CN110737866B - Bearing rotor system initial bifurcation point rotating speed identification method based on 3 sigma method - Google Patents

Bearing rotor system initial bifurcation point rotating speed identification method based on 3 sigma method Download PDF

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CN110737866B
CN110737866B CN201910971476.2A CN201910971476A CN110737866B CN 110737866 B CN110737866 B CN 110737866B CN 201910971476 A CN201910971476 A CN 201910971476A CN 110737866 B CN110737866 B CN 110737866B
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蒋勉
刘双奇
王道勇
李学军
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Abstract

The invention provides a bearing rotor system initial bifurcation point rotating speed identification method based on a 3 sigma method, which comprises the steps of establishing a sliding bearing rotor system dynamic model, solving a differential equation and obtaining a response signal sequence of a nonlinear dynamics model; carrying out taylor expansion on nonlinear terms of the nonlinear model to obtain a linear approximate dynamics model, and solving differential equations to obtain a response signal sequence of the linear model; calculating a nonlinearity value for nonlinear rotor system dynamics models and linear rotor dynamics model response sequences with different input rotation speeds to obtain a nonlinearity measure curve; and calculating an average value and a variance value for the nonlinear measurement sequence according to a 3 sigma rule, setting an alarm threshold value, and identifying the rotating speed of an initial bifurcation point of the sliding bearing rotor system. The invention realizes the identification of the rotating speed of the initial bifurcation point of the rotor system, has good identification effect and higher calculation speed, and can provide a new and reliable reference basis for the design of the rotor system.

Description

Bearing rotor system initial bifurcation point rotating speed identification method based on 3 sigma method
Technical Field
The invention relates to the technical field of mechanical system state monitoring and fault diagnosis, in particular to a bearing rotor system initial bifurcation point rotating speed identification method based on a 3 sigma method.
Background
The bearing rotor system is a core component of power machines such as an aero-engine, a gas turbine, a traction motor and the like, and the running stability of the bearing rotor system is directly related to the safety and the reliability of equipment. Today's rotor system instability is mostly caused by some non-linear phenomena, so that avoiding parameter points or areas where non-linear phenomena occur during rotor-bearing system design and operation is a popular choice. Bifurcation is a typical nonlinear phenomenon, and the nonlinear judgment system in the present stage can adopt tools or methods such as a Floquet multiplier, a poincare mapping and the like. However, in the case of an uncertain nonlinear system, only the system time signal sequence can be acquired, because the necessary system parameter information is lacking, the method for determining the numerical calculation based on the system parameter is not applicable any more, and the method such as poincare mapping can see the bifurcation condition through the mapping diagram corresponding to the dynamic response time signal sequence, but has no good determination condition for the bifurcation critical point. Therefore, the method for identifying the rotating speed of the bifurcation point by utilizing the time signal sequence to calculate the nonlinear measure curve of the dynamic response of the nonlinear system and utilizing the 3 sigma rule to set the alarm threshold is proposed.
Disclosure of Invention
The invention aims to avoid the defects in the prior art and provide a method for identifying the rotating speed of an initial bifurcation point of a bearing rotor system based on a 3 sigma method.
The aim of the invention is achieved by the following technical scheme:
a bearing rotor system initial bifurcation point rotating speed identification method based on a 3 sigma method comprises the following steps:
step 1, a dynamic model of a sliding bearing rotor system is established, and a differential equation is solved to obtain a response signal sequence of a nonlinear dynamic model;
step 2, carrying out taylor expansion on nonlinear terms of the nonlinear model to obtain a linear approximate dynamics model, and solving a differential equation to obtain a response signal sequence of the linear model;
step 3, calculating a nonlinearity value for nonlinear rotor system dynamics models and linear rotor dynamics model response sequences with different input rotation speeds to obtain a nonlinearity measure curve;
and 4, calculating an average value and a variance value for the nonlinear measurement sequence according to a 3 sigma rule, setting an alarm threshold value, and identifying the rotating speed of an initial bifurcation point of the sliding bearing rotor system.
