CN111677806B - Method and system for determining damping force of magnetorheological shock absorber - Google Patents

Method and system for determining damping force of magnetorheological shock absorber Download PDF

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CN111677806B
CN111677806B CN202010342570.4A CN202010342570A CN111677806B CN 111677806 B CN111677806 B CN 111677806B CN 202010342570 A CN202010342570 A CN 202010342570A CN 111677806 B CN111677806 B CN 111677806B
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shock absorber
damping force
yield stress
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CN111677806A (en
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彭志召
危银涛
张进秋
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Tsinghua University
Academy of Armored Forces of PLA
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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
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F9/00—Springs, vibration-dampers, shock-absorbers, or similarly-constructed movement-dampers using a fluid or the equivalent as damping medium
    • F16F9/32—Details
    • F16F9/53—Means for adjusting damping characteristics by varying fluid viscosity, e.g. electromagnetically
    • F16F9/535—Magnetorheological [MR] fluid dampers
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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
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2224/00—Materials; Material properties
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Abstract

The invention relates to a method and a system for determining damping force of a magneto-rheological shock absorber. The method comprises the following steps: constructing a liquid flow mechanics analysis model, and obtaining the set structure size parameters of the magneto-rheological shock absorber; acquiring the viscosity of the magnetorheological fluid and the yield stress under the induction of a magnetic field; determining the area flow of the magnetorheological fluid according to the structural size parameter and the piston speed; determining the dimensionless yield stress according to the area flow; determining a fitted slope between the dimensionless yield stress and the dimensionless pressure gradient; determining the pressure difference in the induction channel according to the fitting slope and the gap length of the induction area; determining the pressure difference in the non-induction channel according to the viscosity, the structural parameters of the gap in the non-induction area and the area flow; determining the damping force of the magneto-rheological shock absorber according to the pressure difference in the induction channel and the pressure difference in the non-induction channel; the damping force of the magneto-rheological shock absorber is used for designing the magneto-rheological shock absorber. By adopting the determination method and the determination system, the estimation accuracy of the damping force can be improved.

Description

Method and system for determining damping force of magnetorheological shock absorber
Technical Field
The invention relates to the field of determining the damping force of a magneto-rheological shock absorber, in particular to a method and a system for determining the damping force of the magneto-rheological shock absorber.
Background
The vibration damper or damper is an indispensable component in a vibration damping system or a vibration isolation system. Once the damping force of the traditional shock absorber is designed and shaped, the damping force can not be adjusted along with the vibration condition of the system or the change of the excitation working condition, and the shock absorption system is difficult to keep stable performance under variable or random working conditions; the advanced vibration reduction system is provided with a vibration reducer with adjustable damping force so as to improve the vibration reduction performance of the system and improve the adaptability of the system to different working conditions. The magneto-rheological damper realizes damping force adjustment by utilizing viscosity change of magneto-rheological fluid under the induction of a magnetic field, is an ideal adjustable damping damper due to the advantages of quick response, good controllability, compact structure and the like, and has a very good application prospect in a damping system.
When designing the magneto-rheological shock absorber, the accurate estimation of the damping force is the key to ensure that the performance of the magneto-rheological shock absorber meets the design requirements, however, at present, when designing the magneto-rheological shock absorber, the estimation of the damping force is greatly simplified, for example, the relation between the dimensionless yield stress and the dimensionless pressure gradient when establishing a shock absorber mechanical model in the structural vibration control-active, semi-active and intelligent control document is simplified into P*＝1+3T*Or
Figure GDA0002897485970000011
Due to over simplification, larger calculation errors can be brought, larger errors are caused, and the estimation accuracy of the damping force is greatly reduced, so that the damping performance of the designed magnetorheological damper does not necessarily meet the design requirement.
Disclosure of Invention
The invention aims to provide a damping force determination method and a damping force determination system of a magneto-rheological shock absorber, and aims to solve the problem that the accuracy of damping force estimation of the existing damping force estimation method is low.
In order to achieve the purpose, the invention provides the following scheme:
a damping force determination method of a magnetorheological shock absorber comprises the following steps:
constructing a liquid flow mechanics analysis model, and obtaining the set structure size parameters of the magneto-rheological shock absorber; the set structural size parameters comprise the radius of the cylinder body, the radius of the piston rod, the gap height, the median radius of the damping gap, the gap length of the induction area, the gap length of the non-induction area and the number of turns of the coil; under the set structural size parameters, in a gap of the hydrodynamics analysis model, magnetorheological fluid flows at a one-dimensional laminar flow at a plane flow speed under the action of pressure difference;
estimating the magnetic field in the gap when the coil loads current by using a finite element method or a numerical method;
acquiring the viscosity and yield stress of the magnetorheological fluid under the magnetic field induction of the magnetic field;
determining the area flow of the magnetorheological fluid according to the radius of the cylinder body, the radius of the piston rod, the median radius of the damping gap and the piston speed;
determining a dimensionless yield stress according to the viscosity, the yield stress, the gap height and the area flow;
determining a fitted slope between the dimensionless yield stress and a dimensionless pressure gradient according to the dimensionless yield stress;
determining a differential pressure within a sensing channel based on the fitted slope, the viscosity, the yield stress, the sensing zone gap length, the gap height, the piston velocity, and the area flow;
determining the pressure difference in a non-induction channel according to the viscosity, the length of the gap in the non-induction area, the height of the gap and the area flow;
determining the damping force of the magneto-rheological shock absorber according to the pressure difference in the induction channel and the pressure difference in the non-induction channel; the damping force of the magneto-rheological shock absorber is used for designing the magneto-rheological shock absorber.
