CN114091314B - Vibration prediction method of rotor system model based on magneto-rheological damper - Google Patents
Vibration prediction method of rotor system model based on magneto-rheological damper Download PDFInfo
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- CN114091314B CN114091314B CN202210076860.8A CN202210076860A CN114091314B CN 114091314 B CN114091314 B CN 114091314B CN 202210076860 A CN202210076860 A CN 202210076860A CN 114091314 B CN114091314 B CN 114091314B
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Abstract
The invention provides a vibration prediction method of a rotor system model based on a magneto-rheological damper, which relates to the technical field of vibration prediction methods of rotor system models and comprises the following steps: establishing a magnetorheological damper oil film force model to obtain a magnetorheological damper oil film force; establishing a rub-impact fault dynamic model based on the magnetorheological damper to obtain rub-impact force; establishing a bearing support model to obtain a bearing force; establishing a disc rotor eccentric model to obtain an eccentric force; establishing a rotor system dynamic model based on the magneto-rheological damper according to the oil film force, the friction force, the bearing force and the eccentric force of the magneto-rheological damper; and solving a rotor system dynamic model based on the magneto-rheological damper by utilizing a Newmark-beta method to obtain system dynamic response. The consideration factors are more comprehensive, the established rotor system dynamic model based on the magnetorheological damper is more in line with the working conditions, and the obtained system dynamic response is more accurate, reasonable and scientific.
Description
Technical Field
The invention relates to the technical field of vibration prediction methods of rotor system models, in particular to a vibration prediction method of a rotor system model based on a magneto-rheological damper.
Background
With the improvement of the performance of the aero-engine, the aero-engine has higher working temperature and worse environment, and due to the manufacturing, process and material, and later use, maintenance and management level limitations of the engine, the aero-engine is easy to generate abnormal vibration in the working process, and various faults are induced. In flight failure, engine failure is a high incidence of failure, often resulting in catastrophic failure. In the routine maintenance of an aircraft, the maintenance and replacement cost of an engine is very huge, and accounts for more than 60% of the whole maintenance cost. Therefore, in order to enable the engine to operate safely and efficiently and save maintenance cost, the operating state of the engine under various working conditions must be known, the vibration change rule of the engine is mastered, and the rotor system is used as a core component of the aircraft engine, so that the vibration performance of the rotor system has a great influence on the safety and reliability of the aircraft engine. Although the structural design and service life of the existing engine rotating parts are greatly improved, the engine rotating parts still have serious faults due to more uncontrollable factors when the engine rotating parts operate in a severe working environment with high speed and severe vibration for a long time under the action of complex alternating load. Because the friction phenomenon between the rotor and the stator is caused by large-deflection deformation of a rotor system, the vibration of the rotor system can be effectively reduced by arranging a damper between a bearing and a supporting structure, the friction fault is prevented, the magnetorheological damper can control the magnetorheological fluid in the magnetorheological damper in an external magnetic field mode, so that the active control of the rotor power is realized, the magnitude of the magnetic field strength is controlled by external current, and the optimal current strength is obtained by applying different external current and observing the dynamic response condition of the system under different current strengths.
Disclosure of Invention
The invention aims to at least solve one of technical problems in the prior art or the related art, and discloses a vibration prediction method of a rotor system model based on a magneto-rheological damper.
The invention is realized by the following scheme: a vibration prediction method of a rotor system model based on a magnetorheological damper comprises the following steps:
s1, establishing a magneto-rheological damper oil film force model, and obtaining magneto-rheological damper oil film force according to the magneto-rheological damper oil film force model;
s2, establishing a rub-impact fault dynamic model based on the magnetorheological damper, and obtaining rub-impact force according to the rub-impact fault dynamic model based on the magnetorheological damper;
s3, establishing a bearing support model, and obtaining a bearing force according to the bearing support model;
s4, establishing a disc rotor eccentric model, and obtaining an eccentric force according to the disc rotor eccentric model;
s5, establishing a rotor system dynamic model based on the magneto-rheological damper according to the oil film force, the rubbing force, the bearing force and the eccentric force of the magneto-rheological damper;
and S6, solving the rotor system dynamic model based on the magneto-rheological damper by using a Newmark-beta method to obtain the system dynamic response.
