research article investigation into the impact and

Research ArticleInvestigation into the Impact and Buffering Characteristics of aNon-Newtonian Fluid Damper Experiment and Simulation

Jingya Sun Sujuan Jiao Xiuchang Huang and Hongxing Hua

Institute of Vibration Shock and Noise Shanghai Jiao Tong University No 800 Dongchuan Road Shanghai 200240 China

Correspondence should be addressed to Hongxing Hua hhxsjtueducn

Received 15 March 2014 Revised 30 May 2014 Accepted 30 May 2014 Published 24 June 2014

Academic Editor Alicia Gonzalez-Buelga

Copyright copy 2014 Jingya Sun et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Dampers are widely applied to protect devices or human body from severe impact or harmful vibration circumstances Consideringthat dampers with low velocity exponent have advantages in energy absorption they have beenwidely used in antiseismic structuresand shock buffering Non-Newtonian fluid with strong shear-thinning effect is commonly adopted to achieve this goal To obtainthe damping mechanism and find convenient methods to design the nonlinear fluid damper in this study a hydraulic damper isfilled with 500000 cSt silicone oil to achieve a low velocity exponent Drop hammer test is carried out to experimentally obtain itsimpact and buffering characteristics Then a coupling model is built to analyze its damping mechanism which consists of a modelof impact system and a computational fluid dynamics (CFD) model Results from the coupling model can be consistent with theexperiment results Simulation method can help design non-Newtonian fluid dampers more effectively

1 Introduction

To promote working precision or avoid impact-vibrationdamage dampers are widely used in vehicles [1ndash3] civilbuildings [4ndash6] weapons [7ndash12] spacecraft [13 14] and soon to absorb energy of vibrations or shocks and suppressthe resonance or alleviate the shock acceleration Amongkinds of dampers because of high energy absorption capacityhydraulic damper always appeals to lots of researchersrsquoattention

To enhance the energy absorption capacity non-Newtonian fluid with shear-thinning effect is commonlyadopted as the flow media of the damper For most doublerod hydraulic dampers the damping force can be describedas

119891 (119905) = 1198881003816100381610038161003816100381612057510038161003816100381610038161003816119899minus1 120575 (1)

where 120575 is the relative displacement across the damper 120575that represents the derivation of 120575 is the relative velocity 119888 isthe damping coefficient 119899 is the velocity exponent [5 15ndash17]Ruzicka and Derby [15] considered the influence of suchvelocity-119899th power damping on vibration isolation and it is

concluded that under the same excitation amplitude if thevelocity exponent is less than unity the damping can leadto better displacement transmissibility than traditional lineardamping Peng et al [18] Kovacic et al [16] and Guo et al[6] derived similar conclusions with those from Ruzicka andDerby In buffering applications to absorb the shock energyin a certain permitted travel the max damping force shouldbe as small as possible to prevent objects or human frombeinginjured therefore in certain conditions dampers with the lowvelocity exponent are preferred [10]

However velocity exponent of dampers is determined notonly by the shape of damping orifice but also by Reynoldsnumbers of the flow through the damping orifice and prop-erties of media fluid Considering the eddy flow throng thedamping orifice will enlarge the velocity exponent to obtaina damper with low velocity exponent it is necessary to makethe flow through the orifice be laminar In this conditionthe velocity exponent is approximate to the rheological indexof the fluid filled in the damper [19] Therefore it is alsonecessary to make the rheological index of the fluid as low aspossible In [19] it is mentioned that high apparent viscosityfluid has a stronger shear-thinning effect which is helpfulto achieve low velocity exponent In practical applications

Hindawi Publishing CorporationShock and VibrationVolume 2014 Article ID 170464 10 pageshttpdxdoiorg1011552014170464

2 Shock and Vibration

silicone oil is commonly used as fluid media because ofits nontoxicity and stability Though in most applicationsviscosity of commonly adopted silicone oil is higher thanthat of hydraulic oil it is still relatively low Characteristics ofdamper with higher viscosity are seldom found in literatures

Moreover it is difficult to design a non-Newtonian fluiddamper Formulas derived from Newtonian fluid dynamicsare nomore suitable Because non-Newtonian fluid dynamicsis abstruse it is difficult to get a simple and generalized designformula that can guide to make the damper handily Withouta doubt numerical simulation method is the most efficientway which supplies a useful tool to predesign the non-Newtonian fluid damper and cut down the product cost Inthis study a damper filledwith high viscosity non-Newtonianfluid 500000 cSt silicone oil is manufactured The dampingorifice is of ring gap Jia et al [17] derived the semianalyticformula for this kind of damper by considering the flowamong the ring gap is purely sheared However this flow is ofCouette type and the pressure difference cannot be ignoredso the results are untrustful Hou [20 21] investigated thiskind of damper using fluid with 1000 cSt viscosity under theharmonic excitationThe experimental and numerical resultscanmatch together but the error is bigThismay be due to theinaccurate viscosity and unreasonable numerical method

In this study characteristics of a damper with highviscosity silicone oil under a shock condition are investigatedA drop hammer test is carried out to obtain the impact andbuffering characteristics of the damper A coupling model isbuilt to predict the impact and the buffering process Themodel consists of the model of impact system and the CFDmodel of the damper The supposed model not only can beused to guide the design of the detailed structure such as thesize of the damping orifice but also can supply suggestions indesigning the moving parts reasonably

