Design and optimization of shear mode MR damper using GRGand GRA methods: experimental validation

DIPAL M PATEL1,* , RAMESH V UPADHYAY2 and D V BHATT3

1Department of Mechanical Engineering, C S Patel Institute of Technology, Charotar University of Science and

Technology, CHARUSAT Campus, Changa 388421, India2Dr K C Patel R&D Center, Charotar University of Science and Technology, CHARUSAT Campus,

Changa 388421, India3Department of Mechanical Engineering, SVNIT, Surat 395007, India

e-mail: dipalpatel.me@charusat.ac.in

MS received 6 April 2021; revised 25 July 2021; accepted 1 September 2021

Abstract. The Generalized Reduced Gradient (GRG) and Grey Relation Analysis (GRA) optimization

techniques are used to optimize the parameters of shear mode magneto-rheological (MR) damper design to

achieve the defined objectives. The purpose is to develop a smart damper for washing machine application. The

main objective is to optimize parameters like magnetic coil height, width, radius of piston road and optimum

fluid volume (as this contributes to 60% cost of MR damper). The anisotropic-particle-based MR fluid (having

high stress at low magnetic field strength) properties are used in optimization. GRG and GRA gave similar

results for the optimized parameter values. GRA method gives additional advantages in design validation.

ANOVA Minitab software is used to analyse significant contributions of each parameter in the design part. The

practical shear mode MR damper was fabricated using optimized design parameters. The force–displacement

curve was recorded using the damper test rig. The obtained force values at each magnetic field strength agree

well with the calculated ones. The fluid volume used was 1.5 ml, and power and force values were, respectively,

5 W and 55 N. The reduced volume of MR fluid and power will help in commercializing this damper for

washing machines.

Keywords. Grey relation analysis (GRA); generalized reduced gradient (GRG); magneto-rheological fluid;

shear mode damper.

1. Introduction

To provide isolation to mechanical systems, hydraulic

dampers, friction dampers or spring type isolators are used

[1, 2]. These dampers provide constant damping force, thus

known as passive dampers. However, these dampers are

very effective and widely used because of their cost ben-

efits. For example, in front-loaded washing machines, a

friction damper is used (which has a constant damping

force) for each operating cycle (e.g. washing cycle, rinse

cycle and drying cycle) [3–5]. In reality, one needs dif-

ferent damping forces for each cycle to get the best per-

formance [6–8]. This is not possible with a friction damper

or a hydraulic damper. To improve the machine perfor-

mance, by reducing wear and improving the damping force,

‘‘smart’’-material-based dampers are used. These materials

respond to external stimuli. Among these, electro-rheo-

logical (ER) and magneto-rheological (MR) fluids are such

class of smart materials. In these fluids, their rheological

properties like viscosity, yield stress (minimum stress

required to flow the fluid), relaxation, etc. can be tuned

using external stimuli like electric fields (for ER) and

magnetic fields (for MR) [9–14]. These tuneable phase

changes, i.e. liquid to a semi-solid, have large industrial

applications in many areas such as dampers, clutches, shock

absorbing systems, ER/MR polishing, hepatic devices, etc.

[12–14].

ER fluid consists of electrical polarizable particles dis-

persed in an insulating medium. This fluid can be polarized

by applying an electric field. Though having potential in

many applications the use of this fluid in industry is ham-

pered by the low value of ER effect, which is defined as

ratio of change in yield stress with electric field to off-state

value [14]. In recent years the discovery of the Giant ER

effect, known as GER, has given a paradigm shift in the use

of ER fluids in different applications. The value of yield

stress achieved is as high as 130 kPa at 6 kV/mm electric

field [15, 16]. The requirement of higher power to achieve

the desire yield stress slows down the pace of ER fluid

applications. This has given a boost to MR fluids research*For correspondence

Sådhanå (2021) 46:217 � Indian Academy of Sciences

https://doi.org/10.1007/s12046-021-01746-6Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)

[17–20]. The next para discusses about MR fluid and its

applications in brief.

