A calculation method for the crack growth life of a wheel considering the limiting load condition

Abstract

The present application belongs to the field of fatigue life calculation, and particularly relates to a method for calculating the crack propagation life of a wheel considering a restricted load condition. The method comprises: obtaining the stress or strain distribution of the wheel under the action of a Class I cyclic peak load condition; prefabricating an initial crack at a characteristic portion of the wheel to obtain a stress intensity factor distribution curve of the initial crack front; performing crack propagation under the action of the Class I cyclic peak load condition according to the first crack propagation plan to obtain crack propagation morphologies of different crack propagation sizes; obtaining the stress or strain distribution of the wheel under the restricted load condition; calculating the maximum stress intensity factor of the crack front corresponding to each of the crack propagation morphologies; fitting the relationship curve between the crack propagation size and the maximum stress intensity factor to predict the critical crack size; and calculating the crack propagation life. The crack propagation life given in the present application is more conservative and safer.

Description

Technical Field

[0001] The present application belongs to the field of fatigue life calculation, and in particular relates to a method for calculating the crack growth life of a wheel considering a limited load condition. Background Art

[0002] Aircraft engine discs are the most critical components in aircraft engine structures. The primary mode of failure is low-cycle fatigue damage. Once damaged during use, these damages can have non-containment consequences, jeopardizing aircraft safety. Therefore, aircraft engine discs are typically designed as life-limited components. The impact of defects or cracks arising from material preparation, blank forming, manufacturing, assembly, transportation, and use on the disc's service life must be considered during design. Fatigue crack growth analysis under typical missions is required to determine whether the crack growth life from an initial defect to a critical crack size meets the requirements for aircraft engine maintenance intervals.

[0003] At present, in the analysis and verification of crack growth of domestic aero-engine discs, through analysis based on mission profiles, Class I (0~maximum~0), Class III (slow~maximum~slow) and Class IV (cruise~maximum~cruise) cycles and their cycle numbers are obtained, and according to the equal damage method or the 1:4:40 conversion method, the equivalent number of cycles corresponding to Class I cycles is obtained. By analyzing the fatigue crack growth of the disc under Class I cyclic load, the fatigue crack growth cycle life is obtained and compared with the converted equivalent number of cycles to verify whether it meets the requirements.

[0004] In actual use, due to the presence of initial defects or cracks in the characteristic parts of the wheel, under the action of cyclic loads, the initial defects or cracks in the characteristic parts begin to expand, thereby weakening the wheel's load-bearing capacity and causing the wheel's residual strength to gradually decrease as the crack grows. When the crack length in the characteristic part of the wheel expands to a certain size (generally referred to as the critical crack size), under the maximum limiting load of the wheel, when the stress intensity factor of the crack front reaches the fracture toughness of the material, the crack in the characteristic part will undergo unstable expansion, causing the wheel to disintegrate and fail. Therefore, the maximum limiting load condition of the wheel in use is the most important load factor that determines the allowable crack expansion length of the characteristic part of the wheel. Under the conditions of a certain initial crack size and a certain material expansion rate, the allowable crack expansion length is the determining factor in determining the crack expansion life. However, in use, the peak load condition corresponding to the Type I cycle is often smaller than the maximum limit load condition that the wheel may experience in the mission profile (including overspeed considering the influence of control system accuracy). This makes the critical crack size determined only according to the Type I cycle peak load longer than the actual situation, and the estimated crack propagation cycle life is also longer than the actual propagation cycle life, which leads to unreliable prediction results.

[0005] Therefore, it is desired to have a technical solution to overcome or at least alleviate at least one of the above-mentioned deficiencies of the prior art. Summary of the Invention

[0006] The purpose of this application is to provide a method for calculating the crack growth life of a wheel disc taking into account a limited load condition, so as to solve at least one problem existing in the prior art.

[0007] The technical solution of this application is:

[0008] A calculation method for the crack growth life of a wheel considering a limiting load condition includes:

[0009] Step 1: Obtain a Class I cyclic peak load condition and a stress or strain distribution of the wheel under the Class I cyclic peak load condition;

[0010] Step 2: Prefabricate an initial crack at a characteristic portion of the wheel disc, and calculate a stress intensity factor distribution curve at the front edge of the initial crack under the Class I cyclic peak load condition;

[0011] Step 3: obtaining a first crack growth plan, and performing crack growth under the type I cyclic peak load condition according to the first crack growth plan to obtain crack growth morphologies of different crack growth sizes;

