CN110750932A - Digital simulation method for rub-impact dynamic characteristics of blade disc-casing system - Google Patents
Digital simulation method for rub-impact dynamic characteristics of blade disc-casing system Download PDFInfo
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Abstract
The invention relates to a digital simulation method of rub-impact dynamic characteristics of a blade disc-casing system, S1, establishing a wheel disc finite element model of elastic support by adopting a shell unit and a spring unit, and establishing a blade finite element model and an elastic casing finite element model by adopting the spring unit and a Ferro-Cisco beam unit; s2, establishing an interface coupling unit between the wheel disc finite element model and the blade finite element model obtained in the S1, and obtaining a primary wheel disc dynamic model; s3, performing dimensionality reduction on the preliminary leaf disc dynamic model and the preliminary case dynamic model by adopting a Craig-Bampton method; finally, obtaining a reduced dynamic model of the leaf disc-casing system through grouping; and S4, solving the rub-impact dynamic characteristics of the reduced dynamic model of the leaf disc-casing system by combining a Lagrange multiplier method and a central difference method. The digital simulation method provided by the invention not only saves the financial cost and the time cost of the test, but also greatly improves the calculation efficiency of obtaining the fault characteristics.
Description
Technical Field
The invention belongs to the technical field of rub-impact fault simulation between a rotor system and a stator system, and particularly relates to a digital simulation method for rub-impact dynamic characteristics of a blade disc-casing system.
Background
High performance aircraft engines are developing in the direction of light weight, high reliability and low cost, and the blisk is a key component of the aircraft engine, and the structure and performance of the blisk play an important role in the design of the high performance aircraft engine. Reducing the clearance between the blade tip and the casing is the most direct and effective way to increase the aerodynamic efficiency and reduce the fuel consumption of an aircraft engine, but also increases the possibility of rubbing between the blade tip and the casing.
In addition, the circular symmetry of the structure of the blisk is difficult to ensure in the blisk processing and manufacturing process, and the vibration of the blisk is further amplified by potential faults such as eccentricity and detuning, so that the risk of collision and friction of the blade tip and the casing is further aggravated.
Disclosure of Invention
Technical problem to be solved
Aiming at the existing technical problems, the invention provides a digital simulation method for the rub-impact dynamic characteristics of a blisk-cartridge receiver system.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that:
a digital simulation method for rub-impact dynamic characteristics of a blade disc-casing system,
s1, establishing a wheel disc finite element model of the elastic support by adopting a shell unit and a spring unit, and establishing a blade finite element model and an elastic case finite element model by adopting the spring unit and a Ferro-Cisco beam unit;
s2, establishing a coupling unit between the wheel disc finite element model and the blade finite element model obtained in the S1 to obtain a primary wheel disc dynamic model;
s3, respectively reducing dimensions of the preliminary leaf disc-casing system dynamic model by adopting a Craig-Bampton method; finally, obtaining a reduced dynamic model of the leaf disc-casing system through grouping;
and S4, solving the rub-impact dynamic characteristics of the reduced dynamic model of the leaf disc-casing system by combining a Lagrange multiplier method and a central difference method.
Preferably, the method further comprises: s2, establishing a coupling relation by using an interface coupling unit;
wherein the coupling relationship comprises coupling between a center point of the disk and a center hole of the disk and coupling between an outer edge of the disk and the blade.
Preferably, the method further comprises: and performing convergence processing on the reduced dynamic model of the blade disc-casing system obtained in the step S3 to obtain a dynamic model of the blade disc-casing system with higher precision.
Preferably, the method further comprises: and S3, performing two-time dimensionality reduction on the twisted blade finite element model and the variable-section wheel disc finite element model respectively, and performing one-time dimensionality reduction on the elastic casing finite element model.
Preferably, the penalty function method is adopted to obtain the center point O of the wheel discdThe unit stiffness matrix of the coupling relation of the ith rigid coupling node pair between the central hole of the wheel disc is
kp＝max(diag(Kd,e) Add to penalty stiffness, Kd,eIs a structural stiffness matrix of the wheel disc, so that the stiffness matrix of the entire stiffness region isWherein N isIIndicating the number of nodes in the center hole of the wheel disc.
Preferably, the kth interface coupling list between the outer edge of the wheel disc and the blade is obtained by a penalty function methodThe stiffness matrix of the elements is
k represents the kth blade;
the total coupling stiffness matrix between the outer edge of the wheel disk and the blades is
NbIndicating the number of blades.
