A Method to Simulate the MR Fluid in ANSYS

ZHANG Zheng-xin1,LIU Qian-hui2,HUANG Fang-lin1 (1.School of Civil Engineering,Central South University,Changsha 410075,China; 2.Vocational Technical

College,Guizhou University,Guiyang 550001,China)  The magnetorheological fluid(MRF) is consistent with the mechanical properties of

Newtonian fluid when no external magnetic field is present,at this time it can be modeled using

FLUID142 in ANSYS.However,when exposed to a magnetic field,the MRF is also showing

some solid-like characteristics,at present,there is no exactly appropriate element type in ANSYS

to model MRF.This paper presents a method to simulate the mechanical behavior of

magnetorheological fluid subjected to magnetic field in the pre-yield region in ANSYS.The main

idea is devide an MRF element into two coincident elements,one of them has density and

viscosity without shear modulus while another has shear modulus without density and

viscosity.Take a simply supported MRF sandwich beam as an example,comparing the results

with the theoretical analysis and experimental study of Ref.[1],this method can obtain good

results and reasonable conclusion,verified the validity of finite element analysis in this

paper.This kind of method which can be called Coincident Elements Method provides a new way

to model the structures with MRF or MR dampers in ANSYS,and it also has some inspiration for

the future development of related elements in ANSYS.

【Key Words】： magnetorheological fluid yield stress viscosity complex shear modulus

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OPTIMIZATION OF MAGNETO-RHEOLOGICAL DAMPER

Done by

S.DINESH KUMAR (3rd year)

email: sdkmit@gmail.com

contact no:+91 9894999261

S.SHANMUGARAJ (3rd year)

email : shanmu36@gmail.com

contact no: +91 9994410105

DEPARTMENT OF PRODUCTION TECHNOLOGY,

MADRAS INSTITUTE OF TECHNOLOGY

ANNA UNIVERSITY

ABSTRACT:

Magnetorheological Fluid Dampers (MR damper) have provided technology that has enabled

effective semi-active control in a number of real world applications like vibration isolation of

systems etc.

This paper throws light on the design optimization of a high-efficiency magnetorheological

(MR) damper based on the non-dimensional damping coefficients for various damper

geometries to reduce the vibrations in the tool. The MR damper is composed of a core, a wound

coil, and a cylinder-shaped flux return. The core and flux return form the annulus through which

the MR fluid flows. The MR damper was constrained within a cylindrical volume of fixed height

and diameter. Within this volume, candidate geometries were constructed on the basis of the

number of wire coils desired in the valve. These candidate geometries were imported into an

ANSYS magnetic finite element analysis (FEA) routine and the magnetic flux densities

through the MR damper was calculated. We have fabricated and found experimentally that the

magnitude of the vibration has been reduced by 30% than the existing damper.

KEYPOINTS:DAMPING, DESIGN OPTIMIZATION, FINITE ELEMENT ANALYSIS,MR-

DAMPER

CONTROLLABLE FLUID:

Smart fluids are such that they have a low viscosity in the absence of an influencing field, but

become quasi-solid with the application of such a field.

There are two types of controllable fluids.

Magneto rheological fluids (MR fluids).

Electro rheological fluids (ER fluids).

ADVANTAGES OF MR FLUIDS OVER ER FLUIDS:

1. YIELD STRESS:

MR fluids have a yield stress an order of magnitude greater than their ER counterpart

ER fluids yield stress= 2-5 kPa,

MR fluids yield stress =50-100 kPa

2. POWER:

ER and MR fluid devices have similar power requirements of ~ 50 watts. But the voltage and

current requirements for ER fluids and MR fluids are;

ER fluids

Voltage = 2000–5000 Volts

Current = 1–10 m Amps

MR fluids

Voltage = 12–24 Volts

Current = 1–2 Amps.

3. STABILITY:

ER fluids are highly sensitive to contaminants or impurities. Contaminants have little effect on

the MR fluids.

WORKING PRINCIPLE OF MR FLUID:

The magnetic particles contained within the carrier oil are distributed randomly in suspension

under normal circumstances, as in figure 1.1

FIGURE 1.1 MR FLUIDS SHOWING MAGNETIC PARTICLES.

FIGURE 1.2 ALIGNMENTS OF MAGNETIC PARTICLES

When a magnetic field is applied, however, the microscopic particles align themselves along the

lines of magnetic flux, see figure 1.2. When the fluid is contained between two poles, the

resulting chains of particles restrict the movement of the fluid, perpendicular to the direction of

flux, effectively increasing its viscosity.This yield stress is dependent on the magnetic field

applied to the fluid, but will reach a maximum point after which increases in magnetic flux

density have no further effect, as the fluid is then magnetically saturated. MR fluids are also

known to be subject to shear thinning, whereby the viscosity above yield decreases with

increased shear rate.