MR fluid is a non-colloidal solution of magnetically

polarizable particles like iron/magnetic particles in a polar

or non-polar carrier fluid. Generally, dispersed particles are

of a few microns size. Owing to the difference in the

density of iron particle (7.86 gm/cm3) and the carrier liquid

(* 1–2 gm/cm3), the particle sedimentation under the

gravity is an issue. However, this is addressed by adopting

stability enhancer additives in the solution [9–11]. Thus, in

the absence of magnetic field (off-state) this fluid nearly

exhibits Newtonian behaviour for lower volume fraction of

dispersed particles. In the presence of a magnetic field (on-

state) the fluid changes its phase from liquid like to a semi-

solid, depending on the intensity of magnetic field and

volume fraction of dispersed particles. This property of the

rheology is widely used in different applications of MR

fluid [21–28]. The applications that have gained the market

place are MR dampers [28]. Three different modes of

operations of dampers are classified based on the fluid flow

behaviour. They are as follows. (i) Flow mode damper – the

fluid flows in the MR fluid gap, and the magnetic flux lines

are perpendicular to the fluid flow direction. As a result, it

is possible to produce high damping force. (ii) Shear mode

– here fluid is sheared in the gap, and magnetic flux lines

are normal to the shear plane. (iii) Squeeze mode – fluid is

squeezed between the gap and field is normal to squeeze

direction [13]. Each mode has its own advantages and

limitations. For example, in flow mode, fluid volume

requirement is large ([50 ml) based on the applications; in

shear mode, force generated is below 100 N but the volume

requirement is low (\3 ml); in squeeze mode, operating

amplitude must be low (\7 mm) [13, 29–31].

The wide application potentiality of the flow mode MR

dampers allowed researchers to focus on the design,

optimization and performance evaluation of flow mode

dampers [13, 32–37]. Different optimization tools were

used, like particle swarm optimization [38–41], response

surface method [40, 42, 43], neuro-fuzzy [43] and genetic

algorithm [44–49]. In addition, a few researchers have

used optimization techniques like genetic algorithm

[47, 48], neuro-fuzzy logic [48–50] and grasshopper

algorithm [51] to control the damper operations. Using

these optimization techniques, a considerable state has

been achieved in flow mode damper design. Dampers

incorporating these optimization methods and the control

system are now termed as active dampers, i.e. feedback

loops are used for controlling the damping coefficient in-

situ. However, in certain applications semi-active con-

trolled dampers are also used [13].

The research on the performance of a shear mode MR

damper (SMMD) is very limited, mainly because of its

limitation on damp force (30–100 N at moderate power\10

W) [29–31]. Another approach used in design of shear

mode dampers is to use a magneto-rheological elastomer

(MRE) rather than MR fluid itself [52, 53]. The advantage

of using MRE is to reduce the leakage problem in the shear

mode damper as well as ease of manufacturing. On the

other hand the compatibility of particles and elastomer

material remains a bottle-neck in the applications [53, 54].

However, MREs are used in many applications; their

details are given in references [53–55]. This issue can be

addressed by the use of MR fluid in shear mode dampers

and a few researchers have reported the performance

evaluation of the shear mode MR fluid dampers

[29–31, 56]. Attempts were made to optimize the parame-

ters for these dampers like the materials used in manufac-

turing of dampers, flow gap and the number of turns on

magnetic coil. The work reported focuses on finite-element

simulation-based optimization techniques [29, 57–59]. The

part less addressed in this mode is geometric optimization

of the shear mode damper.

The major difference between flow mode damper

optimization and shear mode damper optimization is the

number of parameters to be optimized. In case of flow

mode, it is greater than 10; on the contrary, it is less than

5 for shear mode. Therefore, the use of high-end opti-

mization techniques is not required while performing

shear mode damper geometrical optimization. For this,

Grey Relation Analysis (GRA) and Generalized Reduced

Gradient (GRG) methods can be used [60–63]. The ear-

lier GRA method is used in design optimization of wave

mixture [64], strain gauge [65], automobile [66, 67],

parameter selection of different manufacturing processes

like electrical discharge machining (EDM) [68, 69], wire

electrical discharge machining (WEDM) [70–72] and

drilling [73–75]. This technique was also explored in MR

fluid-based finishing application [76] and optimization in

rotary MR dampers [77]. GRG method was also used to

find out the optimum parameters in grinder design [60]

and robot design [78, 79].

