CN110826012B - Qualitative analysis method for vibration energy of rotor system - Google Patents

Qualitative analysis method for vibration energy of rotor system Download PDF

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CN110826012B
CN110826012B CN201911075069.XA CN201911075069A CN110826012B CN 110826012 B CN110826012 B CN 110826012B CN 201911075069 A CN201911075069 A CN 201911075069A CN 110826012 B CN110826012 B CN 110826012B
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energy
rotor
phase
space
plane
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刘军
汪畅
葛为民
王肖锋
韩竹
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Tianjin University of Technology
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Abstract

The invention relates to a qualitative analysis method of rotor system vibration energy, which comprises the steps of obtaining deformation of a rotor in the x and y directions, rotor elastic potential energy time sequences x (t), y (t) and V (t), constructing an x-y-V three-dimensional energy space, obtaining coordinates of an energy point i, and forming an energy track; acquiring a first order derivative of a rotor elastic potential energy time sequence, applying a concept of taking conjugate vectors in a phase space to form a phase plane to an energy space, establishing an energy-phase plane V-V 'plane, obtaining coordinates of phase points, and forming an energy-phase track on the V-V' plane by the phase points; and applying the concept of Poincare mapping in the phase plane to the energy-phase plane V-V' to calculate the energy-Poincare mapping, and finally, qualitatively analyzing the change rule of the rotor vibration energy. The invention introduces an energy concept into nonlinear vibration analysis and proposes an energy track, an energy phase track and an energy-poincare map to perform qualitative analysis on the vibration energy of a rotor system.

