Lubricating grease accelerated degradation modeling and reliability evaluation method

Abstract

The invention discloses a lubricating grease accelerated degradation modeling and reliability evaluation method, and relates to the technical field of lubricating grease performance degradation research. The method comprises the following steps: determining a lubricating grease performance degradation characterization index, and constructing a lubricating grease nonlinear accelerated degradation reliability model by adopting a gamma function; introducing an error term obeying normal distribution; deducing a life distribution function of each performance degradation characterization index; a Frank Copula function is adopted as a connection function, and a reliability function of coupling between performance degradation characterization indexes is established; deducing estimated values of all unknown parameters in the model under actual working conditions by adopting a maximum likelihood estimation method and combining a nonlinear regression method; and substituting the estimated value of each unknown parameter into the reliability function, and calculating the equivalent life of the lubricating grease under the actual working condition. By means of the method, lubricating grease degradation reliability evaluation considering multi-source randomness and multiple performance degradation indexes is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of grease performance degradation research, and in particular to a grease accelerated degradation modeling and reliability assessment method. Background Art

[0002] Grease is a commonly used lubricating material in key functional components of mechanical equipment. Its lubricating performance directly affects the working performance and service life of mechanical products. However, in the core transmission mechanism of mechanical equipment, due to the complex structure and small space, it is difficult to add and replace grease. Therefore, studying the degradation law of grease is of great significance for evaluating the reliability of mechanical products, formulating reasonable maintenance strategies, and improving the service life of equipment.

[0003] Traditional grease reliability assessment methods mainly rely on failure data. However, due to the high reliability of grease itself, failure data is very difficult to obtain, and these data cannot accurately describe its degradation law in actual working conditions. Even if some failure data can be collected, these data are often affected by environmental and human factors and have poor accuracy, which makes it difficult for the accuracy of reliability assessment results to meet requirements. Therefore, developing a grease reliability assessment method based on accelerated degradation is not only of great significance in theory, but also plays a key role in engineering applications.

[0004] Grease has a complex composition and different requirements for lubricity in different usage scenarios, so multiple performance parameters are needed to characterize it. However, there are often certain inline properties between the performance characterization parameters. Therefore, describing the correlation between the performance characterization parameters is also an important part of ensuring the accuracy of reliability modeling and evaluation. Existing methods often select the performance indicators with the most obvious degradation trend as the evaluation target, ignoring the relationship between the performance indicators, which affects the accuracy of the degradation model. Summary of the invention

[0005] The present invention provides a method for modeling and reliability assessment of accelerated degradation of grease, aiming to solve the technical problems mentioned in the above background technology.

[0006] To achieve the above-mentioned purpose, the present invention adopts the following technical scheme: According to one aspect of the present invention, a method for modeling and reliability assessment of accelerated degradation of grease is provided, including: determining a grease performance degradation characterization index, setting the degradation increment of the performance degradation characterization index to obey the gamma distribution, and using the gamma function to construct a nonlinear accelerated degradation reliability model of the grease, wherein the nonlinear accelerated degradation reliability model is used to describe the degradation process of the grease performance under different stress conditions; based on the nonlinear accelerated degradation reliability model, an error term obeying the normal distribution is introduced in the nonlinear gamma accelerated degradation process of the grease, and a grease accelerated degradation reliability model considering the measurement error is established; according to the grease accelerated degradation reliability model, the life distribution function of each performance degradation characterization index is derived, and the life distribution function is used to describe the probability distribution of grease performance degradation at different time points; using Frank Copula function is used as a connection function to establish a reliability function that couples the performance degradation characterization indicators. The maximum likelihood estimation method is used in combination with the nonlinear regression method to derive the estimated values ​​of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions. The estimated values ​​of the unknown parameters are substituted into the reliability function to calculate the equivalent life of the grease under actual working conditions, thereby realizing reliability evaluation.

[0007] Optionally, a nonlinear accelerated degradation reliability model of grease is constructed using a gamma function including: The performance degradation path of the grease obeys the gamma process. According to the characteristics of the gamma process, the nonlinear accelerated degradation reliability model of the grease is expressed as: ; In the formula, Grease Performance degradation characterization indicators, , The total number of indicators that characterize the degradation of grease performance; Indicates the accelerated stress level Next, the grease sample was When measuring for the first time, The degradation increment of a performance degradation characterization indicator; Indicates accelerated stress levels; Indicates Performance degradation indicators at accelerated stress levels The shape parameters below: Indicates the measurement interval between two adjacent measurements; Indicates The diffusion coefficient of each performance degradation indicator; Indicates that the degradation path follows a gamma distribution; To which The Arrhenius model is used to describe the grease under different accelerated stress levels. The impact of the degradation increment of the performance degradation characterization index, wherein the Arrhenius model is expressed as: ; In the formula, Indicates A first unknown parameter of a performance degradation characterization indicator; Indicates A second unknown parameter of a performance degradation characterization indicator; represents the normalized value of stress level; Indicates the normal working stress of grease; Indicates the maximum accelerated stress of grease.