According to the vibration prediction method of the rotor system model based on the magnetorheological damper disclosed by the invention, preferably, the oil film force model of the magnetorheological damper in the step S1 is as follows:
wherein the content of the first and second substances,
is the radial oil film force of the magneto-rheological damper>
Is the radial oil film force of the magneto-rheological damper, L is the length of the damper in the Z direction, and>
is the oil film pressure of the magneto-rheological damper>
Is the oil film azimuth angle relative to the minimum oil film position,
the radius of the rotor is obtained according to the expression of the oil film force model of the magneto-rheological damper, and the expression of the component force of the oil film force of the magneto-rheological damper in the x direction and the component force of the oil film force of the magneto-rheological damper in the y direction is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is the component force of the oil film force of the magneto-rheological damper in the x direction>
Is the component force of the oil film force of the magneto-rheological damper in the y direction>
For the displacement of the center of the inner ring of the magnetorheological damper in the x direction, the magnet is arranged on the inner ring of the magnetorheological damper>
The displacement of the oil film force of the magnetorheological damper in the y direction is realized.
According to the vibration prediction method of the rotor system model based on the magnetorheological damper disclosed by the invention, preferably, the rub-impact fault dynamic model based on the magnetorheological damper in the step S2 is as follows:
wherein the content of the first and second substances,
is a normal contact force between rotor and stator>
Is a tangential friction between the rotor and the stator>
Is an initial gap between rotor and stator, is>
Is a radial displacement of the center of the disk, is adjusted>
For radial contact stiffness, <' >>
The component force expression of the rub-impact force in the x direction and the y direction obtained according to the rub-impact fault dynamic model of the magneto-rheological damper is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is a component force of the rubbing force in the x direction>
For a component of the rubbing force in the y direction>
Is the initial clearance between the rotor and the stator, device for combining or screening>
Is a radial displacement of the center of the disk, is adjusted>
For radial contact stiffness, <' >>
For a rotor/stator friction coefficient>
And &>
Displacement of the disc center in the x and y directions, respectively.
According to the vibration prediction method of the rotor system model based on the magnetorheological damper, preferably, the bearing support model is established in the step S3, and the expression of the bearing force obtained according to the bearing support model is as follows:
wherein, the first and the second end of the pipe are connected with each other,
for a component of the bearing force in the x direction>
For a component of the bearing force in the y direction>
Is the first->
Normal contact deformation of the balls and the roller path>
Is the first->
The angular position of the individual ball at the instant t>
Hertz contact stiffness.
According to the vibration prediction method based on the rotor system model of the magnetorheological damper, disclosed by the invention, preferably,
as a function of Heaviside, can be expressed as:
wherein the content of the first and second substances,
is an initial gap between rotor and stator, is>
Is the radial displacement of the center of the disc.
According to the vibration prediction method of the rotor system model based on the magnetorheological damper disclosed by the invention, preferably, the expression of the eccentric force obtained according to the disc rotor eccentric model in the step S4 is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is a component of the eccentric force in the x direction>
Is a component of the eccentric force in the y direction>
Is the eccentric amount of the disc, is used for selecting the position of the disc>
For the quality of the disc rotor>
For the rotational speed of the disc rotor, in conjunction with a motor>
Is an initial phase angle.
According to the vibration prediction method of the rotor system model based on the magnetorheological damper disclosed by the invention, preferably, the rotor system dynamic model based on the magnetorheological damper in the step S5 is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is broadly shifted and/or is based on>
Is a generalized speed->
In the form of generalized acceleration>
Is a mass matrix of the rotor shaft, is based on the rotor shaft>
Gyro force matrix for a rotor shaft>
Is a stiffness matrix of the rotor shaft>
A generalized force matrix for the rotor shaft;
wherein the content of the first and second substances,
for a component of the bearing force in the x direction>
Is the component force of the bearing force in the y direction; />
Is the component force of the oil film force of the magneto-rheological damper in the x direction>
The component force of the oil film force of the magneto-rheological damper in the y direction is shown; />
The component force of the eccentric force in the x direction; />
Is a component of the rubbing force in the x direction>
Is the component force of the rubbing force in the y direction.
Due to the adoption of the technical scheme, the invention has the following advantages:
according to the invention, the oil film force and the friction force of the magnetorheological damper are taken as consideration factors to be added into the rotor system dynamic model based on the magnetorheological damper, the consideration factors are more comprehensive, the established rotor system dynamic model based on the magnetorheological damper is more consistent with the working condition, and the obtained system dynamic response is more accurate, more reasonable and more scientific.
Drawings
FIG. 1 shows a schematic block diagram of the steps of a vibration prediction method for a model of a magnetorheological damper based rotor system according to an embodiment of the invention.
FIG. 2 shows a schematic representation of a magnetorheological damper coordinate system in accordance with an embodiment of the invention.
Fig. 3 shows a schematic view of a magnetorheological fluid flow curve with bilinear properties according to an embodiment of the invention.
