CN111257023A - Performance accelerated degradation method based on wiener process and gamma process - Google Patents
Performance accelerated degradation method based on wiener process and gamma process Download PDFInfo
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Abstract
The invention belongs to the technical field of performance accelerated degradation tests, and particularly relates to a performance accelerated degradation method of a functional milling head of a numerical control machine tool. Comprising determining a stress factor of the product; performance degradation testing: testing the product according to a preset step stress value, and determining a single stress model and a single stress performance degradation model of the product; and determining an accelerated degradation equation of performance according to the stress factor of the product and the single stress performance degradation model. The technical scheme provided by the invention can be used for obtaining the performance accelerated degradation test data of the product under the conditions of small sample amount and conventional test load equipment, the data can accurately reflect the relation between the product degradation rule and the environmental stress (stress factor), the obtained information and data of the product performance degradation can be used for guiding and predicting the performance degradation of a newly used product, and a foundation is provided for a manufacturer of the product to determine the stress of a rated working condition and compile an operation instruction.
Description
Technical Field
The invention belongs to the technical field of performance accelerated degradation tests, and particularly relates to a performance accelerated degradation method based on a wiener process and a gamma process.
Background
With the acceleration of product updating and the aggravation of market competition, how to improve the reliability of products becomes a key problem of practical engineering. For products with slow performance degradation processes, it is difficult to obtain sufficient degradation information in a short period of time.
The acceleration performance degradation equation is used to describe the relationship between the product degradation law and the environmental stress (acceleration stress). Accelerated performance degradation testing accelerates product performance degradation by improving product conditions or environmental stress, thereby obtaining sufficient product performance degradation information in a shorter time. The acceleration performance degradation equation is divided into a physical acceleration performance degradation equation and an empirical acceleration performance degradation equation, similar to fatigue failure under a defect. In addition, the acceleration performance degradation equation may be divided into a single stress acceleration performance degradation equation and a multi-stress acceleration performance degradation equation according to the number of acceleration stresses. For example, the acceleration degradation equation may be divided into constant stress acceleration performance according to different stress acceleration modes. The degradation test of the product can be divided into two types, namely a step stress acceleration performance degradation test and a sequential stress acceleration performance degradation test. In practical engineering, the constant stress acceleration degradation test requires relatively more test samples, while the sequential stress acceleration degradation test requires higher test load equipment. Therefore, the two performance accelerated degradation test methods are not suitable for the test conditions of small sample size and conventional test load equipment.
Disclosure of Invention
In view of the above technical problems in the background art, it is desirable to provide an accelerated performance degradation method based on a wiener process and a gamma process, where the accelerated performance degradation method needs to be able to obtain test data that accurately reflects the relationship between the product degradation rule and the environmental stress (stress factor) under the conditions of a small sample amount and conventional test load equipment, and the obtained information and data about product performance degradation is used to guide the prediction of product performance degradation for new use.
To achieve the above object, the inventors provide a performance accelerated degradation method based on a wiener process and a gamma process, comprising the steps of:
determining the stress factor of the product;
performance degradation testing: testing a product according to a preset step stress value, wherein the testing comprises the following steps: recording the test time when the product fails under the preset step stress value, or setting the preset time for stopping the test;
determining a single stress model and a single stress performance degradation model of the product by combining an Arrhenius model according to the relation between the preset step stress value and the test time or preset time; and
and determining an acceleration performance degradation equation according to the stress factor and the single stress performance degradation model of the product and combining with an Arrhenius model.
Different from the prior art, the technical scheme at least has the following beneficial effects:
the technical scheme provided by the invention can be used for obtaining the performance accelerated degradation test data of the product under the conditions of small sample amount and conventional test load equipment, the data can accurately reflect the relation between the product degradation rule and the environmental stress (stress factor), the obtained information and data of the product performance degradation can be used for guiding and predicting the performance degradation of a newly used product, and a foundation is provided for a manufacturer of the product to determine the stress of a rated working condition and compile an operation instruction. The technical scheme can also provide reference for the task arrangement and process preparation of the user of the product in the actual use of the machine tool type product.
