CN111353199A - Rotor system bearing parameter determination method for weak nonlinear dynamic behavior - Google Patents
Rotor system bearing parameter determination method for weak nonlinear dynamic behavior Download PDFInfo
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Abstract
The invention provides a method for determining the parameters of a rotor system bearing facing weak nonlinear dynamic behavior, namely selecting the parameters to be determined and the range thereof; determining the size interval of each parameter according to needs, and dispersing each parameter interval; selecting a parameter value group from each interval, and establishing a rotor system nonlinear dynamic model containing the determined parameter value; carrying out Taylor expansion on the nonlinear terms of the nonlinear model in the step 3 to obtain a linear approximate dynamic model; carrying out numerical solution and calculation on nonlinear metric values according to the nonlinear and linear dynamic models; calculating to obtain a non-linearity set according to all the ergodic parameter values, and selecting a minimum value in the set; and 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. The invention utilizes the nonlinearity to construct the rotor system bearing parameter determination method facing the weak nonlinear dynamic behavior, so that the rotor system can be subjected to state identification and fault diagnosis by adopting a method under a linear framework.
Description
Technical Field
The invention relates to the technical field of state monitoring and fault diagnosis of a mechanical system, in particular to a rotor system bearing parameter determination method for weak nonlinear dynamic behavior.
Background
The bearing rotor system is a core component of power machinery such as an aircraft engine, a gas turbine, a traction motor and the like, and the operation stability of the bearing rotor system is directly related to the safety and reliability of equipment. As rotor systems increase in rotational speed and the application of various new materials and structures, rotor systems exhibit more and more nonlinear dynamic behavior. For weak nonlinear dynamic behaviors, the dynamic behavior of the rotor system can be approximated by a linear approximation method, and then the rotor system can be monitored and diagnosed by adopting a mature linear monitoring and diagnosing method system. If the rotor system has strong nonlinear dynamic behavior, a monitoring and diagnosing method system aiming at nonlinear phenomena does not exist to realize the monitoring and diagnosis of the rotor system. Corresponding non-linear monitoring and diagnostic methods can only be designed according to the characteristics of different non-linear phenomena. This greatly increases the difficulty of effectively monitoring and accurately diagnosing rotor systems with strong nonlinear dynamic behavior. Because the selection of the rotor system bearing parameters has a great influence on the strength of the nonlinear degree of the dynamic behavior, the invention provides a rotor system bearing parameter determination method for weak nonlinear dynamic behavior, which is used for determining appropriate parameters on a rotor system bearing to enable the dynamic behavior of the rotor system 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 for weak nonlinear dynamic behavior, which is used for determining appropriate parameters of a rotor system to enable the dynamic behavior of the rotor system to be weak nonlinear and can realize effective monitoring and diagnosis by adopting a linear method system.
The purpose of the invention is realized by the following technical scheme:
a method for determining a rotor system bearing parameter oriented to weak nonlinear dynamic behavior comprises the following steps:
step 1, selecting parameters to be determined and ranges thereof;
step 6, calculating according to all the ergodic parameter values to obtain a nonlinear degree set, and selecting a minimum value in the set;
and 7, further determining the bearing parameter value of the rotor system according to the obtained minimum value to evaluate the non-linear degree of the dynamic behavior of the 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 actual physical conditions.
Optionally, in step 2, the variation interval of the parameters is determined according to different characteristics of the parameters and actual achievable physical conditions, and the parameter interval is equidistantly dispersed.
Optionally, in step 3, the parameters to be determined in the nonlinear dynamic model of the rotor system are obtained and substituted by adopting constant values.
Optionally, in step 4, the method for obtaining the linear approximate dynamic model of the rotor system is obtained by substituting a linear approximate term obtained by taylor expansion at the equilibrium point position for the nonlinear term of the dynamic model.
Optionally, in step 5, the nonlinear metric is obtained by quantizing the difference between the numerical computation responses of the nonlinear dynamical model and the linear approximation model in the norm sense.
In step 6, traversing all possible values of the parameter to be determined to obtain a calculation result set of the nonlinearity, and then obtaining the minimum value in the set through retrieval.
Optionally, in step 7, the strength of the nonlinearity degree of the dynamic behavior of the system is evaluated according to the obtained minimum value, and the corresponding bearing value of the rotor system at the time is determined.
The invention has the following beneficial effects: the invention takes a sliding bearing rotor system with one end supporting loose fault as an example, selects parameters to be determined and the range thereof, then establishes a dynamic model of the rotor system and a corresponding linear approximate model, numerically solves a dynamic differential equation to obtain a dynamic response signal, calculates under different parameter values to obtain a non-linear degree quantized value, and finally determines the corresponding parameter value thereof by retrieving the minimum value of the non-linear degree, so that the rotor system has weak non-linear behavior.
