A design method for fatigue strength of bevel gears under traveling wave vibration considering test dispersion

Abstract

The present invention provides a design method for the traveling wave vibration fatigue strength of bevel gears considering the test dispersion, including: step 1, determining the position, number and distribution form of the bevel gear strain gauge patch; step 2, determining the validity of the vibration stress test data obtained by the dynamic stress test of the bevel gear; step 3, determining the maximum value of the single test data according to all the vibration stress test data with validity in step 2; step 4, repeating steps 1 to 3 to perform multiple bevel gear dynamic stress tests to obtain the maximum value of each test data; step 5, determining the maximum value of multiple test data according to the sample formed by the maximum value of each test data; step 6, evaluating the fatigue strength of the bevel gear through the Goodman high cycle fatigue and other life curves according to the maximum value of multiple test data. The present invention can reduce the risk of accidents and economic losses caused by the traveling wave vibration fatigue failure of bevel gears.

Description

Technical Field

[0001] The invention relates to the technical field of aeroengines, and in particular to a bevel gear traveling wave vibration fatigue strength design method considering test dispersion. Background Art

[0002] Aircraft engine bevel gears are important engine parts. Due to the heavy workload, high speed, and wide operating speed range, the design of bevel gear traveling wave vibration becomes a design difficulty. This vibration often has high destructive energy and strong concealment. There have been many flight accidents caused by fatigue failure of bevel gear traveling wave vibration. Therefore, dynamic stress tests on aircraft engine bevel gears have become particularly important. Although the vibration stress of some gears measured during dynamic testing is not large, gear traveling wave vibration fatigue damage has occurred in some individual engine units. When the manufacturing, assembly, and working loads are severe, the gear vibration stress has a certain increase compared to the dynamic test results. The existing evaluation methods do not fully consider the dispersion of such tests, and have not established a systematic statistical analysis method for multiple tests. The maximum vibration stress obtained in a single test is often selected for analysis and evaluation, which makes it difficult to comprehensively estimate the failure risk of gear traveling wave vibration. Summary of the invention

[0003] In view of this, the present invention provides a bevel gear traveling wave vibration fatigue strength design method taking into account test dispersion, so as to effectively improve the ability to predict the traveling wave vibration fatigue failure of the bevel gear.

[0004] The present invention provides the following technical solution: a bevel gear traveling wave vibration fatigue strength design method considering test dispersion, comprising:

[0005] Step 1: Determine the position, number and distribution of bevel gear strain gauge patches;

[0006] Step 2: Determine the validity of the vibration stress test data obtained from the bevel gear dynamic stress test;

[0007] Step 3: Determine the maximum value of the single test data based on all the valid vibration stress test data in step 2;

[0008] Step 4: Repeat steps 1 to 3 to perform multiple bevel gear dynamic stress tests to obtain the maximum value of the test data for each test;

[0009] Step 5: Determine the maximum value of the test data of multiple tests based on the sample formed by the maximum value of the test data of each test;

[0010] Step 6: Based on the maximum value of multiple test data, the fatigue strength of the bevel gear is evaluated through the Goodman high cycle fatigue isolife curve.

[0011] Furthermore, step 2 includes:

[0012] Set the average stress, use the small sample test method to test and screen the sampled samples, and eliminate the samples whose difference between the sample data and the average stress is greater than the set threshold range;

[0013] By formula Calculate the observed value of each sample data t k ,in, is the single test sample value, is the sample mean of a single trial, and S is the sample variance of a single trial;

[0014] Determine the t distribution test value when the observed value of each sample data t k When it is greater than the t-distribution test value, the vibration stress test data is valid.

[0015] Furthermore, the t distribution test value when the number of patches is n is determined according to the test significance level α .

[0016] Furthermore, step three includes: by formula Determine the maximum value of the test data for a single trial .

[0017] Furthermore, step five includes:

[0018] By formula Determine the maximum value of multiple test data. is the sample mean of m trials, is the sample variance of m trials, is the t distribution test value when the number of trials is m.

[0019] Furthermore, step one includes: the bevel gear strain gauge patch is located at the origin of the fatigue crack where the stress concentration is significant.

[0020] Furthermore, step one includes: the direction of the bevel gear strain gauge patch is perpendicular to the fatigue crack propagation direction.

[0021] Furthermore, the number of the bevel gear strain gauge patches is 6-10, and the multiple bevel gear strain gauge patches are symmetrically distributed on the bevel gear.