FIG. 4 illustrates an illustration of the state characteristics of magnetorheological fluid in a damper gap according to an embodiment of the invention.
Fig. 5 shows an intention of magnetorheological fluid to be squeezed out of a damper from a surrounding space according to an embodiment of the invention.
Fig. 6 shows a schematic view of a magnetorheological fluid being sucked into a damper from a surrounding space according to an embodiment of the invention.
FIG. 7 shows a rotor-stator rub-impact model schematic according to an embodiment of the invention.
Fig. 8 shows a schematic view of a rolling bearing model according to an embodiment of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and thus the present invention is not limited to the specific embodiments disclosed below.
As shown in FIG. 1, the invention provides a vibration prediction method of a rotor system model based on a magnetorheological damper, which comprises the following steps:
step S1, establishing a magneto-rheological damper oil film force model, and obtaining magneto-rheological damper oil film force according to the magneto-rheological damper oil film force model;
s2, establishing a rub-impact fault dynamic model based on the magnetorheological damper, and obtaining rub-impact force according to the rub-impact fault dynamic model based on the magnetorheological damper;
s3, establishing a bearing support model, and obtaining a bearing force according to the bearing support model;
s4, establishing a disc rotor eccentric model, and obtaining eccentric force according to the disc rotor eccentric model;
s5, establishing a rotor system dynamic model based on the magneto-rheological damper according to the oil film force, the friction force, the bearing force and the eccentric force of the magneto-rheological damper;
and S6, solving a rotor system dynamic model based on the magneto-rheological damper by using a Newmark-beta method to obtain system dynamic response.
According to the above embodiment, preferably, the oil film force model of the magnetorheological damper in step S1 is:
wherein the content of the first and second substances,
is the radial oil film force of the magneto-rheological damper>
Is the radial oil film force of the magneto-rheological damper, L is the length of the damper in the Z direction, and is based on the length of the damper in the Z direction>
Is the oil film pressure of the magneto-rheological damper>
Is the azimuthal angle of the oil film relative to the minimum oil film position,
obtaining the expressions of the component force of the magnetorheological damper oil film force in the x direction and the component force of the magnetorheological damper oil film force in the y direction according to the expression of the magnetorheological damper oil film force model as the radius of the rotor:
wherein the content of the first and second substances,
is the component force of the oil film force of the magneto-rheological damper in the x direction>
Is the component force of the oil film force of the magnetorheological damper in the y direction>
For a displacement of the center of the inner ring of the magnetorheological damper in the x direction>
The displacement of the oil film force of the magnetorheological damper in the y direction is realized.
As shown in FIG. 2, where inner ring represents the inner ring and outer ring represents the outer ring, in this embodiment, a coordinate system
For defining the position and velocity components of the fluid flow, the expression can be approximated as:
wherein the content of the first and second substances,
is the eccentric amount of the inner ring and is used for selecting the position>
Is azimuth angle of the oil film relative to the minimum oil film position>
The oil film thickness at the corresponding azimuth angle.
In the process of establishing the magnetorheological damper oil film force model, the following assumptions are based:
(1) Assuming the fluid is incompressible, the effect of the inertia of the fluid is ignored;
(2) Neglecting the volume force influence of the magnetorheological fluid;
(3) The magnetorheological fluid is attached to the contact surface of the squirrel cage and the shell, and does not slide relative to the squirrel cage and the shell;
(4) The oil film is very thin, and the oil film pressure of the magnetorheological fluid along the thickness direction of the oil film is unchanged, namely:
(5) The magnetorheological fluid in the gap of the magnetorheological damper is assumed to flow in a laminar manner;
(6) The magnetorheological damper meets the end bearing condition.
Based on the above assumptions, the equilibrium equation and continuity equation of the magnetorheological fluid can be expressed as:
wherein the content of the first and second substances,
indicates oil film pressure->
And &>
Respectively, represents the magnetorheological fluid along->
And &>
Directional flow velocity.
As shown in fig. 3, the magneto-rheological fluid bilinear constitutive equation can be expressed as:
in the formula (I), the compound is shown in the specification,
,/>
and->
Respectively shear stress between adjacent magnetorheological fluid layers, yield stress of the magnetorheological fluid and shear stress of the magnetorheological fluid at the boundary of the hard core (namely a yield area); eta is the viscosity of the magnetorheological fluid when no current is applied; define >>
Is a viscosity ratio>
Indicates the viscosity of the magnetorheological fluid at the hard nucleus (namely the yielding area)>
Is magnetorheological fluid along>
The velocity of the flow in the direction.
