Life prediction method suitable for high-temperature multi-axis random vibration load

Abstract

The invention discloses a life prediction method suitable for a high-temperature multi-axis random vibration load, relates to data acquisition, processing and life calculation of a random vibration test, and belongs to the field of fatigue performance of a material under the random vibration load. According to the method, a time domain method and a frequency domain method are combined, and an interaction factor is introduced to correct a von Mises equivalent formula, so that the corrected life prediction model is more accurate in life prediction under a multi-axis working condition; and meanwhile, the normal-temperature S-N curve is corrected, so that the corrected life prediction model is more accurate in life prediction under the high-temperature working condition. And mathematical expressions of the parameters are obtained through a multi-axis random vibration fatigue test. The method provided by the invention has clear physical significance and can be used for predicting the fatigue life of the high-temperature multi-axis random vibration.

Description

Technical Field

[0001] The present invention is applied to the field of life prediction under high-temperature multi-axial conditions, and particularly refers to a method for predicting the fatigue life of high-temperature multi-axial random vibration based on a time-domain and frequency-domain hybrid method and the correction of the normal-temperature S-N curve. Background Art

[0002] The cyclic loads suffered by an aero-engine in its actual service environment include random vibration loads and high-temperature environmental loads. Among them, vibration fatigue generally refers to the fatigue failure phenomenon caused by the resonance of a structure due to the intersection or proximity of the frequency distribution of alternating loads (such as vibration, impact, noise loads, etc.) and the natural frequency distribution of the structure. When an aero-engine is working, it is subjected to high-temperature random vibration loads in multiple directions due to blade rotation, air combustion, etc. The random vibration load and the high-temperature environmental load are coupled to form a high-temperature multi-axial random vibration composite load. At present, the research on predicting the random vibration fatigue life under high-temperature multi-axial conditions is still insufficient, and the research on the prediction model for the random vibration fatigue life of signals under high-temperature multi-axial conditions is also relatively lacking. Therefore, establishing a prediction model for the random vibration fatigue life applicable to high-temperature multi-axial conditions can improve the accuracy of the fatigue life prediction of aero-engines and provide theoretical and technical support for the safe and reliable operation of aero-engines. Summary of the Invention

[0003] The object of the present invention is to propose a method for predicting the random vibration fatigue life applicable to high-temperature multi-axial conditions based on a time-domain and frequency-domain hybrid method and the correction of the normal-temperature S-N curve. In the time-domain and frequency-domain hybrid method, the von Mises equivalent model has been widely studied by scholars due to its advantages such as high prediction accuracy and simple calculation, but the von Mises model does not consider non-proportional loading under multi-axial conditions. In complex actual working conditions, due to the diversity of loading paths, different stresses may be applied to the specimen in each cycle, and this non-proportional loading will exacerbate the damage accumulation of the material, thereby shortening its fatigue life. Therefore, in order to improve the accuracy of fatigue life prediction in a multi-axial random vibration environment, it is necessary to fully consider the influence of non-proportional loading on material damage in the multi-axial equivalent life prediction method.

[0004] The technical solution of the present invention is to adopt a time-domain and frequency-domain hybrid method and combine it with a high-temperature curve, which is applicable to the prediction of the random vibration fatigue life under high-temperature multi-axial conditions. The time-domain and frequency-domain hybrid method is used to predict the vibration fatigue life. Based on the von Mises equivalent formula, the interaction factor in each cycle is calculated and corrected, and at the same time, the linear damage accumulation theory and the high-temperature S-N curve are combined to realize the prediction of the multi-axial random vibration fatigue life. The relevant parameters used are the zero-order spectral distance, the interaction factor, and the high-temperature parameter. The implementation steps of this method are as follows:

[0005] (1) First, under normal temperature conditions, obtain the strain-time history in the multi-axis directions (assumed to be the X direction and the Y direction) at the critical point through a contact or non-contact strain gauge, and convert the strain-time history into a stress-time history through the elastic modulus of the material, represented by the symbols X(t) and Y(t) respectively, where t represents the time point.

