CN114282315A - Method for calculating critical rotating speed of water-lubricated bearing-multi-annular seal-rotor system - Google Patents
Method for calculating critical rotating speed of water-lubricated bearing-multi-annular seal-rotor system Download PDFInfo
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Abstract
The invention provides a method for calculating the critical rotating speed of a water lubricated bearing-multi-annular seal-rotor system, which comprises the steps of calculating the dynamic characteristic coefficient of the water lubricated bearing; calculating the dynamic characteristic coefficient of the annular seal; and calculating the critical rotating speed of the whole rotor system. According to the invention, the influence of the dynamic characteristic of the water lubrication bearing and the dynamic characteristic of the annular seal on the critical rotating speed of the rotor system is considered when the critical rotating speed of the rotor system is calculated, and the dynamic characteristic coefficient of the water lubrication bearing based on the finite difference method and the dynamic characteristic coefficient of the annular seal based on the quasi-steady state method are embedded into the calculation of the critical rotating speed of the rotor system, so that the calculation of the critical rotating speed is more accurate.
Description
Technical Field
The invention relates to a method for calculating the critical rotating speed of a water-lubricated bearing-multi-annular seal-rotor system, and belongs to the technical field of rotating machinery.
Background
The rotors are core components of the rotating machinery, each rotor has a natural frequency, and because the rotors always have certain unbalance, the rotors can excite a certain order of mode to generate a resonance phenomenon when running at a critical rotating speed. In a rotating machine, when the working rotating speed of a rotor system is too close to the natural frequency of the rotor system to break through a safety margin, the vibration of the rotor system is remarkably increased to generate resonance, and even irreparable damage is brought to the mechanical system, so that the critical rotating speed of the rotor system is accurately calculated, and the working rotating speed is controlled in a safe and reasonable range to avoid the resonance.
The early scholars regard the support of the rotor as rigid support to calculate the critical rotating speed of the rotor, and with the research of a dynamic model of the sliding bearing, the later scholars construct a dynamic model of describing the dynamic characteristics of the bearing by four rigidity coefficients and four damping coefficients, so that the calculation of the critical rotating speed is more accurate after the dynamic model of the dynamic characteristics of the bearing is coupled in a rotor calculation model. With the development of rotary machinery, a rotor system becomes more complex, and in a multi-stage rotor system, the critical rotating speed of a rotor is influenced not only by the dynamic characteristics of a water lubrication bearing but also by the dynamic characteristics of a plurality of annular seals, so that a set of water lubrication bearing-multi-annular seal-rotor system critical rotating speed calculation method is established, and the method has important significance for improving the accuracy of the multi-stage rotor system critical rotating speed calculation.
Through searching the existing research results and patents, although some research results about the critical rotating speed of the multi-stage rotor system exist, the dynamic characteristic model of the water lubrication bearing and the dynamic characteristic model of the annular seal cannot be well coupled in the rotor system model, and the calculation method is rough.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: at present, a water lubrication bearing dynamic characteristic model and an annular sealing dynamic characteristic model cannot be well coupled in a multistage rotor system critical rotating speed calculation model, and a calculation method is rough.
