Analysis method for key parameters of a fighter structure DFR

Abstract

The application provides a method for analyzing key parameters of a fighter structure DFR, including determination of a fighter DFR reference stress ratio, including load spectrum processing and damage calculation; determination of a fighter DFR reference life; and influence of an S-N curve form on DFR calculation results, so that the method has the advantages that a load spectrum of multiple fighters is analyzed based on a Miner theory, key parameters such as a fighter DFR reference stress ratio and a reference life are determined from the perspective of damage accumulation, errors generated in a derivation process of a DFR expression are analyzed from the perspective of fatigue damage, influence of an S-N curve form on DFR calculation results is researched, and a reference for selection of DFR basic assumptions is provided.

Description

Technical Field

[0001] This invention belongs to the field of engineering equipment durability design technology, and specifically relates to a DFR analysis method for fighter jet structural durability. Background Technology

[0002] In the 1980s, Boeing proposed the Detail Fatigue Rating (DFR) method for durability (fatigue) design of large civil transport aircraft. The DFR method is not only simple and reliable, and easy for designers to accept and master, but more importantly, it allows for durability assessment of all fatigue-critical components in the preliminary design stage of new aircraft, significantly improving design efficiency and quality. For this reason, the DFR method also has broad development prospects in other engineering fields. However, directly applying the civil aircraft DFR method is not advisable, because the core essence of the civil aircraft DFR method lies in objectively and accurately characterizing the inherent fatigue performance and life loss patterns of a structure under civil aircraft service conditions. In different engineering fields, the usage requirements and service conditions of structures cannot be treated uniformly, and materials will exhibit different fatigue properties. Therefore, if the civil aircraft DFR method is used indiscriminately for structural durability design under different engineering backgrounds, then DFR cannot objectively and accurately characterize the inherent fatigue performance and life loss patterns of the structure under different service conditions, which is tantamount to trying to find a sword by marking the boat where it fell into the water. The scientific approach is to first thoroughly analyze the similarities and differences in the design intent and usage methods of structures in different engineering fields, and then make appropriate adjustments to the key parameters of the DFR method for civil aircraft to make it applicable to different engineering fields.

[0003] Based on the DFR method for civil aircraft, the DFR for fighter jets is defined as: the basic reliability requirement of 99.9% reliability at a 90% confidence level of a log-normal distribution during service life when the stress ratio R = 0.1, which can reach 5 × 10 4 The maximum stress (MPa) of the second cycle. The literature initially established the DFR method suitable for fighter jet durability analysis, contributing new ideas to the durability design of fighter jet structures. However, in practical applications, industry sectors have found that, compared with methods such as the nominal stress method and the stress severity coefficient method, structures designed using this method have excessive fatigue margins and prominent overweight issues. The reason for this is that the key DFR parameters for fighter jets given in the literature are not accurate enough and cannot truly reflect the inherent fatigue performance and life loss characteristics of the structure under fighter jet flight load conditions.

[0004] Besides the differences in key parameters, the fundamental assumptions of the DFR method for civil aircraft and fighter jets also differ significantly. These fundamental assumptions include the form of the SN curve and the form of the isochronous lifetime curve. The differences in these fundamental assumptions do not affect the correctness and feasibility of the two DFR methods, as these assumptions are derived from years of experience in their respective fields. However, if the fundamental assumptions do not match the material properties or actual conditions, the accuracy of the DFR calculation will be affected. Research on the influence of the lifetime curve form on the DFR calculation results shows that the DFR method based on the Goodman model is suitable for brittle materials, while the DFR method based on the Gerber model is suitable for ductile materials. Existing technologies have derived DFR expressions based on different SN curve forms, but the impact of the SN curve form on the DFR calculation results has not been discussed in depth. Currently, research on the isochronous lifetime curve in the fundamental assumptions of DFR is relatively abundant, while the discussion on the SN curve is insufficient. The exact impact of the SN curve form on the DFR calculation results remains unclear. Summary of the Invention

[0005] This invention proposes an analysis method for key parameters of the damping force ratio (DFR) of fighter jet structures, studying the selection principles and methods of the DFR reference stress ratio from the perspectives of theoretical analysis and engineering applications. Then, based on Miner's theory, the load spectra of various fighter jets are analyzed, and key parameters such as the DFR reference stress ratio and reference life are determined from the perspective of damage accumulation. Finally, the errors generated in the derivation of the DFR expression are analyzed from the perspective of fatigue damage, and the influence of the SN curve form on the DFR calculation results is studied, providing a reference for the selection of basic assumptions of DFR.

[0006] The technical solution of this invention is implemented as follows: a method for analyzing key parameters of the DFR (Device Frame Reduction) of a fighter jet structure, including...

[0007] Determining the DFR reference stress ratio for fighter jets includes load spectrum processing and damage calculation;

[0008] Determining the DFR (Depth Free) reference life of fighter jets;

[0009] The influence of the SN curve form on the DFR calculation results;

[0010] Load spectrum processing includes processing the test spectrum or design spectrum. The peak and valley overload values ​​and their pairings of the test spectrum are given, and damage calculation and damage distribution can be directly performed. The design spectrum requires high load truncation, low load truncation, interpolation selection, and peak and valley pairing before damage calculation and damage distribution analysis.

[0011] The impact of the SN curve form on DFR calculation results includes the derivation and analysis of DFR expressions based on different SN curve forms, and error analysis of the DFR expression derivation process. The derivation and analysis of DFR expressions based on different SN curve forms includes the derivation of DFR expressions based on SN curves with a constant stress ratio, the derivation of DFR expressions based on SN curves with a constant mean stress, and analysis of DFR calculation results based on different SN curve forms. The error analysis of the DFR expression derivation process includes the equivalent overload calculation method based on equal-life curves, the error analysis of the DFR expression derivation process based on SN curves with a constant stress ratio, the error analysis of the DFR expression derivation process based on SN curves with a constant mean stress, and error analysis of DFR calculation.

[0012] In a preferred embodiment, the overload removal method is based on fitting the design spectrum data to obtain a frequency exceedance curve according to the following calculation formula, and then determining the load corresponding to a frequency of 10 through interpolation, and deleting overloads greater than this load:

[0013] lg[F(n z )]=a0+a1n z +a2n z 2 +a3n z 3 +a4lg(n z )

[0014] Where, n z For overload at each stage of the load spectrum; F(n) z ) represents the cumulative frequency of each overload level; a0, a1, a2, a3, and a4 are the fitting coefficients;

[0015] The low-load interception adopts the overload cutoff ratio criterion method applied to low-load interception of fighter jets and takes a value of 3, that is, the loads less than 1 / 3 of the maximum overload after high-load interception are deleted.

