CN110826012A - Qualitative analysis method for vibration energy of rotor system - Google Patents
Qualitative analysis method for vibration energy of rotor system Download PDFInfo
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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 quantities of a rotor in x and y directions and a rotor elastic potential energy time sequence 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 derivative of a rotor elastic potential energy time sequence, applying a concept of taking a conjugate vector in a phase space to form a phase plane to an energy space, establishing an energy-phase plane V-V 'plane, and obtaining coordinates of phase points which form an energy-phase track on the V-V' plane; and applying the Poincare mapping concept in the phase plane to the energy-phase plane V-V' to calculate the energy-Poincare mapping, and finally realizing qualitative analysis of the change rule of the rotor vibration energy. The invention introduces an energy concept into nonlinear vibration analysis, and provides an energy orbit, an energy phase orbit and an energy-Poincare mapping to carry out qualitative analysis on the vibration energy of a rotor system.
Description
Technical Field
The invention belongs to the technical field of rotor system energy analysis, and particularly relates to a qualitative analysis method for vibration energy of a rotor system.
Background
Various nonlinear excitation sources always exist in a rotary mechanical system, and a plurality of complex nonlinear vibration phenomena are caused. The complex vibration phenomenon of the rotor system is effectively analyzed, so that the normal work of the rotating machinery is maintained, and the major loss is avoided. Researchers have made a lot of research work in the field of nonlinear rotor dynamics, and phase space-based nonlinear dynamics analysis means such as an axis trajectory, poincare mapping, a bifurcation diagram, and a lyapunov exponent are widely applied to nonlinear vibration analysis of a rotor system. However, as the rotating machinery becomes more complex, the nonlinear vibration phenomenon of the multi-rotor system becomes more prominent, and the phase space-based nonlinear vibration analysis method gradually shows limitations. In a multi-rotor system, the coupling relationship between rotors causes rotor modal coupling and nonlinear vibration coupling, and a phase space analysis method can lose part of vibration response information due to the reduction of analysis dimensionality, so that the coupling relationship 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 use energy concepts as a medium for mathematical derivation, and do not invest in research to account for energy variations of rotor systems. The energy change is an inherent expression of nonlinear vibration, and the research on the vibration energy change of the rotor is beneficial to disclosing the nonlinear vibration generation mechanism of the rotor. Therefore, it is necessary to develop an analysis method of the vibration energy of the rotor system.
Therefore, based on the problems, the 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 orbit, the energy phase orbit and the energy-poincare mapping has important practical significance.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for qualitatively analyzing the vibration energy of a rotor system by introducing an energy concept into nonlinear vibration analysis and providing an energy orbit, an energy phase orbit and an energy-Poincare mapping.
The technical problem to be solved by the invention is realized by adopting the following technical scheme:
a qualitative analysis method for 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 quantities of the rotor in the x direction and the y direction respectively, and the time sequence of the elastic potential energy of the rotor is calculated as follows:
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 S1i),y(ti),V(ti) Energy points form a set of tracks in space, referred to as energy tracks;
s3, analyzing the energy orbit in the step S2, thereby preliminarily and qualitatively analyzing the change rule of the rotor vibration energy;
s4, deriving the time series x (t), y (t) in step S1 to obtain a first derivative time series x '(t), y' (t) of the rotor in x, y directions, wherein the first derivative time series of the rotor elastic potential energy is calculated as follows:
V′(t)＝k(xx′+yy′)
wherein k is the stiffness of the rotor shaft;
s5, applying the concept of taking conjugate vector in the phase space to form the phase plane to the energy space, establishing an energy-phase plane V-V' plane, and obtaining the coordinate (V (t) of the phase point according to the rotor elastic potential energy and the time sequence of the first derivative of the rotor elastic potential energy in the steps S1 and S4i),V′(ti) The phase points form an energy-phase orbit on the V-V' plane, so that the change rule of the vibration energy of the rotor is further qualitatively analyzed;
and S6, based on the step S5, calculating the energy-Poincare mapping on the energy-phase plane V-V' plane by combining the calculation principle of the Poincare mapping, and finally realizing the qualitative analysis of the change rule of the rotor vibration energy.
The invention has the advantages and positive effects that:
the nonlinear vibration analysis method is used for carrying out nonlinear vibration analysis on the high-dimensional dynamic system based on the energy space, completely retains the dynamic response information of the system, avoids the problems of subspace parameter coupling and different subspace coupling in a phase space analysis method, and does not need to carry out very complicated decoupling treatment; 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 shown; based on the research on the change of the vibration energy of the system, the invention is beneficial to disclosing the generation mechanism of the nonlinear vibration.
