CN116361959B - Dynamic modeling method for complex central pull rod rotor system - Google Patents
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Abstract
The application relates to the technical field of driving devices, in particular to a dynamic modeling method of a complex central pull rod rotor system. The modeling method comprises the following steps: carrying out structural division on a model of the central pull rod rotor system to obtain a shaft section substructure, an impeller plate structure, an accessory substructure and an end tooth substructure; performing structural equivalent treatment on the shaft segment substructure to obtain a dynamic matrix of the shaft segment substructure; carrying out structural equivalent treatment on the impeller plate structure to obtain a dynamic matrix of the impeller plate structure; carrying out structural equivalent treatment on the accessory substructure to obtain a dynamic matrix of the accessory substructure; performing structure equivalent treatment on the end tooth structure to obtain a dynamic matrix of the end tooth structure; simulating the coupling relation of the joint surface by using a spring unit, and establishing a coupling stiffness matrix of the joint surface; and integrating the dynamic matrix of each substructure and the coupling stiffness matrix of each joint surface to obtain a dynamic model of the central pull rod rotor system. The method solves the problems of improving the accuracy of the rotor dynamics model and reducing the calculation cost.
Description
Technical Field
The application relates to the technical field of driving devices, in particular to a dynamic modeling method of a complex central pull rod rotor system.
Background
Establishing a reasonable and efficient rotor dynamics model is a key to developing rotor dynamics design and researching rotor vibration characteristics. At present, scholars at home and abroad conduct a great deal of research on the modeling aspect of the high-speed rotor system of the aviation, and the adopted modeling method comprises a lumped parameter method, a transmission matrix method, a finite element method, a modal synthesis method and the like. These methods mostly simplify the rotor structure into a combination of constant cross-section beams and rigid disks, with little consideration of the local detail characteristics of the rotor. Doing so, while simplifying the solution process, makes it difficult to obtain the true dynamics of the rotor system. While the use of commercial finite element software modeling can well characterize complex variable cross-section characteristics of a rotor system, the overall degree of freedom of the model is too large, and the problem of low calculation efficiency exists in calculating transient characteristics and nonlinear dynamics characteristics of the system.
The central pull rod rotor has the structural forms of components of central pull rod pretightening and end face circular arc tooth torque transmission, the axial variable cross section characteristics are complex, the structural connecting surfaces are multiple, and the dynamic characteristics of the central pull rod rotor system are more complex due to the factors of central pull rod pretightening force, end tooth connecting contact rigidity and the like. In order to enable the conclusion rule obtained by simulation to better guide the actual design, a general dynamics model which has small calculated amount and high efficiency and can truly reflect the complex structural characteristics of the rotor needs to be established in a targeted manner.
Disclosure of Invention
The application provides a dynamic modeling method of a complex center pull rod rotor system, which aims to solve the problems of improving the accuracy of a rotor dynamic model and reducing the calculation cost.
In a first aspect, the present application provides a dynamic modeling method for a complex center pull rod rotor system, comprising:
s1, carrying out structural division on a model of a central pull rod rotor system to obtain a shaft section substructure, an impeller plate structure, an accessory substructure and an end tooth substructure;
s2, finite element division is carried out on the shaft section substructure to obtain a shaft section constant cross-section beam unit, a shaft section conical variable cross-section beam unit and a shaft section irregular variable cross-section beam unit, and the shaft section irregular variable cross-section beam unit is equivalently processed into the shaft section constant cross-section beam unit to obtain a dynamic matrix of the shaft section substructure;
wherein, the S2 includes: s21, carrying out finite element division on the shaft section substructure based on the inner and outer diameter change of the section to obtain a shaft section constant cross section beam unit, a shaft section conical variable cross section beam unit and a shaft section irregular variable cross section beam unit;
s22, calculating the mass and the polar moment of inertia of the irregular variable cross-section beam units of the shaft section, so that the axial length, the material density, the mass and the polar moment of inertia of the cross-section beam units of the shaft section are the same as the parameters of the irregular variable cross-section beam units of the shaft section, and the irregular variable cross-section beam units of the shaft section are equivalent to the cross-section beam units of the shaft section;
s23, processing the axial section equal-section beam units and the conical variable-section beam units by using Timoshenko Liang Jiashe and a Lagrange equation to obtain a dynamic matrix of the axial section substructure;
s3, carrying out finite element division on the impeller plate structure to obtain impeller plate constant cross-section beam units, impeller plate conical variable cross-section beam units and impeller plate irregular variable cross-section beam units, and equivalently processing the impeller plate irregular variable cross-section beam units into impeller plate constant cross-section beam units to obtain a dynamic matrix of the impeller plate structure;
s4, finite element division is carried out on the accessory substructure to obtain accessory constant cross-section beam units, accessory conical variable cross-section beam units and accessory irregular variable cross-section beam units, and the accessory irregular variable cross-section beam units are equivalently processed into accessory constant cross-section beam units to obtain a dynamic matrix of the accessory substructure;
s5, carrying out finite element division on the end tooth substructure to obtain an end tooth constant cross-section beam unit, an end tooth conical variable cross-section beam unit and an end tooth irregular variable cross-section beam unit, and carrying out equivalent treatment on the end tooth irregular variable cross-section beam unit to obtain a dynamics matrix of the end tooth substructure;
s6, utilizing a spring unit to simulate the coupling relation of the joint surfaces among the shaft section substructure, the impeller plate substructure, the accessory substructure and the end tooth substructure, and establishing a coupling stiffness matrix of the joint surfaces;
s7, integrating a dynamic matrix of the shaft section substructure, a dynamic matrix of the impeller plate substructure, a dynamic matrix of the accessory substructure, a dynamic matrix of the end tooth substructure and a coupling stiffness matrix of the joint surface to obtain a dynamic model of the central pull rod rotor system.