[0022] Compared with the prior art, the beneficial effects that can be achieved by at least one of the above-mentioned technical solutions adopted by the present invention include at least the following: the present invention adopts a small sample analysis method to consider the dispersion of the dynamic stress test of bevel gears, and the obtained analysis results cover the greater vibration stress conditions brought about by these dispersions, which are more statistically significant than the results of a single test, and reduce the risk of accidents and economic losses caused by the traveling wave vibration fatigue failure of bevel gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0024] Fig. 1 is a schematic diagram of a process of the present invention;

[0025] Figure 2 It is a schematic diagram of the number and distribution of gear patches;

[0026] Figure 3 Goodman high cycle fatigue iso-life curve considering stress concentration and safety margin;

[0027] Figure 4 It is a schematic diagram of the relationship between t distribution and normal distribution;

[0028] Figure 5 Schematic diagram of the definition of the significance level α of the t distribution. DETAILED DESCRIPTION

[0029] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0030] The following describes the implementation methods of the present application through specific specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work belong to the scope of protection of the present application.

[0031] like Figure 1 As shown, the present invention provides a bevel gear traveling wave vibration fatigue strength design method considering test dispersion, comprising:

[0032] Step 1: Determine the position, number and distribution of bevel gear strain gauge patches;

[0033] Step 2: Determine the validity of the vibration stress test data obtained from the bevel gear dynamic stress test;

[0034] Step 3: Determine the maximum value of the single test data based on all the valid vibration stress test data in step 2;

[0035] Step 4: Repeat steps 1 to 3 to perform multiple bevel gear dynamic stress tests to obtain the maximum value of the test data for each test;

[0036] Step 5: Determine the maximum value of the test data of multiple tests based on the sample formed by the maximum value of the test data of each test;

[0037] Step 6: Based on the maximum value of multiple test data, the fatigue strength of the bevel gear is evaluated through the Goodman high cycle fatigue isolife curve.

[0038] The present invention adopts a small sample statistical method to analyze the manufacturing, assembly, and working load dispersion of gears, and estimates the possible maximum fatigue stress of traveling wave vibration. On this basis, a fatigue stress assessment method considering the local stress concentration of gears is established, which can effectively improve the ability to predict the traveling wave vibration fatigue failure of bevel gears.

[0039] The specific step one is:

[0040] In order to accurately obtain the traveling wave vibration fatigue stress of the bevel gear, the bevel gear strain gauge patch should be located at the origin of the fatigue crack with significant stress concentration, and the direction of the patch should be perpendicular to the fatigue crack propagation direction.

[0041] In order to fully obtain the manufacturing and processing dispersion of the fatigue crack origin with significant stress concentration, the number of measuring points is determined to be 6 to 10. In order to minimize the self-imbalance caused by the patch, the patch distribution is symmetrical and uniform. Figure 2 A schematic diagram of the number and distribution of gear patches is given.

[0042] Step 2 includes:

[0043] Usually, the vibration stress obtained by the bevel gear dynamic stress test is at a stress level, but some data may appear to be particularly large or small, which is obviously abnormal compared with other data. At this time, the small sample t test method is used to test and screen the data that may be abnormal in the sampled samples (that is, the average stress is set, and the small sample test method is used to test and screen the sampled samples, and the samples whose difference between the sample data and the average stress is greater than the set threshold range are eliminated). The observation value t of each sample data is calculated according to the following formula k :

[0044] ;

[0045] Where: is the single test sample value, is the sample mean of a single trial, and S is the sample variance of a single trial.

[0046] Select a certain test significance level α to determine the t distribution test value , n is the number of patches (sample degrees of freedom), when tk is greater than If it is, it is a valid value; otherwise, it is invalid.

[0047] Step three includes: Determine the maximum value of the test data for a single trial .

[0048] Step 4 includes: multiple tests should be conducted on gears of the same technical status from different production batches and repeatedly assembled and disassembled to fully obtain the gear manufacturing, assembly, and working load dispersion, and estimate the maximum value of each test data according to the previous steps 1 to 3.

[0049] Step five includes:

[0050] By formula Determine the maximum value of multiple test data. is the sample mean of m trials, is the sample variance of m trials, is the t distribution test value when the number of trials is m.