Drawings
The technical solutions 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 illustrative purposes only and thus do not limit the scope of the present invention. Furthermore, unless otherwise indicated, the drawings are intended to be illustrative of the structural configurations described herein and are not necessarily drawn to scale.
FIG. 1a is a harmonic motion energy orbit provided by an embodiment of the present invention;
FIG. 1b is a schematic cycle motion energy orbit provided by an embodiment of the present invention;
FIG. 1c is a chaotic motion energy trajectory provided by an embodiment of the present invention;
FIG. 2a is a schematic diagram of harmonic motion energy-phase trajectory provided by an embodiment of the present invention;
FIG. 2b is a schematic diagram of the almost periodic motion energy-phase trajectory provided by the embodiment of the present invention;
FIG. 2c is a schematic diagram of a chaotic motion energy-phase trajectory according to an embodiment of the present invention;
FIG. 3a is a schematic diagram of a harmonic motion energy-Poincare mapping according to an embodiment of the present invention;
FIG. 3b is a schematic diagram of an almost-periodic motion energy-Poincare mapping according to an embodiment of the present invention;
FIG. 3c is a schematic diagram of a chaotic motion energy-Poincare mapping according to an embodiment of the present invention;
Detailed Description
First, it should be noted that the specific structures, features, advantages, etc. of the present invention will be specifically described below by way of example, but all the descriptions are for illustrative purposes only and should not be construed as limiting the present invention in any way. Furthermore, any individual technical features described or implicit in the embodiments mentioned herein may still be continued in any combination or subtraction between these technical features (or their equivalents) to obtain still further embodiments of the invention that may not be mentioned directly herein.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
The present invention will be described in detail with reference to the accompanying drawings.
FIG. 1a is a harmonic motion energy orbit provided by an embodiment of the present invention; FIG. 1b is a schematic cycle motion energy orbit provided by an embodiment of the present invention; FIG. 1c is a chaotic motion energy trajectory provided by an embodiment of the present invention; FIG. 2a is a schematic diagram of harmonic motion energy-phase trajectory provided by an embodiment of the present invention; FIG. 2b is a schematic diagram of the almost periodic motion energy-phase trajectory provided by the embodiment of the present invention; FIG. 2c is a schematic diagram of a chaotic motion energy-phase trajectory according to an embodiment of the present invention; FIG. 3a is a schematic diagram of a harmonic motion energy-Poincare mapping according to an embodiment of the present invention; FIG. 3b is a schematic diagram of an almost-periodic motion energy-Poincare mapping according to an embodiment of the present invention; FIG. 3c is a schematic diagram of a 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 by this embodiment includes the following steps:
s1, defining time sequences x (t) and y (t), which are the time sequences of the deformation quantity of the rotor in the x direction and the y direction respectively, and calculating the time sequence of the elastic potential energy of the rotor according to the following formula:
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 S1i),y(ti),V(ti) Energy points form a set of tracks in space, referred to as energy tracks; for example, fig. 1a, 1b, 1c show three morphologically distinct energy orbits;
s3, analyzing the energy orbit in the step S2, thereby preliminarily and qualitatively analyzing the change rule of the rotor vibration energy; for example, in fig. 1a, the time series x (t) and y (t) are both harmonic motions, the energy orbits form a closed loop in space, and the vibrational energy varies with the loop; in fig. 1b, the time series x (t) and y (t) are both almost periodic motions, the energy orbit forms a regular curved surface in space, and the vibration energy changes on the curved surface; in fig. 1c, the time sequences x (t) and y (t) are chaotic motions, the energy orbit 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 annular surface;
s4, deriving the time series x (t), y (t) in step S1 to obtain a first derivative time series x '(t), y' (t) of the rotor in x, y directions, wherein the first derivative time series of the rotor elastic potential energy is calculated as follows:
V′(t)＝k(xx′+yy′)
wherein k is the stiffness of the rotor shaft;
s5, applying the concept of taking conjugate vector in the phase space to form the phase plane to the energy space, establishing an energy-phase plane V-V' plane, and obtaining the coordinate (V (t) of the phase point according to the rotor elastic potential energy and the time sequence of the first derivative of the rotor elastic potential energy in the steps S1 and S4i),V′(ti) The phase points form an energy-phase orbit on the V-V' plane, so that the change rule of the vibration energy of the rotor is further qualitatively analyzed; for example, fig. 2a, 2b, 2c present three morphologically distinct sets of energy-phase orbitals: FIG. 2a shows the vibrational energy as a single cycle, FIG. 2b shows the vibrational energy as a triple cycle, and FIG. 2c shows the vibrational energy as an almost cycle;
it should be noted that the phase space contains all the information about the position and the velocity in a system generalized coordinate system, such as x and x' characterizing the displacement and the velocity of the system in the x direction. Typically, phase space analysis will select a set of conjugated quantities, such as x and x', to form a phase plane and project the phase trajectory onto the phase plane. This is actually to lower the phase trajectory of the system from a high-dimensional phase space to a two-dimensional phase plane, which is likely to cause information loss for the actual trajectory in a high-dimensional system. The concept of taking conjugate vectors in phase space to form phase planes is applied to energy space, which is a technique that can be realized by those skilled in the art.
