CN114896715A - Aero-engine wheel disc balancing weight design method based on multi-objective optimization - Google Patents

Aero-engine wheel disc balancing weight design method based on multi-objective optimization Download PDF

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CN114896715A
CN114896715A CN202210345070.5A CN202210345070A CN114896715A CN 114896715 A CN114896715 A CN 114896715A CN 202210345070 A CN202210345070 A CN 202210345070A CN 114896715 A CN114896715 A CN 114896715A
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balancing weight
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design
weight
blade
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郭跃
刘一雄
吴云伍
韩方军
郭勇
陈育志
马青超
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AECC Shenyang Engine Research Institute
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Abstract

The application provides an aeroengine roulette counterweight block design method based on multi-objective optimization, which comprises the following steps: determining key design parameters of the balancing weight, wherein the key design parameters comprise the radial height sum of a balancing weight design domain, the axial length of the balancing weight, the axial centroid of the front end surface of the balancing weight, the axial centroid of an initial domain of the balancing weight, the radial centroid of the initial domain, the distance between the top surface of the initial design domain and an engine rotating shaft, the circumferential width of the balancing weight, the area of the top surface of the initial design domain, the average radius of the balancing weight and the circumferential offset; constructing a balancing weight multi-objective optimization mathematical model comprising the key design parameters; and optimizing the structural parameters of the balancing weight according to the mathematical model to obtain the structural parameters of the balancing weight.

