherical bearings according to claim 1 or 3, characterized in that, In step 2, the short-term wear depth The calculation method is as follows: Step 2.1: Establish an assembly model including the bearing inner ring, outer ring, self-lubricating liner, and spindle; define a contact pair between the inner surface of the self-lubricating liner and the outer surface of the bearing inner ring; and define a binding constraint between the outer surface of the self-lubricating liner and the inner surface of the outer ring. Step 2.2, apply a dynamic load spectrum including swing angle, radial load and axial load, where a swing cycle completed in one loading is defined as a load cycle; Step 2.3: In each incremental step, calculate the node wear based on the Archard wear model. In the formula, The wear constant is To contact pressure, For material hardness, The sliding distance increment is used, and the wear node is driven to move along the normal direction through the UMESHMOTION user subroutine; at the same time, ALE adaptive meshing technology is used to re-mesh the distorted mesh in real time, and the values ​​calculated for all increment steps within a load cycle are used. Accumulate the values ​​to obtain the short-term wear depth. .

5. The method for predicting the probabilistic wear life of self-lubricating spherical bearings in aerospace according to claim 2, characterized in that, Step 3 specifically involves: Step 3.1: Establish wear constants for each stage. Maximum contact pressure at median The functional relationship between them: ， In the formula, The median maximum contact pressure on the self-lubricating gasket is extracted from the finite element simulation. , , These correspond to the wear constants during the break-in period, the stable period, and the rapid wear period, respectively. It is the inverse function of the cubic relationship between the logarithmic wear constant during break-in and the median maximum pressure. , , , , , , , The coefficients are to be fitted. Step 3.2, Establish short-term wear depth Wear constants at each stage Wear rate The proportional relationship between them: , In the formula, This is the simulated wear constant; Step 3.3: Define the objective function as the root mean square error between the simulated wear rate and the experimentally measured wear rate. Use the particle swarm optimization algorithm to solve for the coefficients to be fitted, and substitute them into steps 3.1 and 3.2 to obtain the corrected wear rate for each stage.

6. The method for predicting the probabilistic wear life of aerospace self-lubricating spherical bearings according to claim 5, characterized in that, The objective function is: ， In the formula, θ is the vector set composed of all the coefficients to be fitted in step 3.1; Let be the wear rate in the i-th wear stage; is the test wear rate for the corresponding stage; N is the number of wear stages involved in the correction. The particle swarm optimization algorithm is used to solve for the minimum value of the objective function, thereby obtaining the optimal undetermined coefficients θ. * , θ * Substituting the values ​​from steps 3.1 and 3.2, the corrected wear rates for each stage are calculated. , , .

7. The method for predicting the probabilistic wear life of aerospace self-lubricating spherical bearings according to claim 1 or 6, characterized in that, In step 4, the cumulative wear depth is established based on the segmented wear rate. The definite integral expression for the number of revolutions n is as follows: ， In the formula, , , The revolutions interval; Wherein, the integration constant , Through the boundary condition equations: The solution is obtained; when When the allowable wear depth threshold is reached, the corresponding revolutions n is the predicted service life.

8. The method for predicting the probabilistic wear life of self-lubricating spherical bearings in aerospace according to claim 1, characterized in that, In step 5, the uncertainty propagation method is as follows: based on the statistical distribution characteristics of each key parameter, random parameter samples are generated using Latin hypercube sampling. Each sample group is substituted into the expression for cumulative wear depth described in step 4 to calculate the failure rotations, and the probability density distribution of wear life is obtained using the kernel density estimation method. .

9. The method for predicting the probabilistic wear life of self-lubricating spherical bearings in aerospace according to claim 8, characterized in that, Step 5 further includes: based on the probability density distribution of the wear life. Calculate the confidence interval for the end of the lifetime and determine the safe service life under a given reliability.

10. The method for predicting the probabilistic wear life of aerospace self-lubricating spherical bearings according to claim 8 or 9, characterized in that, The kernel density function is expressed as: In the formula, Let x be the estimated probability density function value at position x, and M be the total number of random samples generated by the Monte Carlo simulation. For bandwidth, Let x be the kernel function, representing the wear life of the bearing. The observed value of the j-th sample, i.e., the j-th group of random sampling parameters, is substituted into the cumulative wear depth. Then, the single-cycle wear life result was calculated.

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