2 Structures of the Damper

The schematic of a non-Newtonian fluid damper is shownin Figure 1 The damper has a two-rod piston which is usedto form two symmetrical piston chambers in order to obtainthe symmetrical characteristicsThe piston stroke is plusmn55mmThe diameters of the piston rod and the piston are 8mmand 20mm respectively The length of the piston is 20mmThe inner diameter of the cylinder is 34mm so there is anannular gap between the piston and the inner cylinder wallwhose width is (34 minus 20)2 = 7 (mm) The width of theannular gap between the piston rod and the cylinder wall is(34 minus 8)2 = 13 (mm) The piston chambers are fully filledwith 500000 cSt silicone oil

When an external force is applied to the left piston rodthe piston rodmoves toward the right Silicone oil in the rightpiston chamber is compressed and flows through the annulargap into the left chamber (as the arrows shown in Figure 1) Inthis process damping force is raised to balance the externalforceThe flow through the ring gap is of typical Couette typeand the damping force consists of two kinds of componentsThe first is the friction force on the surfaces of the rod and

End closure Silicone oil Annular gap Seal Rod

Externalforce

Cylinder Piston Flow direction

Figure 1 Sketch of the non-Newtonian fluid damper

z

o

r120579

Figure 2 Coordinate system for the flow field

the piston due to shearing the fluid The other is from thepressure difference on the piston along the moving axis

3 Govern Equations forthe Non-Newtonian Fluid

To describe the govern equations clearly cylindrical coordi-nate system is built for the flow field of the damper seen inFigure 2 Supposing that the fluid is incompressible and itsdensity is constant anywhere with the flow field being axis-symmetric the flow velocity can be considered as

V119903= 119906 (119903 119911 119905) V

119911= 119908 (119903 119911 119905) V

120579= 0 (2)

The continuity equation and the momentum equation are asfollows

1

119903

120597 (119903119906)

120597119903+120597119908

120597119911= 0 (3)

120588119889119906

119889119905= minus120597119901

120597119903+120597120591119903119903

120597119903+120597120591119903119911

120597119911+120591119903119903

119903 (4)

120588119889119908

119889119905= minus120597119901

120597119911+1

119903

120597 (119903120591119903119911)

120597119903+120597120591119911119911

120597119911 (5)

where 120591119903119903 120591119911119911 and 120591

119903119911are partial stress components 119901 is the

pressure of the flow field 120588 is the fluid density

Shock and Vibration 3

Because of the strong shear-thinning effect the viscositywill degrade remarkably as the shear rate is increasedThere-fore the non-Newtonian fluid is commonly considered asthe generalized Newtonian fluid which results from a minormodification of the Newtonian fluid constitutive equation[19] The equations are as follows

120591119903119903= 2120578 ( 120574)

120597119906

120597119903

120591119911119911= 2120578 ( 120574)

120597119908

120597119911

120591119903119911= 120578 ( 120574) [

120597119906

120597119911+120597119908

120597119903]

(6)

where 120578( 120574) is the viscosity function of the shear rate Manymodels are supposed to describe the relationship betweenthe viscosity and the shear rate such as power-law modelCarreau model Ellis model and Bingham model Carreaumodel can be used to describe the viscosity property ofsilicone oil [20 21] The model is expressed by

120578 ( 120574) = 1205780[1 + (119896 120574)

2

](119899minus1)2

(7)

where 1205780is the apparent viscosity 119896 is a parameter which is

related to the elastic time constant 120574 is the shear rateIn this study the Carreau model is adopted Parameters

in the model are identified according to the measured resultsbased on the method of least squares The model withidentified parameters is as follows

120578 ( 120574) = 43908[1 + (00478 120574)2

]minus02319

(8)

Figure 3 shows the relationship between the viscosity andthe shear rate It is clear that the viscosity goes down whenbeing sheared and the relationship can be well described byCarreau model

4 Drop Hammer Test

The shock characteristics of the damper are tested on a dropmachine Figure 4 shows the sketch of the test rigThedamperis fixed to the foundation A drop hammer is lifted to acertain height and then falls freely to impact the piston rodof the damperThe damper supplies a damping force to brakethe hammer An acceleration transducer is installed at thetop of the drop hammer whose signal is amplified by anamplifier A data acquisition system is used to record theacceleration of the drop hammer as it falls According to theexperiment results the hammer will not rebound after it hitson the piston so it can be considered that the hammermovestogether with the piston in the impact and buffering process

The lifted height of the drop hammer is from 200mm to1000mmwith a step 200mmThe theoretical impact velocity119881119905when the hammer contacts the piston can be calculated by

the following formula

119881119905= radic2119892ℎ (9)

Table 1 Impact velocity of the drop hammer

Drop height (mm) 400 600 800 1000Theoretical velocity (ms) 280 343 395 443Impact velocity (ms) 275 332 374 430Error (times) 182 329 588 296

where 119892 is the gravity ℎ is the drop height The practicalimpact velocity 119881

119901can be approximately derived by integrat-

ing the acceleration The error of 119881119905and 119881

119901is defined as

119864V = |119881119905 minus 119881119901||119881119905| All values abovementioned are shownin Table 1 From the table it is clear that the practical value isin good agreement with the theoretical one and can be usedas the initial impact velocity in the following simulation