[0051] Step six includes:

[0052] Considering the stress concentration and safety margin of bevel gears, the Goodman high cycle fatigue isolife curve is drawn for evaluation. The fatigue limit is selected as the lowest value of -3σ under the stress concentration factor, and the tensile strength should also be selected as the lowest value of -3σ under the stress concentration factor. The steady-state stress is the average steady-state stress along the patch direction at the patch position. According to engineering experience, the appropriate safety margin is selected. The stress value estimated in step 5 is the safety stress within the Goodman high cycle fatigue isolife curve considering the safety margin. Figure 3 A schematic diagram of Goodman high cycle fatigue isolife curve is given considering stress concentration of bevel gears.

[0053] A specific embodiment is used for description, which is as follows:

[0054] In order to accurately obtain the fatigue stress of the traveling wave vibration of the bevel gear, the bevel gear strain gauge patch position should be located at the origin of the fatigue crack, and the direction of the patch should be perpendicular to the fatigue crack propagation direction. In the case that the failure mode is not known yet, based on the crack development characteristics of the typical traveling wave vibration of the bevel gear that have been widely statistically analyzed, the gear traveling wave resonance failure morphology is similar to the pitch diameter vibration mode, and the initial crack usually originates from the bottom of the gear tooth groove where the stress is obviously concentrated. Therefore, the patch position can be determined as a patch close to the bottom of the gear tooth groove along the circumferential direction.

[0055] The characteristics of gear damage are that initial cracks initiate at the bottom of multiple gear grooves, and the cracks first expand and fall off at the weakest groove bottom. Due to differences in processing and manufacturing, the stress at the bottom of each gear tooth groove is different, and the cracks initiate and fall off first at the point where the stress at the bottom of the gear tooth groove is the largest. The direct way to find the weakest point is to paste strain gauges at the bottom of all gear tooth grooves to obtain the maximum stress. Obviously, this brings a large test cost and cycle, so it is necessary to use mathematical statistical methods to randomly select a few gear tooth groove bottoms for dynamic stress measurement. Assume that the stress at the bottom of each gear tooth groove is a random variable and obeys the normal distribution. The manufacturing and processing level at the bottom of each gear tooth groove directly affects the size of the groove bottom stress. This event is a random event. At the same time, the strain gauge patch error and test error can also be regarded as random events. Therefore, it can be assumed that the groove bottom stress is a random variable. The variable can be approximated as a normal distribution overall. The small sample random sampling variable obeys the t distribution. When the number of samples gradually increases, the probability density curve of the t distribution gradually coincides with the normal distribution. When the number of samples is small, the difference between the two is large, such as Figure 4 , the statistical error is large. In order to fully obtain the manufacturing and processing dispersion of the fatigue crack origin with significant stress concentration, the number of measuring points is determined to be 6 to 10. In order to minimize the self-unbalance caused by the patch, the patch distribution is symmetrical and uniform to reduce the error caused by the patch to the dynamic stress measurement. Figure 2 A case study on the fatigue cracks and patch positions of traveling wave vibration of bevel gears is provided. Six strain gauge patches are selected in this case, and the patches are evenly distributed symmetrically.

[0056] Usually, the vibration stress obtained by the bevel gear dynamic stress test is at a certain stress level, but some data may be particularly large or small, which is obviously abnormal compared with other data. In this case, the small sample t test method is used to test and screen the data that may have abnormalities in the sample. The test significance level is α=0.005, and the test value tα(n-1) is defined in Figure 5 , when the observed value t is greater than the test value tα(n-1), its probability of occurrence is less than 0.005. Statistically, the event is considered to be a low-probability event with no statistical significance, and the test data is an invalid test. Table 1 provides a data validity judgment case with a test significance level of α=0.005. This case is Figure 2 In this implementation case, the validity of the 6 strain gauges obtained from the test was determined, and it was found that there was no invalid data in the data of strain gauge No. 2.

[0057] Table 1 T-test analysis results of dynamic stress test results of a bevel gear

[0058]

[0059] refer to Figure 2Table 2 provides the maximum value estimate of the single test data with a significance level of α=0.005. After excluding the strain gauge No. 2 measuring point, the maximum dynamic strain is estimated to be 192 according to the statistical law of the remaining 5 measuring points. The confidence level of 99.5% means that the probability that the measured stress is less than or equal to 192 is 99.5%. The statistically estimated stress in this paper is greater than the measured stress of 181. This method is more conservative, but more statistically convincing.

