Ergonomic Level Improving of Armoured Fighting Vehicle Crew

13 Pages·2017·1.19 MB·English

Defence Science Journal, Vol. 68, No. 1, January 2018, pp. 33-45, DOI : 10.14429/dsj.68.11321
 2018, DESIDOC
Ergonomic Level Improving of Armoured Fighting Vehicle Crew
N.V. Ramamurthy#,*, B.K. Vinayagam@ and J. Roopchand#
#DRDO-Combat Vehicles Research and Development Establishment, Chennai - 600 054, India
@Department of Mechatronics, SRM University, Kattankulathur - 603 203, India
*E-mail: [email protected]
ABSTRACT
The armoured fighting vehicle (AFV) - occupant composite system is modelled as a lumped parameter system,
in this paper, wherein the 4 degrees of freedom (dof) biodynamic occupant model is integrated with 10 dof in-
plane AFV model including the crew seat, thus leading to the 14 dof vehicle-occupant composite model and the
governing equations of motion are obtained. The composite model is subjected to idealised road input simulating
the ground reaction forces. Natural frequencies and the frequency domain vibration responses of various masses
of model are obtained. The natural frequency of chassis thus obtained is compared with the result established by
an earlier research work, to validate the model. The study is focused on crew seat location. A 2 dof occupant-
seat suspension model is formulated and validated through case study. The optimised values of seat suspension
parameters for ride comfort are obtained using the said model, through two methods of Invariant points theory and
genetic algorithm toolbox of Matlab 2014a software. Acceleration responses of body for the current and optimised
parameter values obtained illustrate that comfort of crew is improved with optimised values through minimization
in the acceleration responses.
Keywords: Vibration responses; Vehicle-occupant system; Seat suspension system; Mathematical model, Optimisation
algorithms; GA
NomENCLATuRE
M Chassis mass for half/ in-plane model (kg) Yp Vertical displacement of Passenger/ driver seat mass (m)
Y Vertical displacement of c.g (m) Yw1,..Yw7 Vertical displacement of wheels at road wheel stations
mp Passenger/driver seat mass (kg) 1- 7 (m)
mw1,....mw7 Mass of road wheel + track pad distributed at 7 l1,...l7 Distance from vertical C.L of wheels 1-7 to the c.g of
stations (kg) chassis (sprung) mass (m)
Iy Mass M.I of half/ in-plane chassis mass about a1,...a7 Road input - vertical displacement of wheels 1-7 (m)
pitch axis (kg.m2) Xp Horizontal distance of seat centre position from c.g of
K1,...K7 Stiffness/ spring const. of suspension unit at chassis (sprung) mass (m)
stations 1- 7 (N/m) g Acceleration due to gravity (m/s2)
Kp Stiffness/ spring const. of Passenger/ driver seat fn Natural frequency (Hz)
(N/m) ω Circular frequency (rad/s)
C1,...C7 Damping coeff. of suspension unit at stations 1-
7 (N.s/m)
1. INTRoDuCTIoN
Cp Damping coeff. of Passenger / driver seat Armoured fighting vehicle (AFV) is a typical tracked
(N.s/m)
military vehicle, capable of running at far higher speeds.
θ Pitch displacement of chassis (sprung) mass
High speed tracked vehicle like AFV are generally provided
about vehicle c.g (rad.)
with passive suspension systems using torsion bar and shock
Kw1,...Kw7 Stiffness/ spring const. of road wheel rubber +
track pad at stations 1 - 7 (N/m) absorbers, which contribute in the attenuation of terrain
Cw1,…Cw7 Damping coeff. of road wheel rubber + track pad vibrations. Although such tracked vehicles vary widely
at stations 1- 7 (N.s/m) in size, shape and physical appearance, they share many
Yh,Yut,Ylt&Yth Vertical displacement of human body parts viz. common characteristics in track and suspension assembly.
head, upper torso, lower torso & thorax, thigh For analytical modelling purpose, components of such vehicle
with pelvis, respectively (m) may be divided into two groups viz. track with suspension
Y1,...Y7 Vertical displacement of chassis mass directly components and hull components. Track, hull/ bogie wheels,
above the road wheels at stations 1- 7 (m)
road wheel assemblies and suspension components fall under
first group. All remaining components of vehicle are covered
Received: 31 May 2017, Revised: 03 October 2017
under the name ‘Hull’. Typical AFV additionally possess a
Accepted: 09 October 2017, Online published: 18 December 2017
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DeF. SCI. J., VOL. 68, NO. 1, JANuARy 2018
rotating top part known as ‘Turret’. Ride dynamics of off-road and the low frequency problems of vibration4.
vehicles has drawn extensive research and development efforts However, LPM still remains as one of the most popular
to improve suspension system to achieve comfort of vehicle methods used by researchers as its validity is found to be much
operator, considering the adverse effects of terrain induced suitable for the analysis in the low frequency range i.e. below
vibrations1. However in this work, a cost effective method of 100 Hz5. Also LPM is found to be one of the most popular
locally modifying the seat suspension system by optimising its analytical methods in the study of biodynamic responses of
parameter values, to achieve the same goal of attaining comfort seated human subjects, though it is limited to one directional
of vehicle operator is discussed. analysis. However as the vertical vibration exposure of driver
Fatigue and safety of the crew of an off-road heavy vehicle is our main concern6, LPM is suited for the current problem.
like AFV is very well dominated by the vibration environment Also reports reveal that an off-road vehicle is subjected
during the riding of such vehicle over cross-country terrains. to a ride vibration environment of low frequency and large
earlier studies revealed that both the wheeled and tracked off- amplitude1. Summarising the above facts, it may be justified that
road heavy vehicles were subjected to low frequency and high LPM method is best suited for the current problem, wherein we
amplitude vibration environment during the riding. It was also focus our study on low frequency vertical vibration of vehicle
found that the continuous exposure to such vibrations was the occupant.
cause for the bodily discomfort, insufficient performance and Scientists and engineers pay more attention now-a-
physiological damage of the operators of such heavy vehicles. days, on the study of comfortness of driver and occupants of
Ride characteristics of such ground vehicles are evaluated vehicle, because of the wide spread development of variety
using their analytical models through computer simulation. of kinds of vehicles. Both the security and comfort level of
This avoids the need to resort to repeated testing involving passengers are much dominated by the suspension system,
expense and time consumption. However it should be kept in which is an important device in any type of vehicle. While
view that computer simulations are beneficial, if and only if taking a comparative look on the conventional passive and
the vehicles analytical model accurately reflect the vehicles the two modern suspension systems viz. active and semi-
behaviour during its running1. Accordingly an attempt is made active suspensions, it may be understood that the later i.e non-
here to include the detailed model of AFV. conventional system suffer from few major short comings like
It should be kept in mind that vehicle vibration not only consumption of large energy, bad reliability, etc. Hence these
causes just one part of the body but it causes whole body of the two modern systems are not used widely. On the other side,
operator to vibrate2. When the exposure time of the operator to conventional passive suspension system is comparatively more
vibration exceeds the standard recommended and set by ISO reliable and economic. This makes the control performance
(ISO 2631-1, 1997)3, harmful effect of whole - body vibration improving study of passive suspension as meaningful, still.
will be experienced. Now-a-days, people are more concerned Vehicle body acceleration is still the most important indicator,
about the vibrations to seek better and comfortable environment. among the various comfort level evaluation methods. An
Mostly the interaction between the road and vehicle only leads important functional device for reducing the acceleration of
to vibrations which the vehicle crew is exposed to, with the vehicle body is the vehicle suspension. Thus, comfort level
increase in his travelling activity. Discomfort, fatigue and even of driver and the other occupants of the vehicle would be
injury are the possible effects of vibration. Specifically in the enhanced by selecting reasonably good suspension parameters
seated posture, vehicle occupant is more sensitive to whole thus achieving good isolation effects7. Thus the necessity of
body vibrations. This is the reason for the bio-dynamics of optimising the suspension parameters either for the whole
seated vehicle occupant to become the topic of interest since vehicle suspension or locally for the seat suspension alone, as
long. Also varieties of mathematical models were derived for done in the current work is very well justified, for enhancing
analytical purposes. experimental method for estimating the the comfort level of vehicle occupants.
discomfort and fatigue of vehicle occupant is a time consuming Analysing the comfort level of occupant of typical heavy