Drawings
FIG. 1 is a flow chart of a method for accelerating performance degradation based on a wiener process and a gamma process according to an embodiment.
Detailed Description
The accelerated degradation method of performance based on the wiener process and the gamma process proposed by the present invention is explained in detail below.
The performance accelerated degradation method based on the wiener process and the gamma process comprises the following steps:
determining the stress factor of the product;
performance degradation testing: testing a product according to a preset step stress value, wherein the testing comprises the following steps: recording the test time when the product fails under the preset step stress value, or setting the preset time for stopping the test;
determining a single stress model and a single stress performance degradation model of the product by combining an Arrhenius model according to the relation between the preset step stress value and the test time or preset time; and
and determining an acceleration performance degradation equation according to the stress factor and the single stress performance degradation model of the product and combining with an Arrhenius model.
The operating condition or environmental stress (i.e., acceleration stress) in the accelerated degradation test of product performance is a stress factor that is determined from an analysis of the mechanism of product performance degradation and affects the rate of degradation of product performance. Under the condition of ensuring the mechanism of product performance degradation, the product shows different performance degradation speeds under different stress factors (accelerated stress). And converting the performance degradation data under different stress factors (acceleration stress) into the performance degradation data under the rated working stress through an acceleration performance degradation equation.
The performance degradation test will test all products in order of increasing (some further value) stress. This test requires a pressure test that is kept constant for each time period at each pressure. And stopping the test until the product fails or the test time reaches a preset value, and recording the test time when the product fails under the preset step stress value or automatically setting the preset time for stopping the test.
The relationship between the preset step stress value and the test time or the preset time can be expressed by a function. The Arrhenius model is the most typical and widely applied acceleration model when a temperature stress test is used, the relationship between a step stress value and test time or preset time is combined with the Arrhenius model to obtain a single stress model and a single stress performance degradation model of a product,
as an improved technical solution of the present invention, preferably, in the performance degradation testing step, the preset step stress value is a stress that gradually increases according to a preset step value.
As an improved technical solution of the present invention, in the performance degradation testing step, a preset step stress value should be kept constant within the testing time or a preset time.
As an improved technical solution of the present invention, preferably, the single stress model based on the wiener process is:
wherein the content of the first and second substances,
the single stress performance degradation model based on the wiener process is as follows:
wherein, Xw,l(t + Δ t) is the angle of the degradation increment, Xw,l(t) is the initial angle of the degradation increment, a is the acceleration performance coefficient, b is the stress coefficient, N is the single stress acceleration performance decreasing function, t is the duration under the corresponding stress, Δ t is the time variable, σ is the posterior distribution, SlIs the magnitude of the stress.
As an improved technical solution of the present invention, preferably, for a given gamma process-based single stress performance degradation model, in combination with an arrhenius model, an accelerated performance degradation equation is constructed as follows:
or
Or
η(t，S)＝aexp(-b/S)exp(t/a) (7)
Wherein the single stress performance degradation model based on the gamma process is as follows:
XG，l(t+Δt)-XG，l(t)～Ga(Δη(t，Sl)，β)，tl-1＜t＜t+Δt≤tl
wherein the content of the first and second substances,
Δη(t，Sl)＝η(t+Δt，Sl)-η(t，Sl)
XG，1(t + Δ t) is the angle of the degradation increment, XG，1(t) is the initial angle of the degradation increment, a is the acceleration performance coefficient, b is the stress coefficient, S is the corresponding stress magnitude, t is the duration under the corresponding stress, G is the single stress acceleration performance degradation function, β is the posterior distribution, η (t, S) is the shape function.
As an improved technical solution of the present invention, preferably, the stress factor of the product is determined by a degradation mechanism analysis of product performance, where the degradation mechanism analysis includes:
determining a failure mode of the product;
analyzing the fault influence and damage of the product according to the fault mode of the product;
determining a key subsystem and a failure mode of the product according to the fault influence and hazard analysis result; and
and collecting the key subsystems, the failure modes of the key subsystems and vibration signal amplitude values.