[0012] Step 4: Obtaining a limiting load condition and the stress or strain distribution of the wheel under the limiting load condition;

[0013] Step 5: calculating the stress intensity factor distribution curve of the crack front corresponding to each of the crack extension morphologies under the limiting load condition, and obtaining the maximum stress intensity factor of the crack front corresponding to each of the crack extension morphologies;

[0014] Step 6: According to the first crack extension plan and the maximum stress intensity factor, a relationship curve between the crack extension size and the maximum stress intensity factor is obtained by fitting, and the material fracture toughness K is obtained by interpolation. C The corresponding crack extension size;

[0015] Step 7: Obtain a second crack extension plan, in which the maximum crack extension size is the material fracture toughness K C The corresponding crack propagation size is obtained, and according to the second crack propagation plan, crack propagation is carried out under the action of the Class I cyclic peak load to obtain a relationship curve between the crack propagation length and the corresponding stress intensity factor under the specified crack propagation path. Combined with the crack propagation rate model, the crack propagation length and propagation life curve is calculated, and the crack propagation life is obtained according to the crack propagation life curve.

[0016] In at least one embodiment of the present application, in step 1, obtaining a Class I cyclic peak load condition and a stress or strain distribution of the wheel under the Class I cyclic peak load condition includes:

[0017] Obtain the Class I cyclic peak load condition: the rotation speed n = 13500 r / min, and the blade centrifugal tensile stress on the wheel rim is 364.5 MPa;

[0018] The linear elastic finite element method is used to obtain the circumferential stress distribution in the center area of the wheel disk under the action of the Class I cyclic peak load condition.

[0019] In at least one embodiment of the present application, in step 2, the size of the initial crack is:

[0020] For surface cracks, the initial crack size is: length × depth = 0.76 mm × 0.38 mm;

[0021] For corner cracks, the initial crack size is: length × depth = 0.38 mm × 0.38 mm.

[0022] In at least one embodiment of the present application, in step 2, preforming an initial crack at a characteristic portion of the wheel disc is specifically: preforming an initial crack at the center of the wheel disc, wherein the initial crack is a surface crack with a crack length of 0.76 mm and a crack depth of 0.38 mm.

[0023] In at least one embodiment of the present application, in step three, the first crack extension plan includes:

[0024] The p% of the crack extension length corresponding to the midpoint of the stress intensity factor of the previous crack front is used as the crack extension increment at the midpoint of the stress intensity factor of the next crack front:

[0025] Δa median =a medeian ×p%

[0026] The crack extension increments at other points on the crack front are calculated according to the following formula:

[0027] Δa i =Δa median ×(K i / K median ) 2

[0028] Among them, a medeian is the crack extension length at the midpoint of the stress intensity factor of the crack front, Δa median K is the crack extension increment at the midpoint of the stress intensity factor of the next crack front, iis the stress intensity factor value of the i-th point on the crack front, K median is the median value of the stress intensity factor at the crack front.

[0029] In at least one embodiment of the present application, the p% is 15%.

[0030] In at least one embodiment of the present application, in step 4, obtaining the limiting load condition and the stress or strain distribution of the wheel under the limiting load condition includes:

[0031] Obtain the limiting load condition: speed n = 15000 r / min, blade centrifugal tensile stress on the wheel rim is 450 MPa;

[0032] The circumferential stress distribution in the center area of the wheel disc under the action of the limiting load condition is obtained using the linear elastic finite element method.

[0033] In at least one embodiment of the present application, in step six, the relationship curve between the crack extension size and the maximum stress intensity factor is fitted according to the first crack extension plan and the maximum stress intensity factor, and the material fracture toughness K is obtained by interpolation. C The corresponding crack growth size includes:

[0034] According to the first crack growth plan and the maximum stress intensity factor, the expression of the relationship curve between the crack growth size and the maximum stress intensity factor is fitted as follows:

[0035] Y=0.8865X 7 -7.15X 6 +21.52X 5 -31.33X 4 +29.23X 3 -25.98X 2 +28.24X

[0036] +102.6

[0037] The fracture toughness of the material is obtained by interpolation The corresponding crack extension length is a critical =20.92mm.