And S6, based on the step S5, calculating the energy-Poincare mapping on the energy-phase plane V-V' plane by combining the calculation principle of the Poincare mapping, and finally realizing the qualitative analysis of the change rule of the rotor vibration energy. For example, three different energy-poincare maps are presented in fig. 3a, 3b, 3 c: fig. 3a shows that the vibration energy is periodic, fig. 3b shows that the vibration energy is almost periodic, and fig. 3c shows that the vibration energy changes to chaos.
It should be noted that poincare mapping is a mapping defined by phase trajectories in the 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 motion of the power system is overall known. At present, the poincare mapping drawing method is mature. The invention expands the concept of Poincare mapping and can still adopt the prior Poincare mapping drawing method to obtain the energy-Poincare mapping.
It is to be noted that the implementation basis of the present invention is the numerical solution of each kinetic parameter of the nonlinear dynamical equation of the known rotor system, i.e. the time series, and the numerical solution of the nonlinear dynamical model is obtained by the numerical integration algorithm. Because the nonlinear differential equation has no accurate theoretical solution, algorithms such as an Eulerian method, a Rungestota method, a linear multi-step algorithm and the like are generally adopted in the current research to complete the numerical solution of solving the nonlinear kinetic equation. The numerical solution required by the invention has no requirement on the solving algorithm. Additionally, a time series is a time history of a numerical solution over time.
Finally, harmonic motion, almost periodic motion, chaotic motion and the like are typical vibration types. The vibration energy analysis of different vibration types by the present invention is not limited to the above vibration types.
The present invention has been described in detail with reference to the above examples, but the description is only for the preferred examples of the present invention and should not be construed as limiting the scope of the present invention. All equivalent changes and modifications made within the scope of the present invention shall fall within the scope of the present invention.
Claims (1)
1. A qualitative analysis method for vibration energy of a rotor system is characterized by comprising the following steps: the method comprises the following steps:
s1, acquiring time sequences x (t) and y (t), which are time sequences of the deformation of the rotor in the x direction and the y direction respectively, and calculating the time sequence of the elastic potential energy of the rotor, wherein the time sequence is as follows:
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 S1i),y(ti),V(ti) Energy points form a set of tracks in space, referred to as energy tracks;
s3, analyzing the energy orbit in the step S2, thereby preliminarily and qualitatively analyzing the change rule of the rotor vibration energy;
s4, deriving the time series x (t), y (t) in step S1 to obtain a first derivative time series x '(t), y' (t) of the rotor in x, y directions, wherein the first derivative time series of the rotor elastic potential energy is calculated as follows:
V′(t)＝k(xx′+yy′)
wherein k is the stiffness of the rotor shaft;
s5, applying the concept of forming phase plane by taking conjugate vector in phase space to energy space to establish energy-phaseA plane V-V' and obtaining coordinates (V (t) of the phase point according to the rotor elastic potential energy and the time sequence of the first derivative of the rotor elastic potential energy in the steps S1 and S4i),V′(ti) The phase points form an energy-phase orbit on the V-V' plane, so that the change rule of the vibration energy of the rotor is further qualitatively analyzed;
and S6, based on the step S5, calculating the energy-Poincare mapping on the energy-phase plane V-V' plane by combining the calculation principle of the Poincare mapping, and finally realizing the qualitative analysis of the change rule of the rotor vibration energy.
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Citations (2)
| 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 |
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Patent Citations (2)
| 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)
| Title |
|---|
| JUNGUO WANG 等: "Nonlinear dynamic analysis of a rub-impact rotor supported by oil film bearings" * |
| YAMAMOTO T 等: "Theoretical discussions on vibrations of a rotating shaft with nonlinear spring characteristics" * |
| 刘浩宇 等: "水下杆状结构三维振动数值模拟" * |
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