[0006] (2) Use the von Mises formula to convert X(t) and Y(t) of the entire process into equivalent stress:

[0007]

[0008] where, σ M is the equivalent stress, σ x is the stress in the X direction, σ y is the stress in the Y direction, and t represents the time point.

[0009] (3) Use the Wang-Brown counting method for the stress-time histories X(t) and Y(t) to obtain the start and end time points t si and t ei for each cycle, where t si represents the start point of the i-th cycle, and t ei represents the end point of the i-th cycle.

[0010] (4) Calculate the interaction factor within each cycle according to the start and end time points of each cycle:

[0011]

[0012] where, l max is the maximum chord length within this loading path (if there are multiple identical maximum values, it is the first one), t si is the start point of the i-th cycle, t ei is the end point of the i-th cycle, l(t) is the chord length at time t, f(t) is the rotation factor, F(i) is the interaction factor within the i-th cycle, m X , 0 is the zero-order spectral moment of the power spectral density function in the X direction, m Y，0 is the zero-order spectral moment of the power spectral density function in the Y direction, is the angle between the rotation factor and the X-axis, and C is calculated as a constant.

[0013] (5) Based on step (4), considering the influence of non-proportional loading, correct the sum of the squares of the equivalent stress within each cycle:

[0014]

[0015] where, E(i) is the sum of the squares of the equivalent stress in the i-th cycle, σeq is the equivalent stress after correction within the cycle, α is the material sensitivity parameter, σ M is the equivalent stress, and F(i) is the interaction factor within the cycle.

[0016] (6) Based on step (5), obtain the equivalent time-domain spectrum and calculate the root mean square, and then obtain the zero-order spectral distance of the equivalent power spectral density function:

[0017]

[0018] where, m eq，0 is the zero-order spectral distance of the equivalent time-domain spectrum, n to is the total number of time points included in the history, and to is the total number of all cycles in the history.

[0019] (7) Based on step (6), obtain the equivalent power spectral density function, and the formula is as follows:

[0020]

[0021] where, m eq，0 is the zero-order spectral distance of the equivalent time-domain spectrum, m X，0 is the zero-order spectral distance in the X direction, and G X is the power spectral density function in the X direction.

[0022] (8) Based on step (7), perform an inverse Fourier transform on the equivalent power spectral density function and further obtain the amplitude probability density distribution function (PDF).

[0023] (9) Calculate the fatigue life according to the amplitude probability density distribution function (PDF) and in combination with the material's high-temperature S-N curve (stress-life curve). Based on the fatigue test data of titanium alloy materials, the expression of the fitted high-temperature S-N curve of the material is:

[0024]

[0025] m(T) = m 0 (8×10 -8 T + 2.2×10 -5 T + 1)

[0026] where, S a is the stress amplitude of the specimen, N is the fatigue life, m 0 and C 0 are the material constants at room temperature obtained by fitting, T is the temperature, and m(T) and C(T) are the material constants at temperature T.

[0027] The stress amplitude probability density function P(S a) Analyze by combining the S-N curve of the material and the linear cumulative damage theorem, and the fatigue damage expression of the structure is obtained as follows:

[0028]

[0029] Among them, E[P] is the peak crossing rate, S a is the amplitude stress, m(T) and C(T) are material constants at temperature T, and P(S a ) is the probability density distribution function.

[0030] (10) Based on steps (8) and (9), the random vibration fatigue life under multi-axial working conditions can be predicted:

[0031]

[0032] Among them, D is the fatigue damage per unit time, and at this time the L value is the predicted high-temperature multi-axial random vibration fatigue life of the structure.

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] (1) The life prediction method in the prior art solution ignores the influence of non-proportional loading on the fatigue life. The present invention proposes an interaction factor that can quantitatively describe the additional damage caused by non-proportional loading, improving the life prediction accuracy.

