Calculation method for accumulated fatigue damage value of ball screw based on dynamic threshold LLC (Logical Link Control) method

Abstract

The invention discloses a ball screw accumulated fatigue damage value calculation method based on a dynamic threshold LLC method, and is applied to the technical field of ball screw pair bearing life research. Comprising the following steps: simplifying a load spectrum of a ball screw based on a dynamic threshold Level-Crossing Counting method; extracting a complete load cycle from the simplified load spectrum by using a rain flow counting method; correcting the stress cycle of the ball screw in combination with a Goodman model; and calculating an accumulated fatigue damage value caused by the corrected stress cycle on the basis of a Palmron-Miner linear accumulated damage theory. According to the method, the calculation accuracy of the accumulated fatigue damage value in the fatigue failure process of the ball screw pair is improved, and the design and performance improvement of the ball screw pair can be better guided.

Description

Technical Field

[0001] The present invention relates to the technical field of research on the load-bearing life of ball screw pairs, and more specifically, to a method for calculating the cumulative fatigue damage value of ball screws based on the dynamic threshold LLC method. Background Art

[0002] At present, the research on the load-bearing life of ball screw pairs mainly focuses on cyclic variable loads. However, in the actual operation of ball screws, cyclic variable loads are rarely used, and mainly non-cyclic variable loads that change rapidly are applied. When studying the fatigue failure mechanism of ball screw pairs, there is a large gap between the theoretically calculated load-bearing load type in the traditional fatigue damage value calculation model and the actual working load. In order to calculate the cumulative fatigue damage value of ball screw pairs more accurately, in the existing technical solutions, the cumulative fatigue damage value of ball screw pairs is calculated based on the dynamic threshold Level-Crossing Counting method. At present, during the load-bearing life of ball screw pairs, only the Level-Crossing Counting method and the rain flow counting method exist, and the research on their combination is less, and the dynamic threshold is rarely used. The relevant direction mainly lies in using the single rain flow counting method to calculate the number of load cycles, and there is little research on calculating the number of load cycles by combining the dynamic threshold Level-Crossing Counting method and the rain flow counting method. Therefore, how to provide a method for calculating the cumulative fatigue damage value of ball screws based on the dynamic threshold LLC method is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0003] In view of this, the present invention provides a method for calculating the cumulative fatigue damage value of ball screws based on the dynamic threshold LLC method, which improves the accuracy of calculating the cumulative fatigue damage value during the failure process of ball screw pairs and better guides the process and design applications of related functional components.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] A method for calculating the cumulative fatigue damage value of ball screws based on the dynamic threshold LLC method, comprising the following steps:

[0006] S1. Simplify the load spectrum of the ball screw based on the dynamic threshold Level-Crossing Counting method;

[0007] S2. Extract complete load cycles from the simplified load spectrum using the rain flow counting method;

[0008] S3. Correct the stress cycle of the ball screw in combination with the Goodman model;

[0009] S4. Calculate the cumulative fatigue damage value caused by the corrected stress cycle based on the Palmgren-Miner linear cumulative damage theory.

[0010] Optionally, S1 is specifically:

[0011] S11. Set a reference threshold, taking the average value of the load sequence as the reference threshold. At the same time, based on the sliding window statistical method, calculate the local load mean and standard deviation in real time, and dynamically adjust the reference threshold:

[0012]

[0013] In the formula, is the local load mean, represents the reference threshold within window t, represents the local load mean within window t, S i is the i-th load in the load sequence, n is the total number of loads in the load sequence, r is the dynamic adjustment coefficient, σ t is the standard deviation;

[0014] S12. Set a secondary level value, taking the average value of the load change amount in the load sequence as the secondary level value:

[0015]

[0016] In the formula, is the average value of the load change amount, ΔS j is the j-th load change amount, ΔS = |S i+1 -S i |, S i+1 is the (i + 1)-th load in the load sequence, S i is the i-th load in the load sequence, K is the total number of load change amounts;

[0017] S13. Count the number of positive and negative crossings of the threshold in the load history:

[0018]

[0019] In the formula, m is the number of times of crossing the threshold, and Δi is the number of cycles of the i-th time of crossing the threshold;

[0020] S14. Generate a simplified load sequence:

[0021]

[0022] In the formula, S(t) is the original load value of the load sequence, is the reference threshold, is the secondary level value.

