An accelerated life modeling and prediction method for an insulating bearing

Abstract

The application provides a kind of insulation bearing accelerated life modeling and prediction method, it includes the following steps: S1, constructs insulation bearing model S2, insulation bearing model is converted into accelerated model lnη ji =β0‑β1lnP j +β2lnV i +β3lnP j ·lnV i ;S3, obtains quasi-sample data t1 (β1, β2, β3) < t2 (β1, β2, β3) < … < t r (β1, β2, β3), obtains the best unbiased estimate of shape parameter m r of Weibull distribution using quasi-sample data t1 (β1, β2, β3) < t2 (β1, β2, β3) < … < t ‑1 (β1, β2, β3) S4, the parameter in accelerated model is tested.The application proposes a double stress modeling method under the coupling action of fatigue and electric double stress, which is based on the physical model of bearing, establishes an accelerated model, can predict the life of insulation bearing, solves the problem of time-consuming and low test efficiency of conventional insulation bearing test.

Description

Technical Field

[0001] This invention relates to the field of insulated bearing technology, and more specifically, to a method for accelerated life modeling and prediction of insulated bearings. Background Technology

[0002] With the continuous development of the motor industry, motor products are widely used in various fields. However, motors often experience failures, and approximately 45% to 55% of mechanical failures are caused by the coupling effect of shaft voltage and load on rolling bearings.

[0003] Currently, insulated rolling bearings are used instead of ordinary rolling bearings, and insulated bearings play a crucial role in preventing induced current corrosion. Life testing is an important basis for the type approval of insulated bearings and a necessary process for factory inspection. Insulated bearings have a long lifespan, and conventional testing is time-consuming, costly, and inefficient.

[0004] The applicant's research revealed a lack of methods, equipment, and standards for accelerated life testing of insulated bearings that simultaneously consider electrical damage and fatigue wear. Therefore, it is necessary to propose a modeling and life prediction method for accelerated life testing under the coupled effects of fatigue and electrical stresses. Summary of the Invention

[0005] Based on this, in order to overcome the problems existing in the background technology, the present invention provides an accelerated life modeling and prediction method for insulated bearings, the specific technical solution of which is as follows:

[0006] An accelerated life modeling and prediction method for insulated bearings includes the following steps:

[0007] S1, Constructing the Insulated Bearing Model

[0008] S2, convert the insulated bearing model into the acceleration model inη ji =β0-β1lnP j +β2lnV i +β3lnP j ·lnV i ;

[0009] S3, Obtain quasi-sample data t1(β1,β2,β3) <t2(β1,β2,β3)<…<t r (β1,β2,β3), using quasi-sample data t1(β1,β2,β3)<2(β1,β2,β3)<… <t r (β1,β2,β3) Obtain the shape parameter m of the Weibull distribution. -1 The best unbiased estimate

[0010] S4, verify the parameters in the acceleration model, specifically including the following steps:

[0011] S40, using Nelson's cumulative failure assumption, performs failure time conversion to obtain quasi-sample moments;

[0012] S41, construct the population moments of the exponential distribution to measure the quasi-sample moments, and obtain the parameters β1, β2, β3 in the quasi-sample moments;

[0013] S42, Reconstruct the parent moment to measure the characteristic life η under the first level stress. 11 Seeking

[0014] S43, based on the obtained parameters β0, β1, β2, β3 and η 11 Calculate the characteristic life η of the insulated bearing under rated stress level. 00 ;

[0015] S44, according to and η 00 Calculate the rated horizontal stress Reliability R(t0) and reliability life t p Point estimate;

[0016] Where B is the life correlation coefficient of voltage-load coupling, ε is the coefficient in the life formula, C is the basic rated dynamic load, and P i For the i-th radial load stress level, V i For the i-th electrical stress level, β0 = lnB + εlnC, β1 = -ε. β2=γ, It is the interaction between load and voltage.

[0017] The accelerated life modeling and prediction method for insulated bearings described in this invention proposes a dual-stress modeling method for the coupled effects of fatigue and electrical stress. Based on the physical model of the bearing, an accelerated model is established, which can predict the life of the insulated bearing and solves the problems of time-consuming and inefficient conventional insulated bearing tests.