The relation between the yield stress of the magnetorheological fluid and the shear stress of the magnetorheological fluid at the boundary of the hard core (namely the yield zone) obtained by the equation (5) and the equation (6) is as follows:
wherein, the first and the second end of the pipe are connected with each other,
defining ^ the magnetorheological fluid shear stress at the boundary of the hard nucleus (namely the yield zone)>
In order to obtain a viscosity ratio,
represents the viscosity of the magnetorheological fluid at the hard nucleus (namely the yield area), eta is the viscosity of the magnetorheological fluid when no current is applied, and the temperature of the magnetorheological fluid is greater than or equal to the preset temperature>
Is the yield stress of the magnetorheological fluid.
As shown in FIG. 4, under the action of a magnetic field, the magnetorheological fluid behaves as a non-Newtonian fluid under the action of the magnetic field
The cross-section includes a yielding region and an unyielding region. In the figure, inner ring is an Inner ring, outer ring is an Outer ring, core is a hard Core (i.e. yielding zone), S1 is an unyielding zone, and four unyielding zones S1' and/or>
Is a damper in>
Length in the direction. />
Is hard nucleus (i.e. yield zone) in->
The axial coordinate position of the starting point which is full of the whole oil film gap in the direction. />
Is the distance between the surface of the hard nucleus (i.e. the yield zone) and the outer ring of the oil film, is/are>
The oil film thickness at the corresponding azimuth angle. Because the inner and outer rings of the damper are restrained from axial movement and the oil film gap is small compared to the damper radius, the velocity of the magnetorheological fluid in the damper is relative to the gap intermediate gaugeSurface symmetry, then>
And &>
Can be expressed as:
because the outer ring of the magneto-rheological damper is fixed, and the inner ring is limited to only do radial whirling motion, the boundary condition of the flowing speed of the magneto-rheological fluid in the damper gap can be expressed as follows:
in expressions (10), (11), (12) and (13),
is the magnetorheological fluid along->
The velocity of the flow in the direction.
For magnetorheological fluid yield region: (
And &>
) Substituting constitutive relation (5) or (7) into equation (3), and integrating the two sides of the obtained equation along the radial direction to obtain:
in the formula (I), the compound is shown in the specification,
is an integration constant. Continue integrating the two sides of this equation along the radial direction to obtain:
in the formula (I), the compound is shown in the specification,
is an integration constant.
The integration constant can be obtained by substituting the boundary condition equations (10) and (11) into the equation (15)
，/>
The expression is as follows:
substituting the expression (16) into the expression (15), the expression of the axial speed of the magnetorheological fluid in the yielding zone is obtained as follows:
for the same reason, for the unyielding region: (
) Substituting the constitutive relation (6) into equation (3), performing twice integration on two sides of the obtained equation along the radial direction, and applying the boundary condition expression (11) and the expression (12) to obtain an expression of the axial speed of the unyielding area: />
Integrating the two sides of equation (4) along the radial direction to obtain:
applying conditional equation (9), this equation can be expressed as:
substituting expression (17) and expression (18) into expression (20) and deriving:
wherein the radial distance between the surface of the hard core (namely the yield zone) and the outer ring of the oil film
Obtainable from constitutive relation (6): />
The expression (18) is substituted into the expression (22) and the expression (23), respectively, and hardRadial distance between surface of core (i.e. yield zone) and outer ring of oil film
The expression of (c) is:
wherein the content of the first and second substances,
is the pressure gradient of the oil film along the axial direction.
In the expressions (14) to (25),
indicates oil film pressure, <' > based on>
Is the magnetorheological fluid along->
The flowing speed in the direction eta is the viscosity of the magnetorheological fluid when no current is applied, and the temperature is greater than or equal to>
Is the distance between the surface of the hard nucleus (i.e. the yield zone) and the outer ring of the oil film, is/are>
Is->
Is greater than or equal to>
Indicating the flow of the magnetorheological fluid in the Y directionSpeed,. Or>
For oil film thickness at the corresponding azimuth angle>
For the rate of change of the oil film thickness in the corresponding azimuth angle>
Is the shear stress of the magnetorheological fluid at the boundary of the hard core (namely the yield zone),
is a viscosity ratio>
Indicating the viscosity of the magnetorheological fluid at the hard core (i.e., the yield region).