Description

Qualitative analysis method for vibration energy of rotor system
Technical Field
The invention belongs to the technical field of rotor system energy analysis, and particularly relates to a qualitative analysis method of rotor system vibration energy.
Background
There are always many kinds of nonlinear excitation sources in the rotary mechanical system, which cause many complicated nonlinear vibration phenomena. The rotor system complex vibration phenomenon is effectively analyzed, so that the normal operation of the rotary machine is maintained, and the serious loss is avoided. In the field of nonlinear rotor dynamics, students have made a lot of research work, and nonlinear dynamics analysis means based on phase space such as axis trajectories, poincare maps, bifurcation maps, and lyapunov indexes are widely applied to nonlinear vibration analysis of rotor systems. However, as the rotating machinery becomes more and more complex, the nonlinear vibration phenomenon of the multi-rotor system becomes more and more prominent, and nonlinear vibration analysis means based on phase space gradually show limitations. In a multi-rotor system, the coupling relation among rotors causes rotor modal coupling and nonlinear vibration coupling, and the phase space analysis method can lose part of vibration response information due to the reduction of analysis dimension, so that the coupling relation of the system is weakened, and the vibration analysis result is inaccurate and incomplete. In addition, in a large number of rotordynamic studies, researchers often employ energy concepts as a medium for mathematical derivation, without investigative efforts to account for energy changes in the rotor system. The energy change is an inherent expression of nonlinear vibration, and research on the vibration energy change of the rotor is beneficial to revealing the nonlinear vibration generation mechanism of the rotor. Therefore, it is necessary to develop a method of analyzing the vibration energy of the rotor system.
Based on these problems, therefore, a method for qualitatively analyzing the vibration energy of the rotor system by introducing the energy concept into the nonlinear vibration analysis and adopting the energy track, the energy phase track and the energy-poincare mapping is provided, which has important practical significance.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a method for introducing an energy concept into nonlinear vibration analysis and provides an energy track, an energy phase track and an energy-poincare mapping to perform qualitative analysis on vibration energy of a rotor system.
The invention solves the technical problems by adopting the following technical scheme:
a qualitative analysis method of vibration energy of a rotor system comprises the following steps:
s1, acquiring time sequences x (t) and y (t), wherein the time sequences are time sequences of deformation amounts of the rotor in the x and y directions respectively, and the time sequences of the elastic potential energy of the rotor are calculated according to the following formula:
Figure BDA0002262174580000021
wherein k is the stiffness of the rotor shaft;
s2, constructing an x-y-V three-dimensional space, namely an energy space, and obtaining coordinates (x (t) of an energy point i in the energy space according to the three groups of time sequences in the step S1 i ),y(t i ),V(t i ) The energy points form a set of tracks in space, called energy tracks;
s3, primarily qualitatively analyzing the change rule of the rotor vibration energy by analyzing the energy track in the step S2;
s4, deriving the time sequences x (t) and y (t) in the step S1 to obtain first-order derivative time sequences x '(t) and y' (t) of the rotor in the x and y directions, wherein the first-order derivative time sequences of the elastic potential energy of the rotor are calculated according to the following formula:
V′(t)＝k(xx′+yy′)
wherein k is the stiffness of the rotor shaft;
s5, applying the concept of taking conjugate vectors in the phase space to form a phase plane to the energy space, establishing an energy-phase plane V-V' plane, and obtaining coordinates (V (t) i ),V′(t i ) The phase points form an energy-phase track on a V-V' plane, so that the change rule of the rotor vibration energy is further qualitatively analyzed;
and S6, calculating the energy-Poincare mapping on the energy-phase plane V-V' based on the step S5 by combining the calculation principle of Poincare mapping, and finally, qualitatively analyzing the change rule of the rotor vibration energy.
The invention has the advantages and positive effects that:
according to the invention, nonlinear vibration analysis is carried out on the high-dimensional dynamic system based on the energy space, so that the dynamic response information of the system is completely reserved, the problems of subspace parameter coupling and different subspace coupling in a phase space analysis method are avoided, and very complex decoupling treatment is not needed; by the method, the nonlinear vibration form of the system can be effectively identified, and the change rule of the vibration energy of the system can be displayed; based on the research on the change of the vibration energy of the system, the invention is beneficial to revealing the generation mechanism of nonlinear vibration.
Drawings
The technical solution of the present invention will be described in further detail below with reference to the accompanying drawings and examples, but it should be understood that these drawings are designed for the purpose of illustration only and thus are not limiting the scope of the present invention. Moreover, unless specifically indicated otherwise, the drawings are intended to conceptually illustrate the structural configurations described herein and are not necessarily drawn to scale.
FIG. 1a is a schematic diagram of a harmonic motion energy track provided by an embodiment of the present invention;
FIG. 1b is a schematic periodic motion energy track provided by an embodiment of the present invention;
FIG. 1c is a chaotic motion energy track provided by an embodiment of the present invention;
FIG. 2a is a schematic diagram of harmonic motion energy-phase trajectories according to an embodiment of the present invention;
FIG. 2b is a schematic diagram of a general periodic motion energy-phase trajectory provided by an embodiment of the present invention;
fig. 2c is a schematic diagram of chaotic motion energy-phase trajectory according to an embodiment of the present invention;
FIG. 3a is a schematic diagram of harmonic motion energy-Poincare mapping according to an embodiment of the present invention;
FIG. 3b is a schematic diagram of a schematic periodic motion energy-Poincare mapping according to an embodiment of the present invention;
fig. 3c is a schematic diagram of chaotic motion energy-poincare mapping according to an embodiment of the present invention;
Detailed Description
First, it should be noted that the following detailed description of the specific structure, characteristics, advantages, and the like of the present invention will be given by way of example, however, all descriptions are merely illustrative, and should not be construed as limiting the present invention in any way. Furthermore, any single feature described or implicit in the embodiments referred to herein may still be combined or truncated in any way between such features (or equivalents thereof) to obtain still further embodiments of the invention that may not be directly referred to herein.