[0035] (2) The high-temperature fatigue life prediction method in the prior art solution is not yet perfect. In actual working conditions, high temperature will have a significant impact on the fatigue life of materials. The present invention uses the high-temperature S-N curve to describe the influence of temperature on the fatigue performance of materials and predicts the failure life with high accuracy.

[0036] (3) The life prediction method for high-temperature multi-axial random vibration loads proposed by the present invention considers the additional damage caused to materials when multi-random vibration loads and temperature loads act together, further improving the life prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flowchart for predicting the random vibration fatigue life applicable to high-temperature multi-axial working conditions;

[0038] Figure 2 is a schematic diagram of the power spectral density function in the X direction;

[0039] Figure 3 is a schematic diagram of the power spectral density function in the Y direction;

[0040] Figure 4 is a schematic diagram of the von Mises equivalent power spectral density function;

[0041] Figure 5 Schematic diagram of the corrected von Mises equivalent power spectral density function;

[0042] Figure 6 Schematic diagram of the high-temperature S-N curve;

[0043] Figure 7 High-temperature multiaxial random vibration test diagram;

[0044] Figure 8 Schematic diagram for calculating the interaction factor;

[0045] Figure 9 Octave band diagram of the predicted results of high-temperature multiaxial random vibration life. Specific implementation manners

[0046] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0047] The present invention is a life prediction method applicable to high-temperature multiaxial random vibration loads, which involves data acquisition, processing, and life calculation of random vibration tests, and belongs to the field of fatigue performance of materials under random vibration loads. The present invention combines the time-domain method and the frequency-domain method, introduces an interaction factor to correct the von Mises equivalent formula, so that the corrected life prediction model is more accurate in predicting the life under multiaxial working conditions; at the same time, the normal-temperature S-N curve is corrected, so that the corrected life prediction model is more accurate in predicting the life under high-temperature working conditions. And mathematical expressions of these parameters are obtained through multiaxial random vibration fatigue tests. The proposed method has clear physical meanings and can be used for predicting high-temperature multiaxial random vibration fatigue life.

[0048] Titanium alloy materials are widely used in key parts of aeroengines due to their high strength-to-weight ratio, excellent corrosion resistance, and oxidation resistance. The present invention will be further described based on the life prediction process of titanium alloy materials under constant-temperature uniaxial and multiaxial random vibration loads under different conditions.

[0049] In terms of fatigue tests, all tests were carried out on a random vibration test system, as Figure 7 shown. The application of the temperature load was realized by an induction coil, and the cooling was realized by an air-cooling pipe. The strain during the test was measured by a strain gauge, and the temperature measurement during the test was realized by an infrared thermometer. In addition, all tests were carried out in the air. In this embodiment, random vibration fatigue tests with different temperatures and different intensities were carried out respectively, and the details of these tests are listed in Table 1 and

[0050] Table 2. The failure criterion for all tests was defined as a sharp mutation of the strain gauge at a certain moment.

[0051]

[0052] Step (1): In the normal temperature experiment, obtain the strain-time history in the multi-axis direction at the critical point through a contact or non-contact strain gauge, and convert the strain-time history into a stress-time history by the elastic modulus of the material, denoted by symbols X(t) and Y(t) respectively, where t represents the time point. Meanwhile, convert the stress-time histories in the two directions into power spectral density functions through Fourier transform. The equivalent power spectral density functions are as shown in Appendix Figure 2 and Appendix Figure 3 as shown.

[0053] Step (2): Use the von Mises formula to convert X(t) and Y(t) of the entire process into equivalent stress:

[0054]

[0055] where, σ M is the equivalent stress, σ x is the stress in the X direction, σ y is the stress in the Y direction, and t represents the time point.

[0056] Step (3): Use the Wang-Brown counting for the stress-time histories X(t) and Y(t) to obtain the start and end time points t si and t ei of each cycle. Among them, t si represents the start point of the i-th cycle, and t ei represents the end point of the i-th cycle.