5 Coupling Model forthe Shock Buffering Experiment

51 Coupling Model In the drop hammer test the wholeprocess can be approximately divided into two parts Thefirst is the impact process In this duration the hammer willcollide with the piston and accelerate themoving parts whichmainly includes the rod and the piston to move at the samespeed with itself In the second process the hammer and themoving parts will be braked by the damper The sketch of thewhole model is shown in Figure 5(a) In the figure the modelcan be considered as two coupling systems The upper oneis the impact system while the low is the energy absorbingsystem which only contains a damper

In the impact and buffering process the impact systemsupplies a certain size of velocity to the piston The damperwill feed back damping force to the impact system accordingto the input velocity The two systems affect each other bytwo parameters the damping force and the velocity of thepiston rod Technical process to simulate the coupling modelis described in Figure 5(b)

52 Model of Impact System In Figure 5 1198981represents the

hammer and 1198982is the mass of moving parts of the damper

such as the piston and its rod1198981and119898

2connect each other

through spring element 119896 and damping element 1198881which

are the stiffness and the damping coefficient in the collisionbetween the drop hammer and the piston rod 119896 and 119888

1are

mainly dominated by the isolation rubber The whole impactsystem is supported by a damper

Based on the supposed model the differential motionequations of the system are given by

11989811+ 119896 (119909

1minus 1199092) + 1198881(1minus 2) = 119898

1119892

11989822+ 119896 (119909

2minus 1199091) + 1198881(2minus 1) + 119891DM = 1198982119892

(10)

where 1199091and 119909

2are the displacement of 119898

1and 119898

2

respectively 119891DM is the output damping force of the damper119892 represents the size of the gravity

In the experiment the hammer mass is 32 kg The totalmass of the piston and its rod is 017 kg The parameters 119888

1

and 119896 in the collision can try out approximately based on


100

100

100

200

300

400

500

1000

Shear rate (sminus1)ExperimentCarreau

Visc

osity

(Pamiddot

s)

Figure 3 Relationship between the viscosity and the shear rate

Accelerometer

Mechanical filter

Drop hammer

Guideway

Rubber pad

Shock absorber

Foundation

Figure 4 Sketch of the test rig

Hammer

Movingparts

DM

Impact system

Damper

(a) (b)

Impact system

Initial condition

Damper

Damping force

x2

x1

k

V

c1

Rod velocity

Figure 5 Model for the shock buffering experiment (a) Sketch ofthe coupling model (b) technical process for coupling numericalsimulation

Table 2 Identified parameters of the damper

Parameter Drop height (mm) Averaging400 600 800 1000

Experiment 119899 04399 04524 04148 03890 04240119888 47672 44224 44393 42680 44742

Simulation 119899 05410 05306 05245 05164 05281119888 44237 43968 43857 43827 43972

the experiment results The approximate values of 119896 and 1198881

are 119896 = 34 times 106Nsdotm and 1198881= 400Nsdotsm respectively The

initial velocity of1198981is set to the practical velocity in Table 2

The initial velocity of1198982is set to zero

53 CFD Model of the Damper Govern equations (2) (3)and (4) can be solved in CFD software FLUENT whenthe flow can be considered as laminar Viscosity functionequation (8) can be inserted into the software program bybeing compiled as a user defined functionThe density of thesilicone oil is about 950 kgm3

Due to the axis symmetry characteristic of the damperfluid zone in Figure 2 can be simplified as shown in Figure 6The quad elements are used to discretize the computationaldomain Meshes are refined at regions where there existsbigger velocity gradient such as regions close to the pistonand the piston rod The height of the cell close to the pistonand the piston rod is 02mm the height of the others is05mmThere are 3418 nodes 6655 faces and 3238 cells Thenonslip condition is employed in the nodes located at thewalls

Walls of the fluid zone can be divided into two kinds Oneis the stationary wall which includes the end surfaces and thecylinder surface as seen in the blue bold line in Figure 6 Inthe simulation these walls will keep stationary that is thevelocity is set to zero The other is the moving walls whichinclude surfaces of the rod and piston submerging in fluidas seen in the red bold line in the figure In the simulationthe velocity of moving walls is variable The surfaces mustmove continuously from time to time It belongs to a movingboundary problem Dynamic layering scheme offered by thecomputed fluid dynamic package FLUENT is used to describethe mesh motionThe mesh is updated at each time step Thepiston velocity can be derived from (10)

1198811198982

=1

1198982

int119905

0

[1198982119892 minus 119896 (119909

2minus 1199091) minus 1198881(2minus 1) minus 119891DM] 119889119905

(11)

where the initial velocity of the piston is set to zeroDuring the cosimulation process in every time step the

output damping force will be extracted from FLUENT solverby a user defined function and feed back to the solver of(10) The solver of (10) will calculate the velocity of pistonand feed back to FLUENT Then in the following time stepthe velocity of the piston in the damper will be changedand the output damping force will be got for the next useto calculate the velocity of 119898

1and 119898

2 Once the velocity is

determined in a time step and transferred to the solver of


Axis

Axial symmetry model

Model details

Moving wall

Stationary wall

Figure 6 Simplified CFDModel of the flow field

FLUENT the damping force can be calculated in the nexttime step Similarly the impact and buffering behavior in thewhole process can be obtained

