CN111237338A - Single-degree-of-freedom magnetic-liquid double-suspension bearing control system and method - Google Patents

Single-degree-of-freedom magnetic-liquid double-suspension bearing control system and method Download PDF

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CN111237338A
CN111237338A CN202010038345.1A CN202010038345A CN111237338A CN 111237338 A CN111237338 A CN 111237338A CN 202010038345 A CN202010038345 A CN 202010038345A CN 111237338 A CN111237338 A CN 111237338A
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liquid
cavity
bearing
supporting
electromagnetic
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赵建华
韩放
闫伟东
王永强
李胜
马旭超
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Yanshan University
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Yanshan University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C32/00—Bearings not otherwise provided for
    • F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
    • F16C32/0402—Bearings not otherwise provided for using magnetic or electric supporting means combined with other supporting means, e.g. hybrid bearings with both magnetic and fluid supporting means
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C32/00—Bearings not otherwise provided for
    • F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
    • F16C32/0406—Magnetic bearings
    • F16C32/044—Active magnetic bearings
    • F16C32/0444—Details of devices to control the actuation of the electromagnets
    • F16C32/0446—Determination of the actual position of the moving member, e.g. details of sensors
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C32/00—Bearings not otherwise provided for
    • F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
    • F16C32/0406—Magnetic bearings
    • F16C32/044—Active magnetic bearings
    • F16C32/0444—Details of devices to control the actuation of the electromagnets
    • F16C32/0451—Details of controllers, i.e. the units determining the power to be supplied, e.g. comparing elements, feedback arrangements with P.I.D. control
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C32/00—Bearings not otherwise provided for
    • F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
    • F16C32/0406—Magnetic bearings
    • F16C32/044—Active magnetic bearings
    • F16C32/0474—Active magnetic bearings for rotary movement
    • F16C32/0476—Active magnetic bearings for rotary movement with active support of one degree of freedom, e.g. axial magnetic bearings
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C32/00—Bearings not otherwise provided for
    • F16C32/06—Bearings not otherwise provided for with moving member supported by a fluid cushion formed, at least to a large extent, otherwise than by movement of the shaft, e.g. hydrostatic air-cushion bearings
    • F16C32/0629—Bearings not otherwise provided for with moving member supported by a fluid cushion formed, at least to a large extent, otherwise than by movement of the shaft, e.g. hydrostatic air-cushion bearings supported by a liquid cushion, e.g. oil cushion
    • F16C32/064—Bearings not otherwise provided for with moving member supported by a fluid cushion formed, at least to a large extent, otherwise than by movement of the shaft, e.g. hydrostatic air-cushion bearings supported by a liquid cushion, e.g. oil cushion the liquid being supplied under pressure
    • F16C32/0644—Details of devices to control the supply of liquids to the bearings

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Magnetic Bearings And Hydrostatic Bearings (AREA)

Abstract

The invention discloses a single-degree-of-freedom magnetic-liquid double-suspension bearing control system and a method. Wherein, the PID controller, the differential power amplifier, the displacement sensor and the single-degree-of-freedom magnetic-liquid double-suspension bearing are sequentially connected in a closed manner to form an electromagnetic closed loop. The displacement sensor is used for detecting the offset of the single-degree-of-freedom magnetic-liquid double-suspension bearing rotor and outputting corresponding analog quantity voltage U1Output analog voltage U1Voltage U corresponding to the position of the shaft in the center0And comparing to obtain a voltage difference value delta U, outputting a control current i through a PID controller, and outputting a current meeting the requirements of the upper and lower electromagnetic coils through a differential power amplifier by the control current i so as to obtain the required electromagnetic attraction. The invention respectively adopts the electromagnetic closed loop with PID and the PM flow controller dual control, so that the electromagnetic force and the static pressure jointly compensate the external load according to a certain proportion, and finally the rotor returns to the central position. Regulating capacity of the control methodLarge size, fast response and good dynamic property.

Description

Single-degree-of-freedom magnetic-liquid double-suspension bearing control system and method
Technical Field
The invention relates to the technical field of control, in particular to a single-degree-of-freedom magnetic-liquid double-suspension bearing control system and a single-degree-of-freedom magnetic-liquid double-suspension bearing control method.
Background
The magnetic-hydraulic double-suspension bearing adopts double support of electromagnetic force and static pressure supporting force, is a novel non-mechanical contact bearing, and has the advantages of no friction, no abrasion, large bearing capacity, high motion precision, long service life and the like. The magnetic-hydraulic double-suspension bearing comprises two sets of supporting systems, namely an electromagnetic support and a hydrostatic support, and the traditional control method is single and the recovery response is slow; the invention adopts electromagnetic closed loop regulation electromagnetic force with PID controller, PM flow controller regulates static pressure, to make it compensate external load together according to proportion. When the balance is achieved again under the control method, the rotor returns to the central position, and the control method has the advantages of large adjusting capacity, quick response and good dynamic characteristic, effectively makes up for the defect of slow static pressure response, and greatly improves the running stability of the magnetic-liquid double-suspension bearing.