The main objective of this study was to explore GRG and

GRA optimization techniques for optimizing the perfor-

mance of SMMD for the use of the washing machine. The

proposed optimization technique is able to predict opti-

mized design parameters, which give higher performance

of SMMD damper at lower volume of MR fluid as well as

lower power. To achieve this, first we have used Multi-

physics software to evaluate the magnetic field distribution

for the designed magnetic coil [36, 57]. This is very

essential and for this we have used COMSOL Magnetic

field software. The flake-shaped particle-based MR fluid –

which gives higher MR effect at low field – parameters and

this coil design are used to optimize the design parameters

of SMMD. Minitab software was used to find out the

influence of design parameters on SMMD damping force,

and the results are compared to those obtained from

experimentally designed MR damper performance. The

agreement between the designed MR damper’s results and

the optimized values allows use of the proposed GRG and

GRA methods for shear mode damper geometric opti-

mization purpose.

217 Page 2 of 17 Sådhanå (2021) 46:217

2. Design background and theory

The MR damper consists of various components like a

magnetic coil, piston rod, outer cylinder, oil seals and upper

and lower covers. Figure 1 shows the basic engineering

design of SMMD with an internal configuration and

dimension parameters. The stationary magnetic coil design

used here avoids movement of the coil during the motion of

the piston rod. The current through this coil produces a

magnetic field and outer cylinder provides a field path

through an MR fluid. The intensity of the field depends on

the input current value and the gap between the coil and

piston road, known as fluid gap (x). Based on the earlier

studies, the fluid gap in the present case is 1 mm [29, 30].

The oil seals are used to avoid any leakage during the

process. Utmost care is needed while selecting the oil seal

so as to avoid degradation of the seal during the contact

with the fluid. Lower cover and upper covers help support

the whole assembly. The minimum volume needed for this

configuration will be based on the design optimization.

The present magnetic coil design allows one to model the

MR fluid between two parallel plate configurations in

which magnetic field is perpendicular to the shear plane.

Magnetic particles in the MR fluid will align when sub-

jected to a magnetic field and will hinder the flow. The

resistance to the shear stress is known as damping effect in

MR dampers. Wereley and Pang [80] gave a model to

calculate the damping force for this configuration.

According to this model, the damping force

Fd ¼ shear stress� area of the piston rod in contact with MR fluid:

ð1ÞIn MR fluid, according to the Bingham theory the shear

stress in the magnetic field is given by

s ¼ syðHÞ þ g _c for s[ sy¼ 0 for s� sy

ð2Þ

g is the viscosity of the fluid; _c is a shear rate and sy (H) isthe yield stress, defined as the minimum stress required to

flow the fluid. In the absence of the field the first term in

equation 2 becomes zero and only stress due to viscous

force will come into play. In addition to these stresses, the

Figure 1. Internal configuration and detail dimensions of SMMD. The dimensions are in mm.

Sådhanå (2021) 46:217 Page 3 of 17 217

friction stress (sf) will also contribute to the total stress.

This force is defined as the friction force (Fr). This is due tothe oil seals used.

The area of the piston (A) based on figure 1 can be cal-

culated. For a given configuration

A ¼ circumference of the piston rod� active length of coil

¼ 2pRpr

� �4Lacð Þ ð3Þ

Here, Rpr is the radius of the piston rod and 4Lac is the

active length of the coil (Lac) that is in contact with MR

fluid. So the total damping force is

Figure 2. SEM image of flake shape particles.

-250

-150

-50

50

150

250

-1 -0.6 -0.2 0.2 0.6 1

M(k

A/m

)

H(T)

Figure 3. Magnetization curves of MR fluid.

Table 1. Properties of MR fluid for SMMD.

Properties

Values

MRF

Density (kg/m3) 2200

Yield stress (kPa) @ 0.83 T 21 ± 01

Plastic viscosity (mPa s) @ 40�C 98 ± 01

Weight fraction (%) 73

Magnetic permeability, relative @low field 4

Response time (s) 0.001

Flash point (�C) [ 150

(a)

0

5,000

10,000

15,000

20,000

25,000

0 100 200 300 400 500 600

Str

ess

(Pa)

Shear rate (1/s)

I = 0.5A I = 1.0A I = 1.5A I = 2.0A

(b)

R² = 1

0

10

20

30

0 0.2 0.4 0.6 0.8

Dynam

ic y

ield

S

tres

s

(kP

a)

Magnetic flux density B (T)

Figure 4. (a) Flow curve for different current values and

(b) variation in shear stress with magnetic flux density B (T);

the line is a polynomial fit given by equation (5).

Figure 5. Response time of current and MR fluid. The line is for

current and points are for MR fluid stress values.