Optionally, the determining the area flow of the magnetorheological fluid according to the radius of the cylinder body, the radius of the piston rod, the median radius of the damping gap, and the piston speed specifically includes:
according to the formula
Figure GDA0002897485970000021
Determining the area flow of the magnetorheological fluid; wherein Q issIs the area flow of the magnetorheological fluid; a. thepIn order to be the effective area of the piston,
Figure GDA0002897485970000022
Rcis the radius in the cylinder body, RrIs the piston rod radius; rmThe median radius of the damping gap; vpIs the piston velocity.
Optionally, the determining a dimensionless yield stress according to the viscosity, the yield stress, the gap height, and the area flow specifically includes:
according to the formula
Figure GDA0002897485970000031
Determining a dimensionless yield stress; wherein, T*Is a dimensionless yield stress; tau is0Is the yield stress; h is the gap height; eta is viscosity.
Optionally, the determining a differential pressure in the sensing channel according to the fitting slope, the viscosity, the sensing area gap length, the gap height, the piston speed, the area flow, and the yield stress specifically includes:
according to the formula
Figure GDA0002897485970000032
Determining a pressure differential within the sensing channel; wherein,
Figure GDA0002897485970000033
sensing the pressure difference in the channel; l ismrIs the gap length of the induction area; k is the fitting slope.
Optionally, the determining the pressure difference in the non-inductive channel according to the viscosity, the length of the gap in the non-inductive area, the height of the gap, and the area flow specifically includes:
according to the formula
Figure GDA0002897485970000034
Determining a pressure differential within the non-sensing channel; wherein, Δ PelseIs the pressure difference in the non-inductive channel; l isfIs the length of the gap in the non-sensing area.
Optionally, the determining a damping force of the magnetorheological shock absorber according to the pressure difference in the sensing channel and the pressure difference in the non-sensing channel further includes:
acquiring an expected damping force;
judging whether the damping force of the magneto-rheological shock absorber is within the expected damping force range or not to obtain a first judgment result;
if the first judgment result shows that the damping force of the magneto-rheological shock absorber is within the range of the expected damping force, designing the magneto-rheological shock absorber according to the set structure size parameter;
and if the first judgment result shows that the damping force of the magneto-rheological shock absorber is not in the expected damping force range, adjusting the set structure size parameter.
A damping force determination system for a magnetorheological shock absorber, comprising:
the set structure size parameter acquisition module is used for constructing a fluid flow mechanics analysis model and acquiring set structure size parameters of the magneto-rheological shock absorber; the set structural size parameters comprise the radius of the cylinder body, the radius of the piston rod, the gap height, the median radius of the damping gap, the gap length of the induction area, the gap length of the non-induction area and the number of turns of the coil; under the set structural size parameters, in a gap of the hydrodynamics analysis model, magnetorheological fluid flows at a one-dimensional laminar flow at a plane flow speed under the action of pressure difference;
the magnetic field estimation module is used for estimating the magnetic field in the gap when the coil is loaded with current by using a finite element method or a numerical method;
the viscosity and yield stress acquisition module is used for acquiring the viscosity and yield stress of the magnetorheological fluid under the magnetic field induction of the magnetic field;
the area flow determining module is used for determining the area flow of the magnetorheological fluid according to the radius in the cylinder body, the radius of the piston rod, the median radius of the damping gap and the piston speed;
a dimensionless yield stress determination module for determining a dimensionless yield stress according to the viscosity, the yield stress, the gap height, and the area flow;
the fitting slope determining module is used for determining the fitting slope between the dimensionless yield stress and the dimensionless pressure gradient according to the dimensionless yield stress;
a differential pressure determination module in the sensing channel for determining a differential pressure in the sensing channel according to the fitting slope, the viscosity, the sensing zone gap length, the gap height, the piston velocity, the area flow and the yield stress; the pressure difference determining module in the non-induction channel is used for determining the pressure difference in the non-induction channel according to the viscosity, the length of the gap in the non-induction area, the height of the gap and the area flow;
the damping force determining module is used for determining the damping force of the magneto-rheological shock absorber according to the pressure difference in the induction channel and the pressure difference in the non-induction channel; the damping force of the magneto-rheological shock absorber is used for designing the magneto-rheological shock absorber.
Optionally, the area flow determining module specifically includes:
an area flow rate determining unit for determining the flow rate according to the formula
Figure GDA0002897485970000041
Determining the area flow of the magnetorheological fluid; wherein Q issIs the area flow of the magnetorheological fluid; a. thepIn order to be the effective area of the piston,
Figure GDA0002897485970000042
Rcis the radius in the cylinder body, RrIs the piston rod radius; rmThe median radius of the damping gap; vpIs the piston velocity.