[0057] Step (4): Calculate the interaction factor within each cycle according to the start and end time points of each cycle. The schematic diagram is as shown in Appendix Figure 8 :

[0058]

[0059]

[0060] where, l max is the maximum chord length within the loading path, t si is the start point of the i-th cycle, t ei is the end point of the i-th cycle, l(t) is the chord length at time t, f(t) is the rotation factor, F(i) is the interaction factor within the i-th cycle, m X，0 is the zero-order spectral moment of the power spectral density function in the X direction, m Y，0 is the zero-order spectral moment of the power spectral density function in the Y direction, is the angle between the rotation factor and the X axis, and C is a constant.

[0061] Step (5), based on Step (4), considering the influence of non-proportional loading, correct the sum of squares of equivalent stress within each cycle:

[0062]

[0063] where E(i) is the sum of squares of equivalent stress after correction for the i-th cycle, σ eq is the equivalent stress after correction within the cycle, α is the material sensitivity parameter, σ M is the equivalent stress, and F(i) is the interaction factor within the cycle.

[0064] Step (6), based on Step (5), obtain the equivalent time domain spectrum and calculate the root mean square, and then obtain the zero-order spectral moment of the equivalent power spectral density function:

[0065]

[0066] where m eq，0 is the zero-order spectral moment of the equivalent time domain spectrum, n to is the total number of time points included in the history, and to is the total number of all cycles in the history.

[0067] Step (7), based on Step (6), obtain the equivalent power spectral density function, and the formula is as follows:

[0068]

[0069] where m eq，0 is the zero-order spectral moment of the equivalent time domain spectrum, m X，0 is the zero-order spectral moment in the X direction, and G X is the power spectral density function in the X direction.

[0070] The von Mises equivalent stress power spectral density function is as shown in the appendix Figure 4 The corrected von Mises equivalent stress power spectral density function is as shown in the appendix Figure 5 as shown.

[0071] Step (8), based on Step (7), perform an inverse Fourier transform on the equivalent power spectral density function and further obtain the amplitude probability density distribution function PDF.

[0072] Step (9), calculate the fatigue life according to the amplitude probability density distribution function PDF and in combination with the material's high-temperature S-N curve, i.e., the stress-life curve. Based on the fatigue test data of titanium alloy materials, the expression of the material's high-temperature S-N curve fitted is:

[0073]

[0074] m(T) = m 0 (8×10-8 T + 2.2×10 -5 T + 1)

[0075] Among them, S a is the stress amplitude of the specimen, N is the fatigue life, m 0 and C 0 are the material constants at room temperature obtained by fitting. T is the temperature, and m(T) and C(T) are the material constants at temperature T.

[0076] The high-temperature S-N curve obtained by fitting the fatigue test data is as Figure 8 shown. Further, by combining the stress amplitude probability density function P(S a ), the S-N curve of the material, and the linear cumulative damage theorem for analysis, the fatigue damage expression of the structure is obtained as:

[0077]

[0078] Among them, E[P] is the peak crossing rate, S a is the amplitude stress, m(T) and C(T) are the material constants at temperature T, and P(S a ) is the probability density distribution function.

[0079] Step (10), predicting the random vibration fatigue life under multi-axial conditions based on steps (8) and (9):

[0080]

[0081] Among them, D is the fatigue damage per unit time, and at this time, the value of L is the predicted high-temperature multi-axial random vibration fatigue life of the structure.

[0082] Taking the high-temperature multi-axial random vibration fatigue test of titanium alloy material as an example to illustrate the correctness of this method: First, according to step (1), obtain the vibration response power spectral density curves in two directions of the titanium alloy material, as shown in Appendix Figure 3 and Appendix Figure 4 shown. According to steps (2)-(7), obtain the corrected von Mises equivalent power spectral density curve values, and the power spectral density curve is as shown in Appendix Figure 5 shown. Finally, combine the high-temperature S-N curve and the linear damage accumulation theorem to complete the fatigue life prediction, and the high-temperature S-N curve is as shown in Appendix Figure 6 shown. The final life prediction result is as shown in Appendix Figure 9 shown, and the prediction effect is good.