Disclosure of Invention
The invention aims to provide a novel single-degree-of-freedom magnetic-liquid double-suspension bearing control method, which adopts an electromagnetic closed loop with a PID (proportion integration differentiation) controller and a PM (particulate matter) flow controller for control and respectively regulates and controls electromagnetic force and static pressure.
In order to achieve the purpose, the invention provides the following scheme:
the system comprises a PID controller, a differential power amplifier, a displacement sensor, a single-degree-of-freedom magnetic-liquid double-suspension bearing, a hydraulic pump, an overflow valve, a pressure gauge, a one-way valve, a filter and a PM flow controller;
the PID controller, the differential power amplifier, the single-degree-of-freedom magnetic-liquid double-suspension bearing and the displacement sensor are sequentially connected in a closed manner to form an electromagnetic closed-loop control system, and the hydraulic pump, the overflow valve, the pressure gauge, the one-way valve, the filter, the PM flow controller and the single-degree-of-freedom magnetic-liquid double-suspension bearing are sequentially connected to form a static pressure control system;
the displacement sensor is used for detecting the offset of the rotor of the single-degree-of-freedom magnetic-liquid double-suspension bearing and outputting corresponding analog quantity voltage U1The output analog quantity voltage U1Corresponding to the voltage U when the shaft is in the central position0Comparing to obtain voltage difference value delta U, outputting control current i by PID controller, making control current i pass through differential power amplifier, and changing upper coil current into i0+icLower coil current becomes i0-icWherein i0Is the initial current of the solenoid coil, icIn order to change the value of the current,
formula of calculation by electromagnetic force
Figure BDA0002366819980000021
Knowing that the electromagnetic force is a function of this variable i of the currentcThe current is uniquely determined, and the rotor is assisted to return to the original position under the action of the electromagnetic force generated by the current;
the PM flow controller changes the output flow q by the corresponding deformation of the metal film inside the PM flow controller depending on the change of the pressure difference of the supporting cavity of the single-degree-of-freedom magnetic-liquid double-suspension bearing, namely the PM flow controller is self-adaptive adjustment, when the adjustment of the electromagnetic ring is determined, the static pressure adjustment is determined accordingly, namely the static pressure output flow and the electromagnetic adjustment result, namely the current change icThe hydraulic pressure fLiquid is in one-to-one correspondence with the output flow q of the PM flow controller, and the rotor rotates back to the central position again under the combined action of the fElectricity and the fLiquid;
the electromagnetic closed-loop control system is used for controlling the current parameters of the single-degree-of-freedom magnetic-liquid double-suspension bearing electromagnetic supporting system so as to change the electromagnetic force;
the static pressure control system is used for controlling the flow parameters of the single-degree-of-freedom magnetic-liquid double-suspension bearing static pressure supporting system, so that the static pressure of the upper supporting cavity and the lower supporting cavity is changed.
Preferably, when the hydraulic pump gallery pressure is less than or equal to 0.9 times the oil supply pressure ps, the supply flow rate linearly increases with the gallery pressure.
Preferably, the single-free magnetic-liquid double-suspension bearing is provided with 4 radial magnetic poles, each magnetic pole is bound with a coil, and every two adjacent magnetic poles form a supporting unit; the bottom of each magnetic pole is provided with a supporting cavity, and each two adjacent magnetic poles share one oil inlet.
Preferably, the two pairs of poles are arranged on the same mounting plane and spaced 180 degrees apart from each other.
Preferably, the invention also provides a single-degree-of-freedom magnetic-liquid double-suspension bearing control method, which comprises the following steps:
s1, in an initial state, under the action of no external load, the rotor has no deflection, the deflection of the rotor detected by the displacement sensor is 0, the output current of the PID controller is 0, the driving current output by the power amplification module is a reference current i0, the currents of the upper electromagnetic coil and the lower electromagnetic coil are equal, the supporting forces of the upper electromagnetic coil and the lower electromagnetic coil are equal, the flow and the liquid resistance of the upper supporting cavity and the lower supporting cavity are equal, and the upper static pressure supporting force and the lower static pressure supporting force are equal;
s2, when the rotor is deviated from the center position under the interference of the external load f, the rotor deviation amount detected by the displacement sensor is x, the output current of the PID controller is i, and the electromagnetic supporting forces generated by the upper electromagnetic coil and the lower electromagnetic coil are respectively fElectricity, 1、fElectricity, 2Resultant electromagnetic force of fElectricity, alloy＝(fElectricity, 1-fElectricity, 2)cosθ；
The thickness of an oil film is changed due to the deviation of a rotor, and the change of the liquid resistance of an upper supporting cavity and the liquid resistance of a lower supporting cavity is accompanied, so that the pressure of the upper supporting cavity and the pressure of the lower supporting cavity are changed, a PM flow controller in a static pressure control system makes a metal film in the PM flow controller generate corresponding deformation to control the flow q by depending on the change of the pressure difference of a supporting cavity of a single-degree-of-freedom magnetic-liquid double-suspension bearing, the formula p is qR, wherein the liquid resistance R is a function of displacement x, the static pressure supporting force of the magnetic-liquid double-suspension bearing is determined accordingly, and at the moment, the static pressure supporting forces respectively received by the upper supporting cavity and the lower supportingLiquid, 1、fLiquid, 2Bearing resultant force f of static pressureLiquid, composition＝(fLiquid, 2-fLiquid, 1) cos theta, thereby realizing the electromagnetic supporting force and the static pressure supportThe bearing force compensates the external load f together, and the rotor returns to the central position again under the combined action of the bearing force and the external load f.
