Life prediction method based on error function model

Abstract

The life prediction method based on the error function model relates to the technical field of reliability test. The purpose of the present invention is to solve the problem of poor prediction accuracy in the existing method of predicting product life. An error function model is established based on statistical mechanics to obtain four historical temperatures of the product and four historical lifespans corresponding to the four historical temperatures. Each historical temperature and the corresponding historical lifespan are brought into an error function model to obtain a model group composed of the four error function models after being brought in. The model group is analyzed to obtain four parameter values ​​of b; the four parameter values ​​of b are brought into an error function model to obtain the error function model to be output, the current temperature of the product is input into the error function model to be output, and the lifespan of the product at the current temperature is predicted. It is used to predict product lifespan.

Description

Technical Field

[0001] The invention relates to the technical field of reliability testing, and in particular to a calculation method for predicting the life of an electromechanical component. Background Art

[0002] In order to avoid the loss of life and property caused by product failure, it is necessary to replace or repair the product before the end of its life. This requires consumers to carry out life prediction for the product. Generally speaking, accurate life prediction requires a huge time cost, which takes five to ten years under normal pressure, which is unacceptable. Usually, unconventional stress (also called accelerated stress) is introduced, and the relationship between the magnitude of the stress and the length of life is explained. This degradation test that introduces accelerated stress and shows no difference from normal stress is called an accelerated degradation test. In the accelerated degradation test, the most common abnormal stress is high temperature. Accordingly, the Arrhenius model is used to describe the relationship between life and temperature. However, the Arrhenius model is used to describe the temperature characteristics of chemical reactants per unit time, and is not suitable for life prediction of electronic component products, because the degradation of electronic components is not a chemical reaction; in addition, the Arrhenius model will also have deviations when describing the temperature characteristics of chemical reactants, so the Arrhenius model has the problem of inaccurate prediction. Summary of the invention

[0003] The purpose of the present invention is to solve the problem of poor prediction accuracy in the existing method of predicting product life, and proposes a life prediction method based on an error function model.

[0004] A life prediction method based on an error function model, the method comprising:

[0005] Step 1: Establish an error function model based on statistical mechanics:

[0006]

[0007] Where h is Planck's constant, v is the quantum fundamental frequency, and k B is the Boltzmann constant, is the average vibration energy of the crystal, a and b are the model coefficients, p is the threshold, σ is the standard deviation of the crystal vibration energy, F(T) is the product life, T is the temperature, x is the integral variable, and d is the differential;

[0008] Step 2: Obtain four historical temperatures of the product and four historical lifespans corresponding to the four historical temperatures, bring each historical temperature and corresponding historical lifespan into an error function model, and obtain a model group consisting of the four error function models after being brought in. Analyze the model group and obtain b four parameter values;

[0009] Step 3: b four parameter values ​​are brought into an error function model to obtain the error function model to be output, the current temperature of the product is input into the error function model to be output, and the life of the product at the current temperature is predicted.

[0010] Preferably, in step 2, the four historical lifespans are obtained by using degradation tests.

[0011] Preferably, the method further comprises step 4;

[0012] Step 4: Verify the correctness of the error function model to be output.

[0013] Preferably, the correctness of the error function model to be output is verified, specifically:

[0014] Measure the current temperature of the product and the product life at this temperature, bring the current temperature into the error function model to be output, output the predicted value of the product life, and determine whether the predicted value of the product life at the current temperature is the same as the measured product life. If so, determine that the error function model to be output is correct; if not, determine that the error function model to be output is incorrect.

[0015] Preferably, in step 1,

[0016] The average vibration energy of the crystal It is expressed as:

[0017]

[0018] Preferably, the specific process of establishing the error function model based on statistical mechanics is:

[0019] The product lifespan obtained when the product crystal vibration energy is normally distributed:

[0020]

[0021] In the formula, ζ ω is the vibration energy of the wth crystal;

[0022] Rearranging formula 3 yields formula 1.