(III) advantageous effects
The invention has the beneficial effects that: the digital simulation method for the rub-impact dynamic characteristic of the blisk-cartridge receiver system provided by the invention has the following beneficial effects:
firstly, the mathematical model construction is considered comprehensively, and theoretical support can be provided for aircraft engine designers or related practitioners. The simulation method can enable designers to optimize design schemes, and can also provide theoretical guidance for technicians in the fault detection process of the rotor-stator systems of the aircraft engine and the like. The method has the advantages of high operation speed and high precision.
Secondly, the financial cost and the time cost of the test are saved by adopting digital simulation, and meanwhile, the working efficiency is greatly improved.
Drawings
Fig. 1 is a schematic flow chart of a digital simulation method for rub-impact dynamics characteristics of a blisk-casing system according to the present invention.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
As shown in fig. 1: the embodiment discloses a digital simulation method for rub-impact dynamic characteristics of a blisk-cartridge receiver system, which comprises the following steps of:
s1, establishing a wheel disc finite element model of the elastic support by adopting a shell unit and a spring unit, and establishing a blade finite element model and an elastic case finite element model by adopting the spring unit and a Ferro-Cisco beam unit;
s2, establishing an interface coupling unit between the wheel disc finite element model and the blade finite element model obtained in the S1, and obtaining a primary dynamic model of the blade disc-casing system;
s3, respectively reducing dimensions of the preliminary leaf disc-casing system dynamic model by adopting a Craig-Bampton method; finally, obtaining a reduced dynamic model of the leaf disc-casing system through grouping;
and S4, solving the rub-impact dynamic characteristics of the reduced dynamic model of the leaf disc-casing system by combining a Lagrange multiplier method and a central difference method.
It should be noted that: the method described in this embodiment further includes: s2, establishing a coupling relation by using an interface coupling unit;
wherein the coupling relationship comprises coupling between a center point of the disk and a center hole of the disk and coupling between an outer edge of the disk and the blade.
The method described in this embodiment further includes: and performing convergence processing on the reduced dynamic model of the blisk-case system obtained in the step S3, and obtaining the dynamic model of the blisk-case system with higher computational efficiency on the premise of ensuring the model accuracy.
The method described in this embodiment further includes: and S3, performing two-time dimensionality reduction on the twisted blade finite element model and the variable-section wheel disc finite element model respectively, and performing one-time dimensionality reduction on the elastic casing finite element model.
In this embodiment, a penalty function method is used to obtain the center point O of the wheel diskdThe rigidity matrix of the coupling unit of the ith rigid coupling node pair between the central hole of the wheel disc is
kp＝max(diag(Kd,e) Add to penalty stiffness, Kd,eIs a structural stiffness matrix of the wheel disc, so that the stiffness matrix of the entire stiffness region isWherein N isIIndicating the number of nodes in the center hole of the wheel disc.
In the embodiment, the rigidity matrix of the kth interface coupling unit between the outer edge of the wheel disc and the blade is obtained by a penalty function method
k represents the kth blade;
the unit total rigidity matrix of the coupling relation between the outer edge of the wheel disc and the blades is
NbIndicating the number of blades.
The blade disc-casing system supported elastically in this embodiment is mainly divided into three parts, namely a wheel disc, a blade and a casing.
Center of the blade disc OdConsisting of three wire springs (k)d,X，kd,Y，kd,Z) And three torsion springs (k)d,rotX，kd,rotY，kd,rotZ) And is connected with the central hole of the blade disc through a rigid zone. The casing is composed of a series of uniformly distributed radial directions (k)c,ri) And tangential direction (k)c,ti) Is supported by the wire spring.
It should be noted that the case only considers in-plane (XOY-plane) motion.
In the embodiment, the wheel disc is dispersed by adopting a self-woven eight-node Mindlin-Reissner shell unit, and the blades and the casing are dispersed by adopting a self-woven two-node ironwood Cisco beam unit. It should be particularly noted that, when a finite element model of the blade disc is established, there are two key interface coupling relationships, namely, coupling between the center point of the blade disc and the center hole of the blade disc and coupling between the outer edge of the blade disc and the blades. Center point O of wheel discdAnd the wheel disc center hole is a rigid surface constraint. With the ith node pair Od-iFor example, the displacement constraint equations in XOY, YOZ, and ZOX are unified as follows:
wherein,
based on formula (1), obtaining a stiffness matrix of a coupling unit of the ith rigid coupling node pair by using a penalty function method
kp＝max(diag(Kd,e) Add to penalty stiffness, Kd,eIs a structural stiffness matrix of the wheel disc.