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other.
The invention will be described in detail below with reference to the drawings.
FIG. 1a is a schematic diagram of a harmonic motion energy track provided by an embodiment of the present invention; FIG. 1b is a schematic periodic motion energy track provided by an embodiment of the present invention; FIG. 1c is a chaotic motion energy track provided by an embodiment of the present invention; FIG. 2a is a schematic diagram of harmonic motion energy-phase trajectories according to an embodiment of the present invention; FIG. 2b is a schematic diagram of a general periodic motion energy-phase trajectory provided by an embodiment of the present invention; fig. 2c is a schematic diagram of chaotic motion energy-phase trajectory according to an embodiment of the present invention; FIG. 3a is a schematic diagram of harmonic motion energy-Poincare mapping according to an embodiment of the present invention; FIG. 3b is a schematic diagram of a schematic periodic motion energy-Poincare mapping according to an embodiment of the present invention; fig. 3c is a schematic diagram of chaotic motion energy-poincare mapping according to an embodiment of the present invention; as shown in the figure, the qualitative analysis method for vibration energy of a rotor system provided in this embodiment includes the following steps:
s1, defining time sequences x (t) and y (t), wherein the time sequences are time sequences of deformation amounts of the rotor in the x and y directions respectively, and the time sequences of the elastic potential energy of the rotor are calculated according to the following formula:
Figure BDA0002262174580000051
wherein k is the stiffness of the rotor shaft;
s2, constructing an x-y-V three-dimensional space, namely an energy space, and obtaining coordinates (x (t) of an energy point i in the energy space according to the three groups of time sequences in the step S1 i ),y(t i ),V(t i ) The energy points form a set of tracks in space, called energy tracks; for example, three sets of morphologically distinct energy tracks are presented in fig. 1a, 1b, 1 c;
s3, primarily qualitatively analyzing the change rule of the rotor vibration energy by analyzing the energy track in the step S2; for example, in fig. 1a, the time series x (t) and y (t) are both harmonic motions, the energy tracks form a closed loop in space, and the vibration energy varies with the loop; in fig. 1b, the time sequences x (t) and y (t) are all generally periodic movements, the energy tracks form a regular curved surface in space, and the vibration energy varies on the curved surface; in fig. 1c, the time sequences x (t) and y (t) are both chaotic motions, and the energy track also forms a curved surface in space, but the edge of the curved surface is irregularly distributed, and the vibration energy changes on the irregular ring surface;
s4, deriving the time sequences x (t) and y (t) in the step S1 to obtain first-order derivative time sequences x '(t) and y' (t) of the rotor in the x and y directions, wherein the first-order derivative time sequences of the elastic potential energy of the rotor are calculated according to the following formula:
V′(t)＝k(xx′+yy′)
wherein k is the stiffness of the rotor shaft;
s5, applying the concept of taking conjugate vectors in the phase space to form a phase plane to the energy space, establishing an energy-phase plane V-V' plane, and obtaining coordinates (V (t) i ),V′(t i ) The phase points form an energy-phase track on a V-V' plane, so that the change rule of the rotor vibration energy is further qualitatively analyzed; for example, three morphologically distinct sets of energy-phase orbitals are presented in fig. 2a, 2b, 2 c: FIG. 2a shows a single periodic variation of the vibration energy, FIG. 2b shows a triple periodic variation of the vibration energy, and FIG. 2c shows a rough periodic variation of the vibration energy;
it should be noted that the phase space contains all information about position and velocity in a system generalized coordinate system, for example x and x' characterize the displacement and velocity of the system in the x direction. Typically, phase space analysis will choose a set of conjugate quantities, such as x and x', to make up the phase plane and project the phase trajectory onto the phase plane. This is in effect a reduction of the phase trajectory of the system from a high-dimensional phase space to a two-dimensional phase plane, which in high-dimensional systems easily results in a loss of information on the actual trajectory. The concept of taking conjugate vectors in the phase space to form a phase plane is applied to the energy space, which belongs to the technology that can be realized by those skilled in the art.
And S6, calculating the energy-Poincare mapping on the energy-phase plane V-V' based on the step S5 by combining the calculation principle of Poincare mapping, and finally, qualitatively analyzing the change rule of the rotor vibration energy. Three different sets of energy-poincare maps are presented in fig. 3a, 3b, 3c, for example: fig. 3a shows a periodic variation of the vibration energy, fig. 3b shows a general periodic variation of the vibration energy, and fig. 3c shows a chaotic variation of the vibration energy.
Note that poincare mapping is a mapping defined by phase trajectories in a phase space. When the phase trajectory repeatedly passes through the same section in the phase space, the shape and the topological structure of the trajectory on the section can be qualitatively obtained, so that the global motion of the power system can be known. Currently, the drawing method of poincare mapping is well established. The invention expands the concept of poincare mapping, and can still obtain energy-poincare mapping by adopting the existing drawing method of poincare mapping.
It should be noted that the invention is based on the realization that the numerical solution of each kinetic parameter of the nonlinear kinetic equation of the known rotor system, i.e. the time series, is obtained by a numerical integration algorithm. Because the nonlinear differential equation has no accurate theoretical solution, the numerical solution for solving the nonlinear dynamic equation is generally completed by adopting the algorithms such as an Euler method, a Longku tower method, a linear multi-step algorithm and the like in the current research. The numerical solution required by the invention has no requirement on the solving algorithm. In addition, the time series is the time history of the numerical solution over time.
Finally, harmonic motion, periodic motion, chaotic motion, etc. are typical vibration types. The invention is not limited to the above-described vibration types for analysis of vibration energy of different vibration types.
The foregoing examples illustrate the invention in detail, but are merely preferred embodiments of the invention and are not to be construed as limiting the scope of the invention. All equivalent changes and modifications within the scope of the present invention are intended to be covered by the present invention.

