Vibration Analysis and Modeling of an Off-Road Vibratory ...downloads.hindawi.com/journals/sv/2018/8527574.pdf · 5 l 6 l 7 l 3 l 4 l 2 l 1 l 8 0 F d M dy c L＠ z L＠ m ﬀ (a)

Research ArticleVibration Analysis and Modeling of an Off-RoadVibratory Roller Equipped with Three Different CabrsquosIsolation Mounts

Vanliem Nguyen 12 Jianrun Zhang 1 Vanquynh Le2 and Renqiang Jiao3

1School of Mechanical Engineering Southeast University Nanjing China2Faculty of Automotive and Power Machinery Engineering Thai Nguyen University of Technology Thai Nguyen Vietnam3School of Mechanical and Electrical Engineering Hubei Polytechnic University Huangshi China

Correspondence should be addressed to Jianrun Zhang zhangjrseueducn

Received 12 December 2017 Revised 9 March 2018 Accepted 28 March 2018 Published 15 May 2018

Academic Editor Edoardo Sabbioni

Copyright copy 2018 VanliemNguyen et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study proposes a dynamic model of the vibratory roller interacting with the off-road deformed terrain to analyze the low-frequency performance of three different cabrsquos isolation mounts under the different operating conditions In order to evaluate theride comfort of the vibratory roller with the different cabrsquos isolation mounts a three-dimensional nonlinear dynamic model isestablished The power spectral density (PSD) and the weighted root mean square (RMS) of acceleration responses of the verticaldriverrsquos seat cabrsquos pitch and roll vibrations are chosen as objective functions in the low-frequency range Contrastive analysisof low-frequency vibration characteristics of the vibratory roller with the traditional rubber mounts the hydraulic mounts andthe pneumatic mounts is carried out Experimental investigations are also used to verify the accuracy of models The researchresults show that the hydraulic mounts have an obvious effect on mitigating the cab vibration and improving the ride comfort incomparison with the traditional rubber mounts and the pneumatic mounts

1 Introduction

The vibratory roller is a type of the soil compactor whichis mainly used in the field of the construction project onroads railways airports and so on There is a combinationof the static force of the vehicle and the dynamic force ofthe vibratory drum yielded by an eccentric mass rotatingaround the drum axis to compact soil asphalt and othermaterials in its work process [1ndash3] Therefore the vibrationdynamics of the vehicle are generated from twomain sourcesOne is the wheels interacting the deformable terrain whenthe vehicle travels and the other is interactions between thedrumtyres and the elastoplastic terrain when the vehiclecompacts the soil ground [3 4] Basic researches of thetyre-soft soil interaction models which were proposed byBekker andWong [5 6] had been applied for researching theeffect of soil deformation on off-road vehicle ride responses[4 7 8] Besides based on the theoretical approach ofAS2TM a model of elastic tyre-soil interaction was proposedto investigate the tyre dynamic behaviours on various soil

deformations [9]The dynamic pressure-sinkage relationshipof a smooth rigid wheel-terrain interaction model was alsostudied from the literature and experimental observations[10] In addition the effect of the rough terrain surfaces andvarious off-road terrains had been researched for wheels-soil contact model of earth-moving machinery [8 11 12] Allthe above results indicated that the vibration responses ofinteractive models are greatly influenced by deformable soilground

The traditional interactive models between the drumand elastoplastic soil ground were carried out by Adamand Kopf and Rinehart and Mooney [2 13] to study thedeformable properties of elastic-plastic soil ground in theactual operation conditions Besides the excitation force ofthe drum on the soil grounds was also controlled to enhancethe performance of the compaction process [3] The simula-tion and experiment methods of the vibratory roller-terraininteraction model with the optimal parameters of the wheelsthe drum isolation mounts and the drum mass were thenexamined by Li et al [14] However all the above researches

HindawiShock and VibrationVolume 2018 Article ID 8527574 17 pageshttpsdoiorg10115520188527574

2 Shock and Vibration

almost focus on exploring the soil compression efficiencywith wheels-terrain interactionmodels Ride dynamics of thevibratory roller received only a little attention

The low-frequency excitation arising from the wheels-terrain interaction is mostly transmitted to the driver viacabrsquos isolation mounts and seatrsquos suspension Furthermorevibrations in the low-frequency range of 05ndash10Hz causedby terrain roughness can lead to the main risk factors whichseriously affect the driverrsquos mental and physical health [1516] Consequently cabrsquos isolation mounts are one of themost important factors to improve the driverrsquos ride comfortThe isolation mounts used for the vibratory roller cab aremostly equipped with the traditional rubber mounts withtheir stiffness and damping constants [3 13 14]The influenceof the design parameters of the cab rubber mounts on theride dynamics of the soil compactor was investigated viathe analytical and experimental methods [12] and theirparameters were then optimized to enhance the driverrsquos ridecomfort [17] however the vertical driverrsquos seat and cabrsquospitch vibrations are still great under operation conditionsConsequently the traditional rubber mounts of the cab aredifficult to satisfy the driverrsquos ride comfort

Nowadays the cabrsquos isolation mounts of constructionequipment industrial vehicle and earth-moving machineryare being replaced by the increasing use of the hydraulicmounts to improve the ride comfort [18ndash20] A six-degree-of-freedom (DOF) cab model of earth-moving machinerywith the hydraulic mounts involving quadratic damping wasalso investigated under the road roughness excitation withina frequency range below 10Hz [21] The results showed thatthe root mean square (RMS) of acceleration responses andthe power spectral density (PSD) of displacement responsesof the cabrsquos mass centre are all reduced remarkably with thecomparison between hydraulic and rubbermounts Althoughthe paper has not yet considered the influence of wheels-terrain interactions however the research results are anobvious basis for study and application of the hydraulicmounts into cabrsquos isolation mounts of machines working ondeformable soil grounds especially the soil compactors

Besides the pneumatic suspension systems which wereused in the suspension systems of the car heavy truck andrail vehicles to improve the ride dynamics and noise levels[22ndash24] were also investigated and applied for cabrsquos isolationmounts and the driverrsquos seat suspension to enhance the ridecomfort as well as the driverrsquos health and safety [25ndash27]The research results showed that the vehicle ride comfortwas obviously improved by using the pneumatic suspensionsystems Moreover the theory studies also showed that thepneumatic mounts used in vibration isolation mounts canresult in their stiffness being almost 10 times higher than thelowest stiffness at approximately 8Hz [28] thus this leads tothe application in a low-frequency range of vibration isolationsystems being necessary Air springs have not only lowerresonance frequencies but also smaller overall length thanmechanical springs with equivalent properties [23] Howeverthe pneumatic mounts have not yet been studied to apply oncabrsquos isolation mounts of the off-road vehicles especially thevibratory roller

In this study a three-dimensional nonlinear dynamicmodel of a single drum vibratory roller was establishedbased on Adam and Kopf rsquos elastic-plastic soil model [2] andBekker hypothesis of the soft soil ground [5] The vibrationexcitations consisted of the interactions of the drumwheels-terrain roughness surface when the vehicle travelled on a softsoil ground and a lowhigh excitation frequency 2835Hz ofthe drum when the vehicle compacted an elastoplastic soilground Experimental investigations were used to validatethe models and verify their accuracy Three different cabrsquosisolation mounts including the traditional rubber mountsthe hydraulic mounts and the pneumatic mounts wererespectively simulated The performance of three differentisolationmounts was then evaluated through the accelerationPSD and the weighted RMS acceleration responses of thevertical driverrsquos seat cabrsquos pitch and roll vibrations in boththe frequency and time domains

The innovation in this paper is that an 11-DOF vehicledynamics model which can fully reflect the pitch and rollvibrations of the cab is established The vibration responsesof the vibratory roller under the low excitation frequencyespecially the pitch and roll response of cab with threedifferent isolation mounts are compared and analyzed Theresults showed that the low-frequency and high-stiffnesscharacteristics of the hydraulic mounts have a good effect onisolating low-frequency vibration transmitted and control-ling the cab shaking of the vibratory roller

2 Materials and Methods

21 The Vibratory Roller Dynamic Model As shown inFigure 1(a) the basic structure of the vibratory roller consistsof the rigid drumwheels the frontrear vehicle frame thecab and the seat Moreover the drum and the front frame areconnected by the rubber mounts and the front frame and therear frame are linked by an articulation connectionThe cab isconnected with the rear frame via the cabrsquos isolation mountswhich contains the traditional rubber mounts the hydraulicmounts and the pneumatic mounts as shown in Figures 1(b)1(c) and 1(d) respectively In this study three different cabrsquosisolation mounts are used for analyzing the low-frequencyperformance of the vibratory roller considering the interac-tion between wheels and off-road deformable terrain

A three-dimensional nonlinear dynamic model with 11DOF of a single drum vibratory roller considering theinteraction between the drumwheels and the deformableterrain is built as in Figure 2

See Figure 2 where 119911119904 is the vertical motion at the driverrsquosseat 119911119888 120601119888 and 120579119888 are the vertical the pitch and the rollmotions at the cab respectively and those are described as119911rf 120601rf and 120579rf at the rear vehicle frame The vertical and rollmotions of the front frame and the drum are described as 119911ff 120579ff and 119911119889 120579119889 The mass of the driverrsquos seat the cab the frontframe the engine and the rear frame and the roller drum isdescribed as 119898119904 119898119888 119898ff 119898rf and 119898119889 respectively 119897119906 and 119887Vare the longitudinal and lateral distances of the seat the caband the vehicle (119906 = 1ndash8 V = 1ndash7) 119902119905119895 and 119902119889119895 are the terrainroughness surface at wheels and drum contacts The driverrsquosseat suspension drum mounts and tyres are characterized

Shock and Vibration 3

to Frame

to CabAir bag

Surge pipe

to Air reservoir

13

Cab

WheelRear frame DrumFront frame

z

Rear frame

Cab

(a) Single drum vibratory roller

X

Y

Z

to Frame

to Cab

Damping plate Lower chamberAnnular orificeUpper chamber

Vibration isolation mounts

(b) Simple rubber mount

(c) Simple hydraulic mount

(d) Simple pneumatic mount

Main rubberOrifice

Rubber

zf

zc

Fkc

Fkc

Figure 1 Schematic of vibratory roller with three different cabrsquos isolation mounts

qt1 qd1

cs

kt1

ks

zs

zc

mc

ms

zff

md

Fkc1Fk

c3

zd

cd1kd1

ct1

mＬ

l5l6

l7

l3

l4

l2

l1

l8

0

Fd

Mdy

c

Ｌ

zＬ

mff

(a) Side view

qd1 b4 b5 qd2

kd2 cd2

cs

cd1kd1

b2

b1

b3

ks

zs

zc

zd

ms

mc

md

zff

m

d

Fkc1 Fk

c2

c

ff ff

(b) Front view

Figure 2 Lumped-parameter model

by the linear stiffness coefficients 119896119904 119896119889119895 119896119905119895 and the lineardamping coefficients 119888119904 119888119889119895 119888119905119895 respectively (119895 = 1-2) V0 is thevehicle forward speed

The vertical dynamic forces generated by the cabrsquos iso-lation mounts are described by 119865119896119888119894 Herein superscript 119896denotes R H or P which is the abbreviation of traditionalrubber mounts hydraulic mounts or pneumatic mountsrespectively (119894 = 1ndash4)

The vertical dynamic force of the driverrsquos seat suspensionis described by

119865119904 = 119896119904 (119911119904 minus 119911119888 minus 1198971120601119888 minus 1198871120579119888)+ 119888119904 (119904 minus 119888 minus 1198971 120601119888 minus 1198871 120579119888) (1)

Moreover the vertical dynamic forces 119865119889119895 at thearticulated-frame steered can be described by the verticalforce 119865119889 the rotation moment of pitch axis 119872119889119910 and therotation moment of roll axis119872119889119909 as follows

119865119889 = 1198651198891 + 1198651198892119872119889119910 = (1198651198891 + 1198651198892) 1198978119872119889119909 = 11986511988911198874 + 11986511988921198875