Optionally, the non-dimensional yield stress determining module specifically includes:
a dimensionless yield stress determining unit for determining the yield stress according to a formula
Figure GDA0002897485970000043
Determining a dimensionless yield stress; wherein, T*Is a dimensionless yield stress; tau is0Is the yield stress; h is the gap height; eta is viscosity.
Optionally, the pressure difference determining module in the sensing channel specifically includes:
in the induction channelA differential pressure determining unit for determining the differential pressure according to the formula
Figure GDA0002897485970000051
Figure GDA0002897485970000052
Determining a pressure differential within the sensing channel; wherein,
Figure GDA0002897485970000053
sensing the pressure difference in the channel; l ismrIs the gap length of the sensing area.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a method and a system for determining damping force of a magnetorheological damper, which focus on the damping force generated when magnetorheological fluid flows through a damping gap, and do not set the fitting slope as a fixed value by introducing the fitting slope between dimensionless yield stress and dimensionless pressure gradient, but change the fitting slope based on the dimensionless yield stress, thereby improving the fitting precision, reducing the calculation error of the damping force and improving the estimation accuracy of the damping force.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic view of a hydrodynamics analysis model provided by the present invention;
FIG. 2 is a flow chart of a method for determining a damping force of a magnetorheological shock absorber according to the present invention;
FIG. 3 is a graph of the velocity and shear stress of a Bingham fluid between parallel plates;
FIG. 4 is a graph of the relationship between dimensionless yield stress T and dimensionless pressure gradient P;
FIG. 5 is a schematic view of a magnetorheological damper;
FIG. 6 is a graph of damping force as a function of piston velocity;
FIG. 7 is a graph of T vs. P for different piston speeds;
FIG. 8 is a graph of K as a function of piston speed;
FIG. 9 is a schematic diagram of the variation law of damping force with piston displacement;
FIG. 10 is a block diagram of a damping force determination system for a magnetorheological shock absorber in accordance with the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for determining a damping force of a magneto-rheological shock absorber, which can improve the estimation accuracy of the damping force.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The damping channel of the magneto-rheological shock absorber is generally an annular gap, the height of the gap is far smaller than the diameter of the gap, the annular gap can be approximated to a parallel flat plate model, and the perimeter of the gap is calculated by the middle diameter of the annular gap to serve as the width of the parallel flat plate.
Taking a infinitesimal parallel to the liquid flow direction in a gap of a parallel plate model, fig. 1 is a schematic diagram of a liquid flow mechanics analysis model provided by the invention, as shown in fig. 1.
Fig. 2 is a flowchart of a method for determining a damping force of a magnetorheological shock absorber, and as shown in fig. 2, the method for determining a damping force of a magnetorheological shock absorber includes:
step 201: constructing a liquid flow mechanics analysis model, and obtaining the set structure size parameters of the magneto-rheological shock absorber; the set structural size parameters comprise the radius of the cylinder body, the radius of the piston rod, the gap height, the median radius of the damping gap, the gap length of the induction area, the gap length of the non-induction area and the number of turns of the coil; and under the set structural size parameters, in the gap of the hydrodynamics analysis model, the magnetorheological fluid flows in one-dimensional laminar flow at a plane flow speed under the action of pressure difference.
Step 202: estimating the magnetic field in the gap when the coil loads current by using a finite element method or a numerical method;
step 203: acquiring the viscosity and yield stress of the magnetorheological fluid under the magnetic field induction of the magnetic field;
step 204: determining the area flow of the magnetorheological fluid according to the radius of the cylinder body, the radius of the piston rod, the median radius of the damping gap and the piston speed;
the step 204 specifically includes: according to the formula
Figure GDA0002897485970000061
Determining the area flow of the magnetorheological fluid; wherein Q issIs the area flow of the magnetorheological fluid; a. thepIn order to be the effective area of the piston,
Figure GDA0002897485970000071
Rcis the radius in the cylinder body, RrIs the piston rod radius; rmThe median radius of the damping gap; vpIs the piston velocity.
Step 205: determining a dimensionless yield stress according to the viscosity, the yield stress, the gap height and the area flow;
the step 205 specifically includes: according to the formula
Figure GDA0002897485970000072
Determining a dimensionless yield stress; wherein, T*Is a dimensionless yield stress; tau is0Is the yield stress; h is the gap height; eta is viscosity.
Step 206: determining a fitted slope between the dimensionless yield stress and a dimensionless pressure gradient according to the dimensionless yield stress;
step 207: determining a differential pressure within a sense channel based on the fit slope, the viscosity, the sense zone gap length, the gap height, the piston velocity, the area flow, and the yield stress;
step 207 specifically includes: according to the formula
Figure GDA0002897485970000073
Figure GDA0002897485970000074
Determining a pressure differential within the sensing channel; wherein,
Figure GDA0002897485970000075
sensing the pressure difference in the channel; l ismrIs the gap length of the induction area; k is the fitting slope.
Step 208: determining the pressure difference in a non-induction channel according to the viscosity, the length of the gap in the non-induction area, the height of the gap and the area flow;
the step 208 specifically includes: according to the formula
Figure GDA0002897485970000076
Determining a pressure differential within the non-sensing channel; wherein, Δ PelseIs the pressure difference in the non-inductive channel; l isfIs the length of the gap in the non-sensing area.