[0016] Interpolation with a step size of 0.1g is used to obtain the corresponding cumulative frequency.

[0017] As a preferred implementation, according to Miner's linear damage accumulation theory, the expression for fatigue damage D is:

[0018]

[0019] In the formula: Δσ i =σ max，i -σ min，i , is the load range of the i-th cycle; R i =σ min，i / σ max，i σ is the stress ratio in the i-th cycle.dl，i It is the equivalent overload converted to the pulsating cycle in the i-th cycle. The subscript dl represents the equivalent overload, and m is the damage index.

[0020] σ dl，i The calculation uses the Odin transformation formula, which is as follows:

[0021]

[0022] 0.08 was chosen as the DFR benchmark stress ratio for fighter jets.

[0023] As a preferred implementation, the determination of the fighter jet's DFR reference life requires converting the random load spectrum into an equal amplitude spectrum while adhering to the principle of equal damage. Given that the fighter jet's DFR reference stress ratio is already determined to be 0.08, two additional parameters need to be determined: the peak value of the equal amplitude spectrum and the number of cycles. The specific operation steps are as follows:

[0024] Step 1: For the design spectrum, randomly pair peak and valley values ​​to form load cycles; skip this step for the test spectrum.

[0025] Step 2: Use the Odin transformation formula to convert any load cycle in the load spectrum into a pulsating cycle, and calculate the equivalent overload;

[0026] Step 3: Calculate the equivalent damage caused by each equivalent overload according to the Miner linear damage accumulation criterion;

[0027] Step 4: Determine the median of the equivalent overload, that is, the cumulative damage above and below this overload is equivalent, and determine this median overload as the peak value of the equal amplitude spectrum;

[0028] Step 5: Calculate the cumulative damage per unit hour of the random spectrum, and then calculate the equivalent number of cycles per unit hour of the equal amplitude spectrum according to the Miner linear damage accumulation criterion and the equal damage principle.

[0029] Step 6: Multiply the number of equal amplitude spectrum unit hour equivalent cycles by the target flight hours to obtain the number of equal amplitude spectrum cycles.

[0030] In a preferred embodiment, during the derivation of the DFR expression based on the SN curve with a constant stress ratio, the SN curve with a constant stress ratio can be represented in the form of a power function:

[0031]

[0032] Where: σ max Peak load; N is fatigue life; m1 and C1 are material constants;

[0033] r0 and N0 represent the DFR reference stress ratio and DFR reference life, respectively. rThe DFR is derived from the SN curve with a constant stress ratio, where the subscript r represents the stress ratio. r Substituting N0 into the above formula, we get:

[0034]

[0035] Therefore, when the stress ratio is r0, the SN curve with a constant stress ratio can be expressed as:

[0036]

[0037] Where, σ maxD For any maximum stress on the SN curve when the stress ratio is constant and the stress ratio is r0;

[0038] Based on the fundamental assumptions of the DFR method, the material life relationship can be represented by the Goodman model, from which the maximum stress σ corresponding to any stress ratio R can be established. max The maximum stress σ corresponding to the stress ratio r0 maxD Relationship:

[0039]

[0040] Substitute this into The DFR derived from the SN curve with a constant stress ratio can then be obtained. r expression:

[0041]

[0042] In the formula

[0043] As a preferred embodiment, the expression derived from the DFR expression based on the SN curve with a constant mean stress is as follows:

[0044]

[0045] in,

[0046] As a preferred implementation, in the process of analyzing DFR calculation results based on different forms of SN curves, substituting the same fatigue data into different DFR calculation formulas will yield different DFR calculation results. This obviously contradicts the uniqueness of DFR, which also shows that the different forms of SN curves in the basic assumption will lead to different DFR calculation results.

[0047] In a preferred embodiment, the equivalent overload calculation method based on the isochronous lifetime curve uses the Goodman model, and its expression is:

[0048]

[0049] In the formula: σ m The mean stress; σ a σ is the stress amplitude; -1 The point where the life curve intersects the vertical axis represents the material's rotational fatigue limit; σ m0 The point where the life curve intersects the horizontal axis represents the material's tensile strength. It is easy to see that when the stress ratio is 0, σ... m =σ a Equivalent overload σ dl =2σ a Then the above expression can be rewritten as:

[0050]

[0051] Then the equivalent overload σ dl It can be represented as:

[0052]

[0053] As a preferred embodiment, the error analysis process of the derivation process of the DFR expression based on the SN curve with a constant stress ratio includes the first step of obtaining the reliability life N of the material under any stress ratio R and any peak load. At this time, the critical fatigue damage of the structure can be calculated according to Miner's theory.

[0054] The second step is to convert the stress ratio R to the DFR reference stress ratio r0 and peak load σ based on the life curve. max Converted to σ maxD If the reliability life N remains unchanged during the conversion process, then the critical fatigue damage D of the structure at this time is... r2 It can be represented as D r2 =σ maxD，dl m ·N;

[0055] The third step involves converting the reliability life N to the DFR reference life N0 and peak load σ based on the SN curve where the stress ratio is constant. maxD When converted to DFR, the stress ratio r0 remains constant during the conversion process. Therefore, the critical fatigue damage D of the structure at this point is... r3 It can be represented as D r3 =DFR r，dl m ·N0.

[0056] As a preferred embodiment, the error analysis process for deriving the DFR expression based on the SN curve with a constant mean stress includes: First, obtaining the material at any mean stress σ... m Arbitrary stress amplitude σ a The reliability life N is given, and the critical fatigue damage D of the structure is given.m1 =σ max，dl m ·N;

[0057] The second step is to calculate the mean stress σ based on the life curve. m Converted to Stress amplitude σ a Converted to σ aD If the reliability life N remains unchanged during the conversion process, then the critical fatigue damage D of the structure at this time is... m2 It can be represented as D m2 =σ maxD，dl m ·N;

[0058] The third step involves converting the reliability life N to the DFR reference life N0 and stress amplitude σ based on the SN curve with a constant mean stress. aD Converted to σ during the conversion process m If the value remains unchanged, then the critical fatigue damage D of the structure at this time is... m3 It can be represented as D m3 =DFR m，dl m ·N0.

[0059] After adopting the above technical solution, the beneficial effects of the present invention are:

[0060] The key parameters of the fighter jet structure DFR obtained by this method can more objectively and accurately characterize the inherent fatigue performance and life loss law of the fighter jet structure under service load; the DFR calculation error derived from the SN curve with a constant mean stress is smaller, which can improve the design accuracy of the fighter jet structure durability design DFR method. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 This is a schematic diagram illustrating the derivation process of DFR based on the SN curve with a constant stress ratio in this invention.