(2)

On the basis of Newtonrsquos second law of motion themotion equations of the driverrsquos seat cab and frontrearframe can be written as follows

119898119904119904 = minus119865119904119898119888119888 = 119865119904 minus (1198651198961198881 + 1198651198961198882 + 1198651198961198883 + 1198651198961198884) 119868119888119910 120601119888 = 1198651199041198971 + (1198651198961198881 + 1198651198961198882) 1198972 minus (1198651198961198883 + 1198651198961198884) 1198973119868119888119909 120579119888 = 1198651199041198871 + (1198651198961198881 + 1198651198961198883) 1198872 minus (1198651198961198882 + 1198651198961198884) 1198873


Rear frame

Cab

z kr crzrf

zc

(a) Traditional rubber mount

Cab

Rear frame

z kr cr cf

zrf

zc

(b) Hydraulic mount

w

Cab

M

Rear frame

zke

kv

zrf

zc

c

(c) Pneumatic mount

Figure 3 Lumped-parameter models of three cabrsquos isolation mounts

119898rf rf = (1198651198961198881 + 1198651198961198882 + 1198651198961198883 + 1198651198961198884) minus (119865119889 + 1198651199051 + 1198651199052) 119868rf119910 120601rf = (1198651198961198883 + 1198651198961198884) 1198974 minus (1198651198961198881 + 1198651198961198882) 1198975 + 1198651198891198976

minus (1198651199051 + 1198651199052) 1198977 +119872119889119910119868rf119909 120579rf = (1198651198961198882 + 1198651198961198884) 1198873 minus (1198651198961198881 + 1198651198961198883) 1198872 + 11986511990511198876 minus 11986511990521198877

minus119872119889119909119898ff ff = 1198651198891 + 1198651198892119868ff119909 120579ff = 11986511988911198874 minus 11986511988921198875

(3)

The system of the above differential equations can berepresented in the matrix form as follows

[M] Z + [C] Z + [K] Z = F (119905) (4)

where [M] [C] and [K] are (119898 times 119898) mass damping andstiffnessmatrices respectively Z is the (119898times1) displacementvector F(119905) is the (119898times 1) exciting force vector and119898 is thenumber of DOF (119898 = 9)22 Modeling of Three Cabrsquos Isolation Mounts

221 Mathematic Model of the Traditional Rubber MountsThe traditional rubber mounts are widely used for cabrsquos iso-lation mounts of the vibratory roller to reduce the vibrationsThe viscoelastic properties of the traditional rubber mountare mainly modeled by a linear stiffness 119896119903 and dampingcoefficient 119888119903 as shown in Figure 3(a) The correspondingdynamic force of themount 119894 of rubbermounts in the verticaldirection can be written as follows

119865119877119888119894 = 119896119903119894 (119911119888119894 minus 119911rf 119894) + 119888119903119894 (119888119894 minus rf 119894) (5)

119911119888119894 = 119911119888 + (minus1)120572 119897120572+1120601119888 + (minus1)119894 119887120575120579119888119911rf 119894 = 119911rf minus 119897120592120601rf + (minus1)119894 119887120575120579rf (6)

119888119894 = 119888 + (minus1)120572 119897120572+1 120601119888 + (minus1)119894 119887120575 120579119888rf 119894 = rf minus 119897120592 120601rf + (minus1)119894 119887120575 120579rf (7)

where 119911119888119894 119911rf 119894 and 119888119894 rf 119894 are the displacements and thevelocities of the cab floor and the rear frame at mount 119894 of

the isolation mounts when 119894 = 1-2 then 120572 = 1 120592 = 5 and120575 = 119894 + 1 when 119894 = 3-4 then 120572 = 2 120592 = 4 and 120575 = 119894 minus 1222 MathematicModel of the HydraulicMounts It is shownin Figure 1(c) that the hydraulic mount consists of the mainrubber a damping plate driven by the bolt and a closed cham-ber filled with the fluid The fluid flow in the upper-lowerchamber is derived by the transfer of damping plate throughthe annular orifice and the orifices Assuming the inertialforces in the annular orifice and the orifices are very smalltheir values can be neglected The dynamic behaviour ofthe fluid flow through the annular orifice and the orifices ismainly in the vertical direction 119911 Thus the unequal pressurebetween two chambersΔ119901 can be computed by the sumof thepressure losses through the annular orifice (Δ119901119886 = 119888119886|119886|119886)[20] and the orifices (Δ119901119900 = 119888119900|119900|119900) [29] as follows

Δ119901 = Δ119901119886 + Δ119901119900 = 119888119886 10038161003816100381610038161198861003816100381610038161003816 119886 + 119888119900 10038161003816100381610038161199001003816100381610038161003816 119900 (8)

where 119886 and 119900 are the average flow velocities in the annularorifice and the orifices and 119888119886 and 119888119900 are the constantsdetermined by the geometric dimensions of the annularorifice and the orifices respectively

The flow 119876119888 in the closed chamber through the annularorifice and the orifices is described by the equations ofcontinuity

119876119888 = 119860119888 = 119860119886119886or 119876119888 = 119860119888 = 119860119900119900 (9)

where 119860119888 119860119886 and 119860119900 are the effects of the chamber annularorifice and orifices area respectively and is the relativevelocity between the cab floor and the rear frame

Equation (8) thus can be computed by as followsΔ119901 = [119888119886 (119860119888119860119886

)2 + 119888119900 (119860119888119860119900

)2] || (10)

With effect of the damping plate area119860119889 and the unequalpressure between two chambersΔ119901 the liquid damping force119891 is derived by

119891 = 119860119889Δ119901 = 119888119891 || (11)

where 119888119891 = 119860119889[119888119886(119860119888119860119886)2 + 119888119900(119860119888119860119900)2] is the dampingconstant


Therefore the hydraulic mount applied for cabrsquos isolationmounts can be modeled by the lumped-parameter modelshown in Figure 3(b) The corresponding dynamic force ofthe mount 119894 of hydraulic mounts in the vertical direction isdescribed by

119865H119888119894 = 119896119903119894 (119911119888119894 minus 119911rf 119894) + 119888119903119894 (119888119894 minus rf 119894)+ 119888119891119894 1003816100381610038161003816119888119894 minus rf 1198941003816100381610038161003816 (119888119894 minus rf 119894) (12)

where 119911119888119894 119911rf 119894 and 119888119894 rf 119894 are derived in (6) and (7)

223 Mathematic Model of the Pneumatic Mounts Thepneumatic mount includes an air bag that is connected toan air reservoir via a surge pipe system The structure ofa simple pneumatic mount is shown in Figure 1(d) Themechanical behaviour mainly based on fluid dynamic andthermodynamic mechanisms is often very complicatedwhich is determined by the characteristic parameters of thepressure temperature volume mass density and energy ofthe air as well as the shape of the air bag

According to the method of calculation of a simplepneumatic mount in [22] assume that air bag is deflectedin the vertical direction 119911 After the deflection the new airbag volume 119881119887 and the new reservoir volume 119881119903 with thepolytropic process are

119881119887 = 1198811198870 minus 119860119890119911 + 119860 119904119908119881119903 = 1198811199030 minus 119860 119904119908 (13)

where 1198811198870 and 1198811199030 are the initial volumes of the air bag andthe reservoir119860119890 is the effective area of air bag119860 119904 is the cross-section area of the pipeline and 119908 is the displacement of airin surge pipe

The GENSYS model of the pneumatic mount as illus-trated in Figure 3(c) has polytropic gas state change For thismodel the static and viscous stiffness constants 119896119890 and 119896V andthe mass119872 can be respectively written by [23]

119896119890 = 119901011986021198901205821198811198870 + 1198811199030 119896V = 11989611989011988111990301198811198870 119872 = 119860 119904119897119904120588(119860119890119860 119904

11988111990301198811198870 + 1198811199030)2

(14)

where 120582 is the polytropic rate (1 lt 120582 lt 14) 1199010 is the initialpressure in the air bag 119897119904 is the length of the surge pipe and120588 is the air density

The nonlinear viscous damper 119888120573 is only related to thevelocity over the damper (119888120573) and the vertical viscous force119865V119911 is expressed by [30]

119865V119911 = 119896V (119911 minus 119908) = 119888120573 ||120573 sign () + 119872119872 = 119896V (119911 minus 119908) minus 119888120573 ||120573 sign () (15)

The relationship between the nonlinear damping 119888120573 andthe damping 119888119904 is described by

119888120573 = 119888119904 (119860119890119860 119904

11988111990301198811198870 + 1198811199030)1+120573 (16)

in which 119888119904 = (12)120588119860 119904119888st = (12)120588119860 119904(119888fr + 119888en + 119888119888 + 119888119887)where 119888st is total loss coefficient 119888fr is the loss coefficient dueto friction 119888en is the loss coefficient due to enlargement 119888119888is the loss coefficient due to contraction and 119888119887 is the losscoefficient due to bends in the pipe

The dynamic force of pneumatic mount in the verticaldirection can be derived by

119865119875119888 = 119896119890119911 + 119896V (119911 minus 119908) (17)

By combining (15) and (17) the corresponding dynamicforce of the mount 119894 of pneumatic mounts in the verticaldirection can be written as follows

119872119894119894 = 119896V119894 (119911119888119894 minus 119911rf 119894 minus 119908119894) minus 119888120573119894 10038161003816100381610038161198941003816100381610038161003816120573119894 sign (119894) 119865P119888119894 = 119896119890119894 (119911119888119894 minus 119911rf 119894) + 119896V119894 (119911119888119894 minus 119911rf 119894 minus 119908119894)

(18)

where 119911119888119894 and 119911rf 119894 are also derived in (6) and (7)

23 Dynamic Off-Road Vehicle and Deformable Soil Inter-action Models In actual operation conditions the drumand wheels often interact with the deformable soil groundsTherefore a rigid drum- and the elastic tyres-deformablesoil contact when the vehicle travels on the soft terrain anda rigid drum-elastoplastic soil interaction when the vehiclecompacts the elastoplastic soil ground are given to establishthe interactional models

231 The Rigid Drum-Deformable Soil Contact Model Theride vibration responses of vehicles are greatly influenced bythe rough terrain surfaces apart from the operating factorsand various designs Accordingly the random excitation onvarious off-road terrains of the wheel-soft terrain contactmodel [6] of the elastic tyre-soft terrain contact model [11]and of the rigid drum-elastic soil interaction model [17] isconcerned to evaluate the vehicle ride vibration respectively

In this study a single rigid drum-deformable soil contactmodel with the terrain roughness surface is investigatedbased on the traditional model of Bekker and Wong [5 6]When the drum traverses on a random terrain surface 119902(119905) ofa deformable terrain under the effect of the static anddynamic loads of the drum the terrain is then sunk 119911119900119886 asshown in Figure 4(a) The pressure 119901119892 and the shear stress120591119892 arising from the soil compression in the deformable arearegion (arc of 119900119886) thus impact contrarily the drum Conse-quently the vertical reaction force 119865119892 of the soil under thedrum is given by

119865119892 = int120579119886(119905)0

119861119889119901119892119903119889 cos 120579 119889120579 + int120579119886(119905)0

119861119889120591119892119903119889 sin 120579 119889120579= int119897(119905)

0119861119889119901119892119889119909 + int119897(119905)

0119861119889120591119892119909 (1199032119889 minus 1199092)minus12 119889119909

(19)


Δo

terrain surface

ar

zd

zx

zoaz0

x

rd Fd

md

l(t)

d

q(t)

0

a

gpg

a(t)q(t + x

0)q(t + x

0)

(a) The rigid drum-deformable soil

ob

terrain surface

ar

zt

z0

m

a

t

q(t)

t

r t

l1(t) l

x

2(t)

b pgg

a

0

zx

Ft

q(t + x

0)

(b) The elastic tyre-deformable soil

Figure 4 The wheels-soil interaction models [7]

where 120579119886(119905) and 119897(119905) are the angle and length in the hori-zontal direction of the drum-soil contact which are generallychanged and depend on the rough terrain properties