Description

Aero-engine wheel disc balancing weight design method based on multi-objective optimization
Technical Field
The application belongs to the technical field of aero-engines, and particularly relates to a design method of a wheel disc balancing weight of an aero-engine based on multi-objective optimization.
Background
The disk of the aero-engine is a part which is easy to generate structural damage in the aero-engine due to the complex load working conditions such as higher centrifugal load, thermal load and the like. Therefore, safety assessment tests are usually carried out on the disk of the aircraft engine, and if real blades are adopted for balancing weights of hollow air-cooled blades, particularly high in manufacturing cost, the test cost is overhigh, and unnecessary waste is caused. Therefore, in an aircraft engine wheel disc examination test, a balancing weight is often adopted to replace a real blade to simulate blade load. Although the balancing weight is only a test accompanying test piece, the quality of the design of the balancing weight has important influence on the test examination of the strength and the service life of the wheel disc, and the unreasonable design can cause the problem that the wheel disc is damaged in advance due to over examination or the wheel disc is not examined and can not be fully exposed, so that the design of the balancing weight is important in the test design of the strength of the wheel disc.
The method for designing the balancing weight in the prior art is generally based on the equivalent principle of weight moment and bending moment, namely, the weight moment of the balancing weight and the bending moment of the rabbet throat are ensured to be consistent with those of a real blade.
Disclosure of Invention
The application aims to provide a design method of an aeroengine roulette counterweight block based on multi-objective optimization, so as to solve or alleviate at least one problem in the background art.
The technical scheme of the application is as follows: a design method of a disk balancing weight of an aero-engine based on multi-objective optimization, the method comprises the following steps:
determining key design parameters of the balancing weight, wherein the key design parameters comprise radial height h of a balancing weight design domain 1 And h 2 Axial length l of balancing weight, axial mass center X of front end face of balancing weight s Axial mass center X of the balancing weight c Initial domain axial mass center X of balancing weight 0 Initial domain radial centroid Z 0 Distance Z between top surface of initial design domain and rotating shaft of engine s Circumferential width w of counter weight, initial design area top surface area S 0 The average radius r of the balancing weight and the circumferential offset a;
constructing a balancing weight multi-objective optimization mathematical model comprising the key design parameters;
and optimizing the structural parameters of the balancing weight according to the mathematical model to obtain the structural parameters of the balancing weight.
Further, based on the weight moment and bending moment equivalent principle, when the balancing weight is designed, the structure of the balancing weight is divided into an initial domain and a design domain, wherein the initial domain is consistent with the tenon structure of the real blade and is used for ensuring the assembly performance of the balancing weight and the wheel disc mortise so as to simulate the tenon mass distribution of the real blade; the design domain is divided into a rectangular region and a triangular region, and the mass of the balancing weight and the mass center are adjusted by changing the parameters of the design domain so as to simulate the blade body mass distribution of a real blade.
Further, the mathematical model is as follows:
Figure BDA0003576244820000021
in the formula: sigma k,p The stress of the main checking part under the action of the balancing weight;
σ k,b the stress of the main assessment part under the action of the blade;
σ i,p the stress of the ith secondary assessment part under the action of the balancing weight;
σ i,b the stress of the ith secondary assessment part under the action of the blade;
lambda is the weight moment amplification factor of the balancing weight;
r is the average radius of the counterweight;
n is the number of blades;
w is the circumferential width of the balancing weight;
a is a circumferential offset;
V p is the volume of the balancing weight;
Z p is the radial mass center of the balancing weight;
V b is the volume of the blade;
Z b is the radial center of mass of the blade.
Further, radial height h of rectangular area of counterweight block design domain 1 And the radial height h of the triangular area 2 Satisfies the following conditions:
Figure BDA0003576244820000031
Figure BDA0003576244820000032
wherein D, E, F is a dimensionless parameter, including:
Figure BDA0003576244820000033
in the formula, V 0 Is the initial domain volume;
Z 0 is the initial domain radial centroid;
l is the axial length of the balancing weight;
X s is the axial mass center of the front end surface of the balancing weight;
X c is the axial mass center of the balancing weight;
X 0 an initial design domain axial centroid;
S 0 designing the area of the top surface of the domain for the initial design;
Z s the distance between the top surface of the initial design domain and the rotating shaft of the engine is set;
V b is the volume of the blade;
Z b is the radial center of mass of the blade;
lambda is the weight moment amplification factor of the balancing weight;
xi is the blade density/weight density.
Further, the radial height h of the rectangular area of the design domain of the balancing weight 1 And the radial height h of the triangular area 2 The radial weight moment of the real blade is equal to the sum of the radial weight moment of the initial domain of the balancing weight, the radial weight moment of the rectangular region in the design domain and the radial weight moment of the triangular region in the design domain, and the equivalent principle of the balancing weight and the blade to the bending moment of the throat of the tenon is obtained, and the equivalent principle of the balancing weight and the blade to the bending moment of the throat of the tenon comprises the following steps:
Figure BDA0003576244820000041
Figure BDA0003576244820000042
in addition, the application also provides an aeroengine roulette counterweight block, and the configuration block is obtained through the aeroengine roulette counterweight block design method based on multi-objective optimization.
Aiming at the problem that the conventional balancing weight designed based on the weight moment and bending moment equivalent principle cannot meet the requirement of service life test precision, the invention develops multi-objective optimization by establishing an optimized mathematical model of the balancing weight design, obtains a design scheme of a balancing weight structure with higher precision by design constraints of theoretical solution and equal local stress, and meets the requirement of safety examination test on the strength and service life of the wheel disc.
Drawings
In order to more clearly illustrate the technical solutions provided by the present application, the following briefly introduces the accompanying drawings. It is to be expressly understood that the drawings described below are only illustrative of some embodiments of the invention.