S23, processing the axial section equal-section beam units and the conical variable-section beam units by using Timoshenko Liang Jiashe and a Lagrange equation to obtain a dynamic matrix of the axial section substructure.
In some embodiments, the step S3 of performing finite element division on the impeller plate structure to obtain an impeller plate constant cross-section beam unit, an impeller plate conical variable cross-section beam unit and an impeller plate irregular variable cross-section beam unit, and equivalently processing the impeller plate irregular variable cross-section beam unit into the impeller plate constant cross-section beam unit to obtain a dynamic matrix of the impeller plate structure, where the dynamic matrix comprises:
s31, dividing the impeller plate structure into a blade part and a wheel disc part;
s32, calculating the mass and the moment of inertia of the blade part to obtain an additional mass matrix of the blade part;
s33, carrying out finite element division on the wheel disc part to obtain a wheel disc equal cross-section beam unit, a wheel disc conical variable cross-section beam unit and a wheel disc irregular variable cross-section beam unit;
s34, processing the equal cross-section beam units of the wheel disc, the conical variable cross-section beam units of the wheel disc and the irregular variable cross-section beam units of the equal wheel disc in the S33 by using Timoshenko Liang Jiashe and Lagrange equations to obtain a dynamic matrix of the complete degree of freedom of the wheel disc part;
s35, reducing the unit degrees of freedom of the wheel disc part by adopting Guyan static force reduction to obtain a wheel disc dynamic matrix only retaining the main degrees of freedom;
s36, integrating the additional mass matrix of the blade part onto the wheel disc dynamics matrix with the reduced unit freedom degree to obtain the dynamics matrix of the impeller disc structure.
In some embodiments, the step S4 of performing finite element division on the accessory substructure to obtain an accessory equal-cross-section beam unit, an accessory tapered variable-cross-section beam unit and an accessory irregular variable-cross-section beam unit, and performing equivalent processing on the accessory irregular variable-cross-section beam unit to obtain a dynamics matrix of the accessory equal-cross-section beam unit, where the dynamics matrix comprises:
s41, carrying out finite element division on the accessory substructure to obtain accessory constant cross-section beam units, accessory conical variable cross-section beam units and accessory irregular variable cross-section beam units;
s42, processing the accessory constant cross-section beam unit, the accessory conical variable cross-section beam unit and the accessory irregular variable cross-section beam unit in S41 by using Timoshenko Liang Jiashe and a Lagrange equation to obtain a dynamic matrix of an accessory substructure;
s43, the dividing nodes of the accessory sub-structure are consistent with the corresponding shaft segment sub-structures, and the dynamic matrix of the accessory sub-structure in S42 is superimposed on the dynamic matrix of the corresponding shaft segment sub-structure.
In some embodiments, the step S5 of performing finite element division on the end tooth substructure to obtain an end tooth constant cross-section beam unit, an end tooth tapered variable cross-section beam unit and an end tooth irregular variable cross-section beam unit, and performing equivalent processing on the end tooth irregular variable cross-section beam unit to obtain a dynamics matrix of the end tooth constant cross-section beam unit, where the dynamics matrix comprises:
s51, obtaining normal force and tangential force received on a single pair of end tooth contact surfaces based on a GW contact model and a friction theory;
s52, deriving the normal rigidity and tangential rigidity of the contact surface by the normal force and tangential force on the contact surface, and converting the normal rigidity and tangential rigidity into equivalent connection rigidity of the single-pair end teeth in the horizontal axis direction;
s53, summing the equivalent connection rigidity of all the opposite end teeth in the horizontal axial direction to obtain the equivalent connection rigidity of the whole end teeth in the horizontal axial direction;
s54, connecting the equivalent connecting rigidity of the horizontal axis of the end tooth and the rigidity of the body of the end tooth in series to obtain the integral connecting rigidity of the end tooth;
s55, the end teeth are integrally connected with the rigidity to obtain the equivalent elastic modulus of the end tooth structure;
s56, using the equivalent elastic modulus of the end tooth structure, and obtaining a dynamic matrix of the end tooth structure by using Timoshenko Liang Jiashe and Lagrangian equation.
In some embodiments, the step S6 of using the spring unit to simulate the coupling relationship of the joint surfaces among the shaft segment substructure, the impeller plate structure, the accessory substructure and the end tooth substructure to establish a coupling stiffness matrix of the joint surfaces includes:
s61, dividing the joint surface into a thread joint surface and a boss joint surface;
s62, connecting coupling springs of a threaded joint surface are established, distributed springs are arranged on the joint surface, and each group of springs comprises a translation spring and a rotation spring;
s63, connecting coupling springs of a boss joint surface are established, distributed springs are arranged on the joint surface, and each group of springs comprises a translation spring;
s64, giving spring stiffness, obtaining generalized coupling force between each pair of coupling nodes on the joint surface, converting the generalized coupling force into a coupling stiffness matrix, and integrating the coupling stiffness matrix between all pairs of nodes in the joint surface to obtain the coupling stiffness matrix of the joint surface.
In some embodiments, the step S7 of integrating the dynamic matrix of the shaft segment substructure, the dynamic matrix of the impeller plate substructure, the dynamic matrix of the accessory substructure, the dynamic matrix of the end tooth substructure, and the coupling stiffness matrix of the joint surface to obtain a dynamic model of the center pull rod rotor system includes:
s71, simplifying the bearing support 18 into an elastic structure with support rigidity and damping, and obtaining a rigidity matrix and a damping matrix of the bearing support;
s72, adopting Rayleigh damping to establish a structural damping matrix of the central pull rod rotor system;
s72, integrating the dynamic matrix of each substructure, the coupling stiffness matrix of the joint surface, the bearing stiffness matrix, the bearing damping matrix and the system structure damping matrix to obtain a dynamic model of the central pull rod rotor system. The coupling stiffness matrix of the joint surface solves the problems of improving the accuracy of the rotor dynamics model and reducing the calculation cost, and the application has the following advantages:
the application provides a modeling method for a central pull rod rotor with complex variable cross section and interface contact characteristics, which adopts UG software to assist equivalent processing and discrete modeling of a complex rotor structure, introduces Guyan static reduction and GW interface contact models to perform equivalent modeling on a complex impeller disc structure and an end tooth substructure in a rotor system, and characterizes a dynamic coupling relation on a subsystem joint surface based on distributed spring unit combination. The modeling method has the advantages of good reduction degree, high precision and higher calculation efficiency, and can be used for rapidly calculating the dynamic characteristics of the rotor system and supporting the rotor dynamic design and vibration characteristic analysis. The method can be similarly generalized to rotor system or spindle system modeling with similar structural features.