Optionally, the sliding bearing rotor system nonlinear dynamics model established in step 1 is:
Figure BDA0002232241340000021
wherein m is 1 The mass is concentrated for the equivalent of the rotor at the bearings at the two ends; m is m 2 The equivalent concentrated mass of the rotor at the disc; m is m 3 The equivalent concentrated mass of the loose end bearing support seat is obtained; k is the linear stiffness of the elastic axisCoefficients; c 1 Equivalent damping at the bearings at the two ends; c 2 Damping of the rotor at the disc; k (k) b 、c b Respectively equivalent rigidity and equivalent damping of the foundation to the loose end supporting seat; x is x 1 ，y 1 The vibration displacement of the axle center at the right end bearing relative to the balance position in the horizontal and vertical directions is respectively; x is x 2 ，y 2 The vibration displacement of the center of the turntable relative to the balance position in the horizontal direction and the vertical direction is respectively; x is x 3 ，y 3 The left end bearing axle center is respectively in the horizontal and vertical direction relative to the vibration displacement of the balance position; the loose clearance between the left end bearing support and the foundation is delta; y is 4 The vibration displacement is carried out in the vertical direction of the bearing support; e is the mass eccentricity of the turntable; omega is the angular velocity of the rotor of the plain bearing rotor system;
Figure BDA0002232241340000022
and->
Figure BDA0002232241340000023
The components of nonlinear oil film force on sliding bearings at the left end and the right end in the horizontal direction and the vertical direction are respectively; ky (ky) 4 、/>
Figure BDA0002232241340000024
Representing the linear and nonlinear parts of the elastic force, respectively.
Wherein, the equivalent rigidity and equivalent damping of the foundation to the loose end supporting seat are respectively expressed as:
Figure BDA0002232241340000025
optionally, in step 2, the linear approximation dynamics model establishment process of the nonlinear model is as follows;
nonlinear oil film force F in nonlinear model x ，F y Performing Taylor expansion, and removing higher-order terms to obtain linear approximate oil film force as follows:
Figure BDA0002232241340000026
h in xx ,h xy ,h yx ,h yy For oil film stiffness, d xx ,d xy ,d yx ,d yy F is oil film damping x0 ，F y0 Is the oil film force at the static equilibrium position.
Similarly, the nonlinear elastic force generated by the loosening fault of the rotor system
Figure BDA0002232241340000036
The linear approximation elastic force can be obtained by taylor expansion at the equilibrium point and discarding the higher order term as follows:
Figure BDA0002232241340000031
substituting the result of the nonlinear term taylor expansion into the original equation can obtain a linear approximation dynamic model L (ω) of the sliding bearing rotor system as follows:
Figure BDA0002232241340000032
in the middle of
Figure BDA0002232241340000033
Representing the oil film force component F x ,F y Is a linear approximation of (a).
Optionally, in step 3, a calculation formula used for calculating the nonlinear measure value of the sliding bearing rotor system is:
φ L ＝||N(ω)-L(ω)||
in the formula of I, I representing norms; n is a nonlinear dynamic system; l is a linear approximation system obtained by adopting Taylor expansion; n (ω) and G (ω) represent the output response of the nonlinear system and the linear system, respectively, at the input ω; phi (phi) L Is a non-linearity estimation value.
Optionally, in step 4, the algorithm flow for identifying the initial bifurcation point rotation speed of the bearing rotor system based on the 3-sigma rule is as follows:
1) Let t=1, 2,3, … denote the rotational speed, phi, used to calculate the nonlinearity L,1 ,φ L,2 ,φ L,3 … represents the value of the nonlinearity at the corresponding rotational speed; starting from t=2, the mean and variance values of the nonlinear measurement sequence are calculated according to the 3 sigma rule, as follows:
Figure BDA0002232241340000034
2) According to 3 sigma rule, according to formula
Figure BDA0002232241340000035
Setting an alarm threshold;
3) Judging phi L，t+1 Upper limit +. ω )+3σ(φ L ) If so, the rotating speed at the time t+1 is the initial bifurcation rotating speed; if not, let t=t+1, continue steps 1), 2), 3) until φ is satisfied L，t+1 Upper limit +. ω )+3σ(φ L )。
The beneficial effects obtained by the invention are as follows: in the invention, a sliding bearing rotor system with one end supporting loosening fault is taken as an example, a dynamic model of the rotor system and a corresponding linear approximation model are established, a dynamic differential equation is solved numerically to obtain a dynamic response signal, and the nonlinear degree is utilized to realize the identification of a bifurcation point of the rotor system, so that the identification effect is good and the calculation speed is higher.
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The invention will be further understood from the following description taken in conjunction with the accompanying drawings, with emphasis instead being placed upon illustrating the principles of the embodiments.