Step 209: determining the damping force of the magneto-rheological shock absorber according to the pressure difference in the induction channel and the pressure difference in the non-induction channel; the damping force of the magneto-rheological shock absorber is used for designing the magneto-rheological shock absorber.
Said step 209 further comprises, after: acquiring an expected damping force range; judging whether the damping force of the magneto-rheological shock absorber is within the expected damping force range, if so, designing the magneto-rheological shock absorber according to the set structure size parameter; if not, adjusting the set structure size parameter.
The method for determining the damping force of the magnetorheological shock absorber is applied to the actual application, a fluid flow mechanics analysis model is adopted, and according to the symmetry, the magnetorheological fluid can be assumed to flow at a plane speed Q in a gap under the action of a pressure difference dpsWhen z is more than or equal to 0, the relation between the pressure gradient of the magnetorheological fluid along the direction parallel to the flat plate and the shear stress is as follows:
Figure GDA0002897485970000081
since the flow of the fluid is symmetrical along the middle symmetry plane of the parallel plates, the boundary conditions can be obtained: when z is 0, τ is 0, the formula (1) is integrated, and from this condition, the condition can be obtained
Figure GDA0002897485970000082
When the pressure difference across the flat plate is not sufficient to yield the magnetorheological fluid, the magnetorheological fluid does not flow. The critical pressure gradient for the magnetorheological fluid to start flowing is:
Figure GDA0002897485970000083
since shear stress is greatest near the wall, when the pressure gradient is greater than or equal to this threshold, the fluid near the wall yields first and begins to flow. And a part of the fluid near the central symmetry plane of the gap is subjected to a shearing stress smaller than the shearing yield stress of the magnetorheological fluid, and the velocity gradient in the part of the fluid is zero, so that the part of the fluid is similar to a piston which moves in the gap in parallel. From equation (3), the thickness of the "piston" is:
Figure GDA0002897485970000084
from equation (4), the thickness of this unyielding "piston" depends on the shear yield strength of the fluid and the pressure gradient within the plate.
From the symmetry, consider h firstcWhen z is more than or equal to 2 and less than or equal to h/2, the following formulas (2) and
Figure GDA0002897485970000085
substitution type Bingham model
Figure GDA0002897485970000091
Can obtain the product
Figure GDA0002897485970000092
Equation (6) is integrated and based on the boundary conditions:
Figure GDA0002897485970000093
when u is 0, there are
Figure GDA0002897485970000094
When z is more than or equal to 0 and less than or equal to hcAt/2, the flow rate of MRF is equal everywhere and equal to the flow rate of fluid hcFlow rate at/2. According to the symmetry, the flow velocity of each point of the comprehensively-obtained cross section is as follows:
Figure GDA0002897485970000095
the flow rate of the magnetorheological fluid between the two plates and the shear stress distribution within the fluid are shown in fig. 3. Integrating the section velocity distribution curve along the z-axis to obtain the area flow of the fluid:
Figure GDA0002897485970000096
is deformed into
Figure GDA0002897485970000097
Calculated from the structural parameters and the piston velocity, the area flow
Figure GDA0002897485970000098
ApIn order to be the effective area of the piston,
Figure GDA0002897485970000099
Rcis the radius in the cylinder body, RrIs the piston rod radius; rmThe median radius of the damping gap; vpIs the piston velocity.
Let τ be0The above formula (10) is simplified to a pressure gradient calculation formula of newtonian fluid as 0
Figure GDA0002897485970000101
The zero field viscosity of the magnetorheological fluid can be tested by using the formula.
The formula (10) is dimensionless and can be obtained by arranging:
Figure GDA0002897485970000102
in the formula, P*、T*Dimensionless pressure gradient and dimensionless yield stress:
Figure GDA0002897485970000103
for the convenience of calculation, the existing document structural vibration control-active, semi-active and intelligent control simplifies the formula (12) into P when establishing a mechanical model of the shock absorber*＝1+3T*Or
Figure GDA0002897485970000104
Figure GDA0002897485970000105
Large calculation errors are introduced.
In the present invention, formula (12) is a standard Cardan equation with T as a variable, and
Figure GDA0002897485970000106
formula (12) is changed to
T*3+aT*+b＝0 (14)
This equation can be solved by trigonometric transformation:
4cos3θ-3cosθ-cos3θ≡0 (15)
order to
T*＝mcosθ (16)
Then
m3cos3θ+amcosθ+b≡4cos3θ-3cosθ-cos3θ (17)
Thus, it is possible to provide
Figure GDA0002897485970000107
Then:
Figure GDA0002897485970000108
from the formula (16):
Figure GDA0002897485970000111
in the formula (4), hcH, available:
Figure GDA0002897485970000112
the physical significance of which is the minimum pressure gradient required to cause the magnetorheological fluid to flow between the parallel plates. Thus, the
Figure GDA0002897485970000113
Therefore, it is not only easy to use
Figure GDA0002897485970000114
Thereby to obtain
Figure GDA0002897485970000115
The cosine function is monotonous over this interval. Thus T*Can be represented by P*To show that:
Figure GDA0002897485970000116
this formula establishes T*In respect of P*The analytical expression of (2). However, what needs to be established when estimating the damping force of the shock absorber is P*About T*And (3) an analytical expression of (c), i.e. an inverse function of the above equation, to find the differential pressure of the damping gap.
