CN111353199B - Method for determining bearing parameters of rotor system oriented to weak nonlinear dynamic behaviors - Google Patents

Method for determining bearing parameters of rotor system oriented to weak nonlinear dynamic behaviors Download PDF

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CN111353199B
CN111353199B CN202010135601.9A CN202010135601A CN111353199B CN 111353199 B CN111353199 B CN 111353199B CN 202010135601 A CN202010135601 A CN 202010135601A CN 111353199 B CN111353199 B CN 111353199B
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rotor system
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CN111353199A (en
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蒋勉
刘双奇
何宽芳
王宇华
李学军
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Foshan University
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Abstract

The invention provides a method for determining the bearing parameters of a rotor system facing weak nonlinear dynamic behaviors, namely, selecting parameters and ranges thereof to be determined; determining the size interval of each parameter according to the requirement, and dispersing each parameter interval; selecting parameter value groups from each interval, and establishing a nonlinear dynamic model of the rotor system containing determined parameter values; carrying out taylor expansion on the nonlinear term of the nonlinear model in the step 3 to obtain a linear approximate dynamic model; carrying out numerical solution calculation on nonlinear measurement values according to nonlinear and linear dynamic models; calculating to obtain a nonlinear degree set according to all parameter values traversed, and selecting a minimum value in the set; and evaluating the intensity of the nonlinear degree of the dynamic behavior of the system according to the obtained minimum value, and further determining the bearing value of the rotor system. The method for determining the rotor system bearing parameters oriented to weak nonlinear dynamic behaviors is constructed by utilizing the nonlinearity, so that the method under a linear frame can be used for carrying out state identification and fault diagnosis on the rotor system.

Description

Method for determining bearing parameters of rotor system oriented to weak nonlinear dynamic behaviors
Technical Field
The invention relates to the technical field of mechanical system state monitoring and fault diagnosis, in particular to a rotor system bearing parameter determining method oriented to weak nonlinear dynamic behaviors.
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. With the increase in rotational speed of rotor systems and the application of various new materials and new structures, rotor systems exhibit increasing nonlinear dynamic behavior. For weak nonlinear dynamic behavior, a linear approximation method can be adopted to approximate the dynamic behavior of the rotor system, and then a mature linear monitoring and diagnosis method system is adopted to realize the monitoring and diagnosis of the rotor system. If the rotor system has strong nonlinear dynamic behavior, a monitoring and diagnosing method system for nonlinear phenomenon does not exist to realize the monitoring and diagnosing of the rotor system. Corresponding nonlinear monitoring and diagnosis methods can only be designed according to the characteristics of different nonlinear phenomena. This greatly increases the difficulty of effectively monitoring and accurately diagnosing rotor systems having strong nonlinear dynamic behavior. The rotor system bearing parameter determination method for the weak nonlinear dynamic behavior is used for determining the proper parameters on the rotor system bearing to enable the rotor system dynamic behavior to be weak nonlinear, and can realize effective monitoring and diagnosis by adopting a linear method system.
Disclosure of Invention
The invention aims to provide a rotor system bearing parameter determining method oriented to weak nonlinear dynamic behaviors, which is used for determining proper parameters of a rotor system to enable the dynamic behaviors of the rotor system to be weak nonlinear, and can realize effective monitoring and diagnosis by adopting a linear method system.
The aim of the invention is achieved by the following technical scheme:
a method for determining the bearing parameters of a rotor system facing weak nonlinear dynamic behavior comprises the following steps:
step 1, selecting parameters to be determined and a range thereof;
step 2, determining the size interval of each parameter according to the requirement, and dispersing each parameter interval;
step 3, selecting parameter value groups from each interval, and establishing a nonlinear dynamic model of the rotor system containing determined parameter values;
step 4, carrying out Taylor expansion on the nonlinear term of the nonlinear model in the step 3 to obtain a linear approximate dynamic model;
step 5, carrying out numerical solution calculation on nonlinear measurement values according to nonlinear and linear dynamic models;
step 6, calculating to obtain a non-linearity set according to all parameter values traversed, and selecting the minimum value in the set;
and 7, evaluating the strength of the nonlinear degree of the dynamic behavior of the system according to the obtained minimum value, and further determining the bearing parameter value of the rotor system.
Optionally, the parameters to be determined in step 1 include bearing clearance and oil film viscosity, and the variable range of each parameter is determined according to the actual physical conditions.
Optionally, in step 2, the variation interval of the parameters is determined according to different characteristics of each parameter and physical conditions actually achievable, and the parameter intervals are equidistantly scattered.
Optionally, in step 3, the parameters to be determined in the nonlinear dynamic model of the rotor system are obtained by substituting constant values.