217 Page 4 of 17 Sådhanå (2021) 46:217

Fd ¼ sy Hð Þ þ g _c� �

2pRpr

� �4Lacð Þ� �þ Fr ð4Þ

In this equation _c ¼ mx where m is the velocity of the piston

and x is the MR fluid gap.

In the absence of magnetic field the term sy(H) is zero,and the force generated due to the rest of the terms is

known as ‘‘off-state’’ damping force FD (off-state). When

subjected to magnetic field, the damping force produced is

called Fd (on-state). The ratio of these two forces, on-state

to off-state, is called the Bingham number [81]. To have a

higher damper performance, a high Bingham number is

preferred. This again is a function of MR fluid properties

and damper design. In the next section we will discuss the

fluid properties, followed by the optimization of the MR-

damper design based on these properties.

Equation 4 leads us to believe that damping effect is

influenced by MR fluid properties as well as damper design

aspect. The yield stress depends on fluid properties and

magnetic field (equation 4) while damping force is tuned by

an MR fluid gap (x). In literature, many researchers have

reported the influence of fluid gap on the damping perfor-

mance for a damper and shown that the fluid gap between

0.75 and 1.2 mm is a reasonable gap to evaluate the per-

formance [29–31, 35–37, 56, 57]. Thus, in this work 1 mm

fluid gap is fixed. With this parameter fixed, other design

parameters of the damper were optimized to achieve the

best performance. The next section shows the details of MR

fluid.

3. MR fluid synthesis and properties

The major components in MR fluid are carrier liquid, which

takes around 60–80% of total volume, micron-sized mag-

netic iron particles (having loading from 20 to 40% by

volume) and a few additives to keep MR fluid stable and re-

dispersible. In the absence of magnetic field, MR fluid

exhibits viscous Newtonian or shear thinning behaviour.

When this fluid is subjected to a magnetic field, interaction

between induced dipoles causes particles to form a chain-

like structure of a low volume fraction of particles; how-

ever at a higher volume fraction it forms a columnar

structure in MR fluid. The mechanical energy required to

overcome this field-induced structure is known as yield

stress [9, 11, 13].

The micron-sized iron particles (procured from Industrial

Metal Powder, Pune, India) having flake-shaped structure

Figure 6. Protocol for calculation of damping force based on design variables.

Table 2. Three levels of input parameters (all dimensions are in

mm).

Lower Middle Higher

Rpr 5 7.5 10

Lac 5 10 15

hc 4 8 12

Wc 4 8 12

Sådhanå (2021) 46:217 Page 5 of 17 217

(figure 2) is used to prepare MR suspension. The particles

have the length of 6.5 lm (r = 2), width of 4.4 lm (r = 0.7)

and an aspect ratio of 1.5 (r = 0.5). Here, r is the standard

deviation. The use of non-spherical shape particle has the

advantage of slow settling characteristics as shown in our

earlier paper [29, 30]. In addition it has a higher Bingham

number, as derived from the rheological studies [81]. The

magnetization curve is recorded using a vibrating sample

magnetometer (VSM) for flake-shaped iron particles, and

the saturation value thus obtained (from 1/H versus

M curve) is 1714 kA/m (2.34 T @ 800 kA/m). The fluid

magnetization is shown in figure 3. The details of MR fluid

preparation and its characterisation are given in reference

[30]. Table 1 gives the properties of synthesised MR fluid.

The most important property of the MR fluid in the

present application is field response time and variation of

dynamic yield stress with magnetic field. A commercial

Anton Paar Physica MCR 301 rheometer was used to

investigate the flow behaviour of the MR fluids. A parallel

plate–plate geometry (plate diameter 20 mm, gap 1 mm) is

used for this purpose. A magneto-rheological device (MRD

170/1T) is used to apply magnetic field, which is perpen-

dicular to the flow direction. To maintain temperature, a

constant temperature batch having an accuracy ± 1�C is

used. In parallel-plate configuration, shear rate is consid-

ered at the outer radial edge of the rotor plate. The response

signals are processed through RHEOPLUS software pro-

vided with the equipment.

A typical flow curve obtained for the present MR fluid is

shown in figure 4(a). The shear stress increases with the

increase in magnetic field. This is due to the increase in

magneto-static interaction between the particles, which

generates chain or columnar meso-structure. The variation

in dynamic yield stress with magnetic field derived using

the Bingham model is shown in figure 4(b). The second-

order polynomial fit (equation 5) gives the variation of

yield stress with field at R2 value of 1.

sv ¼ �1:99þ 77:12B� 54:063B2 ð5ÞThis variation is used while validating the results with the

theory derived from the optimization of damper parameters.