The pressure 119901119892 and the shear stress 120591119892 in (19) were givenby Bekker [5] as follows

119901119892 = (119896119888119887 + 119896120593)119911119899119909120591119892 = (119888 + 119901119892 tan120593) (1 minus 119890minus119895119889119870)

(20)

where 119896119888 and 119896120593 are the soil stiffness coefficients for sink-age and internal friction 119899 is the sinkage exponent 119887 =min119861119889 119897(119905) is the smaller dimension of the contact patchin which 119861119889 is the width of the drum 119888 is the soil cohesioncoefficient 120593 is the angle of the internal friction 119895119889 =119903119889119904119889[120579119886(119905) minus 120579] in which 119904119889 is the slip ratio of the drum and119870is the shear deformation modulus

Assuming ar is the average roughness line of the terrainsurface thus the sinking of the soil 119911119909 can be determined asfollows

119911119909 = 119902(119905 + 119909V0) + 119911119900119886 minus Δ= 119902(119905 + 119909

V0) + 119911119889 minus 1199110 minus (119903119889 minus radic1199032119889 minus 1199092)

(21)

where 119903119889 is the radius of the drum 1199110 is the static sinkage119911119889 is the vertical displacement of the drum centre and 119902(119905 +119909V0) is the random excitation of an off-road terrain and it isdescribed in Section 234

The vertical excitation forces 119865119889119895 arising due to the drummounts are described by

119865119889119895 = 119896119889119895 [119911ff minus 119911119889 + (minus1)119895 119887119895+3 (120579ff minus 120579119889)]+ 119888119889119895 [ff minus 119889 + (minus1)119895 119887119895+3 ( 120579ff minus 120579119889)] (22)

The motion equations of the rigid drum-soft terraincontact can be written as follows

119898119889119889 = 1198651198891 + 1198651198892 minus 119865119892 + 119898119889119892119868119889119909 120579119889 = 11986511988911198874 minus 11986511988921198875 (23)

232The Elastic Tyre-Deformable Soil Contact Model Whenthe elastic tyre traverses on the deformable terrain under theeffect of the static and dynamic loads of the wheel the terrainis also sunk Two deformation characteristics are presented inthe tyre-soil contact region One is the deformation betweenthe tyre and the soil (the region of 1198871199001198871015840) and the other is theunique soil (the region of 1198871015840119886) as shown in Figure 4(b)Herein 119911119905 1199110 and 119911119909 are the vertical displacements of thetyre centre the static deformation and the sinkage of terrainrespectively 119898119905 120596119905 and 119903119905 are the mass the angular velocityand radius of the wheel and119865119905 is the vertical dynamic force attyre centre

The regions of 1198871199001198871015840 and 1198871015840119886 are assumed to be a straightline 1198871199001198871015840 with the length of contact 1198971(119905) and an arc of 1198871015840119886with the length of contact in the horizontal direction 1198972(119905)respectively 119901119892 and 120591119892 arising in the deformable regions of1198871199001198871015840 and 1198871015840119886 are described by the vertical reaction forces ofterrain under the tire 1198651199111198921 and 1198651199111198922 [7]

The vertical reaction force 1198651199111198921 in the region of 1198871199001198871015840 iscalculated by

1198651199111198921 = 1198651199111199011198921 = 2119861119905 (119896119888119887 + 119896120593)int11989712(119905)

0119911119899119909119889119909 (24)

where 119911119909 = 119902(119905 + 119909V0) + 1199110 minus 119911119905 and 119887 = min119861119905 1198971(119905)The vertical reaction force 1198651199111198922 in the region of 1198871015840119886 is also

calculated as follows

1198651199111198922 = 1198651199111199011198922 + 1198651199111205911198922= int11989712(119905)+1198972(119905)

11989712(119905)119861119905119901119892119889119909

+ int11989712(119905)+1198972(119905)11989712(119905)

119861119905120591119892119909 (1199032119905 minus 1199092)minus12 119889119909(25)

where the pressure 119901119892 and the shear stress 120591119892 are determinedin (20) 119887 = min119861119905 1198972(119905) and 119895119905 = 119903119905119904119905[120579119886(119905) minus 120579] in which 119904119905is the slip ratio of the tyre

The total reaction force of the terrain is given by

119865119892 = 1198651199111198921 + 1198651199111198922 (26)


see

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(a) Loading phase

se

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(b) Unloading phase

mg

se

kＭＪ

cＭ kＭ

zＭ

zd

0Fd

Fe

md

me

(c) Drum-hop phase

Figure 5 The rigid drum and elastoplastic soil interaction model

The vertical excitation forces119865119905119895 exerted on the rear frameare described as follows

119865119905119895 + 119865119892119895 minus 119898119905119895119892 = 0119865119905119895= 119896119905119895 [119911rf minus 1198977120601rf + (minus1)119895 119887119895+5120579rf minus 119911119892119895]+ 119888119905119895 [rf minus 1198977 120601rf + (minus1)119895 119887119895+5 120579rf minus 119892119895]

(27)

where119898119905119895 is the portion of total vehicle mass supported at thetyres and 119892 is the gravitational acceleration233TheRigidDrumand Elastoplastic Soil InteractionModelThe vibration response of the drum is arising not only fromthe self-excitation but also from the interaction between therigid drum and elastoplastic soil In this study based on theelastoplastic properties of the terrain [2] a lumped-parametermodel of the drum-soil interaction in the vertical directionis built which can be divided into three phases as shown inFigure 5

In Figure 5 119911119889 and 119911se are the vertical motion of the drumand the elastic terrain deformation119898 is the total mass of thefront frame and the drum 119898119889 is the mass of the drum 119896spand 119896se are the plastic and elastic stiffness constants 119888se isthe elastic damping constant se is the abbreviation ofthe static equilibrium 119865119890 = 1198981198901198901205962 sin120596119905 is the verticalprojection of the rotating eccentric mass 119898119890 in which 120596 isthe vibrator rotational velocity and 119890 is the eccentricity of therotating mass 119865119892 is the dynamic force yielded by the plasticdeformation of the soil surface layer or the elastoplasticdeformation of the soil subsequence layers which is writtenas follows

119865119892 = 119896sp (119911119889 minus 119911se) = 119896se119911se + 119888sese (28)

The motion equation of the drum and elastoplastic soilinteraction can be described by

119898119889119889 = 119865119889 minus 119865119892 + 1198981198901198901205962 sin120596119905 (29)

According to Adam and Kopf [2] the elastoplastic prop-erty can be expressed by a plasticity factor 120576 and a soildamping to plasticity ratio 120574 as follows

120576 = 119896sp(119896sp + 119896se)

120574 = 119888se119896sp (30)

where the mutation parameter 120576 is from 0 to 1 The value120576 = 0 achieved as 119896sp = 0 refers to purely plastic soil propertywhich degrades the loss of the drum-soil contact The value120576 = 1 refers to an ideal elastic soil property achieved as 119896sp rarrinfin Over each cycle of the vibratory drum-soil interactionthere are two or three distinct phases which are described asfollows

(i) Loading Phase As shown in Figure 5(a) this phase ischaracterized by the elastic and the plastic soil deformationsThe drum moves downward while its compressive force isapplied to the terrainThe necessary conditions for this phaseare 119865119892 + 119898119892 gt 0 and 119889 gt 0

In order to describe the relation of 119911119889 120576 and 120574 the third-order differential equation of the vertical roller drum-soilinteraction is calculated by

120576120574119898119889

119911119889 + 119898119889119889 = 120576120574119889 + 119865119889 minus 120576119888se119889 + (120576 minus 1) 119896sp119911119889+ 1205761205741198981198901198901205963 cos120596119905 + 1198981198901198901205962 sin120596119905 (31)

(ii) Unloading Phase In this phase the drum moves upwardwhile the drum-soil contact is retained as illustrated inFigure 5(b) The soil recovers its elastic deformation whilethe plastic deformation represents the soil compaction Theplastic stiffness 119896sp is thus assumed to be infinite Thenecessary conditions for this phase are 119865119892 + 119898119892 gt 0 and119889 lt 0

119898119889119889 = 119865119889 minus 119888se119889 + 1198981198901198901205962 sin120596119905 (32)

(iii) Drum-Hop Phase The drum continues upward motionand the drum-soil contact is broken as seen in Figure 5(c)


minus004

minus002

0

002

004H

eigh

t (m

)

10 20 30 40 500Time (s)

(a) The off-road terrain profile

Terrain PSD

Medium

Good

Poor Very poor

10minus8

10minus6

10minus4

10minus2

100

Off-

road

PSD

(Ｇ2（Ｔminus

1)

100 10110minus1

Frequency (Hz)

(b) Spectral densities

Figure 6 Generation of the off-road terrain roughness according to unpaved off-road classification

The full elastic property of soil is thus recovered while theplastic stiffness of soil vanishes (119896sp = 0) which yields 120576 = 0The necessary conditions for this phase are 119865119892 + 119898119892 = 0

The drum-soil contact in this phase is broken and thestatic loads of the front frame and the drum are not balancedby any static reaction force of the terrain The gravitycomponent 119898119892 is now considered in the motion equation ofdrum rewritten by

119898119889119889 = 119865119889 + 119898119892 + 1198981198901198901205962 sin120596119905 (33)

The motions of the drum and the elastoplastic soilinteraction can be described in (31) (32) and (33) Based onthe vertical motion of the drum 119911119889 the vertical excitationforces 119865119889 in (22) are then determined

234 The Random Excitation of the Off-Road Terrain Thevehicle ride comfort is strongly influenced not only by thevibratory drum and the terrain deformation but also bythe rough terrain surfaces The terrain behaviour underwheel-soil contact is nonlinear Thus the off-road vehiclesmust be performed in the frequency domain apart from thetraditional time domain to analyze the ride comfort Off-roadterrain surface in the frequency domain is calculated usingthe PSD value [6 31] The spatial PSD of the road surfaceprofile 119878(Ω) is generally described as a function of thespatial frequency Ωcyclemminus1 The spectral density of off-road terrain is thus written in accordance with ISO proposal[32] over different spatial frequency ranges as

119878 (Ω) = 119878 (Ω0) sdot ( ΩΩ0

)minus1199080 (34)

where 1199080 = 3 for Ω le Ω0 and 1199080 = 225 for Ω gt Ω0 thevalue 119878(Ω0) provides a measure for the random terrain withthe reference spatial frequencyΩ0 = 12120587 cycle mminus1

Table 1 The parameters of the unpaved off-road classification

Classification Good Medium Poor Very poor1199080 225 225 214 214119878(Ω0) times 10minus6m3 cycminus1 1998 9739 37825 102416

More specifically assuming the vehicle travels with aforward speed V0 the off-road terrain irregularities in thetime domain can then be simulated by the series

119902 (119905) = 119873sum119894=1

119904119894 sin (119894Δ120596119905 + 120593119894) (35)

where 119873 is the number of intervals 119904119894 = radic2119878(119894Δ119899)Δ119899 isthe amplitude of each excitation harmonic in which 119878 is thetarget spectral density Δ119899 = 2120587119871 and 119871 is the length ofroad segment 120593119894 is a random phase uniformly distributedbetween 0 and 2120587 and Δ120596 = Δ119899V0 is the fundamentaltemporal frequency Mitschke [33] extended the spectraldensity ranges for the unpaved off-road classifications apartfrom the traditional asphalt road classifications includingthe classification ranges from good to very poor as listed inTable 1 and shown in Figure 6(b) and a desired terrainroughness can be yielded by choosing a value in the spectraldensity ranges

In order to develop an off-road terrain roughness inputfor the vibratory roller close to the actual terrain conditionthe simulation parameters used for generating the timedomain of a poor terrain roughness as shown in Figure 6(a)are V0 = 167msminus1 119871 = 84m Δ119905 = 0005 s 1199080 = 214and 119878(Ω0) = 37825 times 10minus6m3 cycleminus1 The PSD of the off-road terrain irregularity obtained from the time domain isdepicted in Figure 6(b) The frequency region of the inputsignal is mainly below 10Hz