6 Results and Discussion

61 Experiment Results Figure 7 shows time history of theshock acceleration of the hammer under different dropheights It can be found that in the impact process thehammer always contacts the piston rod because the size ofacceleration is always larger than the gravity To compareeasily acceleration of the free drop is offset to zero So theacceleration multiplying the hammer mass represents theoutput damping force In the figure the whole duration lastsfrom about 20ms to 35ms It can be divided into two stagesthe impact process and the buffering process

In the impact process the shock acceleration changessharply with time which is mainly due to the collisionbetween the hammer and the piston rod The piston rodis accelerated to the same velocity of the hammer in anextremely short time This duration lasts for no more than2ms and the duration seems independent of the dropheight The maximum of the acceleration in this processis remarkably large From the scaled figure in Figure 7it is clear to find that with the drop height increasingthe maximum is approximately increasing linearly and therebound acceleration is also reinforced Many factors canaffect this process such as the mass of the piston and the rodthe mass of the liquid in the damper and the rubber pad onthe top end of the rod

In the buffering process the acceleration changes rela-tively smoothly but most of the shock energy is absorbed bythe damper in this process Obviously under different heightthe acceleration shape is similar though the magnitude isdifferent With the drop height increased though the magni-tude is increasing the magnitude increment goes downThisis because the silicone oil belongs to non-Newtonian fluidwhose viscosity is shear-thinningWith initial piston velocityincreasing fluid among the damping orifice is sheared more

Impact

800

400

600800

1000

600

400

200

00 1 2

00

200

5 10 20 3015 25 35

minus1

Time (ms)

Shoc

k ac

cele

ratio

n (m

s2)

Buffering

h200h400h600

h800h1000

Figure 7 Time history of the shock accelerations

severely and its viscosity is degraded which leads to a lowerdamping force increment

62 Simulation Results and Comparisons The simulatedshock acceleration of the hammer is shown in Figure 8 Withcomparisons between the simulated and the experimentalwhich are shown in Figure 8 it is easy to find that bothresults match well with each other In the impact processthe peak value of the shock acceleration increases as the dropheight is increasedThe simulated peak value shows the sametendency The shock duration which seems independent ofthe drop height also matches well

In the buffering process the duration time and the mag-nitude of the calculated results are approximate to those of theexperimental results Certain level errors still can be observedfrom the calculated and the experimental resultsThese errorsare caused by the measurement and the simplification in thesimplified model

Generally speaking the calculated resultsmatchwell withthose from the experimental ones The supposed couplingmodel can be used to analyze the influence of parameters onthe shock characteristics

63 Analysis on the Output Damping Force To clearly under-stand the dampingmechanismof the damper a stress analysissketch is shown in Figure 9 The output damping force canbe divided into three parts The first part is caused by thepressure differential on the piston 119891

1= int119860end119901119889119860 where

119860end is the two end surfaces of the piston The second part isthe friction force on the piston 119891

2= int119860cylinder

120591piston119889119860 where119860cylinder is the outer cylinder surface of the piston The lastpart is the friction force on the rod 119891

3= int119860rod120591rod119889119860 where


0 5 10 15 20 25 30

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

35

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

ExperimentSimulation

(c)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(d)

Figure 8 Comparison between the calculation and the experimental curves Drop height in (a) 400mm (b) 600mm (c) 800mm (d)1000mm In figures solid lines represent data from the experiment dashed lines are from the simulation

120591rod 120591rodprightpleft

VFr

z

120591pistion

Figure 9 Forces imposed on the piston and the rod

119860 rod is the outer cylinder surface of the rod merging in thefluid So the total output force is 119891DM = 1198911 + 1198912 + 1198913

Figure 10 shows components of the output damping forceEach component nearly keeps the same proportion of thetotal in the whole process In the impact process the forcefluctuates obviously It is mainly caused by coupling behaviorbetween the damper and the hammer In the following

buffering process the damper force is rather smooth In thisstage the damping force is supplied to stop the hammerand most of shock energy is absorbed From the point ofthe damping force components 119891

1 the force on the piston

due to pressure is the main component 1198912and 119891

3 forces on

the rod and piston caused by shearing the fluid also occupyremarkable ratio of the total This means that different fromthe traditional damper filled with low viscosity fluid it isnecessary to consider the shear force on the moving parts fordampers with high viscosity fluid

To understand the damping characteristics of the damperdeeply (1) is used to describe its mechanics behavior atthe buffering process The identified parameter values fromexperimental results and simulations are shown in Table 2while the experimental data at the buffering process is usedas the samples It can be found in the table that parameters


00

150

300

450

5 10 15 20 25 30 35

Time (ms)

Dam

ping

forc

e (N

)

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(c)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(d)

Figure 10 Components of the damping force from the simulation of drop height 600mm In figures solid line 1198911 dashed line 119891

2 dotted

line 1198913

from the experimental and the simulation results match wellwith each other although there are some differences Theparameters show a decreasing tendency as the drop heightincreases

64 Influence of the Mass of the Moving Parts Mass 1198982of

the moving parts has great effects on the peak of the shockacceleration To know about the regularity (10) is solved withdifferent values of 119898