process involving lot of efforts. Alternatively bio-mechanical vehicle like tractor, it is apparent that the occupant of such
models are much useful to predict the vibration response of vehicle is not equipped to tolerate the vibration levels in the
bodily parts of vehicle occupant in a vibration environment. 0.5 Hz to 11 Hz discomfort range for extended periods of time,
Thus the dynamic characteristics of vehicle occupant can be which he is exposed to during the operation of such vehicle.
estimated through simulation of human mechanical models. It was observed that the earlier design works done for tractor
In common, mathematical models are found to be suitable for suspension systems to isolate the occupants from the pitch
bio-dynamic response studies, as they describe the vehicle and vertical vibrations were not very effective, due to the
occupant in the best way under vertical whole body vibration simple reason that such designs were based only on seat level
conditions. Lumped parameter modelling (LPM), finite measurement of vibration transmissibilities, as the vibration
element modelling (FeM) and multi-body dynamic modelling measurement on the suspended seat alone does not truly reflect
(MBDM) are few groups of modelling techniques. Considering the vibration level, which the human body parts are exposed
human body as several concentrated masses interconnected to. Thus it is obvious that the seat suspension designs done
by springs and dashpots is the approach followed under LPM without taking into account the combined effect of the vehicle
method. Analysis being simple and the experimental validation and occupant do not yield satisfactory results. This is also
task being easier are the common advantages of this method. supported by the work at the National Institute of Agricultural
But their application is restricted to one-directional analysis engineering, united Kingdom, who stressed that a mechanical
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RAMAMuRTHy, et al.: eRGONOMIC LeVeL IMPROVING OF ARMOuReD FIGHTING VeHICLe CReW
simulation of human body characteristics together with the seat wherein the vehicle model has not been included in the study and
is necessary8. also un-damped bio-dynamic model only has been considered,
The task of modelling the occupant and the tractor together thus ignoring the damping characteristics of connective tissues
in the form of lumped mass system interconnected by springs between various body segments.
and dashpots was carried out by Patil and Palanichamy8, based Abbas6, et al. arrived at an optimal seat design using
on the above concept. Said composite model was subjected to genetic algorithm, wherein 4 dof biodynamic model interfaced
sinusoidal i.e idealised field or road profile vibration at the tire with an on-road vehicle model is considered for study. Thus
contact points. It is pertinent to mention here that for vibration it does not discuss about off-road vehicle. Said 4 dof bio-
elimination, seating system designs of on-road as well as dynamic model6 is adopted in the present work. Also the widely
off-road vehicles are optimised using mathematical models accepted in-plane model of AFV, proposed in AMC Pamphlet12
of vehicle occupants through the estimation and prediction has been adopted by modifying the number of wheel stations
of vibration response of vehicle occupant4. Accordingly and both models were integrated for use in the present study.
said researchers found out the resulted responses of various The natural frequencies and the frequency domain vibration
body parts through computer simulation which were further responses of various masses of the vehicle-occupant composite
studied for the selection of new seat suspension parameters model are obtained by subjecting the model to idealised road
i.e optimised parameter values so that the intensity of vehicle inputs simulating the ground reaction forces. Matlab 2014 a
occupant vibration was reduced in the 0.5 Hz - 11 Hz harmful software package has been used in these simulations. Natural
frequency range to a minimum level8. frequency of major mass segment viz. the chassis thus obtained
The methodology followed by the above researchers in is compared with the value established by an earlier research
their work for the wheeled off-road heavy vehicle viz. tractor work, to validate the vehicle-occupant model.
is adopted in the present work for the tracked off-road heavy Liu7, et al., presented the Invariant Points Theory, wherein
vehicle viz. Armoured fighting vehicle (AFV), to arrive at the the authors have arrived at the invariant equation of suspension
ideal parameter values for the crew seat suspension system using from the differential equations of a 2 dof quarter vehicle
the 14 dof vehicle - occupant composite model. However, the suspension model and illustrated that there are no suspension
suspension parameters giving minimum vibration response i.e parameters in the said invariant equation demonstrating that the
the optimised values were obtained by the above researchers8 vehicle suspensions are all under the control of the invariant
in their work, by varying the parameters involved in their study equation. Same concept is adopted in the present work for
i.e. by the conventional trial and error method. In the said optimising the seat suspension parameters.
conventional method, values of design variables are iteratively In the current work, first a vehicle-occupant composite
changed and the system is reanalysed until acceptable design model is formulated and output values for specified road input
criteria are achieved. This is both time-consuming and tedious. forces applied to the model, are obtained through simulation
But in the present work, modern optimisation techniques are and analysis study. The results of such study are compared
used to arrive at the ideal suspension parameter values of with those obtained in an earlier research, to validate the
vehicle. formulated model. Then the study is focused on driver seat
Limited works are reported in the literature considering location and the optimal values of seat suspension parameters
off-road vehicle-occupant composite model, that too, not are obtained by visualising a 2 dof occupant-seat suspension
relating to AFV applications. Ramamurthy and Patil9 developed model. The formulated model is validated using driver seat
a seat suspension system for the use of AFV and assessed the level vibration data acquired through case study, before using
improvement achieved in crew comfort, through case study. the model to obtain optimal seat suspension parameter values.
However the parameter values used in the said seat design were Then said optimal values for ride comfort are obtained, using
adopted from the results of earlier research works carried out the two methods of Invariant points theory proposed by
for optimising the parameter values of crew seat suspension of Liu7, et al. involving direct mathematical formula and also
other heavy vehicle viz. tractor. G.A optimisation algorithm. Driver seat level acceleration
Rakheja10, et al. made an analytical experimental graphs obtained for old and optimal parameter values are given
investigation of the Driver-seat suspension system, for the ride to demonstrate the improvement achieved in ride comfort, with
vibration environment of off-road vehicles, but the work was the new optimal seat suspension parameter values. Thus, one
not specific to the AFV environment. Dhir and Sankar1 carried purpose of the current work is to derive, first, a detailed i.e
out a simulation study with field validation on the ride dynamics 14 dof vehicle – occupant (man – machine) composite model
of high speed tracked vehicles, but the study was exclusively for the use of future researchers in this area and validate the
done for a conventional military armoured personnel carrier said model. The other purpose of the current work is to obtain
(APC) and not exactly for the AFV like military tank, as done optimal parameter values for the driver seat suspension system
in the present work. using a simplified model duly validated, to improve the ride
Shirahatt11, et al. made a study on optimal design of comfort i.e ergonomic level of AFV crew/ driver in a cost
passenger car suspension for ride and road holding, but the effective manner.
mathematical model covered the chassis with the passenger
seat only and not the body segments of vehicle occupant. 2. mATHEmATICAL moDEL FoRmuLATIoNS
Singh4, et al. have done the modal analysis of human body 2.1 Proposed model
vibration model for Indian subjects under sitting posture, This section is devoted to the mathematical modelling
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DeF. SCI. J., VOL. 68, NO. 1, JANuARy 2018
of proposed system i.e. the biodynamic lumped human linear the composite model of 14 dof. In the Fig.1, a1,...a7 refer to
model coupled with the in-plane model of AFV. As mentioned the road input vertical displacement of wheels 1-7 (m), which
earlier, the 4 dof biodynamic model proposed by Abbas6, are defined such that:
et al. wherein the human body was constructed with four a1=A'.sin (ωt);a2 = A'.sin (ω(t−α1));
separate mass segments interconnected by four sets of springs
& dampers with the arms and legs combined with the upper a3 = A'.sin (ω(t−α2));a4 = A'.sin (ω(t−α3));

