Weighted average wheel disc circumferential rupture rotating speed analysis method

Abstract

The invention provides a weighted average wheel disc circumferential rupture rotating speed analysis method, and belongs to the technical field of aero-engines, and the method specifically comprises the steps: dividing a wheel disc into a plurality of units for circumferential bearing according to the structural characteristics of the wheel disc; calculating the effective bearing area of the meridian plane of the wheel disc according to the area of each unit of the meridian plane of the wheel disc in the limit state; calculating the weighted average ultimate strength of the meridian plane of the wheel disc based on the effective bearing area; calculating the weighted average circumferential stress of the meridian plane of the wheel disc based on the effective bearing area; and according to the weighted average ultimate strength and the weighted average circumferential stress, the circumferential rupture rotation speed reserve of the meridian plane of the wheel disc is obtained. According to the processing scheme, the problem that the theoretical predicted value of the circumferential rupture rotation speed of the wheel disc is large in deviation from the actual value under high temperature and large temperature gradient is solved, and the prediction precision of the circumferential rupture rotation speed of the wheel disc is improved.

Description

Technical Field

[0001] The present application relates to the field of aero-engine technology, and in particular to a weighted average wheel disc circumferential fracture rotation speed analysis method. Background Art

[0002] The rotor disc is a critical component of turbine machinery, such as engines. During normal engine acceleration, transient overspeed, fuel regulator failure, and afterburner malfunction can cause the disc to overspeed or even rupture. Disc rupture is typically considered an uncontained failure. To ensure flight safety, engine standards set a minimum rotor speed limit. Therefore, preventing rotor rupture is a key criterion in rotor strength design. Accurately estimating the rotor rupture speed is crucial during disc design.

[0003] In the design of small engines, to reduce development costs, most use an integral blisk structure, using integral precision casting and forging processes to reduce the number of parts. Due to the small size of the engine, the boundary layer effect in the airflow path is severe, and the engine thrust needs to be increased by increasing the temperature before the turbine. This requires the impeller to be able to withstand higher temperatures and greater temperature gradients.

[0004] Currently, the main method used in China to predict the fracture speed of a wheel is the mean stress method of linear elastic analysis. This method uses the mean stress of the critical section of the wheel, the ultimate strength corresponding to the mean temperature of the section, and the material correction factor to predict the fracture speed. However, this method assumes a linear relationship between the ultimate strength of the wheel material and temperature. When the temperature difference between the center and rim of the wheel is small, the ultimate strength corresponding to the mean temperature of the wheel meridian plane is similar to the actual value, and the error between the analysis result and the actual fracture speed is small. However, when there is a large temperature gradient between the center and rim of the wheel, the temperature-induced ultimate strength of the material decreases significantly. The ultimate strength corresponding to the mean temperature of the wheel meridian plane is higher than the actual value, and the predicted fracture speed is too high, posing a safety hazard to the design analysis.

[0005] Based on the above considerations, those skilled in the art are committed to studying a method for analyzing the circumferential fracture speed of a wheel based on the finite element weighted average ultimate strength to overcome the above problems. Summary of the Invention

[0006] In view of this, an embodiment of the present application provides a weighted average wheel circumferential rupture speed analysis method, which at least partially solves the problem in the prior art that when there is a large temperature gradient between the temperature of the wheel center and the wheel edge, the predicted rupture speed is too high, which brings safety hazards to the design analysis.

[0007] The present application provides a weighted average wheel disk circumferential fracture rotation speed analysis method, the method comprising:

[0008] According to the structural characteristics of the wheel disc, the wheel disc is divided into several circumferentially loaded units;

[0009] Calculate the effective bearing area of ​​the wheel meridian surface according to the area of ​​each unit of the wheel meridian surface under the limit state;

[0010] Calculate the weighted average ultimate strength of the wheel meridian surface based on the effective bearing area;

[0011] Calculate the weighted average circumferential stress of the wheel meridian surface based on the effective load-bearing area;

[0012] The circumferential fracture speed reserve of the wheel meridian surface is obtained according to the weighted average ultimate strength and the weighted average circumferential stress.