2while the other parameters are kept

constant The corresponding results are shown in Figure 11where the acceleration curves of 400mm drop height areplotted

Obviously the influence of 1198982mainly locates in the

impact process With increasing 1198982 the max acceleration

and the overshoot magnitude are increasing For the shockacceleration it needs more time to approach the quasi-steadystate as119898

2is increased So the mass119898

2should be as small as

possible while the piston and rod can meet the strength anddeformation requirements

65 Influence of the Collision Parameters 119896 and 1198881are the

main collision parameters which are mainly determined bythe isolation rubber at the top of the piston To analyze theinfluence of parameters 119896 119888

1on the impact process (10) is

solved with different 119896 1198881 and119898

2while the other parameters

are kept constantIn Figure 12 the acceleration curves of drop height

400mm with different parameters 119896 and 1198881are shown


800800

0

0

0

0 10 20 30

1 2 3 4 5 6200

200

400

600600

400

Shoc

k ac

cele

ratio

n (m

s2)

Time (ms)

01m2

05m2

15m2

10m2

20m2

Figure 11 Shock acceleration curves from the simplifiedmodel withdifferent 119898

2under the drop height 400mm In figures solid line

011198982 dashed line 05119898

2 dotted line 10119898

2 dashed-dotted line

151198982 dashed-dotted-dotted line 20119898

2

The influence of 119896 and 1198881mainly locates in the collision

process The max acceleration as the values of 119896 and 1198881

increases and the overshoot becomes small The wholeduration will last for a longer time under the small size of 119896and 1198881 but the buffering process seems to be delayed in a little

time So in realistic applications the isolation rubber shouldbe thick enough to reduce the shock magnitude to a certainlevel

66 Analysis on Flow Fields In the whole impact andbuffering process the distribution of flow field parametersalmost keeps the same except their magnitudes so we choosethe distributions at the simulation time 5ms to show itscharacteristics

The pressure distribution map is shown in Figure 13Because the piston moves towards right pressure in the rightchamber is higher than that in the left The pressure gradientat the piston gap is nearly linear Near the piston stage thepressure distribution is disordered It is easy to find that inthe corner formed by the rod and the end cap the value isextremely high or lowThis is because values near these valuesare singular so their values are untractable However it ishard to settle because of the shortcoming of the model

Figure 14 describes the velocity magnitude of the flowfield The velocity of the rod surface is always equal to thesame value while the other walls are stationary Silicone oilin the right chamber is squeezed through the piston gap intothe left The flow is running towards the left and the peakvalue appears at the middle of the gap

Because of the high viscosity silicone oil with strongshear thinning effect the viscosity will be degrading with

0 1 2 3 4 5 6

800

0

200

400

600

0 10 20 30Time (ms)

800

0

200

600

400

Shoc

k ac

cele

ratio

n (m

s2)

01k 01c1 15k 15c105k 05c110k 10c1

20k 20c1

Figure 12 Shock acceleration curves from the simplifiedmodelwithdifferent 119896 and 119888

1under the drop height 400mm In figures solid

line 011198982 dashed line 05119898


2 dashed-dotted

line 151198982 dashed-dotted-dotted line 20119898

2

539e+004

246e+005

439e+005

631e+005

823e+005

102e+006

121e+006

178e+006

198e+006

140e+006

159e+006

minus110e+006

minus908e+005

minus715e+005

minus523e+005

minus331e+005

minus138e+005

(Pa)

Figure 13 Pressure distribution map of the flow field at simulationtime 5ms

000e+000

104e+000

913eminus001

783eminus001

652eminus001

117e+000

130e+000

143e+000

157e+000

196e+000

209e+000

170e+000

183e+000

130eminus001

261eminus001

391eminus001

522eminus001

(m sminus1)

Figure 14 Velocity distribution map of the flow field at simulationtime 5ms

Shock and Vibration 9213e+001

468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)

Figure 15 Viscosity distribution map of the flow field at simulationtime 5ms

the velocity gradient increasing Figure 15 shows the viscositydistributions This characteristic is different from Newtonianfluid whose viscosity is always constant In the figure fluidviscosity near walls is reduced sharply which means that thefluid shear rate is great At corners the fluid is hard to besheared so the viscosity keeps its initial value the apparentviscosity

The abovementioned three maps which are helpful todetermine which structural details will have main influenceon the output damping force can be used to guide the damperstructure design For example the manufacture quality atcorners will have little effect on the output force

7 Conclusions

In this paper a non-Newtonian fluid damper filled with500000 cSt silicone oil is made and investigated in a drophammer test firstly to get the impact and buffering charac-teristics experimentallyThen a couplingmodel is establishedto predict the shock acceleration and analyze the outputdamping mechanism Results from the coupling model canmatch well with the experiment results Some conclusions areconcluded as follows

(i) With the drop height being increased the impactvelocity becomes larger In the impact process thepeak shock acceleration is increasing and the impactduration is independent of the impact velocity whichis determined by the nature of the impact system Soit is necessary to design the impact system reasonablyto reduce the max shock acceleration

(ii) In different conditions the shock acceleration curveslook similar The buffering characteristic is mainlyaffected by the velocity exponent