Transforming the formula (12) into
P*3-(1+3T*)P*2+4T*3＝0 (23)
Replacing variables:
P*＝x-λ (24)
substituting formula (23) to make the quadratic term coefficient zero, can obtain
Figure GDA0002897485970000117
Then, equation (23) becomes:
Figure GDA0002897485970000118
order to
Figure GDA0002897485970000121
The above equation can be written as a standard form of the Cardan equation:
x3+Ax+B＝0 (27)
still adopting the method of three times of constant angle cosine formula to make
Figure GDA0002897485970000122
Then
Figure GDA0002897485970000123
Thus, it is possible to provide
Figure GDA0002897485970000124
As a result of this, the number of the,
Figure GDA0002897485970000125
Figure GDA0002897485970000126
therefore, the temperature of the molten metal is controlled,
Figure GDA0002897485970000127
namely, it is
Figure GDA0002897485970000128
From the formulae (24), (25), (28):
Figure GDA0002897485970000129
thus, P*The algebraic solution of (a) may be:
Figure GDA00028974859700001210
(n＝0)
Figure GDA00028974859700001211
(n is 1) and has a positive sign
Figure GDA0002897485970000131
(n is 1) and has a negative sign
However, from the point of view of the correlation between the pressure difference and the yield strength of the magnetorheological fluid, P*And T*Is a one-to-one correspondence relationship, but cannot be determined only from an algebraic relationship
Figure GDA0002897485970000132
Which is the true solution.
Since the formula (22) is T obtained under strict algebraic constraints*In respect of P*Can thus be used to verify P*About T*The solution of (1). Taking a specific magnetorheological damping gap as an example, the relevant parameters are as follows: gap height h is 1.0mm, area flow Qs is 0.0013m2The viscosity eta of the magnetorheological fluid is 0.3Pa.s, and the yield strength tau0∈[0，100]kPa, the parameter is substituted for the formula (1-13b) to calculate T*Then substituted into P*Three algebraic solutions of
Figure GDA0002897485970000133
Then substituting the formula (22) to obtain
Figure GDA0002897485970000134
Verified to be only
Figure GDA0002897485970000135
Thus determining
Figure GDA0002897485970000136
Is a correct solution.
In addition, let τ0When the value is 0, then T *0, in
Figure GDA0002897485970000137
To obtain
Figure GDA0002897485970000138
Figure GDA0002897485970000139
Tau is shown by the formulas (11) and (13a)0When the content is equal to 0, the content,
Figure GDA00028974859700001310
for reasonable values, can also be determined
Figure GDA00028974859700001311
Is a correct solution.
Thus, the
Figure GDA00028974859700001312
From this formula, it is found that limP when T → 0*＝1+3T*(ii) a When the temperature is T → ∞ times,
Figure GDA00028974859700001313
a general formula (35) and P*＝1+3T*Plotted in fig. 4, from the general trend, the theoretical value is better in linearity, but as T increases, P is used*＝1+3T*The accuracy of the fit gradually deteriorates. From the previous analysis, T*When equal to 0, P*Therefore, it is reasonable to fit equation (35) to 1:
P*＝1+KT* (36)
as can be seen in FIG. 4, with T*The slope K of the fitting straight line changes with the value of T in order to improve the fitting accuracy and reduce the error:
Figure GDA0002897485970000141
for a length LmrThe magnetic field induced gap of (1) and (35) can obtain the pressure difference delta P between two ends of the gapmrComprises the following steps:
Figure GDA0002897485970000142
as can be seen from equations (13) and (36), equation (38) can be simplified as:
Figure GDA0002897485970000143
since in the derivation process, T is used*≥0、P*≥0、QsThe condition is assumed to be ≧ 0, and attention should be paid to the application of the above formula. When it is necessary to consider the positive and negative values of the piston velocity direction, for example, when drawing a schematic diagram, the tensile force is generally positive and the compression force is generally negative, and equations (38) and (39) need to be corrected as follows:
Figure GDA0002897485970000144
Figure GDA0002897485970000151
the theoretical value and the estimated value of the damping force of the shock absorber are respectively as follows:
Fd＝(ΔPmr+ΔPelse)Ap (42)
Figure GDA0002897485970000152
in the formula,. DELTA.PelseIs the pressure difference caused by other damping passages and flow channels, ApIs the effective area of the piston.