Optionally, in step 4, the method for obtaining the linear approximation dynamic model of the rotor system is obtained by substituting the nonlinear term of the original dynamic model by using taylor expansion at the equilibrium point position to obtain the linear approximation term.
Optionally, in step 5, the nonlinear metric value is obtained by quantifying a difference of numerical calculation responses of the nonlinear dynamic model and the linear approximation model in a norm sense, respectively.
In step 6, traversing the calculation result set of which all possible values of the parameters need to be determined to obtain nonlinearity, and then obtaining the minimum value in the set through retrieval.
Optionally, in step 7, the intensity of the nonlinear degree of the dynamic behavior of the system is estimated according to the obtained minimum value, and the corresponding bearing value of the rotor system at the moment is determined.
The beneficial effects obtained by the invention are as follows: taking a sliding bearing rotor system with one end supporting loosening fault as an example, selecting parameters to be determined and a range thereof, then establishing a dynamic model of the rotor system and a corresponding linear approximation model, numerically solving a dynamic differential equation to obtain a dynamic response signal, calculating under different parameter values to obtain a nonlinear degree quantized value, and finally determining a corresponding parameter value by searching a nonlinear degree minimum value to enable the rotor system to have weak nonlinear behavior.
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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 flow chart of a method for determining the bearing parameters of a rotor system facing weak nonlinear dynamic behavior;
FIG. 2 is a simplified schematic diagram of a sliding bearing rotor system according to the present invention;
FIG. 3 is a graph of the result of nonlinearity at a rotation of 500rad/s with an eccentricity of 0.01mm in the present invention;
FIG. 4 is a graph of the result of non-linearities at a rotation speed of 885rad/s, an eccentricity of 0.01mm, in the invention;
FIG. 5 is a graph of the result of nonlinearity at a rotational speed of 500rad/s and an eccentricity of 0.1mm in the present invention;
FIG. 6 is a graph showing the result of nonlinearity at a rotational speed of 885rad/s and an eccentricity of 0.1mm in 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 determining a rotor system bearing parameter oriented to weak nonlinear dynamic behavior, which comprises the following steps: (please refer to FIG. 1)
Step 1, selecting parameters to be determined as bearing clearance c and lubricating oil viscosity mu, and assuming a corresponding parameter range of c E [ c ] min ,c max ]，μ∈[μ min ,μ max ]。
Step 2, assume interval c e c of bearing gap min ,c max ]Divided into k 1 Equally dividing the interval mu E [ mu ] of the viscosity of the lubricating oil min ,μ max ]Divided into k 2 Aliquoting, determining the discrete intervals of the bearing gaps as follows:
Figure BDA0002397195740000041
the discrete intervals for determining the viscosity of the lubricating oil are:
Figure BDA0002397195740000042
step 3, the i-th parameter value of the bearing clearance is taken out to be
c i ＝c min +(i-1)Δc (3)
The j-th parameter value of the viscosity of the extracted lubricating oil is
μ j ＝μ min +(j-1)Δμ (4)
The plain bearing-rotor system with support looseness failure is simplified to a simplified model as shown in fig. 2. The rotor being supported at both ends by 2 identical slide bearings, O 1 Is the geometric center of the bearing bush, O 2 For rotor geometric centre, O 3 Is the center of mass of the rotor. m is m 1 For equivalent concentrated mass of rotor at bearings at both ends, m 2 For rotor in circleEquivalent concentrated mass at disk, m 3 For loosening the equivalent concentrated mass of the end bearing support seat, k is the linear rigidity coefficient of the elastic shaft, c 1 C is equivalent damping at the bearings at both ends 2 Damping of the rotor at the disc. k (k) b 、c b The equivalent rigidity and the equivalent damping of the foundation to the loose end supporting seat are respectively. And a mass-free shaft is arranged between the turntable and the bearing.
Assuming that the vibration displacement of the shaft center at the right end bearing of the bearing rotor system relative to the balance position in the horizontal and vertical directions is x 1 ，y 1 The vibration displacement of the center of the turntable relative to the balance position in the horizontal and vertical directions is x 2 ，y 2 The vibration displacement of the left end bearing axle center relative to the balance position in the horizontal and vertical directions is x respectively 3 ，y 3 . Assuming that the left end bearing support has loosening fault, the loosening clearance between the bearing support and the foundation is delta, and only the vertical vibration displacement y of the bearing support is considered because the horizontal vibration of the loosening end bearing support is very small 4 。
The vibration generated by the rotor system is determined by exciting force and rigidity and damping of a mechanical structure, when a bearing support is in loose fault, the system generates large vibration due to tiny unbalance or misalignment of the system, the connection rigidity and the mechanical damping of the system are reduced, and the supporting characteristic is in piecewise linearity, so that the equivalent rigidity and the equivalent damping of a foundation to a loose end supporting seat are respectively expressed as:
Figure BDA0002397195740000051
the nonlinear factor in the loose clearance of the supporting seat is one of the common nonlinear factors, and the nonlinear factor is particularly remarkable in the situations of aging and loosening of a rotor system and the like. The vertical spring force generated by the bearing clearance of the plain bearing rotor system in this example is defined by the following nonlinearity:
Figure BDA0002397195740000052
/>
middle ky 4 、
Figure BDA0002397195740000053
Representing the linear and nonlinear parts of the elastic force, respectively.