(iii) From the components of the damping force it isclear that the friction force occupies a big part ofthe whole which is different from the traditionalhydraulic damper where the friction force is usuallyignored In design damper with high viscosity fluidthis point should be paid attention

(iv) Through the flow fields the rule of structures whichaffected the flow can be summarized easily It ishelpful to design structure details

Generally speaking numerical simulation technology is anefficient way to investigate the impact on and bufferingcharacteristics of non-Newtonian fluid damper And thismethod is deserved to be used to design high quality fluiddamper and cut down research costs for companies

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors gratefully acknowledge the support of theNational Science Foundation of China (no 10872132 and no11202128) for this work

References

[1] J Dixon The Shock Absorber Handbook John Wiley amp SonsNew York NY USA 2008

[2] P Mao W Rui-ming and X Ming-xiang ldquoSimulation andexperiment study of hydraulic buffer of track vehiclerdquo inProceedings of the International Conference on ComputationalIntelligence and Software Engineering (CiSE rsquo09) pp 1ndash5WuhanChina December 2009

[3] F Wang M Tanaka N Nakada T Hayase and S ChonanldquoDevelopment of an ER bypass damper for railway car reliefcouplersrdquo International Journal of Applied Electromagnetics andMechanics vol 19 no 1ndash4 pp 269ndash274 2004

[4] J Hwang and Y Huang ldquoSeismic design of structures with vis-cous dampersrdquo in International Training Programs For SeismicDesign of Building Structures 2002

[5] D Taylor and M Constantinou ldquoTesting procedures for highoutput fluid viscous dampers used in building and bridgestructures to dissipate seismic energyrdquo Shock and Vibration vol2 no 5 pp 373ndash381 1995

[6] P Guo Z Lang and Z Peng ldquoAnalysis and design of the forceand displacement transmissibility of nonlinear viscous damperbased vibration isolation systemsrdquoNonlinear Dynamics vol 67no 4 pp 2671ndash2687 2012

[7] M Ahmadian R Appleton and J A Norris ldquoAn analyticalstudy of fire out of battery using magneto rheological dampersrdquoShock and Vibration vol 9 no 3 pp 129ndash142 2002

[8] M Ahmadian and J C Poynor ldquoAn evaluation of magnetorheological dampers for controlling gun recoil dynamicsrdquo Shockand Vibration vol 8 no 3-4 pp 147ndash155 2001

[9] MAhmadian B Reichert andX Song ldquoSystemnon-linearitiesinduced by skyhook dampersrdquo Shock and Vibration vol 8 no2 pp 95ndash104 2001

[10] H Bao-lin ldquoInfluence of fluid behavior index on performanceof a gun recoil magneto-rheological damperrdquo Explosion andShock Waves no 3 pp 245ndash249 2006

[11] Z Li and J Wang ldquoA gun recoil system employing a magne-torheological fluid damperrdquo SmartMaterials and Structures vol21 no 10 Article ID 105003 2012


[12] K Li and A Darby ldquoAn approach to the design of bufferfor a buffered impact damperrdquo Structural Control and HealthMonitoring vol 17 no 1 pp 68ndash82 2010

[13] A Rittweger J Albus E Hornung H Ory and P MoureyldquoPassive damping devices for aerospace structuresrdquo Acta Astro-nautica vol 50 no 10 pp 597ndash608 2002

[14] J Chen H Nie and J-C Zhao ldquoReview of the development ofsoft-landing buffer for lunar explorationsrdquo Journal of Astronau-tics vol 29 no 3 pp 731ndash735 2008

[15] J Ruzicka and T Derby Influence of Damping in VibrationIsolation DTIC Document 1971

[16] I Kovacic Z Milovanovic and M Brennan ldquoOn the relativeand absolute transmissibility of a vibration isolation systemsubjected to base excitationrdquo Facta Universitatis-SeriesWorkingandLiving Enviromental Protection vol 5 no 1 pp 39ndash48 2008

[17] J H Jia J Y Du Y Wang and H X Hua ldquoDesign method forfluid viscous dampersrdquoArchive of AppliedMechanics vol 78 no9 pp 737ndash746 2008

[18] Z K Peng Z Q Lang and G Meng ldquoEvaluation of trans-missibility for a class of nonlinear passive vibration isolatorsrdquoFrontiers of Mechanical Engineering vol 7 no 4 pp 401ndash4092012

[19] R Bird R Armstrong and O HassagerDynamics of PolymericLiquids vol 1 of Fluid Mechanics 2nd edition 1987

[20] C Hou ldquoFluid dynamics and behavior of nonlinear viscousfluid dampersrdquo Journal of Structural Engineering vol 134 no1 pp 56ndash63 2008

[21] C Hou ldquoBehavior explanation and a new model for nonlinearviscous fluid dampers with a simple annular orificerdquo Archive ofApplied Mechanics vol 82 no 1 pp 1ndash12 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



silicone oil is commonly used as fluid media because ofits nontoxicity and stability Though in most applicationsviscosity of commonly adopted silicone oil is higher thanthat of hydraulic oil it is still relatively low Characteristics ofdamper with higher viscosity are seldom found in literatures