The calculation process of the damping force is described by taking the schematic diagram of the magnetorheological shock absorber shown in fig. 5 as an example. Radius R in cylinder bodyc25mm, piston dampingMedian radius R of the gapm21.5mm, gap height h 1mm, piston rod radius RrTotal length L of the sensing zone in the damping gap, 8mmmr＝L1+L2Length L of non-sensing area f15 mm. Effective area of piston
Figure GDA0002897485970000153
Figure GDA0002897485970000154
Piston velocity Vp. The viscosity eta of the magnetorheological fluid is 0.3Pa.s, and when the coil is loaded with 3A current, the yield strength tau of the magnetorheological fluid in the gap under the induction of a magnetic field 030 kPa. Damping gap cross section area flow
Figure GDA0002897485970000155
Dimensionless yield stress
Figure GDA0002897485970000156
The theoretical value Δ P of the differential pressure in the sensing area can be calculated according to equation (38)mrAn estimate of the differential pressure in the sensing region can be calculated according to equation (39)
Figure GDA0002897485970000157
Damping gap non-inductive zone pressure difference
Figure GDA0002897485970000158
Finally, theoretical and estimated values of the damping force are calculated from equations (40), (41), respectively. FIG. 6 is piston velocity VpDamping forces of 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6m/s, respectively. Visible P*＝1+3T*The result of the simplified calculation is greatly different from the theoretical value, and the P of the invention is used*＝1+KT*The accuracy of the estimation is high. At VpAt 0.05m/s, the theoretical value of the damping force is 2558N, using P*＝1+3T*The simplified calculation result is 3317N (error is 29.67%), and P is obtained by the present invention*＝1+KT*2572N (error only 0.55%) of the estimate was made; at Vp＝06m/s, the theoretical value of the damping force is 4591N with P*＝1+3T*The result of the simplified calculation was 4911N (error: 7%), P according to the invention*＝1+KT*The estimated 4592N (error almost 0) is performed. As can be seen from FIG. 7, T*And P*All decrease with increasing piston speed, with the invention P*＝1+KT*Calculated P*Has better consistency with the theoretical value, and uses P*＝1+3T*Calculated P*The difference from the theoretical value becomes larger as the piston speed decreases, because with P*＝1+KT*To P*When fitting to the theoretical value of (c) in (see fig. 8), the lower the piston speed, the farther K is from K3 (the closer K is to 2), and P is used*＝1+3T*The larger the error caused by the estimation.
FIG. 9 is a graphical representation of the damping force versus piston displacement for analyzing the energy dissipation performance of the shock absorber. Taking a vehicle suspension shock absorber as an example, the working diagram is a 'damping force-displacement' diagram under sinusoidal displacement excitation with the frequency of 1.67Hz and the amplitude of +/-50 mm. Under this excitation, the piston velocity Vp＝2π×1.67×0.05×cos(2π×1.67×t)。
Area flow Q in damping gap when shock absorber piston movessIs variable, resulting in T*And the variation is carried out, so that if the whole working diagram of the shock absorber needs to be accurately estimated, the working diagram needs to be drawn along with the piston speed Vp(or displacement S) to calculate | T*And further the value of K is changed according to equation (37). When estimating the damping force in designing the magnetorheological shock absorber, attention is often paid to the damping force when the piston speed is maximum (displacement S is 0), and therefore, T when the piston speed is maximum (displacement S is 0) can be calculated*Then, the corresponding K value is obtained by the formula (36), the K value is kept constant, and the formula (43) is replaced to calculate the estimated value of the pressure difference of the sensing area
Figure GDA0002897485970000161
Damping gap non-inductive zone pressure difference
Figure GDA0002897485970000162
Finally, the damping force is estimated from equation (43)
Figure GDA0002897485970000163
Plotting the theoretical value (. DELTA.P)mrCalculated by equation (40), P*＝1+KT*(including K varying with the shift S, for only two cases where S is 0), P*＝1+3T*The schematic diagram in four cases is shown in fig. 9. It can be seen that with the process P of the invention*＝1+KT*(K is taken as a value according to equation (37) with the change of the displacement S) the estimated damping force is very consistent with a theoretical value. When S is 0, piston velocity Vp＝2π×1.67×0.05＝0.525m/s，T*When K is 2.67 from equation (37) and K is 2.22, the damping force at the other values of S is estimated from equations (39) and (43) with the K value kept constant, and it is seen that only a small error exists at both ends of the schematic diagram as shown by the dotted line in fig. 9. And with P*＝1+3T*The estimated damping force has large errors on the whole work drawing, and the accuracy of the estimation of the damping force can be influenced when the shock absorber is designed.
Fig. 10 is a structural view of a damping force determining system of a magnetorheological shock absorber provided in accordance with the present invention, and as shown in fig. 10, a damping force determining system of a magnetorheological shock absorber comprises:
a set structure size parameter obtaining module 1001 for constructing a fluid flow mechanics analysis model and obtaining set structure size parameters of the magneto-rheological shock absorber; the set structural size parameters comprise the radius of the cylinder body, the radius of the piston rod, the gap height, the median radius of the damping gap, the gap length of the induction area, the gap length of the non-induction area and the number of turns of the coil; and under the set structural size parameters, in the gap of the hydrodynamics analysis model, the magnetorheological fluid flows in one-dimensional laminar flow at a plane flow speed under the action of pressure difference.
And a magnetic field estimation module 1002, configured to estimate a magnetic field in the gap when the coil is loaded with current by using a finite element method or a numerical method.
A viscosity and yield stress obtaining module 1003, configured to obtain the viscosity and yield stress of the magnetorheological fluid under the magnetic field induction of the magnetic field.