In order to solve the technical problem, the technical scheme of the invention is to provide a method for calculating the critical rotating speed of a water-lubricated bearing-multi-annular sealing-rotor system, which is characterized by comprising the following steps of:
step 1, giving initial calculation parameters of a water lubrication bearing based on a rotor system;
step 3, calculating the dynamic characteristic coefficient of the water lubrication bearing;
the annular seal does not serve as a supporting component, and when the rotor balance position is located at the center of the annular seal, the relation between the exciting force and displacement and speed disturbance is linearly expressed as follows:
in the formula, Fx、FyActing forces of the sealing fluid on the rotor in the X-axis direction and the Y-axis direction are respectively; k is a main stiffness coefficient, and K is a cross stiffness coefficient; c is a main damping coefficient, and C is a cross damping coefficient; m is a main mass coefficient; (x, y) is the displacement of the center of the rotor whirl,
is the speed of the central vortex motion of the rotor,
is the rotor whirl central acceleration;
when the eccentricity of the rotor is e and the rotor performs concentric vortex motion around the center of the annular seal at an angular velocity omega, the motion equation of the vortex motion center is as follows:
wherein t is a time variable; when t is 0, the displacement of the vortex center is (e,0), and the corresponding speed and acceleration are (0, e Ω) (-e Ω)20), the functional relationship of the exciting force and the dynamic characteristic coefficient is expressed as:
step 6, calculating the dynamic characteristic coefficient of the annular seal;
step 7, establishing a three-dimensional calculation model of the rotor system;
and 8, calculating the critical rotating speed of the water lubrication bearing-multi-annular sealing-rotor system, which comprises the following steps:
two ends of the water lubricated bearing-multi-annular seal-rotor system are supported by two same cylindrical radial dynamic pressure water lubricated bearings, the impeller, the balance hub and the balance disc are asymmetrically placed between the bearings at the two ends, the dynamic characteristic of the bearing and the dynamic characteristic of the annular seal are embedded into a motion differential equation of the rotor system by a dynamic characteristic coefficient matrix, and then the motion differential equation of the rotor system is established as follows:
in the formula, C is an asymmetric damping matrix of the system, G is a gyro matrix, K is a symmetric part of a system stiffness matrix, and S is the systemThe asymmetric portion of the stiffness matrix, M being the mass matrix, U,
And
the generalized coordinate vector of the mechanical system, the speed of the mechanical system and the acceleration of the mechanical system are respectively shown, and Q is a generalized external force acting on the mechanical system;
and extracting complex eigenvalues and complex eigenvectors from the rotor system motion differential equation by adopting a Damped method, calculating modal frequencies of the rotor system at different rotating speeds, and reading the critical rotating speed from the modal frequencies.
Preferably, in step 1, the initial calculation parameters of the water-lubricated bearing include bearing length, bearing diameter, bearing radius clearance, bearing thrust force, lubricating hydraulic pressure viscosity, rotating speed, preset offset angle and preset eccentricity.
Preferably, in step 2, the static characteristic coefficient of the water-lubricated bearing comprises: liquid film pressure distribution, liquid film bearing capacity, bearing deflection angle and bearing eccentricity ratio, and the method specifically comprises the following steps:
step 201, two ends of a rotor system are supported by two same cylindrical radial dynamic hydraulic lubrication bearings, and the pressure distribution of a liquid film is obtained by solving a two-dimensional Reynolds equation by adopting a finite difference method;
202, integrating the pressure distribution of the liquid film to solve the liquid film bearing capacity in the X-axis direction and the Y-axis direction;
step 203, correcting the bearing deflection angle theta according to the characteristic that the load of the bearing is vertical downward, and setting the bearing deflection angle obtained by the ith calculation as thetaiThen, there are:
in the formula: thetai-1Calculating the bearing deflection angle for the (i-1) th time;
is the bearing capacity of a dimensionless liquid film in the X-axis direction,
is a dimensionless liquid film bearing capacity in the Y-axis direction and has
Step 204, correcting the eccentricity epsilon of the bearing based on the principle that the load of the bearing is balanced with the bearing capacity of the liquid film, and setting the eccentricity epsilon of the bearing obtained by the ith calculationiThen, there are:
in the formula: epsiloni-1Calculating the bearing eccentricity obtained in the (i-1) th time;
in order to have a dimensionless bearing load,
is a dimensionless liquid film bearing capacity and has
Preferably, in step 3, the dynamic characteristic coefficient includes a main stiffness coefficient, a cross stiffness coefficient, a main damping coefficient, and a cross damping coefficient.
Preferably, the step 3 comprises the steps of:
the rigidity and the damping coefficient of the liquid film reflect the change condition of the liquid film force when the shaft neck is disturbed by displacement or speed at a static balance position, various disturbance parameters of a Reynolds equation under an unsteady working condition are derived to obtain a differential equation of each disturbance pressure, and the dynamic characteristic coefficient of the water-lubricated bearing is obtained by solving the disturbance pressure differential equation by combining the Reynolds equation.
Preferably, in step 5, the three-dimensional physical model includes: the sealing device comprises the annular sealing length, the annular sealing outer diameter, the annular sealing inner diameter, the sealing fluid average film thickness, the sealing inlet and outlet pressure difference, the working rotating speed, the sealing fluid density, the sealing fluid dynamic pressure coefficient and the rotor whirling center eccentricity.
