A method for adaptive determination of the failure time of a rolling bearing

Abstract

The present application belongs to the technical field of failure time determination, and discloses a kind of adaptive determination method of rolling bearing failure time, which includes the following steps: calculating rolling bearing health index increment;Gaussian processing rolling bearing health index increment;The mean and standard deviation estimation of health index increment after Gaussian processing is carried out;Based on 6-sigma rule, the upper and lower limits of the adaptive failure threshold of rolling bearing are calculated;Combined with the failure threshold, the continuous trigger mechanism is used to finally determine the failure time of rolling bearing.The present application can adaptively determine the failure threshold and corresponding failure time of rolling bearing, is not limited to the fixed failure threshold given by human, is not affected by equipment difference and working condition difference, and has the characteristics of self-adaptation in the determination process of rolling bearing failure time.

Description

Technical Field

[0001] This invention belongs to the field of failure time determination technology, and particularly relates to an adaptive method for determining the failure time of rolling bearings. Background Technology

[0002] In industrial manufacturing and testing, rolling bearing failure is an unavoidable occurrence in equipment. To ensure safe operation and extend the service life of equipment, it is necessary to reasonably determine the bearing failure threshold. The failure threshold refers to the value at which a certain indicator will cause the equipment to malfunction and shut down. By reasonably determining the failure threshold, equipment shutdown can be triggered in a timely manner, preventing accidents and ensuring the smooth operation of the production process.

[0003] Determining the failure threshold is crucial for the safe conduct of fatigue failure experiments and the calculation of the total service life of equipment bearings. Fatigue failure experiments require prolonged operation and testing of equipment bearings to determine the failure threshold of rolling bearings, enabling timely shutdown and ensuring experimental safety. Furthermore, the failure threshold is a critical parameter in predicting the remaining service life of rolling bearings. By rationally determining the failure threshold, the remaining service life of equipment bearings can be calculated more accurately, providing a basis for equipment maintenance and upkeep.

[0004] However, determining the failure threshold presents certain difficulties and challenges. Traditional failure thresholds are determined through experience and regulations, lacking scientific basis and reliability. Furthermore, failure thresholds may vary under different operating conditions and with different equipment, requiring adjustments and optimizations for different situations. Therefore, a scientific method and technology are needed to adaptively determine the failure threshold and corresponding failure time of rolling bearings. Summary of the Invention

[0005] To address the problems existing in current technologies, particularly regarding the determination of rolling bearing failure time, this invention proposes an adaptive method for determining rolling bearing failure time. The incremental data of rolling bearing health indicators are Gaussianized, and the upper and lower limits of the bearing failure threshold are obtained based on the 6-sigma criterion. A continuous triggering mechanism is then employed to adaptively determine the failure time of the rolling bearing. This method can adaptively determine the failure threshold and corresponding failure time of rolling bearings, without being limited by a manually given fixed failure threshold. Furthermore, it is unaffected by differences in equipment and operating conditions, exhibiting adaptive characteristics in the determination of rolling bearing failure time.

[0006] The technical solution of this invention is as follows:

[0007] An adaptive method for determining the failure time of a rolling bearing includes the following steps:

[0008] Step 1: Calculate the increment of rolling bearing health indicators;

[0009] ΔHI(t)=HI(t)-HI(t-1) (1)

[0010] Where HI(t) is the value of the rolling bearing health index HI at time t, and ΔHI(t) is the increment of the rolling bearing health index at time t;

[0011] Step 2: Gaussianize the incremental health indicators of rolling bearings;

[0012]

[0013] Where, ΔHI (ξ) This is the result after Gaussianizing the incremental health index of rolling bearings; ε is a small positive number; ξ is solved using the maximum likelihood estimation method.

[0014] The log-likelihood function for solving ξ is derived as follows:

[0015]

[0016] Where lnL(ξ) is the log-likelihood function with respect to ξ, and ΔHI (ξ) (t) represents ΔHI (ξ) At time t, N is the total time length; when formula (3) reaches its maximum value, the corresponding ξ is the final solution result;

[0017] Step 3: Estimate the mean and standard deviation;

[0018] After Gaussianizing the increment of rolling bearing health indicators, the resulting ΔHI (ξ) It follows a normal distribution with mean μ and standard deviation σ, i.e., ΔHI (ξ) ~N(μ,σ 2 Regarding μ and σ 2 The likelihood function is:

[0019]