The area flow determining module 1004 is configured to determine an area flow of the magnetorheological fluid according to the radius of the cylinder, the radius of the piston rod, the median radius of the damping gap, and the piston speed.
The area flow determining module 1004 specifically includes: an area flow rate determining unit for determining the flow rate according to the formula
Figure GDA0002897485970000171
Determining the area flow of the magnetorheological fluid; wherein Q issIs the area flow of the magnetorheological fluid; a. thepIn order to be the effective area of the piston,
Figure GDA0002897485970000172
Rcis the radius in the cylinder body, RrIs the piston rod radius; rmThe median radius of the damping gap; vpIs the piston velocity.
A dimensionless yield stress determining module 1005 configured to determine a dimensionless yield stress according to the viscosity, the yield stress, the gap height, and the area flow.
The non-dimensional yield stress determination module 1005 specifically includes: a dimensionless yield stress determining unit for determining the yield stress according to a formula
Figure GDA0002897485970000181
Determining a dimensionless yield stress; wherein, T*Is a dimensionless yield stress; tau is0Is the yield stress; h is the gap height; eta is viscosity.
A fitting slope determination module 1006, configured to determine a fitting slope between the dimensionless yield stress and the dimensionless pressure gradient according to the dimensionless yield stress.
And a pressure difference determining module 1007 in the sensing channel, configured to determine a pressure difference in the sensing channel according to the fitting slope, the viscosity, the sensing zone gap length, the gap height, the piston velocity, the area flow, and the yield stress.
Pressure differential determination module 10 in the sensing channel07 specifically includes: a pressure difference determining unit in the sensing passage for determining the pressure difference according to the formula
Figure GDA0002897485970000182
Determining a pressure differential within the sensing channel; wherein,
Figure GDA0002897485970000183
sensing the pressure difference in the channel; l ismrIs the gap length of the sensing area.
And a pressure difference determining module 1008 in the non-sensing channel, configured to determine a pressure difference in the non-sensing channel according to the viscosity, the gap length of the non-sensing area, the gap height, and the area flow.
A damping force determining module 1009, configured to determine a damping force of the magnetorheological shock absorber according to the pressure difference in the sensing channel and the pressure difference in the non-sensing channel; the damping force of the magneto-rheological shock absorber is used for designing the magneto-rheological shock absorber.
Compared with the existing damping force estimation method of the magnetorheological shock absorber, the method provided by the invention not only provides a theoretical calculation method, but also provides a simple estimation method with very high accuracy, and provides a means and a method for designing the magnetorheological shock absorber meeting the requirements.
The method is not only used for designing the magnetorheological damper, and the damping force modeling of the device with the constitutive equation the same as that of the device with the formula (5) and the fluid flowing through the damping channel, such as the magnetorheological valve, the electrorheological damper/damper or the valve, can adopt the method.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A method for determining a damping force of a magnetorheological shock absorber, comprising:
constructing a liquid flow mechanics analysis model, and obtaining the set structure size parameters of the magneto-rheological shock absorber; the set structural size parameters comprise the radius of the cylinder body, the radius of the piston rod, the gap height, the median radius of the damping gap, the gap length of the induction area, the gap length of the non-induction area and the number of turns of the coil; under the set structural size parameters, in a gap of the hydrodynamics analysis model, magnetorheological fluid flows at a one-dimensional laminar flow at a plane flow speed under the action of pressure difference;
estimating the magnetic field in the gap when the coil loads current by using a finite element method or a numerical method;
acquiring the viscosity and yield stress of the magnetorheological fluid under the magnetic field induction of the magnetic field;
determining the area flow of the magnetorheological fluid according to the radius of the cylinder body, the radius of the piston rod, the median radius of the damping gap and the piston speed;
determining a dimensionless yield stress according to the viscosity, the yield stress, the gap height and the area flow;
determining a fitted slope between the dimensionless yield stress and a dimensionless pressure gradient according to the dimensionless yield stress;
determining a differential pressure within a sensing channel based on the fitted slope, the viscosity, the yield stress, the sensing zone gap length, the gap height, the piston velocity, and the area flow;
determining the pressure difference in a non-induction channel according to the viscosity, the length of the gap in the non-induction area, the height of the gap and the area flow;
determining the damping force of the magneto-rheological shock absorber according to the pressure difference in the induction channel and the pressure difference in the non-induction channel; the damping force of the magneto-rheological shock absorber is used for designing the magneto-rheological shock absorber.
2. The method for determining the damping force of a magnetorheological shock absorber according to claim 1, wherein the determining the area flow of the magnetorheological fluid according to the radius of the cylinder body, the radius of the piston rod, the median radius of the damping gap and the piston velocity specifically comprises:
according to the formula
Figure FDA0002897485960000011
Determining the area flow of the magnetorheological fluid; wherein Q issIs the area flow of the magnetorheological fluid; a. thepIn order to be the effective area of the piston,
Figure FDA0002897485960000012
Rcis the radius in the cylinder body, RrIs the piston rod radius; rmThe median radius of the damping gap; vpIs the piston velocity.
3. The method for determining the damping force of a magnetorheological shock absorber according to claim 2, wherein the determining the dimensionless yield stress according to the viscosity, the yield stress, the gap height and the area flow specifically comprises:
according to the formula
Figure FDA0002897485960000021
Determining a dimensionless yield stress; wherein, T*Is a dimensionless yield stress; tau is0Is the yield stress; h is the gap height; eta is viscosity.