Preferably, in step S1, the method for calculating the mechanical balance equation of the rotor includes the following steps:
s11, in a balanced state, the magnetic-liquid double-suspension bearing adopts a PM flow controller to regulate and control the flow parameters of the static pressure bearing system, neglecting the mass of the rotor, at the initial moment, the rotor is balanced, the pressures of the upper bearing cavity and the lower bearing cavity are equal, and the flow passing through the upper bearing cavity and the lower bearing cavity is equal, namely:
q1,0＝q2,0；
in the formula, q1,0For upper support chamber flow, q2,0The lower support cavity flow rate;
s12, obtaining the static pressure supporting force f of the upper supporting cavity and the lower supporting cavity according to the Navier-Stokes equationLiquid, 1,0、fLiquid, 2,0Comprises the following steps:
Figure BDA0002366819980000041
in the formula, theta is an included angle between the central line of the supporting cavity and the central line of the rotating shaft;
p1,0the pressure of the initial upper bearing cavity is expressed in MPa;
p2,0the pressure of the initial lower supporting cavity is expressed in MPa;
Aeis the bearing area of the bearing cavity and has the unit of m2；
S13, obtaining the electromagnetic suspension supporting force f of the upper supporting unit and the lower supporting unit according to the Maxwell attraction formulaElectric, 1,0、fElectric, 2,0Comprises the following steps:
Figure BDA0002366819980000042
in the formula, k is an electromagnetic constant and has a unit of H.m; the formula for k is as follows:
Figure BDA0002366819980000043
wherein h is0Initial liquid film thickness in m;
i0is the initial bias current of the electromagnetic coil, and the unit is A;
l is the thickness of the zinc coating of the electromagnet, and the unit is m;
μ0air permeability in units of H/m;
n is the number of turns of the electromagnetic coil;
a is the area of the iron core and is m2；
S14, obtaining a mechanical balance equation of the rotor according to Newton' S second law:
felectric, 1,0+fLiquid, 2,0-fElectric, 2,0-fLiquid, 1,0＝0。
Preferably, in step S2, the calculation method of the control current i generated by the PID controller is: when there is an external disturbance fOuter coverWhen the rotor acts on the bearing rotor, the displacement of the bearing rotor is changed into x, and the liquid film thickness h of the upper bearing cavity and the lower bearing cavity is determined1、h2Comprises the following steps:
Figure BDA0002366819980000044
at this time, the currents passing through the upper and lower electromagnetic coils are respectively (i)0+ic)、(i0-ic) Therefore, the electromagnetic supporting forces of the upper supporting unit and the lower supporting unit are respectively:
Figure BDA0002366819980000051
in the formula icControl current is induced for rotor displacement in units of a;
the rotor deflects due to external load, so that the thicknesses of the hydraulic films of the upper supporting cavity and the lower supporting cavity are changed, the hydraulic resistance and the pressure of the upper supporting cavity and the lower supporting cavity are changed, and the static pressure supporting force f of the upper supporting cavity and the lower supporting cavity is obtainedLiquid, 1、fLiquid, 2Comprises the following steps:
Figure BDA0002366819980000052
Pr1is the pressure of the upper bearing chamber;
Pr2is the pressure of the lower bearing chamber;
determining parameters of a PM flow controller for each bearing chamber and determining a pump pressure psThen, the pressure expressions of the upper supporting cavity and the lower supporting cavity are obtained as follows:
Figure BDA0002366819980000053
in the formula, q01、q02The initial flow rates of the PM flow controllers corresponding to the upper supporting cavity and the lower supporting cavity respectively; c. C1，c2The specific flow of the PM flow controllers corresponding to the upper and lower supporting cavities respectively has the following values:
Figure BDA0002366819980000054
and q isp1、qp2The PM flow controllers corresponding to the upper bearing cavity and the lower bearing cavity respectively have the pressure equal to the oil supply pressure psFlow rate of water passing through, R1The unit is the liquid resistance of the upper supporting cavity and is N.s/m5；
Figure BDA0002366819980000055
R2The liquid resistance of the lower supporting cavity is expressed in the unit of N.s/m5；
Figure BDA0002366819980000056
Wherein mu is the dynamic viscosity of the oil liquid, and the unit is Pa.s;
Figure BDA0002366819980000057
supporting the flow coefficient for the support cavity;
from the above formula, the expression of the hydrostatic bearing force is:
Figure BDA0002366819980000061
according to Newton's second law, obtaining a mechanical equilibrium equation of the rotating shaft:
Figure BDA0002366819980000062
wherein f is the external load of the rotor and has the unit of N; m is the rotor mass;
to fElectricity, alloyAnd (3) carrying out linearization processing at the position where x is 0 and i is 0 to obtain:
felectricity, alloy＝kx1+kii
In the formula, kx1Is the displacement stiffness coefficient with the unit of N/m; k is a radical ofiThe current stiffness coefficient is expressed in the unit of N/A.