The nonlinear dynamic model of the rotor system comprising the determination of bearing clearance and lubricant viscosity parameter values is:
Figure BDA0002397195740000054
wherein e is the mass eccentricity of the turntable; omega is the angular velocity of the rotor of the plain bearing rotor system;
Figure BDA0002397195740000055
Figure BDA0002397195740000056
and->
Figure BDA0002397195740000057
The components of the nonlinear oil film force on the sliding bearings at the left end and the right end in the horizontal direction and the vertical direction are respectively. The nonlinear oil film force component calculation formula is as follows:
F x ＝sf x ,F y ＝sf y
f in the formula x ，F y Representing the horizontal and vertical components of the oil film. s is a correction coefficient:
Figure BDA0002397195740000058
omega is the rotating speed of the rotating shaft, R is the radius of the bearing, L is the length of the bearing, and c i Mu, for bearing radial clearance j Mu is the viscosity of the lubricating oil.
Wherein the dimensionless Reynolds equation is simplified according to the short cylindrical bearing theory:
Figure BDA0002397195740000059
solving the above to obtain dimensionless oil film pressure as follows:
Figure BDA00023971957400000510
wherein: r represents the journal radius; d represents the journal diameter; l represents the bearing length; θ represents an angle radius;
Figure BDA00023971957400000511
representing the dimensionless thickness of the lubricating oil film; c i Representing the bearing clearance.
Assuming that the lubricating film acts over an angle range [ beta, beta + pi ], the angle beta is defined as:
Figure BDA0002397195740000061
based on boundary conditions: the cavity area and the two ends of the bearing are p=0, the oil film pressure is integrated along the lubrication action angle of the bearing, the nonlinear oil film force is solved, and then the oil film force is decomposed into f along the x and y directions x And f y ：
Figure BDA0002397195740000062
The above is transformed to obtain:
Figure BDA0002397195740000063
Figure BDA0002397195740000064
/>
Figure BDA0002397195740000065
Figure BDA0002397195740000066
and carrying out numerical integration solution on a nonlinear dynamic differential equation by adopting a 4-5-order variable step length Runge-Kutta method to obtain a nonlinear dynamic 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 BDA0002397195740000067
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；c b2 ＝500N·s/m；
Step 4, performing taylor expansion on the nonlinear term of the nonlinear model in the step 3 to obtain a linear approximate dynamic model, wherein the linear approximate dynamic 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 BDA0002397195740000068
h in xx ,h xy ,h yx ,h yy For oil film stiffness, d xx ,d xy ,d yx ,d yy Is oil film damping.
Similarly, the nonlinear elastic force generated by the loosening fault of the rotor system
Figure BDA0002397195740000069
The linear approximation elastic force can be obtained by taylor expansion at the equilibrium point and discarding the higher order term as follows:
Figure BDA00023971957400000610
substituting the result of the nonlinear term Taylor expansion into the original equation to obtain the linear approximate dynamic model L (c) i ,μ j ) The following are provided:
Figure BDA0002397195740000071
in the middle of
Figure BDA0002397195740000072
Representing the oil film force component F x ,F y Is a linear approximation of (a).
And carrying out numerical integration solving on the linear approximate dynamic model by adopting a 4-5-order variable step length Runge-Kutta method to obtain a response signal sequence of the linear approximate dynamic model, wherein the step length h=pi/512 is selected in simulation in order to ensure the convergence of the solution and reduce calculation errors. Take x= [ X ] 1 ,y 1 ,x 2 ,y 2 ,x 3 ,y 3 ]'dimensionless, X' =x/c as follows,
Figure BDA0002397195740000073
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；c b2 ＝500N·s/m。/>
Step 5, carrying out numerical solution calculation on nonlinear measurement values according to nonlinear and linear dynamic models; the specific operation is as follows:
introduction of L 2 Norms:
Figure BDA0002397195740000074
the non-linearity degree calculation formula is defined as:
Figure BDA0002397195740000075
omega in 0 For a certain fixed rotating speed of the rotor system, N is a nonlinear dynamic system; l is a linear approximation system obtained by adopting Taylor expansion; n (c) i ,μ j ) And L (c) i ,μ j ) Representing the nonlinear system and the linear system at parameter c, respectively i ,μ j Output response at time; phi (phi) ij Is a non-linearity estimation value. Value range phi ij ≥0。
Step 6, i is not less than 1 and not more than k is taken 1 ,1≤j≤k 2 Calculating to obtain a non-linearity set according to all parameter values
Figure BDA0002397195740000076
And determining the minimum value in the set as:
Figure BDA0002397195740000077
step 7, according to the obtained minimum value phi min At the collection
Figure BDA0002397195740000081
And (3) determining the corresponding parameter value sequence number and determining the parameter pairs which can be selected by the rotor system.