torso & thigh respectively, finally amounting to a total human
a5 = A'.sin (ω(t−α4));a6 = A'.sin (ω(t−α5));
mass of 60.67 kg., is adopted here for use as occupant model
but with slight changes in the notations. With the modified a7 = A'.sin (ω(t−α6));
notations, the four masses represent following body segments:
head and neck (mh), upper torso (mut), lower torso (mlt) α1,..α7 refer to the time lag between adjacent wheels to
and thigh with and pelvis (mth).The stiffness and damping cross the same obstacle as explained in section 2.2.
Said composite model is subjected to sinusoidal vibrations
properties of thigh with pelvis are Kth&Cth, those of lower
simulating the ground reaction forces, that the AFV model
torso areKlt&Clt, upper torso are Kut,Ktth&Cut,Ctth and
would be subjected to, at its speed range, while negotiating
those of head are Kh&Ch. Yh,Yut,Ylt&Ythare the vertical
the cross country. While deriving the governing equations of
displacements of body parts viz. head, upper torso, lower torso,
motion, pitch motion of AFV chassis, in addition to its vertical
and thorax, thigh with pelvis about the c.g of chassis (sprung)
motion is included. The equation of motion of each mass
mass. The biomechanical parameters of the model are listed in
consists of the inertia terms and forces exerted on the mass by
Table 1.
the springs and dashpots due to the relative motion between the
In-plane model of AFV of 10 dof duly integrated with the
connected masses. Description of variables with respect to the
seat and biodynamic model is illustrated in Fig. 1, thus making
in-plane vehicle model is given in Table 2 and the parameters
Table 1. The biomechanical parameters of occupant model,
of the AFV model obtained from literature and reports12-14 are
as adopted from Abbas model6
listed in Table 3.
mass (kg) Damping coeff. (N.s/m) Spring constant (N/m)
2.2 Governing Equations of motion
mh=4.17 Ch=310 Kh=166990
The governing second order coupled ordinary differential
mut=15 Cut=200 Kut=10000 equations of various masses of the composite model of Fig. 1
mlt=5.5 Clt =330 Klt=20000 are put down as:
Head
mth=36 Ctth=909.1 Ktth=144000
Cth=2475 Kth=49340 (mh. Yh) + Kh.(Yh - Yut) + Ch.( Yh - Yut) = 0 (1)
Figure 1. Vehicle-occupant composite model.
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RAMAMuRTHy, et al.: eRGONOMIC LeVeL IMPROVING OF ARMOuReD FIGHTING VeHICLe CReW
Table 2. Description of variables of in-plane AFV model upper Torso
Symbol Description (mut .Yut) + Kh . (Yut − Yh) + Ch . (Yut − Yh)
M Chassis mass for half/ in-plane model (kg) + [Kut (Yut – Ylt) +Cut . (Yut − Ylt)  (2)
 
Y Vertical displacement of centre of gravity (c.g) (m)
mp Passenger/ driver Seat mass (kg) + Ktth . (Yut − Yth) + Ctth . (Yut − Yth) = 0
mw1,....mw7 Mass of road wheel + track pad distributed at 7 Lower Torso
stations (kg)
Iy Mass M.I of half/ in-plane Chassis mass about pitch (mlt .Ylt) + Kut . (Ylt – Yut) + Cut . (Ylt − Yut) (3)
axis (kg.m2) + Klt . (Ylt – Yth) + Clt . (Ylt − Yth) = 0
K1,...K7 Stiffness/ spring const. of suspension unit at stations
1- 7 (N/m) Thigh (Pelvic):
Stiffness/ spring const. of Passenger/ driver seat
Kp (mth .Yth) + Klt . (Yth − Ylt) +
(N/m)
(4)
C1,...C7 Damping coeff. of suspension unit at stations 1- 7 Clt . (Yth − Ylt) + Ktth . (Yth − Yut) +
(N.s/m) Ctth . (Yth − Yut) + Kth . (Yth − Yp) + Cth . (Yth − Yp)] = 0
 
Cp Damping coeff. of Passenger/ driver seat (N.s/m)
θ Pitch displacement of chassis (sprung) mass about Driver Seat
vehicle c.g (rad.) (mp .Yp )+{ Kp . Yp − Y − (Xp .θ)}
Kw1,...Kw7 Stiffness/ spring const. of road wheel rubber + track
pad at stations 1 - 7 (N/m) +{ Cp . Yp − Y − (Xp .θ)} (5)
 