[0063] Figure 2 This is a schematic diagram illustrating the derivation process of DFR based on the SN curve with a constant mean stress in this invention.

[0064] Figure 3 DFR in this invention rDFR m A schematic diagram showing the relationship between N / N0. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] A method for DFR (Device-Free Ratio) analysis of fighter jet structural durability, with the following principles for determining the reference stress ratio in the fighter jet DFR method: 1.1 The reference stress ratio for civil aircraft DFR cannot be used. The reference stress ratio for DFR should be a concentrated reflection of the load-time history characteristics of the aircraft during flight. Since the main mission of civil aircraft is to complete manned (or cargo-carrying) flight routes, their flight profile is relatively simple, and damage caused by the ground-to-air-to-ground cycle accounts for the majority of the total damage. Therefore, focusing on the ground-to-air-to-ground cycle characteristics, Boeing's setting of the reference stress ratio for civil aircraft DFR at 0.06 is feasible and has been verified through extensive engineering practice. However, the main mission of fighter jets is to complete prescribed combat missions. The negative overload generated when performing high-maneuverability maneuvers such as loops and dives in the air is often lower than the minimum ground load. Therefore, the damage caused by the ground-to-air-to-ground cycle is not as prominent for fighter jets as it is for civil aircraft. For this reason, if the approach used for civil aircraft is simply to determine the fighter jet DFR stress ratio from the perspective of the ground-to-air-to-ground cycle, it will not objectively reflect the characteristics of the load-time history of the fighter jet during flight, and will also lead to distortion of subsequent calculation results.

[0067] 1.2 The focus should be on the stress ratio characteristics of maneuvering loads. A significant difference between the load-time history of fighter jets and that of civil aircraft is that it is difficult to identify representative typical load cycles for fighter jets; instead, all levels of load cause some damage. Therefore, determining the DFR stress ratio for fighter jets should follow the general principle of "focusing on the major and neglecting the minor," that is, focusing on the load characteristics that cause significant damage to the airframe and have a significant impact on crack initiation life. Fighter jets undergo numerous, large-amplitude, and complex maneuvers during flight, and the damage caused by maneuvering loads accounts for the vast majority of the total damage, while the damage caused by other loads such as gust loads is minimal. Therefore, the baseline stress ratio for the fighter jet DFR method should be determined starting with the maneuvering loads, which dominate the damage assessment.

[0068] 1.3 Focusing on the stress ratio characteristics of maneuvering loads, 1) Overloads resulting from loads with non-zero stress ratios, converted into pulsating loads, are called equivalent overloads. The equivalent large overload in the load spectrum represents the load that causes severe damage to the fighter jet structure during flight, and its stress ratio represents the load characteristics of the harshest parts of the fighter jet's service life. Using the large overload stress ratio as the benchmark stress ratio for the fighter jet's DFR method is equivalent to conducting durability design on the fighter jet structure under harsh conditions, thus obtaining a conservative and safe design result. This is a key premise and important guarantee for the practical feasibility of the fighter jet DFR method in engineering.

[0069] 2) Analysis of the fighter jet load spectrum reveals that equivalent large overloads, with a cumulative frequency of only 3% of the total frequency, cause approximately 40% of the total damage, with some models even exceeding 50%. However, equivalent small overloads, with a cumulative frequency exceeding 60% of the total frequency, cause less than 10% of the total damage. Furthermore, test results show that when the peak load increases from 16.5g to 18g (with a trough of 5g), the crack initiation life of the titanium alloy sample decreases from 3034h to 1766h, a decrease of 41.8%; the crack initiation life of the aluminum alloy sample decreases from 3747h to 3351h, a decrease of 10.6%. Analysis of these data indicates that equivalent large overloads have a particularly significant impact on airframe damage and crack initiation life. Therefore, equivalent large overloads in the load spectrum must be given special attention during fighter jet durability design.

[0070] 3) When fighter jets perform maneuvers in the air, the movements are intense and vary greatly. Observation of the fighter jet's test spectrum (program block spectrum) also reveals that large positive overloads are often paired with large negative overloads to form a load cycle. Therefore, the equivalent large overload has a large stress range and a small stress ratio. Thus, using the equivalent large overload stress ratio as the benchmark stress ratio for the fighter jet's DFR method has an engineering advantage: in DFR testing, a smaller stress ratio combined with fewer loading cycles can accumulate to a larger fatigue damage, thereby shortening the test cycle and saving manpower costs.

[0071] 1.4 The DFR reference stress ratio for some critical components needs to be considered separately. During fighter jet flight, although the load magnitude and characteristics of different parts such as the fuselage and wings are not exactly the same, the differences are not significant. Therefore, when using the DFR method for durability design, the same DFR reference stress ratio can be selected. However, for components such as landing gear, horizontal stabilizer, vertical stabilizer, and carrier-based aircraft arresting systems, not only does their structural integrity play a crucial role in ensuring the safe flight of the fighter jet, but their load spectrum characteristics also differ significantly from those of other parts such as the fuselage. Therefore, for these critical structures, the DFR reference stress ratio needs to be considered separately.

[0072] 2. Method for determining the reference stress ratio of fighter jets using the DFR method

[0073] 2.1 Load Spectrum Processing Method: The DFR (Damage-Free Ratio) reference stress ratio is a concentrated reflection of the load-time history characteristics of a fighter jet during flight. Calculating the stress ratio range of damage concentration from the load spectrum is a common approach to determining the DFR stress ratio. Currently, our research group has collected test or design spectra of various fighter jets. For test spectra, since the peak and valley overload values ​​and their pairings are already given, the damage distribution can be directly analyzed. However, for design spectra, the following processing is required:

[0074] 1) High-load cut-off

[0075] The overload hysteresis effect caused by high loads in the load spectrum can increase the fatigue life of the structure, making the test results more dangerous. In order to reduce the beneficial effect of high load hysteresis on fatigue life, this paper adopts the high load removal method commonly used in engineering, that is, to delete high loads with a frequency of less than 10 times within 1000 flight hours. The specific method is to obtain the frequency exceedance curve by fitting the design spectrum data according to Equation (1), and then determine the load corresponding to the frequency of 10 by interpolation, and delete the overloads greater than this load.