[0020] lnL(μ,σ) 2 |ΔHI (ξ) ) respectively with respect to μ and σ 2 Find the partial derivatives and set them to zero. The corresponding likelihood equations are derived as follows:

[0021]

[0022] Solving formula (5) yields μ and σ. 2 The maximum likelihood estimates are as follows:

[0023]

[0024] Step 4: Calculate the adaptive failure threshold;

[0025] Based on the 6-sigma criterion, the upper and lower limits of the adaptive failure threshold for rolling bearings are as follows:

[0026]

[0027] Step 5: Determine the failure time of the rolling bearing;

[0028] A continuous triggering mechanism is adopted, that is, when l+1 consecutive ΔHI (ξ) Value in the interval [T] down ,T up When the bearing fails outside the specified range, the formula for determining the bearing failure time is as follows:

[0029] T = inf{t{ΔHI} (ξ) (t-τ)} τ＝0:l ≥T up ∪{ΔHI (ξ) (t-τ)} τ＝0:l ≤T down} (8)

[0030] Where T is the failure time of the rolling bearing, and inf{·} denotes the infimum; {ΔHI (ξ) (t-τ)} τ＝0:l It contains l+1 elements, and the value of τ is in the range of 0, 1, 2...l, where l is a positive integer.

[0031] The incremental data of rolling bearing health indicators are Gaussianized, and the upper and lower limits of the adaptive failure threshold of rolling bearings are obtained based on the 6-sigma criterion. A continuous triggering mechanism is adopted to determine the time corresponding to the occurrence of rolling bearing failure.

[0032] The beneficial effects of this invention are as follows: This invention proposes an adaptive method for determining the failure time of rolling bearings. This method can automatically adjust the failure threshold according to different working conditions and load conditions to flexibly cope with different working conditions and usage environments of rolling bearings. It provides theoretical guidance for determining the failure shutdown time during accelerated fatigue testing of rolling bearings, and also provides an important reference for timely failure warning of mechanical equipment in actual production operation. Attached Figure Description

[0033] Figure 1 This is a flowchart of an adaptive method for determining the failure time of a rolling bearing provided by the present invention;

[0034] Figure 2 These are the original vibration signal data of the rolling bearing throughout its entire lifespan in this embodiment of the invention;

[0035] Figure 3 These are health indicators in embodiments of the present invention;

[0036] Figure 4 This is the rolling bearing failure time determined in the embodiments of the present invention. Detailed Implementation

[0037] The specific embodiments of the present invention are described in detail below with reference to the technical solutions and accompanying drawings.

[0038] This embodiment presents an adaptive method for determining the failure time of a rolling bearing. Figure 1 This flowchart illustrates the adaptive method for determining the failure time of a rolling bearing, including the following steps:

[0039] Step 1: Calculate the increment of rolling bearing health indicators;

[0040] Collect acceleration and vibration signal data of rolling bearings throughout their entire lifespan, such as... Figure 2 As shown; specifically, in this embodiment, the accelerated fatigue test bench for rolling bearings is the PRONOSTIA test platform; the effective value of the original vibration signal data of the rolling bearing is used as a health indicator of the rolling bearing performance degradation process, such as... Figure 3 As shown; then calculate the increment of the rolling bearing health index:

[0041] ΔHI(t)=HI(t)-HI(t-1) (9)

[0042] Where HI(t) is the value of the rolling bearing health index HI at time t, and ΔHI(t) is the increment of the rolling bearing health index at time t;

[0043] Step 2: Gaussianize the incremental health indicators of rolling bearings;

[0044]

[0045] Where, ΔHI (ξ) This is the result after Gaussianizing the incremental health index of rolling bearings; ε is a small positive number; ξ is solved using the maximum likelihood estimation method.

[0046] The log-likelihood function for solving ξ is derived as follows:

[0047]

[0048] Where, ln L(ξ) is the log-likelihood function with respect to ξ, and ΔHI (ξ) (t) represents ΔHI (ξ) At time t, N is the total time length; when formula (3) reaches its maximum value, the corresponding ξ is the final solution result;

[0049] Step 3: Estimate the mean and standard deviation;

[0050] After Gaussianizing the increment of rolling bearing health indicators, the resulting ΔHI (ξ) It follows a normal distribution with mean μ and standard deviation σ, i.e., ΔHI (ξ) ~N(μ,σ 2 Regarding μ and σ 2 The likelihood function is:

[0051]

[0052] lnL(μ,σ) 2 |ΔHI (ξ) ) respectively with respect to μ and σ 2 Find the partial derivatives and set them to zero. The corresponding likelihood equations are derived as follows:

[0053]

[0054] Solving formula (13) yields μ and σ. 2 The maximum likelihood estimates are as follows:

[0055]

[0056] Step 4: Calculate the adaptive failure threshold;

[0057] Based on the 6-sigma criterion, the upper and lower limits of the adaptive failure threshold for rolling bearings are as follows:

[0058]

[0059] Step 5: Determine the failure time of the rolling bearing;

[0060] A continuous triggering mechanism is adopted, that is, when l+1 consecutive ΔHI (ξ) Value in the interval [T] down ,T up When the bearing fails outside the specified range, the formula for determining the bearing failure time is as follows:

[0061] T = inf{t{ΔHI} (ξ) (t-τ)} τ＝0:l ≥T up ∪{ΔHI (ξ) (t-τ)} τ＝0:l ≤T down} (16)

[0062] Where T is the failure time of the rolling bearing, and inf{·} denotes the infimum; {ΔHI (ξ) (t-τ)} τ＝0:lIt contains l+1 elements, and the value of τ ranges from 0, 1, 2…l, where l is a positive integer; the failure time determination of the rolling bearing is as follows: Figure 4 As shown.

[0063] Specifically, such as Figure 4 As shown, the upper and lower limits of the adaptive failure threshold of the rolling bearing are -0.1734 and -1.4904, respectively, and the identified failure time of the rolling bearing is 4260s. The proposed method can adaptively determine the failure threshold and corresponding failure time of the rolling bearing, without being limited by a fixed failure threshold given by humans, and is not affected by differences in equipment and operating conditions. It has the characteristic of being adaptive in the process of determining the failure time of the rolling bearing.

[0064] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and should not be construed as limiting the present invention. Those skilled in the art can make modifications and substitutions to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. An adaptive method for determining the failure time of a rolling bearing, characterized in that, Includes the following steps: Step 1: Calculate the increment of rolling bearing health indicators; ΔHI(t)=HI(t)-HI(t-1) (1) Where HI(t) is the value of the rolling bearing health index HI at time t, and ΔHI(t) is the increment of the rolling bearing health index at time t; Step 2: Gaussianize the incremental health indicators of rolling bearings; Where, ΔHI (ξ) This is the result after Gaussianizing the incremental health index of rolling bearings; ε is a small positive number; ξ is solved using the maximum likelihood estimation method. The log-likelihood function for solving ξ is derived as follows: Where lnL(ξ) is the log-likelihood function with respect to ξ, and ΔHI (ξ) (t) represents ΔHI (ξ) At time t, N is the total time length; when formula (3) reaches its maximum value, the corresponding ξ is the final solution result; Step 3: Estimate the mean and standard deviation; After Gaussianizing the increment of rolling bearing health indicators, the resulting ΔHI (ξ) It follows a normal distribution with mean μ and standard deviation σ, i.e., ΔHI (ξ) ~N(μ,σ 2 Regarding μ and σ 2 The likelihood function is: lnL(μ,σ) 2 |ΔHI (ξ) ) respectively with respect to μ and σ 2 Find the partial derivatives and set them to zero. The corresponding likelihood equations are derived as follows: Solving formula (5), we obtain μ and σ. 2 The maximum likelihood estimates are as follows: Step 4: Calculate the adaptive failure threshold; Based on the 6-sigma criterion, the upper and lower limits of the adaptive failure threshold for rolling bearings are as follows: Step 5: Determine the failure time of the rolling bearing; A continuous triggering mechanism is adopted, that is, when l+1 consecutive ΔHI (ξ) Value in the interval [T] down ,T up When outside the range, The formula for determining the bearing failure time when a rolling bearing fails is expressed as follows: T=inf{t|{ΔHI (ξ) (t-τ)} τ＝0:l ≥T up ∪{ΔHI (ξ) (t-τ)} τ＝0:l ≤T down } (8) Where T is the failure time of the rolling bearing, and inf{·} denotes the infimum; {ΔHI (ξ) (t-τ)} τ＝0:l It contains l+1 elements, and the value of τ is in the range of 0, 1, 2...l, where l is a positive integer.

2. The adaptive method for determining the failure time of a rolling bearing according to claim 1, characterized in that, The incremental health indicators are Gaussianized, and the upper and lower limits of the adaptive failure threshold of the rolling bearing are obtained based on the 6-sigma criterion. A continuous triggering mechanism is used to determine the time corresponding to the occurrence of rolling bearing failure.

Images