Drawings
FIG. 1 illustrates a flow chart of a method of dynamic modeling of a complex center tie rotor system of an embodiment;
FIG. 2 illustrates a flow chart of a dynamic matrix of a build shaft segment substructure of a dynamic modeling method of a complex center tie rotor system of an embodiment;
FIG. 3 illustrates a flow chart of a method of dynamic modeling of a complex center tie rotor system of an embodiment for constructing a dynamic matrix of an impeller plate structure;
FIG. 4 illustrates a flow chart of a dynamics matrix of a construction attachment substructure of a dynamics modeling method of a complex center tie rotor system of an embodiment;
FIG. 5 illustrates a flow chart of a dynamic matrix of a build end tooth substructure of a dynamic modeling method of a complex center tie rotor system of an embodiment;
FIG. 6 illustrates a flow chart of a coupling stiffness matrix of a build interface of a dynamic modeling method of a complex center tie rotor system of an embodiment;
FIG. 7 illustrates a flow chart of a dynamic modeling method of a complex center tie rotor system of another embodiment;
FIG. 8 illustrates a dynamic model diagram of a dynamic modeling method of a complex center tie rotor system of an embodiment.
Reference numerals
11-shaft segment substructure; 12-impeller tray structure; 13-accessory substructure; 14-end tooth structure; 15-node; 16-thread interface spring; 17-boss faying surface springs; 18-bearing support.
Detailed Description
The disclosure will now be discussed with reference to several exemplary embodiments. It should be understood that these embodiments are discussed only to enable those of ordinary skill in the art to better understand and thus practice the present disclosure, and are not meant to imply any limitation on the scope of the present disclosure.
As used herein, the term "comprising" and variants thereof are to be interpreted as meaning "including but not limited to" open-ended terms. The term "based on" is to be interpreted as "based at least in part on". The terms "one embodiment" and "an embodiment" are to be interpreted as "at least one embodiment. The term "another embodiment" is to be interpreted as "at least one other embodiment".
The embodiment discloses a dynamic modeling method for a complex central pull rod rotor system, as shown in fig. 1 and fig. 2, which may include:
s1, carrying out structural division on a model of a central pull rod rotor system to obtain a shaft section substructure 11, an impeller plate structure 12, an accessory substructure 13 and an end tooth substructure 14;
s2, carrying out finite element division on the shaft section substructure 11 to obtain a shaft section constant cross-section beam unit, a shaft section conical variable cross-section beam unit and a shaft section irregular variable cross-section beam unit, and carrying out equivalent treatment on the shaft section irregular variable cross-section beam unit to obtain a shaft section constant cross-section beam unit to obtain a dynamic matrix of the shaft section substructure 11;
s3, carrying out finite element division on the impeller plate structure 12 to obtain impeller plate constant cross-section beam units, impeller plate conical variable cross-section beam units and impeller plate irregular variable cross-section beam units, and equivalently processing the impeller plate irregular variable cross-section beam units into impeller plate constant cross-section beam units to obtain a dynamic matrix of the impeller plate structure 12;
s4, carrying out finite element division on the accessory substructure 13 to obtain accessory constant cross-section beam units, accessory conical variable cross-section beam units and accessory irregular variable cross-section beam units, and carrying out equivalent treatment on the accessory irregular variable cross-section beam units to obtain a dynamic matrix of the accessory substructure 13;
s5, carrying out finite element division on the end tooth substructure 14 to obtain an end tooth constant cross-section beam unit, an end tooth conical variable cross-section beam unit and an end tooth irregular variable cross-section beam unit, and carrying out equivalent treatment on the end tooth irregular variable cross-section beam unit to obtain a dynamics matrix of the end tooth substructure 14;
s6, utilizing a spring unit to simulate the coupling relation of the joint surfaces among the shaft section substructure 11, the impeller plate substructure 12, the accessory substructure 13 and the end tooth substructure 14, and establishing a coupling stiffness matrix of the joint surfaces;
s7, integrating the dynamic matrix of the shaft segment sub-structure 11, the dynamic matrix of the impeller plate sub-structure 12, the dynamic matrix of the accessory sub-structure 13, the dynamic matrix of the end tooth sub-structure 14 and the coupling stiffness matrix of the joint surface to obtain a dynamic model of the central pull rod rotor system.
In the present embodiment, as shown in fig. 8, the rotating body supported by the bearing 18 is referred to as a rotor. Rotors are often used in rotary machines such as aircraft engines and gas turbines. When the rotor rotates at a high speed, unbalance of the rotor can cause the precession axis of the rotor to deviate from the original central axis, harmful vibration is generated, and the engine parts are damaged by the collision and abrasion in severe cases, and even the engine stops. Therefore, it is necessary to accurately predict the dynamic behavior of the rotor, and avoid resonance points as much as possible in the working rotation speed interval.
To ensure accuracy of the model, one typically uses a finite element method to build the rotor model. However, for aerorotors with complex structures, the finite element model built usually has a high dimension, and the model solving also costs a high time cost.