FIG. 1 is a flow chart of a design method of a multi-objective optimization-based aircraft engine roulette counterweight block.
Fig. 2 is a schematic diagram of a weight parameter in the present application.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application.
As shown in fig. 1, the design method of an aircraft engine disk configuration block based on multi-parameter optimization provided by the present application includes the following steps:
(1) determining key design parameters for a counterweight
The weight block design is generally based on the weight moment and bending moment equivalent principle, as shown in fig. 2, and affects key design parameters of weight moment and mass center distribution of the weight block. When the balancing weight is designed, the structure of the balancing weight is divided into an initial domain and a design domain, the initial domain is consistent with the tenon structure of a real blade, the assembling performance of the balancing weight and a wheel disc mortise is ensured, and the balancing weight is used for simulating the tenon quality of the blade; the design domain is divided into a rectangular region and a triangular region and is used for simulating the blade body mass of the blade, and the mass of the balancing weight and the mass center are adjusted by changing the parameters of the design domain.
The key design parameters of the balancing weight finally determined according to the method mainly comprise: radial height h of design area of balancing weight 1 And h 2 Axial length l of balancing weight, axial mass center X of front end face of balancing weight s Axial mass center X of the balancing weight c Initial domain axial mass center X of balancing weight 0 Initial domain radial centroid Z 0 Distance Z between top surface of initial design domain and rotating shaft of engine s Circumferential width w of balancing weight, top surface area S of initial design area 0 The average radius r of the balancing weight, the circumferential offset a and the like.
(2) Multi-objective optimization mathematical model for building balancing weight
The principle of the design of the balancing weight is to ensure that the average stress and the local point stress of the wheel disc are consistent with those of a real blade under the action of the balancing weight, the specific physical parameter indexes are decomposed to ensure that the weight moment of the balancing weight and the bending moment of the throat of the tenon are consistent with those of the blade, and a mathematical model designed by the balancing weight is established according to the principle.
According to the radial weight moment of the real blade equal to the sum of the radial weight moment of the initial domain of the balancing weight, the radial weight moment of the rectangular area in the design domain and the radial weight moment of the triangular area in the design domain, and meanwhile according to the dispersibility of the weight of the blade, in order to guarantee the effectiveness of the examination, the amplification factor lambda of the weight moment of the balancing weight is introduced, and the following equation is established:
Figure BDA0003576244820000061
according to the equivalent principle of the balancing weight and the blade to the bending moment of the throat of the tenon, the following equation is established:
Figure BDA0003576244820000062
in the formula: v 0 Is the initial domain volume, mm 3 ；
Z 0 Is the initial domain radial centroid, mm;
l is the axial length of the balancing weight in mm;
X s is the axial mass center of the front end surface of the balancing weight in mm;
X c is the axial mass center of the balancing weight in mm;
X 0 the axial centroid, mm, of the initial design domain;
S 0 for initial design of the area of the top surface of the domain, mm 2 ；
Z s The distance between the top surface of the initial design domain and the rotating shaft of the engine is mm;
V b is the volume of the blade, mm 3 ；
Z b Is the radial centroid of the blade, mm;
lambda is the weight moment amplification factor of the balancing weight;
xi is the blade density/weight density.
The theoretical solutions of formula 1 and formula 2 are:
Figure BDA0003576244820000063
Figure BDA0003576244820000064
wherein D, E, F in equations 3 and 4 are defined dimensionless parameters:
Figure BDA0003576244820000071
theoretical calculation results of key design parameters of the balancing weight can meet the test requirements of the excessive rotation, the breakage and other examination average bearing capacity of the wheel disc, but the design precision is not enough for the service life test of examining the local point stress, particularly the test that the examined part is positioned at the bottom of the groove. At the moment, the stress relative error minimization of the wheel disc checking part under the action of the balancing weight and the blade is taken as an optimization target, the mean square error of the stress relative error of the weight moment and the secondary checking part is taken as a constraint condition, meanwhile, the condition that the circumferential direction is not interfered (a gap of 0.5mm is reserved in the circumferential direction) during the assembly of the balancing weight is taken as a geometric constraint, and a mathematical model for multi-objective optimization of the balancing weight is established as follows:
Figure BDA0003576244820000072
in the formula: sigma k,p The stress of the main checking part under the action of the balancing weight;
σ k,b the stress of the main assessment part under the action of the blade;
σ i,p the stress of the ith secondary assessment part under the action of the balancing weight;
σ i,b the stress of the ith secondary assessment part under the action of the blade;
lambda is the weight moment amplification factor of the balancing weight;
r is the average radius of the counterweight;
n is the number of blades;
w is the circumferential width of the balancing weight;
a is a circumferential offset;
V p is the volume of the balancing weight;
Z p is the radial mass center of the balancing weight;
V b is the volume of the blade;
Z b is the radial center of mass of the blade.
(3) Developing counterweight multi-objective optimization
And optimizing the structural parameters of the balancing weight by the multi-objective optimization mathematical model.
In order to improve the solving efficiency and precision of the multi-objective optimization, the key design parameters or range of the balancing weight can be obtained through a theoretical solution, the key design parameters or range can be used as the initial design parameters of the multi-objective optimization, the multi-objective optimization design can be carried out, and the iterative computation is carried out until the key design parameters meet the precision requirement.
Aiming at the problem that the conventional balancing weight designed based on the weight moment and bending moment equivalent principle cannot meet the requirement of service life test precision, the invention develops multi-objective optimization by establishing an optimized mathematical model designed by the balancing weight, obtains a design scheme of a balancing weight structure with higher precision by theoretical solution and design constraint of equal local stress, and meets the requirement of safety examination test on the strength and service life of the wheel disc.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (6)