So the coupling stiffness matrix of the whole stiffness region can be written asWherein N isIIndicating the number of nodes in the center hole of the wheel disc.
The element matrix of the disk is constructed on the basis of a fixed coordinate system OXYZ, while the element matrix of the blade is based on a local coordinate system okxkykzkConstructed, where the subscript k denotes the kth blade.
Therefore, when matrix grouping of the blades and the wheel disc is carried out, the main node of the outer edge of the wheel disc and the main node of the root of the blades need to meet the compatibility condition of interface displacement.
Take the coupling of the disk to the kth blade as an example, fromkxkykzkThe transformation matrix from the coordinate system to the xyz coordinate system is:
according to the displacement coordination, the displacement constraint equation of the kth interface coupling unit in the xyz can be expressed as:
[I6×6Tk]·qk＝0 (3)
in the formula,then obtaining a stiffness matrix of the kth interface coupling unit by a penalty function method
The total stiffness matrix of the interface coupling units of the disk and all the blades can be written uniformly asNbIndicating the number of blades.
The differential equation of motion of the blisk-case system containing rub-impact failure in this embodiment can be written as:
wherein M, C, D and K are respectively a mass matrix, a Coriolis force (gyro) matrix, a Rayleigh damping matrix and a stiffness matrix; b iscIs a contact constraint matrix;
and u are acceleration, velocity and displacement vectors, respectively; lambda [ alpha ]NAnd FextLagrange multipliers and external force vectors, respectively. While 
In the formula, NcpIndicating the number of blades coming into contact with the casing.
Considering that the blade disc-casing system has a large number of degrees of freedom, in order to improve the calculation efficiency, necessary model dimension reduction is carried out. In the embodiment, a Craig-Bampton method (CBM) is adopted to establish a dimension reduction model of the system. According to the basic principle of CBM method dimension reduction, the freedom degrees of a wheel disc, a blade and a casing are firstly divided into a slave freedom degree and a master freedom degree, and the corresponding motion equation is as follows:
in the formula, the superscript X represents a wheel disc, a blade or a casing; m, C and K are respectively a mass matrix, a Coriolis force (gyro) matrix and a rigidity matrix; f is an external force vector; subscripts s and m represent the slave degree of freedom and the master degree of freedom, respectively; u is the sum of the total weight of the components,
and
representing displacement, velocity and acceleration vectors, respectively.
Physical displacement uXAnd generalized displacement qXCan be written as:
in the formula,
the interface canonical mode is fixed for the first l orders preserved.
Substituting the formula (6) into the formula (5) can obtain the motion equation of the wheel disc, the blade or the casing after dimensionality reduction:
in the formula,
in order to establish a final dimension reduction model of the blade disk-casing system, in this embodiment, a two-step dimension reduction method is adopted for the blade disk, and a one-step dimension reduction method is adopted for the casing.
The present embodiment is a numerical example of the previous embodimentThe parameters set for the disk, blade and case are shown in Table 1. Note that the component level frequency error is calculated relative to the unreduced model when the blade modal cutoff number η is equal to the unreduced modelbWhen the frequency is more than or equal to 3, the maximum frequency error of the first 7-step natural frequency of the reduced blade is 3.456%, and the mode truncation number of the wheel disc is ηdWhen the reduction ratio of the blade model to the disk model is larger than or equal to 1, the maximum frequency error of the reduction ratio disk is 1.728 percent, the first reduced blade and the disk model are assembled, the disk is further reduced into the disk model with lower degree of freedom through secondary dimensionality reduction, and when the reduction ratio of the modal truncation order of the disk model is ηbdIs greater than or equal to 86 and the rotation speed n epsilon [0,15000 ∈ ]]The maximum frequency error of the first 100 order natural frequency of the second order disk model is 2.061% in rpm. Further, it is assumed in this patent that the elastically supported blisk system is centered on OdSubject to unbalanced loads with an excitation frequency of 1 xn/60. in order to maximize the computational efficiency and reduce the number of degrees of freedom of the system, η is chosen in this patentbdThe dynamic frequency characteristics of the system were verified at 2, 4 and 86 to ηbd86 as a basis when n ∈ [0,15000 ]]Rpm, ηbd4 is sufficient to guarantee the accuracy of the reduced model results.