Preferably, in step 6, the dynamic characteristic coefficient of the annular seal comprises a main stiffness coefficient, a cross stiffness coefficient, a main damping coefficient and a cross damping coefficient.
Preferably, in step 6, the calculation of the dynamic characteristic coefficient of the annular seal includes the following steps:
based on CFD value, calculating out 10 groups of exciting forces F corresponding to different vortex speed omegax、FyAnd solving the dynamic characteristic coefficient of the annular seal according to the functional relation between the exciting force and the dynamic characteristic coefficient.
Preferably, in step 7, the three-dimensional calculation model of the rotor system includes: the dynamic sealing device comprises a main shaft, an impeller, a balance hub, a balance disc, rotor material density, rotor material elastic modulus, rotor material Poisson's ratio, bearing dynamic characteristic coefficient, annular sealing dynamic characteristic coefficient, rotor rotating speed and a mode extraction method.
Preferably, in step 7, the method for establishing the three-dimensional calculation model of the rotor system is as follows:
and establishing a three-dimensional model of the rotor system in modal calculation software, and setting rotor material density, rotor material elastic modulus, rotor material Poisson's ratio, bearing dynamic characteristic coefficient, annular sealing dynamic characteristic coefficient, rotor rotating speed and a modal extraction method.
The invention researches a method for calculating the critical rotating speed of a water-lubricated bearing-multi-annular seal-rotor system based on the dynamic characteristic coefficient calculation of the water-lubricated bearing and the dynamic characteristic coefficient calculation of the annular seal according to the rotor dynamics principle, and can calculate the critical rotating speed of the rotor system under the comprehensive consideration of the dynamic characteristic of the water-lubricated bearing and the dynamic characteristic of the annular seal. By contrast, the dynamic characteristic of the annular seal has a large influence on the critical rotating speed of the rotor system, and the method established by the invention is adopted to calculate the critical rotating speed, so that the calculation precision of the critical rotating speed is improved, and the occurrence of rotor resonance is effectively avoided.
Drawings
FIG. 1 is a schematic analysis flow chart of a method for calculating the critical rotation speed of a water-lubricated bearing-multiple annular seal-rotor system according to the invention;
FIG. 2 is a schematic diagram of the multi-stage rotor stress in the method for calculating the critical rotation speed of the water-lubricated bearing-multi-annular seal-rotor system according to the invention;
FIG. 3 is a schematic diagram of a hydrodynamic model of a water-lubricated bearing in a method for calculating the critical speed of a water-lubricated bearing-multiple annular seal-rotor system according to the present invention, wherein the hydrodynamic characteristics of the bearing are represented by the coefficient of the hydrodynamic characteristics;
FIG. 4 is a schematic diagram of an annular seal power model in a method for calculating the critical rotation speed of a water-lubricated bearing-multiple annular seal-rotor system according to the present invention, wherein 4 is an annular seal fixed wall surface, and 5 is a rotor;
FIG. 5 is a schematic diagram of a multi-stage rotor system in the method for calculating the critical speed of a water-lubricated bearing-multi-annular seal-rotor system according to the present invention, wherein 1, 2, and 3 are annular seals, and B1 and B2 are water-lubricated bearings;
FIG. 6 is a schematic diagram of a finite element model of a multi-stage rotor in the method for calculating the critical rotation speed of a water-lubricated bearing-multi-annular seal-rotor system according to the invention.
Detailed Description
The sizes, proportions and the like shown in the drawings in the specification are only schematic, are used for matching with the contents described in the specification, are not used for limiting the implementation conditions of the invention, and do not influence the efficacy of the invention. The positional relationships such as "upper", "lower", "inner" and "outer" in the present specification are for convenience of description only and are not intended to limit the implementable scope of the present invention, and variations in the relative relationships thereof are considered to be within the implementable scope of the present invention without substantial changes in the technical contents.
As shown in fig. 1, the method for calculating the critical rotation speed of a water-lubricated bearing-multi-annular seal-rotor system comprises the following steps:
firstly, calculating the dynamic characteristic coefficient of a water lubrication bearing in a rotor system;
secondly, calculating the dynamic characteristic coefficient of the annular seal in the rotor system;
thirdly, establishing a rotor system calculation model based on the dynamic characteristic coefficients in the first step and the second step and inputting parameters;
fourthly, carrying out mesh division on the rotor system to establish a finite element model;
and fifthly, carrying out numerical calculation of the critical rotating speed based on the finite element model in the fourth step.