The technical scheme provided by the invention can be used for obtaining the performance accelerated degradation test data of the product under the conditions of small sample amount and conventional test load equipment, the data can accurately reflect the relation between the product degradation rule and the environmental stress (stress factor), the obtained information and data of the product performance degradation can be used for guiding and predicting the performance degradation of a newly used product, and a foundation is provided for a manufacturer of the product to determine the stress of a rated working condition and compile an operation instruction. The technical scheme also provides reference for the task arrangement and process preparation of the users of the products in the actual use of the machine tool products.
For the purpose of explaining technical contents, structural features, objects and effects of the technical solutions in detail, the following detailed description is given with reference to the accompanying drawings in conjunction with the specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present application.
In the embodiment, the performance accelerated degradation method based on the wiener process and the gamma process is explained by taking the performance accelerated degradation of a certain type of numerically-controlled machine tool milling head as an example. The milling head is used as a key subsystem of a machine tool, has the characteristics of long production period, high test cost, long service life and the like, and the problem to be solved is how to obtain a method for accelerating the performance degradation of the milling head in a short time under the conditions of small samples and low cost. By determining the failure mode of the milling head and analyzing the influence and damage of the failure mode, the main drive bevel gear and the main shaft bearing of the functional milling head are key subsystems, and the corresponding main failure modes are gear wear and bearing damage. From a performance degradation perspective, wear of the main drive bevel gear of the functional milling head and damage to the main shaft bearing correspond to an increase in the amplitude of the vibration signal. By collecting various information sources in the stages of designing, developing and using the milling head with the mining function, the performance accelerated degradation test can be carried out, a single stress performance degradation model can be obtained, a manufacturer of a product is further guided to determine the stress of a rated working condition and write an operation instruction, and reference can be provided for the task arrangement and the process preparation of the user of the milling head of the numerical control machine tool for actually using the product.
The main driving bevel gear abrasion and the main shaft bearing damage are stress factors of the machine tool functional milling head in the embodiment, and are determined through a descending mechanism analysis on product performance, wherein the descending mechanism analysis step comprises the following steps:
determining a fault mode of a functional milling head product of the mining machine tool in the design, development and use stages of the functional milling head of the mining machine tool;
analyzing fault influence and damage aiming at a fault mode of a functional milling head product of a machine tool;
determining a key subsystem and a failure mode of the product according to the fault influence and hazard analysis result; and collecting the key subsystems and the failure modes and vibration signal amplitude values thereof.
Under the step acceleration performance degradation test of the 3-level acceleration stress, the performance degradation data of the vibration signal amplitude of the functional milling head sample 1 and the functional milling head sample 2 are respectively shown in table 1 and table 2.
Table 1 acceleration performance degradation data for functional milling head sample 1
Table 2 acceleration performance degradation data for functional milling head sample 2
According to the data in the tables 1 and 2, a classical Arrhenius model is combined, an acceleration performance degradation equation is constructed based on a wiener process and a gamma process, and a single stress model and a single stress performance degradation model of the product are determined according to the relation between the preset step stress value and the test time or the preset time and the Arrhenius model. The single stress performance degradation model based on the wiener process is as follows:
wherein, Xw，1(t + Δ t) is the angle of the degradation increment, Xw，1(t) is the initial angle of the degradation increment, a is the acceleration performance coefficient, b is the stress coefficient, N is the single stress acceleration performance decreasing function, t is the duration under the corresponding stress, Δ t is the time variable, σ is the posterior distribution, SlIs the magnitude of the stress.
The single stress performance degradation model based on the gamma process is as follows:
XGl(t+Δt)-XG，l(t)～Ga(Δη(t，Sl)，β)，tl-1＜t＜t+Δt≤tl
wherein the content of the first and second substances,
Δη(t，Sl)＝η(t+Δt，Sl)-η(t，Sl)
XG，l(t + Δ t) is the angle of the degradation increment, XG，l(t) is the initial angle of the degradation increment, a is the acceleration performance coefficient, b is the stress coefficient, S is the corresponding stress magnitude, t is the duration under the corresponding stress, G is the single stress acceleration performance degradation function, β is the posterior distribution, η (t, S) is the shape function.