Table 2The reference parameters of a single drum vibratory roller

Parameter Value119898119904kg 85119898119888kg 891119898ff kg 2822119898frkg 4464119898119889kg 4378119868119888119909kgm2 560119868119888119910kgm2 523119868rf119909kgm2 31 times 103119868rf119910kgm2 12 times 104119868ff119909kgm2 19 times 103119868119889119909kgm2 30 times 1031198871m 0551198872m 071198873m 0681198874m 09451198875m 09451198971m 03831198972m 011198973m 05241198974m 01361198975m 0761198976m 091198977m 061198978m 15119896119904Nmminus1 12 times 10411989611988912Nmminus1 39 times 10611989611990512Nmminus1 05 times 106119888119904Nsmminus1 12 times 10211988811988912Nsmminus1 29 times 10311988811990512Nsmminus1 40 times 103119891Hz 28351198650MN 028019

3 Results and Discussion

The performance of three different cabrsquos isolation mountsis evaluated under the interaction of wheels and off-roadterrain in both time and frequency domain The referenceparameters of the vehicle are given in Table 2 In additionfor the lumped parameters of three cabrsquos isolation mounts aslisted in Table 3 herein the traditional rubber mounts andthemain rubber of hydraulicmounts are the same stiffness 119896119903119894and damping constants 119888119903119894 [21] The static stiffness constants119896119890119894 of pneumatic mounts are also equivalently calculated withthe above two isolation mounts The vehicle ride comfort isthe main goal for evaluation performance

31 Evaluation Criteria The performance of the vehiclesuspension systemwas evaluated by threemain indices in thetime domain including the ride comfort working space androad holding characteristics Among these three indices theride comfort performance evaluated via the weighted RMSacceleration response was considered to be the most impor-tant index [21] In addition in the international standard ISO2631-1 [34] the acceleration PSD response was also applied

to estimate the effect of vibration on the endurance limit ofthe human body in the frequency domain It was suggestedthat a low-frequency range of 4ndash10Hz for the vertical and of05ndash2Hz for the rotational vibrations seriously affected thedriverrsquos health and safety

In this study the performance of three different cabrsquosisolation mounts is evaluated through the acceleration PSDresponses and the weighted RMS acceleration responses ofthe vertical driverrsquos seat cabrsquos pitch and roll vibrations in boththe frequency and time domains Thus the smaller valuesof the acceleration PSD and the weighted RMS accelerationmean better ability of the corresponding isolation mountsThe expression of the weighted RMS acceleration response isdefined by

119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)

where superscript 119896 denotes R H or P of three cabrsquos isolationmounts respectively subscript 119897 refers to the vertical driverrsquosseat (119911119904) cabrsquos pitch (120601119888) or cab roll (120579119888) vibrations 119886119896119908119897(119905) isthe acceleration response of R H or P in the 119897 as a functionof time and 119879 = 50 s is the duration of the simulation

32 Experiment Results In this section comparisons are usedto validate the vibratory roller model with the cab rubbermounts and verify its accuracy through experiment inves-tigations The experiment was carried out under the sameconditions of the dynamic simulationwhen the vehiclemovesand compacts an elastic-plastic soil ground Three steps inexperiments were described as follows

(i) Preparation step instruments for the experimentincluding a single drum vibratory roller XS120 ICPthree-direction acceleration sensors Belgium LMSdynamic test and analysis system were used to mea-sure the vibration accelerations The sensors werecalibrated and installed on the driverrsquos seat and thecab floor at four locations of isolation mounts Thearrangement of measuring points and instrumenta-tions is shown in Figure 7

(ii) Measurement step the multipoint measurementmethod for the vehicle ride comfort was applied foranalysis and comparison The process of measure-ment was performed under four different conditionssuch as at lowhigh excitation frequency 2835Hz ofthe rigid drum when the vehicle compacted an origi-nal place and when the vehicle moved and compactedon an elastic-plastic soil ground at 083m sminus1 forwardspeed

(iii) Data extraction step the data measurements werecarried out including the vertical acceleration on thedriverrsquos seat and the vertical accelerations at fourmeasurement points on the cab floor

The acceleration responses of cabrsquos pitch and roll angleswere derived from themeasured vertical accelerations at fourmeasurement points on the cab floor by using kinematic


Table 3 The lumped parameters of rubber (R) hydraulic (H) and pneumatic (P) mounts

Parameter R and H P119896119903119894Nmminus1 119888119903119894Nsmminus1 119888119891119894Ns2mminus2 119896119890119894Nmminus1 119896V119894Nmminus1 119872119894kg 119888120573119894Ns2mminus2

Font-end mount 91 times 105 218 20 times 103 91 times 105 153 times 105 98 124 times 103

Rear-end mount 12 times 105 29 45 times 103 12 times 105 201 times 105 33 107 times 103

Table 4 The lumped parameters of the Grenville loam

Terrain type Moisture content 119899 119896119888Nmminus(119899+1) 119896120593Nmminus(119899+2) 119888Pa 120593∘Grenville loam 24 101 006 times 103 5880 times 103 31 times 103 298

Cab floor accelerometer The driverrsquos seataccelerometer

13

X

Y

Z

5

Signal processor and display the results

Rear frame accelerometer

Figure 7 Diagrammatic sketch of the experimental setup

relations of the cab Assuming small angular motions andnegligible contribution due to structure flexibility thus theacceleration responses of cabrsquos pitch and roll angles arecalculated by

120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)

where 119888119894 (119894 = 1ndash4) are the vertical accelerations at fourmeasurement points on the cab floor and 119897119888 and 119887119888 are thedistance between measurement points

The acceleration PSD responses and the weighted RMSacceleration responses of the vertical driverrsquos seat cabrsquos pitchand roll vibrations are compared with the experimentalresults under the same condition of a low excitation fre-quency 28Hz of the drum when the vehicle moves andcompacts the elastic-plastic soil ground at 083m sminus1 forwardspeed as shown in Figures 8 and 9

As plotted in Figure 8 comparison between simulationand experimental results shows that the simulation resultsalmost agree with the tests regarding the frequency of the var-ious peaks in the responses and the trend Besides the sim-ulation results of the weighted RMS acceleration responsesof the vertical drivers seat cabrsquos pitch and roll vibrationsalso are a small deviation of 1013 1136 and 1267 incomparisonwith theirmeasured results as shown in Figure 9It implies that the mathematical model of the vibratoryroller is accurate and feasible for low-frequency vibrationperformances analysis of cabrsquos isolation mounts

33 Ride Comfort Analysis When the Vehicle Travels on theDeformable Terrain The five types of soft terrain from LETEsand to Grenville loam had been given byWong [35] throughthe data of field measurement In this study the vehicle isassumed to be travelling on a terrain type of Grenville loam at167m sminus1 forward speed The Grenville loamrsquos parameters inTable 4 and its off-road terrain in Figures 6(a) and 6(b) are therandom excitation inputs Simulations are then carried out tocompare the performances of three cabrsquos isolation mounts

331 Frequency Acceleration Responses The simulationresults of the acceleration PSD responses of the verticaldriverrsquos seat cabrsquos pitch and roll vibrations with three cabrsquosisolation mounts are plotted in Figure 10 The peaks ofacceleration PSD responses of vertical driverrsquos seat and cabrsquospitch vibrations shown in Figures 10(a) and 10(b) exhibit thatthe resonance frequencies occur at 079 179 209 249 and839Hz with both traditional rubber mounts and hydraulicmounts and at 089 18 22 26 and 839Hz with pneumatic


ExperimentalSimulation

1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

(a) Vertical driverrsquos seat


1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

(b) Cabrsquos pitch angle


1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

(c) Cabrsquos roll angle

Figure 8 The acceleration PSD responses under a low excitation frequency 28Hz of the drum

mounts Meanwhile the resonance peaks of accelerationPSD responses of cabrsquos roll angle shown in Figure 10(c) occurat 209 259 and 839Hz with both rubber mounts andhydraulic mounts and at 26 and 839Hz with pneumaticmounts Particularly the results show that hydraulic mountswith the nonlinear damping characteristics have almostno effect on the resonance frequencies in comparison withtraditional rubber mounts which had been proved by Sunand Zhang [21] However at low-frequency range from 079to 26Hz the resonance frequencies with pneumatic mountsare higher in comparison with both traditional rubber andhydraulic mounts in all three directions This can be due tothe influence of the elastic stiffness of air bags which may bechanged and depended on the pressure volume mass anddensity of the air in air bags

Also at a low-frequency range of 079ndash26Hz the resultsspecifically emphasize that traditional rubber mounts showmore resonance frequencies than those on the off-roadterrain in comparison with those on the rigid road whichonly show a resonance frequency near 21 Hz [7] or near277Hz [21] It implies that the driverrsquos ride comfort is

strongly influenced by an off-road deformable terrain inlow-frequency region Consequently the maximum values ofacceleration PSD responses with three cabrsquos isolation mountsat 079ndash26Hz are given to compare the performances of threecabrsquos isolation mounts

The maximum PSD values with three cabrsquos isolationmounts are listed in Table 5 The maximum PSD values ofthe vertical driverrsquos seat cabrsquos pitch and roll vibrations withhydraulic mounts are strongly reduced by 5528 5765and 3516 compared with traditional rubbermountsMean-while with pneumatic mounts the maximum PSD values ofthe vertical driverrsquos seat and cabrsquos pitch vibrations are alsolower by 3902 and 3294 however those of cabrsquos rollvibration are higher by 714 in comparison with traditionalrubber mounts

Besides at the frequency range above 10Hz Figure 10shows that the acceleration PSD responses with hydraulicmounts are all clearly lower in comparison with traditionalrubber mounts whereas their values with pneumatic mountsare all higher compared with traditional rubber mounts in allthree directions It can be seen from the above analysis that


Table 5 The maximum PSDs of the acceleration responses with three cabrsquos isolation mounts

Parameters 119891Hz Maximum PSD 119891Hz Maximum PSDR H P

Vertical vibrationm2 sminus3 209 123 055 26 075Pitch vibrationrad2 sminus3 209 085 036 26 057Roll vibrationrad2 sminus3 259 0091 0059 26 0098

Table 6 The parameters of an elastoplastic ground deformation with a high density soil

Road ground 120576 119896spNmminus1 119896seNmminus1 119888seNsmminus1

Elastoplastic soil 087 283 times 106 423 times 106 371 times 103

Table 7 The resonance frequencies of three cabrsquos isolation mounts

Isolation mounts Low excitation frequency 28Hz of the drum High excitation frequency 35Hz of the drum1198911 1198912 1198913 1198914 1198915 1198916 1198911 1198912 1198913 1198914 1198915 1198916

R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2

Figure 9 The weighted RMS acceleration responses under a lowexcitation frequency 28Hz of the drum

the improveddriverrsquos health and safetywith hydraulicmountsare especially evident in comparisonwith both the pneumaticand traditional rubber mounts in the low-frequency range

332 The Weighted RMS Acceleration Responses The resultsof the weighted RMS acceleration responses of the verti-cal driverrsquos seat cabrsquos pitch and roll vibrations with threedifferent isolation mounts are shown in Figure 11 Withtraditional rubber mounts the weighted RMS values of thevertical driverrsquos seat and cabrsquos pitch vibrations are quite greatwhich can make the driver tired and uncomfortable [34]however those of cabrsquos roll vibration are relatively small andthese results are similarly the basis of measurements andsimulations results by Kordestani et al and Quynh [12 17]In addition the weighted RMS values of the vertical driverrsquosseat cabrsquos pitch and roll vibrations with hydraulic mountsare respectively decreased by 3248 2631 and 6303 incomparison with traditional rubber mounts and by 1311

1624 and 142 in comparison with pneumatic mountsThus the driverrsquos ride comfort can be clearly improved byusing the hydraulic mounts