As shown in figures 5 and 6 of the drawings,
is the distance between the surface of the hard nucleus (i.e. the yield zone) and the outer ring of the oil film, is/are>
Is the oil film thickness at the corresponding azimuth angle>
For the rate of change of the oil film thickness at the corresponding azimuth angle, <' >>
Is the magnetorheological fluid along->
The velocity of the flow in the direction. In position->
At a speed gradient->
Indicating that the magnetorheological fluid is pressed out of the damper (>
) Which is at->
Speed in axial direction greater than 0 (& ltwbr/& gt)>
) (ii) a Speed gradient->
Indicating that the magnetorheological fluid is sucked into the damper (pick-up or pick-up) from the surrounding space>
) Which is at->
Speed in axial direction less than 0 (& lt & gt)>
) In order to obtain an axial speed at the boundary of the hard nucleus (i.e. the yield zone)>
And respectively substituting an expression (17) of the axial speed of the magnetorheological fluid in the yield region into an equation (5) and an equation (7), and deriving:
substituting expressions (26) and (27) into expression (21) may result in:
continuing to integrate expressions (28) and (29) in the axial direction:
in the formula (I), the compound is shown in the specification,
and &>
Is an integration constant whose value can be determined from an axial position +>
The oil film pressure boundary condition is determined, namely:
when in use
When the hard nucleus (namely the yielding area) is contacted with the inner ring and the outer ring of the damper, the hard nucleus is in contact with the inner ring and the outer ring of the damper, and the hard nucleus is in contact with the inner ring and the outer ring of the damper at the moment>
=0. Substituting the condition into expression (24) and expression (25), respectively, may result in: />
The Reynolds equation can be obtained by arranging the expression (30) and the expression (31):
(1) When the temperature is higher than the set temperature
When the temperature of the water is higher than the set temperature,
(2) When in use
When the temperature of the water is higher than the set temperature,
expressions (35) and (36) express the pressure gradient of the oil film in the axial direction
In relation to an axial coordinate->
I.e.:
and then, the pressure gradient value of the oil film along the axial direction can be obtained by solving a one-element cubic equation. By integrating the expression (37) in the axial direction and using the following boundary conditions:
the pressure distribution of the oil film along the axial direction can be obtained:
wherein, the first and the second end of the pipe are connected with each other,
is atmospheric pressure, for expression (39), its coordinates @>
This is true when the following conditions are satisfied:
when in
The hardmac (i.e., the yield zone) is in contact with the damper inner and outer rings. In this region, the magnetorheological fluid exhibits a viscosity of ≥ er>
The oil film pressure distribution of the Newtonian liquid can be obtained by a classical Reynolds equation:
according to the boundary conditions:
the following can be obtained:
pair the two sides of expression (43)
Obtaining a pressure gradient expression of the oil film along the axial direction by differentiating:
then it can be obtained
The expression of (a) is:
when in
When the oil film pressure distribution is expressed by the formula (41), the boundary conditions are:
expression (41) becomes:
in view of the above, it can be seen that,
(1) When in use
The method comprises the following steps:
① 
magnetorheological damper oil film pressure>
Is formula (43);
② 
and oil film pressure of magnetorheological damper>
Is the expression (39).
(2) When in use
Oil film pressure of magnetorheological damper>
Is represented by formula (47).
Obtaining the oil film pressure of the magneto-rheological damper
Then, by pressing on the oil film->
Is axially based>
And circumferential direction->
And integrating to obtain the expression of the tangential and radial oil film forces of the magnetorheological damper as follows:
the inner ring of the magneto-rheological damper is assumed to be centered
And &>
A displacement in the direction of ^ is respectively ^>
And &>
And then the oil film force edge of the magneto-rheological damper is->
And &>
The directional component can be expressed as:
in the expressions (26) to (51),
indicates oil film pressure, <' > based on>
Is magnetorheological fluid along>
The flowing speed in the direction eta is the viscosity of the magnetorheological fluid when no current is applied, and the temperature is greater than or equal to>
Is a hard core (namely a yield region) surface and an oil filmThe distance between the outer rings->
For the rate of change of the oil film thickness in the corresponding azimuth angle>
Is->
In a particular value of (a), in a predetermined range of values>
Representing the flow speed of the magnetorheological fluid in the Y direction>
For oil film thickness at the corresponding azimuth angle>
Is the shear stress of the magnetorheological fluid at the boundary of the hard core (namely the yield zone),
is a viscosity ratio>
Indicates the viscosity of the magnetorheological fluid at the sclerotic nucleus (i.e., the yield region)>
Is the yield stress of the magnetorheological fluid,
is a pressure gradient of the oil film in the axial direction>
Is when>
The pressure of the oil film>
Is at atmospheric pressure and is at or near the blood pressure>
Is the rotor radius.