Another parameter that is very important is the response

time of the MR fluid with magnetic field. To record this, it

is very essential to understand the response time of power

supply that provides current to the coil. To record this, for a

given current (here 2 A) time profile was recorded using

rheometer software programs. The response time thus

obtained is shown in figure 5 (black line). It is clear that to

achieve the required current (or magnetic field), the time

taken is 50 ms. In a similar way, the MR fluid response time

measurement was recorded. The points in figure 5 are the

10.07.55.0

120

105

90

75

601284

1284

120

105

90

75

6015105

Radius of Piston Rod

Mea

n

Coil Height

Coil Width Active length of coil

Main Effects Plot for Damping ForceData Means

Figure 7. Main effect plot of damping force deduced using Minitab software for different parameters given in table 2.

217 Page 6 of 17 Sådhanå (2021) 46:217

values of stress obtained. The MR fluid response after

reaching the desired current is\1 ms.

4. Optimization of the damper

The damping force is calculated using equation 4. Here,

piston radius (Rpr) and active length of piston road (Lac) arethe key parameters. However, the yield stress value, sy (H),depends upon the magnetic field intensity. This is a func-

tion of magnetic coil height (hc) and coil width (Wc).

Considering the values of these two parameters, number of

turns can be finalized as this influences power required to

energize the magnetic coil. In any design optimization,

initialization value parameters are very important. Thus the

lower and upper limits were defined for piston radius,

length of piston road, magnetic coil height and coil width.

They are given in table 2. The base for the choice of these

limits is discussed in detail later. This makes totally 34

combinations.

A protocol used to calculate the damping force is as

shown in figure 6. Damping force values were obtained

after performing 34 iterations. The influence of four vari-

ables (given in table 2) is understood using the main effect

plot. This is generated using Minitab software and the same

is shown in figure 7.

The variations of these parameters on the damping force

help in the design parameter optimization. This plot helps

select the right parameters to maximize the damping force.

Thus, for design optimization all these four parameters are

considered. As discussed earlier, with only four parameters

to optimize, we have used (i) GRG and (ii) GRA techniques

for the design optimization. The results of the same are

discussed in the subsequent sections.

Figure 8. Flow chart of Generalized Reduced Gradient (GRG).

Table 3. Optimized dimensions derived from GRG method.

Parameters Rpr hc Wc Lac Damping force Volume of fluid Power

Values 5 mm 8 mm 8 mm 5 mm 52.22 N 1.5 ml 10 W

Sådhanå (2021) 46:217 Page 7 of 17 217

Figure 9. Flow analysis step of Grey Relation Analysis.

Table 4. Grey relation grade and rank based on the grey relation co-efficient of volume of fluid, damping force and power.

Radius of piston rod

Rpr (mm)

Coil height

hc mm

Coil width Wc

(mm)

Active length of coil

Lac (mm)

Volume of

fluid (ml)

Force

(N)

Power

(W)

Grey relation

grade Rank

5 4 4 5 1267.12 28.37 3.88 0.7777 1

5 8 4 5 1267.12 34.93 6.30 0.7322 2

7.5 4 4 5 1706.72 36.55 4.34 0.7170 3

5 12 4 5 1267.12 39.09 9.48 0.6886 6

5 4 4 10 1957.92 40.06 3.88 0.7056 5

5 4 8 5 1543.44 41.48 5.56 0.7126 4

10 4 4 5 2146.32 44.74 4.81 0.6721 7

7.5 8 4 5 1706.72 46.40 7.24 0.6687 8

5 8 8 5 1543.44 52.33 10.41 0.6484 155 8 4 10 1957.92 51.31 6.30 0.6627 10

5 4 4 15 2648.72 51.76 3.88 0.6631 9

7.5 12 4 5 1706.72 52.63 10.88 0.6257 17

7.5 4 4 10 2711.52 54.09 4.34 0.6503 13

5 4 12 5 1819.76 54.57 7.24 0.6618 11

7.5 4 8 5 2108.64 56.23 6.49 0.6498 14

10 8 4 5 2146.32 57.86 8.17 0.6223 19

5 4 8 10 2234.24 57.86 5.56 0.6577 12

5 12 4 10 1957.92 58.44 9.48 0.6210 20

5 4 8 15 2925.04 74.25 5.56 0.6263 16

Table 5. Optimized dimensions of damper to satisfy optimum fluid volume objective using GRA method (rank 15 in table 4).