34 Ride Comfort AnalysisWhen Vehicle Compacts the Elasto-plastic Soil Ground The soil properties are changed duringthe interaction between wheels and soil ground In the initialphase the soil is relatively soft thus a continuous contactbetween the drum and soil can exist The soil density thenbecomes higher after the repeated phase of the drum And inthe final phase the drum-soil contact could be broken dueto the interaction of the drum with the high-density soil(elastoplastic soil) The elastoplastic soil properties are rep-resented by three different values of the plasticity parameter120576 including a low density soil 120576 = 034 medium densitysoil 120576 = 072 and high-density soil 120576 = 087 [2] Howeverthe property of a low density soil (120576 = 034) is similar tothe property of a soft soil deformation which is simulated inSection 33 Thus an elastoplastic soil concerned with amedium- or high-density soil is chosen in this part

In the compaction condition the vibratory roller invari-ably moves at very slow speed on the terrain deformationThus the vehicle forward speed at 083m sminus1 and an excita-tion frequency of 2835Hz of the drum on a high-density soilground with parameters listed in Table 6 are chosen as theinput parameters of the model in Figure 5 Meanwhile theelastic tyres are assumed to be moving on a soil deformationof the model in Figure 4(b) The vehicle model is thensimulated to evaluate the performance of three cabrsquos isolationmounts

341 Frequency Acceleration Responses The accelerationPSD responses with three cabrsquos isolationmounts at a lowhighexcitation frequency 2835Hz of the drum are given inFigures 12 and 13 The results of the resonance frequenciesare also listed in Table 7 Similarly in the vehicle travellingcondition the resonance peaks of the acceleration PSD



ParametersLow excitation frequency 28Hz of the drum High excitation frequency 35Hz of the drum

119891Hz Maximum PSD 119891Hz Maximum PSD 119891Hz Maximum PSD 119891Hz Maximum PSD

R H P R H P

Vertical vibrationm2 sminus3 209 068 037 18 065 209 054 032 18 051

Pitch vibrationrad2 sminus3 209 042 019 18 048 209 042 018 18 035

Roll vibrationrad2 sminus3 249 0048 0032 22 0042 249 0054 0026 569 0041

X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP


Figure 10 The acceleration PSD responses under an excitation of the off-road terrain of Grenville loam

responses with hydraulic rubber mounts are not changed incomparison with traditional rubber mounts Meanwhile theresonance frequencies with pneumatic mounts are slightlyhigher in comparison with both traditional rubber andhydraulic mounts Besides at a low-frequency range of169ndash249Hz traditional rubber mounts also occur showresonance frequencies thus the ride comfort is strongly

influenced by an elastoplastic soil ground in low-frequencyregion

In order to compare the performances of three cabrsquosisolationmounts themaximumPSD values of three cabrsquos iso-lation mounts are also carried out in Table 8 The maximumPSD values of the vertical driverrsquos seat cabrsquos pitch and rollvibrations with hydraulic mounts are strongly reduced by


Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio

ns0141 rad Ｍminus2

117 rad Ｍminus2

122 m Ｍminus2106 m Ｍminus2

157 m Ｍminus2

0139 rad Ｍminus20376 rad Ｍminus2


Figure 11 The weighted RMS acceleration responses under an excitation of the off-road terrain of Grenville loam

X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


Figure 12 The acceleration PSD responses on a high-density soil ground at low excitation frequency 28Hz of the drum


X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


Figure 13 The acceleration PSD responses on a high-density soil ground at high excitation frequency 35Hz of the drum

4558 5476 and 3333 at a low excitation frequency28Hz and by 4074 5714 and 5185 at a high excitationfrequency 35Hz in comparison with traditional rubbermounts Meanwhile with pneumatic mounts the maximumPSD values of the vertical driverrsquos seat and cabrsquos roll vibrationsare also smaller by 441 and 1250 and those of cabrsquospitch vibration are higher by 1250 at a low excitationfrequency 28Hz however all the maximum PSD valuesare respectively lower by 555 1667 and 2407 at ahigh excitation frequency 35Hz comparable with traditionalrubber mounts

At the frequency range above 10Hz the resonance peaksof the acceleration PSD responses in Figures 12 and 13 showthat the resonance frequencies with cabrsquos isolation mountsalso occur at 2818Hz or 3518Hz in all three directionsThis can be due to the resonance of an excitation frequency2835Hz of the vibratory drum In addition the resonancefrequency of the acceleration PSD responses clearly appearsat 1849Hz in both graphs of Figures 12 and 13 whereasthis resonance frequency does not occur in the graph of

Figure 10 especially with traditional rubber mounts Thisparticularity may be due to the effect of the soil stiffnesswith the high-density soil ground Besides the results of theacceleration PSD responses with hydraulic mounts are allclearly lower whereas their values with pneumatic mountsare all strongly enhanced comparable with traditional rubbermounts in three directions especially at a high excitation fre-quency 35HzConsequently all the above analysis results alsosuggest that the driverrsquos health and safety with hydraulicmounts are obviously improved in comparison with both thepneumatic and traditional rubbermounts on elastoplastic soilground

342TheWeighted RMSAcceleration Responses Figure 14(a)shows that at a low excitation frequency 28Hz of thedrum the weighted RMS values of the vertical driverrsquosseat and cabrsquos pitch vibrations with pneumatic mounts areenhanced by 405 and 488 in comparisonwith traditionalrubber mounts Thus pneumatic mounts have a little effect


RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions

Degrees of freedomc czs

041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2

0085 rad Ｍminus20085 rad Ｍminus20131 rad Ｍminus2

(a) Under a low excitation frequency 28Hz of the drum

RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2



(b) Under a high excitation frequency 35Hz of the drum

Figure 14 The weighted RMS acceleration responses on a high-density soil ground

on improving the driverrsquos ride comfort Meanwhile withhydraulic mounts their weighted RMS values are all respec-tively smaller by 845 1795 and 3511 compared withtraditional rubber mounts Therefore the driverrsquos ride com-fort is clearly improved by using hydraulic mounts

Besides Figure 14(b) also shows that at a high excitationfrequency 35Hz the weighted RMS values of the verticaldriverrsquos seat and cabrsquos pitch vibrationswith pneumaticmountsare slightly reduced by 307 and 303 in comparison withtraditional rubber mounts Contrary to that with pneumaticmounts their weighted RMS values with hydraulic mountsare all strongly decreased by 2153 2727 and 4554compared with traditional rubber mounts

In addition the driverrsquos ride comfort is also significantlyinfluenced by the excitation frequencies of the vibratorydrum As shown in Figures 14(a) and 14(b) the weightedRMS acceleration responses of the vertical driverrsquos seat cabrsquospitch and roll vibrations at a high excitation frequency 35Hzcomparable with a low excitation frequency 28Hz are allrespectively lower by 845 1538 and 1603 with tradi-tional rubber mounts by 1486 2195 and minus341 withpneumatic mounts and by 2154 25 and 2823 withhydraulic mounts Therefore all the above analysis resultsshow that the driverrsquos ride comfort can be improved clearlywith hydraulicmounts when the vehiclemoves and compactsan elastoplastic soil ground in low-frequency region

4 Conclusions

Modeling and low-frequency performance analysis of anoff-road vibratory roller equipped with three different cabrsquosisolationmounts are addressed in thisworkTheperformanceof three cabrsquos isolationmounts is evaluated through the accel-eration PSD responses and the weighted RMS accelerationresponses of the vertical driverrsquos seat cabrsquos pitch and the rollvibrations in both the frequency and the time domains

The results show that the maximum PSD values of thevertical driverrsquos seat cabrsquos pitch and roll vibrations with thehydraulic mounts are strongly reduced by 5528 5765and 3516 compared with traditional rubber mountsBesides the weighted RMS values of the vertical driverrsquosseat cabrsquos pitch and roll vibrations with hydraulic mountsare also respectively lower by 1311 1624 and 142 incomparison with pneumatic mounts when the vehicle travelson a deformable terrain

When the vehicle moves and compacts an elastoplasticsoil ground with hydraulicmounts the weighted RMS valuesof the vertical driverrsquos seat cabrsquos pitch and roll vibrationsare greatly decreased by 845 1795 and 3511 at a lowexcitation frequency 28Hz of the drum and theirmaximumPSD values are strongly reduced by 4558 5476 and3333 at a low excitation frequency 28Hz and by 40745714 and 5185 at a high excitation frequency 35Hzcomparable with the traditional rubber mounts

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This study is supported by the Science and TechnologySupport Program of Jiangsu China (no BE2014133) and theProspective Joint Research Program of Jiangsu China (noBY2014127-01)

References

[1] D Pietzsch and W Poppy ldquoSimulation of soil compaction withvibratory rollersrdquo Journal of Terramechanics vol 29 no 6 pp585ndash597 1992


[2] D Adam and F Kopf ldquoTheoretical analysis of dynamicallyloaded soilsrdquo in Proceedings of the European Workshop Com-paction of Soils and Granular Materials pp 207ndash220 ParisFrance 2000

[3] R Anderegg and K Kaufmann ldquoIntelligent compaction withvibratory rollers feedback control systems in automatic com-paction and compaction controlrdquo Transportation ResearchRecord no 1868 pp 124ndash134 2004

[4] K Tateyama S Ashida R Fukagawa and H TakahashildquoGeomechatronics - Interaction between ground and construc-tion machinery and its application to construction roboticsrdquoJournal of Terramechanics vol 43 no 3 pp 341ndash353 2006

[5] M Bekker Introduction to Terrain-Vehicle Systems University ofMichigan Press Ann Arbor Mich USA 1969

[6] J Wong Theory of Ground Vehicles John Wiley amp Sons NewYork NY USA 2001

[7] X ZhangModelling simulation and optimization of ride comfortfor off road articulated dump trucks [PhD thesis] SoutheastUniversity 2010

[8] A Pakowski and D Cao ldquoEffect of soil deformability onoff-road vehicle ride dynamicsrdquo SAE International Journal ofCommercial Vehicles vol 6 no 2 pp 362ndash371 2013

[9] C Harnisch B Lach R Jakobs M Troulis and O NehlsldquoA new tyre-soil interaction model for vehicle simulation ondeformable groundrdquo Vehicle System Dynamics vol 43 pp 384ndash394 2005

[10] R A Irani R J Bauer and A Warkentin ldquoDynamic wheel-soil model for lightweight mobile robots with smooth wheelsrdquoJournal of Intelligent amp Robotic Systems vol 71 no 2 pp 179ndash193 2013

[11] S Park A A Popov and D J Cole ldquoInfluence of soil deforma-tion on off-road heavy vehicle suspension vibrationrdquo Journal ofTerramechanics vol 41 no 1 pp 41ndash68 2004

[12] A Kordestani S Rakheja P Marcotte A Pazooki and D JurasldquoAnalysis of ride vibration environment of soil compactorsrdquoSAE International Journal of Commercial Vehicles vol 3 no 1pp 259ndash272 2010

[13] R V Rinehart and M A Mooney ldquoInstrumentation of a rollercompactor to monitor vibration behavior during earthworkcompactionrdquoAutomation in Construction vol 17 no 2 pp 144ndash150 2008

[14] J Li Z Zhang H Xu and Z Feng ldquoDynamic characteristicsof the vibratory roller test-bed vibration isolation systemSimulation and experimentrdquo Journal of Terramechanics vol 56pp 139ndash156 2014

[15] M Griffin Handbook of Human Vibration Academic PressLondon UK 1990

[16] J De Temmerman K Deprez I Hostens J Anthonis and HRamon ldquoConceptual cab suspension system for a self-propelledagricultural machine - part 2 operator comfort optimisationrdquoBiosystems Engineering vol 90 no 3 pp 271ndash278 2005

[17] V Quynh Vibration study and control for cab of vibratory roller[PhD thesis] Southeast University 2013

[18] P Lee J Vogt and S Han ldquoApplication of hydraulic bodymounts to reduce the freeway hop shake of pickup trucksrdquo SAETechnical Papers 2009-01-2126 2009

[19] T Higuchi and K Miyaki ldquoWork machine with operatorscabinrdquo Tech Rep 1999 US Patent No 5984036