In the steps 1 to 6 of the present invention, each step may be preferably performed as follows:
optionally, in step 1, the number of parameters to be determined and the corresponding range size thereof may be changed;
optionally, in step 2, the size interval of each parameter needs to be determined and can be adjusted according to the object and the physical condition, and the method for dispersing each parameter interval can be selected according to the actual situation, and can be selected to be equidistant or set to be unequal;
optionally, in step 3, a nonlinear dynamic model of the rotor system including the determined parameter values is established according to the subject of study;
optionally, in step 4, the linear approximation dynamic model may be obtained by taylor expansion of the nonlinear term, or may be obtained by optimization or other methods;
optionally, in step 5, the nonlinear metric value is calculated by performing numerical solution according to the nonlinear and linear dynamic models in a certain norm sense, where the definition of the norm can be determined according to the specific object and the actual application situation;
alternatively, in step 6, the determination of the minimum value of the set of non-linearities may select a different retrieval 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 (4)

1. A method for determining the bearing parameters of a rotor system facing weak nonlinear dynamic behavior comprises the following steps:
step 1, selecting parameters to be determined and a range thereof;
the parameters to be determined in the step 1 comprise bearing clearance and oil film viscosity, and the variable range of each parameter is determined according to actual physical conditions; the parameters to be determined are selected as bearing clearance c and lubricating oil viscosity mu, and the corresponding parameter range is assumed to be c E [ c min ,c max ]，μ∈[μ min ,μ max ]；
Step 2, determining the size interval of each parameter according to the requirement, and dispersing each parameter interval;
in the step 2, the change interval of the parameters is determined according to different characteristics of each parameter and physical conditions which can be realized practically, and the parameter intervals are equidistantly scattered; interval c e of bearing gap c min ,c max ]Divided into k 1 Equally dividing the interval mu E [ mu ] of the viscosity of the lubricating oil min ,μ max ]Divided into k 2 Aliquoting, determining the discrete intervals of the bearing gaps as follows:
Figure FDA0004221971060000011
the discrete intervals for determining the viscosity of the lubricating oil are:
Figure FDA0004221971060000012
step 3, selecting parameter value groups from each interval, and establishing a nonlinear dynamic model of the rotor system containing determined parameter values; in the step 3, parameters to be determined in the nonlinear dynamic model of the rotor system are obtained and substituted by constant values;
the i-th parameter value of the bearing clearance is taken out to be
c i ＝c min +(i-1)Δc
The j-th parameter value of the viscosity of the extracted lubricating oil is
μ j ＝μ min +(j-1)Δμ
Step 4, carrying out Taylor expansion on the nonlinear term of the nonlinear model in the step 3 to obtain a linear approximate dynamic model;
step 5, carrying out numerical solution calculation on nonlinear measurement values according to nonlinear and linear dynamic models;
step 6, calculating to obtain a non-linearity set according to all parameter values traversed, and selecting the minimum value in the set;
and 7, evaluating the strength of the nonlinear degree of the dynamic behavior of the system according to the obtained minimum value, and further determining the bearing value of the rotor system.
2. The method for determining the bearing parameters of the rotor system facing weak nonlinear dynamic behavior according to claim 1, wherein in the step 4, the method for obtaining the linear approximation dynamic model of the rotor system is obtained by substituting the nonlinear terms of the original dynamic model by using taylor expansion at the equilibrium point position to obtain the linear approximation terms.
3. The method for determining the bearing parameters of the rotor system for weak nonlinear dynamic behavior according to claim 1, wherein in step 5, the nonlinear metric value is obtained by quantifying the difference of the numerical calculation responses of the nonlinear dynamic model and the linear approximation model in the normative sense, respectively.
4. The method for determining the bearing parameters of the rotor system for weak nonlinear dynamic behavior according to claim 1, wherein in step 6, a set of calculation results of nonlinearity is obtained by traversing all possible values of the parameters to be determined, and then the minimum value in the set is obtained by searching.
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