According to the above embodiment, preferably, the magnetorheological damper rub-impact fault dynamics model in step S2 is:
wherein the content of the first and second substances,
is a normal contact force between rotor and stator>
Is a tangential friction between rotor and stator, in the absence of a pressure sensor>
Is the initial clearance between the rotor and the stator, device for combining or screening>
Is a radial displacement of the center of the disk, is adjusted>
For radial contact stiffness>
For the friction coefficient of a rotor and a stator, the component force expressions of the rub-impact force in the x direction and the y direction obtained according to the rub-impact fault dynamic model of the magneto-rheological damper are as follows:
wherein, the first and the second end of the pipe are connected with each other,
is a component force of the rubbing force in the x direction>
For a component of the rubbing force in the y direction>
Is an initial gap between rotor and stator, is>
Is a radial displacement of the center of the disk, is adjusted>
For radial contact stiffness>
In order to rotate the coefficient of friction of the stator,
and &>
A displacement of the disc center in the x and y direction, respectively>
Is a Heaviside function and can be expressed as:
in the embodiment, as shown in fig. 7, stator represents a Stator, disc at initial state represents a Disc in an initial state, and Disc at contact state represents a Disc in a contact state, and the rub-impact force is added to a general force term at a node of the Disc of the finite element model of the rotor system through model analysis, so that a rub-impact rotor system dynamic model with the magnetorheological damper can be obtained. Wherein
Is the initial clearance between the rotor and the stator, device for combining or screening>
Is a radial displacement of the center of the disk, which can be expressed as->
Wherein is present>
And &>
Displacement of the disc center in the x and y directions, respectively. />
And &>
Normal contact force and tangential friction force between rotors and stators, respectively. When +>
In the meantime, a rubbing fault occurs, and assuming that the friction conforms to the coulomb friction law, the rubbing force can be expressed as:
in the formula (I), the compound is shown in the specification,
is a normal contact force between rotor and stator>
Is a tangential friction between the rotor and the stator>
For radial contact stiffness>
For a rotor friction coefficient, based on the number of revolutions per minute>
Is an initial gap between rotor and stator, is>
Is a radial displacement of the center of the disk, is adjusted>
Is a Heaviside function and can be expressed as:
then the rubbing force is
And &>
The force components in the direction are respectively->
And/or>
Expressed as:
according to the above embodiment, preferably, the step S3 of establishing the bearing support model is to establish the bearing support model based on the nonlinear Hertz contact theory, and the bearing force expression obtained according to the bearing support model is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is a component of the bearing force in the x direction>
For a component of the bearing force in the y direction>
Is the first->
Normal contact deformation of the balls and the roller path>
Is the number of the balls>
Is the first->
Each ball is at>
The angular position of the moment of time>
Based on the Hertz contact stiffness>
As a function of Heaviside, can be expressed as:
as shown in fig. 8, the
th ball is denoted as ^ h->
And balls, inner Ring of the bearing, outer Ring of the bearing, shaft of the Shaft, cage of the Cage and Ball of the Ball, wherein the Outer Ring of the bearing is connected with the elastic support of the squirrel Cage, and the Inner Ring of the bearing is connected with the rotating Shaft and rotates along with the rotating Shaft. It is assumed that the balls are arranged at equal intervals on the bearing cage and perform pure rolling. />
Is the inner raceway radius>
Is the radius of the outer raceway->
Is the first->
Each ball is at>
The angular position of the moment of time, namely:
in the formula (I), the compound is shown in the specification,
is the ball center angular velocity->
Is the number of balls. Is/are>
Normal contact deformation of balls and roller path>
Can be expressed as: />
Wherein the content of the first and second substances,
is the bearing play.
Based on the nonlinear Hertz contact theory, the first
The normal contact force of each ball with the raceway can be expressed as:
in the formula (I), the compound is shown in the specification,
rigidity to Hertz contact>
Is a Heaviside function and has the expression as follows:
then the bearing force is
And &>
The force component in the direction can be expressed as:
according to the above embodiment, preferably, the expression of the eccentric force obtained from the disk rotor eccentric model in step S4 is:
in the expressions (59) to (63),
is the distance of the ball from the center in the x direction>
Is the distance of the ball from the center in the y direction>
Is the first->
In combination with a ball>
Angular position of the instant, <' >>
Based on the Hertz contact stiffness>
For a component of the bearing force in the x direction>
For a component of the bearing force in the y direction>
Is the first->
Normal contact deformation of the balls and the roller path>
Is a component of the eccentric force in the x direction>
For a component of the eccentric force in the y direction>
Is the eccentric amount of the disc, is used for selecting the position of the disc>
Is the quality of the disc rotor>
For the rotational speed of the disc rotor, in conjunction with a motor>
Is an initial phase angle, which can be expressed as:
wherein the content of the first and second substances,
is an initial gap between rotor and stator, is>
Is the radial displacement of the center of the disc.