TYPES OF MR FLUIDS:

Three types of MR fluids manufactured by the LORD Corporation are now commercially

available. MRF- 132LD (oil based), MRF- 240BS (water based) and MRF- 336AG (silicon oil

based). Since the flash point of MRF- 336AG is high (200°C.) we have chosen it for our

optimization process.

INTRODUCTION TO MAGNETORHEOLOGICAL DAMPER:

Magnetorheological Fluid Dampers (MR damper) have provided technology that has enabled

effective semi-active control in a number of real world applications like vibration isolation of

systems under harmonic loading, civil structural vibration reduction, vibration control in washing

machines, and automobiles. MR fluid dampers are similar to conventional viscous dampers

except that the viscous fluid viscosity is controlled by an applied magnetic field.

APPLICATIONS OF MR DAMPER:

o In Skyscrapers and long bridges susceptible to resonance created by high winds

and seismic activity in order to mitigate the resonance effect.

o Dampers are used in machines that are likely in use every day, including car

suspension systems and clothes washing machines.

o A damping system in a building is much larger and is also designed to absorb the

violent shocks of an earthquake.

INTRODUCTION DESIGN OPTIMIZATION OF MR DAMPER:

The design optimization of magnetorheological damper is carried out using a constrained volume

cylindrical geometry with fixed height and diameter. An optimization methodology based on the

non-dimensional damping coefficients for various damper geometries was carried out.

SCHEMATIC OF MR DAMPER:

FIGURE 1.3 SCHEMATIC OF MR DAMPER

METHODOLOGY OF DESIGN OPTIMIZATION:

The framework of the optimization procedure was based on physical design needs. A damper

was considered with a fixed cylindrical volume allotted for a damper.

Parameters Symbol Units

Total Damper length L mm

Diameter of Damper D mm

Height of the coil hc mm

Annual gap D mm

Coil width mm

Bobbin core radius ta mm

Flange height tb mm

Active length LA mm

Viscosity Pa·s

Magnetic Flux Density or Magnetic

BSUM Tesla

Induction

Current Density Js A/m2

Numbers of turns of wires

N turns

Number of wraps NW No unit

Wire diameter dc mm

TABLE 1 VARIOUS PARAMETERS USED IN THE DESIGN OPTIMIZATION

The MR damper was constrained within a cylindrical volume of fixed height and diameter.

Within this volume, candidate geometries were constructed on the basis of the number of wire

coils desired in the valve. These candidate geometries were imported into an ANSYS magnetic

finite element analysis (FEA) routine and the magnetic flux densities through the MR damper

was calculated.

The MR valve was shaped to guide the magnetic flux axially through the bobbin, across the

bobbin flange and fluid gap at one end, through the flux return, and across the fluid gap and

bobbin flange again at the opposite end (figure 1.4).

FIGURE1.4 MAGNETIC FLUX THROUGH MR DAMPER

FIGURE 1.5 ACTIVE AND PASSIVE FLUID LENGTH.

La - Active Fluid length

Lp - Passive Fluid length

The volume of fluid through which the magnetic field passes was defined as the active volume; it

is only within this active volume that MR effects occur. In order to make the valve most

effective, it was desirable to have a high magnetic flux density passing through a large active

volume. However, producing large magnetic fields required large numbers of magnetic coils. An

optimized circuit would maintain a balance between the field produced and power required by

the magnetic coils, and a valve design that would make best use of the field to activate the MR

fluid yield stress.

A viable candidate geometry was one in which the various critical areas though which the

magnetic field passes were the same size. This was necessary to keep the magnetic flux density

constant throughout the circuit, which ensured that one region of the magnetic

circuit did not saturate prematurely and cause a bottleneck effect. There are three critical

areas in the magnetic circuit: the circular cross-section of the bobbin core A1, the annular cross-

sectional area of the flux return A2, and the cylindrical area at the interior of the bobbin flanges

A3.

FIGURE 1.6 MR VALVE GEOMETRY NOMENCLATURE

Thus, the critical areas were defined by,

The volume constraint on the circuit was specified by prescribing maximum values for R and L.

Small changes in the valve gap, d, would drastically alter the performance of different valves, so

a fixed gap was also prescribed to ensure an unbiased evaluation. For these constraints, the

optimized geometry of the valve could be calculated algebraically.

By solving the equations 1,2&3 the resulting equations for ta, tb, la, hc are;

(4)

(5) (5)

La = 2tb (6)

hc = L – 2tb (7)

PROCEDURE FOR CALCULATING THE CANDIDATE GEOMETRY:

For calculating the candidate geometry, the damper height, diameter are fixed i.e. height=21mm,

diameter= 21mm. The fluid gap is also fixed which is equal to 1mm.

By using the equations 4,5,6,7 the various parameters such as ta, tb, hc, La and number of wraps

are calculated for various coil width.

It was noted from equations 4 and 5 that wc was the only variable necessary to characterize the

geometry of the damper. Since radius of the valve, R and the fluid gap width, d are fixed.