[0038] The invention has at least the following beneficial technical effects:

[0039] The calculation method of the wheel crack growth life considering the limited load conditions in this application can predict the crack growth life of the wheel under the action of Class I cyclic peak load based on the wheel limited load conditions determined by the working envelope and usage of the aircraft engine. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of a method for calculating the crack growth life of a wheel disc considering a limited load condition according to one embodiment of the present application;

[0041] Figure 2 This is a schematic diagram of the circumferential stress distribution at the center of the wheel disc under a Class I cyclic peak load condition according to one embodiment of the present application;

[0042] Figure 3 This is a schematic diagram of a wheel disc with an initial crack prefabricated at the center of the disc according to one embodiment of the present application;

[0043] Figure 4 is a stress intensity factor distribution curve of the initial crack front under a Class I cyclic peak load condition according to one embodiment of the present application;

[0044] Figure 5 This is a schematic diagram of crack extension morphologies corresponding to different crack extension sizes according to an embodiment of the present application;

[0045] Figure 6 This is a schematic diagram of the circumferential stress distribution at the center of the wheel disc under a limited load condition in one embodiment of the present application;

[0046] Figure 7 is a stress intensity factor distribution curve of the crack front corresponding to each crack propagation morphology in one embodiment of the present application;

[0047] Figure 8 is a relationship curve between the crack extension size and the maximum value of the stress intensity factor in one embodiment of the present application;

[0048] Figure 9 This is a curve showing the relationship between the length of the deepest point of crack propagation and the number of life cycles in one embodiment of the present application. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below in conjunction with the drawings in the embodiments of this application. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of this application, not all of the embodiments. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain this application, and should not be understood as limitations on this application. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The embodiments of this application are described in detail below in conjunction with the drawings.

[0050] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be understood as limiting the scope of protection of this application.

[0051] The following is combined with Figures 1 to 9 This application is described in further detail.

[0052] The present application provides a method for calculating the crack growth life of a wheel disc considering a limited load condition, comprising the following steps:

[0053] Step 1: Obtain a Class I cyclic peak load condition and the stress or strain distribution of the wheel under the Class I cyclic peak load condition;

[0054] Step 2: Prefabricate an initial crack at a characteristic location of the disc and calculate the stress intensity factor distribution curve at the initial crack front under a Type I cyclic peak load condition;

[0055] Step 3: Obtain a first crack growth plan, and perform crack growth under a Type I cyclic peak load condition according to the first crack growth plan to obtain crack growth morphologies of different crack growth sizes;

[0056] Step 4: Obtain the limiting load condition and the stress or strain distribution of the wheel under the limiting load condition;

[0057] Step 5: Calculate the stress intensity factor distribution curve of the crack front corresponding to each crack growth morphology under the action of the limiting load condition, and obtain the maximum stress intensity factor of the crack front corresponding to each crack growth morphology;

[0058] Step 6: According to the first crack extension plan and the maximum stress intensity factor, a relationship curve between the crack extension size and the maximum stress intensity factor is obtained by fitting, and the material fracture toughness K is obtained by interpolation. C The corresponding crack extension size;

[0059] Step 7: Obtain the second crack extension plan. The maximum crack extension size in the second crack extension plan is the material fracture toughness K CThe corresponding crack extension size is obtained, and according to the second crack extension plan, crack extension is carried out under the action of type I cyclic peak load to obtain the relationship curve between the crack extension length and the corresponding stress intensity factor under the specified crack extension path. Combined with the crack extension rate model, the crack extension length and extension life curve is calculated, and the crack extension life is obtained according to the crack extension life curve.

[0060] The present invention relates to a method for calculating the crack growth life of a disk considering a restricted load condition. First, in step 1, a Class I cyclic peak load is obtained. Under the Class I cyclic peak load condition, the stress or strain distribution of the disk is obtained using the linear elastic finite element method. In one embodiment of the present invention, a Class I cyclic peak load of a disk is known to be: a rotational speed n = 13500 r / min, and the centrifugal tensile stress of the blades on the rim is 364.5 MPa. Under the above load, the circumferential stress distribution in the disk center region, where the disk has the greatest stress and is the most dangerous, is as follows: Figure 2 shown.

[0061] In a preferred embodiment of the present application, in step 2, an initial defect is prefabricated at a characteristic portion of the wheel disc. For surface cracks, the initial crack size is generally: length × depth = 0.76 mm × 0.38 mm; for corner cracks, the initial crack size is generally: length × depth = 0.38 mm × 0.38 mm. In this embodiment, Figure 3 As shown in Figure 1, an initial surface crack was prefabricated at the center of the wheel disc, with a crack length of 0.76 mm and a crack depth of 0.38 mm. The stress intensity factor distribution curve of the crack front corresponding to the initial crack morphology under the action of the Type I cyclic peak load condition is obtained, see Figure 4 .