[0008] Optionally, the method further comprises converting the shape parameter in the nonlinear accelerated degradation reliability model into Randomization introduces differences between sample individuals to describe the different effects of sample individuals on grease The influence of the degradation increment on the performance degradation characterization index, the shape parameter It is expressed as: ; In the formula, For the The mean coefficient of randomization of shape parameters of performance degradation characterization indicators; For the The variance coefficient of the randomization of the performance degradation characterization indicators; Indicates The shape parameters of the performance degradation characterization indicators follow a normal distribution.

[0009] Optionally, the error term obeying the normal distribution is introduced in the nonlinear gamma accelerated degradation process of the grease to establish a grease accelerated degradation reliability model taking into account the measurement error; based on the grease accelerated degradation reliability model, the life distribution function of each performance degradation characterization index is derived, including: Without considering the measurement error, the Birnbaum-Saunders distribution is used to approximate the distribution of the degradation process. The probability density function of the nonlinear accelerated degradation reliability model is expressed as: ; ; ; in, Indicates The probability density function of the degradation increment of each performance degradation characterization indicator; Indicates the measurement time; Indicates Shape parameters of performance degradation indicators; Indicates A scale parameter of a performance degradation characterization indicator; Indicates The failure threshold of a performance degradation amount; The introduced error term follows a normal distribution and is expressed as: ; in, represents the amount of measured degradation; represents the actual degradation amount; Represents random measurement error, which is related to the accuracy of the measuring instrument. ; represents the standard deviation of measurement error; Introducing the error term into the general nonlinear Gamma process of accelerated grease degradation, the probability density function is expressed as follows when the measurement error is taken into account: ; ; in, Indicates life span; Indicates the case where measurement error is taken into account. The probability density function of the performance degradation characterization index; The probability density function representing the measurement error; Indicates The diffusion coefficient of a performance degradation indicator.

[0010] Optionally, after deriving the life distribution function of each performance degradation characterization index according to the grease accelerated degradation reliability model, the method further comprises: According to the grease accelerated degradation reliability model, the cumulative distribution function of each performance degradation characterization index is constructed: ; in, Indicates The cumulative distribution function of the degradation increment of each performance degradation characterization indicator; , indicating that at the accelerated stress level Next, the grease sample was When measuring for the first time, The degradation increment of a performance degradation characterization indicator, Indicates The time point of the measurement; , which means that after considering the error The failure threshold of a performance degradation indicator; Indicates Performance degradation indicators at accelerated stress levels The shape parameters below: Indicates The diffusion coefficient of each performance degradation indicator; represents the measurement error; Indicates no measurement error The simplified form of the probability density function of the performance degradation characterization index is shown in Figure 2.

[0011] Optionally, the Frank Copula function is used as a connection function to establish a reliability function for coupling between performance degradation characterization indicators, including: The reliability function of the performance degradation characterization index coupling is: ; in, Indicates A reliability function coupled with performance degradation characterization indicators; represents the Copula linear correlation coefficient under normal temperature stress; represents the reliability function of the first performance degradation characterization index; represents the reliability function of the second performance degradation characterization index; Represents the corresponding Copula distribution function; Select Frank Copula as the link function. .

[0012] Optionally, the maximum likelihood estimation method is used in combination with the nonlinear regression method to derive the estimated values ​​of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions, including: Obtain unknown parameters in the grease accelerated degradation reliability model to form an unknown parameter set; Constructing a log-likelihood function of the unknown parameter set, solving it using a multivariate optimization search algorithm, and finding the parameter value that maximizes the log-likelihood function; Based on the solved parameter values, the maximum likelihood method is used to calculate the unknown parameter values ​​at each stress level; According to the unknown parameter values ​​solved at each stress level, the estimated values ​​of each parameter under natural storage stress are extrapolated using nonlinear regression analysis method.