FIG. 1 is a flowchart of a method for detecting a bifurcation point of a sliding bearing rotor system according to an embodiment of the present invention
FIG. 2 is a graph showing the comparison of the nonlinearity of the simulation signal and the conventional response bifurcation provided in the embodiment of the present invention;
FIG. 3 is a flowchart of branch point rotation speed recognition according to an embodiment of the present invention;
fig. 4 is a graph showing the result of identifying the initial bifurcation point of the sliding bearing rotor system provided in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following examples thereof; it should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. Other systems, methods, and/or features of the present embodiments will be or become apparent to one with skill in the art upon examination of the following detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims. Additional features of the disclosed embodiments are described in, and will be apparent from, the following detailed description.
The same or similar reference numbers in the drawings of embodiments of the invention correspond to the same or similar components; in the description of the present invention, it should be understood that, if there is an azimuth or positional relationship indicated by terms such as "upper", "lower", "left", "right", etc., based on the azimuth or positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but it is not indicated or implied that the apparatus or component referred to must have a specific azimuth, be constructed and operated in a specific azimuth, and thus terms describing the positional relationship in the drawings are merely illustrative and should not be construed as limitations of the present patent, and specific meanings of the terms described above may be understood by those skilled in the art according to specific circumstances.
The invention relates to a method for identifying the rotation speed of an initial bifurcation point of a bearing rotor system based on a 3 sigma rule, which comprises the following steps: (please refer to FIG. 1)
Step 1, a dynamic model of a sliding bearing rotor system is established, and a differential equation is solved to obtain a response signal sequence of a nonlinear dynamic model;
the nonlinear dynamics model of the sliding bearing rotor system established in the step 1 is as follows:
Figure BDA0002232241340000051
wherein m is 1 The mass is concentrated for the equivalent of the rotor at the bearings at the two ends; m is m 2 The equivalent concentrated mass of the rotor at the disc; m is m 3 The equivalent concentrated mass of the loose end bearing support seat is obtained; k is the linear stiffness coefficient of the elastic shaft; c 1 Equivalent damping at the bearings at the two ends; c 2 Damping of the rotor at the disc; k (k) b 、c b Respectively equivalent rigidity and equivalent damping of the foundation to the loose end supporting seat; x is x 1 ，y 1 The vibration displacement of the axle center at the right end bearing relative to the balance position in the horizontal and vertical directions is respectively; x is x 2 ，y 2 The vibration displacement of the center of the turntable relative to the balance position in the horizontal direction and the vertical direction is respectively; x is x 3 ，y 3 The left end bearing axle center is respectively in the horizontal and vertical direction relative to the vibration displacement of the balance position; the loose clearance between the left end bearing support and the foundation is delta; y is 4 The vibration displacement is carried out in the vertical direction of the bearing support; e is the mass eccentricity of the turntable; omega is the angular velocity of the rotor of the plain bearing rotor system;
Figure BDA0002232241340000052
and->
Figure BDA0002232241340000053
The components of nonlinear oil film force on sliding bearings at the left end and the right end in the horizontal direction and the vertical direction are respectively; ky (ky) 4 、/>
Figure BDA0002232241340000054
Representing the linear and nonlinear parts of the elastic force, respectively.
Wherein, the equivalent rigidity and equivalent damping of the foundation to the loose end supporting seat are respectively expressed as:
Figure BDA0002232241340000055
and carrying out numerical integration solution on a nonlinear dynamics differential equation by adopting a 4-5-order variable step length Runge-Kutta method to obtain a nonlinear dynamics response signal sequence.
To ensure convergence of the solution and reduce calculation errors, a step h=pi/512 is chosen for simulation. Take x= [ X ] 1 ,y 1 ,x 2 ,y 2 ,x 3 ,y 3 ]'dimensionless, X' =x/c as follows,
Figure BDA0002232241340000061
where c is the bearing radial clearance (i.e., the average thickness of the lubricating film). Other parameters employed in the calculation are as follows: δ=0.0002 m; e=0.5×10 - 4 m；m 1 ＝4kg；m 2 ＝32.1kg；m 3 ＝50kg；k＝2.5×10 7 N/m；k b1 ＝7.5×10 7 N/m；R＝0.025m；k b2 ＝2.5×10 9 N/m；c 1 ＝1050N·s/m；l＝0.012m；c 2 ＝2100N·s/m；c b1 ＝350N·s/m；μ＝0.018pa°s；c b2 ＝500N·s/m；c＝0.00011m；
Step 2, carrying out taylor expansion on nonlinear terms of the nonlinear model to obtain a linear approximate dynamics model, and solving a differential equation to obtain a response signal sequence of the linear model;
the linear approximate dynamics model establishment process of the nonlinear model is as follows;
nonlinear oil film force F in nonlinear model x ，F y Performing Taylor expansion, and removing higher-order terms to obtain linear approximate oil film force as follows:
Figure BDA0002232241340000062
h in xx ,h xy ,h yx ,h yy For oil film stiffness, d xx ,d xy ,d yx ,d yy F is oil film damping x0 ，F y0 Is the oil film force at the static equilibrium position.