[0018] Furthermore, in step S40, the specific method for calculating the failure time using the Nelson cumulative failure assumption to obtain the quasi-sample moments includes the following steps:

[0019] When the failure time T follows a Weibull distribution W(m,η), T m Obey the mean lifetime θ of η m If the exponential distribution E(1 / θ) is followed, then Randomly vary W1, W2, ..., W r Independent and identically distributed, with a mean lifetime θ of ηm The exponential distribution E(1 / θ);

[0020] Random variables X1, X2, ..., X r Independent and identically distributed α and β follow an exponential distribution E(1 / θ), denoted as α. If k = 1, 2, ..., r, then we have The independent and identically distributed pairs follow an exponential distribution (1 / θ);

[0021] make but

[0022] according to The k-th order raw moments of the quasi-sample are obtained as follows: For k = 1, 2, 3, the first, second, and third raw moments of the standard exponential distribution are 1, 2, and -6, respectively.

[0023] Further, in step S41, the specific method for constructing the population moments of the exponential distribution to measure the quasi-sample moments and obtaining the parameters β1, β2, and β3 in the quasi-sample moments includes the following steps:

[0024] The system of equations is obtained based on the idea of ​​inverse moment estimation.

[0025] The shape parameter m of the Weibull distribution -1 The best unbiased estimate Substitute into the system of equations Solving

[0026] in, The inverse moment estimates are β1, β2, and β3, respectively.

[0027] Furthermore, in step S42, the parent moment is reconstructed to measure the characteristic lifetime η under the first level stress. 11 Seeking The specific method includes the following steps:

[0028] W1,W2,…,W r ~E(1 / θ), where Therefore, quasi-sample Independent and identically distributed standard exponential distribution E(1);

[0029] Using the idea of ​​inverse moment estimation, we can obtain After simplification, we get

[0030] Will and substitute quasi-sample data achievable

[0031] Depend on Seek

[0032] Further, in step S43, based on the obtained parameters β0, β1, β2, β3, and η 11 Calculate the characteristic life η of the insulated bearing under rated stress level. 00 The specific method includes the following steps: by Then the characteristic life η under the rated stress level combination (0,0) can be obtained. 00 The estimate is Attached Figure Description

[0033] The invention will be further understood from the following description taken in conjunction with the accompanying drawings. The components in the drawings are not necessarily drawn to scale, but rather the emphasis is on illustrating the principles of the embodiments. In different views, the same reference numerals designate corresponding parts.

[0034] Figure 1 This is a schematic diagram of the overall process of an accelerated life modeling and prediction method for an insulated bearing according to an embodiment of the present invention.

[0035] Figure 2 This is a schematic diagram of the overall process of an accelerated life modeling and prediction method for an insulated bearing according to another embodiment of the present invention.

[0036] Figure 3 This is a schematic diagram of the step stress combination of an accelerated life modeling and prediction method for an insulated bearing in another embodiment of the present invention.

[0037] Figure 4 This is a schematic diagram illustrating the failure time conversion of an accelerated life modeling and prediction method for an insulated bearing, according to another embodiment of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to its embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of protection of the invention.

[0039] It should be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0040] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0041] In this invention, "first" and "second" do not represent a specific quantity or order, but are merely used to distinguish names.

[0042] like Figure 1-4 As shown, an accelerated life modeling and prediction method for an insulated bearing according to an embodiment of the present invention includes the following steps:

[0043] S1, Constructing the Insulated Bearing Model

[0044] Specifically, an insulating bearing model is constructed based on LP theory and an inverse power law model.

[0045] Based on the failure modes of insulated bearings, it is determined that the insulated bearings are mainly subjected to load stress and voltage stress. According to the ISO 281[8] relationship between life and load... Where: a1 is the lifespan adjustment coefficient; a ISO ε is the life correction factor; C is the basic rated dynamic load; and P is the equivalent dynamic load.

[0046] According to the inverse power law model: Where: V i Let represent the i-th electrical stress level, A be the lifetime-related coefficient, and γ be the correlation constant under voltage failure mode.

[0047] Because a ISO As a lifetime correction factor, this invention mainly addresses the influence of voltage, without considering other factors, so a is... ISO replace An insulated bearing model can then be established: Where B is the life correlation coefficient of voltage-load coupling, ε is the coefficient in the life formula, C is the basic rated dynamic load, and P j For the j-th radial load stress level, V i Let i be the i-th electrical stress level.

[0048] S2, convert the insulated bearing model into the acceleration model lnη ji = β 0-β1lnP j +β2lnV i +β3lnP j ·lnV i .

[0049] Step 2: Convert the insulated bearing model into an acceleration model;

[0050] Specifically, the general expression for the dual-stress acceleration model is: Taking the logarithm of both sides of the equation for the insulated bearing model established in step S1, we can obtain lnη. ji = (ln B + εln C) - εln P j +γln V i .