[0023] Optionally, S2 is specifically:

[0024] S21. Convert the simplified load sequence into a peak-valley point sequence:

[0025] P = [P1, P2, P3, …, P M

[0026] S22. Sequentially extract P i , P i+1 , P i+2 , P i+3 , and at the same time satisfy:

[0027] |P i+1 - P i | ≥ |P i+2 - P i+1 |

[0028] |P i+3 - P i+2 | ≥ |P i+2 - P i+1 |

[0029] Then extract the cyclic amplitude mean value Remove P i+1 and P i+2 ;

[0030] S23. Statistically analyze all the extracted cycles to form a cycle matrix:

[0031]

[0032] In the formula, K is the total number of cycles, n (k) is the number of repetitions of the kth cycle, is the amplitude of the kth cycle, is the mean value of the kth cycle, δ is an indicator function, which is 1 when the condition is satisfied and 0 when the condition is not satisfied.

[0033] Optionally, S3 is specifically:

[0034] S31. Damage calculation based on the S-N curve:

[0035] S m ·N = C

[0036] In the formula, S is the load amplitude, N is the maximum number of cyclic loads corresponding to the load, m is the Wohler index, and C is a constant;

[0037] S32. Use the Goodman curve to correct the damage:

[0038] ​

[0039] Wherein, S ai is the amplitude value of the i-th cycle calculated in the first step, S i is the load amplitude value when the equivalent mean value is 0, S mi is the mean value of the i-th cycle calculated in the first step, and σ b is the maximum load value at the tensile fracture of the material.

[0040] Optionally, S4 is specifically:

[0041] Calculate the cumulative fatigue damage value caused by the corrected stress cycle based on the Palmgren-Miner linear cumulative damage theory:

[0042]

[0043] Wherein, D total is the cumulative fatigue damage value, α is the correction coefficient, and D noise is the equivalent damage value caused by the filtered noise, N(σ a , σ m ) is the reference life at the amplitude mean value H ij is the element in the cycle matrix, representing the number of cycles satisfying the amplitude in the interval i and the mean value in the interval j, N is the number of amplitude intervals, and M is the number of mean value intervals. is the amplitude of the i-th cycle, is the mean value of the j-th cycle.

[0044] Optionally, the equivalent damage value caused by the filtered noise is specifically:

[0045]

[0046] Wherein, Δt is the load application time, PSD(f k ) is the power at the frequency f k , and N ref (f k ) is the reference life corresponding to the frequency f k .

[0047] Optionally, the reference life of each cycle is specifically:

[0048]

[0049] Wherein, σ' f is the fatigue strength coefficient, and b is the fatigue strength index.

[0050] As can be seen from the above technical solutions, compared with the prior art, the present invention provides a method for calculating the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method, which has the following beneficial effects:

[0051] 1. Through the dynamic threshold Level-Crossing Counting method and the rainflow counting method, the present invention simplifies the load spectrum and filters noise for rapidly changing non-periodic loads based on the dynamic threshold Level-Crossing Counting method, calculates the simplified load spectrum using the rainflow counting method, and constructs a complete load cycle counting model;

[0052] 2. Based on the S-N curve, the present invention optimizes the cycle of fatigue failure of the ball screw pair using the Goodman model;

[0053] 3. Based on the Palmgren-Miner linear cumulative damage theory, the present invention improves the calculation of the cumulative fatigue damage value caused by each cycle, takes into account the damage caused by the filtered noise, and can calculate the fatigue damage value of the ball screw more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the provided drawings.

[0055] Figure 1 It is a flow chart of the method for calculating the cumulative fatigue damage value of the ball screw of the present invention;

[0056] Figure 2 It is a comparison diagram of the original load and the simplified load in the embodiment of the present invention;

[0057] Figure 3 It is a schematic diagram of the H matrix in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0059] The embodiment of the present invention discloses a method for calculating the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method, as Figure 1As shown in the figure, it includes the following steps:

[0060] S1. Simplify the load spectrum of the ball screw based on the dynamic threshold Level-Crossing Counting method;

[0061] S2. Extract complete load cycles from the simplified load spectrum using the rainflow counting method;

[0062] S3. Correct the stress cycles of the ball screw in combination with the Goodman model;

[0063] S4. Calculate the cumulative fatigue damage value caused by the corrected stress cycles based on the Palmgren-Miner linear cumulative damage theory.