Similarly, the nonlinear elastic force generated by the loosening fault of the rotor system
Figure BDA0002232241340000063
The linear approximation elastic force can be obtained by taylor expansion at the equilibrium point and discarding the higher order term as follows:
Figure BDA0002232241340000064
substituting the result of the nonlinear term taylor expansion into the original equation can obtain a linear approximation dynamic model L (ω) of the sliding bearing rotor system as follows:
Figure BDA0002232241340000065
in the middle of
Figure BDA0002232241340000066
Representing the oil film force component F x ,F y Is a linear approximation of (a).
And carrying out numerical integration solution on the linear approximate dynamics model by adopting a 4-5-order variable step length Runge-Kutta method to obtain a response signal sequence of the linear approximate dynamics model.
To ensure convergence of the solution and reduce calculation errors, a step h=pi/512 is chosen for simulation. Take x= [ X ] 1 ,y 1 ,x 2 ,y 2 ,x 3 ,y 3 ]'dimensionless, X' =x/c as follows,
Figure BDA0002232241340000067
where c is the bearing radial clearance (i.e., the average thickness of the lubricating film). Other parameters employed in the calculation are as follows: δ=0.0002 m; e=0.5×10 - 4 m；m 1 ＝4kg；m 2 ＝32.1kg；m 3 ＝50kg；k＝2.5×10 7 N/m；k b1 ＝7.5×10 7 N/m；R＝0.025m；k b2 ＝2.5×10 9 N/m；c 1 ＝1050N·s/m；l＝0.012m；c 2 ＝2100N·s/m；c b1 ＝350N·s/m；μ＝0.018pa°s；c b2 ＝500N·s/m；c＝0.00011m；。
Step 3, calculating a nonlinearity value for nonlinear rotor system dynamics models and linear rotor dynamics model response sequences with different input rotation speeds to obtain a nonlinearity measure curve;
in step 3, a calculation formula adopted for calculating the nonlinear measure value of the sliding bearing rotor system is as follows:
φ L ＝||N(ω)-L(ω)||
in the formula of I, I representing norms; n is a nonlinear dynamic system; l is a linear approximation system obtained by adopting Taylor expansion; n (ω) and G (ω) represent the output response of the nonlinear system and the linear system, respectively, at the input ω; phi (phi) L Is a non-linearity estimation value.
And calculating corresponding nonlinearity degree values according to the nonlinearity degree calculation formula for the nonlinear dynamics model response signals and the linear approximation model dynamics response signals, drawing a trend graph of the nonlinearity degree values along with the change of the rotating speed, comparing the trend graph with a rotor system response bifurcation graph, and as shown in a result of a graph in fig. 2, when the rotating speed of a rotor system is low, the nonlinearity degree of the dynamics behavior is weak, the nonlinearity measure value fluctuates in a small amplitude range from 24.3 to 28, and when bifurcation occurs in the system response, the nonlinearity value of the system starts to rapidly increase, and finally the nonlinearity degree is kept at a high level. According to the characteristic that the nonlinearity curve increases rapidly when the system response bifurcation starts to appear, a 3 sigma method is adopted to calculate an alarm threshold value and identify the rotating speed of the system response bifurcation point.
And 4, calculating an average value and a variance value for the nonlinear measurement sequence according to a 3 sigma rule, setting an alarm threshold value, and identifying the rotating speed of an initial bifurcation point of the sliding bearing rotor system.