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The present invention will be further understood from the following description taken in conjunction with the accompanying drawings, the emphasis instead being placed upon illustrating the principles of the embodiments.
FIG. 1 is a flow chart of a method for determining a rotor system bearing parameter for weak nonlinear dynamic behavior according to the present invention;
FIG. 2 is a simplified model schematic of a plain bearing rotor system provided by the present invention;
FIG. 3 is a graph showing the results of the nonlinearity of the present invention at a rotation speed of 500rad/s and an eccentricity of 0.01 mm;
FIG. 4 is a graph showing the results of the nonlinearity of the present invention at a rotation speed of 885rad/s and an eccentricity of 0.01 mm;
FIG. 5 is a graph showing the results of the nonlinearity of the present invention at a rotation speed of 500rad/s and an eccentricity of 0.1 mm;
FIG. 6 is a graph showing the results of the nonlinearity of the present invention at a rotation speed of 885rad/s and an eccentricity of 0.1 mm.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to embodiments thereof; it should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Other systems, methods, and/or features of the present embodiments will become apparent to those skilled in the art upon review 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 detailed description that follows.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by the terms "upper", "lower", "left", "right", etc. based on the orientation 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 intended to indicate or imply that the device or component referred to must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and are not to be construed as limiting the present patent, and the specific meaning of the terms described above will be understood by those of ordinary skill in the art according to the specific circumstances.
The invention relates to a method for determining a rotor system bearing parameter for weak nonlinear dynamic behavior, which comprises the following steps: (please refer to FIG. 1)
Step 1, selecting parameters needing to be determined as a bearing clearance c and a lubricating oil viscosity mu, and assuming that a corresponding parameter range is c ∈ [ c [ [ c ]min,cmax],μ∈[μmin,μmax]。
the discrete intervals for determining the viscosity of the lubricating oil are:
ci=cmin+(i-1)Δc (3)
The jth parameter value of the viscosity of the taken lubricating oil is
μj=μmin+(j-1)Δμ (4)
The plain bearing-rotor system with bearing loosening failure is simplified to the simplified model shown in fig. 2. Both ends of the rotor being supported by 2 identical sliding bearings, where O1Is the geometric center of the bearing bush, O2Is the geometric center of the rotor, O3Is the center of mass of the rotor. m is1For equivalent concentrated mass of rotor at bearings at both ends, m2For equivalent concentrated mass of the rotor at the disk, m3For loosening the equivalent concentrated mass of the end bearing support, k is the linear stiffness coefficient of the elastic shaft, c1For equivalent damping at the bearings at both ends, c2Damping of the rotor at the disc. k is a radical ofb、cbRespectively the equivalent rigidity and the equivalent damping of the loose end supporting seat. An unbalancedness shaft is assumed between the rotary table and the bearing.
Suppose that the vibration displacement of the axle center at the right end bearing of the bearing rotor system in the horizontal and vertical directions relative to the balance position is x respectively1,y1The vibration displacement of the center of the turntable in the horizontal and vertical directions relative to the equilibrium position is x2,y2The vibration displacement of the left end bearing axis in the horizontal and vertical directions relative to the balance position is x3,y3. If the bearing support at the left end has a loosening fault, the loosening gap between the bearing support and the foundation is delta, and the vibration of the bearing support at the loosening end in the horizontal direction is very small, so that the vibration displacement y of the bearing support in the vertical direction is only considered4。
The vibration generated by the rotor system is determined by the exciting force and the rigidity and damping of a mechanical structure, when a bearing support has a loosening fault, the system generates large-amplitude vibration due to micro unbalance or misalignment of the system, the connection rigidity and mechanical damping of the system are reduced, and the support characteristic is piecewise linear, so that the equivalent rigidity and equivalent damping of the base to the support seat at the loosening end are respectively expressed as:
the nonlinear factors in the bearing seat loosening clearance are one of common nonlinear factors, and are particularly remarkable under the conditions of aging and loosening of a rotor system and the like. In this example, the vertical elastic force generated by the bearing loose clearance of the sliding bearing rotor system is defined by the following nonlinearity:
in the formula ky4、Representing the linear and non-linear portions of the spring force, respectively.