As shown in fig. 1, a model of the central pull rod rotor system is first divided into a structural division, which can be divided into a shaft segment sub-structure 11, an impeller plate sub-structure 12, an accessory sub-structure 13 and an end tooth sub-structure 14, depending on the actual structure of the rotor. Because the forces received by different structures in the using process of the rotor system model are different, the model is divided into different structures to carry out different treatments, the state of each structure of the rotor model in the using process can be calculated more accurately, errors between the rotor model and the actual situation are reduced, and the simulation precision is improved.
Because the section of the shaft segment substructure 11 is more changeable and the calculation difficulty is higher, finite element division is needed by adding the nodes 15 to the shaft segment substructure 11, and the method is divided into an equal-section beam unit, a conical variable-section beam unit and an irregular variable-section beam unit which are convenient to calculate. And carrying out equivalent treatment on the irregular variable-cross-section beam units, wherein the equivalent treatment is simple and convenient to calculate. Resulting in a mass matrix, a gyroscopic matrix and a stiffness matrix of the impeller dish structure 12.
The impeller dish structure 12 also has a variable cross section, which needs to be separated, the separated structure divided into a blade structure and a disk structure, and an additional mass matrix of the blade is obtained. Because the section of the wheel disc structure in the axial direction is changeable, the dynamic matrix of the wheel disc structure cannot be directly obtained. The wheel disc thus needs to be divided into constant cross-section beam units, tapered variable cross-section beam units and irregular variable cross-section beam units for easy calculation to obtain the mass matrix, gyro matrix and stiffness matrix of the impeller dish structure 12.
The accessory substructure 13 may include accessories of various structures, and since the sections of the accessory substructure 13 are variable, the calculation difficulty is high, so that it is necessary to add nodes 15 on the accessory substructure 13, and perform finite element division on the accessory substructure 13, and divide the accessory substructure into constant-section beam units, tapered variable-section beam units and irregular variable-section beam units which are convenient to calculate, and keep the same with the corresponding shaft section substructure 11 in unit node 15 division. Thereby obtaining a mass matrix, a gyro matrix and a stiffness matrix of the accessory substructure 13.
The end tooth substructure 14 may likewise be partitioned into substructures using finite element methods. Considering that the rough surface characteristics of the end tooth contact surface can affect the end tooth connection stiffness, the end tooth equivalent elastic modulus is introduced to characterize the stiffness variation of the end tooth substructure 14. Thereby obtaining a mass matrix, a gyroscopic matrix and a stiffness matrix of the end tooth substructure 14.
Next, the dynamics matrix of the shaft segment sub-structure 11, the dynamics matrix of the impeller plate sub-structure 12, the dynamics matrix of the attachment sub-structure 13, the dynamics matrix of the end tooth sub-structure 14 and the coupling stiffness matrix of the joint surface are based.
And finally, as the third part, the rotor system integral model is the integration of all the sub-structural systems, and the integral dynamic equation of the central pull rod rotor system is obtained by carrying out carrying-in and calculation according to the system quality matrix, the system gyro matrix, the system generalized displacement vector, the system rigidity matrix and the like obtained in the process.
In some embodiments, S21, finite element division is performed on the shaft section substructure 11 based on the inner and outer diameter variation of the cross section, resulting in constant cross section beam units, tapered variable cross section beam units, and irregular variable cross section beam units;
s21, carrying out finite element division on the shaft section substructure based on the inner and outer diameter change of the section to obtain a shaft section constant cross section beam unit, a shaft section conical variable cross section beam unit and a shaft section irregular variable cross section beam unit;
s22, calculating the mass and the polar moment of inertia of the irregular variable cross-section beam units of the shaft section, so that the axial length, the material density, the mass and the polar moment of inertia of the cross-section beam units of the shaft section are the same as the parameters of the irregular variable cross-section beam units of the shaft section, and the irregular variable cross-section beam units of the shaft section are equivalent to the cross-section beam units of the shaft section;
s23, processing the constant cross-section beam unit, the conical variable cross-section beam unit and the constant cross-section beam unit after the equivalent in the step S21 by using Timoshenko Liang Jiashe and a Lagrange equation to obtain a dynamic matrix of the axial segment substructure. In this embodiment, as shown in fig. 2, the shaft section substructure 11 may include a tone wheel and a center pull rod, and the tone wheel and center pull rod may be divided according to the inner and outer diameter variation of the cross section. When the shaft section is too long, the section change is large, the calculation difficulty is possibly increased, and the related parameters of the shaft section cannot be effectively analyzed. Thus, nodes 15 may be provided at abrupt changes in the section of the shaft segment, dividing the shaft segment structure 11, between every two adjacent nodes 15 being considered a beam unit. Each shaft segment sub-structure 11 is divided into a constant cross-section beam unit, a tapered variable cross-section beam unit, and an irregular variable cross-section beam unit.
The shaft sections with the same left and right cross sections after the shaft sections are cut according to the nodes 15 are equal-cross-section beam units, the shaft sections with different left and right cross sections after the shaft sections are cut according to the nodes 15 and are changed linearly are called tapered variable-cross-section beam units, and the shaft sections with different left and right cross sections after the shaft sections are cut according to the nodes 15 and are changed irregularly are called irregular variable-cross-section beam units.
In step S22, the irregular variable cross section beam unit has variable cross sections, which is difficult to calculate. Because the distance between the nodes 15 is smaller, the nodes can be equivalent to the cross-section beam units such as the shaft sections, and the calculation difficulty is reduced. By acquiring axial length, material density, mass, polar moment of inertia and other data of the axial section irregular variable cross-section beam unit, an equivalent axial section equal cross-section beam unit is established, and the axial length, material density, mass and polar moment of inertia of the axial section equal cross-section beam unit are identical to parameters of the irregular variable cross-section beam unit, so that the internal and external radius parameters of the equivalent equal cross-section beam unit are obtained as follows:
；
；
wherein ,the outer radius of the equal-section beam unit is the equivalent shaft section;
the inner radius of the equal cross-section beam unit is the equivalent shaft section;
polar moment of inertia of the beam unit with the irregular variable cross section for the shaft section;
is an axle sectionThe mass of the irregular variable cross-section beam unit;
ρ is the material density of the axial section irregular variable cross section beam unit;
the axial length of the cross-section beam unit is irregularly changed for the shaft section.