[0013] Optionally, the unknown parameter set composed of the unknown parameters is: ; in, Indicates A set of unknown parameters that characterize performance degradation indicators; The log-likelihood function of the unknown parameter set for: ; in, represents the Copula connection log-likelihood function, represents the marginal log-likelihood function; ; ; in, represents the stress level number; represents the sample size; Indicates the number of sample tests; Represents the probability density function of Copula; represents the normalized form of the first performance degradation characterization indicator after the degradation increment is deformed; represents the normalized form of the degradation increment of the second performance degradation characterization indicator after deformation; Represents the Copula correlation coefficient under each stress to be estimated; For the The normalized form of the degradation increment of each performance degradation characterization indicator after deformation; Indicates accelerated stress levels; Indicates The drift coefficient of a performance degradation indicator; Indicates The mean coefficient of randomization of shape parameters of performance degradation characterization indicators; ; in, Indicates the total number of measurements; Indicates The approximate matrix of the variance matrix of the degradation amount of samples; Indicates The degradation vector of samples; Indicates The measurement time of each sample; upper right It means to find the derivative.

[0014] Optionally, substituting the estimated values ​​of each unknown parameter into the reliability function, calculating the equivalent life of the grease under actual working conditions includes: obtaining relevant parameters of the grease accelerated degradation reliability model under normal temperature storage state according to the temperature of the grease in the natural storage state; defining a failure threshold, substituting the relevant parameters of the model under normal temperature storage state and the failure threshold into the reliability function, and obtaining the reliability under each normal temperature storage stress state; based on the solved reliability, predicting the reliability median life of the grease during natural storage.

[0015] The beneficial effects of the present invention are as follows: the present invention establishes a grease accelerated degradation model that takes into account measurement uncertainty and multiple performance degradation characterization indicators. Compared with traditional methods, the present method has a more conservative reliability curve and a lower information criterion value, with higher prediction accuracy and more in line with the actual detection process. The present invention uses the Frank Copula function to express the correlation between multiple performance degradation characterization indicators of grease, thereby improving the accuracy and reliability of the evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 1 is a flow chart of a method for modeling and reliability assessment of accelerated degradation of grease in an embodiment of the present invention; Figure 2 It is the commonly used Copula function and its corresponding joint distribution function expression; Figure 3 It is the expression of rank correlation coefficient and information content equation; Figure 4 is a comparison between the rank correlation coefficient and the amount of information in an embodiment of the present invention; Figure 5 is the parameter estimation value of the grease accelerated degradation reliability model in the embodiment of the present invention; Figure 6 are estimated values ​​of various parameters of the grease accelerated degradation reliability model under actual working conditions in the embodiment of the present invention; Figure 7 : The median life and AIC of the grease reliability in the embodiment of the present invention. DETAILED DESCRIPTION

[0017] In order to enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only embodiments of a part of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0018] The terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0019] Reference Figure 1 , Figure 1 is a flow chart of a method for modeling and evaluating the reliability of grease accelerated degradation in an embodiment of the present invention, such as Figure 1 As shown, the method comprises the following steps: S1, determining a grease performance degradation characterization index, setting the degradation increment of the performance degradation characterization index to obey the gamma distribution, and using the gamma function to construct a nonlinear accelerated degradation reliability model of the grease, wherein the nonlinear accelerated degradation reliability model is used to describe the degradation process of the grease performance under different stress conditions; Grease is a semi-solid oily substance mainly used for gears, bearings and other mechanical moving parts to lubricate, protect and seal. It is made of base oil and thickener, and some of them contain additives. The base oil can be mineral oil or synthetic oil, the thickener includes soap-based, hydrocarbon-based, organic and inorganic thickeners, and the additives include scaling improvers, antioxidant additives, anti-rust additives, anti-wear and extreme pressure additives.

[0020] The performance degradation characterization indicators of grease are used to reflect the performance degradation of grease during use, including cone penetration, dropping point, evaporation loss, colloid stability, oxidation stability, water resistance, oil separation, etc. Among them, cone penetration (needle penetration) is the depth of a standard cone that sinks into the grease within 5 seconds under specified temperature and load. It is an indicator used to measure the consistency of the grease. The larger the value, the softer the grease, and vice versa. The dropping point is the temperature at which the grease softens with increasing temperature when heated under specified conditions and reaches a certain fluidity. The dropping point can generally determine the operating temperature of the grease. Evaporation loss refers to the percentage of evaporation of grease to the total amount of grease under specified conditions. It is an important factor affecting the service life of the grease. It is expressed as mass fraction. The smaller the evaporation loss, the better. Colloidal stability (oil separation) refers to the ability of grease to retain oil in the skeleton of its thickener under the action of external forces. Oxidation stability refers to the ability of grease to resist oxidation during storage and use. Water resistance refers to the ability of grease to not dissolve in water, not absorb water from the surrounding medium, and not be washed away by water. Oil separation refers to a small amount of oil precipitation in the storage and use of grease. Grease with better quality has less oil separation.