[0076] lg[F(n z )]=a0+a1n z +a2n z 2 +a3n z 3 +a4lg(n z (1)

[0077] Where: n z For overload at each stage of the load spectrum; F(n) z ) represents the cumulative frequency of each overload level; a0, a1, a2, a3, and a4 are the fitting coefficients.

[0078] 2) Low-load interception

[0079] Low-load frequencies are high in the load spectrum, but they cause minimal damage to the airframe. Therefore, removing low-loads that have little impact on the test results using appropriate criteria can help shorten the test cycle. This paper adopts the overload cutoff ratio criterion method, which has been successfully applied to low-load interception in fighter jets, and sets its value to 3, that is, removing loads less than 1 / 3 of the maximum overload after high-load interception.

[0080] 3) Interpolation

[0081] When compiling fighter jet design spectra, measured data are often subjected to hierarchical statistical processing, that is, the loads within a certain range are assigned to a specific load, and the specific load and frequency represent the loads and total frequencies of the entire range. Although this processing can represent the complex load situation of the fighter jet relatively simply, its accuracy is greatly reduced when calculating the stress ratio. For example, the stress ratio is 0.125 when the peak value is 5.6g and the valley value is 0.7g; the stress ratio is 0.047 when the peak value is 6.4g and the valley value is 0.3g. However, after hierarchical statistical processing, the stress ratio of the above two loads is expressed as 0.5 / 6 = 0.833, which is obviously unacceptable. In order to obtain more accurate calculation results, this paper first fits the frequency transcendence curves of the peak and valley values ​​based on equation (1), and then interpolates with a step size of 0.1g to obtain the corresponding cumulative frequency, and uses this as the basis for subsequent calculations.

[0082] 4) Pairing of peak and trough values

[0083] Fighter jet design spectra often represent peak and trough values ​​separately. Therefore, when calculating damage, the first issue to address is how to pair peak and trough values. Currently, the commonly used method is to pair them randomly. However, observation of fighter jet test spectra reveals a pattern in the combination of peak and trough values: large positive overloads often correspond to large negative overloads. Therefore, while randomly pairing peak and trough values ​​is simpler, it clearly deviates from the actual load conditions experienced by fighter jets during flight. This paper employs an analogy analysis method to solve the peak and trough value pairing problem. First, based on test spectra of similar aircraft, the proportion of equivalent large overload trough values ​​and their frequencies is statistically analyzed. Then, the trough values ​​from various similar aircraft are weighted and combined to form trough overload values ​​and frequencies to be paired. Finally, peak and trough values ​​are randomly paired to form load cycles.

[0084] 2.2 Damage Calculation

[0085] Section 1.3 explains from three aspects why the reference stress ratio of the fighter jet's DFR method should be determined based on the equivalent large overload. This paper selects the equivalent large overload, which accounts for 3% of the frequency in the fighter jet's load spectrum, as the basic data to calculate its stress ratio and fatigue damage. According to Miner's linear damage accumulation theory, the expression for fatigue damage D is:

[0086]

[0087] In the formula: Δσ i =σ max，i -σ min，i , is the load range of the i-th cycle; R i =σ min，i / σ max，i σ is the stress ratio in the i-th cycle; dl，iσ is the equivalent overload converted to the pulsating cycle in the i-th cycle (the subscript dl represents the equivalent overload, the same below); m is the damage index, given a range of approximately 3 to 6, with 4 generally taken in engineering. Currently, σ is calculated... dl，i The commonly used methods are the Odin transformation formula method and the equal life curve method. Since the latter requires knowledge of some material constants, the Odin transformation method is chosen here without involving the material system. The calculation formula is shown in equation (3), and the calculation results are summarized in Table 1.

[0088]

[0089] Based on Table 1, 0.08 was selected as the baseline stress ratio for the DFR method of fighter jets for the following reasons:

[0090] 1) For the models in Table 1, (0.06, 0.09] is the stress ratio range where damage is particularly concentrated;

[0091] 2) For the models in Table 1, 0.08 is close to the damage median, meaning that the damage caused by loads with stress ratios greater than 0.08 and less than 0.08 is roughly equivalent;

[0092] 3) In addition to the aircraft types listed in Table 1, the equivalent damage of a certain type of fighter jet and a certain type of Russian Air Force fighter jet was also analyzed. It was found that the stress ratio ranges with the most concentrated damage were 0.08–0.23 and 0.05–0.15, respectively. It can be seen that for the above aircraft types, choosing 0.08 as the DFR benchmark stress ratio for fighter jets is also acceptable.

[0093] Table 1 Equivalent damage distribution of fighter jets at various stress ratios

[0094]

[0095] After determining the baseline stress ratio for the DFR method of fighter jets to be 0.08, one more issue needs to be addressed: the selection of the stress ratio interval length in Table 1. The stress ratio interval length should obviously not be set too large, as a wide interval would obscure the range of stress ratios where damage is truly concentrated, hindering the determination of the final stress ratio. At the same time, the interval length should not be set too small, because both test and design spectra are mostly subject to hierarchical statistical processing during compilation. This can lead to damage being overly concentrated in a few stress ratios during damage calculation, affecting the judgment of the calculation results. A narrower stress ratio interval is more susceptible to the influence of hierarchical statistical processing. After several trials, 0.03 was finally chosen as the stress ratio interval length.

[0096] Determination of the DFR (Depth-Frequency) Reference Life of 3 Fighter Jets

[0097] To determine the DFR reference life of a fighter jet, the random load spectrum must be converted into an equal amplitude spectrum under the principle of equal damage. Given that the DFR reference stress ratio for the fighter jet is determined to be 0.08 in Section 2, two more parameters need to be determined: the peak value and the number of cycles of the equal amplitude spectrum. The specific steps are as follows: 1. For the design spectrum, randomly pair the peak and valley values ​​to form load cycles; skip this step for the test spectrum. 2. Use the Odin transformation formula (Equation (3)) to convert any load cycle in the load spectrum into a pulsating cycle and calculate the equivalent overload. 3. Calculate the equivalent damage caused by each equivalent overload according to the Miner linear damage accumulation criterion (Equation (2)). 4. Determine the median of the equivalent overload, i.e., the damage accumulated above and below this overload is equivalent. This median overload is determined as the peak value of the equal amplitude spectrum. 5. Calculate the cumulative damage per unit hour of the random spectrum, and then calculate the number of equivalent cycles per unit hour of the equal amplitude spectrum according to the Miner linear damage accumulation criterion and the principle of equal damage. 6. The number of constant amplitude spectrum cycles can be obtained by multiplying the equivalent number of cycles per hour of the constant amplitude spectrum by the target flight hours. Based on the above method, the calculation results for each aircraft type are summarized in Table 2.