[0064] Furthermore, S1 is specifically as follows:

[0065] S11. Set a reference threshold, use the average value of the load sequence as the reference threshold, and at the same time, based on the sliding window statistical method, calculate the local load mean and standard deviation in real time, and dynamically adjust the reference threshold:

[0066]

[0067] In the formula, is the local load mean, represents the reference threshold within window t, represents the local load mean within window t, S i is the i-th load in the load sequence, n is the total number of loads in the load sequence, r is the dynamic adjustment coefficient, σ t is the standard deviation;

[0068] S12. Set a secondary level value, use the average value of the load change amount in the load sequence as the secondary level value:

[0069]

[0070] In the formula, is the average value of the load change amount, ΔS j is the j-th load change amount, ΔS = |S i+1 -S i |, S i+1 is the (i + 1)-th load in the load sequence, S i is the i-th load in the load sequence, K is the total number of load change amounts;

[0071] S13. Count the positive and negative crossing times exceeding the threshold in the load history:

[0072]

[0073] Where m is the number of times of crossing the threshold, and Δi is the number of cycles for the i-th time of crossing the threshold;

[0074] S14. Generate a simplified load sequence:

[0075]

[0076] Where S(t) is the original load value of the load sequence, is the reference threshold, is the secondary level value. In the embodiments of the present invention, the comparison between the original load and the simplified load is as Figure 2 shown.

[0077] Further, S2 is specifically:

[0078] S21. Convert the simplified load sequence into a peak-valley point sequence:

[0079] P = [P1, P2, P3, …, P M

[0080] S22. Sequentially extract P i , P i+1 , P i+2 , P i+3 , and at the same time satisfy:

[0081] |P i+1 - P i | ≥ |P i+2 - P i+1 |

[0082] |P i+3 - P i+2 | ≥ |P i+2 - P i+1 |

[0083] Then extract the cycle amplitude mean value Remove P i+1 and P i+2 ;

[0084] S23. Statistically analyze all the extracted cycles to form a cycle matrix:

[0085]

[0086] Where K is the total number of cycles, n (k) is the number of repetitions of the k-th cycle, is the amplitude of the k-th cycle, is the mean value of the k-th cycle, δ is an indicator function, which is 1 when the condition is satisfied and 0 when the condition is not satisfied. In the embodiments of the present invention, the cycle matrix is as​Figure 3 as shown

[0087] Further, S3 is specifically as follows:

[0088] S31. Damage calculation based on the S-N curve:

[0089] S m ·N = C

[0090] In the formula, S is the load amplitude, N is the maximum cyclic load times corresponding to the load, m is the Wohler exponent, and C is a constant;

[0091] S32. Use the Goodman curve to correct the damage:

[0092]

[0093] In the formula, S ai is the amplitude of the i-th cycle calculated in the first step, S i is the load amplitude when the equivalent mean value is 0, S mi is the mean value of the i-th cycle calculated in the first step, σ b is the maximum load value at the tensile fracture of the material.

[0094] Further, S4 is specifically as follows:

[0095] Calculate the cumulative fatigue damage value caused by the corrected stress cycle based on the Palmgren-Miner linear cumulative damage theory:

[0096]

[0097] In the formula, D total is the cumulative fatigue damage value, α is the correction coefficient, D noise is the equivalent damage value caused by the filtered noise, N(σ a ,σ m ) is the reference life under the amplitude mean value H ij is the element in the cycle matrix, representing the number of cycles satisfying the amplitude in the interval i and the mean value in the interval j, N is the number of amplitude intervals, M is the number of mean value intervals, is the amplitude of the i-th cycle, is the mean value of the j-th cycle.

[0098] Further, the equivalent damage value caused by the filtered noise is specifically as follows:

[0099]

[0100] In the formula, Δt is the load application time, PSD(fk ) is the power at frequency f k , and N ref (f k ) is the reference life corresponding to frequency f k .

[0101] Furthermore, the reference life of each cycle is specifically as follows:

[0102]

[0103] In the formula, σ' f is the fatigue strength coefficient, and b is the fatigue strength index.

[0104] Furthermore, in an embodiment of the present invention, the dynamic threshold Level-Crossing Counting method is combined with the rainflow counting method. The number of load points calculated by the rainflow counting method is 200, and the simplified number of load points is 140, with a compression rate reaching 30%. At the same time, cycle correction is performed using the Goodman model. Finally, according to Palmgren-Miner linear cumulative damage, the cumulative fatigue damage value caused by each cycle is effectively calculated theoretically, considering the damage caused by noise, and the cumulative fatigue damage value of the ball screw can be calculated more accurately.