For a given gamma process-based single stress performance degradation model, in combination with an Arrhenius model, an accelerated performance degradation equation is constructed as:
η(t，s)＝aexp(-b/S)t (5)
or
Or
η(t，S)＝aexp(-b/S)exp(t/a) (7)
It should be noted that, although the above embodiments have been described herein, the invention is not limited thereto. Therefore, based on the innovative concepts of the present invention, the technical solutions of the present invention can be directly or indirectly applied to other related technical fields by making changes and modifications to the embodiments described herein, or by using equivalent structures or equivalent processes performed in the content of the present specification and the attached drawings, which are included in the scope of the present invention.
Claims (6)
1. The performance accelerated degradation method based on the wiener process and the gamma process is characterized by comprising the following steps of:
determining the stress factor of the product;
performance degradation testing: testing a product according to a preset step stress value, wherein the testing comprises the following steps: recording the test time when the product fails under the preset step stress value, or setting the preset time for stopping the test;
determining a single stress model and a single stress performance degradation model of the product by combining an Arrhenius model according to the relation between the preset step stress value and the test time or preset time; and
and determining an acceleration performance degradation equation according to the stress factor and the single stress performance degradation model of the product and combining with an Arrhenius model.
2. The method according to claim 1, wherein in the performance degradation testing step, the preset step stress value is a stress that is gradually increased by a preset step value.
3. The method according to claim 1, wherein in the performance degradation testing step, the preset step stress value is kept constant for the testing time or the preset time.
4. The method of claim 1, wherein the single stress model based on wiener process is:
wherein the content of the first and second substances,
the single stress performance degradation model based on the wiener process is as follows:
wherein, Xw，l(t + Deltat) isAngle of incremental degradation, Xw，l(t) is the initial angle of the degradation increment, a is the acceleration performance coefficient, b is the stress coefficient, N is the single stress acceleration performance decreasing function, t is the duration under the corresponding stress, Δ t is the time variable, σ is the posterior distribution, SlIs the magnitude of the stress.
5. The method of claim 4, wherein for a given gamma process based single stress performance degradation model, in combination with an Arrhenius model, an accelerated performance degradation equation is constructed as:
η(t，s)＝aexp(-b/S)t (5)
or
Or
η(t，S)＝aexp(-b/S)exp(t/a) (7)
Wherein the single stress performance degradation model based on the gamma process is as follows:
XG，l(t+Δt)-XG，l(t)～Ga(Δη(t，Sl)，β)，tl-1＜t＜t+Δt≤tl
wherein the content of the first and second substances,
Δη(t，Sl)＝η(t+Δt，Sl)-η(t，Sl)
XG，1(t + Δ t) is the angle of the degradation increment, XG，1(t) is the initial angle of the degradation increment, a is the acceleration performance coefficient, b is the stress coefficient, S is the corresponding stress magnitude, t is the duration under the corresponding stress, G is the single stress acceleration performance degradation function, β is the posterior distribution, η (t, S) is the shape function.
6. The method of claim 1, wherein the stress factor of the product is determined by a degradation mechanism analysis of product performance, the degradation mechanism analysis comprising:
determining a failure mode of the product;
analyzing the fault influence and damage of the product according to the fault mode of the product;
determining a key subsystem and a failure mode of the product according to the fault influence and hazard analysis result; and
and collecting the key subsystems, the failure modes of the key subsystems and vibration signal amplitude values.
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| CN115795928A (en) * | 2023-02-10 | 2023-03-14 | 中国电子产品可靠性与环境试验研究所（（工业和信息化部电子第五研究所）（中国赛宝实验室）） | Accelerated degradation test data processing method and device based on gamma process |
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