[0023] The beneficial effects of the present invention are:

[0024] The error function model established in the present application does not describe the temperature characteristics of chemical reactants, but directly establishes a relationship between temperature and product crystal vibration energy. Therefore, the present application can more directly predict the product life according to temperature, which is more accurate than existing models. In addition, the present application has good applicability and is not only suitable for predicting the life of electronic components. When it is applied to the field of electronic components, the error function model is used to obtain the changes in the crystal vibration energy inside the electronic components affected by temperature, thereby predicting the product life. Therefore, the present application has good applicability and is more accurate than the Arrhenius model. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a flow chart of a life prediction method based on an error function model;

[0026] Figure 2 It is an effect diagram of the simulation error function model, and reference numeral 1 represents a threshold value p;

[0027] Figure 3 The temperature characteristics of the spring force are used to preliminarily verify the error function model;

[0028] Figure 4 The figure is a curve comparison chart of the lifespan predicted by the method of the present application and the lifespan predicted by the existing method. DETAILED DESCRIPTION

[0029] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0030] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0031] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0032] Embodiment 1:

[0033] Combination Figure 1 This embodiment describes a life prediction method based on an error function model, the method comprising:

[0034] Step 1: Establish an error function model based on statistical mechanics:

[0035]

[0036] Where h is Planck's constant, v is the quantum fundamental frequency, and k B is the Boltzmann constant, is the average vibration energy of the crystal, a and b are the model coefficients, p is the threshold, σ is the standard deviation of the crystal vibration energy, F(T) is the product life, T is the temperature, x is the integral variable, and d is the differential;

[0037] Step 2: Obtain four historical temperatures of the product and four historical lifespans corresponding to the four historical temperatures, bring each historical temperature and corresponding historical lifespan into an error function model, and obtain a model group consisting of the four error function models after being brought in. Analyze the model group and obtain b four parameter values;

[0038] Step 3: b four parameter values ​​are brought into an error function model to obtain the error function model to be output, the current temperature of the product is input into the error function model to be output, and the life of the product at the current temperature is predicted.

[0039] In this embodiment, in order to solve the limitations of the Arrhenius model, the present application provides a life prediction method based on an error function model. This method, based on the crystal vibration energy in statistical mechanics, proposes a hypothesis between microscopic properties and macroscopic properties, establishes a model between temperature and macroscopic characteristics, and life span, thereby realizing a replacement for the Arrhenius model.

[0040] The products in this application include electromechanical components, such as coil current switching devices, spring forces, electromagnetic relays, etc.

[0041] Taking the electromagnetic relay as an example, its degradation is mainly caused by the relaxation of the spring stress of the relay, so the error function model proposed in this application should be applicable to this product.

[0042] like Figure 4 As shown, there is a large deviation between the predicted life of the Arrhenius model and the model of the present application at 298K. The huge time cost hinders better verification of the model in predicting life. Instead, we focus on the fitting effect. Therefore, the sum of squared errors is used to compare the Arrhenius model and the model of the present application. The smaller the sum of squared errors, the better the acceleration model. The sum of squared errors of the Arrhenius model is 98985.29, and the sum of squared errors of the error function model is 2.31. Therefore, in terms of electromagnetic relays, the life prediction using the error function model is more advantageous than the prediction using the Arrhenius model. From Figure 4 It can be seen that the characteristic of life is that it decreases with increasing temperature, but it tends to be stable in relatively high or relatively low temperature sections.

[0043] In a preferred embodiment, in step 2, four historical life spans are obtained by using degradation tests.

[0044] In a preferred embodiment, the method further comprises step 4;

[0045] Step 4: Verify the correctness of the error function model to be output.

[0046] A preferred implementation method verifies the correctness of the error function model to be output, specifically:

[0047] Measure the current temperature of the product and the product life at this temperature, bring the current temperature into the error function model to be output, output the predicted value of the product life, and determine whether the predicted value of the product life at the current temperature is the same as the measured product life. If so, determine that the error function model to be output is correct; if not, determine that the error function model to be output is incorrect.