[20] S Jiao Y Wang L Zhang and H Hua ldquoShock wave character-istics of a hydraulic damper for shock test machinerdquoMechanicalSystems and Signal Processing vol 24 no 5 pp 1570ndash1578 2010

[21] X Sun and J Zhang ldquoPerformance of earth-moving machinerycab with hydraulic mounts in low frequencyrdquo Journal of Vibra-tion and Control vol 20 no 5 pp 724ndash735 2014

[22] P Sundvall ldquoComparisons between predicted and measuredride comfort in trains-a case study on modelingrdquo TRITAFKTReport Division of Railway Technology Department of VehicleEngineering Royal Institute of Technology Stockholm Swe-den 2001

[23] M Presthus Derivation of air spring model parameters for trainsimulation [MS thesis] Lulea University of Technology 2002

[24] H J Abid J Chen and A A Nassar ldquoEquivalent air springsuspension model for quarter-passive model of passenger vehi-clesrdquo International Scholarly Research Notices vol 2015 ArticleID 974020 pp 1ndash6 2015

[25] I Hostens K Deprez and H Ramon ldquoAn improved designof air suspension for seats of mobile agricultural machinesrdquoJournal of Sound and Vibration vol 276 no 1-2 pp 141ndash1562004

[26] J Yan Z Yin X Guo and C Fu ldquoFuzzy control of semi-activeair suspension for cab based on genetic algorithmsrdquo SAETechnical Papers 2008-01-2681 2008

[27] G Tang H Zhu Y Zhang and Y Sun ldquoStudies of air springmathematical model and its performance in cab suspensionsystem of commercial vehiclerdquo SAE Technical Papers vol 2015no 4 pp 341ndash348 2015

[28] C Harris and A PiersolHarrisrsquo Shock and Vibration HandbookMcGraw-Hill New York NY USA 5th edition 2002

[29] T Ushijima and T Dan ldquoNonlinear BBA for predicting vibra-tion of vehicle with hydraulic engine mountrdquo SAE TechnicalPapers 860550 1986

[30] M Berg ldquoA three-dimensional air spring model with frictionand orifice dampingrdquo in Proceedings of the 16th IAVSD Sympo-siumThe Dynamics of Vehicles on Roads And on Tracks vol 33pp 528ndash539 Pretoria South Africa 1999

[31] J D Robson ldquoRoad surface description and vehicle responserdquoInternational Journal of Vehicle Design vol 1 no 1 pp 25ndash351979

[32] International Organization for Standardization ldquoReportingvehicle road surface irregularitiesrdquo Tech Rep ISOTC108SC2WG4 N57 Thieme Medical Publishers Stuttgart Germany1982

[33] M Mitschke Dynamik der Kraftfahrzeuge Springer-VerlagBerlin Germany 1972

[34] International Organization for Standardization ldquoMechanicalvibration and shock-evaluation of human exposure to wholebody vibration-part 2 General requirdquo Tech Rep ISO 2631-11997 ISO Geneva Switzerland 1997

[35] J Y Wong ldquoData processing methodology in the character-ization of the mechanical properties of terrainrdquo Journal ofTerramechanics vol 17 no 1 pp 13ndash41 1980

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almost focus on exploring the soil compression efficiencywith wheels-terrain interactionmodels Ride dynamics of thevibratory roller received only a little attention

The low-frequency excitation arising from the wheels-terrain interaction is mostly transmitted to the driver viacabrsquos isolation mounts and seatrsquos suspension Furthermorevibrations in the low-frequency range of 05ndash10Hz causedby terrain roughness can lead to the main risk factors whichseriously affect the driverrsquos mental and physical health [1516] Consequently cabrsquos isolation mounts are one of themost important factors to improve the driverrsquos ride comfortThe isolation mounts used for the vibratory roller cab aremostly equipped with the traditional rubber mounts withtheir stiffness and damping constants [3 13 14]The influenceof the design parameters of the cab rubber mounts on theride dynamics of the soil compactor was investigated viathe analytical and experimental methods [12] and theirparameters were then optimized to enhance the driverrsquos ridecomfort [17] however the vertical driverrsquos seat and cabrsquospitch vibrations are still great under operation conditionsConsequently the traditional rubber mounts of the cab aredifficult to satisfy the driverrsquos ride comfort

Nowadays the cabrsquos isolation mounts of constructionequipment industrial vehicle and earth-moving machineryare being replaced by the increasing use of the hydraulicmounts to improve the ride comfort [18ndash20] A six-degree-of-freedom (DOF) cab model of earth-moving machinerywith the hydraulic mounts involving quadratic damping wasalso investigated under the road roughness excitation withina frequency range below 10Hz [21] The results showed thatthe root mean square (RMS) of acceleration responses andthe power spectral density (PSD) of displacement responsesof the cabrsquos mass centre are all reduced remarkably with thecomparison between hydraulic and rubbermounts Althoughthe paper has not yet considered the influence of wheels-terrain interactions however the research results are anobvious basis for study and application of the hydraulicmounts into cabrsquos isolation mounts of machines working ondeformable soil grounds especially the soil compactors

Besides the pneumatic suspension systems which wereused in the suspension systems of the car heavy truck andrail vehicles to improve the ride dynamics and noise levels[22ndash24] were also investigated and applied for cabrsquos isolationmounts and the driverrsquos seat suspension to enhance the ridecomfort as well as the driverrsquos health and safety [25ndash27]The research results showed that the vehicle ride comfortwas obviously improved by using the pneumatic suspensionsystems Moreover the theory studies also showed that thepneumatic mounts used in vibration isolation mounts canresult in their stiffness being almost 10 times higher than thelowest stiffness at approximately 8Hz [28] thus this leads tothe application in a low-frequency range of vibration isolationsystems being necessary Air springs have not only lowerresonance frequencies but also smaller overall length thanmechanical springs with equivalent properties [23] Howeverthe pneumatic mounts have not yet been studied to apply oncabrsquos isolation mounts of the off-road vehicles especially thevibratory roller

In this study a three-dimensional nonlinear dynamicmodel of a single drum vibratory roller was establishedbased on Adam and Kopf rsquos elastic-plastic soil model [2] andBekker hypothesis of the soft soil ground [5] The vibrationexcitations consisted of the interactions of the drumwheels-terrain roughness surface when the vehicle travelled on a softsoil ground and a lowhigh excitation frequency 2835Hz ofthe drum when the vehicle compacted an elastoplastic soilground Experimental investigations were used to validatethe models and verify their accuracy Three different cabrsquosisolation mounts including the traditional rubber mountsthe hydraulic mounts and the pneumatic mounts wererespectively simulated The performance of three differentisolationmounts was then evaluated through the accelerationPSD and the weighted RMS acceleration responses of thevertical driverrsquos seat cabrsquos pitch and roll vibrations in boththe frequency and time domains

The innovation in this paper is that an 11-DOF vehicledynamics model which can fully reflect the pitch and rollvibrations of the cab is established The vibration responsesof the vibratory roller under the low excitation frequencyespecially the pitch and roll response of cab with threedifferent isolation mounts are compared and analyzed Theresults showed that the low-frequency and high-stiffnesscharacteristics of the hydraulic mounts have a good effect onisolating low-frequency vibration transmitted and control-ling the cab shaking of the vibratory roller

2 Materials and Methods

21 The Vibratory Roller Dynamic Model As shown inFigure 1(a) the basic structure of the vibratory roller consistsof the rigid drumwheels the frontrear vehicle frame thecab and the seat Moreover the drum and the front frame areconnected by the rubber mounts and the front frame and therear frame are linked by an articulation connectionThe cab isconnected with the rear frame via the cabrsquos isolation mountswhich contains the traditional rubber mounts the hydraulicmounts and the pneumatic mounts as shown in Figures 1(b)1(c) and 1(d) respectively In this study three different cabrsquosisolation mounts are used for analyzing the low-frequencyperformance of the vibratory roller considering the interac-tion between wheels and off-road deformable terrain

A three-dimensional nonlinear dynamic model with 11DOF of a single drum vibratory roller considering theinteraction between the drumwheels and the deformableterrain is built as in Figure 2

See Figure 2 where 119911119904 is the vertical motion at the driverrsquosseat 119911119888 120601119888 and 120579119888 are the vertical the pitch and the rollmotions at the cab respectively and those are described as119911rf 120601rf and 120579rf at the rear vehicle frame The vertical and rollmotions of the front frame and the drum are described as 119911ff 120579ff and 119911119889 120579119889 The mass of the driverrsquos seat the cab the frontframe the engine and the rear frame and the roller drum isdescribed as 119898119904 119898119888 119898ff 119898rf and 119898119889 respectively 119897119906 and 119887Vare the longitudinal and lateral distances of the seat the caband the vehicle (119906 = 1ndash8 V = 1ndash7) 119902119905119895 and 119902119889119895 are the terrainroughness surface at wheels and drum contacts The driverrsquosseat suspension drum mounts and tyres are characterized


to Frame

to CabAir bag

Surge pipe

to Air reservoir

13

Cab


z

Rear frame

Cab


X

Y

Z

to Frame

to Cab






Main rubberOrifice

Rubber

zf

zc

Fkc

Fkc


qt1 qd1

cs

kt1

ks

zs

zc

mc

ms

zff

md

Fkc1Fk

c3

zd

cd1kd1

ct1

mＬ

l5l6

l7

l3

l4

l2

l1

l8

0

Fd

Mdy

c

Ｌ

zＬ

mff

(a) Side view

qd1 b4 b5 qd2

kd2 cd2

cs

cd1kd1

b2

b1

b3

ks

zs

zc

zd

ms

mc

md

zff

m

d

Fkc1 Fk

c2

c

ff ff

(b) Front view







119865119889 = 1198651198891 + 1198651198892119872119889119910 = (1198651198891 + 1198651198892) 1198978119872119889119909 = 11986511988911198874 + 11986511988921198875

(2)




Rear frame

Cab

z kr crzrf

zc


Cab

Rear frame

z kr cr cf

zrf

zc

(b) Hydraulic mount

w

Cab

M

Rear frame

zke

kv

zrf

zc

c

(c) Pneumatic mount





(3)


[M] Z + [C] Z + [K] Z = F (119905) (4)



119865119877119888119894 = 119896119903119894 (119911119888119894 minus 119911rf 119894) + 119888119903119894 (119888119894 minus rf 119894) (5)





Δ119901 = Δ119901119886 + Δ119901119900 = 119888119886 10038161003816100381610038161198861003816100381610038161003816 119886 + 119888119900 10038161003816100381610038161199001003816100381610038161003816 119900 (8)



119876119888 = 119860119888 = 119860119886119886or 119876119888 = 119860119888 = 119860119900119900 (9)



)2 + 119888119900 (119860119888119860119900

)2] || (10)


119891 = 119860119889Δ119901 = 119888119891 || (11)








119881119887 = 1198811198870 minus 119860119890119911 + 119860 119904119908119881119903 = 1198811199030 minus 119860 119904119908 (13)



119896119890 = 119901011986021198901205821198811198870 + 1198811199030 119896V = 11989611989011988111990301198811198870 119872 = 119860 119904119897119904120588(119860119890119860 119904

11988111990301198811198870 + 1198811199030)2

(14)





119888120573 = 119888119904 (119860119890119860 119904

11988111990301198811198870 + 1198811199030)1+120573 (16)



119865119875119888 = 119896119890119911 + 119896V (119911 minus 119908) (17)



(18)





119865119892 = int120579119886(119905)0

119861119889119901119892119903119889 cos 120579 119889120579 + int120579119886(119905)0

119861119889120591119892119903119889 sin 120579 119889120579= int119897(119905)

0119861119889119901119892119889119909 + int119897(119905)

0119861119889120591119892119909 (1199032119889 minus 1199092)minus12 119889119909

(19)


Δo

terrain surface

ar

zd

zx

zoaz0

x

rd Fd

md

l(t)

d

q(t)

0

a

gpg

a(t)q(t + x

0)q(t + x

0)


ob

terrain surface

ar

zt

z0

m

a

t

q(t)

t

r t

l1(t) l

x

2(t)

b pgg

a

0

zx

Ft

q(t + x

0)