Parameters Rpr hc Wc Lac Damping force Volume of fluid Power

Values 5 mm 8 mm 8 mm 5 mm 52.22 N 1.5 ml 10 W

217 Page 8 of 17 Sådhanå (2021) 46:217

4.1 GRG method

GRG non-linear method is used to obtain the optimum

values of the dimension mentioned in table 2 [60]. To

execute this, solver function of Microsoft office excel is

used along with a GRG non-linear method for the solution

[61]. The algorithm of GRG method is shown in figure 8.

The range of the design variables is selected by imposing

constraint on the outer radius of damper (Ro) (\25 mm).

This is the first constraint related to the design parameter.

The second design constraint is the length of the damper,

\100 mm. Having defined constraints and requirements,

the next step was to define objective functions for the

optimization. In this paper the objective functions are

(a) optimum fluid volume, (b) damping force between 50

and 55 N and (c) minimum power consumption (\15 W).

These calculations were carried out based on the dimension

of the damper, magnetic coil resistance, current and MR

fluid parameters specified in table 1. The optimized

parameters derived from GRG method are given in table 3.

Because of manufacturing constraints, only integer values

are considered in the design.

4.2 GRA

To select the best combination of multi-objectives and

parameters, GRA method is used. This method works on

the basis of data normalized with reference based on sets

objective function and thereafter set into sequences using

grey relation grade [62–67, 77]. The basic flow analysis

steps are shown in figure 9.

Using the parameters specified in tables 2 and 1, damp-

ing force values, fluid volume and power requirement are

set as objectives with defined constraints in the GRG

method. The best objectives assigned are larger damping

force, minimum fluid volume and low power consumption.

Considering the flow defined in figure 9, first 20 combi-

nations out of total 81 results were identified based on the

higher grey relation grade and they are given in table 4.

In table 4, till rank 8, the damping force values are below

the objective defined; therefore they are eliminated from

the design part. The remaining data sets are used to design

the damper. To satisfy other objectives of the minimum

fluid volume (as defined in table 2) rank 15 is the best

option (shown in italics in table 4). On the contrary, the

lower power objective is achieved without compromising

the damping force, in rank 9, but it needs higher fluid

volume (approximately 1.7 times). As discussed earlier the

major cost involved in the MR damper is fluid cost, nearly

60%. Therefore, in the present case, rank 15 is considered

as a good choice. The optimized parameters are shown in

table 5. This analysis (Table 4) can be used based on the

end use applications for the design of SMMD.

The values of parameters obtained (Tables 3 and 5) after

the optimization seem to be identical. Thus both methods

can be used to achieve defined objective, but the GRA

method explores permutation–combination possibilities for

different user defined requirements. Therefore, the GRA

method can be used for the optimization of SMMD. In the

next sections we present the fabrication of shear mode

damper using the optimized parameters given in table 5.

This will be followed by experimental results and its

validation.

Figure 10. Magnetic field distribution in SMMD in T.

Sådhanå (2021) 46:217 Page 9 of 17 217

5. Damper fabrication

Based on these optimized parameters a shear mode damper

is fabricated. Manufacturing the piston, casing and mag-

netic coil needs materials having high magnetic perme-

ability. This will ensure high magnetic field in the fluid gap.

The material used is 1018 grade steel, having the magnetic

permeability of 529 [82]. The permeability of the magnetic

materials was confirmed using the vibrating sample mag-

netometer (VSM Lakshore 7404). Other parameter values

were taken from the manufacturer’s data sheet. A tolerance

of ± 1% was considered in the manufacturing of the

components.

The most important part in the design and fabrication

was the magnetic coil. To confirm the field needed in the

fluid gap, magnetic field analysis was carried out using

COMSOL Multiphysics software to optimize design

parameters. The field distribution in the optimized coil

Figure 11. Magnetic flux density (T) along the length of MR fluid gap in SMMD.

Figure 12. 3D model and manufactured components of SMMD.

217 Page 10 of 17 Sådhanå (2021) 46:217

design is shown in figure 10. Enlarged image shows (left

side) the magnetic field distribution in the MR fluid gap,

which is around 0.25 T, shown in blue colour. The field

distributions along the MR fluid gap for different current

values are shown in figure 11. The value agrees with that

required for the present damper design.