[0098] Based on Table 2, select 5×10 4 Using this cycle as the baseline lifespan for fighter jet DFR is consistent with the conclusions given in the literature, for the following reasons. Most of the aircraft types in Table 2 are third-generation fighters, with approximately 5 cycles per hour equivalent of the constant amplitude spectrum. The fatigue life of third-generation fighters is generally 3000–4000 flight hours, therefore the number of cycles per hour equivalent of the constant amplitude spectrum is 1.5 × 10⁻⁶. 4 ~2×10 4 The target lifespan of newly developed aircraft is generally 6000 flight hours. Considering that the usage conditions of newly developed fighter jets may be more severe, the number of equivalent cycles per hour of constant amplitude spectrum is calculated as 6 to 7. Therefore, the number of equivalent cycles per hour of constant amplitude spectrum is 3.6 × 10⁻⁶. 4 ~4.2×10 4 Next. Select 5×10 4 The secondary cycle, as the DFR benchmark life for fighter jets, takes into account the fatigue life design indicators of both existing and newly developed aircraft, while also leaving a certain margin, ensuring the safety and accuracy of the fighter jet DFR method.

[0099] Table 2 Peak values ​​of the fighter jet's constant amplitude spectrum and number of equivalent cycles per hour

[0100]

[0101] The influence of the 4S-N curve form on DFR calculation results: Fighter jets and civilian aircraft differ significantly in mission objectives, usage methods, and accumulated experience. Therefore, the basic assumptions of the DFR method for fighter jets and civilian aircraft also differ considerably, as summarized in Table 3. If the basic assumptions do not match the material properties or actual conditions, the accuracy of the DFR calculation will be affected. Therefore, the applicability of different basic assumptions and their impact on the DFR calculation results should be clearly understood. This section begins with the derivation process of the DFR expression, studying the errors generated during the derivation process from the perspective of fatigue damage, and further investigates the influence of the SN curve form on the DFR calculation results.

[0102] Table 3. Similarities and differences in DFR methods for fighter jets and civil aircraft.

[0103]

[0104] 4.1 Derivation and Analysis of DFR Expressions Based on Different Forms of SN Curves

[0105] 4.1.1 Derivation of the DFR expression based on the SN curve with a constant stress ratio

[0106] The SN curve with a constant stress ratio can be represented by a power function:

[0107]

[0108] In the formula: σ max is the peak load; N is the fatigue life; m1 and C1 are material constants.

[0109] r0 and N0 represent the DFR reference stress ratio and DFR reference life, respectively. r The DFR is derived from the SN curve where the stress ratio is constant (the subscript r represents the stress ratio, the same below). The DFR... r Substituting N0 into equation (4), we get:

[0110]

[0111] Therefore, when the stress ratio is r0, the SN curve with a constant stress ratio can be expressed as:

[0112]

[0113] In the formula: σ maxD Let r be any maximum stress on the SN curve when the stress ratio is constant and r0 is the stress ratio.

[0114] Based on the fundamental assumptions of the DFR method, the material life relationship can be represented by the Goodman model, from which the maximum stress σ corresponding to any stress ratio R can be established. max The maximum stress σ corresponding to the stress ratio r0maxD Relationship:

[0115]

[0116] Simplifying, we get:

[0117]

[0118] Substituting equation (7-b) into equation (6) yields the DFR derived from the SN curve with a constant stress ratio. r expression:

[0119]

[0120] In the formula:

[0121] 4.1.2 Derivation of the DFR expression based on the SN curve with a constant mean stress

[0122] The SN curve with a constant mean stress can be represented by a power function:

[0123]

[0124] In the formula: σ a is the stress amplitude; m2 and C2 are material constants.

[0125] DFR m The DFR (subscript m represents the mean stress, the same below) is derived from the SN curve with a constant mean stress. Therefore, according to the definition of DFR, σ a Substituting N0 into equation (9), we get:

[0126]

[0127] Therefore, when the average stress When the mean stress is constant, the SN curve can be expressed as:

[0128]

[0129] In the formula: σ aD The average stress At that time, any stress amplitude on the SN curve with a constant mean stress value.

[0130] Based on the fundamental assumptions of the DFR method, the material life relationship can be represented by the Goodman model, from which the maximum stress σ corresponding to any stress ratio R can be established. max With average stress The maximum stress DFR corresponding to the time m Relationship:

[0131]

[0132] Simplifying, we get:

[0133]

[0134] Substituting equation (12-b) into equation (11), we obtain the expression derived from the SN curve and the Goodman-type isochronous life curve based on the constant mean stress:

[0135]

[0136] In the formula

[0137] 4.1.3 Analysis of DFR Calculation Results Based on Different Forms of SN Curves

[0138] As defined by DFR, given that r0, N0, fatigue life distribution, and reliability indicators are all determined, a structure should have one and only one DFR value. The uniqueness of DFR is precisely why it can characterize the inherent fatigue performance of a material / structure. Therefore, substituting the same fatigue data into equations (8) and (13) respectively should yield the same calculation results, i.e.:

[0139] DFR r =DFR m (14-a)

[0140] Right now:

[0141]

[0142] Simplifying, we get:

[0143]

[0144] Observing equation (14-c), we can see that the equation holds if and only if N = N0, that is, DFR only holds if the reliability life (obtained through DFR testing) equals the DFR reference life. r Only equals DFR m When N≠N0, DFR r ≠DFR mSubstituting the same fatigue data into different DFR calculation formulas yields different DFR calculation results, which clearly contradicts the uniqueness of DFR. This also indicates that different forms of the SN curve in the basic assumption lead to different DFR calculation results. This conclusion raises two questions: 1. Since different forms of SN curves are objective reflections of structural fatigue performance, why do different SN curve forms lead to different DFR calculation results? 2. Based on which form of SN curve can the derived DFR expression more objectively and accurately describe the inherent fatigue performance of the material / structure? To clarify and resolve these questions, the following analysis examines the errors generated during the derivation of the DFR expression from the perspective of fatigue damage, and studies the influence of the SN curve form on the DFR calculation results.

[0145] 4.2 Error Analysis in the Derivation of the DFR Expression

[0146] 4.2.1 Equivalent Overload Calculation Method Based on Equal Life Curve

[0147] Solving fatigue damage requires calculating the equivalent overload under arbitrary loads. Section 2.2 mentions two conversion methods: the Odin transformation method and the constant life curve method. Literature compares and analyzes these two methods, concluding that the constant life curve method has a smaller conversion error. Although the constant life curve method is superior, it requires knowledge of some material constants. Section 2.2, without considering the material system, cannot provide these constants, therefore the Odin transformation method is used to calculate the equivalent overload. However, this is a theoretical analysis without numerical calculations; therefore, the constant life curve method, with its smaller conversion error, is used to calculate the equivalent overload.