Referring to fig. 3, in step 4, the algorithm flow for identifying the initial bifurcation point rotation speed of the bearing rotor system based on the 3 sigma rule is as follows:
1) Expressed as t=1, 2,3,..Rotation speed of degree phi L,1 ,φ L,2 ,φ L,3 ,. the non-linearity values at the corresponding rotational speeds; starting from t=2, the mean and variance values of the nonlinear measurement sequence are calculated according to the 3 sigma rule, as follows:
Figure BDA0002232241340000071
2) According to 3 sigma rule, according to formula
Figure BDA0002232241340000072
Setting an alarm threshold;
3) Judging phi L，t+1 Upper limit +. ω )+3σ(φ L ) If so, the rotating speed at the time t+1 is the initial bifurcation rotating speed; if not, let t=t+1, continue steps 1), 2), 3) until φ is satisfied L，t+1 Upper limit +. ω )+3σ(φ L )。
According to the method for identifying the rotation speed of the initial bifurcation point of the bearing rotor system, the nonlinear measurement sequence is identified, the identification result is shown in figure 4, when the rotation speed of the rotor system is low, the dynamic behavior nonlinearity degree is weak, the nonlinear measurement value fluctuates between 24.3 and 28 in a small amplitude, the curve is in the alarm threshold range, when the bifurcation starts to appear in the system response, the dynamic behavior nonlinearity value of the system starts to grow rapidly, and when the rotation speed reaches 626rad/s, the corresponding dynamic response nonlinearity measurement value of the rotor system exceeds the alarm threshold range, and finally the nonlinearity degree is kept at a high level. Thus, a rotor system response initial bifurcation speed of 626rad/s is obtained, which is consistent with the results shown in the response bifurcation diagram shown in FIG. 3, thus proving the effectiveness of the present method.
While the invention has been described above with reference to various embodiments, it should be understood that many changes and modifications can be made without departing from the scope of the invention. That is, the methods, systems and devices discussed above are examples. Various configurations may omit, replace, or add various procedures or components as appropriate. For example, in alternative configurations, the methods may be performed in a different order than described, and/or various components may be added, omitted, and/or combined. Moreover, features described with respect to certain configurations may be combined in various other configurations, such as different aspects and elements of the configurations may be combined in a similar manner. Furthermore, as the technology evolves, elements therein may be updated, i.e., many of the elements are examples, and do not limit the scope of the disclosure or the claims.
Specific details are given in the description to provide a thorough understanding of exemplary configurations involving implementations. However, configurations may be practiced without these specific details, e.g., well-known circuits, processes, algorithms, structures, and techniques have been shown without unnecessary detail in order to avoid obscuring configurations. This description provides only an example configuration and does not limit the scope, applicability, or configuration of the claims. Rather, the foregoing description of the configuration will provide those skilled in the art with an enabling description for implementing the described techniques. Various changes may be made in the function and arrangement of elements without departing from the spirit or scope of the disclosure.
It is intended that the foregoing detailed description be regarded as illustrative rather than limiting, and that it be understood that it is the following claims, including all equivalents, that are intended to define the spirit and scope of this invention. The above examples should be understood as illustrative only and not limiting the scope of the invention. Various changes and modifications to the present invention may be made by one skilled in the art after reading the teachings herein, and such equivalent changes and modifications are intended to fall within the scope of the invention as defined in the appended claims.

Claims (1)

1. A bearing rotor system initial bifurcation point rotating speed identification method based on a 3 sigma method comprises the following steps:
step 1, a dynamic model of a sliding bearing rotor system is established, and a differential equation is solved to obtain a response signal sequence of a nonlinear dynamic model;
step 2, carrying out taylor expansion on nonlinear terms of the nonlinear model to obtain a linear approximate dynamics model, and solving a differential equation to obtain a response signal sequence of the linear model;
step 3, calculating a nonlinearity value for nonlinear rotor system dynamics models and linear rotor dynamics model response sequences with different input rotation speeds to obtain a nonlinearity measure curve;
step 4, calculating an average value and a variance value for the nonlinear measurement sequence according to a 3 sigma rule, setting an alarm threshold value, and identifying the rotating speed of an initial bifurcation point of the sliding bearing rotor system;