4. The method for determining damping force of a magnetorheological shock absorber according to claim 3, wherein determining the pressure differential in the sensing channel based on the fit slope, the viscosity, the sensing zone gap length, the gap height, the piston velocity, the area flow, and the yield stress comprises:
according to the formula
Figure FDA0002897485960000022
Determining a pressure differential within the sensing channel; wherein,
Figure FDA0002897485960000023
sensing the pressure difference in the channel; l ismrIs the gap length of the induction area; k is the fitting slope.
5. The method for determining the damping force of the magnetorheological shock absorber according to claim 4, wherein the determining the pressure difference in the non-inductive passage according to the viscosity, the gap length of the non-inductive region, the gap height and the area flow specifically comprises:
according to the formula
Figure FDA0002897485960000024
Determining a pressure differential within the non-sensing channel; wherein, Δ PelseIs the pressure difference in the non-inductive channel; l isfIs the length of the gap in the non-sensing area.
6. The method for determining the damping force of a magnetorheological shock absorber according to any one of claims 1 to 5, wherein the determining the damping force of the magnetorheological shock absorber is based on the pressure difference in the sensing channel and the pressure difference in the non-sensing channel, and then further comprising:
acquiring an expected damping force;
judging whether the damping force of the magneto-rheological shock absorber is within the expected damping force range or not to obtain a first judgment result;
if the first judgment result shows that the damping force of the magneto-rheological shock absorber is within the expected damping force range, designing the magneto-rheological shock absorber according to the set structure size parameter;
and if the first judgment result shows that the damping force of the magneto-rheological shock absorber is not in the expected damping force range, adjusting the set structure size parameter.
7. A damping force determination system for a magnetorheological shock absorber, comprising:
the set structure size parameter acquisition module is used for constructing a fluid flow mechanics analysis model and acquiring set structure size parameters of the magneto-rheological shock absorber; the set structural size parameters comprise the radius of the cylinder body, the radius of the piston rod, the gap height, the median radius of the damping gap, the gap length of the induction area, the gap length of the non-induction area and the number of turns of the coil; under the set structural size parameters, in a gap of the hydrodynamics analysis model, magnetorheological fluid flows at a one-dimensional laminar flow at a plane flow speed under the action of pressure difference;
the magnetic field estimation module is used for estimating the magnetic field in the gap when the coil is loaded with current by using a finite element method or a numerical method;
the viscosity and yield stress acquisition module is used for acquiring the viscosity and yield stress of the magnetorheological fluid under the magnetic field induction of the magnetic field;
the area flow determining module is used for determining the area flow of the magnetorheological fluid according to the radius in the cylinder body, the radius of the piston rod, the median radius of the damping gap and the piston speed;
a dimensionless yield stress determination module for determining a dimensionless yield stress according to the viscosity, the yield stress, the gap height, and the area flow;
the fitting slope determining module is used for determining the fitting slope between the dimensionless yield stress and the dimensionless pressure gradient according to the dimensionless yield stress;
a differential pressure determination module in the sensing channel for determining a differential pressure in the sensing channel according to the fitting slope, the viscosity, the sensing zone gap length, the gap height, the piston velocity, the area flow and the yield stress;
the pressure difference determining module in the non-induction channel is used for determining the pressure difference in the non-induction channel according to the viscosity, the length of the gap in the non-induction area, the height of the gap and the area flow;
the damping force determining module is used for determining the damping force of the magneto-rheological shock absorber according to the pressure difference in the induction channel and the pressure difference in the non-induction channel; the damping force of the magneto-rheological shock absorber is used for designing the magneto-rheological shock absorber.
8. The system for determining the damping force of a magnetorheological shock absorber of claim 7, wherein the area flow determination module comprises:
an area flow rate determining unit for determining the flow rate according to the formula
Figure FDA0002897485960000041
Determining the area flow of the magnetorheological fluid; wherein Q issIs the area flow of the magnetorheological fluid; a. thepIn order to be the effective area of the piston,
Figure FDA0002897485960000042
Rcis the radius in the cylinder body, RrIs the piston rod radius; rmThe median radius of the damping gap; vpIs the piston velocity.
9. The system for determining damping force of a magnetorheological shock absorber of claim 8, wherein the non-dimensional yield stress determining module comprises:
a dimensionless yield stress determining unit for determining the yield stress according to a formula
Figure FDA0002897485960000043
Determining a dimensionless yield stress; wherein, T*Is a dimensionless yield stress; tau is0Is the yield stress; h is the gap height; eta is viscosity.
10. The system for determining damping force of a magnetorheological shock absorber of claim 9, wherein the pressure differential determining module in the sensing channel comprises:
a pressure difference determining unit in the sensing passage for determining the pressure difference according to the formula
Figure FDA0002897485960000044
Figure FDA0002897485960000045
Determining a pressure differential within the sensing channel; wherein,
Figure FDA0002897485960000046
sensing the pressure difference in the channel; l ismrIs the gap length of the induction area; k is the fitting slope.
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