[0048] In this embodiment, for example, when the product is a spring, the curve of the spring force changing with temperature is measured, that is, the temperature characteristic is as follows: Figure 3 As shown in the figure, the spring force-temperature characteristic shows an inverse "S" shape, which is the same as the simulation result. Therefore, the model can be considered reasonable. In addition, Figure 3 The force loss in is the integrated form of the model of this application. In conventional temperature stress accelerated degradation tests, the Arrhenius model originated from describing the temperature characteristics of chemical reactants per unit time. In 1985, Campell, a US Navy laboratory, applied this to the life prediction of cables. Since then, the Arrhenius model has been widely used in accelerated degradation experiments. Similar to the Arrhenius model, the error function model is suitable for describing the temperature characteristics of spring force, and accordingly, it is also suitable for life prediction related to spring stress relaxation degradation.

[0049] In a preferred embodiment, in step 1,

[0050] The average vibration energy of the crystal It is expressed as:

[0051]

[0052] In this embodiment, the microscopic substances arranged in an orderly manner in the macroscopic product are called crystals. As the temperature increases, the average amplitude of the crystals will increase accordingly, thereby obtaining Formula 2.

[0053] In a preferred embodiment, the specific process of establishing the error function model based on statistical mechanics is as follows:

[0054] The product lifespan obtained when the product crystal vibration energy is normally distributed:

[0055]

[0056] In the formula, ζ ω is the vibration energy of the wth crystal;

[0057] Rearranging formula 3 yields formula 1.

[0058] In this implementation, Formula 1 obtained by rearranging Formula 3 is a conventional mathematical transformation.

[0059] Assumption: The macroscopic properties of an object are proportional to the sum of the vibrational energies of the crystals greater than a threshold value p:

[0060]

[0061] Among them, F(T) is the macroscopic performance of the object, ζ ω is the vibration energy of the wth crystal, M is the sum of the number of crystals, M p is the sum of the number of crystals whose vibration energy is greater than the threshold p, a and b are the model coefficients, Indicates any.

[0062] The distribution of crystal vibration energy can be approximated as a normal distribution, then:

[0063]

[0064] σ is the standard deviation of the crystal vibration energy, which is considered a constant here. For the convenience of calculation, we further have:

[0065]

[0066] This model is similar to the standard error function model, so it is named the error function model. Through simulation, the model should show the following Figure 2 shown.

[0067] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A life prediction method based on an error function model, characterized in that: The method comprises: Step 1: Establish an error function model based on statistical mechanics: Where h is Planck's constant, v is the quantum fundamental frequency, and k B is the Boltzmann constant, is the average vibration energy of the crystal, a and b are the model coefficients, p is the threshold, σ is the standard deviation of the crystal vibration energy, F(T) is the product life, T is the temperature, is the integral variable, d is the differential; Step 2: Obtain four historical temperatures of the product and four historical lifespans corresponding to the four historical temperatures, bring each historical temperature and corresponding historical lifespan into an error function model, and obtain a model group consisting of the four error function models after being brought in. Analyze the model group and obtain b four parameter values, the product is an electromechanical component; Step 3: b four parameter values ​​are brought into an error function model to obtain the error function model to be output, the current temperature of the product is input into the error function model to be output, and the life of the product at the current temperature is predicted.

2. The life prediction method based on the error function model according to claim 1 is characterized in that: In step 2, four historical lives are obtained using degradation tests.

3. The life prediction method based on the error function model according to claim 1 is characterized in that: The method further comprises step 4; Step 4: Verify the correctness of the error function model to be output.

4. The life prediction method based on the error function model according to claim 3 is characterized in that: Verify the correctness of the error function model to be output, specifically: Measure the current temperature of the product and the product life at this temperature, bring the current temperature into the error function model to be output, output the predicted value of the product life, and determine whether the predicted value of the product life at the current temperature is the same as the measured product life. If so, determine that the error function model to be output is correct; if not, determine that the error function model to be output is incorrect.

5. The life prediction method based on the error function model according to claim 1 is characterized in that: In step 1, The average vibration energy of the crystal It is expressed as:

6. The life prediction method based on the error function model according to claim 5 is characterized in that: The specific process of establishing the error function model based on statistical mechanics is as follows: The product lifespan obtained when the product crystal vibration energy is normally distributed: Rearranging formula 3 yields formula 1.

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