The method for obtaining the mass of the irregular variable cross-section beam unit of the shaft section and the polar moment of inertia through the mass mandrel is not limited, and can be real measurement or calculation through the function of a measuring body in the UG analysis module.
For the axle section equal cross-section beam unit and the axle section conical variable cross-section beam unit, the axle section equal cross-section beam unit is influenced by the gyroscopic effect and the own mass and rigidity in the rotating process, and a mass matrix, a gyroscopic effect matrix and a rigidity matrix with two nodes 15 and eight degrees of freedom can be obtained based on Timoshenko Liang Jiashe and Lagrange equations.
In some embodiments, S31, dividing the impeller plate structure into a blade portion and a disk portion;
s32, calculating the mass and the moment of inertia of the blade part to obtain an additional mass matrix of the blade part;
s33, carrying out finite element division on the wheel disc part to obtain a wheel disc equal cross-section beam unit, a wheel disc conical variable cross-section beam unit and a wheel disc irregular variable cross-section beam unit;
s34, processing the equal cross-section beam units of the wheel disc, the conical variable cross-section beam units of the wheel disc and the irregular variable cross-section beam units of the equal wheel disc in the step S33 by using Timoshenko Liang Jiashe and Lagrange equations to obtain a dynamic matrix of the complete degree of freedom of the wheel disc part;
s35, reducing the unit degrees of freedom of the wheel disc part by adopting Guyan static force reduction to obtain a wheel disc dynamic matrix only retaining the main degrees of freedom;
s36, integrating the additional mass matrix of the blade part onto the wheel disc dynamics matrix with the reduced unit freedom degree to obtain the dynamics matrix of the impeller disc structure. In this embodiment, as shown in fig. 3, since the impeller plate structure 12 is relatively complex and has a variable cross section, the impeller plate structure 12 can be divided into a blade structure and a wheel disc structure with relatively simple structure, so as to facilitate subsequent calculation and processing. The method of how the blade structure is peeled from the impeller plate structure 12 is not limited, and the hub curve of the blade structure can be constructed by the "sketch" function in the UG analysis module, and the blade structure is peeled from the impeller plate along the hub curve using the "boolean intersection" function.
The rotation of the blade structure is mainly affected by the moment of inertia and the concentrated mass. After obtaining the blade structure, in order to analyze the rotational process of the blade structure, an additional mass matrix of the blade structure may be obtained by obtaining the mass and moment of inertia of the blade structure. The method for obtaining the integral mass and the rotational inertia of the blade structure can be directly calculated through a measuring body function in the UG analysis module.
Because the wheel disc structure has a complex variable cross section in the axial direction, the related factors are excessive, and the direct calculation is difficult. Therefore, the method is divided into a wheel disc constant cross-section beam unit, a wheel disc conical variable cross-section beam unit and a wheel disc irregular variable cross-section beam unit, and the wheel disc irregular variable cross-section beam unit is converted into the wheel disc constant cross-section beam unit by utilizing the mass and moment of inertia equivalent principles.
And (3) processing the cross-section beam units such as the wheel disc and the like, the wheel disc conical variable cross-section beam units and the equivalent wheel disc and the like in the step (S33) by using Timoshenko Liang Jiashe and Lagrange equations to obtain a mass matrix, a gyro matrix and a rigidity matrix of the beam units.
In order to ensure the accuracy of the model, the number of subunits of the wheel disc structure is usually more, the dimension of the overall dynamic matrix is larger, and the degree of freedom is higher. The higher the degree of freedom is, the higher the calculated time and cost are, so in order to improve the calculation efficiency under the condition of ensuring the precision, the degree of freedom of the wheel disc part can be reduced by adopting Guyan static reduction, and a wheel disc dynamic matrix which only keeps the main degree of freedom is obtained.
The attachment mass matrix of the blade portion is integrated into the reduced cell degree of freedom wheel dynamics matrix to yield the dynamics matrix of the impeller dish structure 12.
It should be noted that to make a connection with other substructures, both the two end nodes 15 of the element of the disk structure and the blade structure centroid point need to be defined as the main degrees of freedom, and the choice of other nodes 15 may be dependent on the requirements.
In some embodiments of the present application, in some embodiments,
s41, carrying out finite element division on the accessory substructure to obtain accessory constant cross-section beam units, accessory conical variable cross-section beam units and accessory irregular variable cross-section beam units;
s42, processing the accessory constant cross-section beam unit, the accessory conical variable cross-section beam unit and the accessory irregular variable cross-section beam unit in the step S41 by using Timoshenko Liang Jiashe and a Lagrange equation to obtain a dynamic matrix of an accessory substructure;
s43, the dividing nodes of the accessory sub-structure are consistent with the corresponding shaft segment sub-structures, and the dynamic matrix of the accessory sub-structure in S42 is superimposed on the dynamic matrix of the corresponding shaft segment sub-structure. In this embodiment, as shown in fig. 4, the accessory substructure 13 may include an adjusting washer, a bearing inner ring, a lock nut, and the like, and has a relatively complex cross section due to the different structures of the adjusting washer, the bearing inner ring, the lock nut, and the like. Therefore, the nodes 15 are required to be arranged on the accessory substructure 13 for division, so that the constant cross-section beam units, the conical variable cross-section beam units and the equivalent constant cross-section beam units are obtained, and the calculation difficulty is reduced.
And processing the cross-section beam units such as the accessories, the conical variable cross-section beam units and the equivalent accessories in the step S41 by using Timoshenko Liang Jiashe and a Lagrangian equation to obtain a dynamic matrix of the accessory substructure 13.