[0062] In a preferred embodiment of the present application, in step three, the first crack extension plan includes:

[0063] The p% of the crack extension length corresponding to the midpoint of the stress intensity factor of the previous crack front is used as the crack extension increment at the midpoint of the stress intensity factor of the next crack front. The recommended p% value is 15%:

[0064] Δa median =a medeian ×p%

[0065] The crack extension increments at other points on the crack front are calculated according to the following formula:

[0066] Δa i =Δa median ×(K i / K median ) 2

[0067] Among them, amedeian is the crack extension length at the midpoint of the stress intensity factor of the crack front, Δa median K is the crack extension increment at the midpoint of the stress intensity factor of the next crack front, i is the stress intensity factor value of the i-th point on the crack front, K median is the median value of the stress intensity factor at the crack front.

[0068] In this embodiment, a crack growth plan at the midpoint of the stress intensity factor of the crack front is formulated based on the initial crack size. Each crack growth increment is 15% of the crack growth length, resulting in the crack growth length and growth increment plan shown in Table 1.

[0069] Table 1

[0070] Crack growth increment Crack size (mm) Crack extension increment size (mm) 0 0.380 0.0 1 0.437 0.057 2 0.503 0.066 3 0.578 0.075 … … … 31 28.935 3.774 32 33.275 4.340 33 38.266 4.991

[0071] Based on the above crack growth plan, the crack is grown under the type I cyclic peak load condition, and the morphology of the crack growth sheet corresponding to different crack growth lengths is obtained, as shown in Figure 2. Figure 5 shown.

[0072] In a preferred embodiment of the present application, in step 4, the limiting load condition is obtained as follows: the rotation speed n = 15000 r / min, and the centrifugal tensile stress of the blade on the rim portion is 450 MPa; the circumferential stress distribution of the disk center area, where the disk stress is the largest and most dangerous, under the limiting load condition is obtained using the linear elastic finite element method, as shown in FIG. Figure 6 shown.

[0073] In this embodiment, in step five, based on the crack extension morphology under the type I cyclic peak load condition obtained in step three as the crack geometry, the stress intensity factor distribution curves of the crack front under different crack extension morphologies under the maximum limit load condition are calculated in sequence, and the calculation data of the maximum value of the stress intensity factor of the crack front are obtained, as shown in Table 7.

[0074] Furthermore, in step 6, according to the first crack extension plan prepared in step 3 and the maximum stress intensity factor obtained in step 5, a relationship curve between the crack extension size and the maximum stress intensity factor is obtained by fitting, see Figure 8 , and the material fracture toughness K is obtained by interpolation C Corresponding crack extension size. In this embodiment, the relationship between the crack extension size and the maximum stress intensity factor is expressed as follows:

[0075] Y=0.8865X 7 -7.15X 6 +21.52X 5 -31.33X 4+29.23X 3 -25.98X 2 +28.24X

[0076] +102.6

[0077] The fracture toughness of the material is obtained by interpolation The corresponding crack extension length is a critical =20.92mm.

[0078] Finally, in step seven, following the first crack extension plan in step three and the a obtained in step six critical , a new second crack extension plan is formulated, and the last step of the extension increment is a critical The crack length is determined in the previous step. In this embodiment, the crack extension plan at the midpoint of the stress intensity factor of the crack front has a maximum crack length of a critical , as shown in Table 2.

[0079] Table 2

[0080] Crack growth increment Crack size (mm) Crack extension increment size (mm) 0 0.380 0.0 1 0.437 0.057 2 0.503 0.066 3 0.578 0.075 … … … 27 16.543 2.158 28 19.025 2.482 29 20.920 1.895

[0081] According to the above content, the crack growth plan is carried out to obtain the relationship curve between the crack growth length and the corresponding stress intensity factor under the specified crack growth path. Combined with the crack growth rate model, the crack growth life curve is calculated. This process is realized by the existing life calculation software. Finally, the relationship curve between the crack growth length at the midpoint of the crack front and the life cycle number is calculated, as shown in the figure below: Figure 9 As shown, the corresponding cycle life from the initial crack expansion to the critical crack size is 20103 cycles.

[0082] The present invention's calculation method for the crack growth life of a wheel disc, taking into account the restricted load conditions, predicts a crack growth life of 20,103 cycles. Without the restricted load conditions, the predicted crack growth life is 24,886 cycles. This demonstrates that the crack growth life given in this application is more conservative and offers greater safety.