Claims

1. A life prediction method suitable for high-temperature multi-axial random vibration loads, considering the interaction factor under non-proportional loading, that is, the additional interaction load on the structure under non-proportional loading, so as to reduce the failure life; defining the interaction factor F; considering the influence of high temperature on the SN curve; high temperature will change the slope and intercept of the SN curve, thereby reducing the failure life; defining the correction functions c(T) and m(T) of the high-temperature SN curve; Features: The implementation steps of the life prediction method are as follows: Step (1), obtaining the strain-time history of the dangerous point in multi-axial directions by means of a contact or non-contact strain gauge, and converting the strain-time history into a stress-time history by means of the elastic modulus of the material, represented by symbols X(t) and Y(t), respectively, where t represents the time point; Step (2), use the von Mises formula to convert X(t) and Y(t) of the entire process into equivalent stress: Among them, σ M is the equivalent stress, σ x is the stress in the X direction, σ y is the stress in the Y direction, and t represents the time point; Step (3): Use Wang-Brown counting to obtain the start and end time points t of each cycle for the stress-time history X(t) and Y(t). si With t ei , where t si represents the starting point of the ith cycle, t ei Indicates the end point of the i-th cycle; Step (4), calculate the interaction factor within each cycle based on the start and end time points of each cycle: f(t)=|sinθ(t)| Among them, l max is the maximum chord length within the loading path, t si is the starting point of the ith cycle, t ei is the end point of the ith cycle, l(t) is the chord length at time t, f(t) is the rotation factor, F(i) is the interaction factor within the ith cycle, and m X，0 is the zero-order spectral distance of the power spectral density function in the X direction, m Y，0 is the zero-order spectrum distance of the power spectral density function in the Y direction, α is the angle between the rotation factor and the X axis, and C is a constant; Step (5), based on step (4), consider the effect of non-proportional loading and correct the sum of squares of equivalent stress in each cycle: Where E(i) is the sum of squares of the equivalent stress of the ith cycle, σ eq is the equivalent stress after correction in the cycle, α is the material sensitive parameter, σ M is the equivalent stress, F(i) is the interaction factor within the cycle; Step (6), based on step (5), the equivalent time domain spectrum is obtained and the root mean square is calculated, and then the zero-order spectrum distance of the equivalent power spectrum density function is obtained: Among them, m eq，0 is the zero-order spectral distance of the equivalent time domain spectrum, n to is the total number of time points in the process, and to is the total number of all cycles in the process; Step (7), based on step (6), the equivalent power spectrum density function is obtained, and the formula is as follows: Among them, m eq，0 is the zero-order spectral distance of the equivalent time domain spectrum, m X，0 is the zero-order spectral distance in the X direction, G X is the power spectral density function in the X direction; Step (8), based on step (7), performing an inverse Fourier transform on the equivalent power spectrum density function, and further obtaining an amplitude probability density distribution function PDF; Step (9), the fatigue life is calculated based on the amplitude probability density distribution function PDF and the material high temperature SN curve, i.e., the stress-life curve. The high temperature SN curve of the titanium alloy material is: m(T)=m0(8×10 -8 T+2.2×10 -5 T+1) Among them, S a is the stress amplitude of the specimen, N is the fatigue life, m0 and C0 are the material constants at room temperature, m(T) and C(T) are the material constants at T temperature, and T is the temperature; The stress amplitude probability density function P(S a ), the SN curve of the material and the linear cumulative damage theorem are combined to analyze and obtain the fatigue damage expression of the structure: Where E[P] is the peak penetration rate, S a is the amplitude stress, m(T) and C(T) are material constants at T, T is temperature, P(S a ) is the probability density distribution function; Step (10), predicting the random vibration fatigue life under multi-axis conditions based on steps (8) and (9): Among them, D is the fatigue damage per unit time, and the L value is the predicted high-temperature multi-axial random vibration fatigue life of the structure.

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