[0021] In one embodiment of the present invention, by analyzing the degradation degree of each performance index parameter that can characterize the failure of grease, the performance degradation characterization indexes of the accelerated degradation test with temperature as the sensitive stress, cone penetration and oil separation as the degree are determined, and the corresponding accelerated degradation model is constructed using the gamma function. Specifically, it includes: S11, assuming that the performance degradation path of the grease obeys the Gamma process. According to the characteristics of the Gamma process, the performance degradation increment of the grease obeys the Gamma distribution. Then the nonlinear accelerated degradation reliability model of the grease is expressed as: ; In the formula, Grease performance degradation characterization indicators, , The total number of indicators that characterize the degradation of grease performance; Indicates the accelerated stress level Next, the grease sample was When measuring for the first time, The degradation increment of a performance degradation characterization indicator; Indicates accelerated stress levels; Indicates Performance degradation indicators at accelerated stress levels The shape parameters below: Indicates the measurement interval between two adjacent measurements; Indicates The diffusion coefficient of each performance degradation indicator; Indicates that the degradation path follows the gamma distribution.

[0022] S12, for which The Arrhenius model is used to describe the grease under different accelerated stress levels. The impact on the degradation increment of each performance degradation indicator; The Arrhenius model is a model used for accelerated life testing. It is mainly used to shorten the test time by increasing the test stress, so as to evaluate the life characteristics of the product under normal stress. The model was proposed by Arrhenius of Sweden in 1889. It was originally used to describe the relationship between the chemical reaction rate constant and the temperature, but was later widely used in accelerated life testing. The Arrhenius model is expressed as: ; In the formula, Indicates A first unknown parameter of a performance degradation characterization indicator; Indicates A second unknown parameter of a performance degradation characterization indicator; represents the normalized value of stress level; Indicates the normal working stress of grease; It represents the maximum accelerated stress of grease. The first unknown parameter and the second unknown parameter are parameters in the accelerated degradation model, one is the activation energy, and the other is a factor related to temperature. Different degradation characterization indicators correspond to different parameters.

[0023] S13, the shape parameters in the model Randomization introduces differences between sample individuals to describe the different effects of sample individuals on grease The influence of the degradation increment on the performance degradation characterization index, the shape parameter It is expressed as: ; In the formula, For the The mean coefficient of randomization of shape parameters of performance degradation characterization indicators; For the The variance coefficient of the randomization of the performance degradation characterization indicators; Indicates The shape parameters of the performance degradation characterization indicators follow a normal distribution.

[0024] S2, based on the nonlinear accelerated degradation reliability model, an error term that obeys normal distribution is introduced in the nonlinear gamma accelerated degradation process of grease, and a grease accelerated degradation reliability model that takes measurement error into consideration is established; based on the grease accelerated degradation reliability model, a life distribution function of each performance degradation characterization index is derived, and the life distribution function is used to describe the probability distribution of grease performance degradation at different time points; S21, without considering the measurement error, the probability density function is expressed as: ; in, Indicates The probability density function of the degradation increment of each performance degradation characterization indicator; Indicates The shape parameters of the performance degradation characterization indicators; Indicates A scale parameter of a performance degradation characterization indicator; Indicates The diffusion coefficient of each performance degradation indicator; Indicates the measurement time; when hour, hour, ; , which is the Gamma function; the mean of the Gamma process is , the variance is ; is the shape parameter of the Gamma process; S22, the Birnbaum-Saunders distribution (also known as fatigue life distribution) is used to approximate the distribution of the degradation process. The probability density function (PDF) of the Birnbaum-Saunders distribution is as follows: Assume that the random variable t follows the Birnbaum-Saunders distribution, and its probability density function is: ; in, is the scale parameter, is the shape parameter.

[0025] After the embodiment of the present invention is sorted by Birnbaum-Saunders distribution, the probability density function is expressed as: ; in, , indicating the The shape parameters of the performance degradation characterization indicators; , indicating the A scale parameter of a performance degradation characterization indicator; Failure thresholds representing the amount of degradation of each performance; Indicates The probability density function of the degradation increment of each performance degradation characterization indicator; S23, the error term is introduced into the general nonlinear Gamma process of grease accelerated degradation, and the error term obeys the normal distribution, which is expressed as: ; in, represents the amount of measured degradation; represents the actual degradation amount; represents the random measurement error, , usually related to the accuracy of the measuring instrument; represents the standard deviation of measurement error; S24, then in the case of taking measurement error into account, the probability density function is expressed as: ; in, Indicates life span; Indicates the case where measurement error is taken into account. The probability density function of the performance degradation characterization index; , which represents the probability density function of the measurement error.