Cw1,…Cw7 Damping coeff. of road wheel rubber + track pad at
stations 1- 7 (N.s/m) + Kth.(Yp−Yth) + Cth.(Yp − Yth)} =0
Yh, Yut Ylt Vertical displacement of human body parts viz.
& Yth head, upper torso, lower torso & thorax thigh with Chassis (Bounce)
pelvis, respectively (m)
M. Y + [K1 . (Y+l1.θ− Yw1)] +M [. CY1 +. ( Y[K +1 .l 1(Y.θ+−l 1Y.wθ1−)] Y+w1 [)K] 2+ . [(YC1 +. (lY2 . θ+− l1 Y.θw−2) ]Yw1)] + [K2 . (Y + l2. θ− Yw2)]
Y1,...Y7 Vertical displacement of chassis mass directly above
M. Y + [K1 t.h e(Y ro+adl w1.hθee−ls aYtw st1a)ti]o n+s 1 M-[ 7C. (1Ym .) +(Y [ K+1 l.1 (.Yθ−+l 1Y.wθ1−)] Y Mw++[1.C ) [Y]2K .++ 2(Y [.[ KC(+Y11l .2. +(.( YθY −l+ 2+ lY.1 θw .lθ1−2.−)θ ]Y −Yw+w Y2 1[M)w)K]]1. 3)+Y+ ][. C ([++Y2C [1[.+ K K(.Y 1 (l2 Y3 . .+( . θY +l(−Y2+ .l θ1Yl1+.w−θ.θ3 − l)−Y2] w . YY θ+2ww)−1 1][)) C]Y]+ 3w++ [.2 K([)[Y]KC3 1 2+. . ( . Y (l(Y3Y . θ+ + −+ l l3Y 1l.w2. θθ3. −θ−)]− YY wwY13w))2]] )]++ [[KC23 .. ((YY ++ ll23.. θθ −− YYww32))]]
+[YCp 2 . (YM +. YlV2 e.+r θti c[−aKl 1Y dw.i s(2pY)la]+c el+m1.e θn[t−K o3Yf w .+ 1MP[()CYa]s. 2 sYe++ n. g (+[elYCr3 /[ d.1 Kθr+ i.v 1−l(e 2Y.r .Y( θYsw+e−a+3 tl ) 1Yl1].wθ .θ2+−−) ]Y[ YCw+M++w1[3[C1 ).K[ )].Y2K ] 4( + .Y3+. + ( (Y [. Y  [[+K( KCY++ 211l l 3 +.2..l .4.θ((( θYY.Yl θ−3− +− .++Y θ lY 1wY −wll.wθ1322 .)4.Y−θ) θ])w] −]− YM3 ++ w) Y Y.1[] + w[ w)CY[1K]+C24 )+3)+ +]2.][[ K. C( .+ [ Y[((K4C3YY [ 11+ .. K +.+(.(l YY42((l YY.l 2  θ3.+. ++ .θ(− +θY l −l 1l− 4Y 3l. 1.θw+Y . θYθ.w4−θ w− l−)2− 23]Y ) .YY) ]w θY+w] w1 w+− 4)3+[1]) ) K)[Y ] ]][K ++w5 C +3 2.[[3 )C( .C ]Y [.( 14KY( Y −.. 2 ( +(l YY.5+ .( l θY3l++3.− θ l.+lθ 41−Y .− . wθθl  Y2Y5−−w.)w θ] 3 YY3−)w)w]] 14Y+))w]] 2 [+C)+] 3 [[ .KK (Y25 .. +((YY l 3+−.θl −l52 .Y θ. θw−−3 )Y ]Yww52)]) ]
mass (m)
+[YKw14,. .Y. w(Y7+ [ C+M2 Vl .e.4 r(Y.tYi θc a +−l+ [dlYK2isw.1p θ l4.a −)c(Ye] m Y++ew nl[12tC .)θo]4−f +. +w Y+( [whY[[Ke1CKe )4l+]23s .l+.. a (4t((Y YY.[ θrC o+1−a++d . l llY2(4w3Y.w. .θh θ θ4e+−e−−)l ]l Y 1 YYw.+θww2−34 )[)) ]KY]]  + w++++5+[[1[ KC C)[ .[] [C245 K(CY + 4...3 3 ( (( . [YYY. −. ( K( Y ( lYY−+2+5 l.l.+ 5 + θl+2(.4lY. θ − θ4.ll θ 3−.3− +θY.−. θθ Y w−Y l −w−Y2w5 w5.Y Y) 2θY)]w4w)] −w) ]43] 3++ ))Y ++)[]] wC] [ +[ 2[K+2C[+)KK ]6 .4+ [ 3 [4( [.K .Y(CC .Y. ( 5 (35Y( YY+ −. .. l+(((l+2+YYY6l.. 4θ  θll−.3−+4− θ−..l l θ θ −5 l5YY3−.−.w wθ .θYθ 26−YYw− −))ww4 ]] Y43Y ) Yw)+])+ww ]]5 3 +5+)[[)+)C] K] ][ [ 6C+[3K C 4. . 5[ (3(. YK .Y  (. ( Y6 Y(−Y + . l(+ 6 Y−l+l.3 lθ45. −. lθ− θ.3 lθ− .6−Yθ−. w θ−YY 6Yw w−Y)w3]4w Y)5)3]w)]) ] ]6 ++) ][[ CK+35 [ ..C ((Y6Y . +−(Yl l5 3.− θ.θl− 6−. YθYww−53 )Y)]]w 6)]
+[C5 . (Y+ [−K+l4s5[t Ca.. tθ(i2oY− n. s( +YY1-w l7+45 (l.)m θ2]). − θ+− Y [wYKw4)26]) +].+ ( +Y[+[C[C K [5−4K4 .l. 3 6.( ( Y.(Y. Yθ( Y −−++ l l+5Y 4l. w.4l θ θ3.6 −.θ− θ)− ] −YY  w w+YY5w4w )[)43]C])) ]]+6+++ ++[+ [[ C. K[K [[ ([5KCKY47C  . 645 . .3 ( −(( Y....YY  ( ((Yl (YY Y6− −+. −l θl+−+ 57ll.−4ll. 6 θ l5θ4.3. θ.−. Yθ−. θθθ−w − Y−−−Y 6wY w YY)YYw57w]www))43]6]5)4) )])]+)++] ]+[] K +[[+[+C[K4CC [7[+64.5 C K[ (. ..Y K. (6( 5(YY( Y 7Y .+. .( −−( Y +Y−(lllY4l 67l 45. −..− θ θ.θ.− θθll−−−6l5−−7. . Y θ.YθY θYYwww−−ww−476 5 4)) YY))Y]])]ww] w++] 56+[ 7++[))K) ]C] [ ] [p[ C4K K+. 6.6( 5 Y ( [.. Y C(. ( YY− (7Y+ −Y. −l p−(4llY6 .6l θ.− 5. θ θ−.− θ−X−l p7−Y Y . wY .θw Yθw46−w))6])5] )]Y ]) ]w++ 7 [)[K]C +56[ ..K ((pYY . −−(Yll6 5.−. θ θ −Y−p YY w−w65 X))]]p . θ)]