Moreover it is difficult to design a non-Newtonian fluiddamper Formulas derived from Newtonian fluid dynamicsare nomore suitable Because non-Newtonian fluid dynamicsis abstruse it is difficult to get a simple and generalized designformula that can guide to make the damper handily Withouta doubt numerical simulation method is the most efficientway which supplies a useful tool to predesign the non-Newtonian fluid damper and cut down the product cost Inthis study a damper filledwith high viscosity non-Newtonianfluid 500000 cSt silicone oil is manufactured The dampingorifice is of ring gap Jia et al [17] derived the semianalyticformula for this kind of damper by considering the flowamong the ring gap is purely sheared However this flow is ofCouette type and the pressure difference cannot be ignoredso the results are untrustful Hou [20 21] investigated thiskind of damper using fluid with 1000 cSt viscosity under theharmonic excitationThe experimental and numerical resultscanmatch together but the error is bigThismay be due to theinaccurate viscosity and unreasonable numerical method

In this study characteristics of a damper with highviscosity silicone oil under a shock condition are investigatedA drop hammer test is carried out to obtain the impact andbuffering characteristics of the damper A coupling model isbuilt to predict the impact and the buffering process Themodel consists of the model of impact system and the CFDmodel of the damper The supposed model not only can beused to guide the design of the detailed structure such as thesize of the damping orifice but also can supply suggestions indesigning the moving parts reasonably

2 Structures of the Damper

The schematic of a non-Newtonian fluid damper is shownin Figure 1 The damper has a two-rod piston which is usedto form two symmetrical piston chambers in order to obtainthe symmetrical characteristicsThe piston stroke is plusmn55mmThe diameters of the piston rod and the piston are 8mmand 20mm respectively The length of the piston is 20mmThe inner diameter of the cylinder is 34mm so there is anannular gap between the piston and the inner cylinder wallwhose width is (34 minus 20)2 = 7 (mm) The width of theannular gap between the piston rod and the cylinder wall is(34 minus 8)2 = 13 (mm) The piston chambers are fully filledwith 500000 cSt silicone oil

When an external force is applied to the left piston rodthe piston rodmoves toward the right Silicone oil in the rightpiston chamber is compressed and flows through the annulargap into the left chamber (as the arrows shown in Figure 1) Inthis process damping force is raised to balance the externalforceThe flow through the ring gap is of typical Couette typeand the damping force consists of two kinds of componentsThe first is the friction force on the surfaces of the rod and

End closure Silicone oil Annular gap Seal Rod

Externalforce

Cylinder Piston Flow direction

Figure 1 Sketch of the non-Newtonian fluid damper

z

o

r120579

Figure 2 Coordinate system for the flow field

the piston due to shearing the fluid The other is from thepressure difference on the piston along the moving axis

3 Govern Equations forthe Non-Newtonian Fluid

To describe the govern equations clearly cylindrical coordi-nate system is built for the flow field of the damper seen inFigure 2 Supposing that the fluid is incompressible and itsdensity is constant anywhere with the flow field being axis-symmetric the flow velocity can be considered as

V119903= 119906 (119903 119911 119905) V

119911= 119908 (119903 119911 119905) V

120579= 0 (2)

The continuity equation and the momentum equation are asfollows

1

119903

120597 (119903119906)

120597119903+120597119908

120597119911= 0 (3)

120588119889119906

119889119905= minus120597119901

120597119903+120597120591119903119903

120597119903+120597120591119903119911

120597119911+120591119903119903

119903 (4)

120588119889119908

119889119905= minus120597119901

120597119911+1

119903

120597 (119903120591119903119911)

120597119903+120597120591119911119911

120597119911 (5)

where 120591119903119903 120591119911119911 and 120591

119903119911are partial stress components 119901 is the

pressure of the flow field 120588 is the fluid density



120591119903119903= 2120578 ( 120574)

120597119906

120597119903

120591119911119911= 2120578 ( 120574)

120597119908

120597119911

120591119903119911= 120578 ( 120574) [

120597119906

120597119911+120597119908

120597119903]

(6)


120578 ( 120574) = 1205780[1 + (119896 120574)

2

](119899minus1)2

(7)




120578 ( 120574) = 43908[1 + (00478 120574)2

]minus02319

(8)


4 Drop Hammer Test




119881119905= radic2119892ℎ (9)






119901is defined as








2connect each other



1are



11989811+ 119896 (119909

1minus 1199092) + 1198881(1minus 2) = 119898

1119892

11989822+ 119896 (119909

2minus 1199091) + 1198881(2minus 1) + 119891DM = 1198982119892

(10)

where 1199091and 119909


1and 119898

2



1



100

100

100

200

300

400

500

1000


Visc

osity

(Pamiddot

s)


Accelerometer

Mechanical filter

Drop hammer

Guideway

Rubber pad

Shock absorber

Foundation


Hammer

Movingparts

DM

Impact system

Damper

(a) (b)

Impact system

Initial condition

Damper

Damping force

x2

x1

k

V

c1

Rod velocity




Experiment 119899 04399 04524 04148 03890 04240119888 47672 44224 44393 42680 44742

Simulation 119899 05410 05306 05245 05164 05281119888 44237 43968 43857 43827 43972








1198811198982

=1

1198982

int119905

0

[1198982119892 minus 119896 (119909


(11)



1and 119898




Axis


Model details

Moving wall

Stationary wall







Impact

800

400

600800

1000

600

400

200

00 1 2

00

200

5 10 20 3015 25 35

minus1

Time (ms)