[0013] According to a specific implementation of the embodiment of the present application, the calculation formula for the effective load-bearing area of ​​the wheel meridian surface is:

[0014]

[0015] Among them, ∫ A dA is the effective bearing area of ​​the wheel meridian surface, n is the total number of units on the effective bearing surface of the wheel meridian surface; A i is the area of ​​the i-th unit on the effective load-bearing surface of the wheel meridian surface; V i is the volume simulated by the i-th unit on the effective bearing surface of the wheel meridian plane; ri is the centroid radius of the i-th unit on the effective bearing surface of the wheel meridian plane.

[0016] According to a specific implementation of the embodiment of the present application, the calculation of the weighted average ultimate strength of the wheel meridian plane includes:

[0017] According to the ultimate strength of the material at a known temperature, the ultimate strength of each unit on the radial surface of the wheel at the corresponding temperature is obtained;

[0018] According to the ultimate strength of each unit at the corresponding temperature, the total ultimate strength of the wheel meridian surface is calculated with the area of ​​each unit as the weight;

[0019] According to the total ultimate strength and effective bearing area of ​​the wheel meridian surface, the weighted average ultimate strength of the wheel meridian surface is calculated.

[0020] According to a specific implementation of the embodiment of the present application, the calculation formula for the total ultimate strength of the wheel meridian surface is:

[0021]

[0022] in, is the total ultimate strength of the wheel meridian surface; is the ultimate strength of the i-th unit on the effective bearing surface of the wheel meridian surface at the corresponding temperature; Ti is the temperature of the i-th unit on the effective bearing surface of the wheel meridian surface.

[0023] According to a specific implementation of the embodiment of the present application, the calculation formula of the weighted average ultimate strength of the wheel meridian plane is:

[0024]

[0025] Among them, σ bavg It is the weighted average ultimate strength of the wheel meridian surface.

[0026] According to a specific implementation of the embodiment of the present application, the calculation of the weighted average circumferential stress of the wheel meridian plane includes:

[0027] Obtain the circumferential stress of each element on the wheel meridian surface;

[0028] Based on the area of ​​each unit on the wheel meridian surface and the circumferential stress of each unit, the total circumferential stress on the wheel meridian surface is obtained;

[0029] Based on the effective load-bearing area and the total circumferential stress on the wheel meridian surface, the weighted average circumferential stress on the wheel meridian surface is calculated.

[0030] According to a specific implementation of the embodiment of the present application, the calculation formula for the total circumferential stress of the wheel meridian surface is:

[0031]

[0032] Among them, ∫ A σ t dA is the total circumferential stress on the wheel meridian surface, σ ti is the circumferential stress of the i-th unit on the effective load-bearing surface of the wheel meridian surface.

[0033] According to a specific implementation of the embodiment of the present application, the calculation formula of the weighted average circumferential stress of the wheel meridian surface is:

[0034]

[0035] Among them, σ tavg is the weighted average circumferential stress on the wheel meridian surface.

[0036] According to a specific implementation of the embodiment of the present application, the calculation formula of the circumferential fracture speed reserve of the wheel meridian surface is:

[0037]

[0038] Among them, n bis the circumferential rupture reserve speed coefficient of the wheel; k is the correction coefficient.

[0039] Beneficial effects:

[0040] The weighted average wheel circumferential fracture speed analysis method in the embodiment of the present application, with the help of commercial finite element software, based on the finite element calculation results and program writing, accurately obtains the temperature, stress and ultimate strength at the corresponding temperature corresponding to several units of the wheel meridian surface. Taking into account that the size of the average ultimate strength of the wheel meridian surface depends not only on the size of the ultimate strength of several units of the meridian surface at the corresponding temperature, but also on the proportion of the ultimate strength of several units in the meridian surface, the weighted average ultimate strength of the wheel meridian surface is calculated by the improved method of weighted average, which can take into account the influence of the proportion of the ultimate strength of each unit on the ultimate strength of the meridian surface, so that the obtained ultimate strength average value is closer to the actual value. The circumferential fracture speed reserve of the wheel meridian surface is calculated by the obtained weighted average ultimate strength, weighted average circumferential stress and material utilization coefficient, which can improve the prediction accuracy of the circumferential fracture speed of the wheel. This method involves few calculation parameters and has a significant improvement effect.