[0026] According to the accelerated degradation model of the unknown parameter set that has been constructed, the degradation data of the two performance degradation characterization indicators of grease cone penetration and oil separation are fitted to determine the marginal distribution they obey. The degree of fitting is tested by comparing the distribution density image, rank correlation coefficient and information content, and the optimal Copula function is selected to establish the reliability function of the coupling of the two performance parameters. Specifically, it includes: According to the established accelerated degradation model of the unknown parameter set, the cumulative distribution function of the degradation increment of each performance degradation characterization index is constructed, and the cumulative distribution function is expressed as: ; in, , indicating that at the accelerated stress level Next, the grease sample was When measuring for the first time, The degradation increment of a performance degradation characterization indicator, Indicates The time point of the measurement; , which means that after considering the error The failure threshold of a performance degradation indicator; Indicates Performance degradation indicators at accelerated stress levels The shape parameters below: Indicates The diffusion coefficient of each performance degradation indicator; Indicates The cumulative distribution function of the degradation increment of each performance degradation characterization indicator; Indicates no measurement error The simplified form of the probability density function of the performance degradation characterization index is shown in Figure 2.

[0027] The main purpose of constructing the cumulative distribution function is to facilitate subsequent quantitative calculations. The probability density function, also known as the life distribution function, describes the probability density of a continuous random variable near a specific value. The probability density function is first derived, and then the cumulative distribution function is integrated to obtain the cumulative distribution function. The cumulative distribution function calculates the probability of falling within a certain interval, that is, the probability that the random variable is less than or equal to a certain value. The probability density function describes the distribution of the variable, and the cumulative distribution function is the probability of the variable falling within a certain interval, that is, the probability of failure.

[0028] S3, using Frank Copula function as the connection function to establish the reliability function of coupling between multiple performance degradation characterization indicators; The Copula function is a tool for describing the dependency relationship between multi-dimensional random variables. The present invention implements the use of the Copula function to process the correlation between multiple performance degradation characterization indicators.

[0029] When different Copula functions are selected, the joint distribution of multiple performance degradation characterization indicators has different expressions. The commonly used Copula functions and their corresponding joint distribution function expressions are as follows: Figure 2 shown.

[0030] Figure 2 middle, represents the cumulative distribution function of the first performance degradation characterization indicator; represents the cumulative distribution function of the second performance degradation characterization indicator; express and The correlation coefficient between two random variables; Represents a Copula function; Indicates standardized form; According to the rank correlation coefficient and information test results, the Copula function with the best fit is selected, where the rank correlation coefficient and information equation expressions are as follows: Figure 3 shown.

[0031] Figure 3 In the table, * indicates various types of Copula functions; Represents the value of the first measurement of the Debye function; Represents the value of the second measurement Debye function; Represents the squared Euclidean distance of each type of Copula function; Indicates Coupla empirical function value of the feature; represents the overall log-likelihood function; Indicates the number of unknown parameters; ) is the Debye function, ; Analysis of the performance degradation data of cone penetration and oil separation of grease shows that the two characteristic parameters show sharp peaks and thick tails, and the tails are basically symmetrical, so the binary Gaussian Copula function and the binary Frank Copula function are selected to describe the correlation characteristics of the performance index parameters.

[0032] The Pearson linear correlation coefficient, Kendall rank correlation coefficient, and Spearman rank correlation coefficient of the binary Gaussian Copula function and the binary Frank Copula function are solved respectively. The results are as follows Figure 4 shown.

[0033] comprehensive Figure 4 The analysis results show that the embodiment of the present invention selects the Frank Copula function as the connection function to express the binary correlation of multiple performance parameters and establishes a reliability function for coupling the performance degradation characterization indexes. The reliability function can comprehensively consider the influence of multiple indicators on the reliability of the grease. Among them, the reliability function for coupling the two performance parameters for: ; represents the Copula linear correlation coefficient under normal temperature stress; represents the reliability function of the first performance degradation characterization index; represents the reliability function of the second performance degradation characterization index; Represents the corresponding Copula distribution function; Frank Copula is the link function, then .