+[l1K,..7.l7 . (Y+[ C−5+lDo[ 7f.Ki .sc( θtY4haan − .sc s−(e iYY slf r5w(os+.pm7 θr )u l−v4n]e .g r θY)+t iwm−c a5a[ lYs )CCsw] . (7L4m+ )o+.)] +f [([+ [YKwK C[h 7C65e− e 4...l (l s (Y(. 7Y 1Y(. -Y θ7 −− − t−lo+ll6 7 5tl.Yh4. .θ e θwθ. θ−c−7−.−g )Y YY ]wY +www6[574)K))])] ]]p ++++ +++.[ [ [[ K C (C[[[CY5pKK7C6 5..6.7 − ( . (Y ( .Y.Y. ( ( ( YYY(Y  −Yp− − − −−Yll5−−7plll.6.56 l θ θ..7X−. θθ −θ−.p θ−X−− YY.−p  YθwwY.Y  θw)5wY7w])5)]w)66 )]])] 7) =+] +])+[ ]C 0+ + +[[5[K[C K [.K+6 7C7([p YC. 6..( Y (.p(. Y−Y ( (.Y (Yl− Y5−− l . −l6 θl−7−7. −θ.l.Y θ 6θY− p.Y−−p θ  w Y −−YY−5www ) X6Y]X77) pw)p)]+ ] .6]. θ + + θ)[+)][)] K] K[[C=6pC 6 . 7.(0 Y .(. Y ( (YY −− l−6− Y.ll θ6p7. −. θ θ− −−Y Xw YYp6ww ).76 ]θ )))]+]] + [[CKp6 .. ((YY −− lY6p. θ −− XYpw .6 θ))]]
+[aC1,p... a.7(Y + [−K +Y7Rw[p Co.h ae(5d−eY l .is n (X1−pY-up7l t.7 −( -θ.m lvθ)5)e]−.r θti= c−Yaw l 0Yd7wis)p5]l) a]+c+ e++[ m[C[ eCK[pnK7t7 .o 6 (..fY (. ((Y YY− −− −Ylllp776 ... θ θθ−−−− X YYYpww.w θ677)))])] ]] +=++++[[[ CK[K0 C[pp7C6 ... 7( .Y( ( Y(Y. Y ( − Y −−− Yl l−Yp76p. l. θ θ7− .−−− θX −YYXpww.p θY67 ).w))] θ] ]7)+ =])+[]K ++ 0[[7[CCK .p7 p( Y.. ( .Y( Y(−Y −l −7 −.Yl θ7p Y.− θp− −Y −Xw Yp 7Xw.) θp7]) )].+ ] θ =+ )[][ CK07p .. ((YY −−l 7Y.p θ −− YXwp7 .) θ]) +][Kp . (Y − Yp − Xp . θ)]
+[Cp+[ .K(Y7 .− (Y Y p− l−7. θX−p. θY)w] 7)=] +0+[C [pC .7( Y. ( Y− −Ypl7 .− θ− X pY.w θ7))] ] +=+[[ CK0pp .. ((YY −− YYpp −− XXpp. θ. θ)])] +=[C 0p .(Y − Yp − Xp. θ)] = 0
Xp Horizontal distance of seat centre position from c.g
+o[fC cph a.s(Ysis −(sp Yrupn g−) m Xaps.s θ ()m] )= 0 (6)
g Acceleration due to gravity (m/s2) Chassis (Pitch)
Table 3. Parameters of in-plane AFV model as adopted from Iy .θ+ l1.K1 . (Y + l1.θ – Yw1)+ l1 .C1 . (Y + l1.θ− Yw1)
AmCP12, Banerjee13, et al. & Chandramouli14
+l2 .K2 . (Y + l2.θ − Yw2)+ l2 .C2 . (Y + l2. θ − Yw2)
Parameter Value Parameter Value
M 10000 kg Cw1,...Cw7 5793 N.s/m + l3 .K3 . (Y + l3.θ − Yw3)+ l3 .C3 . (Y + l3. θ − Yw3)
mp 10 kg l1 2.5 m + l4 .K4 . (Y + l4.θ − Yw4)+ l4 .C4 . (Y + l4. θ − Yw4) (7)
mw1,...mw7 575 kg (each) l2 1.7 m + l5 .K5 . (Y −l5.θ − Yw5)+ l5 .C5 . (Y −l5. θ − Yw5)
Iy 1.94x105 (kg.m2) l3 0.8 m
K1,...K7 14483 N/m l4 0 + l6 . K6 . (Y −l6.θ − Yw6)+ l6 .C6 . (Y −l6. θ − Yw6)
Kp 90000 N/m l5 0.8 m + l7 .K7 . (Y −l7.θ − Yw7)+ l7 .C7 .(Y −l7. θ − Yw7)
C1,...C7 2,98,188 N.s/m l6 1.6 m − Kp . Xp . (Y − Yp − Xp .θ )− Cp .Xp . (Y − Yp − Xp .θ )= 0
Cp 400 N.s/m l7 2.7 m Vertical displacement of wheels:
Xp 0 g 9.81 m/s2
Kw1,...Kw7 45,00,000 N/m Wheel 1
37
DeF. SCI. J., VOL. 68, NO. 1, JANuARy 2018
(mw1 . Yw1) + Kw1 . (Yw1 −a1) Following state variables have been used:
+Cw1 . (Yw1 −a1)+K1 . (Yw1 − Y1) (8) Yh= X1; Yh= X2; Yut = X3; Yut = X4; Y lt = X5; Ylt = X6; Yth= X7; Yth= X8;
Yh= X1; Yh= X2; Yut = X3; Yut = X4; Ylt = X5; Ylt = X6; Yth= X7; Yth= X8;
+ C1 . (Yw1 −Y1)=Kw1.A.sin ωt + Cw1. A. ω.cosωt
  Yp= X9;Yp= X10; Y = X11; Y = X12;q = X13;q = X14; Yw1= X15; Yw1= X16;
Wheel 2
(mw2 . Yw2) + Kw2 . (Yw2 −aYY2pp)== XX99;;YYpp==XX1100;; Y Y==XX1111;; Y Y==XX1122;;q qθ  ==XX1133;;q q θ==XX1144;; Y Yww11==XX1155;; Y Yww11==XX1166;;
Yw2= X17; Yw2= X18; Yw3= X19; Y w3= X20; Yw4= X21; Yw4= X22;Yw5= X23;
+Cw2 . (Yw2 −a2)+K2 . (Yw2 − Y2)
Yw2= X17; Yw2= X18; Yw3= X19; Yw3= X20; Yw4= X21; Yw4= X22;Yw5= X23;
+ C2 . (Yw2 −Y2)=Kw2.A.sin (ω (t−α1)) (9)
  Yw5= X24;Yw6= X25; Yw6= X26; Yw7= X27; Yw7= X28.
+ Cw2. A. ω.cos (ω (t−α1)) Yw5= X24;Yw6= X25; Yw6= X26; Yw7= X27; Yw7= X28.
Wheel 3 Substituting the above variables in eqns (1) to (14) and
(mw3 . Yw3) + Kw3 . (Yw3 −a3) writing the equations in state space representation form,
X = A.X + B.Q (16)
+Cw3 . (Yw3 −a3)+K3 . (Yw3 − Y3) where A is System Matrix such that
(10)
+ C3 . (Yw3 −Y3)=Kw3.A.sin (ω (t−α2)) A=[A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11
 