To fLiquid, compositionAnd (3) carrying out linearization treatment when x is 0 to obtain:
fliquid, composition＝kxx
In the formula, kxIs the displacement stiffness coefficient with the unit of N/m;
when the single-degree-of-freedom magnetic-liquid double-suspension bearing system is under the action of an external load, the rotor returns to the central position again by changing electromagnetic force and static pressure, balance is achieved, and the effect that the resultant force of the electromagnetic force and the resultant force of the static pressure are equal is achieved:
Figure BDA0002366819980000063
kx1+kii＝kxx
the PID controller generates a control current i of:
Figure BDA0002366819980000064
compared with the prior art, the invention has the following beneficial effects:
the invention aims at an electromagnetic supporting system and a static pressure supporting system of a single-degree-of-freedom magnetic-liquid double-suspension bearing, and respectively adopts an electromagnetic closed loop with PID and dual control of a PM flow controller, so that the electromagnetic force and the static pressure jointly compensate an external load according to a certain proportion, and finally a rotor returns to the central position. The control method has the advantages of large adjusting capacity, quick response and good dynamic characteristic, and greatly improves the stability, rapidness and effectiveness of the operation of the magnetic-liquid double-suspension bearing.
Drawings
FIG. 1 is a schematic diagram of a novel single-degree-of-freedom magnetic-liquid double-suspension bearing control system; and
fig. 2 is a schematic structural diagram of a magnetic-liquid double-suspension bearing.
Detailed Description
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
As shown in fig. 1, a single-degree-of-freedom magnetic-hydraulic double-suspension bearing control system includes a PID controller 14, a differential power amplifier 15, a displacement sensor 16, a single-degree-of-freedom magnetic-hydraulic double-suspension bearing 17, a hydraulic pump 1, an overflow valve 2, a pressure gauge 3, a check valve 4, a filter 5, and a PM flow controller 6.
Wherein, the PID controller 14, the differential power amplifier 15, the single-degree-of-freedom magnetic-liquid double-suspension bearing 17 and the displacement sensor 16 are sequentially connected in a closed manner to form an electromagnetic closed-loop control system.
The hydraulic pump 1, the overflow valve 2, the pressure gauge 3, the check valve 4, the filter 5, the PM flow controller 6 and the single-degree-of-freedom magnetic-liquid double-suspension bearing 17 are sequentially connected to form a static pressure control system.
The displacement sensor is used for detecting the offset of the single-degree-of-freedom magnetic-liquid double-suspension bearing rotor and outputting corresponding analog quantity voltage U1Output analog voltage U1Voltage U corresponding to the reference position set by the PID controller0And comparing to obtain a voltage difference value delta U, outputting a control current i through a PID controller, outputting the control current i through a differential power amplifier to meet the current of an upper electromagnetic coil and a lower electromagnetic coil, and enabling a metal film in the PM flow controller to generate corresponding deformation to control the flow only by depending on the change of the pressure difference of the supporting cavity of the single-degree-of-freedom magnetic-liquid double-suspension bearing without the input of external energy or electronic control.
The electromagnetic closed-loop control system is used for controlling the current parameters of the single-degree-of-freedom magnetic-liquid double-suspension bearing electromagnetic supporting system so as to change the electromagnetic force; and the static pressure control system is used for controlling the flow parameters of the single-degree-of-freedom magnetic-liquid double-suspension bearing static pressure supporting system so as to change the static pressure of the upper supporting cavity and the lower supporting cavity.
As shown in fig. 2, the stator 11 of the single-degree-of-freedom magnetic-liquid double-suspension bearing is provided with 4 radial magnetic poles 300; the upper electromagnetic coil 30 is disposed outside the upper two magnetic poles 300, and the lower electromagnetic coil is disposed outside the lower two magnetic poles. Each magnetic pole 300 is provided with an oil inlet through hole and bound with a coil, and a supporting cavity is processed at the bottom of each magnetic pole and comprises an upper supporting cavity 10 and a lower supporting cavity 20, each 2 magnetic poles form a supporting unit, and the supporting unit comprises an upper supporting unit 100 and a lower supporting unit 200. And share an oil inlet 12 or an oil outlet 13.