119901119892 = (119896119888119887 + 119896120593)119911119899119909120591119892 = (119888 + 119901119892 tan120593) (1 minus 119890minus119895119889119870)

(20)



119911119909 = 119902(119905 + 119909V0) + 119911119900119886 minus Δ= 119902(119905 + 119909


(21)





119898119889119889 = 1198651198891 + 1198651198892 minus 119865119892 + 119898119889119892119868119889119909 120579119889 = 11986511988911198874 minus 11986511988921198875 (23)




1198651199111198921 = 1198651199111199011198921 = 2119861119905 (119896119888119887 + 119896120593)int11989712(119905)

0119911119899119909119889119909 (24)



1198651199111198922 = 1198651199111199011198922 + 1198651199111205911198922= int11989712(119905)+1198972(119905)

11989712(119905)119861119905119901119892119889119909

+ int11989712(119905)+1198972(119905)11989712(119905)

119861119905120591119892119909 (1199032119905 minus 1199092)minus12 119889119909(25)



119865119892 = 1198651199111198921 + 1198651199111198922 (26)


see

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(a) Loading phase

se

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(b) Unloading phase

mg

se

kＭＪ

cＭ kＭ

zＭ

zd

0Fd

Fe

md

me

(c) Drum-hop phase




(27)





119898119889119889 = 119865119889 minus 119865119892 + 1198981198901198901205962 sin120596119905 (29)


120576 = 119896sp(119896sp + 119896se)

120574 = 119888se119896sp (30)




120576120574119898119889



119898119889119889 = 119865119889 minus 119888se119889 + 1198981198901198901205962 sin120596119905 (32)



minus004

minus002

0

002

004H

eigh

t (m

)

10 20 30 40 500Time (s)


Terrain PSD

Medium

Good

Poor Very poor

10minus8

10minus6

10minus4

10minus2

100

Off-

road

PSD

(Ｇ2（Ｔminus

1)

100 10110minus1

Frequency (Hz)





119898119889119889 = 119865119889 + 119898119892 + 1198981198901198901205962 sin120596119905 (33)



119878 (Ω) = 119878 (Ω0) sdot ( ΩΩ0

)minus1199080 (34)





119902 (119905) = 119873sum119894=1

119904119894 sin (119894Δ120596119905 + 120593119894) (35)











119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)















13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



to Frame

to CabAir bag

Surge pipe

to Air reservoir

13

Cab


z

Rear frame

Cab


X

Y

Z

to Frame

to Cab






Main rubberOrifice

Rubber

zf

zc

Fkc

Fkc


qt1 qd1

cs

kt1

ks

zs

zc

mc

ms

zff

md

Fkc1Fk

c3

zd

cd1kd1

ct1

mＬ

l5l6

l7

l3

l4

l2

l1

l8

0

Fd

Mdy

c

Ｌ

zＬ

mff

(a) Side view

qd1 b4 b5 qd2

kd2 cd2

cs

cd1kd1

b2

b1

b3

ks

zs

zc

zd

ms

mc

md

zff

m

d

Fkc1 Fk

c2

c

ff ff

(b) Front view







119865119889 = 1198651198891 + 1198651198892119872119889119910 = (1198651198891 + 1198651198892) 1198978119872119889119909 = 11986511988911198874 + 11986511988921198875

(2)




Rear frame

Cab

z kr crzrf

zc


Cab

Rear frame

z kr cr cf

zrf

zc

(b) Hydraulic mount

w

Cab

M

Rear frame

zke

kv

zrf

zc

c

(c) Pneumatic mount





(3)


[M] Z + [C] Z + [K] Z = F (119905) (4)



119865119877119888119894 = 119896119903119894 (119911119888119894 minus 119911rf 119894) + 119888119903119894 (119888119894 minus rf 119894) (5)





Δ119901 = Δ119901119886 + Δ119901119900 = 119888119886 10038161003816100381610038161198861003816100381610038161003816 119886 + 119888119900 10038161003816100381610038161199001003816100381610038161003816 119900 (8)



119876119888 = 119860119888 = 119860119886119886or 119876119888 = 119860119888 = 119860119900119900 (9)



)2 + 119888119900 (119860119888119860119900

)2] || (10)


119891 = 119860119889Δ119901 = 119888119891 || (11)








119881119887 = 1198811198870 minus 119860119890119911 + 119860 119904119908119881119903 = 1198811199030 minus 119860 119904119908 (13)



119896119890 = 119901011986021198901205821198811198870 + 1198811199030 119896V = 11989611989011988111990301198811198870 119872 = 119860 119904119897119904120588(119860119890119860 119904

11988111990301198811198870 + 1198811199030)2

(14)





119888120573 = 119888119904 (119860119890119860 119904

11988111990301198811198870 + 1198811199030)1+120573 (16)



119865119875119888 = 119896119890119911 + 119896V (119911 minus 119908) (17)



(18)





119865119892 = int120579119886(119905)0

119861119889119901119892119903119889 cos 120579 119889120579 + int120579119886(119905)0

119861119889120591119892119903119889 sin 120579 119889120579= int119897(119905)

0119861119889119901119892119889119909 + int119897(119905)

0119861119889120591119892119909 (1199032119889 minus 1199092)minus12 119889119909

(19)


Δo

terrain surface

ar

zd

zx

zoaz0

x

rd Fd

md

l(t)

d

q(t)

0

a

gpg

a(t)q(t + x

0)q(t + x

0)


ob

terrain surface

ar

zt

z0

m

a

t

q(t)

t

r t

l1(t) l

x

2(t)

b pgg

a

0

zx

Ft

q(t + x

0)





119901119892 = (119896119888119887 + 119896120593)119911119899119909120591119892 = (119888 + 119901119892 tan120593) (1 minus 119890minus119895119889119870)

(20)



119911119909 = 119902(119905 + 119909V0) + 119911119900119886 minus Δ= 119902(119905 + 119909


(21)





119898119889119889 = 1198651198891 + 1198651198892 minus 119865119892 + 119898119889119892119868119889119909 120579119889 = 11986511988911198874 minus 11986511988921198875 (23)




1198651199111198921 = 1198651199111199011198921 = 2119861119905 (119896119888119887 + 119896120593)int11989712(119905)

0119911119899119909119889119909 (24)



1198651199111198922 = 1198651199111199011198922 + 1198651199111205911198922= int11989712(119905)+1198972(119905)

11989712(119905)119861119905119901119892119889119909

+ int11989712(119905)+1198972(119905)11989712(119905)

119861119905120591119892119909 (1199032119905 minus 1199092)minus12 119889119909(25)



119865119892 = 1198651199111198921 + 1198651199111198922 (26)


see

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(a) Loading phase

se

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(b) Unloading phase

mg

se

kＭＪ

cＭ kＭ

zＭ

zd

0Fd

Fe

md

me

(c) Drum-hop phase




(27)





119898119889119889 = 119865119889 minus 119865119892 + 1198981198901198901205962 sin120596119905 (29)


120576 = 119896sp(119896sp + 119896se)

120574 = 119888se119896sp (30)




120576120574119898119889



119898119889119889 = 119865119889 minus 119888se119889 + 1198981198901198901205962 sin120596119905 (32)



minus004

minus002

0

002

004H

eigh

t (m

)

10 20 30 40 500Time (s)


Terrain PSD

Medium

Good

Poor Very poor

10minus8

10minus6

10minus4

10minus2

100

Off-

road

PSD

(Ｇ2（Ｔminus

1)

100 10110minus1

Frequency (Hz)





119898119889119889 = 119865119889 + 119898119892 + 1198981198901198901205962 sin120596119905 (33)



119878 (Ω) = 119878 (Ω0) sdot ( ΩΩ0

)minus1199080 (34)





119902 (119905) = 119873sum119894=1

119904119894 sin (119894Δ120596119905 + 120593119894) (35)











119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)















13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Rear frame

Cab

z kr crzrf

zc


Cab

Rear frame

z kr cr cf

zrf

zc

(b) Hydraulic mount

w

Cab

M

Rear frame

zke

kv

zrf

zc

c

(c) Pneumatic mount





(3)


[M] Z + [C] Z + [K] Z = F (119905) (4)



119865119877119888119894 = 119896119903119894 (119911119888119894 minus 119911rf 119894) + 119888119903119894 (119888119894 minus rf 119894) (5)





Δ119901 = Δ119901119886 + Δ119901119900 = 119888119886 10038161003816100381610038161198861003816100381610038161003816 119886 + 119888119900 10038161003816100381610038161199001003816100381610038161003816 119900 (8)



119876119888 = 119860119888 = 119860119886119886or 119876119888 = 119860119888 = 119860119900119900 (9)



)2 + 119888119900 (119860119888119860119900

)2] || (10)


119891 = 119860119889Δ119901 = 119888119891 || (11)








119881119887 = 1198811198870 minus 119860119890119911 + 119860 119904119908119881119903 = 1198811199030 minus 119860 119904119908 (13)



119896119890 = 119901011986021198901205821198811198870 + 1198811199030 119896V = 11989611989011988111990301198811198870 119872 = 119860 119904119897119904120588(119860119890119860 119904

11988111990301198811198870 + 1198811199030)2

(14)





119888120573 = 119888119904 (119860119890119860 119904

11988111990301198811198870 + 1198811199030)1+120573 (16)



119865119875119888 = 119896119890119911 + 119896V (119911 minus 119908) (17)



(18)





119865119892 = int120579119886(119905)0

119861119889119901119892119903119889 cos 120579 119889120579 + int120579119886(119905)0

119861119889120591119892119903119889 sin 120579 119889120579= int119897(119905)

0119861119889119901119892119889119909 + int119897(119905)

0119861119889120591119892119909 (1199032119889 minus 1199092)minus12 119889119909

(19)


Δo

terrain surface

ar

zd

zx

zoaz0

x

rd Fd

md

l(t)

d

q(t)

0

a

gpg

a(t)q(t + x

0)q(t + x

0)


ob

terrain surface

ar

zt

z0

m

a

t

q(t)

t

r t

l1(t) l

x

2(t)

b pgg

a

0

zx

Ft

q(t + x

0)





119901119892 = (119896119888119887 + 119896120593)119911119899119909120591119892 = (119888 + 119901119892 tan120593) (1 minus 119890minus119895119889119870)

(20)



119911119909 = 119902(119905 + 119909V0) + 119911119900119886 minus Δ= 119902(119905 + 119909


(21)





119898119889119889 = 1198651198891 + 1198651198892 minus 119865119892 + 119898119889119892119868119889119909 120579119889 = 11986511988911198874 minus 11986511988921198875 (23)




1198651199111198921 = 1198651199111199011198921 = 2119861119905 (119896119888119887 + 119896120593)int11989712(119905)

0119911119899119909119889119909 (24)



1198651199111198922 = 1198651199111199011198922 + 1198651199111205911198922= int11989712(119905)+1198972(119905)

11989712(119905)119861119905119901119892119889119909

+ int11989712(119905)+1198972(119905)11989712(119905)

119861119905120591119892119909 (1199032119905 minus 1199092)minus12 119889119909(25)



119865119892 = 1198651199111198921 + 1198651199111198922 (26)


see

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(a) Loading phase

se

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(b) Unloading phase

mg

se

kＭＪ

cＭ kＭ

zＭ

zd

0Fd

Fe

md

me

(c) Drum-hop phase




(27)





119898119889119889 = 119865119889 minus 119865119892 + 1198981198901198901205962 sin120596119905 (29)


120576 = 119896sp(119896sp + 119896se)

120574 = 119888se119896sp (30)




120576120574119898119889



119898119889119889 = 119865119889 minus 119888se119889 + 1198981198901198901205962 sin120596119905 (32)



minus004

minus002

0

002

004H

eigh

t (m

)

10 20 30 40 500Time (s)


Terrain PSD

Medium

Good

Poor Very poor

10minus8

10minus6

10minus4

10minus2

100

Off-

road

PSD

(Ｇ2（Ｔminus

1)