[0148] Commonly used isochronous life curve models include the Goodman, Gerber, and Soderberg models. The basic assumptions of the DFR method for fighter jets and civil aircraft all use the Goodman isochronous life curve. Other isochronous life curve models differ only slightly in form and are essentially the same; therefore, this section only derives the conversion formula based on the Goodman isochronous life curve. The Goodman model expression is:

[0149]

[0150] Where: σ m The mean stress; σ a σ is the stress amplitude; -1 The point where the life curve intersects the vertical axis represents the material's rotational fatigue limit; σ m0 The point where the equal life curve intersects the horizontal axis represents the material's tensile strength. It is easy to see that when the stress ratio is 0, σ... m =σ a Equivalent overload σ dl =2σ aThen equation (15) can be rewritten as:

[0151]

[0152] Then the equivalent overload σ dl It can be represented as:

[0153]

[0154] 4.2.2 Error Analysis of the Derivation Process of the DFR Expression Based on the SN Curve with a Constant Stress Ratio

[0155] The derivation of the DFR expression for the curve can be summarized in three steps. The first step is to obtain the material under arbitrary stress ratio R and arbitrary peak load σ. max Given a reliability life N, the critical fatigue damage D of the structure can be calculated using Miner's theory. r1 =σ max，dl m • N; The second step is to convert the stress ratio R to the DFR reference stress ratio r0 and peak load σ based on the isolife curve. max Converted to σ max D, if the reliability life N remains unchanged during the conversion process, then the critical fatigue damage D of the structure at this time is... r2 It can be represented as D r2 =σ maxD，dl m ·N; The third step is to convert the reliability life N to the DFR reference life N0 and the peak load σ based on the SN curve where the stress ratio is constant. maxD When converted to DFR, the stress ratio r0 remains constant during the conversion process. Therefore, the critical fatigue damage D of the structure at this point is... r3 It can be represented as D r3 =DFR r，dl m ·N0. Figure 1 This is a schematic diagram of the conversion process.

[0156] The following discussion addresses whether the conversion based on the isochronous lifetime curve introduces errors. Due to σ max With σ maxD On the same lifetime curve, therefore σ max，dl =σ maxD，dl , and then σ max , dl m ·N=σ maxD，dl m ·N, i.e. D r1 =D r2 That is, the conversion based on the life curve is converted to the damage conversion, and no error is generated in the conversion process.

[0157] The following discussion addresses whether the conversion of the SN curve based on a constant stress ratio is also an equal-damage conversion. Simplifying equation (6) yields:

[0158]

[0159] Since the SN curve based on a constant stress ratio does not change the stress ratio, therefore:

[0160]

[0161] and then:

[0162]

[0163] and:

[0164]

[0165] Obviously D r2 ≠D r3 Therefore, the conversion based on the constant stress ratio of the SN curve is not an equal damage conversion, and errors will occur in the conversion process.

[0166] 4.2.3 Error Analysis in the Derivation of the DFR Expression Based on the Constant Stress Mean of the SN Curve

[0167] As can be seen from Section 4.1.2, the derivation of the DFR expression based on the SN curve with a constant mean stress can also be summarized in three steps. The first step is to obtain the material under any mean stress σ. m Arbitrary stress amplitude σ a The reliability life N is given, and the critical fatigue damage D of the structure is given. m1 =σ max，dl m ·N;

[0168] The second step is to calculate the mean stress σ based on the life curve. m Converted to Stress amplitude c a Converted to σ aD If the reliability life N remains unchanged during the conversion process, then the critical fatigue damage D of the structure at this time is... m2 It can be represented as D m2 =σ maxD，dl m ·N;

[0169] The third step involves converting the reliability life N to the DFR reference life N0 and stress amplitude σ based on the SN curve with a constant mean stress. aD Converted to σ during the conversion process m If the value remains unchanged, then the critical fatigue damage D of the structure at this time is... m3 It can be represented as Dm3 =DFR m，dl m ·N0. Figure 2 This is a schematic diagram of the conversion process.

[0170] Similar to Section 4.2.2, the conversion based on the equal life curve is an equal damage conversion, and the conversion process does not introduce errors. The following discussion examines whether the conversion based on the SN curve with a constant mean stress is also an equal damage conversion.

[0171] Simplifying expression (11) yields:

[0172]

[0173] And because of this time:

[0174]

[0175] Therefore:

[0176] σ maxD =σ m +σ aD (24-a)

[0177]

[0178] Furthermore, D m2 It can be represented as:

[0179]

[0180] and:

[0181]

[0182] Obviously D m2 ≠D m3 Therefore, the conversion based on the constant stress ratio of the SN curve is not an equal damage conversion, and errors will occur in the conversion process.

[0183] 4.2.4 DFR Calculation Error Analysis

[0184] The calculation results in Sections 4.2.2 and 4.2.3 provide the answer to Question 1 in Section 4.1.3: the reason why the form of the SN curve affects the DFR calculation results is that the conversion based on the SN curve is not an equal-damage conversion, and errors will occur during the conversion process. The answer to Question 1 also provides a research direction for Question 2: the smaller the conversion error of the SN curve, the more objectively and accurately the DFR expression derived from the SN curve can characterize the inherent fatigue performance of the material / structure.

[0185] Observing equations (8) and (13), it can be seen that the DFR expression contains r0, N0, R, and σ. max, N, σ m0 With numerous parameters, and the inherent relationships between these parameters, theoretical analysis is difficult. Therefore, this study chooses to substitute experimental data into various formulas to calculate DFR. r DFR m The DFR error was analyzed based on the calculation results. Fatigue data of commonly used aerospace materials were selected from the literature and substituted into the calculation. The material system, original data and calculation results are summarized in Table 4.

[0186] First, observe the data for serial number 2 in Table 4. At this point, we can approximate N = N0, meaning the reliability lifetime equals the DFR baseline lifetime. Since DFR can be obtained without conversion using the SN curve, there will be no conversion error. Therefore, the DFR calculation result at this point is accurate (denoted as [DFR], the same below). m With DFR r The fact that the calculation results are almost identical also proves this point. Based on this, further comparative analysis of the data in sequence 1 shows that when N≠N0, DFR is obviously... m Compared to DFR r It is closer to [DFR]. Analyzing the data in serial numbers 15 and 16 yields the same conclusion, so it is preliminarily believed that the calculation error of the DFR expression derived from the SN curve with a constant mean stress is smaller.