[0034] S4, using the maximum likelihood estimation method combined with the nonlinear regression method, derives the estimated values ​​of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions; The unknown parameters in the model include shape parameter, diffusion coefficient, drift coefficient, etc.

[0035] S41, obtain unknown parameters in the grease accelerated degradation reliability model and form an unknown parameter set : ; S42, constructing a log-likelihood function of the unknown parameter set : ; in, represents the Copula connection log-likelihood function, represents the marginal log-likelihood function; ; ; in, represents the stress level number; represents the sample size; Indicates the number of sample tests; Represents the probability density function of Copula; represents the normalized form of the first performance degradation characterization indicator after the degradation increment is deformed; represents the normalized form of the degradation increment of the second performance degradation characterization indicator after deformation; Represents the Copula correlation coefficient under each stress to be estimated; For the The normalized form of the degradation increment of each performance degradation characterization indicator after deformation; Indicates accelerated stress levels; Indicates The drift coefficient of a performance degradation indicator; Indicates The mean coefficient of randomization of shape parameters of performance degradation characterization indicators; ; in, Indicates the total number of measurements; Indicates The approximate matrix of the variance matrix of the degradation amount of samples; Indicates The degradation vector of samples; Indicates The measurement time of each sample; upper right represents the derivative; According to the above formula and Find the first-order partial derivative and set it equal to 0, and get its estimated value: ; express An estimated value of express An estimated value of Indicates The first performance degradation indicator The degradation vector matrix of samples; Indicates The sample in The inverse matrix of the approximate matrix of the variance matrix of the degradation amount under each stress level; Indicates The first performance degradation indicator The inverse matrix of the approximate matrix of the variance matrix of the degradation amount of samples; express An estimated value of S43, substituting the obtained parameter estimation value back into the established log-likelihood function, and solving using a multivariate optimization search algorithm to find the parameter value that maximizes the log-likelihood function; S44, based on the solved parameter values, using the maximum likelihood method to calculate the unknown parameter values ​​at each stress level; S45, based on the unknown parameter values ​​at each solved stress level, the estimated values ​​of each parameter under the natural storage stress are extrapolated using a nonlinear regression analysis method.

[0036] Nonlinear regression analysis first determines the model that fits the nonlinear relationship based on the data, and then uses the unknown parameter values ​​at each stress level that have been solved as input to extrapolate the parameter values ​​under normal stress through nonlinear regression analysis. Figure 5 As shown, Figure 5 Parameter estimates for the model are shown.

[0037] S5, substituting the estimated values ​​of the unknown parameters into the reliability function, calculating the equivalent life of the grease under actual working conditions, and realizing reliability evaluation.

[0038] Equivalent life is the time required for the performance of a grease to degrade to a predetermined level under a specific stress level.

[0039] S51, according to the temperature of the lubricating grease in the natural storage state, obtaining relevant parameters of the reliability model of the accelerated degradation of the lubricating grease in the normal temperature storage state; Through experiments, it is determined that the temperature of the grease under actual working conditions is 25°C. The degradation model is established based on the degradation data of the grease cone penetration and oil separation. The relevant parameters obtained are as follows: Figure 6 As shown; S52, defining a failure threshold, substituting the obtained relevant parameters of the model under the normal temperature storage state and the failure threshold into the reliability function, and obtaining the reliability under each normal temperature storage stress state; The failure threshold is used to determine whether the grease has failed and can be set based on experience or experimental data.

[0040] S53, based on the solved reliability, predict the reliability median life of the grease during natural storage.

[0041] The median reliability life refers to the time it takes for the reliability to drop to 0.5.

[0042] like Figure 7 As shown, Figure 7 Median life and AIC of grease reliability for the accelerated degradation reliability model.

[0043] By analyzing Figure 7 It can be seen that the median reliability life of the Frank correlation of the cone penetration and oil separation dual performance parameters considering the measurement error is about 10.49 years, compared with the median reliability life of about 11.57 years of the Frank correlation of the dual performance parameters considering the sample difference, and the median reliability life of about 13.06 years without considering the sample and measurement uncertainty. The potential degradation state of the grease under accelerated stress is not ignored, and the life characteristics are estimated more conservatively. Therefore, the method proposed in the present invention is closer to engineering practice than the method that does not consider multi-source randomness.

[0044] The grease accelerated degradation modeling and reliability assessment method in the embodiment of the present invention can improve the accuracy of assessment results and reduce the cost of grease reliability testing in the field of accelerated degradation modeling and reliability assessment, thus providing an important theoretical basis for improving grease reliability.