The mass matrix, the gyroscopic effect matrix and the stiffness matrix of the accessory substructure 13 are directly superimposed on the corresponding matrix of the shaft segment substructure 11, and are combined to realize the coupling of the accessory substructure 13 and the shaft segment substructure 11.
In some embodiments of the present application, in some embodiments,
s51, obtaining normal force and tangential force received on a single pair of end tooth contact surfaces based on a GW contact model and a friction theory;
s52, deriving the normal rigidity and tangential rigidity of the contact surface by the normal force and tangential force on the contact surface, and converting the normal rigidity and tangential rigidity into equivalent connection rigidity of the single-pair end teeth in the horizontal axis direction;
s53, summing the equivalent connection rigidity of all the opposite end teeth in the horizontal axial direction to obtain the equivalent connection rigidity of the whole end teeth in the horizontal axial direction;
s54, connecting the equivalent connecting rigidity of the horizontal axis of the end tooth and the rigidity of the body of the end tooth in series to obtain the integral connecting rigidity of the end tooth;
s55, the end teeth are integrally connected with the rigidity to obtain the equivalent elastic modulus of the end tooth structure;
s56, using the equivalent elastic modulus of the end tooth structure, and obtaining a dynamic matrix of the end tooth structure by using Timoshenko Liang Jiashe and Lagrangian equation. In this embodiment, as shown in fig. 5, the pre-tightening force affects the connection stiffness of the end tooth structure. In order to facilitate dynamic modeling, the equivalent elastic modulus is used to characterize the overall connection stiffness of the end tooth structure. Wherein the mass matrix, gyroscopic effect matrix and stiffness matrix of the end tooth substructure are identical in form to the matrix form of the conventional beam unit. Therefore, in order to obtain the integral connection rigidity of the end tooth substructure, the influence of the rough surface features of the end tooth contact surface on the end tooth connection rigidity can be represented by adopting a GW model, an end tooth connection rigidity model considering the rough surface features is established, and the connection rigidity change of the end tooth substructure is represented by introducing an equivalent elastic modulus, so that the influence of the surface microscopic morphology on the end tooth contact surface rigidity is obtained. The specific process is as follows:
based on GW model, to single pair end tooth structure, obtain a pair of normal force and a pair of tangential force that receive on the contact surface, wherein, calculate the normal force formula that the contact surface received and be:
；
；
wherein , and />Is the normal force on the contact surface;
n is the number of asperities on the roughened surface;
e is the elastic modulus of the contact surface;
，/> and />Respectively the average rough radii of the two contact surfaces;
and />The height variation values of the two contact surfaces are respectively;
is the root mean square value of the roughness surface.
According to the friction theory, the tangential force received by the contact surface of the end tooth is obtained as follows:
；
；
wherein , and />Is a tangential force on the contact surface;
v is the poisson ratio of the contact surface;
the normal rigidity and the tangential rigidity at the contact surface can be deduced from the normal force and the tangential force on the contact surface, and the normal rigidity and the tangential rigidity on the contact surface are further equivalent to the horizontal axial direction, so that the equivalent connection rigidity of the single-pair end tooth structure is obtained as follows:
；
wherein ,equivalent connection rigidity of a single pair of end tooth structures;
is the pressure angle at the end tooth contact surface.
The equivalent connection rigidity of the integral end tooth structure is the sum of the equivalent connection rigidity of all opposite end teeth in the horizontal axial direction, and comprises the following components:
；
in the formula ,equivalent connection rigidity of the integral end tooth structure;
z is the total logarithm of the end tooth.
The integral connection rigidity of the end tooth structure is formed by the equivalent connection rigidity of the end tooth structure and the rigidity of the body of the end tooth structure together, and the obtained structure is that:
；
wherein ,is of a structure of end teethIs used for the overall connection stiffness of the steel sheet;
is the rigidity of the end tooth structure body.
In this embodiment, as shown in fig. 5, finally, the equivalent elastic modulus of the end tooth structure is used to obtain the kinetic matrix of the end tooth structure by using Timoshenko Liang Jiashe and lagrangian equation.
In some embodiments, S61, dividing the bonding surface into a threaded bonding surface and a boss bonding surface;
s62, connecting coupling springs of a threaded joint surface are established, distributed springs are arranged on the joint surface, and each group of springs comprises a translation spring and a rotation spring;
s63, connecting coupling springs of a boss joint surface are established, distributed springs are arranged on the joint surface, and each group of springs comprises a translation spring;
s64, given spring stiffness, generalized coupling force between each pair of coupling nodes 15 on the joint surface is obtained, the generalized coupling force is converted into a coupling stiffness matrix, and then the coupling stiffness matrices between all pairs of nodes 15 in the joint surface are integrated to obtain the coupling stiffness matrix of the joint surface.
The shaft segment sub-structure 11, the impeller plate structure 12 and the shaft segment attachment sub-structure 13 are connected with each other at the time of installation, and the connection relation needs to be considered. The connection relationship can be divided into a connection manner in which connection is achieved by threads and a connection face has a thread bond of a certain axial length, and a boss bond having a contact relationship and a connection face having a certain axial length.
In order to reduce the calculation difficulty, a spring unit can be used for simulating the coupling relation at the joint surface.
The inner ends of the outer rotor shaft and the central pull rod, and the outer ends of the outer rotor shaft and the central pull rod can be connected through threaded combination, coupling force and moment effect exist between the nodes 15 at the same time, and a coupling relation at a distributed spring simulation joint surface can be set, so that a threaded joint surface spring 16 is established. The spring unit may be composed of a translational spring and a rotational spring.
The boss in the middle of external rotor axle and the center pull rod can be connected through the connected mode that the boss combines, only has the coupling force effect between the node 15, can set up the coupling relation of distributed spring simulation faying face department, establishes boss faying face spring 17 unit. Wherein the spring unit comprises only a translational spring.