The following is specifically illustrated by the examples:
step 1: the mass centers of all parts are extracted based on the multi-stage rotor model, a stress analysis diagram of the rotor system is established according to the extracted quality information, and the stress analysis of the three-stage rotor system is carried out according to stress balance and moment balance to obtain the bearing reaction force at the bearing, as shown in figure 1. Initial calculation parameters of the water lubrication bearing are initially set based on a rotor system.
Step 2: and (3) calculating the static characteristic coefficient of the water lubrication bearing by using a finite difference method based on the step 1.
TABLE 1 static coefficient of performance of water lubricated bearings in rotor system
And step 3: and (3) obtaining a differential equation of each disturbance pressure by derivation of each disturbance parameter of the Reynolds equation under the unsteady working condition based on the step 2, and obtaining dynamic characteristic coefficients (a main stiffness coefficient, a cross stiffness coefficient, a main damping coefficient and a cross damping coefficient) of the water-lubricated bearing by solving the disturbance pressure differential equation by combining the Reynolds equation, wherein a dynamic model of the water-lubricated bearing is shown in FIG. 3.
TABLE 2 dynamic coefficient of performance of water lubricated bearings in rotor system
And 4, step 4: based on a quasi-steady state method, the annular seal dynamic characteristic coefficient is calculated through CFD, and an annular seal dynamic characteristic model is shown in figure 4 and comprises the following steps: main stiffness coefficient, cross stiffness coefficient, main damping coefficient, and cross damping coefficient.
TABLE 3 coefficient of dynamic characteristics of annular seal
And 5: establishing a rotor system calculation model, inputting physical parameters of the model, wherein the main shaft, the balance drum and the balance disc are made of 2205 stainless steel, the density of the main shaft, the balance drum and the balance disc is 7.88 multiplied by 103kg/m3, the elastic modulus of the main shaft, the balance drum and the balance disc is 190GPa, and the Poisson ratio of the main shaft, the balance drum and the balance disc is 0.27; the material of the impeller is CD4MnCu, the density is 7.80 multiplied by 103kg/m3, the elastic modulus is 210GPa, and the Poisson ratio is 0.27. The power characteristic coefficients in tables 2 and 3 were coupled to the rotor calculation model, and the two-dimensional map of the calculation model is shown in fig. 5.
Step 6: the rotor system computational model was gridded using swept and tetrahedral grids, respectively, by ANSYS, and the number of grids of the three-dimensional model was determined to be 48192 after grid independence test, as shown in fig. 6. At Bearing support A, B, the water lubricated Bearing was modeled as an elastic damped Bearing with four stiffness and four damping coefficients using Bearing and the stiffness and damping coefficients of the water lubricated Bearing in table 2 were given to the support. The extended modality, gyroscopic effect and Campbell Diagram (Campbell Diagram) are set in the Analysis Setting (Analysis Setting). Because the damping effect of the system cannot be ignored, a Damped method is selected in the modal extraction method, and the Program Controlled solution type is adopted for analysis and calculation. The rotor system is a special mechanical vibration system, the modal frequency of the rotor system is influenced by the rotating speed, so that a Components speed definition mode is selected in the Rotational Velocity, different rotating speeds of the rotor are input, the modal frequency of the rotor system at different rotating speeds is calculated, and the critical rotating speed is read from the modal frequency.
TABLE 4 rotor system Critical speed value calculation
In order to facilitate comparison of the influence of the annular seal on the critical rotating speed of the rotor system, the critical rotating speed of the rotor system is calculated under the two conditions of considering the dynamic characteristic of the annular seal and not considering the dynamic characteristic of the annular seal.
TABLE 5 comparison of critical rotational speeds of rotor systems
As described above, the method for calculating the critical rotating speed of the water-lubricated bearing-multi-annular sealing-rotor system is established, the critical rotating speed of the rotor is calculated under the condition of comprehensively considering the dynamic characteristics of the water-lubricated bearing and the annular sealing, a multi-stage rotor model closer to the actual condition is established, and the calculation accuracy of the critical rotating speed is improved.