With reference to fig. 1 and 2, the specific working principle is as follows:
the single-degree-of-freedom magnetic-liquid double-suspension bearing 17 comprises a rotor and a stator, wherein the rotor is positioned in an inner hole of the stator, the stator is provided with 4 radial magnetic poles, every 2 magnetic poles are matched in pairs for use, the paired magnetic poles are arranged on the same mounting plane and are separated from each other by 180 degrees, an oil inlet through hole is processed in each magnetic pole, each pair of magnetic poles share one oil inlet, and a supporting cavity is processed at the bottom of each magnetic pole.
1. In an initial state, under the action of no external load, the rotor is in a reference position without deviation, and the rotor deviation amount detected by the displacement sensor is 0, so that the output current of the PID controller is 0, and the driving current output by the power amplification module is reference current i0. As shown in fig. 2, the currents of the upper and lower solenoids are equal, and the upper and lower electromagnetic supporting forces (f) are equal. At this time, the flow rates and hydraulic resistances of the upper support chamber and the lower support chamber are equal, and therefore the upper static pressure support force and the lower static pressure support force (hydraulic) are equal.
In a balanced state, the magnetic-liquid double-suspension bearing adopts a PM flow controller to regulate and control the flow parameters of a static pressure supporting system, neglects the mass of a rotor, and at the initial moment, the rotor is balanced, the pressure of an upper supporting cavity and a lower supporting cavity is equal, and the flow flowing through the upper supporting cavity and the lower supporting cavity is equal, namely:
q1,0＝q2,0；
obtaining the static pressure supporting force f of the upper supporting cavity and the lower supporting cavity according to the Navier-Stokes equationLiquid, 1,0、fLiquid, 2,0Comprises the following steps:
Figure BDA0002366819980000081
in the formula, the central line of the theta-supporting cavity forms an included angle with the central line of the rotating shaft;
p1,0the pressure of the initial upper bearing chamber 10, MPa;
p2,0pressure of the initial lower bearing chamber 20, MPa;
Aebearing chamber bearing area, m2。
Obtaining the electromagnetic suspension supporting force f of the upper supporting unit 100 and the lower supporting unit 200 according to the Maxwell attraction formulaElectric, 1,0、fElectric, 2,0Comprises the following steps:
Figure BDA0002366819980000091
in the formula, k-electromagnetic constant, H.m;
Figure BDA0002366819980000092
h0-initial liquid film thickness, m;
i0-a solenoid initial bias current, a;
l-the thickness of the zinc coating of the electromagnet, m;
μ0-air permeability, H/m;
n-number of turns of electromagnetic coil, dimensionless;
a-area of iron core, m2。
And (3) obtaining a mechanical balance equation of the rotor according to a Newton second law:
felectric, 1,0+fLiquid, 2,0-fElectric, 2,0-fThe liquid is mixed with the raw materials of the raw materials,1,0＝0
2. when the rotor is under the interference of an external load f and deviates from the central position, the rotor offset detected by the displacement sensor is x, the output current of the PID controller is i, the rotor stress is shown in figure 2, the electromagnetic supporting forces generated by the upper electromagnetic coil 1 and the lower electromagnetic coil 2 are respectively f electricity, 1 electricity, 2 electricity and the electromagnetic resultant force is f electricityElectricity, alloy＝(fElectricity, 1-fElectricity, 2) cos θ; the PM flow controller in the static pressure control system controls the flow by generating corresponding deformation of a metal film in the PM flow controller according to the change of the differential pressure of the supporting cavities of the single-degree-of-freedom magnetic-liquid double-suspension bearing so as to realize the automatic regulation of the static pressure supporting force of the magnetic-liquid double-suspension bearing, wherein the static pressure supporting forces borne by the upper supporting cavity and the lower supporting cavity are respectively fLiquid, 1, fLiquid, 2 and a static pressure supporting resultant force fLiquid, composition＝(fLiquid, 2-fLiquid, 1) cos θ, so that the electromagnetic bearing force together with the hydrostatic bearing force compensates the external load f, in the combined action of the two, the rotor is once again returned to the central position.
When there is an external disturbance fOuter coverWhen the displacement of the bearing rotor is changed to x when acting on the rotor, the liquid film thickness h of the upper supporting cavity 10 and the lower supporting cavity 20 is1、h2Comprises the following steps:
Figure BDA0002366819980000101
then the current passing through the upper and lower electromagnetic coils is (i)0+ic)、(i0Ic), the electromagnetic supporting forces of the upper and lower support units 100, 200 are therefore:
Figure BDA0002366819980000102
where ic-rotor displacement causes the control current in units of A.