A MODEL CALCULATION:

For a coil width of 6mm, the various candidate geometries obtained are:

Bobbin core radius, = 11.6 mm.

Flange height, tb = 11.6/2 = 5.7mm.

Coil height = 9.5mm,

No of wraps= 7

Total number of windings = 91.

Similarly, candidate geometries obtained for various coil widths calculated are given below

Wc Ta Tb Hc Wraps N

4 12.7 6.355 8.29 4 44

5 12.1 6.1 8.86 5 60

6 11.6 5.7 9.5 7 91

7 10.9 5.46 10 8 104

TABLE 2 VALUE OF VARIOUS PARAMETERS

FINITE ELEMENT ANALYSIS USING ANSYS:

Due to structural symmetry, the MR damper will be analyzed as a 2D axi-symmetrical

model in ANSYS.

FIGURE1.7 SCHEMATIC AXISYMMETRIC MODEL OF

THE MR VALVE

The main dimensions of the valve are of Dcore, Lcore, Din, Dout, Lactive, Lreturn and g, where

Dcore = diameter of bobbin shaft

Lcore = length of bobbin shaft

Din = inner diameter of the valve

Dout = outer diameter of the valve

Lactive = active core length

g = 0.5mm, fluid gap

Lreturn = thickness of flux return

(Dout - Din)/2 - g

ASSUMPTIONS MADE IN THE ANALYSIS:

Assumptions of ANSYS magnetic analysis are given below.

The element lies in a global X-Y plane

Y-axis is the axis of symmetry for axi-symmetric analysis

An axi-symmetric structure was modeled in the +X quadrants

The only active degrees of freedom are the magnetic vector potential (AZ)

There is no flux leakage. i.e. flux parallel boundary condition is used.

ELEMENTS USED IN THE ANALYSIS

The element used in our analysis is magnetic vector, Quad 4 node 13 (plane 13)

PLANE13 has a 2-D magnetic, thermal, electrical, piezoelectric and structural field capability.

PLANE13 is defined by four nodes with up to four degrees of freedom per node. The element

has nonlinear magnetic capability for modeling B-H curves or permanent magnet

demagnetization curves.

FIGURE1.8 ELEMENT DESCRIPTIONS

MATERIAL PROPERTIES:

1.MR FLUID:

For MR fluid the material properties include relative permeability , magnetic flux density (B),

magnetic field intensity (H) which are chosen from B-H curve of MR fluid.

FIGURE 1.9 THE PLOT OF B-H CURVE FOR MRF 336AG.

s.no Properties Unit Symbol Value

1. Relative Permeability

No unit r 5

2. Magnetic Flux density

Tesla B 0.8,0.9

3. Magnetic Field Intensity

KA/m H 150,200.

TABLE 3 MATERIAL PROPERTIES OF MR FLUID:

2. STEEL:

s.no Properties Unit Value

1. Relative Permeability (r)

No unit 1000

2. Magnetic Flux density(B)

Tesla 1.25,1.45

3. Magnetic Field Intensity(H)

A/m 600,1000.

. MATERIAL PROPERTIES OF COIL AND INSULATION:

The coil and insulation is assumed to have relative permeability of 1.

BOUNDARY CONDITION:

A perimeter boundary condition is applied to obtain a “flux parallel” field solution. This

boundary condition assumes that the flux does not leak out of the iron at the perimeter of the

model.

LOAD CONDITION:

The current density (JS) identified using the formula given in equation (8) was applied over the

coil area. For a 2-D analysis, only the Z component of JS is valid, a positive value indicates

current flowing in the +Z direction in the planar case and the –Z (hoop) direction in the

axisymmetric case.

(8)

Results and Discussions:

After analysis using ANSYS software, the magnetic flux densities for various coil width was

obtained and shown on the table 5.

COIL WIDTH (mm) MAGNETIC FLUX DENSITY (Tesla)

3 0.823

4 1.1

5 1.715

6 0.35

TABLE5 MAGNETIC FLUX DENSITY FOR VARIOUS COIL WIDTHS.

FIGURE 1.11 FLUX DENSITY VS COIL WIDTH.

From the graph the flux density increases as coil width increases. It reaches a maximum value of

1.715 for a coil width of 5mm and then it decreases. The design for which the maximum flux

density is reached gives the optimized design.

The 3 dimensional view of optimized MR damper is shown in the figure 4.13.

The assembled view is shown in figure 1.12.

FIGURE1.12 THE DRAFT FOR THE OPTIMIZED

DESIGN

CONCLUSION:

An optimized magnetorheological damper was designed using volume constrained

optimization methodology with the help of ANSYS software. The optimized design of MR

damper has a magnetic flux density of 1.715 Tesla for a coil width of 5mm and number of wraps

of 7.

The results obtained for optimized MR damper was compared with the results of existing MR

damper. The result shows that the optimized damper has more vibration suppression capability

compared with the existing damper.

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