[0041] This application proposes an improved fracture speed analysis method for discs with circumferential fracture failure. The method features a simple calculation process and is readily applicable in engineering applications. This application addresses the significant temperature-induced decrease in ultimate material strength, addressing the significant deviation between theoretically predicted and actual fracture speeds at high temperatures and large temperature gradients, thereby improving the accuracy of circumferential fracture speed prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0043] Figure 1 Schematic diagram of a unit of the effective bearing surface of the wheel meridian surface according to one embodiment of the present invention;

[0044] Figure 2 Schematic diagram of a cylindrical microelement represented by the i-th unit of the wheel meridian plane according to an embodiment of the present invention;

[0045] Figure 3 Schematic diagram of solving the area of ​​the i-th unit after deformation of the wheel meridian surface according to one embodiment of the present invention;

[0046] Figure 4 FIG. 4 is a comparison diagram of ultimate strength calculation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0048] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the features in the following embodiments and embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative work are within the scope of protection of this application.

[0049] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this application, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0050] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present application. The illustrations only show components related to the present application and are not drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component can be changed at will, and the component layout type may also be more complicated.

[0051] Additionally, in the following description, specific details are provided to provide a thorough understanding of the examples. However, one skilled in the art will appreciate that the aspects described can be practiced without these specific details.

[0052] The embodiment of the present application provides a weighted average wheel circumferential fracture speed analysis method, which is referred to below. Figures 1 to 4 Provide a detailed description.

[0053] In one embodiment, a weighted average wheel disk circumferential fracture rotation speed analysis method is provided, the method comprising the following steps:

[0054] According to the structural characteristics of the wheel disc, the wheel disc is divided into several circumferentially loaded units;

[0055] Calculate the effective bearing area of ​​the wheel meridian surface according to the area of ​​each unit of the wheel meridian surface under the limit state;

[0056] Calculate the weighted average ultimate strength of the wheel meridian surface based on the effective bearing area;

[0057] Calculate the weighted average circumferential stress of the wheel meridian surface based on the effective load-bearing area;

[0058] The circumferential fracture speed reserve of the wheel meridian surface is obtained according to the weighted average ultimate strength and the weighted average circumferential stress.

[0059] In the specific implementation, according to the structural characteristics of the wheel, several units of the wheel circumferential load are selected in the finite element model, see Figure 1 As shown. With OXYZ as the coordinate system, each unit represents a cylindrical microelement with an area of ​​the unit area and a height of the circumference around the central axis of the wheel. Figure 2 .like Figure 3 As shown, the gray unit surrounded by the four points LIJK is the i-th unit of the roulette meridian plane, point P is the center of mass of the unit, and the distance between point O and point P is the radius r of the center of mass of the i-th unit of the roulette meridian plane. i , then the area A of the unit after deformation i is the volume V of the unit i With radius r i The ratio of the circumference of The effective bearing area of ​​the wheel meridian surface can be obtained by obtaining the volume and centroid radius of each unit after deformation and summing up the areas of several units.

[0060] In the selected units, the temperature of each unit on the wheel meridian surface is output through the written calculation program. According to the ultimate strength of the material at the known temperature, the ultimate strength of each unit at the corresponding temperature is obtained. According to the area of ​​each unit calculated in step 2, the total ultimate strength of the wheel meridian surface is calculated by summing the area of ​​each unit on the meridian surface as the weight. The weighted average ultimate strength can be obtained by dividing the total ultimate strength by the effective bearing area.

[0061] Among the selected units, the circumferential stress of each unit on the wheel meridian surface is output through the written calculation program, and then the circumferential stresses of several units are summed up to calculate the total circumferential stress on the wheel meridian surface. The weighted average circumferential stress can be obtained by dividing the total circumferential stress by the effective bearing area with the area of ​​several units on the meridian surface as the weight.

[0062] According to the relationship that stress is proportional to the square of the rotational speed, the circumferential fracture rotational speed reserve of the wheel meridian surface is calculated by dividing the weighted average ultimate strength by the weighted average circumferential stress, multiplying it by the material correction coefficient, and then taking the square root.