In the same way, due to the external load,the static pressure supporting force f of the upper supporting cavity 10 and the lower supporting cavity 20 can be obtained by the deviation of the rotor to change the thicknesses of the hydraulic films of the upper supporting cavity and the lower supporting cavity, so as to cause the hydraulic resistance and the pressure of the upper supporting cavity and the lower supporting cavity to change (neglecting the influence of a sensitive liquid path on a bearing system)Liquid, 1、fLiquid, 2Comprises the following steps:
Figure BDA0002366819980000103
Pr1the pressure of the upper bearing chamber 10;
Pr2the pressure of lower bearing chamber 20;
parameters of the PM flow controller corresponding to each bearing chamber are given, and a pump pressure p is determinedsThen, the pressure expressions of the upper supporting cavity and the lower supporting cavity can be deduced to be respectively:
Figure BDA0002366819980000104
in the formula, q01、q02The initial flow rates of the PM flow controllers corresponding to the upper and lower supporting cavities respectively; c. C1，c2The specific flow of the PM flow controllers corresponding to the upper and lower supporting cavities respectively has the following values:
Figure BDA0002366819980000111
and q isp1、qp2The PM flow controllers corresponding to the upper and lower bearing chambers respectively have a pressure equal to the oil supply pressure psFlow rate of water passing through, R1For the hydraulic resistance of the upper bearing chamber 10, N.s/m5；
Figure BDA0002366819980000112
R2The liquid resistance of the lower bearing chamber 20, N.s/m5；
Figure BDA0002366819980000113
Wherein mu is dynamic viscosity of the oil liquid, Pa.s;
Figure BDA0002366819980000114
the flow coefficient is supported by the supporting cavity without dimension.
To sum up: the expression hydrostatic bearing force can be written as:
Figure BDA0002366819980000115
and similarly, obtaining a mechanical equilibrium equation of the rotating shaft according to the Newton's second law:
Figure BDA0002366819980000116
where f is the external load of the rotor, N; m-rotor mass.
To fElectricity, alloyAnd (3) carrying out linearization processing at the position where x is 0 and i is 0 to obtain:
felectricity, alloy＝kx1+kii
In the formula, kx1-coefficient of displacement stiffness, N/m; k is a radical ofi-current stiffness factor, N/a.
To fLiquid, compositionAnd (3) carrying out linearization treatment when x is 0 to obtain:
fliquid, composition＝kxx
In the formula, kx-coefficient of displacement stiffness, N/m.
When the single-degree-of-freedom magnetic-liquid double-suspension bearing system is under the action of an external load, the rotor returns to the central position again by changing electromagnetic force and static pressure, so that balance is achieved, and the effect that the resultant force of the electromagnetic force and the resultant force of the static pressure are basically equal can be achieved:
Figure BDA0002366819980000117
kx1+kii＝kxx
the PID controller generates a control current i of:
Figure BDA0002366819980000121
compared with the prior art, the invention has the following beneficial effects:
the invention aims at an electromagnetic supporting system and a static pressure supporting system of a single-degree-of-freedom magnetic-liquid double-suspension bearing, and respectively adopts an electromagnetic closed loop with PID and dual control of a PM flow controller, so that the electromagnetic force and the static pressure jointly compensate an external load according to a certain proportion, and finally a rotor returns to the central position. The control method has the advantages of large adjusting capacity, quick response and good dynamic characteristic, and greatly improves the stability, rapidness and effectiveness of the operation of the magnetic-liquid double-suspension bearing.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope defined by the claims of the present invention.

Claims (7)

1. A single-degree-of-freedom magnetic-liquid double-suspension bearing control system is characterized in that: the device comprises a PID controller, a differential power amplifier, a displacement sensor, a single-degree-of-freedom magnetic-liquid double-suspension bearing, a hydraulic pump, an overflow valve, a pressure gauge, a one-way valve, a filter and a PM flow controller;
the PID controller, the differential power amplifier, the single-degree-of-freedom magnetic-liquid double-suspension bearing and the displacement sensor are sequentially connected in a closed manner to form an electromagnetic closed-loop control system, and the hydraulic pump, the overflow valve, the pressure gauge, the one-way valve, the filter, the PM flow controller and the single-degree-of-freedom magnetic-liquid double-suspension bearing are sequentially connected to form a static pressure control system;
the displacement sensor is used for detecting the offset of the rotor of the single-degree-of-freedom magnetic-liquid double-suspension bearing and outputting corresponding analog quantity voltage U1The output analog quantity voltage U1Corresponding to the voltage U when the shaft is in the central position0Comparing to obtain voltage difference value delta U, outputting control current i by PID controller, making control current i pass through differential power amplifier, and changing upper coil current into i0+icLower coil current becomes i0-icWherein i0Is the initial current of the solenoid coil, icIn order to change the value of the current,
formula of calculation by electromagnetic force
Figure FDA0002366819970000011
In the knowledge that,
the variable ic of the electromagnetic force along with the current is uniquely determined, and the rotor is assisted to return to the original position under the action of the electromagnetic force generated by the current;
the PM flow controller changes the output flow q by the corresponding deformation of the metal film inside the PM flow controller depending on the change of the pressure difference of the supporting cavity of the single-degree-of-freedom magnetic-liquid double-suspension bearing, namely the PM flow controller is self-adaptive adjustment, when the adjustment of the electromagnetic ring is determined, the static pressure adjustment is determined accordingly, namely the static pressure output flow and the electromagnetic adjustment result, namely the current change icIs in one-to-one correspondence, and the hydraulic pressure fLiquid is in one-to-one correspondence with the output flow q of the PM flow controller, at fElectric powerAnd fLiquid for treating urinary tract infectionUnder the combined action of the two rotors, the rotors rotate back to the central position again;
the electromagnetic closed-loop control system is used for controlling the current parameters of the single-degree-of-freedom magnetic-liquid double-suspension bearing electromagnetic supporting system so as to change the electromagnetic force;
the static pressure control system is used for controlling the flow parameters of the single-degree-of-freedom magnetic-liquid double-suspension bearing static pressure supporting system, so that the static pressure of the upper supporting cavity and the lower supporting cavity is changed.