the nonlinear dynamics model of the sliding bearing rotor system established in the step 1 is as follows:
Figure FDA0004110882110000011
wherein m is 1 The mass is concentrated for the equivalent of the rotor at the bearings at the two ends; m is m 2 The equivalent concentrated mass of the rotor at the disc; m is m 3 The equivalent concentrated mass of the loose end bearing support seat is obtained; k is the linear stiffness coefficient of the elastic shaft; c 1 Equivalent damping at the bearings at the two ends; c 2 Damping of the rotor at the disc; x is x 1 ，y 1 The vibration displacement of the axle center at the right end bearing relative to the balance position in the horizontal and vertical directions is respectively; x is x 2 ，y 2 The vibration displacement of the center of the turntable relative to the balance position in the horizontal direction and the vertical direction is respectively; x is x 3 ，y 3 The left end bearing axle center is respectively in the horizontal and vertical direction relative to the vibration displacement of the balance position; the loose clearance between the left end bearing support and the foundation is delta; y is 4 The vibration displacement is carried out in the vertical direction of the bearing support; e is the mass eccentricity of the turntable; omega is the angular velocity of the rotor of the plain bearing rotor system;
Figure FDA0004110882110000012
and->
Figure FDA0004110882110000013
Respectively slide at the left end and the right endThe components of the nonlinear oil film force on the dynamic bearing in the horizontal and vertical directions; ky (ky) 4 、/>
Figure FDA0004110882110000014
Respectively representing the linear and nonlinear parts of the elastic force;
wherein k is b 、c b Respectively equivalent rigidity and equivalent damping of the foundation to the loose end supporting seat; the equivalent rigidity and equivalent damping of the foundation to the loose end supporting seat are respectively expressed as follows:
Figure FDA0004110882110000021
in step 2, the linear approximation dynamics model of the established nonlinear model is as follows;
Figure FDA0004110882110000022
in the middle of
Figure FDA0004110882110000023
Representing the oil film force component F x ,F y Is a linear approximation of ky 4 Representing a linear approximate elastic force;
wherein the method comprises the steps of
Figure FDA0004110882110000024
By applying a nonlinear oil film force F in a nonlinear model x ，F y And (3) performing Taylor expansion, and removing higher-order terms to obtain the formula:
Figure FDA0004110882110000025
h in xx ,h xy ,h yx ,h yy For oil film stiffness, d xx ,d xy ,d yx ,d yy Is thatOil film damping, F x0 ，F y0 Is the oil film force at the static equilibrium position;
similarly, the nonlinear elastic force generated by loosening faults of rotor system
Figure FDA0004110882110000026
Taylor expansion is performed at the equilibrium point and the higher order term is truncated to obtain a linear approximate elastic force as follows:
Figure FDA0004110882110000027
in step 3, a calculation formula adopted for calculating the nonlinear measure value of the sliding bearing rotor system is as follows:
φ L ＝||N(ω)-L(ω)||
in the middle of
Figure FDA0004110882110000028
Representing norms; n is a nonlinear dynamic system; l is a linear approximation system obtained by adopting Taylor expansion; n (ω) and G (ω) represent the output response of the nonlinear system and the linear system, respectively, at the input ω; phi (phi) L Is a nonlinearity estimation value;
in step 4, the algorithm flow for identifying the initial bifurcation point rotation speed of the bearing rotor system based on the 3 sigma rule is as follows:
1) Let t=1, 2,3, … denote the rotational speed number, phi, used to calculate the nonlinearity L,1 ,φ L,2 ,φ L,3 … represents the value of the nonlinearity at the corresponding rotational speed; starting from t=2, the mean and variance values of the nonlinear measurement sequence are calculated according to the 3 sigma rule, as follows:
Figure FDA0004110882110000031
2) According to 3 sigma rule, according to formula
Figure FDA0004110882110000032
Setting an alarm threshold;
3) Judging phi L，t+1 Upper limit +. ω )+3σ(φ L ) If so, the rotating speed at the time t+1 is the initial bifurcation rotating speed; if not, let t=t+1, continue steps 1), 2), 3) until φ is satisfied L，t+1 Upper limit +. ω )+3σ(φ L )。
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CN111353199B (en) * 2020-03-02 2023-06-13 佛山科学技术学院 Method for determining bearing parameters of rotor system oriented to weak nonlinear dynamic behaviors

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CN109374300A (en) * 2018-12-13 2019-02-22 西安理工大学 A kind of touch rubbing speed based on UMP-bearing arrangement Analysis of Vibration Characteristic method
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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Publication number Priority date Publication date Assignee Title
CN106706303A (en) * 2017-03-02 2017-05-24 湖南科技大学 Rotor-bearing system pedestal looseness state assessment method
CN109374300A (en) * 2018-12-13 2019-02-22 西安理工大学 A kind of touch rubbing speed based on UMP-bearing arrangement Analysis of Vibration Characteristic method
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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