The upper cover and lower cover were fabricated using

SS310 steel. Details of each component and a schematic

diagram of the damper are shown in figure 12. The overall

damper dimensions are given in table 6. The physical

dimensions met the required criteria for an application in

the washing machine.

5.1 Damper test rig

The damper’s performance was evaluated using a damper

testing machine procured from AG Measurement, Roorkee

(Model: 0100S02; figure 13). To measure the displacement

of the damper, a Liner variable differential transformer

(LVDT; 0100S02) is used. The sensitivity of this sensor is

Table 6. Dimensions of SMMD.

Parameter Symbol

Dimension

(mm)

Outer radius of cylinder Ro 17.5

Radius of magnetic core d 15

Effective length of piston Lac 36

Radius of piston Rpr 5

Outer pole length Lp 5

Coil height hc 8

Coil width Wc 8

Gap between piston and magnetic

core

x 1

Length of magnetic core Lc 50

Figure 13. Damper testing machine.

Figure 14. Assembly of SMMD.

Sådhanå (2021) 46:217 Page 11 of 17 217

10 mV/V/mm. An S-type load cell (Sentronics, 60001-2T-

030B) is fixed on the top to measure the load.

This load cell has force measuring capacity up to 7000 N

with an accuracy of ±1 N. A hydraulic actuator is used to

apply sinusoidal excitation to the moving table. During this

motion, damping force and displacement are recorded using

a data acquisition system (NI USB 6002, National Instru-

ment, sample rate 1000S/s). The displacement applied to

the moving table is ±10 mm and the frequency is set at 1

Hz. Frequency and displacement are controlled by a con-

troller. A magnetic coil is energized using a constant cur-

rent DC power supply. The damper is fitted between the

fixed support and moving table.

6. Results and validation

Using the parameters of the design, as defined in table 2, a

prototype damper was manufactured. The manufactured

components of the damper and the MR damper assembly

are shown in figure 14. The following protocol was set to

evaluate the damper performance: (i) the frequency of

moving table was set at 1 Hz and (ii) displacement at

±10mm. Force–displacement data are recorded for three

cycles at a given value of current (figure 15) and averages

of these are presented in figure 16. The statistical error in

force is ±1 N. All the data are recorded at 313 K. During

the measurement, temperature was recorded and the rise in

damper temperature at the maximum current was within ±

2�C during the measurement time.

The important part in the experiment was to check off-

state (in the absence of magnetic field) force–displacement

behaviour of the damper. The average of three cycles plot

in the absence of the field is shown in figure 16. The off-

state force (which is a combination of friction force and

viscous force) is 12 N ± 1 N.

The damping force increases with an increase in the

current value. The increase in current (magnetic field)

induces the formation of chain structure in MR fluid, which

resists the flow of the fluid. This gives the damping effect.

The degree of orientation and strength of the chain are

functions of applied magnetic field (current). Therefore, as

current increases the damping force increases. The damping

Figure 15. Damping force–time at 10 mm stroke length and 1 Hz

frequency for 0–1 A current (at intervals of 0.2 A).

Figure 16. Damping force variation with displacement for

current of 0–1 A at intervals of 0.2 A for 1 Hz frequency and

10 mm stroke length.

Table 7. ANOVA parameters and percentage contribution of each input parameter.

Source DF Seq SS Adj SS Adj MS F P Percentage contribution (%)

Radius of piston rod 2 39358 39358 19679 179.75 \0.005 32.90

Coil height 2 7468 7468 3734 34.11 \0.005 6.24

Coil width 2 28615 28615 14308 130.69 \0.005 23.92

Active length of coil 2 43970 43970 21985 200.82 \0.005 36.75

Error 72 7882 7882 109

Total 80 127293 59815

S = 10.4632 R-Sq = 93.81% R-Sq (adj) = 93.12%

217 Page 12 of 17 Sådhanå (2021) 46:217

force at 1 A is 52±2 N, which is within the defined

objective limit.

6.1 Validation

To evaluate the significance of each parameter, ANOVA in

Minitab software is used. This provides the percentage

contribution of each parameter on damping performance.