[0187] Further observation of the data in Table 4 reveals DFR r DFR m The following relationship exists between N / N0 and DFR: When N / N0 > 1, DFR r >DFR m When N / N0 = 1, DFR r =DFR m (i.e., [DFR]); when N / N0 < 1, DFR r <DFR m By observing the changing patterns of each group of data, we can further provide DFR. r DFR m A diagram illustrating the relationship between N / N0 is shown below. Figure 3 As shown ( Figure 3 This is for illustrative purposes only and does not represent DFR. r DFR m (A linear relationship exists between N / N0 and 1). The graph clearly shows that when N / N0 ≠ 1 (which is unavoidable in the DFR experiment), regardless of the relationship between N / N0 and 1, DFR will obviously... m Both are closer to [DFR] than DFR, therefore we conclude that DFR mThis allows for a more objective and accurate description of the inherent fatigue properties of materials / structures. This also explains why Boeing's DFR expression is derived from an SN curve with a constant mean stress.

[0188] Table 4. Fatigue life data and DFR calculation results for typical aerospace materials:

[0189]

[0190]

[0191] Note: ① The literature studied σ m0 The influence of the value of on the DFR calculation results shows that DFR affects σ m0 Insensitive, therefore the data given in standard HB7110-94 is used here: if σ b ≤1380MPa, σ m0 =930

[0192] MPa; if σ b >1380MPa, σ m0 =1240MPa.

[0193] ② Based on the fundamental assumptions of the fighter jet DFR method, fatigue life follows a log-normal distribution; therefore, the median life calculation formula here is:

[0194] ③ The reliability index is taken as 99.9% reliability at a 90% confidence level, and the logarithmic standard deviation is taken as 0.14.

[0195] ④ The DFR reference stress ratio r0 is taken as 0.08, and the reference life N0 is taken as 5×10. 4 .

[0196] ⑤ The literature, through studying the slopes of the SN curves of various aerospace materials, concludes that it is feasible to uniformly select values ​​for m1 and m2, and that a value of 4 for m1 is acceptable. Standard HB 7110-94 gives S = 1.8 for high-strength steel, while... The calculation yields m2≈3.917. Therefore, m1 is taken as 4 and m2 as 3.917.

[0197] Although DFR m The calculation error and DFR r Compared to the relatively small, but from Figure 3 As can be seen from Table 4, as the difference between the value of N / N0 and 1 increases, DFR m DFR rThe calculation error will increase accordingly. Therefore, in DFR testing, the reliability life should be as close as possible to the DFR reference life to ensure the accuracy of the DFR calculation results. This is precisely why standard HB 7110-94 requires a range for the median life. At the same time, this also indicates that although DFR... r The error is relatively large, but this does not mean that DFR r The calculation results are unacceptable; as long as the value of N / N0 is sufficiently close to 1, then DFR r The calculation results are also reliable. It's just that they differ from DFR. m In comparison, DFR r The sensitivity to N / N0 is higher, thus placing higher demands on the selection of test loads in DFR tests. Due to the current lack of supporting data, the next step could be to determine DFR based on practical experience. r DFR m The acceptable error magnitude and the corresponding range of N / N0 values ​​provide a reference for the standardization and normalization of DFR testing.

[0198] Although the analysis results in Sections 4.2.2 and 4.2.3 indicate that the conversion based on the isolife curve (i.e., converting the test load stress ratio to the DFR reference stress ratio) will not produce errors, observing the data in numbers 3, 4, 11, and 12 of Table 4 reveals that when the difference between the test load stress ratio and the DFR reference stress ratio is large, regardless of whether it is DFR m or DFR r All results deviated significantly from [DFR]. This deviation may stem from the fact that the isolife curve model cannot fully and accurately represent the true isolife relationship of the material. Therefore, it is recommended to conduct DFR tests at the DFR reference stress ratio to avoid errors arising from conversion based on the isolife curve. If testing is not feasible due to limitations, it is recommended to select data with a test load stress ratio close to the DFR reference stress ratio to calculate DFR.

[0199] 1) When determining the DFR reference stress ratio for fighter jets, the DFR reference stress ratio for civil aircraft should not be directly used. Instead, the focus should be on the load characteristics of large equivalent overloads in the maneuver loads of fighter jets.

[0200] 2) The DFR reference stress ratio for fighter jets can be taken as 0.08, and the DFR reference life can be taken as 5×104 cycles.

[0201] 3) The reason why the form of the SN curve can affect the DFR calculation results is that the conversion based on the SN curve will introduce errors. The DFR expression derived based on the SN curve with a constant mean stress can more objectively and accurately describe the inherent fatigue properties of the material / structure.

[0202] 4) To obtain accurate DFR calculation results, it is recommended to conduct DFR tests under the DFR reference stress ratio, and sufficient attention should be paid to the selection of the test load stress level to ensure that the reliability life is as close as possible to the DFR reference life.

[0203] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing key parameters of the DFR (Design for Frame Reduction) of a fighter jet structure, characterized in that, include Determining the DFR reference stress ratio for fighter jets includes load spectrum processing and damage calculation; Determining the DFR (Depth Free) reference life of fighter jets; The influence of the SN curve form on the DFR calculation results; Load spectrum processing includes processing the test spectrum or design spectrum. The peak and valley overload values ​​and their pairings of the test spectrum are given, and damage calculation and damage distribution can be directly performed. The design spectrum requires high load removal, low load removal, interpolation selection, and peak and valley pairing before damage calculation and damage distribution analysis. The impact of the SN curve form on DFR calculation results includes the derivation and analysis of DFR expressions based on different SN curve forms, and error analysis of the DFR expression derivation process. The derivation and analysis of DFR expressions based on different SN curve forms includes the derivation of DFR expressions based on SN curves with a constant stress ratio, the derivation of DFR expressions based on SN curves with a constant mean stress, and analysis of DFR calculation results based on different SN curve forms. The error analysis of the DFR expression derivation process includes the equivalent overload calculation method based on equal-life curves, the error analysis of the DFR expression derivation process based on SN curves with a constant stress ratio, the error analysis of the DFR expression derivation process based on SN curves with a constant mean stress, and error analysis of DFR calculation. In the derivation of the DFR expression based on the SN curve with a constant stress ratio, the SN curve with a constant stress ratio can be represented in the form of a power function: ； Where: σ max Peak load; N is fatigue life; m 1. C 1 is a material constant; r 0、 N 0. DFR reference stress ratio and DFR reference life respectively. DFR r The DFR is derived from the SN curve with a constant stress ratio, where the subscript r represents the stress ratio. DFR r , N Substituting 0 into the above formula, we get: ； Therefore, when the stress ratio is r When the stress ratio is constant at 0, the SN curve can be expressed as: ； Where, σ maxD The stress ratio is r At 0, the maximum stress on the SN curve where the stress ratio is constant; Based on the fundamental assumptions of the DFR method, the material life relationship can be represented by the Goodman model, from which the maximum stress σ corresponding to any stress ratio R can be established. max The ratio of stress is r The maximum stress σ corresponding to 0 maxD Relationship: ； Substitute this into This allows us to obtain the SN curve derived based on a constant stress ratio. DFR r expression: ； In the formula ; The expression derived from the DFR expression based on the SN curve with a constant mean stress is as follows: ； in, ; In the analysis of DFR calculation results based on different forms of SN curves, substituting the same fatigue data into different DFR calculation formulas will yield different DFR calculation results, which obviously contradicts the uniqueness of DFR. This also shows that the different forms of SN curves in the basic assumption will lead to different DFR calculation results.