1. A design method of a disk balancing weight of an aircraft engine based on multi-objective optimization is characterized by comprising the following steps:
determining key design parameters of the balancing weight, wherein the key design parameters comprise radial height h of a balancing weight design domain 1 And h 2 Axial length l of balancing weight, axial mass center X of front end face of balancing weight s Axial mass center X of the balancing weight c Initial domain axial mass center X of balancing weight 0 Initial domain radial centroid Z 0 Distance Z between top surface of initial design domain and rotating shaft of engine s Circumferential width w of counter weight, initial design area top surface area S 0 The average radius r of the balancing weight and the circumferential offset a;
constructing a balancing weight multi-objective optimization mathematical model comprising the key design parameters;
and optimizing the structural parameters of the balancing weight according to the mathematical model to obtain the structural parameters of the balancing weight.
2. The method for designing a multi-objective optimization-based aircraft engine wheel disc balancing weight according to claim 1, wherein based on the principle of weight moment and bending moment equivalence, when designing the balancing weight, the structure of the balancing weight is divided into an initial domain and a design domain, the initial domain is consistent with the tenon structure of a real blade, and the initial domain is used for ensuring the assembly performance of the balancing weight and a wheel disc mortise so as to simulate the tenon mass distribution of the real blade; the design domain is divided into a rectangular region and a triangular region, and the mass of the balancing weight and the mass center are adjusted by changing the parameters of the design domain so as to simulate the blade body mass distribution of a real blade.
3. The method for designing a multi-objective optimization-based aircraft engine roulette counterweight according to claim 2, wherein the mathematical model is:
Figure FDA0003576244810000021
in the formula: sigma k,p The stress of the main checking part under the action of the balancing weight;
σ k,b stress of main examination part under action of blade；
σ i,p The stress of the ith secondary assessment part under the action of the balancing weight;
σ i,b the stress of the ith secondary assessment part under the action of the blade;
lambda is the weight moment amplification factor of the balancing weight;
r is the average radius of the counterweight;
n is the number of the blades;
w is the circumferential width of the balancing weight;
a is a circumferential offset;
V p is the volume of the balancing weight;
Z p is the radial mass center of the balancing weight;
V b is the volume of the blade;
Z b is the radial center of mass of the blade.
4. The method of claim 3 for designing an aircraft engine roulette counterweight based on multi-objective optimization, wherein the radial height h of the rectangular region of the counterweight design field 1 And the radial height h of the triangular area 2 Satisfies the following conditions:
Figure FDA0003576244810000022
Figure FDA0003576244810000023
wherein D, E, F is a dimensionless parameter, including:
Figure FDA0003576244810000031
in the formula, V 0 Is the initial domain volume;
Z 0 is the initial domain radial centroid;
l is the axial length of the balancing weight;
X s is the axial mass center of the front end surface of the balancing weight;
X c is the axial mass center of the balancing weight;
X 0 for initial design of domain axial centroid
S 0 Designing the area of the top surface of the domain for the initial design;
Z s the distance between the top surface of the initial design domain and the rotating shaft of the engine is set;
V b is the volume of the blade;
Z b is the radial center of mass of the blade;
lambda is the weight moment amplification coefficient of the balancing weight;
xi is the blade density/weight density.
5. The multi-objective optimization-based aircraft engine roulette counterweight design method according to claim 4, wherein the radial height h of the rectangular region of the counterweight design domain 1 And the radial height h of the triangular area 2 The radial weight moment of the real blade is equal to the sum of the radial weight moment of the initial domain of the balancing weight, the radial weight moment of the rectangular region in the design domain and the radial weight moment of the triangular region in the design domain, and the equivalent principle of the balancing weight and the blade to the bending moment of the throat of the tenon is obtained, and the equivalent principle of the balancing weight and the blade to the bending moment of the throat of the tenon comprises the following steps:
Figure FDA0003576244810000032
Figure FDA0003576244810000041
6. an aircraft engine roulette counterweight according to any of claims 1 to 5, wherein the configuration block is obtained by the method for designing an aircraft engine roulette counterweight according to any of claims 1 to 5.
CN202210345070.5A 2022-03-31 2022-03-31 Aero-engine wheel disc balancing weight design method based on multi-objective optimization Pending CN114896715A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117171923A (en) * 2023-11-02 2023-12-05 陕西空天信息技术有限公司 Blade design method, device, equipment and computer storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117171923A (en) * 2023-11-02 2023-12-05 陕西空天信息技术有限公司 Blade design method, device, equipment and computer storage medium
CN117171923B (en) * 2023-11-02 2024-03-22 陕西空天信息技术有限公司 Blade design method, device, equipment and computer storage medium

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