100 10110minus1

Frequency (Hz)





119898119889119889 = 119865119889 + 119898119892 + 1198981198901198901205962 sin120596119905 (33)



119878 (Ω) = 119878 (Ω0) sdot ( ΩΩ0

)minus1199080 (34)





119902 (119905) = 119873sum119894=1

119904119894 sin (119894Δ120596119905 + 120593119894) (35)











119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)















13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








119881119887 = 1198811198870 minus 119860119890119911 + 119860 119904119908119881119903 = 1198811199030 minus 119860 119904119908 (13)



119896119890 = 119901011986021198901205821198811198870 + 1198811199030 119896V = 11989611989011988111990301198811198870 119872 = 119860 119904119897119904120588(119860119890119860 119904

11988111990301198811198870 + 1198811199030)2

(14)





119888120573 = 119888119904 (119860119890119860 119904

11988111990301198811198870 + 1198811199030)1+120573 (16)



119865119875119888 = 119896119890119911 + 119896V (119911 minus 119908) (17)



(18)





119865119892 = int120579119886(119905)0

119861119889119901119892119903119889 cos 120579 119889120579 + int120579119886(119905)0

119861119889120591119892119903119889 sin 120579 119889120579= int119897(119905)

0119861119889119901119892119889119909 + int119897(119905)

0119861119889120591119892119909 (1199032119889 minus 1199092)minus12 119889119909

(19)


Δo

terrain surface

ar

zd

zx

zoaz0

x

rd Fd

md

l(t)

d

q(t)

0

a

gpg

a(t)q(t + x

0)q(t + x

0)


ob

terrain surface

ar

zt

z0

m

a

t

q(t)

t

r t

l1(t) l

x

2(t)

b pgg

a

0

zx

Ft

q(t + x

0)





119901119892 = (119896119888119887 + 119896120593)119911119899119909120591119892 = (119888 + 119901119892 tan120593) (1 minus 119890minus119895119889119870)

(20)



119911119909 = 119902(119905 + 119909V0) + 119911119900119886 minus Δ= 119902(119905 + 119909


(21)





119898119889119889 = 1198651198891 + 1198651198892 minus 119865119892 + 119898119889119892119868119889119909 120579119889 = 11986511988911198874 minus 11986511988921198875 (23)




1198651199111198921 = 1198651199111199011198921 = 2119861119905 (119896119888119887 + 119896120593)int11989712(119905)

0119911119899119909119889119909 (24)



1198651199111198922 = 1198651199111199011198922 + 1198651199111205911198922= int11989712(119905)+1198972(119905)

11989712(119905)119861119905119901119892119889119909

+ int11989712(119905)+1198972(119905)11989712(119905)

119861119905120591119892119909 (1199032119905 minus 1199092)minus12 119889119909(25)



119865119892 = 1198651199111198921 + 1198651199111198922 (26)


see

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(a) Loading phase

se

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(b) Unloading phase

mg

se

kＭＪ

cＭ kＭ

zＭ

zd

0Fd

Fe

md

me

(c) Drum-hop phase




(27)





119898119889119889 = 119865119889 minus 119865119892 + 1198981198901198901205962 sin120596119905 (29)


120576 = 119896sp(119896sp + 119896se)

120574 = 119888se119896sp (30)




120576120574119898119889



119898119889119889 = 119865119889 minus 119888se119889 + 1198981198901198901205962 sin120596119905 (32)



minus004

minus002

0

002

004H

eigh

t (m

)

10 20 30 40 500Time (s)


Terrain PSD

Medium

Good

Poor Very poor

10minus8

10minus6

10minus4

10minus2

100

Off-

road

PSD

(Ｇ2（Ｔminus

1)

100 10110minus1

Frequency (Hz)





119898119889119889 = 119865119889 + 119898119892 + 1198981198901198901205962 sin120596119905 (33)



119878 (Ω) = 119878 (Ω0) sdot ( ΩΩ0

)minus1199080 (34)





119902 (119905) = 119873sum119894=1

119904119894 sin (119894Δ120596119905 + 120593119894) (35)











119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)















13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Δo

terrain surface

ar

zd

zx

zoaz0

x

rd Fd

md

l(t)

d

q(t)

0

a

gpg

a(t)q(t + x

0)q(t + x

0)


ob

terrain surface

ar

zt

z0

m

a

t

q(t)

t

r t

l1(t) l

x

2(t)

b pgg

a

0

zx

Ft

q(t + x

0)





119901119892 = (119896119888119887 + 119896120593)119911119899119909120591119892 = (119888 + 119901119892 tan120593) (1 minus 119890minus119895119889119870)

(20)



119911119909 = 119902(119905 + 119909V0) + 119911119900119886 minus Δ= 119902(119905 + 119909


(21)





119898119889119889 = 1198651198891 + 1198651198892 minus 119865119892 + 119898119889119892119868119889119909 120579119889 = 11986511988911198874 minus 11986511988921198875 (23)




1198651199111198921 = 1198651199111199011198921 = 2119861119905 (119896119888119887 + 119896120593)int11989712(119905)

0119911119899119909119889119909 (24)



1198651199111198922 = 1198651199111199011198922 + 1198651199111205911198922= int11989712(119905)+1198972(119905)

11989712(119905)119861119905119901119892119889119909

+ int11989712(119905)+1198972(119905)11989712(119905)

119861119905120591119892119909 (1199032119905 minus 1199092)minus12 119889119909(25)



119865119892 = 1198651199111198921 + 1198651199111198922 (26)


see

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(a) Loading phase

se

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(b) Unloading phase

mg

se

kＭＪ

cＭ kＭ

zＭ

zd

0Fd

Fe

md

me

(c) Drum-hop phase




(27)





119898119889119889 = 119865119889 minus 119865119892 + 1198981198901198901205962 sin120596119905 (29)


120576 = 119896sp(119896sp + 119896se)

120574 = 119888se119896sp (30)




120576120574119898119889



119898119889119889 = 119865119889 minus 119888se119889 + 1198981198901198901205962 sin120596119905 (32)



minus004

minus002

0

002

004H

eigh

t (m

)

10 20 30 40 500Time (s)


Terrain PSD

Medium

Good

Poor Very poor

10minus8

10minus6

10minus4

10minus2

100

Off-

road

PSD

(Ｇ2（Ｔminus

1)

100 10110minus1

Frequency (Hz)





119898119889119889 = 119865119889 + 119898119892 + 1198981198901198901205962 sin120596119905 (33)



119878 (Ω) = 119878 (Ω0) sdot ( ΩΩ0

)minus1199080 (34)





119902 (119905) = 119873sum119894=1

119904119894 sin (119894Δ120596119905 + 120593119894) (35)











119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)















13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



see

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(a) Loading phase

se

kＭＪcＭ kＭ

zＭ

zd

0Fd

Fe

Fg

(b) Unloading phase

mg

se

kＭＪ

cＭ kＭ

zＭ

zd

0Fd

Fe

md

me

(c) Drum-hop phase




(27)





119898119889119889 = 119865119889 minus 119865119892 + 1198981198901198901205962 sin120596119905 (29)


120576 = 119896sp(119896sp + 119896se)

120574 = 119888se119896sp (30)




120576120574119898119889



119898119889119889 = 119865119889 minus 119888se119889 + 1198981198901198901205962 sin120596119905 (32)



minus004

minus002

0

002

004H

eigh

t (m

)

10 20 30 40 500Time (s)


Terrain PSD

Medium

Good

Poor Very poor

10minus8

10minus6

10minus4

10minus2

100

Off-

road

PSD

(Ｇ2（Ｔminus

1)

100 10110minus1

Frequency (Hz)





119898119889119889 = 119865119889 + 119898119892 + 1198981198901198901205962 sin120596119905 (33)



119878 (Ω) = 119878 (Ω0) sdot ( ΩΩ0

)minus1199080 (34)





119902 (119905) = 119873sum119894=1

119904119894 sin (119894Δ120596119905 + 120593119894) (35)











119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)















13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



minus004

minus002

0

002

004H

eigh

t (m

)

10 20 30 40 500Time (s)


Terrain PSD

Medium

Good

Poor Very poor

10minus8

10minus6

10minus4

10minus2

100

Off-

road

PSD

(Ｇ2（Ｔminus

1)

100 10110minus1

Frequency (Hz)





119898119889119889 = 119865119889 + 119898119892 + 1198981198901198901205962 sin120596119905 (33)



119878 (Ω) = 119878 (Ω0) sdot ( ΩΩ0

)minus1199080 (34)





119902 (119905) = 119873sum119894=1

119904119894 sin (119894Δ120596119905 + 120593119894) (35)











119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)















13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










119886119896119908119897 = radic 1119879 int119879

0[119886119896119908119897 (119905)]2 119889119905 (36)















13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










13

X

Y

Z

5





120601119888 = 1198882 minus 1198884119897119888 120579119888 = 1198881 minus 1198882119887119888

(37)








1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)



1 2 4 8 16 3205Frequency (Hz)

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

















R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











R and H 169 189 209 249 569 859 169 189 209 249 569 859P 18 22 26 52 65 18 22 26 569 679

Degrees of freedom


c czs0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns 079 m Ｍminus2

071 m Ｍminus2

044 rad Ｍminus2

039 rad Ｍminus2

0150 rad Ｍminus2

0131 rad Ｍminus2












R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






R H P R H P




X 079Y 019 X 179

Y 083

X 209Y 123 X 26

Y 075

X 839Y 0084

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

05 1 2 4 8 16 32

X 089Y 024

X 209Y 085 X 26

Y 057X 839Y 018

X 179Y 026

Frequency (Hz)

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)


X 209Y 0036

X 26Y 0098 X 839

Y 0072

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)

RHP







Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Degrees of freedom

RHP

c czs0

05

1

15

2

Wei

ghte

d RM

S ac

cele

ratio


117 rad Ｍminus2


157 m Ｍminus2




X 18Y 065

X 209Y 068

X 249Y 045

X 569Y 0096

X 859Y 0091

X 2818Y 0004

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Vert

ical

acce

lera

tion

PSD

(Ｇ2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 18Y 048

X 209Y 042 X 249

Y 029X 859Y 0074 X 2818

Y 0037

X 1809Y 0004

10minus4

10minus3

10minus2

10minus1

100

101Pi

tch

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


RHP

X 22Y 0042 X 65

Y 0029

X 859Y 0073

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)




X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



X 18Y 051

X 209Y 054 X 249

Y 037

X 569Y 0042

X 859Y 0057

X 3518Y 0002

RHP

10minus4

10minus3

10minus2

10minus1

100

101Ve

rtic

al ac

cele

ratio

n PS

D (Ｇ

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 3518Y 0012

X 1849Y 0002

X 249Y 024

X 859Y 0046

X 209Y 042

X 18Y 035

RHP

10minus4

10minus3

10minus2

10minus1

100

101

Pitc

h ac

cele

ratio

n PS

D (Ｌ

＞2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)


X 249Y 0054 X 569

Y 0041X 859Y 0058

RHP

10minus5

10minus4

10minus3

10minus2

10minus1

100

Roll

acce

lera

tion

PSD

(Ｌ＞

2Ｍminus

3)

1 2 4 8 16 3205Frequency (Hz)








RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



RHP

0

02

04

06

08

1W

eigh

ted

RMS

acce

lera

tions


041 rad Ｍminus2

074 m Ｍminus2

071 m Ｍminus2

032 rad Ｍminus2

065 m Ｍminus2

039 rad Ｍminus2



RHP


0

02

04

06

08

1

Wei

ghte

d RM

S ac

cele

ratio

ns

063 m Ｍminus2

065 m Ｍminus2

051 m Ｍminus2








4 Conclusions






Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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Vibration Analysis and Modeling of an Off-Road Vibratory ...downloads.hindawi.com/journals/sv/2018/8527574.pdf · 5 l 6 l 7 l 3 l 4 l 2 l 1 l 8 0 F d M dy c L＠ z L＠ m ﬀ (a)