Table 6 shows the percentage contribution obtained using

ANOVA software. DF indicates the total degrees of free-

dom and it also indicates the amount of information used

for the analysis. Seq SS is the sequential sum of squared,

which signifies the deviation in different parameters in the

model. Adj SS is adjusted sum of the squares, useful in

calculation of P-value. P-values decide the significance of

the parameters and this value must be \0.005. F-valuesindicate percent contribution of that parameter in the

design. Adj MS is adjusted mean square used to calculate

R-sq.The significant percentage contribution to damping force

comes from the active length of coil. This is followed by

the radius of the piston and coil width. The last contribution

is coil height. Based on the ANOVA parameters (table 7) a

regression analysis was performed. Table 8 shows the

parameter obtained after regression analysis for an applied

current of 1 A. A similar analysis is performed for each

current value and results are presented in table 9.

Coefficients obtained from the analysis help develop the

regression equation between input parameters and output

result. SE-Coef indicates the standard error in the coeffi-

cient; lower the value higher the precision of the model. Tvalue is the ratio of the coefficient to SE-Coef. The

regression equation can be represented as follows:

damping force ¼ �C1þ C2� Rpr þ C3� hc þ C4�Wc

þ C5� Lac:

ð6ÞHere, C1–C5 are coefficients obtained at each current value

from the regression (table 9).

Using the equation of regression and coefficients from

table 9, the theoretical value of damping force is calculated

and presented in figure 17 as square symbols along with

experimental values (circles). The agreement between the

predicted and experimental values validate the optimiza-

tions of SMMD and fabrication. The agreement is within

the experimental error.

7. Conclusion

The present paper shows the use of GRG and GRA tech-

niques to optimize geometrical parameters for the SMMD.

Having a small number of parameters (\5) to be optimized,

these techniques give a better option compared with other

Table 8. Regression coefficient obtained at 1 A current.

Predictor Coefficient SE-Coef T P

Constant –100.52 6.756 –16.81 \0.005

Radius of piston rod (Rpr) 10.7989 0.5806 18.6 \0.005

Coil height (hc) 2.8344 0.3629 7.81 \0.005

Coil width (Wc) 5.7312 0.3629 15.79 \0.005

Active length of coil (Lac) 5.707 0.2903 19.66 \0.005

S = 10.6657 R-Sq = 93.81% R-Sq (adj) = 93.12%

.

Table 9. Values of different coefficients obtained for different

current values.

Current

Regression coefficient

C1 C2 C3 C4 C5

1 A 100.52 10.79 2.83 5.73 5.71

0.8 A 75.02 8.36 2.04 4.27 4.19

0.6 A 60.89 6.24 1.64 3.45 3.41

0.4 A 46.23 4.89 1.24 2.68 2.64

0.2 A 31.25 3.56 0.65 1.98 1.85

Figure 17. Theoretical damping force calculated using equation

6 and experimental damping force for different currents.

Sådhanå (2021) 46:217 Page 13 of 17 217

techniques available. Both methods, GRG and GRA, gave

similar optimized parameter values. However the GRA

method gives a better control of the parameters, which is

not only essential for validation but also useful to design

custom-based shear mode dampers. The ANOVA Minitab

software was used to evaluate significance of four variable

parameters (piston rod radius, magnetic coil width, coil

radius and active coil length) on the performance of the

shear mode damper. The results show that major contri-

bution comes from the active length of the coil; this is

followed by piston radius and magnetic coil width. The

anisotropic-particle-based MR fluid, having high yield

stress at lower magnetic field intensity properties, is used in

the design optimization. Using these parameters, SMMD

was designed and tested at different current values. The

damping force obtained for each value of currents was

verified by theoretical analysis using regression method. A

fair agreement between these values confirms the damper

performance as per the defined objectives, i.e. low volume

of MR fluid (\2 ml), low power (* 5 W) and high

damping force (* 55 N). The optimum fluid volume will

help in cost reduction of this damper. Further work is in

progress to use this damper in washing machines and test its

performance. The proposed optimization techniques can

also be applied to other MR fluid devices like breaks and

certain MRE-based dampers.

List of symbolsFd Damping force

g Viscosity of the fluid

_c Shear rate

sy (H) Yield stress

sf Friction stress

Fr Friction force

A Area of the piston

Rpr Radius of the piston rod

Lac Active length of the coil

m Velocity of the piston

x MR-fluid gap

Wc Coil width

hc Coil height

Ro Outer radius of cylinder

d Radius of magnetic core

Lp Outer pole length

B Magnetic field density

M Magnetic field intensity

FD Off-state damping force

Acknowledgement

The authors would like to thank CHARUSAT for providing

all technical assistance and testing facilities.

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