[0105] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other.

[0106] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A calculation method for the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method, characterized in that, It includes the following steps: S1. Simplify the load spectrum of the ball screw based on the dynamic threshold Level-Crossing Counting method; S2. Extract complete load cycles from the simplified load spectrum using the rainflow counting method; S3. Correct the stress cycles of the ball screw in combination with the Goodman model; S4. Calculate the cumulative fatigue damage value caused by the corrected stress cycles based on the Palmgren-Miner linear cumulative damage theory.

2. A calculation method for the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method according to claim 1, characterized in that, Specifically, S1 is as follows: S11. Set a reference threshold, take the average value of the load sequence as the reference threshold, and at the same time, based on the sliding window statistical method, calculate the local load mean and standard deviation in real time and dynamically adjust the reference threshold: In the formula, is the local load mean value, represents the reference threshold within window t, represents the local load mean value within window t, S i is the i-th load in the load sequence, n is the total number of loads in the load sequence, r is the dynamic adjustment coefficient, σ t is the standard deviation; S12. Set a secondary level value, take the average value of the load change amount in the load sequence as the secondary level value: Wherein, is the average value of the load change amount, and ΔS j is the j-th load change amount, ΔS = |S i+1 - S i |, S i+1 is the (i + 1)-th load in the load sequence, S i is the i-th load in the load sequence, and K is the total number of load change amounts; S13. Count the number of positive and negative crossings exceeding the threshold in the load history: In the formula, m is the number of times of crossing the threshold, and Δi is the number of cycles of the i-th crossing the threshold; S14. Generate a simplified load sequence: where S(t) is the original load value of the load sequence, is the reference threshold, is the secondary level value.

3. A calculation method for the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method according to claim 1, characterized in that Specifically, S2 is as follows: S21. Convert the simplified load sequence into a peak-valley point sequence: P = [P1, P2, P3, …, P M ​ S22. Extract P from the peak-valley point sequence in turn i , P i+1 , P i+2 , P i+3 , while satisfying: |P i+1 -P i |≥|P i+2 -P i+1 | |P i+3 -P i+2 |≥|P i+2 -P i+1 | Then extract the cyclic amplitude Mean value Remove P i+1 and P i+2 ; S23. Count all the extracted cycles to form a cycle matrix: where K is the total number of cycles, and n (k) is the number of repetitions in the k-th cycle, is the amplitude in the k-th cycle, is the mean value in the k-th cycle, δ is an indicator function, which is 1 when the condition is satisfied and 0 when the condition is not satisfied.

4. A calculation method for the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method according to claim 1, characterized in that Specifically, S3 is as follows: S31. Damage calculation based on the S-N curve: S m ·N=C In the formula, S is the load amplitude, N is the maximum cyclic load number corresponding to the load, m is the Wohler index, and C is a constant; S32. Correct the damage using the Goodman curve: where S ai is the amplitude of the i-th cycle calculated in the first step, S i is the load amplitude when the equivalent mean value is 0, S mi is the mean value of the i-th cycle calculated in the first step, and σ b is the maximum load value of the material at tensile fracture.

5. A calculation method for the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method according to claim 1, characterized in that Specifically, S4 is as follows: Calculate the cumulative fatigue damage value caused by the corrected stress cycles based on the Palmgren-Miner linear cumulative damage theory: Where D total is the cumulative fatigue damage value, α is the correction coefficient, D noise is the equivalent damage value caused by the filtered noise, N(σ a , σ m ) is the reference life under the amplitude mean value , H ij is the element in the cyclic matrix, representing the number of cycles that satisfy the amplitude in the interval i and the mean value in the interval j, N is the number of amplitude intervals, M is the number of mean value intervals, is the amplitude of the i-th cycle, is the mean value of the j-th cycle.

6. A calculation method for the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method according to claim 5, characterized in that The equivalent damage value caused by the filtered noise is specifically: where Δt is the load application time, PSD(f k ) is the power at frequency f k , and N ref (f k ) is the reference life corresponding to frequency f k .

7. A calculation method for the cumulative fatigue damage value of a ball screw based on the dynamic threshold LLC method according to claim 5, characterized in that, The reference life of each cycle is specifically: where σ' f is the fatigue strength coefficient and n is the fatigue strength exponent.

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