Claims (1)

1. A qualitative analysis method for vibration energy of a rotor system is characterized in that: the method comprises the following steps:
s1, acquiring time sequences x (t) and y (t), wherein the time sequences are time sequences of deformation amounts of the rotor in the x and y directions respectively, and calculating the time sequences of the elastic potential energy of the rotor, and the formula is as follows:
Figure FDA0002262174570000011
wherein k is the stiffness of the rotor shaft;
s2, constructing an x-y-V three-dimensional space, namely an energy space, and obtaining coordinates (x (t) of an energy point i in the energy space according to the three groups of time sequences in the step S1 i ),y(t i ),V(t i ) The energy points form a set of tracks in space, called energy tracks;
s3, primarily qualitatively analyzing the change rule of the rotor vibration energy by analyzing the energy track in the step S2;
s4, deriving the time sequences x (t) and y (t) in the step S1 to obtain first-order derivative time sequences x '(t) and y' (t) of the rotor in the x and y directions, wherein the first-order derivative time sequences of the elastic potential energy of the rotor are calculated according to the following formula:
V′(t)＝k(xx′+yy′)
wherein k is the stiffness of the rotor shaft;
s5, applying the concept of taking conjugate vectors in the phase space to form a phase plane to the energy space, establishing an energy-phase plane V-V' plane, and obtaining coordinates (V (t) i ),V′(t i ) The phase points form an energy-phase track on a V-V' plane, so that the change rule of the rotor vibration energy is further qualitatively analyzed;
and S6, calculating the energy-Poincare mapping on the energy-phase plane V-V' based on the step S5 by combining the calculation principle of Poincare mapping, and finally, qualitatively analyzing the change rule of the rotor vibration energy.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103151979A (en) * 2013-03-26 2013-06-12 王少夫 Doubly-fed wind-driven generator-based chaotic system
CN109829262A (en) * 2019-04-04 2019-05-31 哈尔滨工程大学 A kind of rotor-bearing system nonlinear dynamic analysis method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103151979A (en) * 2013-03-26 2013-06-12 王少夫 Doubly-fed wind-driven generator-based chaotic system
CN109829262A (en) * 2019-04-04 2019-05-31 哈尔滨工程大学 A kind of rotor-bearing system nonlinear dynamic analysis method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Junguo Wang 等.Nonlinear dynamic analysis of a rub-impact rotor supported by oil film bearings .《Archive of Applied Mechanics》.2012,413-430. *
Yamamoto T 等.Theoretical discussions on vibrations of a rotating shaft with nonlinear spring characteristics.《Ingenieur-Archiv》.1977,125-135. *
刘浩宇 等.水下杆状结构三维振动数值模拟.《港工技术》.2016,第53卷(第5期),5-10. *

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