[0063] In one embodiment, the calculation formula for the effective bearing area of ​​the wheel meridian surface is:

[0064]

[0065] Among them, ∫ A dA is the effective bearing area of ​​the wheel meridian surface, n is the total number of units on the effective bearing surface of the wheel meridian surface; A i is the area of ​​the i-th unit on the effective load-bearing surface of the wheel meridian surface; V i is the volume simulated by the i-th unit on the effective load-bearing surface of the wheel meridian surface; r i is the centroid radius of the i-th unit on the effective load-bearing surface of the wheel meridian plane.

[0066] In one embodiment, the calculating of the weighted average ultimate strength of the wheel meridian plane includes:

[0067] According to the ultimate strength of the material at a known temperature, the ultimate strength of each unit on the radial surface of the wheel at the corresponding temperature is obtained;

[0068] According to the ultimate strength of each unit at the corresponding temperature, the total ultimate strength of the wheel meridian surface is calculated with the area of ​​each unit as the weight;

[0069] According to the total ultimate strength and effective bearing area of ​​the wheel meridian surface, the weighted average ultimate strength of the wheel meridian surface is calculated.

[0070] In one embodiment, the calculation formula for the total ultimate strength of the wheel meridian surface is:

[0071]

[0072] in, is the total ultimate strength of the wheel meridian surface; is the ultimate strength of the i-th unit on the effective bearing surface of the wheel meridian surface at the corresponding temperature; Ti is the temperature of the i-th unit on the effective bearing surface of the wheel meridian surface.

[0073] In one embodiment, the calculation formula of the weighted average ultimate strength of the wheel meridian plane is:

[0074]

[0075] Among them, σ bavg It is the weighted average ultimate strength of the wheel meridian surface.

[0076] In one embodiment, the step of calculating the weighted average circumferential stress of the wheel meridian plane includes:

[0077] Obtain the circumferential stress of each element on the wheel meridian surface;

[0078] Based on the area of ​​each unit on the wheel meridian surface and the circumferential stress of each unit, the total circumferential stress on the wheel meridian surface is obtained;

[0079] Based on the effective load-bearing area and the total circumferential stress on the wheel meridian surface, the weighted average circumferential stress on the wheel meridian surface is calculated.

[0080] In one embodiment, the calculation formula for the total circumferential stress of the wheel meridian surface is:

[0081]

[0082] Among them, ∫ A σ t dA is the total circumferential stress on the wheel meridian surface, σ ti is the circumferential stress of the i-th unit on the effective load-bearing surface of the wheel meridian surface.

[0083] In one embodiment, the calculation formula of the weighted average circumferential stress of the wheel meridian plane is:

[0084]

[0085] Among them, σ tavg is the weighted average circumferential stress on the wheel meridian surface.

[0086] In one embodiment, the calculation formula for the circumferential fracture speed reserve of the wheel meridian surface is:

[0087]

[0088] Among them, n b is the circumferential rupture reserve speed coefficient of the wheel; k is the correction coefficient.

[0089] This application first uses commercial finite element software to accurately obtain the temperature, stress and ultimate strength of several units on the wheel meridian surface at the corresponding temperature based on the finite element calculation results and program writing. Considering that the average ultimate strength of the wheel meridian surface depends not only on the ultimate strength of several units on the meridian surface at the corresponding temperature, but also on the proportion of the ultimate strength of several units in the meridian surface, the improved method of weighted average is used to calculate the weighted average ultimate strength of the wheel meridian surface. This can take into account the influence of the proportion of the ultimate strength of each unit on the ultimate strength of the meridian surface, making the obtained ultimate strength average value closer to the actual value. For specific calculation results, refer to Figure 4The circumferential fracture speed reserve of the wheel's radial surface is calculated using the obtained weighted average ultimate strength, weighted average circumferential stress, and material utilization factor. This method improves the accuracy of the prediction of the wheel's circumferential fracture speed. This method involves fewer calculation parameters and achieves significant improvements.

[0090] This method, specifically designed for discs with circumferential failure, features a simple calculation process and is readily applicable in engineering applications. By employing a weighted average method for fracture speed analysis, and taking into account the significant temperature-induced decrease in the ultimate strength of the material, it addresses the significant discrepancy between theoretically predicted and actual fracture speeds at high temperatures and large temperature gradients, thereby improving the accuracy of the predictions.