Claims (10)
1. A method for calculating the critical rotating speed of a water-lubricated bearing-multi-annular sealing-rotor system is characterized by comprising the following steps of:
step 1, giving initial calculation parameters of a water lubrication bearing based on a rotor system;
step 2, calculating the static characteristic coefficient of the water lubrication bearing;
step 3, calculating the dynamic characteristic coefficient of the water lubrication bearing;
step 4, establishing a dynamic model of the annular seal, which comprises the following steps:
the annular seal does not serve as a supporting component, and when the rotor balance position is located at the center of the annular seal, the relation between the exciting force and displacement and speed disturbance is linearly expressed as follows:
in the formula, Fx、FyActing forces of the sealing fluid on the rotor in the X-axis direction and the Y-axis direction are respectively; k is a main stiffness coefficient, and K is a cross stiffness coefficient; c is a main damping coefficient, and C is a cross damping coefficient; m is a main mass coefficient; (x, y) is the displacement of the center of the rotor whirl,
is the speed of the central vortex motion of the rotor,
is the rotor whirl central acceleration;
when the eccentricity of the rotor is e and the rotor performs concentric vortex motion around the center of the annular seal at an angular velocity omega, the motion equation of the vortex motion center is as follows:
wherein t is a time variable; when t is 0, the displacement of the vortex center is (e,0), and the corresponding speed and acceleration are (0, e Ω) (-e Ω)20), the functional relationship of the exciting force and the dynamic characteristic coefficient is expressed as:
step 5, establishing an annular sealed three-dimensional physical model;
step 6, calculating the dynamic characteristic coefficient of the annular seal;
step 7, establishing a three-dimensional calculation model of the rotor system;
and 8, calculating the critical rotating speed of the water lubrication bearing-multi-annular sealing-rotor system, which comprises the following steps:
two ends of the water lubricated bearing-multi-annular seal-rotor system are supported by two same cylindrical radial dynamic pressure water lubricated bearings, the impeller, the balance hub and the balance disc are asymmetrically placed between the bearings at the two ends, the dynamic characteristic of the bearing and the dynamic characteristic of the annular seal are embedded into a motion differential equation of the rotor system by a dynamic characteristic coefficient matrix, and then the motion differential equation of the rotor system is established as follows:
wherein C is an asymmetric damping matrix of the system, G is a gyro matrix, K is a symmetric part of a stiffness matrix of the system, S is an asymmetric part of the stiffness matrix of the system, M is a mass matrix, U, and,
And
the generalized coordinate vector of the mechanical system, the speed of the mechanical system and the acceleration of the mechanical system are respectively shown, and Q is a generalized external force acting on the mechanical system;
and extracting complex eigenvalues and complex eigenvectors from the rotor system motion differential equation by adopting a Damped method, calculating modal frequencies of the rotor system at different rotating speeds, and reading the critical rotating speed from the modal frequencies.
2. The method for calculating the critical rotation speed of the water-lubricated bearing-multi-ring-shaped sealing-rotor system according to claim 1, wherein in the step 1, the initial calculation parameters of the water-lubricated bearing comprise bearing length, bearing diameter, bearing radius clearance, bearing support reaction force, dynamic pressure viscosity of lubricating fluid, rotation speed, preset deviation angle and preset eccentricity.