[0051] Among them, β0=lnB+εlnC, β1=-ε, β2=γ, If the acceleration model is based on the interaction of load and voltage, then the insulated bearing acceleration model is as follows:

[0052] lnη ji =β0-β1ln P j +β2ln V i +β3lnP j ·lnV i (1)

[0053] S3, parameter estimation for the dual-stress accelerated model of the insulated bearing.

[0054] Specifically, the inverse moment estimation method is used here. The insulated bearing adopts a cross-step stress constant truncation test scheme, such as... Figure 3 As shown, the parameters of the dual-stress accelerated model of the insulated bearing are estimated using the obtained experimental sample data. The process is as follows:

[0055] 1. Several basic assumptions of this invention

[0056] ① The life distribution of insulated bearings under both normal stress and accelerated stress follows the Weibull distribution;

[0057] ②The failure mechanism of the insulated bearings is the same under all stress levels;

[0058] ③ The acceleration model of the rolling bearing is the same under all stress levels;

[0059] ④ Based on Nelson's cumulative failure assumption, the remaining fatigue life of an insulated bearing depends only on the current stress level and the currently accumulated failure portion, and is independent of the accumulation method.

[0060] 2. Calculation of failure time for insulated bearing samples

[0061] Based on the above four assumptions, we can obtain in As an acceleration factor, the failure data under all level combinations are converted into lifetime data under the first level of stress using the acceleration factor, such as... Figure 4 As shown, the obtained quasi-sample data is as follows:

[0062] t1(β1,β2,β3) <t2(β1,β2,β3)<…<t r (β1,β2,β3)

[0063] 3. Inverse Moment Estimation Method for Accelerated Model Parameters

[0064] Using quasi-samples, the shape parameter m of the Weibull distribution is obtained. -1 The best unbiased estimate is:

[0065]

[0066] From the formula, we can know It contains parameters β1, β2, and β3.

[0067] S4, to test the parameters in the acceleration model.

[0068] According to assumption ①, when the failure time T follows a Weibull distribution W(m,η), T m Obey the mean lifetime R of η m If the exponential distribution E(1 / θ) is followed by:

[0069]

[0070] Then the random variables W1, W2, ..., W r Independent and identically distributed, with a mean lifetime θ of η m The exponential distribution is E(1 / θ).

[0071] Based on assumption ②, the random variables X1, X2, ..., X... r Independent and identically distributed (i.e., following an exponential distribution E1 / θ). Let... If k = 1, 2, ..., r, then we have The independent and identically distributed pairs follow an exponential distribution (1 / θ).

[0072] make

[0073] Based on assumptions ① and ②, we have:

[0074]

[0075] The samples are independently and identically distributed according to the standard exponential distribution E(1). The first-order raw moment of the standard exponential distribution is equal to 1, the second-order raw moment is equal to 2, and the third-order raw moment is equal to -6. The k-th order raw moment of the quasi-sample is:

[0076]

[0077] The system of equations can be obtained using the inverse moment estimation method:

[0078]

[0079] The system of equations (6) contains unknown parameters m and β. Substituting the estimate of m (3) into the system of equations, we can obtain the solution. These are the inverse moment estimates of β1, β2, and β3.

[0080] And W1, W2, ..., W r ~E(1 / θ), where Therefore, the quasi-sample is:

[0081]

[0082] The independent and identically distributed standard exponential distribution is E(1).

[0083] Using the idea of ​​inverse moment estimation, we get:

[0084]

[0085] Simplifying, we get:

[0086]

[0087] Will Substituting the quasi-sample (2) into (10), we can obtain

[0088] From assumption ③, we know that:

[0089]

[0090] Therefore, the estimate of β0 can be obtained as follows:

[0091]

[0092] Depend on Then the characteristic life η under the rated stress level combination (0,0) can be obtained. 00 The estimate is

[0093]

[0094] From formulas (3) and (13), we get η 00 The rated horizontal stress can then be obtained. Reliability R(t0) and reliability life t p Point estimate.

[0095] The advantages of this invention are:

[0096] 1. The accelerated life modeling and prediction method for insulated bearings described in this invention proposes a dual-stress modeling method under the coupled effects of fatigue and electrical stress. Based on the physical model of the bearing, an accelerated model is established. By simultaneously considering electrical damage and fatigue wear, accelerated testing of the insulated bearing can be performed, which can predict the life of the insulated bearing, improve the testing efficiency of insulated bearings, reduce the testing time, and solve the problems of time-consuming and inefficient conventional insulated bearing testing.