2. The method for analyzing key parameters of fighter jet structure DFR according to claim 1, characterized in that, The overload removal method is based on fitting the frequency exceedance curve to the design spectrum data according to the following calculation formula, and then determining the load corresponding to the frequency of 10 through interpolation, and deleting overloads greater than this load: lg[F(n z )]=a0+a1n z +a2n z 2 +a3n z 3 +a4lg(n z ); in, n z For overload at each stage of the load spectrum; F ( n z () represents the cumulative frequency of overload at each level; a 0、 a 1. a 2. a 3. a 4 represents the fitting coefficient; The low-load interception adopts the overload cutoff ratio criterion method applied to low-load interception of fighter jets and takes a value of 3, that is, the loads less than 1 / 3 of the maximum overload after high-load interception are deleted. Interpolation with a step size of 0.1g is used to obtain the corresponding cumulative frequency.

3. The method for analyzing key parameters of fighter jet structure DFR according to claim 1, characterized in that, According to Miner's linear damage accumulation theory, the expression for fatigue damage D is: ； In the formula: Δσ i =σ max，i -σ min，i , is the load range of the i-th cycle; R i =σ min，i / σ max，i σ is the stress ratio in the i-th cycle. dl,i It is the equivalent overload converted to the pulsating cycle in the i-th cycle. The subscript dl represents the equivalent overload, and m is the damage index. σ dl,i The calculation uses the Odin transformation formula, which is as follows: ； 0.08 was chosen as the baseline stress ratio for the DFR method in fighter jets.

4. The method for analyzing key parameters of fighter jet structure DFR according to claim 3, characterized in that, The determination of the fighter jet's DFR reference life requires converting the random load spectrum into an equal amplitude spectrum while adhering to the principle of equal damage. Given that the fighter jet's DFR reference stress ratio is already determined to be 0.08, two additional parameters need to be determined: the peak value of the equal amplitude spectrum and the number of cycles. The specific operational steps are as follows: Step 1: For the design spectrum, randomly pair the peak and valley values ​​to form load cycles; Skip this step in the experimental spectrum; Step 2: Use the Odin transformation formula to convert any load cycle in the load spectrum into a pulsating cycle, and calculate the equivalent overload; Step 3: Calculate the equivalent damage caused by each equivalent overload according to the Miner linear damage accumulation criterion; Step 4: Determine the median of the equivalent overload, that is, the cumulative damage above and below this overload is equivalent, and determine this median overload as the peak value of the equal amplitude spectrum; Step 5: Calculate the cumulative damage per unit hour of the random spectrum, and then calculate the equivalent number of cycles per unit hour of the equal amplitude spectrum according to the Miner linear damage accumulation criterion and the equal damage principle. Step 6: Multiply the number of equal amplitude spectrum unit hour equivalent cycles by the target flight hours to obtain the number of equal amplitude spectrum cycles.

5. The method for analyzing key parameters of fighter jet structure DFR according to claim 4, characterized in that, In the equivalent overload calculation method based on the constant lifetime curve, the constant lifetime curve model adopts the Goodman model, and its expression is: ； Where: σ m The mean stress; σ a σ is the stress amplitude; -1 The point where the life curve intersects the vertical axis represents the material's rotational fatigue limit; σ m0 The point where the life curve intersects the horizontal axis represents the material's tensile strength; it is easy to see that when the stress ratio is 0, σ m =σ a Equivalent overload σ dl =2σ a Then the above expression can be rewritten as: ； Then the equivalent overload σ dl It can be represented as:

6. The method for analyzing key parameters of fighter jet structure DFR according to claim 1, characterized in that, The error analysis process of the derivation process of the DFR expression based on the SN curve with a constant stress ratio includes the first step of obtaining the reliability life N of the material under any stress ratio R and any peak load. At this time, the critical fatigue damage of the structure can be calculated according to Miner's theory. The second step is to convert the stress ratio R to the DFR reference stress ratio based on the life curve. r 0. Peak load σ max Converted to σ maxD If the reliability life N remains unchanged during the conversion process, then the critical fatigue damage D of the structure at this time is... r2 It can be represented as D r2 =σ maxD，dl m ·N; The third step involves converting the reliability life N to the DFR reference life N0 and peak load σ based on the SN curve where the stress ratio is constant. maxD Stress ratio converted to DFR during the conversion process r If 0 remains constant, then the critical fatigue damage D of the structure at this time... r3 It can be represented as D r3 =DFR r，d1 m ·N0.

7. The method for analyzing key parameters of fighter jet structure DFR according to claim 1, characterized in that, The error analysis process for deriving the DFR expression based on the SN curve with a constant mean stress includes: First, obtaining the material at any mean stress σ. m Arbitrary stress amplitude σ a Reliability lifespan N At this point, the critical fatigue damage D of the structure ml =σ max，dl m ·N; The second step is to calculate the mean stress σ based on the life curve. m Converted to Stress amplitude σ a Converted to σ aD Reliability life during the conversion process N If the value remains unchanged, then the critical fatigue damage D of the structure at this time is... m2 It can be represented as D m2 =σ maxD，dl m ·N; The third step is based on the fact that the mean stress is constant. SN The curve will indicate reliability lifespan N Converted to DFR reference life N 0. Stress amplitude σ aD Converted to During the conversion process, σ m If the value remains unchanged, then the critical fatigue damage D of the structure at this time is... m3 It can be represented as D m3 =DFR m，dl m ·N0.

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