3. The method for calculating the critical rotation speed of the water-lubricated bearing-multi-annular seal-rotor system according to claim 1, wherein in the step 2, the static characteristic coefficient of the water-lubricated bearing comprises the following steps: liquid film pressure distribution, liquid film bearing capacity, bearing deflection angle and bearing eccentricity ratio, and the method specifically comprises the following steps:
step 201, two ends of a rotor system are supported by two same cylindrical radial dynamic hydraulic lubrication bearings, and the pressure distribution of a liquid film is obtained by solving a two-dimensional Reynolds equation by adopting a finite difference method;
202, integrating the pressure distribution of the liquid film to solve the liquid film bearing capacity in the X-axis direction and the Y-axis direction;
step 203, correcting the bearing deflection angle theta according to the characteristic that the load of the bearing is vertical downward, and setting the bearing deflection angle obtained by the ith calculation as thetaiThen, there are:
in the formula: thetai-1Calculating the bearing deflection angle for the (i-1) th time;
is the bearing capacity of a dimensionless liquid film in the X-axis direction,
is a dimensionless liquid film bearing capacity in the Y-axis direction and has
Step 204, correcting the eccentricity epsilon of the bearing based on the principle that the load of the bearing is balanced with the bearing capacity of the liquid film, and setting the eccentricity epsilon of the bearing obtained by the ith calculationiThen, there are:
in the formula: epsiloni-1Calculating the bearing eccentricity obtained in the (i-1) th time;
in order to have a dimensionless bearing load,
is a dimensionless liquid film bearing capacity and has
4. The method for calculating the critical rotation speed of the water-lubricated bearing-multi-annular sealing-rotor system according to claim 1, wherein in the step 3, the dynamic characteristic coefficients comprise a main stiffness coefficient, a cross stiffness coefficient, a main damping coefficient and a cross damping coefficient.
5. A method for calculating a critical rotation speed of a water lubricated bearing-multiple annular seal-rotor system as claimed in claim 3, wherein said step 3 comprises the steps of:
the rigidity and the damping coefficient of the liquid film reflect the change condition of the liquid film force when the shaft neck is disturbed by displacement or speed at a static balance position, various disturbance parameters of a Reynolds equation under an unsteady working condition are derived to obtain a differential equation of each disturbance pressure, and the dynamic characteristic coefficient of the water-lubricated bearing is obtained by solving the disturbance pressure differential equation by combining the Reynolds equation.
6. The method for calculating the critical rotation speed of the water-lubricated bearing-multi-annular seal-rotor system according to claim 1, wherein the three-dimensional physical model in the step 5 comprises: the sealing device comprises the annular sealing length, the annular sealing outer diameter, the annular sealing inner diameter, the sealing fluid average film thickness, the sealing inlet and outlet pressure difference, the working rotating speed, the sealing fluid density, the sealing fluid dynamic pressure coefficient and the rotor whirling center eccentricity.
7. The method for calculating the critical rotation speed of the water-lubricated bearing-multi-ring seal-rotor system according to claim 1, wherein in the step 6, the dynamic characteristic coefficients of the ring seal comprise a main stiffness coefficient, a cross stiffness coefficient, a main damping coefficient and a cross damping coefficient.
8. The method for calculating the critical rotation speed of the water-lubricated bearing-multi-ring seal-rotor system according to claim 6, wherein in the step 6, the dynamic characteristic coefficient of the ring seal is calculated by the following steps:
based on CFD value, calculating out 10 groups of exciting forces F corresponding to different vortex speed omegax、FyAnd solving the dynamic characteristic coefficient of the annular seal according to the functional relation between the exciting force and the dynamic characteristic coefficient.
9. The method for calculating the critical rotation speed of the water-lubricated bearing-multi-annular sealing-rotor system according to claim 1, wherein in the step 7, the three-dimensional calculation model of the rotor system comprises the following steps: the dynamic sealing device comprises a main shaft, an impeller, a balance hub, a balance disc, rotor material density, rotor material elastic modulus, rotor material Poisson's ratio, bearing dynamic characteristic coefficient, annular sealing dynamic characteristic coefficient, rotor rotating speed and a mode extraction method.
10. The method for calculating the critical rotation speed of the water-lubricated bearing-multi-annular sealing-rotor system according to claim 8, wherein in the step 7, the three-dimensional calculation model of the rotor system is established by the following method:
and establishing a three-dimensional model of the rotor system in modal calculation software, and setting rotor material density, rotor material elastic modulus, rotor material Poisson's ratio, bearing dynamic characteristic coefficient, annular sealing dynamic characteristic coefficient, rotor rotating speed and a modal extraction method.
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| CN109408946A (en) * | 2018-10-19 | 2019-03-01 | 西安交通大学 | Consider the cryogenic liquid expansion machine rotor critical speed prediction technique that sealing force influences |
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| CN109408946A (en) * | 2018-10-19 | 2019-03-01 | 西安交通大学 | Consider the cryogenic liquid expansion machine rotor critical speed prediction technique that sealing force influences |
| 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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