[0097] 2. This invention uses the physical model of bearings as its theoretical basis to establish an acceleration model. Subsequent model construction and derivation are all based on the physical model, ensuring that the parameters in each step of the model construction are evolutions of one or more parameters of the physical model, each with a corresponding clear physical meaning. This guarantees that the model is indeed reliable and conforms to physical theory, enabling the model to obtain accurate prediction results.

[0098] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are 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 this specification.

[0099] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for accelerated life modeling and prediction of insulated bearings, characterized in that, The accelerated life modeling and prediction method for the insulated bearing includes the following steps: S1, Constructing the Insulated Bearing Model S2, convert the insulated bearing model into the acceleration model lnη ji =β0-β1lnP j +β2lnV i +β3lnP j ·lnV i ; S3, Obtain quasi-sample data t1(β1,β2,β3) <t2(β1,β2,β3)<…<t r (β1,β2,β3), using quasi-sample data t1(β1,β2,β3) <t2(β1,β2,β3)<…<t r (β1,β2,β3) Obtain the shape parameter m of the Weibull distribution. -1 The best unbiased estimate S4, verify the parameters in the acceleration model, specifically including the following steps: S40, using Nelson's cumulative failure assumption, performs failure time conversion to obtain quasi-sample moments; S41, construct the population moments of the exponential distribution to measure the quasi-sample moments, and obtain the parameters β1, β2, β3 in the quasi-sample moments; S42, Reconstruct the parent moment to measure the characteristic life η under the first level stress. 11 Seeking S43, based on the obtained parameters β0, β1, β2, β3 and η 11 Calculate the characteristic life η of the insulated bearing under rated stress level. 00 ; S44, according to and η 00 Calculate the rated horizontal stress Reliability R(t0) and reliability life t p Point estimate; Where B is the life correlation coefficient of voltage-load coupling, ε is the coefficient in the life formula, C is the basic rated dynamic load, and P i For the i-th radial load stress level, V i For the i-th electrical stress level, β0 = lnB + εlnC, β1 = -ε. β2=γ, It is the interaction between load and voltage.

2. The accelerated life modeling and prediction method for insulated bearings as described in claim 1, characterized in that, In step S40, the specific method for calculating the quasi-sample moments using the Nelson cumulative failure assumption includes the following steps: When the failure time T follows a Weibull distribution W(m,η), T m Obey the mean lifetime θ of η m If the exponential distribution E(1 / θ) is followed, then Randomly vary W1, W2, ..., W r Independent and identically distributed, with a mean lifetime θ of η m The exponential distribution E(1 / θ); Random variables X1, X2, ..., X r Independent and identically distributed α and β follow an exponential distribution E(1 / θ), denoted as α. Then there is The independent and identically distributed pairs follow an exponential distribution (1 / θ); make but according to The k-th order raw moments of the quasi-sample are obtained as follows: The first, second, and third raw moments of the standard exponential distribution are 1, 2, and -6, respectively.

3. The accelerated life modeling and prediction method for insulated bearings as described in claim 2, characterized in that, In step S41, the specific method for constructing the population moments of the exponential distribution to measure the quasi-sample moments and obtaining the parameters β1, β2, and β3 in the quasi-sample moments includes the following steps: The system of equations is obtained based on the idea of ​​inverse moment estimation. The shape parameter m of the Weibull distribution -1 The best unbiased estimate Substitute into the system of equations Solving in, The inverse moment estimates are β1, β2, and β3, respectively.

4. The accelerated life modeling and prediction method for insulated bearings as described in claim 3, characterized in that, In step S42, the parent moment is reconstructed to measure the characteristic life η under the first level stress. 11 Seeking The specific method includes the following steps: W1,W2,…,W r ~E(1 / θ), where Therefore, quasi-sample Independent and identically distributed standard exponential distribution E(1); Using the idea of ​​inverse moment estimation, we can obtain After simplification, we get Will and substitute quasi-sample data achievable Depend on Seek 5. The accelerated life modeling and prediction method for insulated bearings as described in claim 4, characterized in that, In step S43, based on the obtained parameters as well as Calculate the characteristic life η of the insulated bearing under rated stress level. 00 The specific method includes the following steps: by Then the characteristic life η under the rated stress level combination (0,0) can be obtained. 00 The estimate is

Images