+ Cw3. A. ω.cos (ω (t−α2)) A12 A13 A14 A15 A16 A17 A18 A19A20

A21 A22 A23 A24 A25 A26 A27 A28]T
Wheel 4
X is State Matrix such that
(mw4 . Yw4) + Kw4 . (Yw4 -a4)+Cw4 . (Yw4 -a4)
X =[X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11
+K4 . (Yw4 - Y4)+ C4 . (Yw4 -Y4) (11)
X12 X13 X14 X15 X16 X17 X18 X19 X20
=Kw4.A.sin (ω (t-α3)) + Cw4. A. ω.cos (ω (t-α3))
X21 X22 X23 X24 X25 X26 X27 X28] T

Wheel 5
mw5 . Yw5 + [Kw5 . (Yw5 −a5)]+[Cw5 . (Yw5 −a5)] B is Input Matrix such that,
+[K5 . (Yw5 − Y5)] + [C5 . (Yw5 −Y5)] (12) B=[B1 B2 B3 B4 B5 B6 B7] wherein
=Kw5.A.sin(ω(t−α4))+ Cw5. A. ω.cos(ω(t−α4))
B1=0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Kw1/mw1) 0 0 0 0 0 0 0 0 0 0 0 0T
Wheel 6
(mw6. Yw6) + Kw6 . (Yw6 −a6)+Cw6 . (Yw6 −a6) B2=0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Kw2/mw2) 0 0 0 0 0 0 0 0 0 0T
+K6. (Yw6 − Y6)+ C6 . (Yw6−Y6) (13) B3=0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0(Kw3/mw3) 0 0 0 0 0 0 0 0 T
=Kw6.A.sin (ω (t−α5)) + Cw6. A. ω.cos (ω (t−α5))
B4=0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0(Kw4/mw4) 0 0 0 0 0 0T
Wheel 7
(mw7. Yw7) + Kw7 . (Yw7 −a7)+Cw7 . (Yw7 −a7) B5=0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Kw5/mw5) 0 0 0 0T
+K7. (Yw7 − Y7)+ C7 . (Yw7−Y7) (14) B6=0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Kw6/mw6) 0 0T
=Kw7.A.sin (ω (t−α6)) + Cw7. A. ω.cos (ω (t−α6))
B7=0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Kw7/mw7)T
The set of Auxiliary equations for chassis & wheels (used
while deriving their bounce and pitch equations as shown Q is Input (Scalar) such that Q = [a1 a2 a3 a4 a5 a6 a7]T
above), for small values of angle θ are: where a1,..a7refer to the road input vertical displacement of
Y1 = Y + l1. sin θ = Y + l1. θ and Y1 = Y + (l1. cos θ). θ = Y + l1. θ wheels 1-7 (m), which are defined such that:
Y2 = Y + l2. sin θ = Y + l2. θand Y2 = Y + (l2. cos θ). θ = Y + l2. θ a1= A'.sin (ωt);a2 = A'.sin (ω (t−α1));
Y3=Y+l3.sin θ=Y+l3.θand Y3=Y+(l3.cos θ).θ =Y+l3.θ a3 = A'.sin (ω(t−α2));a4 = A'.sin (ω(t−α3));
Y4 = Y + l4. sin θ = Y + l4. θ and Y4 = Y + (l4. cos θ). θ = Y + l4. θ a5 = A'.sin (ω(t−α4));a6 = A'.sin (ω(t−α5));
Y5 =Y−l5. sin θ =Y−l5. θand Y5=Y+(l5. cos θ). θ =Y+l5.θ a7 = A'.sin (ω(t−α6));
Y6=Y-l6. sin θ=Y-l6.θ and Y6=Y+(l6.cos θ).θ=Y+l6.θ Now for the sinusoidal road profile considered by
Shirahatt11, et al., amplitude and pitch values of the sinusoidal
Y7=Y−l7.sin θ=Y−l7.θand Y7=Y+(l7.cos θ).θ=Y+l7.θ
proving ground used for case study in the current work are
(15)
38
RAMAMuRTHy, et al.: eRGONOMIC LeVeL IMPROVING OF ARMOuReD FIGHTING VeHICLe CReW
implemented as amplitude (A') = 0.15 m and pitch (λ)= 4m A8=[0 0 (Ktth/mth) (Ctth/mth) (Klt/mth) (Clt/mth) ((−Kth−Ktth−Klt)/mth)
as illustrated below. A vehicle velocity of V= 11.11 m/s. is
also derived corresponding to Aa 8v=eh[i0cl 0e (sKptetehd/ omf th40) (kCmt/thhr./ mth) (Klt(/(m−tCht)h A (−C8Cl=tt/[th0m 0−th (C)K l(tt(t)−h/K/mmththt−h) )K ( (tKCthtth−th/K/mlmtt)hth/)m ) ( (tChK)tlht//mmtthh)) 0 ( 0C 0lt 0/ 0m 0t 0h 0) ( 0( 0− 0K 0th 0− 0 0K 0tt 0h 0−]Klt)/mth)

Here, ω refers to the circular (fr(e−qCuAethn8c−=y C[o0tft 0hth (−eK Cdttilhstp)/l/amcmethtmh)e) n ( tC ( Ktthth//mmthth)) ( K (Cltth/m(/(mt−htCh) t) (h 0C− 0lt 0C/ 0tmt 0ht 0h− 0)C ( 0(l 0t−) 0K/ 0tmh 0t 0−h 0)K 0 t ( t0hK 0−t 0hK]/lmt)th/m) t (hC)th/mth) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
applied (rad/s) and 'α1,....α7' refer to the time lag between the
concerned road wheel and first road (w(h−eCelt,h w−hCictht hal−soC islt e)q/umalt h) (Kth/mth) (Cth/mth) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
to the phase angle between the input displacements applied to
them. Taking the typical case of movement of adjacent road A9=[0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
wheels 1 and 2, it may be observed that they follow the same
trajectory with a time delay of which may be defined, by A10=[0 0 0 0 0 0 (Kth/mp) (Cth/mp) ((−Kp−Kth/mp)) ((−Cp –Cth)/ mp) (Kp/mp)
referring to Fig. 1 as:
(l1−l2) (2.5−1.7) A10=[0 0 0 0 0 0 (Kth/mp) (Cth(C/mpp/)m (Ap(1−)0 K(=Kpp[−0 K. 0xtp h0 0// mm 0p 0p) ()) K ( ((Ct−hpC/ p.m x –ppC) / (t mhC)pt/h )m / 0pm 0) p 0()K 0 (p 0(−/ 0mK 0p p0) 0− 0K 0t h0 0/ m0]p)) ((−Cp –Cth)/ mp) (Kp/mp)
α1= = =0.072 s
V 11.11 (Cp/mp) (KAp1 0. x=p [/0 m 0p 0) 0 (C 0p 0 (. xKpt h/ m/mp)(p C 0)p (0C 0/t m0h 0p/ 0)m 0 (p K0) 0p ( 0 (. 0− x 0pK 0 p/ 0 m−]pK)t h (C/pm p. x)p) ( /( m−Cpp) 0– 0C 0th 0) 0/ 0m 0p 0) 0 ( 0K 0p 0/ 0m 0p])

Same way, the time lag between other road wheels and
first road wheel may be arrived at. (Cp/mp) (Kp . xp / mp) (Cp . xp / mp) 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Forcing circular frequency ωof the displacement applied A11=[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
may be used, for the above vehicle velocity as:
ω=2.π.f =2.π.V  = 2.π .(11.11/4) = 17.45 rad/s A12 =[0 0 0 0 0 0 0 0 (Kp/M) (Cp/M)
λ ((−K1−K2−K3−K4−K5−K6−K7−Kp)/M)
Now, for the sinusoidal road profile conditions, for the
+((−C1−C2−C3−C4−C5−C6−C7−Cp)/M)
present case, as function of time and displacements of the
first set of adjacent wheels 1 and 2 as function of time will  K1*l1+K2*l2+K3*l3+K4*l4− 
become11: +− /M
 K5*l5−K6*l6−K7*l7−Kp*Xp 
 A '(1−cos (ωt), if 0≤t≤ 2λand  C1*l1+C2*l2+C3*l3+C4*l4− 
a1 (t)=2 V +− /M
  C5*l5−C6*l6−C7*l7−Cp*Xp 
 0, otherwise
+(K1/M) (C1/M)(K2/M) (C2/M) (K3/M)
 A '(1−cos (ω(t−α1), if 0≤t≤ 2λand (C3/M) (K4/M) (C4/M) (K5/M)
a2 (t)=2 V
 0, otherwise +(C5/M) (K6/M) (C6/M) (K7/M) (C7/M)]
Same is applicable for the other sets of adjacent road A13=[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
wheels also.
Now from the governing eqns (1) to (15), the system A14 = [ 0 0 0 0 0 0 0 0 (−Kp*Xp/Iy) (−Cp*Xp/Iy)
matrices may be defined as:  K1*l1+K2*l2+K3*l3+K4*l4− 
A1=[01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +−K5*l5−K6*l6−K7*l7−Kp*Xp/Iy
A2=[(−Kh/mh)(−Ch/mh)(Kh/mh)(Ch/mh)  C1*l1+C2*l2+C3*l3+C4*l4− 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +−C5*l5−C6*l6−C7*l7−Cp*Xp/Iy
A3=[0 0 01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] +(−(K1*l1*l1+K2*l2*l2+K3*l3*l3+
A4=[(−Kh/mut) (Ch/mut) ((−Kh−Kut−Ktth/mut)) K4*l4*l4+K5*l5*l5+K6*l6*l6
+ K7*l7*l7+ Kp*Xp*Xp)/Iy)
((−Ch−Cut−Ctth)/mut)(Kut/mut) (Cut/mut)
(−(C1*l1*l1+C2*l2*l2+C3*l3*l3+C4*l4*l4+
(Ktth/mut) (Ctth/mut)00000000000000000000]
C5*l5*l5+C6*l6*l6+C7*l7*l7+Cp*Xp*Xp/Iy))
A5=[0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] (K1*l1/Iy) (C1*l1/Iy) (K2*l2/Iy) (C2*l2/Iy)
(K3*l3/Iy) (C3*l3/Iy) (K4*l4/Iy)
A6 = 0 0 (Kut/mlt) (Cut/mlt) ((−Kut−Klt)/mlt)((−Cut−Clt) /(mClt4)* (lK4lt//Iym) l(t− )(K5*l5/Iy)) (−C5*l5/Iy)
A6 = 0 0 (Kut/mlt) (Cut/mlt) ((−Kut−Klt) (/ Cm l lt t/ )m(A(lt6−) =C 0 0u0 t0 −0 0 0C (0lK 0t) 0u /t0m /0m 0lt 0l)t 0 () 0K ( 0lCt 0u/ 0tm 0/ 0lmt 0 )l]t) ((−Kut−Klt)/mlt)((−(C−uKt6−*Cl6lt/)Iy /)m(−lCt)6 (*Kll6t//Imy)l t )
(Clt/mlt) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] (Clt/mlt) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] (−K7*l7/Iy)(−C7*l7/Iy)]