The nonlinear dynamic model of the rotor system comprising the determination of the bearing clearance and the lubricating oil viscosity parameter values is as follows:
wherein e is the mass eccentricity of the turntable; omega is the angular speed of the rotor of the sliding bearing rotor system; andthe 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:
Fx=sfx,Fy=sfy
in the formula Fx,FyRepresenting the horizontal and vertical components of the oil film. s is a correction coefficient:omega is the rotational speed of the rotating shaft, R is the bearing radius, L is the bearing length, ciIs the bearing radial clearance, mujμ is the lubricating oil viscosity.
Wherein a dimensionless Reynolds equation is simplified according to the short cylindrical shoe bearing theory:
solving the above formula to obtain the dimensionless oil film pressure as:
in the formula: r represents the journal radius; d represents the journal diameter; l represents the bearing length; θ represents an angular radius;representing the dimensionless thickness of the lubricating film; c. CiIndicating bearing clearance.
Assuming a lubricating oil film action angle range of [ β + π ], angle β is defined as:
based on the boundary conditions: the oil film pressure is integrated along the bearing lubrication action angle to obtain the nonlinear oil film force, and then the oil film force is decomposed along the directions of x and yTo form fxAnd fy:
The above equation is transformed into:
and (3) carrying out numerical integration solution on the nonlinear dynamic differential equation by adopting a 4-5 order variable step length Runge-Kutta method to obtain a nonlinear dynamic response signal sequence. In order to ensure the convergence of the solution and reduce the calculation error, the step length h is pi/512. Taking X as ═ X1,y1,x2,y2,x3,y3]'dimensionless, X' is processed as follows,where c is the bearing radial clearance (i.e. the average thickness of the lubricating film) other parameters used in the calculation were δ 0.0002m and e 0.5 × 10 m-4m;m1=4kg;m2=32.1kg;m3=50kg;k=2.5×107N/m;kb1=7.5×107N/m;R=0.025m;kb2=2.5×109N/m;c1=1050N·s/m;l=0.012m;c2=2100N·s/m;cb1=350N·s/m;cb2=500N·s/m;
the nonlinear oil film force F in the nonlinear modelx,FyTaylor expansion is carried out, and high-order terms are removed, so that the linear approximate oil film force is obtained as follows:
in the formula hxx,hxy,hyx,hyyOil film stiffness, dxx,dxy,dyx,dyyAnd oil film damping is adopted.
In the same way, the nonlinear elastic force generated by the loosening fault of the rotor systemWith Taylor expansion at the equilibrium point and the rounding off of higher order terms, the linear approximation spring force can be obtained as follows:
substituting the result of Taylor expansion of the nonlinear term into the original equation to obtain the linear approximate dynamic model L (c) of the rotor system of the sliding bearingi,μj) The following were used:
And (3) carrying out numerical integration solution on the linear approximation dynamic model by adopting a 4-5 order variable step length Runge-Kutta method to obtain a response signal sequence of the linear approximation dynamic model, wherein the step length h is pi/512 is selected in simulation in order to ensure the convergence of the solution and reduce the calculation error. Taking X as ═ X1,y1,x2,y2,x3,y3]'dimensionless, X' is processed as followsX/c,Where c is the bearing radial clearance (i.e. the average thickness of the lubricating film) other parameters used in the calculation were δ 0.0002m and e 0.5 × 10 m-4m;m1=4kg;m2=32.1kg;m3=50kg;k=2.5×107N/m;kb1=7.5×107N/m;R=0.025m;kb2=2.5×109N/m;c1=1050N·s/m;l=0.012m;c2=2100N·s/m;cb1=350N·s/m;cb2=500N·s/m。
introduction of L2Norm:
the non-linearity degree calculation formula is defined as:
in the formula of omega0A certain fixed rotation speed of the rotor system, and N is a nonlinear dynamic system; l is a linear approximation system obtained by Taylor expansion; n (c)i,μj) And L (c)i,μj) Respectively representing the non-linear system and the linear system at parameter ci,μjAn output response of time; phi is aijIs an estimate of the non-linearity. Value range phiij≥0。
Step 6, taking i not less than 1 and not more than k1,1≤j≤k2Calculating to obtain a non-linearity set according to the ergodic all parameter valuesAnd determining the minimum value in the set as:
step 7, obtaining the minimum value phiminIn the collectionThe parameter value serial number corresponding to the parameter value serial number is determined, and the parameter pair which can be selected by the rotor system is determined.