[0060] Table 2 Estimation results of the maximum dynamic strain (α=0.005, number of samples 5)

[0061]

[0062] refer to Figure 2 In this paper, gears with the same technical status from different production batches and repeated assembly and disassembly are selected for multiple tests to fully obtain the dispersion of gear manufacturing, assembly and working load. The maximum value of the test data of each test is estimated according to the previous steps. This is used as sample data to estimate the maximum value of the test data of multiple tests. The results are shown in Table 3. The dynamic strain of 309 obtained through multiple tests is 16% higher than the maximum dynamic strain of 266 obtained from multiple measurements. This method is more conservative but more statistically convincing.

[0063] Table 3 shows that the present invention can effectively improve the ability to predict the fatigue failure of bevel gear traveling wave vibration. The dynamic stress of 309με obtained through multiple tests is 16% higher than the maximum value of 266με obtained through multiple actual measurements of the maximum dynamic strain, and 70% higher than the minimum dynamic strain of 181με obtained through multiple actual measurements. Therefore, the use of dynamic stress estimated by considering test dispersion can improve the failure risk assessment ability of gear traveling wave vibration, and reduce the risk of accidents and economic losses caused by fatigue failure of bevel gear traveling wave vibration.

[0064] Table 3 Estimated values ​​of traveling wave vibration stress of bevel gears considering dispersion (taking α=0.005)

[0065]

[0066] Considering the stress concentration and safety margin of bevel gears, the Goodman high cycle fatigue and other life curves are drawn for evaluation. The fatigue limit uses the lowest value of -3σ under the stress concentration factor, and the tensile strength should also use the lowest value of -3σ under the stress concentration factor. When the data under the stress concentration factor of bevel gears is missing, the data when the notch factor is 3 can be referred to based on engineering experience. The steady-state stress selects the average steady-state stress along the patch direction at the patch position. In this implementation case, the safety margin is selected as 1.67 according to engineering experience. Figure 3A schematic diagram of the Goodman high cycle fatigue isolife curve considering the stress concentration and safety factor of bevel gears is given. The stress values ​​estimated by multiple tests are within the Goodman high cycle fatigue isolife curve considering the safety margin and are within the safe stress range. When multiple tests are not performed, a safety margin of 2.5 can be selected to evaluate the fatigue strength of bevel gears based on the results of a single test.

[0067] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A bevel gear traveling wave vibration fatigue strength design method considering test dispersion, characterized in that: include: Step 1: Determine the position, number and distribution of bevel gear strain gauge patches; Step 2: Determine the validity of the vibration stress test data obtained from the bevel gear dynamic stress test; Step 3: Determine the maximum value of the single test data based on all the valid vibration stress test data in step 2; Step 4: Repeat steps 1 to 3 to perform multiple bevel gear dynamic stress tests to obtain the maximum value of the test data for each test; Step 5: Determine the maximum value of the test data of multiple tests based on the sample formed by the maximum value of the test data of each test; Step 6: According to the maximum value of the test data of the multiple tests, the fatigue strength of the bevel gear is evaluated by using the Goodman high cycle fatigue isolife curve; The second step comprises: Set the average stress, use the small sample test method to test and screen the sampled samples, and eliminate the samples whose difference between the sample data and the average stress is greater than the set threshold range; By formula Calculate the observed value of each sample data t k ,in, is the single test sample value, is the sample mean of a single trial, and S is the sample variance of a single trial; Determine the t distribution test value when the observed value of each sample data t k When it is greater than the t-distribution test value, the vibration stress test data is valid; Determine the t distribution test value when the number of patches is n according to the test significance level α .

2. The bevel gear traveling wave vibration fatigue strength design method considering test dispersion according to claim 1 is characterized in that: The step three includes: Determine the maximum value of the test data for a single trial .

3. The bevel gear traveling wave vibration fatigue strength design method considering test dispersion according to claim 2 is characterized in that: The step five comprises: By formula Determine the maximum value of multiple test data. is the sample mean of m trials, is the sample variance of m trials, is the t distribution test value when the number of trials is m.

4. The bevel gear traveling wave vibration fatigue strength design method considering test dispersion according to claim 1, characterized in that: The step 1 comprises: the bevel gear strain gauge patch is located at the origin of the fatigue crack where the stress concentration is significant.

5. The bevel gear traveling wave vibration fatigue strength design method considering test dispersion according to claim 1, characterized in that: The step 1 comprises: the direction of the bevel gear strain gauge patch is perpendicular to the fatigue crack propagation direction.

6. The bevel gear traveling wave vibration fatigue strength design method considering test dispersion according to claim 1, characterized in that: The number of bevel gear strain gauge patches is 6-10, and the multiple bevel gear strain gauge patches are symmetrically distributed on the bevel gear.

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