2. The single degree of freedom magnetic-liquid double suspension bearing control system of claim 1, characterized in that: when the oil chamber pressure of the hydraulic pump is less than or equal to 0.9 times the oil supply pressure ps, the supply flow rate linearly increases with the oil chamber pressure.
3. The single degree of freedom magnetic-liquid double suspension bearing control system of claim 1, characterized in that: the single-free magnetic-liquid double-suspension bearing is provided with 4 radial magnetic poles, each magnetic pole is bound with a coil, and every two adjacent magnetic poles form a supporting unit; the bottom of each magnetic pole is provided with a supporting cavity, and each two adjacent magnetic poles share one oil inlet or one oil outlet.
4. The single degree of freedom magnetic-liquid double suspension bearing control system of claim 3, characterized in that: the two pairs of magnetic poles are arranged on the same mounting plane and are spaced 180 degrees apart from each other.
5. The control method of the single-degree-of-freedom magnetic-liquid double-suspension bearing control system according to claim 1 is characterized in that: which comprises the following steps:
s1, when in initial state, under the action of no external load, the rotor has no offset, the offset of the rotor detected by the displacement sensor is 0, the output current of the PID controller is 0, and the driving current output by the power amplification module is the reference current i0At the moment, the currents of the upper electromagnetic coil and the lower electromagnetic coil are equal, the supporting forces of the upper electromagnetic coil and the lower electromagnetic coil are equal, the flow rates and the liquid resistances of the upper supporting cavity and the lower supporting cavity are equal, and the upper static pressure supporting force and the lower static pressure supporting force are equal;
s2, when the rotor is deviated from the center position under the interference of the external load f, the rotor deviation amount detected by the displacement sensor is x, the output current of the PID controller is i, and the electromagnetic supporting forces generated by the upper electromagnetic coil and the lower electromagnetic coil are respectively fElectricity, 1、fElectricity, 2Resultant electromagnetic force of fElectricity, alloy＝(fElectricity, 1-fElectricity, 2)cosθ；
The thickness of an oil film can be changed along with the change of the liquid resistance of the upper bearing cavity and the liquid resistance of the lower bearing cavity due to the deviation of the rotor, so that the pressure of the upper bearing cavity and the pressure of the lower bearing cavity are changed, a PM flow controller in a static pressure control system makes a metal film in the PM flow controller generate corresponding deformation to control the flow by depending on the change of the pressure difference of the supporting cavity of the single-degree-of-freedom magnetic-liquid double-suspension bearing, and the automatic adjustment of the static pressure supporting force of the magnetic-liquid double-suspension bearing is realizedLiquid, 1、fLiquid, 2Bearing resultant force f of static pressureLiquid, composition＝(fLiquid, 2-fLiquid, 1) cos theta, thereby realizing the electromagnetic supporting force and the static pressure supportThe bearing force compensates the external load f together, and the rotor returns to the central position again under the combined action of the bearing force and the external load f.