A7=[0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] A15=[0000000000000001000000000000]
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DeF. SCI. J., VOL. 68, NO. 1, JANuARy 2018
A16 =[0000000000 (K1/mw1) (C1/mw1) model to idealised road inputs simulating the ground reaction
forces using the approach suggested by Michael15. Matlab
(K1.l1/mw1) (C1.l1/mw1)((−K1−Kw1)/mw1) 2014 a software package has been used in these simulations.
((−C1−Cw1)/mw1) 000000000000 ] Sample vibration response graphs are given in results section.
Natural frequency of major mass segment viz. the chassis thus
A 1 7=[0000000000000000010000000000] obtained is compared with the value established by an earlier
research work, as discussed in the results section, to validate
A18=[0 0 0 0 0 0 0 0 0 0 (K2/mw2) the model.
(C2/mw2) (K2.l2/mw2)
3. oPTImAL AFV SEAT SuSPENSIoN DESIGN
(C2.l2/mw2) 00((−K2−Kw2)/mw2)
uSING INVARIANT PoINTS THEoRy
((−C2−Cw2)/mw2) 0 0 0 0 0 0 0 0 0 0] 3.1 Numerical Simulations

Now the study is focused on crew seat location and the
A19=0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0] optimised values of seat suspension parameters are obtained

by visualising a 2 dof occupant-seat suspension model of
A20=[0 0 0 0 0 0 0 0 0 0 (K3/mw3)(C3/mw3)
Fig. 2, using the two methods of Invariant points theory
(K3.l3/mw3)(C3.l3/mw3)0 0 0 0 proposed by Liu7, et al.
((−K3−Kw3)/mw3)
((−C3−Cw3)/mw3) 0 0 0 0 0 0 0 0]

A21=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0]

A22=[0 0 0 0 0 0 0 0 0 0 (K4/mw4) (C4/mw4)
(K4.l4/mw4) (C4.l4/mw4)
0 0 0 000 ((−K4−Kw4)/mw4)
((−C4−Cw4)/mw4) 0 0 0 0 0 0]

A23=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 0 0 0 0]

A24=[00 0 0 0 0 0 0 0 0 (K5/mw5) (C5/mw5)
Figure 2. occupant-seat suspension model.
(−K5.l5/mw5) (−C5.l5/mw5)
0 0 0 0 0 0 0 0 ((−K5−Kw5)/mw5) Method 1 of invariant points theory involves the use
((−C5−Cw5)/mw5) 0 0 0 0] of direct mathematical formula. Method 2 involves the
formulation of objective function, selection of lower and
A25=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 0 0] upper bounds of parameter values based on earlier studies

and the application of genetic algorithm (G A) toolbox of
A26=[00 0 0 0 0 0 0 0 0 (K6/mw6) (C6/mw6) optimisation App of Matlab 2014a software. G.A, which is
(−K6.l6/mw6) (−C6.l6/mw6) stochastic technique search method, not only increases the
probability of finding the global optimum solution but also
0 0 0 0 0 0 0 0 0 0 ((−K6−Kw6)/mw6)
avoids convergence to a local minimum which is a drawback
((−C6−Cw6)/mw6) 0 0] of gradient based methods6. G.As are global search methods