The junction between the two substructures is divided into n segments, and then comprises n+1 pairs of coupling nodes. For any pair of coupling nodes, when relative motion occurs between the pair of nodes 15, the force and bending moment of action between the pair of nodes 15 is obtained and converted into a matrix of coupling stiffness between the nodes 15. Consider that the pair of nodes are respectively numbered in the overall rotor and ,/>The coupling stiffness matrix between the pair of nodes can be expressed as:
；
wherein ,is translational spring stiffness;
for the rotational spring rate;
the coupling rigidity matrix between each node pair of the contact area is assembled, and the total coupling rigidity matrix of the joint surface is finally established。/>
In some embodiments, S71, simplifying the bearing support 18 into an elastic structure with support stiffness and damping, and deriving its stiffness matrix and damping matrix;
s72, adopting Rayleigh damping to establish a structural damping matrix of the central pull rod rotor system;
s72, integrating the dynamic matrix of each substructure, the coupling stiffness matrix of the joint surface, the bearing stiffness matrix, the bearing damping matrix and the damping matrix of the system structure to obtain the integral dynamic equation of the central pull rod rotor system.
In this embodiment, as shown in FIG. 7, the rotor system overall finite element model is an integrated coupling of the various sub-structural systems and the interface. The rotor is supported by bearings 18, simplifying it into a resilient structure with radial stiffness and damping. The system damping mainly comprises bearing damping and structural damping. Coupling is carried out according to the connection relation between the substructures and the connection relation between the shaft and the bearing, and finally, the overall dynamics model of the rotor system is established:
；
wherein ,is a generalized displacement vector of the system;
is a system quality matrix;
is a system gyro matrix;
is a system stiffness matrix;
is a system damping matrix;
is a generalized exciting force vector.
The application has the beneficial effects that: the application provides a modeling method for a central pull rod rotor with complex variable cross section and interface contact characteristics, which adopts UG software to assist equivalent processing and discrete modeling of a complex rotor structure, introduces Guyan static reduction and GW interface contact models to perform equivalent modeling on a complex impeller disc structure and an end tooth substructure in a rotor system, and characterizes a dynamic coupling relation on a subsystem joint surface based on distributed spring unit combination. The modeling method has the advantages of good reduction degree, high precision and higher calculation efficiency, and can be used for rapidly calculating the dynamic characteristics of the rotor system and supporting the rotor dynamic design and vibration characteristic analysis. The method can be similarly generalized to rotor system or spindle system modeling with similar structural features.
It will be understood by those of ordinary skill in the art that the foregoing embodiments are specific examples of implementing the present disclosure, and that various changes in form and details may be made therein without departing from the spirit and scope of the present disclosure.
Claims (6)
1. The dynamic modeling method of the complex center pull rod rotor system is characterized by comprising the following steps of:
s1, carrying out structural division on a model of a central pull rod rotor system to obtain a shaft section substructure, an impeller plate structure, an accessory substructure and an end tooth substructure;
s2, finite element division is carried out on the shaft section substructure to obtain a shaft section constant cross-section beam unit, a shaft section conical variable cross-section beam unit and a shaft section irregular variable cross-section beam unit, and the shaft section irregular variable cross-section beam unit is equivalently processed into the shaft section constant cross-section beam unit to obtain a dynamic matrix of the shaft section substructure;
s2, carrying out finite element division on a shaft section substructure based on the inner and outer diameter change of the section to obtain a shaft section equal-section beam unit, a shaft section conical variable-section beam unit and a shaft section irregular variable-section beam unit;
s22, calculating the mass and the polar moment of inertia of the irregular variable cross-section beam units of the shaft section, so that the axial length, the material density, the mass and the polar moment of inertia of the cross-section beam units of the shaft section are the same as the parameters of the irregular variable cross-section beam units of the shaft section, and the irregular variable cross-section beam units of the shaft section are equivalent to the cross-section beam units of the shaft section;
s23, processing the axial section equal-section beam units and the conical variable-section beam units by using Timoshenko Liang Jiashe and a Lagrange equation to obtain a dynamic matrix of the axial section substructure;
s3, carrying out finite element division on the impeller plate structure to obtain impeller plate constant cross-section beam units, impeller plate conical variable cross-section beam units and impeller plate irregular variable cross-section beam units, and equivalently processing the impeller plate irregular variable cross-section beam units into impeller plate constant cross-section beam units to obtain a dynamic matrix of the impeller plate structure;
s4, finite element division is carried out on the accessory substructure to obtain accessory constant cross-section beam units, accessory conical variable cross-section beam units and accessory irregular variable cross-section beam units, and the accessory irregular variable cross-section beam units are equivalently processed into accessory constant cross-section beam units to obtain a dynamic matrix of the accessory substructure;
s5, carrying out finite element division on the end tooth substructure to obtain an end tooth constant cross-section beam unit, an end tooth conical variable cross-section beam unit and an end tooth irregular variable cross-section beam unit, and carrying out equivalent treatment on the end tooth irregular variable cross-section beam unit to obtain a dynamics matrix of the end tooth substructure;
s6, utilizing a spring unit to simulate the coupling relation of the joint surfaces among the shaft section substructure, the impeller plate substructure, the accessory substructure and the end tooth substructure, and establishing a coupling stiffness matrix of the joint surfaces; wherein, the coupling rigidity matrix is that,
；
wherein ,is translational spring stiffness;
for the rotational spring rate;
the coupling rigidity matrix between each node pair of the contact area is assembled, and the total coupling rigidity matrix of the joint surface is finally established；
S7, integrating the dynamic matrix of the shaft segment substructure, the dynamic matrix of the impeller plate substructure, the dynamic matrix of the accessory substructure, the dynamic matrix of the end tooth substructure and the coupling stiffness matrix of the joint surface to obtain a dynamic model of the central pull rod rotor system, wherein the dynamic model is,
；
wherein ,is a generalized displacement vector of the system;
is a system quality matrix;
is a system gyro matrix;
is a system stiffness matrix;
is a system damping matrix;
is a generalized exciting force vector.