[0045] An embodiment of the present invention further provides a storage medium, in which a computer program is stored, wherein the computer program is configured to execute the steps of any of the above method embodiments when running.

[0046] For specific examples in this embodiment, reference may be made to the examples described in the above embodiments and optional implementation modes, and this embodiment will not be described in detail here.

[0047] Optionally, in this embodiment, the above-mentioned storage medium may include but is not limited to: a USB flash drive, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk or an optical disk, and other media that can store computer programs.

[0048] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0049] In the above embodiments of the present invention, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0050] The steps in the above-mentioned embodiment of the present invention can be adjusted in order, combined and deleted according to actual needs. The technical features can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the embodiment are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

[0051] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for modeling and reliability assessment of accelerated grease degradation, characterized in that: include: Determine a grease performance degradation characterization index, set the degradation increment of the performance degradation characterization index to obey the gamma distribution, and use the gamma function to construct a nonlinear accelerated degradation reliability model of the grease, wherein the nonlinear accelerated degradation reliability model is used to describe the degradation process of the grease performance under different stress conditions; Based on the nonlinear accelerated degradation reliability model, an error term obeying normal distribution is introduced in the nonlinear gamma accelerated degradation process of grease, and a grease accelerated degradation reliability model considering measurement error is established; According to the grease accelerated degradation reliability model, a life distribution function of each performance degradation characterization index is derived, wherein the life distribution function is used to describe the probability distribution of grease performance degradation at different time points; The Frank Copula function is used as the connection function to establish the reliability function of the coupling between the performance degradation characterization indicators; The maximum likelihood estimation method is used in combination with the nonlinear regression method to derive the estimated values ​​of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions. The estimated values ​​of the unknown parameters are substituted into the reliability function to calculate the equivalent life of the grease under actual working conditions, thereby achieving reliability evaluation.

2. The grease accelerated degradation modeling and reliability assessment method according to claim 1, characterized in that: The nonlinear accelerated degradation reliability model of grease constructed using the gamma function includes: The performance degradation path of the grease obeys the gamma process. According to the characteristics of the gamma process, the nonlinear accelerated degradation reliability model of the grease is expressed as: ； In the formula, Grease performance degradation characterization indicators, , The total number of indicators that characterize the degradation of grease performance; Indicates the accelerated stress level Next, the grease sample was When measuring for the first time, The degradation increment of a performance degradation characterization indicator; Indicates accelerated stress levels; Indicates Performance degradation indicators at accelerated stress levels The shape parameters below: Indicates the measurement interval between two adjacent measurements; Indicates The diffusion coefficient of each performance degradation indicator; Indicates that the degradation path follows a gamma distribution; To which The Arrhenius model is used to describe the grease under different accelerated stress levels. The impact of the degradation increment of the performance degradation characterization index, wherein the Arrhenius model is expressed as: ； In the formula, Indicates A first unknown parameter of a performance degradation characterization indicator; Indicates A second unknown parameter of a performance degradation characterization indicator; represents the normalized value of stress level; Indicates the normal working stress of grease; Indicates the maximum accelerated stress of grease.

3. The grease accelerated degradation modeling and reliability assessment method according to claim 2, characterized in that: The method further comprises converting the shape parameter in the nonlinear accelerated degradation reliability model Randomization introduces differences between sample individuals to describe the different effects of sample individuals on grease The influence of the degradation increment on the performance degradation characterization index, the shape parameter It is expressed as: ; In the formula, For the The mean coefficient of randomization of shape parameters of performance degradation characterization indicators; For the The variance coefficient of the randomization of the performance degradation characterization indicators; Indicates The shape parameters of the performance degradation characterization indicators follow a normal distribution.

4. The grease accelerated degradation modeling and reliability assessment method according to claim 3, characterized in that: The error term obeying the normal distribution is introduced in the nonlinear gamma accelerated degradation process of the grease, and the reliability model of the grease accelerated degradation considering the measurement error is established; according to the reliability model of the grease accelerated degradation, the life distribution function of each performance degradation characterization index is derived, including: Without considering the measurement error, the Birnbaum-Saunders distribution is used to approximate the distribution of the degradation process. The probability density function of the nonlinear accelerated degradation reliability model is expressed as: ； ； ； in, Indicates The probability density function of the degradation increment of each performance degradation characterization indicator; Indicates the measurement time; Indicates Shape parameters of performance degradation indicators; Indicates A scale parameter of a performance degradation characterization indicator; Indicates The failure threshold of a performance degradation amount; The introduced error term follows a normal distribution and is expressed as: ； in, represents the amount of measured degradation; represents the actual degradation amount; Represents random measurement error, which is related to the accuracy of the measuring instrument. ; represents the standard deviation of measurement error; Introducing the error term into the general nonlinear Gamma process of accelerated grease degradation, the probability density function is expressed as follows when the measurement error is taken into account: ； ； in, Indicates life span; Indicates the case where measurement error is taken into account. The probability density function of the performance degradation characterization index; The probability density function representing the measurement error; Indicates The diffusion coefficient of a performance degradation indicator.