[0083] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for calculating the crack growth life of a wheel considering a limited load condition, characterized in that: include: Step 1: Obtain a Class I cyclic peak load condition and a stress or strain distribution of the wheel under the Class I cyclic peak load condition; Step 2: Prefabricate an initial crack at a characteristic portion of the wheel disc, and calculate a stress intensity factor distribution curve at the front edge of the initial crack under the Class I cyclic peak load condition; Step 3: obtaining a first crack growth plan, and performing crack growth under the type I cyclic peak load condition according to the first crack growth plan to obtain crack growth morphologies of different crack growth sizes; The first crack growth plan includes: The p% of the crack extension length corresponding to the midpoint of the stress intensity factor of the previous crack front is used as the crack extension increment at the midpoint of the stress intensity factor of the next crack front: Δa medeian =a medeian ×p% The crack extension increments at other points on the crack front are calculated according to the following formula: Δa i =Δa median ×(K i / K median ) 2 Among them, a medeian is the crack extension length at the midpoint of the stress intensity factor of the crack front, Δa median K is the crack extension increment at the midpoint of the stress intensity factor of the next crack front, i is the stress intensity factor value of the i-th point on the crack front, k median is the median value of the stress intensity factor at the crack front; Step 4: Obtaining a limiting load condition and the stress or strain distribution of the wheel under the limiting load condition; Step 5: calculating the stress intensity factor distribution curve of the crack front corresponding to each of the crack extension morphologies under the limiting load condition, and obtaining the maximum stress intensity factor of the crack front corresponding to each of the crack extension morphologies; Step 6: According to the first crack extension plan and the maximum stress intensity factor, a relationship curve between the crack extension size and the maximum stress intensity factor is obtained by fitting, and the material fracture toughness K is obtained by interpolation. C The corresponding crack growth size includes: According to the first crack growth plan and the maximum stress intensity factor, the expression of the relationship curve between the crack growth size and the maximum stress intensity factor is fitted as follows: Y=0.8865X 7 -7.15X 6 +21.52X 5 -31.33X 4 +29.23X 3 -25.98X 2 +28.24X+102.6 The material fracture toughness K is obtained by interpolation C =120MPa√mThe corresponding crack extension length is a critical =20.92mm; Step 7: Obtain a second crack extension plan, in which the maximum crack extension size is the material fracture toughness K C The corresponding crack propagation size is obtained, and according to the second crack propagation plan, crack propagation is carried out under the action of the Class I cyclic peak load to obtain a relationship curve between the crack propagation length and the corresponding stress intensity factor under the specified crack propagation path. Combined with the crack propagation rate model, the crack propagation length and propagation life curve is calculated, and the crack propagation life is obtained according to the crack propagation life curve.

2. The method for calculating the crack growth life of a wheel disc considering the limiting load condition according to claim 1, characterized in that: In step 1, obtaining a Class I cyclic peak load condition and the stress or strain distribution of the wheel under the Class I cyclic peak load condition includes: Obtain the Class I cyclic peak load condition: the rotation speed n = 13500 r / min, and the blade centrifugal tensile stress on the wheel rim is 364.5 MPa; The linear elastic finite element method is used to obtain the circumferential stress distribution in the center area of the wheel disk under the action of the Class I cyclic peak load condition.

3. The method for calculating the crack growth life of a wheel disc considering the limiting load condition according to claim 2, characterized in that: In step 2, the size of the initial crack is: For surface cracks, the initial crack size is: length × depth = 0.76 mm × 0.38 mm; For corner cracks, the initial crack size is: length × depth = 0.38 mm × 0.38 mm.

4. The method for calculating the crack growth life of a wheel disc considering the limiting load condition according to claim 3 is characterized in that: In step 2, the prefabrication of the initial crack at the characteristic position of the wheel disc is specifically as follows: prefabrication of the initial crack at the center of the wheel disc, the initial crack being a surface crack with a crack length of 0.76 mm and a crack depth of 0.38 mm.

5. The method for calculating the crack growth life of a wheel disc considering the limiting load condition according to claim 4, characterized in that: The p% is 15%.

6. The method for calculating the crack growth life of a wheel disc considering the limiting load condition according to claim 5, characterized in that: In step 4, obtaining the limiting load condition and the stress or strain distribution of the wheel under the limiting load condition includes: Obtain the limiting load condition: speed n = 15000 r / min, blade centrifugal tensile stress on the wheel rim is 450 MPa; The circumferential stress distribution in the center area of the wheel disc under the action of the limiting load condition is obtained using the linear elastic finite element method.

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