In this embodiment, η is preset during model dimension reductionb＝ηd＝ηbdIn addition, for the casing, after the dimension reduction of the model, the model is transferred to the modal coordinate, so that a so-called casing main node does not exist, and in addition, the modal truncation number η of the casing is assumed in the calculation process in the embodimentc11. It should be noted that the degrees of freedom of the blade disk-casing system with elastic support before and after dimensionality reduction are 15021 × 15021 and 125 × 125, respectively, which indicates that the final reduction in the system degrees of freedom is 99.17%.
TABLE 1 materials and geometric parameter settings
The technical principles of the present invention have been described above in connection with specific embodiments, which are intended to explain the principles of the present invention and should not be construed as limiting the scope of the present invention in any way. Based on the explanations herein, those skilled in the art will be able to conceive of other embodiments of the present invention without inventive efforts, which shall fall within the scope of the present invention.
Claims (6)
1. A digital simulation method for rub-impact dynamic characteristics of a bladed disk-casing system is characterized in that,
s1, establishing a wheel disc finite element model of the elastic support by adopting a shell unit and a spring unit, and establishing a blade finite element model and an elastic case finite element model by adopting the spring unit and a Ferro-Cisco beam unit;
s2, establishing an interface coupling unit between the wheel disc finite element model and the blade finite element model obtained in the S1, and obtaining a primary wheel disc dynamic model;
s3, respectively reducing dimensions of the preliminary leaf disc-casing system dynamic model by adopting a Craig-Bampton method; finally, obtaining a reduced dynamic model of the leaf disc-casing system through grouping;
and S4, solving the rub-impact dynamic characteristics of the reduced dynamic model of the leaf disc-casing system by combining a Lagrange multiplier method and a central difference method.
2. The simulation method of claim 1, further comprising: s2, establishing a coupling relation by using an interface coupling unit;
wherein the coupling relationship comprises coupling between a center point of the disk and a center hole of the disk and coupling between an outer edge of the disk and the blade.
3. The simulation method of claim 2, further comprising: and performing convergence processing on the reduced dynamic model of the blisk-case system obtained in the step S3, and obtaining the dynamic model of the blisk-case system with higher computational efficiency on the premise of ensuring the model accuracy.
4. The simulation method of claim 3, further comprising: and S3, performing two-time dimensionality reduction on the twisted blade finite element model and the variable-section wheel disc finite element model respectively, and performing one-time dimensionality reduction on the elastic casing finite element model.
5. The simulation method of claim 4,
obtaining the center point O of the wheel disc by using a penalty function methoddThe rigidity matrix of the coupling unit of the ith rigid coupling node pair between the central hole of the wheel disc is
kp＝max(diag(Kd,e) Add to penalty stiffness, Kd,eIs a structural stiffness matrix of the wheel disc, so that the stiffness matrix of the entire stiffness region is
Wherein N isIIndicating the number of nodes in the center hole of the wheel disc.
6. The simulation method of claim 5,
obtaining a rigidity matrix of a kth interface coupling unit between the outer edge of the wheel disc and the blade by a penalty function method
k represents the kth blade;
the total coupling stiffness matrix between the outer edge of the wheel disk and the blades isNbIndicating the number of blades.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111209639A (en) * | 2020-02-17 | 2020-05-29 | 合肥工业大学 | Efficient quantitative modeling method for impeller-bearing-rotor system |
| CN111783258A (en) * | 2020-07-29 | 2020-10-16 | 江苏省金象传动设备股份有限公司 | Estimation method for inherent characteristics and pitch diameter vibration of thin rim gear system |
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| CN103500287A (en) * | 2013-10-16 | 2014-01-08 | 东北大学 | Rotary blade-box rub-impact force determining method |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111209639A (en) * | 2020-02-17 | 2020-05-29 | 合肥工业大学 | Efficient quantitative modeling method for impeller-bearing-rotor system |
| CN111209639B (en) * | 2020-02-17 | 2024-05-03 | 合肥工业大学 | Efficient quantitative modeling method for impeller-bearing-rotor system |
| CN111783258A (en) * | 2020-07-29 | 2020-10-16 | 江苏省金象传动设备股份有限公司 | Estimation method for inherent characteristics and pitch diameter vibration of thin rim gear system |
| CN111783258B (en) * | 2020-07-29 | 2023-09-26 | 江苏省金象传动设备股份有限公司 | Inherent characteristic and pitch diameter vibration prediction method of thin rim gear system |
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