5. The grease accelerated degradation modeling and reliability assessment method according to claim 4, characterized in that: After deriving the life distribution function of each performance degradation characterization index according to the grease accelerated degradation reliability model, the method further includes: According to the grease accelerated degradation reliability model, the cumulative distribution function of each performance degradation characterization index is constructed: ； in, Indicates The cumulative distribution function of the degradation increment of each performance degradation characterization indicator; , indicating that at the accelerated stress level Next, the grease sample was When measuring for the first time, The degradation increment of a performance degradation characterization indicator, Indicates The time point of the measurement; , which means that after considering the error The failure threshold of a performance degradation indicator; Indicates Performance degradation indicators at accelerated stress levels The shape parameters below: Indicates The diffusion coefficient of each performance degradation indicator; represents the measurement error; Indicates no measurement error The simplified form of the probability density function of the performance degradation characterization index is shown in Figure 2.

6. The grease accelerated degradation modeling and reliability assessment method according to claim 5, characterized in that: The Frank Copula function is used as the connection function to establish the reliability function of coupling between the performance degradation characterization indicators, including: The reliability function of the performance degradation characterization index coupling is: ； in, Indicates A reliability function coupled with performance degradation characterization indicators; represents the Copula linear correlation coefficient under normal temperature stress; represents the reliability function of the first performance degradation characterization index; represents the reliability function of the second performance degradation characterization index; Represents the corresponding Copula distribution function; Select Frank Copula as the link function. 。 7. The grease accelerated degradation modeling and reliability assessment method according to claim 6, characterized in that: The maximum likelihood estimation method is used in combination with the nonlinear regression method to derive the estimated values ​​of all unknown parameters in the grease accelerated degradation reliability model under actual working conditions, including: Obtain unknown parameters in the grease accelerated degradation reliability model to form an unknown parameter set; Constructing a log-likelihood function of the unknown parameter set, solving it using a multivariate optimization search algorithm, and finding the parameter value that maximizes the log-likelihood function; Based on the solved parameter values, the maximum likelihood method is used to calculate the unknown parameter values ​​at each stress level; According to the unknown parameter values ​​solved at each stress level, the estimated values ​​of each parameter under natural storage stress are extrapolated using nonlinear regression analysis method.

8. The grease accelerated degradation modeling and reliability assessment method according to claim 7, characterized in that: The unknown parameter set composed of the unknown parameters is: ； in, Indicates A set of unknown parameters that characterize performance degradation indicators; The log-likelihood function of the unknown parameter set for: ; in, represents the Copula connection log-likelihood function, represents the marginal log-likelihood function; ； ； in, represents the stress level number; represents the sample size; Indicates the number of sample tests; Represents the probability density function of Copula; represents the normalized form of the first performance degradation characterization indicator after the degradation increment is deformed; represents the normalized form of the degradation increment of the second performance degradation characterization indicator after deformation; Represents the Copula correlation coefficient under each stress to be estimated; For the The normalized form of the degradation increment of each performance degradation characterization indicator after deformation; Indicates accelerated stress levels; Indicates The drift coefficient of a performance degradation indicator; Indicates The mean coefficient of randomization of shape parameters of performance degradation characterization indicators; ； in, Indicates the total number of measurements; Indicates The approximate matrix of the variance matrix of the degradation amount of samples; Indicates The degradation vector of samples; Indicates The measurement time of each sample; upper right It means to find the derivative.

9. The grease accelerated degradation modeling and reliability assessment method according to claim 1, characterized in that: Substituting the estimated values ​​of the unknown parameters into the reliability function, the equivalent life of the grease under actual working conditions is calculated, including: According to the temperature of the grease in the natural storage state, the relevant parameters of the reliability model of the accelerated degradation of the grease under the normal temperature storage state are obtained; Define the failure threshold, substitute the relevant parameters of the model under the normal temperature storage state and the failure threshold into the reliability function, and obtain the reliability under each normal temperature storage stress state; Based on the solved reliability, predict the reliability median life of the grease during natural storage.

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