In steps 1-6 of the invention, each step can be optimized as follows:
optionally, in step 1, the number of parameters to be determined and the corresponding range size may be changed;
optionally, in step 2, it is determined that the size interval of each parameter may be adjusted according to the object and physical conditions, and the method for dispersing each parameter interval may also be selected according to the actual situation, and may be selected to be equidistant, or may also be set to be unequal;
optionally, in step 3, establishing a nonlinear dynamic model of the rotor system including the determined parameter values may be determined according to the object under study;
optionally, in step 4, the linear approximation dynamic model may be obtained by taylor expansion of the nonlinear term, or by optimization or other methods;
optionally, in step 5, performing numerical solution to calculate the nonlinear metric value according to the nonlinear and linear dynamic models is under a certain norm meaning, where the definition of the norm may be determined according to a specific object and a practical application condition;
optionally, in step 6, the determination of the minimum value of the set of non-linearities may select a different retrieval method.
Although the invention has been described above with reference to various embodiments, it should be understood that many changes and modifications may 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, substitute, or add various procedures or components as appropriate. For example, in alternative configurations, the methods may be performed in an order different than that 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, as different aspects and elements of the configurations may be combined in a similar manner. Further, elements therein may be updated as technology evolves, i.e., many elements are examples and do not limit the scope of the disclosure or claims.
Specific details are given in the description to provide a thorough understanding of the exemplary configurations including implementations. However, configurations may be practiced without these specific details, for example, well-known circuits, processes, algorithms, structures, and techniques have been shown without unnecessary detail in order to avoid obscuring the configurations. This description provides example configurations only, and does not limit the scope, applicability, or configuration of the claims. Rather, the foregoing description of the configurations 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 are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.
Claims (8)
1. A method for determining a rotor system bearing parameter oriented to weak nonlinear dynamic behavior comprises the following steps:
step 1, selecting parameters to be determined and ranges thereof;
step 2, determining the size interval of each parameter according to the requirement, and dispersing each parameter interval;
step 3, selecting a parameter value group from each interval, and establishing a rotor system nonlinear dynamic model containing the determined parameter value;
step 4, performing Taylor expansion on the nonlinear terms of the nonlinear model in the step 3 to obtain a linear approximate dynamic model;
step 5, carrying out numerical solution and calculation on nonlinear metric values according to the nonlinear and linear dynamic models;
step 6, calculating according to all the ergodic parameter values to obtain a nonlinear degree set, and selecting a minimum value in the set;
and 7, further determining a bearing value of the rotor system according to the obtained minimum value to evaluate the non-linear degree of the dynamic behavior of the system.
2. The weak nonlinear dynamic behavior oriented plain bearing rotor system parameter determination method according to claim 1, wherein the parameters to be determined in step 1 include bearing clearance, oil film viscosity, and a variable range of each parameter is determined according to actual physical conditions.
3. The weak nonlinear dynamic behavior-oriented plain bearing rotor system parameter determination method according to claim 1, characterized in that in step 2, the variation interval of the parameters is determined according to different characteristics and actually achievable physical conditions of each parameter, and the parameter interval is equidistantly dispersed.
4. The weak nonlinear dynamic behavior oriented sliding bearing rotor system parameter determination method according to claim 1, wherein in step 3, the parameter to be determined in the obtained rotor system nonlinear dynamic model is substituted with a constant value.
5. The weak nonlinear dynamic behavior oriented sliding bearing rotor system parameter determination method according to claim 1, wherein in step 4, the method for obtaining the linear approximation dynamic model of the rotor system is obtained by substituting nonlinear terms of the dynamic model with linear approximation terms obtained by taylor expansion at the equilibrium point position.
6. The weak nonlinear-dynamic-behavior-oriented plain bearing rotor system parameter determination method according to claim 1, wherein in step 5, the nonlinear metric is obtained by quantifying differences in numerically calculated responses of the nonlinear dynamic model and the linear approximation model, respectively, in a norm sense.
7. The weak nonlinear-dynamic-behavior-oriented sliding bearing rotor system parameter determination method according to claim 1, characterized in that in step 6, a calculation result set of the nonlinearity is obtained by traversing all possible values of the parameter to be determined, and then the minimum value in the calculation result set is obtained by searching.
8. The method for determining parameters of a sliding bearing rotor system facing weak nonlinear dynamic behavior according to claim 1, characterized in that in step 7, the strength of the nonlinearity degree of the dynamic behavior of the system is evaluated according to the obtained minimum value, and the corresponding bearing value of the rotor system at the moment is determined.
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CN109710964A (en) * | 2018-11-07 | 2019-05-03 | 西安交通大学 | A kind of milling train radial oil film bearing design method |
CN110688720A (en) * | 2019-10-14 | 2020-01-14 | 佛山科学技术学院 | Method for determining chaotic motion rotating speed range of sliding bearing rotor system |
CN110737866A (en) * | 2019-10-14 | 2020-01-31 | 佛山科学技术学院 | bearing rotor system initial bifurcation point rotating speed identification method based on 3 sigma method |
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