and are based on the Darwins principle of natural selection
A27=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 ] and genetic modification16. They operate with a population of
A28=[0 0 0 0 0 0 0 0 0 0 (K7/mw7)(C7/mw7) possible solutions (individuals) of the optimisation problem.
Also they work using three operators viz. selection, cross over
(−K7.l7/mw7) (−C7.l7/mw7) and mutation17. Here, G.A is applied to search for the optimal
0 0 0 0 0 0 0 0 0 0 0 0 ((−K7−Kw7)/mw7) parameters of vehicle seat suspension in order to minimise
bodily vibration response of crew to achieve his best comfort
((−C7−Cw7)/mw7)]
during vehicle operation.
Global Optimisation Toolbox of Matlab 2014a provides
2.3 Numerical Simulation and Validation functions that search for global solutions to problems which
The natural frequencies and the frequency domain contain multiple maxima or minima. The toolbox includes
vibration responses of various lumped masses of the vehicle- solvers like genetic algorithm, pattern search, etc., The genetic
occupant composite model are obtained using transfer functions algorithm is a method for solving both constrained and
obtained from the state space variables formed, utilising the unconstrained optimisation problems. As mentioned above, it
governing equations of motion (1) - (15), by subjecting the is based on natural selection, the process that drives biological
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RAMAMuRTHy, et al.: eRGONOMIC LeVeL IMPROVING OF ARMOuReD FIGHTING VeHICLe CReW
evolution. The algorithm repeatedly modifies a population of
individual solutions. It selects individuals at random from the
current population, at each step, to be parents and uses them to
produce the children for the next generation. The population
‘evolves’ toward an optimal solution over successive
generations. As mentioned earlier, it uses three main types of
rules viz. selection, cross over and mutation at each step to
create the next generation from the current population18.
Optimised parameter values of seat suspension for Figure 4. Layout of data acquisition setup.
ride comfort are chosen from the results obtained at the end
of optimisation process using G.A solver. To illustrate the
improvement obtained in ride comfort with the optimised
parameter values, acceleration response of body for the current
and optimised parameter values are obtained using the above
said occupant-seat suspension model. Then the results are
compared.
3.2 Validation of Formulated 2 dof occupant-seat
Suspension model through Case Study
Acquiring time domain data using data acquisition set up
has been quite familiar since long. use of MeMS sensor as part
of data acquisition set up has been reported by Patel19, et al..
Figure 5. Running of test vehicle in test track.
Though modern sensors like MeMS are widely functional now-
a-days, use of sensors like piezo electric accelerometers are still Sensor, pre-amplifier, recorder, storage medium/ display
popular due to their ruggedness as required in the current case are the components common to the data acquisition setup.
study. Hence by using the said piezo electric accelerometer, Sensor’s function is to detect the mechanical movement and
case study has been carried out, by acquiring data on seat level convert it into a specific, usable electric signal. Accelerometer
vibration of the vehicle, as part of present work, to validate is the sensor used here. The required filtering, gain and cable
the formulated 2 dof Occupant-seat suspension model of drive capability are provided by the pre-amplifier. Spectrum
Fig. 2, before using the same for carrying out the Invariant analyser is the display system used in lab level analysis. In the
Points Theory based optimisation study. current study, vibration data are stored in ASCII codes in time
For this, first, the acceleration responses are obtained for domain on to a laptop connected to the data acquisition system,
the model of Fig. 2 through simulation study, for the idealised by fixing a sampling rate of 100 kHz and sampling period of
sinusoidal road input of amplitude (A') = 0.15 m and pitch 100 ms. The recorded data are further processed & analysed
(λ) = 4 m for vehicle speed of 40 km/hr. Matlab code written in the lab using Signal Processing techniques to obtain the
for the purpose is used for this. Then the case study is carried seat level acceleration. Power for the instruments during data
out by running the AFV in the Sinusoidal test track, with the acquisition is provided by an inverter which is supplied with
accelerometer duly mounted beneath the Crew Seat of AFV, 24V DC from battery placed on rear of the tank.
as shown in Fig. 3. Said accelerometer is stud mounted to the From the vibration data acquired, acceleration response at
installation kit welded in the required location of the vehicle. seat level is obtained, by using the Matlab code developed for
Layout of data acquisition set up is given in Fig. 4. Running of this purpose. Final seat level vibration values are obtained by
test vehicle on test track is as shown in Fig. 5. passing the output through a low pass filter with upper cut-off
frequency as 100 Hz, based on region of interest for our study,
aimed at human comfort analysis. Acceleration levels thus
obtained are compared with those obtained through simulation
study, to validate the optimisation model formulated, as
mentioned in the results section.
3.3 optimisation using Invariant Points Theory
based objective Function
For implementing the optimisation methodology based
on Invariant points theory, as proposed by Liu7, et al., for the
Occupant-seat suspension model of Fig. 2, the parameters are
defined such that the terms m , m , K, C and K represent
s t s s t
seated driver (sprung) mass, driver seat (un sprung) mass,
stiffness and damping coefficients of human body segment viz.
‘thigh with pelvis’ and stiffness of seat suspension respectively.
Figure 3. mounting of accelerometer. Also the terms X, X and X refer to the state variables which
s t r
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DeF. SCI. J., VOL. 68, NO. 1, JANuARy 2018
stand for sprung and un-sprung mass displacements and road 0.8 and objective function accuracy of 1e-15, retaining default
input respectively. For the ride comfort of the crew of AFV., values wherever necessary, optimal values are obtained at 185th
desired objective is proposed as the minimisation of objective iteration.
function formed by the combination of these three state
variables7, et al.. 4. RESuLTS AND DISCuSSIoN
4.1 Validation of Vehicle-occupant Composite
3.3.1 Method 1 model using Established Results
under method 1 of the above approach, expressions for Table 4 shows the values of natural frequencies (f) of
n
optimal suspension parameters, as arrived at by the above various lumped masses of the vehicle-occupant composite
researchers7 are: model for the idealised road inputs, simulating the ground
Ks=(K .m .m )/(m + m )2 and reaction forces, obtained through the current mathematical
t s t s t
modelling and simulation study. From the fact that the value of
Cs= K .m3.m (m + 2m )/( m .m )4 (17) natural frequency of the major mass segment i.e Chassis mass
t s t s t s t
M thus obtained (1.2357 Hz), reasonably agrees with the value
With reference to Fig. 2, for a 2 dof occupant-seat obtained in an earlier analysis carried out by Balamurugan20
suspension model, a group of nominal seat suspension (1.2449 Hz), validity of vehicle-occupant composite model
parameters obtained from earlier studies are considered such formulated as part of present work, is established.
that: m = 61 kg, m = 10 kg, C = 2475 Ns/m, K = 49340 N/m
s t s s
and K = 90000 N/m. Table 4. Natural frequencies (fn) of various masses obtained
t through modelling and simulation
3.3.2 Method 2
mass fn (Hz) mass fn (Hz) mass fn (Hz)
under the method 2 of Invariant points theory proposed
by the authors, the objective function is selected as: mh 3.9955 M 1.2357 mw5 0.6227
F =b1Y12+b2 Y22+b3Y32 +b4Y42 (18) mut 2.8060 mw1 0.7318 mw6 3.6079
where in
mlt 2.1361 mw2 0.0391 mw7 0.6227
Y =C2K +K (−K .m +K .m ) (19)
1 s t s t s s t
mth 2.2460 mw3 0.6227
Y =C2K (m +2m )+2K m (−K m +K .m ) (20) mp 1.4021 mw4 3.6079
2 s t s t s t t s s t
Y =−2K2(m +m )[−K mm +K ((m +m )2) 4.2 Frequency Domain Responses
3 s s t t s t s s t 
(21) Frequency domain vibration responses of various masses
+Cs2Kt −2Ks(ms +mt)2+Ktms(ms +mt) of the vehicle-occupant composite model formulated, are
obtained using Matlab 2014a software, by subjecting the model
Y4=−K mm +K (m +m )2 (22) to idealised road inputs at seven wheel stations, thus simulating
t s t s s t
the ground reaction forces. Figs. 6 and 7 show such graphs for
where as b1,b2,b3 and b4are positive weighing coefficients selected masses viz. head and chassis (bump), respectively,
for the local maximum values, selecting the value of with the magnitude in db. The notation followed for output
b = 1 (i = 1,2,3,4),as suggested by the authors. Now the graphs is such that z13 refers to vibration response of state 1
i
optimal values are obtained under method 2 using optimal due to road input at wheel station 3, and so on. As there are 7
toolbox as suggested by the said researchers7, by solving the road input forces and 14 displacement output state variables
equations with initial values and value ranges of K and C, as considered in the current study, a total of 98 transfer functions
s s
described below. G.A is the optimisation algorithm used for are to be investigated. However due to the similarity in the
this purpose. input forces 1, 3, 5, & 7 and 2, 4, & 6 of the system considered,
it is observed that the transfer functions and thus the resulting
3.3.2.1 Optimisation based on G.A using Method 2 response output graphs are found to be similar in certain cases,
To obtain the optimal values using G.A following the as in Figs. 6 and 7, for instance, Z11=Z13=Z15=Z17
method 2 illustrated above, first a function file has been created and Z111=Z113=Z115=Z117, following the above said
in Matlab 2014a to define the objective function of eqns. notation. This is also supported by the results obtained for the
(18) to (22) of method 2. Then the lower and upper bounds similar case of 3 mass system proposed by Hatch15.
of suspension parameters corresponding to the same nominal
values of method 1 mentioned earlier, are fixed as: 4.3 Validation of occupant-seat Suspension model
60≤ m ≤ 62; 8 ≤ m ≤1 2; 1 980 ≤ C ≤ 2970; through Case Study
s t s (23) Seat level acceleration levels are obtained through
39472 ≤ K ≤ 59208 &72000 ≤ K ≤1 08000
s t simulation study and case study as mentioned earlier. The
Now setting G.A parameters like population size of 50, results are illustrated graphically in Figs. 8(a) and 8(b),
number of variables as 5, number of generations as 5000, fitness respectively. The reasonable agreement between the two results
scaling function as ‘rank’, selection function as ‘uniform’, demonstrates the validity of the occupant-seat suspension
cross over technique as ‘heuristic’, probability of cross over as model formulated in the present work.
42