6. The control method of the single-degree-of-freedom magnetic-liquid double-suspension bearing control system according to claim 5 is characterized in that: in step S1, the method for calculating the mechanical balance equation of the rotor includes the following steps:
s11, in a balanced state, the magnetic-liquid double-suspension bearing adopts a PM flow controller to regulate and control the flow parameters of the static pressure bearing system, neglecting the mass of the rotor, at the initial moment, the rotor is balanced, the pressures of the upper support cavity and the lower support cavity are equal, and the flow passing through the upper support cavity and the lower support cavity is equal, namely:
q1,0＝q2,0；
in the formula, q1,0For upper support chamber flow, q2,0The lower support cavity flow rate;
s12, obtaining the static pressure supporting force f of the upper supporting cavity and the lower supporting cavity according to the Navier-Stokes equationLiquid, 1,0、fLiquid, 2,0Comprises the following steps:
Figure FDA0002366819970000031
in the formula, theta is an included angle between the central line of the supporting cavity and the central line of the rotating shaft;
p1,0the pressure of the initial upper bearing cavity is expressed in MPa;
p2,0the pressure of the initial lower supporting cavity is expressed in MPa;
Aeis the bearing area of the bearing cavity and has the unit of m2；
S13, obtaining the electromagnetic suspension supporting force f of the upper supporting unit and the lower supporting unit according to the Maxwell attraction formulaElectric, 1,0、fElectric, 2,0Comprises the following steps:
Figure FDA0002366819970000032
in the formula, k is an electromagnetic constant and has a unit of H.m; the formula for k is as follows:
Figure FDA0002366819970000033
wherein h is0Initial liquid film thickness in m;
i0is the initial bias current of the electromagnetic coil, and the unit is A;
l is the thickness of the zinc coating of the electromagnet, and the unit is m;
μ0air permeability in units of H/m;
n is the number of turns of the electromagnetic coil;
a is the area of the iron core and is m2；
S14, obtaining a mechanical balance equation of the rotor according to Newton' S second law:
felectric, 1,0+fLiquid, 2,0-fElectric, 2,0-fLiquid, 1,0＝0。
7. The control method of the single-degree-of-freedom magnetic-liquid double-suspension bearing control system according to claim 5 is characterized in that: in step S2, the method for calculating the control current i generated by the PID controller is: when there is an external disturbance fOuter coverWhen the rotor acts on the bearing rotor, the displacement of the bearing rotor is changed into x, and the liquid film thickness h of the upper bearing cavity and the lower bearing cavity is determined1、h2Comprises the following steps:
Figure FDA0002366819970000041
at the moment, the currents passing through the upper electromagnetic coil and the lower electromagnetic coil are respectively i0+ic、i0-icTherefore, the electromagnetic supporting forces of the upper supporting unit and the lower supporting unit are respectively:
Figure FDA0002366819970000042
in the formula icControl current is induced for rotor displacement in units of a;
the rotor deflects due to external load, so that the thicknesses of the hydraulic films of the upper supporting cavity and the lower supporting cavity are changed, the hydraulic resistance and the pressure of the upper supporting cavity and the lower supporting cavity are changed, and the static pressure supporting force f of the upper supporting cavity and the lower supporting cavity is obtainedLiquid, 1、fLiquid, 2Comprises the following steps:
Figure FDA0002366819970000043
Pr1is the pressure of the upper bearing chamber;
Pr2is the pressure of the lower bearing chamber;
determining parameters of a PM flow controller for each bearing chamber and determining a pump pressure psThen, the pressure expressions of the upper supporting cavity and the lower supporting cavity are obtained as follows:
Figure FDA0002366819970000051
in the formula, q01、q02The initial flow rates of the PM flow controllers corresponding to the upper supporting cavity and the lower supporting cavity respectively; c. C1，c2The specific flow of the PM flow controllers corresponding to the upper and lower supporting cavities respectively has the following values:
Figure FDA0002366819970000052
and q isp1、qp2The PM flow controllers corresponding to the upper bearing cavity and the lower bearing cavity respectively have the pressure equal to the oil supply pressure psFlow rate of water passing through, R1The unit is the liquid resistance of the upper supporting cavity and is N.s/m5；
Figure FDA0002366819970000053
R2The liquid resistance of the lower supporting cavity is expressed in the unit of N.s/m5；
Figure FDA0002366819970000054
Wherein mu is the dynamic viscosity of the oil liquid, and the unit is Pa.s;
Figure FDA0002366819970000057
supporting the flow coefficient for the support cavity;
from the above formula, the expression of the hydrostatic bearing force is:
Figure FDA0002366819970000055
according to Newton's second law, obtaining a mechanical equilibrium equation of the rotating shaft:
Figure FDA0002366819970000056
wherein f is the external load of the rotor and has the unit of N; m is the rotor mass;
to fElectricity, alloyAnd (3) carrying out linearization processing at the position where x is 0 and i is 0 to obtain:
felectricity, alloy＝kx1+kii
In the formula, kx1Is the displacement stiffness coefficient with the unit of N/m; k is a radical ofiIs the current stiffness coefficient with the unit of N/A;
to fLiquid, compositionAnd (3) carrying out linearization treatment when x is 0 to obtain:
fliquid, composition＝kxx
In the formula, kxIs the displacement stiffness coefficient with the unit of N/m;
when the single-degree-of-freedom magnetic-liquid double-suspension bearing system is under the action of an external load, the rotor returns to the central position again by changing electromagnetic force and static pressure, balance is achieved, and the effect that the resultant force of the electromagnetic force and the resultant force of the static pressure are equal is achieved:
Figure FDA0002366819970000061
kx1+kii＝kxx
the PID controller generates a control current i of:
Figure FDA0002366819970000062
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CN114165456B (en) * 2021-12-17 2022-10-28 浙江大学 Centrifugal pump based on magnetic-liquid double-suspension structure

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