According to the above embodiment, preferably, the rotor system dynamic model based on the magnetorheological damper in step S5 is:
wherein the content of the first and second substances,
is broadly shifted and/or is based on>
Is a generalized speed->
Is a generalized acceleration, is>
Is a mass matrix of the rotor shaft, is based on the rotor shaft>
A gyro-force matrix being a rotor shaft>
Is a stiffness matrix of the rotor shaft>
Is a generalized force matrix of the rotor shaft,
wherein, the first and the second end of the pipe are connected with each other,
for a component of the bearing force in the x direction>
Is the component force of the bearing force in the y direction; />
Is the component force of the oil film force of the magneto-rheological damper in the x direction>
The component force of the oil film force of the magneto-rheological damper in the y direction is shown; />
The component force of the eccentric force in the x direction; />
Is a component of the rubbing force in the x direction>
Is the component force of the rubbing force in the y direction.
In this embodiment, the
Is the first->
Quality matrix of the section unit axis->
Is the first->
Gyro force matrix for a segment unit shaft>
Is the first->
Stiffness matrix of the section unit axis->
Is the first->
And (3) obtaining a rotor dynamics equation by using the generalized force matrix of the section unit shaft:
wherein, the first and the second end of the pipe are connected with each other,
in the formula (I), the compound is shown in the specification,
the specific form of each element in the matrix is as follows:
combining the dynamic equations of all the unit shaft sections, wherein the dynamic equation of the whole section of the shaft system is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is broadly shifted and/or is based on>
Is a generalized speed->
Is a generalized acceleration, is>
Is a mass matrix of the rotor shaft, is based on the rotor shaft>
A gyro-force matrix being a rotor shaft>
Is a stiffness matrix of the rotor shaft>
Is a generalized force matrix of the rotor shaft>
Is the moment of inertia of the rotor and,
is the density of the substance(s), A is the cross-sectional area->
Is the length of the beam unit>
Is a shear factor->
Is equivalent stiffness, <' > based on the measured signal strength>
And/or>
Are all generalized forces.
By utilizing a magnetorheological damper oil film force model, a rub-impact fault dynamic model, a bearing supporting model and a disc rotor eccentric model, a rotor dynamic model considering the magnetorheological damper oil film force, the rub-impact force, the bearing supporting force and the eccentric force is established based on a Newton's second law,
wherein the content of the first and second substances,
is broadly shifted and/or is based on>
Is a generalized speed->
Is a generalized acceleration, is>
Is a mass matrix of the rotor shaft, is based on the rotor shaft>
A gyro-force matrix being a rotor shaft>
Is a stiffness matrix of the rotor shaft>
Is a generalized force matrix of the rotor shaft>
For a component of the bearing force in the x direction>
Is the component force of the bearing force in the y direction; />
Is the component force of the oil film force of the magneto-rheological damper in the x direction>
Is made of magnetismComponent force of rheological damper oil film force in y direction; />
The component force of the eccentric force in the x direction; />
Is a component of the rubbing force in the x direction>
The component force of the rubbing force in the y direction,
wherein the content of the first and second substances,
the expression is as follows:
and then solving a kinetic equation by utilizing a Newmark-beta method to obtain a system kinetic response. Reasonable and scientific power parameters can be searched according to response conditions, and due to the fact that the consideration factors are more comprehensive, the established rotor system dynamic model based on the magneto-rheological damper is more consistent with working conditions, and the obtained system dynamic response is more accurate, reasonable and scientific.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A vibration prediction method of a rotor system model based on a magnetorheological damper is characterized by comprising the following steps:
s1, establishing a magneto-rheological damper oil film force model, and obtaining magneto-rheological damper oil film force according to the magneto-rheological damper oil film force model;
s2, establishing a rub-impact fault dynamic model based on the magnetorheological damper, and obtaining rub-impact force according to the rub-impact fault dynamic model based on the magnetorheological damper;
s3, establishing a bearing support model, and obtaining a bearing force according to the bearing support model;
s4, establishing a disc rotor eccentric model, and obtaining an eccentric force according to the disc rotor eccentric model;
s5, establishing a rotor system dynamic model based on the magneto-rheological damper according to the oil film force of the magneto-rheological damper, the friction force, the bearing force and the eccentric force;
s6, solving the rotor system dynamic model based on the magneto-rheological damper by using a Newmark-beta method to obtain system dynamic response;
specifically, the oil film force model of the magnetorheological damper in the step S1 is as follows:
wherein, F mr Is the radial oil film force of the magneto-rheological damper F mt Obtaining the radial oil film force of the magneto-rheological damper, wherein L is the length of the damper in the Z direction, p is the oil film pressure of the magneto-rheological damper, theta is the azimuth angle of the oil film relative to the position of the minimum oil film, R is the radius of a rotor, and the expression of the component force of the magneto-rheological damper oil film force in the x direction and the component force of the magneto-rheological damper oil film force in the y direction is obtained according to the expression of the magneto-rheological damper oil film force model and is as follows:
wherein, F mx Is the component force of the oil film force of the magneto-rheological damper in the x direction, F my Is the component force of the oil film force of the magneto-rheological damper in the y direction, x m Is the displacement of the center of the inner ring of the magneto-rheological damper in the x direction, y m The displacement of the oil film force of the magneto-rheological damper in the y direction is realized;
the dynamic model based on the rub-impact fault of the magnetorheological damper in the step S2 is as follows:
F N ＝k r (δ r -δ 0 )H(δ r -δ 0 )
F T ＝μ r F N
wherein, F N Is the normal contact force between rotor and stator, F T Is the tangential friction between rotor and stator, delta 0 Is the initial clearance, δ, between rotor and stator r Radial displacement of the centre of the disc, k r For radial contact stiffness, μ r Obtaining a component force expression of the rub-impact force in the x direction and the y direction according to the rub-impact fault dynamic model of the magneto-rheological damper, wherein the component force expression is the friction coefficient between a rotor and a stator:
wherein, F rx Component of rubbing force in the x direction, F ry Component of rubbing force in the y-direction, k r For radial contact stiffness, μ r Is rotor-stator friction coefficient, x d And y d Displacement of the disc centre in the x and y directions, respectively, delta 0 Is the initial clearance, δ, between rotor and stator r Is the radial displacement of the center of the disc.
2. The vibration prediction method for the rotor system model based on the magnetorheological damper according to claim 1, wherein a bearing support model is established in the step S3, and the expression of the bearing force obtained according to the bearing support model is as follows:
wherein, F bx Component of the bearing force in the x-direction, F by Component of the bearing force in the y-direction, δ i Is the normal contact deformation of the ith ball and the raceway,
angular position of the i-th ball at time t, C b Hertz contact stiffness.
3. The vibration prediction method of a rotor system model based on a magnetorheological damper as claimed in claim 2, wherein H is a Heaviside function expressed as:
wherein, delta 0 Is the initial clearance, δ, between rotor and stator r Is the radial displacement of the center of the disc.
4. The vibration prediction method of a rotor system model based on a magnetorheological damper as claimed in claim 2, wherein the expression of the eccentric force obtained according to the disc rotor eccentric model in step S4 is as follows:
wherein, F ex Is the component of the eccentric force in the x direction, F ey Is the component force of the eccentric force in the y direction, e is the eccentric amount of the disc, m c Is the mass of the disc rotor, omega is the rotational speed of the disc rotor,
is an initial phase angle.
5. The vibration prediction method of the rotor system model based on the magnetorheological damper as claimed in claim 4, wherein the rotor system dynamic model based on the magnetorheological damper in the step S5 is as follows:
wherein, q is a generalized displacement,
is a generalized speed->
For generalized acceleration, M s Is a mass matrix of the rotor shaft, G s Gyro force matrix, K, being rotor shaft s Is a stiffness matrix of the rotor shaft, Q s A generalized force matrix for the rotor shaft;
{Q s }＝[F bx ，F by ，F mx -F bx ，F my -F by ，F ex +F rx ，F ey +F ry ，0，0，···] T
wherein, F bx Component of the bearing force in the x-direction, F by Is the component force of the bearing force in the y direction; f mx Is the component force of the oil film force of the magneto-rheological damper in the x direction, F my For magnetorheological damper oil film force in y directionComponent force; f ex The component force of the eccentric force in the x direction; f rx Component of rubbing force in the x direction, F ry Is the component force of the rubbing force in the y direction.
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| 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 |
| CN110566624A (en) * | 2019-09-27 | 2019-12-13 | 天津大学仁爱学院 | Semi-active vibration damper capable of phase-splitting self-adaptive control |
| 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 |
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| CN104776998A (en) * | 2015-03-26 | 2015-07-15 | 北京工业大学 | Rotor center trail solving method based on dynamic rigidity coefficient and damping coefficient |
| 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 |
| CN110566624A (en) * | 2019-09-27 | 2019-12-13 | 天津大学仁爱学院 | Semi-active vibration damper capable of phase-splitting self-adaptive control |
| 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 |
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