2. The method for modeling dynamics of a complex center tie rod rotor system according to claim 1, wherein the step S3 of performing finite element division on an impeller plate structure to obtain an impeller plate constant cross-section beam unit, an impeller plate tapered variable cross-section beam unit and an impeller plate irregular variable cross-section beam unit, and equivalently processing the impeller plate irregular variable cross-section beam unit into the impeller plate constant cross-section beam unit to obtain a dynamics matrix of the impeller plate structure comprises the steps of:
s31, dividing the impeller plate structure into a blade part and a wheel disc part;
s32, calculating the mass and the moment of inertia of the blade part to obtain an additional mass matrix of the blade part;
s33, carrying out finite element division on the wheel disc part to obtain a wheel disc equal cross-section beam unit, a wheel disc conical variable cross-section beam unit and a wheel disc irregular variable cross-section beam unit;
s34, processing the equal cross-section beam units of the wheel disc, the conical variable cross-section beam units of the wheel disc and the irregular variable cross-section beam units of the equal wheel disc in the S33 by using Timoshenko Liang Jiashe and Lagrange equations to obtain a dynamic matrix of the complete degree of freedom of the wheel disc part;
s35, reducing the unit degrees of freedom of the wheel disc part by adopting Guyan static force reduction to obtain a wheel disc dynamic matrix only retaining the main degrees of freedom;
s36, integrating the additional mass matrix of the blade part onto the wheel disc dynamics matrix with the reduced unit freedom degree to obtain the dynamics matrix of the impeller disc structure.
3. The method for modeling dynamics of a complex center tie rotor system according to claim 1, wherein the step S4 of performing finite element division on the accessory substructure to obtain an accessory constant cross-section beam unit, an accessory tapered variable cross-section beam unit and an accessory irregular variable cross-section beam unit, and performing equivalent processing on the accessory irregular variable cross-section beam unit to obtain a dynamics matrix of the accessory substructure, includes:
s41, carrying out finite element division on the accessory substructure to obtain accessory constant cross-section beam units, accessory conical variable cross-section beam units and accessory irregular variable cross-section beam units;
s42, processing the accessory constant cross-section beam unit, the accessory conical variable cross-section beam unit and the accessory irregular variable cross-section beam unit in S41 by using Timoshenko Liang Jiashe and a Lagrange equation to obtain a dynamic matrix of an accessory substructure;
s43, the dividing nodes of the accessory sub-structure are consistent with the corresponding shaft segment sub-structures, and the dynamic matrix of the accessory sub-structure in S42 is superimposed on the dynamic matrix of the corresponding shaft segment sub-structure.
4. The method for modeling dynamics of a complex center tie rotor system according to claim 1, wherein the step S5 of performing finite element division on the end tooth substructure to obtain an end tooth constant cross-section beam unit, an end tooth tapered variable cross-section beam unit and an end tooth irregular variable cross-section beam unit, and equivalently processing the end tooth irregular variable cross-section beam unit into the end tooth constant cross-section beam unit to obtain a dynamics matrix of the end tooth substructure comprises:
s51, obtaining normal force and tangential force received on a single pair of end tooth contact surfaces based on a GW contact model and a friction theory;
s52, deriving the normal rigidity and tangential rigidity of the contact surface by the normal force and tangential force on the contact surface, and converting the normal rigidity and tangential rigidity into equivalent connection rigidity of the single-pair end teeth in the horizontal axis direction;
s53, summing the equivalent connection rigidity of all the opposite end teeth in the horizontal axial direction to obtain the equivalent connection rigidity of the whole end teeth in the horizontal axial direction;
s54, connecting the equivalent connecting rigidity of the horizontal axis of the end tooth and the rigidity of the body of the end tooth in series to obtain the integral connecting rigidity of the end tooth;
s55, the end teeth are integrally connected with the rigidity to obtain the equivalent elastic modulus of the end tooth structure;
s56, using the equivalent elastic modulus of the end tooth structure, and obtaining a dynamic matrix of the end tooth structure by using Timoshenko Liang Jiashe and Lagrangian equation.
5. The method for dynamically modeling a complex center tie rotor system according to claim 1, wherein S6, using the spring unit to simulate the coupling relationship of the coupling surfaces among the shaft segment substructure, the impeller plate substructure, the accessory substructure, and the end tooth substructure, establishes a coupling stiffness matrix of the coupling surfaces, comprises:
s61, dividing the joint surface into a thread joint surface and a boss joint surface;
s62, connecting coupling springs of a threaded joint surface are established, distributed springs are arranged on the joint surface, and each group of springs comprises a translation spring and a rotation spring;
s63, connecting coupling springs of a boss joint surface are established, distributed springs are arranged on the joint surface, and each group of springs comprises a translation spring;
s64, giving spring stiffness, obtaining generalized coupling force between each pair of coupling nodes on the joint surface, converting the generalized coupling force into a coupling stiffness matrix, and integrating the coupling stiffness matrix between all pairs of nodes in the joint surface to obtain the coupling stiffness matrix of the joint surface.
6. The method for dynamically modeling a complex central pull rod rotor system according to claim 1, wherein the step S7 of integrating the dynamic matrix of the shaft segment substructure, the dynamic matrix of the impeller plate substructure, the dynamic matrix of the accessory substructure, the dynamic matrix of the end tooth substructure and the coupling stiffness matrix of the joint surface to obtain the dynamic model of the central pull rod rotor system comprises the steps of:
s71, simplifying the bearing support into an elastic structure with support rigidity and damping, and obtaining a rigidity matrix and a damping matrix of the bearing support;
s72, adopting Rayleigh damping to establish a structural damping matrix of the central pull rod rotor system;
s72, integrating the dynamic matrix of each substructure, the coupling stiffness matrix of the joint surface, the bearing stiffness matrix, the bearing damping matrix and the system structure damping matrix to obtain a dynamic model of the central pull rod rotor system.
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