[0091] 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 the present 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 weighted average wheel circumferential fracture speed analysis method, characterized in that: The method comprises: According to the structural characteristics of the wheel disc, the wheel disc is divided into several circumferentially loaded units; Calculate the effective bearing area of ​​the wheel meridian surface according to the area of ​​each unit of the wheel meridian surface under the limit state; Calculate the weighted average ultimate strength of the wheel meridian surface based on the effective bearing area; Calculate the weighted average circumferential stress of the wheel meridian surface based on the effective load-bearing area; The circumferential fracture speed reserve of the wheel meridian surface is obtained according to the weighted average ultimate strength and the weighted average circumferential stress.

2. The weighted average wheel disk circumferential fracture speed analysis method according to claim 1, characterized in that: The calculation formula for the effective bearing area of ​​the wheel meridian surface is: Among them, ∫ A dA is the effective bearing area of ​​the wheel meridian surface, n is the total number of units on the effective bearing surface of the wheel meridian surface; A i is the area of ​​the i-th unit on the effective load-bearing surface of the wheel meridian surface; V i is the volume simulated by the i-th unit on the effective load-bearing surface of the wheel meridian surface; r i is the centroid radius of the i-th unit on the effective load-bearing surface of the wheel meridian plane.

3. The weighted average wheel disk circumferential fracture speed analysis method according to claim 2, characterized in that: The calculation of the weighted average ultimate strength of the wheel meridian plane includes: According to the ultimate strength of the material at a known temperature, the ultimate strength of each unit on the radial surface of the wheel at the corresponding temperature is obtained; According to the ultimate strength of each unit at the corresponding temperature, the total ultimate strength of the wheel meridian surface is calculated with the area of ​​each unit as the weight; According to the total ultimate strength and effective bearing area of ​​the wheel meridian surface, the weighted average ultimate strength of the wheel meridian surface is calculated.

4. The weighted average wheel disk circumferential fracture speed analysis method according to claim 3, characterized in that: The calculation formula for the total ultimate strength of the wheel meridian surface is: in, is the total ultimate strength of the wheel meridian surface; is the ultimate strength of the i-th unit on the effective bearing surface of the wheel meridian surface at the corresponding temperature; Ti is the temperature of the i-th unit on the effective bearing surface of the wheel meridian surface.

5. The weighted average wheel disk circumferential fracture rotation speed analysis method according to claim 4, characterized in that: The calculation formula of the weighted average ultimate strength of the wheel meridian plane is: Among them, σ bavg It is the weighted average ultimate strength of the wheel meridian surface.

6. The weighted average wheel disk circumferential fracture rotation speed analysis method according to claim 5, characterized in that: The calculation of the weighted average circumferential stress of the wheel meridian surface includes: Obtain the circumferential stress of each element on the wheel meridian surface; Based on the area of ​​each unit on the wheel meridian surface and the circumferential stress of each unit, the total circumferential stress on the wheel meridian surface is obtained; Based on the effective load-bearing area and the total circumferential stress on the wheel meridian surface, the weighted average circumferential stress on the wheel meridian surface is calculated.

7. The weighted average wheel disk circumferential fracture rotation speed analysis method according to claim 6, characterized in that: The calculation formula of the total circumferential stress of the wheel meridian surface is: Among them, ∫ A σ t dA is the total circumferential stress on the wheel meridian surface, σ ti is the circumferential stress of the i-th unit on the effective load-bearing surface of the wheel meridian surface.

8. The weighted average wheel disk circumferential fracture rotation speed analysis method according to claim 7, characterized in that: The calculation formula of the weighted average circumferential stress of the wheel meridian surface is: Among them, σ tavg is the weighted average circumferential stress on the wheel meridian surface.

9. The weighted average wheel disk circumferential fracture rotation speed analysis method according to claim 8, characterized in that: The calculation formula of the circumferential fracture speed reserve of the wheel meridian surface is: Among them, n b is the circumferential rupture reserve speed coefficient of the wheel; k is the correction coefficient.

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