Shoc

k ac

cele

ratio

n (m

s2)

Buffering

h200h400h600

h800h1000







1= int119860end119901119889119860 where




3= int119860rod120591rod119889119860 where


0 5 10 15 20 25 30

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

35

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(c)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(d)



VFr

z

120591pistion







3 forces on




00

150

300

450

5 10 15 20 25 30 35

Time (ms)

Dam

ping

forc

e (N

)

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(c)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(d)


2 dotted

line 1198913




















800800

0

0

0

0 10 20 30

1 2 3 4 5 6200

200

400

600600

400

Shoc

k ac

cele

ratio

n (m

s2)

Time (ms)

01m2

05m2

15m2

10m2

20m2



011198982 dashed line 05119898




2









0 1 2 3 4 5 6

800

0

200

400

600

0 10 20 30Time (ms)

800

0

200

600

400

Shoc

k ac

cele

ratio

n (m

s2)

01k 01c1 15k 15c105k 05c110k 10c1

20k 20c1





2 dashed-dotted


2

539e+004

246e+005

439e+005

631e+005

823e+005

102e+006

121e+006

178e+006

198e+006

140e+006

159e+006

minus110e+006

minus908e+005

minus715e+005

minus523e+005

minus331e+005

minus138e+005

(Pa)


000e+000

104e+000

913eminus001

783eminus001

652eminus001

117e+000

130e+000

143e+000

157e+000

196e+000

209e+000

170e+000

183e+000

130eminus001

261eminus001

391eminus001

522eminus001

(m sminus1)



468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)




7 Conclusions









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120591119903119903= 2120578 ( 120574)

120597119906

120597119903

120591119911119911= 2120578 ( 120574)

120597119908

120597119911

120591119903119911= 120578 ( 120574) [

120597119906

120597119911+120597119908

120597119903]

(6)


120578 ( 120574) = 1205780[1 + (119896 120574)

2

](119899minus1)2

(7)




120578 ( 120574) = 43908[1 + (00478 120574)2

]minus02319

(8)


4 Drop Hammer Test




119881119905= radic2119892ℎ (9)






119901is defined as








2connect each other



1are



11989811+ 119896 (119909

1minus 1199092) + 1198881(1minus 2) = 119898

1119892

11989822+ 119896 (119909

2minus 1199091) + 1198881(2minus 1) + 119891DM = 1198982119892

(10)

where 1199091and 119909


1and 119898

2



1



100

100

100

200

300

400

500

1000


Visc

osity

(Pamiddot

s)


Accelerometer

Mechanical filter

Drop hammer

Guideway

Rubber pad

Shock absorber

Foundation


Hammer

Movingparts

DM

Impact system

Damper

(a) (b)

Impact system

Initial condition

Damper

Damping force

x2

x1

k

V

c1

Rod velocity




Experiment 119899 04399 04524 04148 03890 04240119888 47672 44224 44393 42680 44742

Simulation 119899 05410 05306 05245 05164 05281119888 44237 43968 43857 43827 43972








1198811198982

=1

1198982

int119905

0

[1198982119892 minus 119896 (119909


(11)



1and 119898




Axis


Model details

Moving wall

Stationary wall







Impact

800

400

600800

1000

600

400

200

00 1 2

00

200

5 10 20 3015 25 35

minus1

Time (ms)

Shoc

k ac

cele

ratio

n (m

s2)

Buffering

h200h400h600

h800h1000







1= int119860end119901119889119860 where




3= int119860rod120591rod119889119860 where


0 5 10 15 20 25 30

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

35

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(c)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(d)



VFr

z

120591pistion







3 forces on




00

150

300

450

5 10 15 20 25 30 35

Time (ms)

Dam

ping

forc

e (N

)

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(c)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(d)


2 dotted

line 1198913




















800800

0

0

0

0 10 20 30

1 2 3 4 5 6200

200

400

600600

400

Shoc

k ac

cele

ratio

n (m

s2)

Time (ms)

01m2

05m2

15m2

10m2

20m2



011198982 dashed line 05119898




2









0 1 2 3 4 5 6

800

0

200

400

600

0 10 20 30Time (ms)

800

0

200

600

400

Shoc

k ac

cele

ratio

n (m

s2)

01k 01c1 15k 15c105k 05c110k 10c1

20k 20c1





2 dashed-dotted


2

539e+004

246e+005

439e+005

631e+005

823e+005

102e+006

121e+006

178e+006

198e+006

140e+006

159e+006

minus110e+006

minus908e+005

minus715e+005

minus523e+005

minus331e+005

minus138e+005

(Pa)


000e+000

104e+000

913eminus001

783eminus001

652eminus001

117e+000

130e+000

143e+000

157e+000

196e+000

209e+000

170e+000

183e+000

130eminus001

261eminus001

391eminus001

522eminus001

(m sminus1)



468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)




7 Conclusions









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










100

100

100

200

300

400

500

1000


Visc

osity

(Pamiddot

s)


Accelerometer

Mechanical filter

Drop hammer

Guideway

Rubber pad

Shock absorber

Foundation


Hammer

Movingparts

DM

Impact system

Damper

(a) (b)

Impact system

Initial condition

Damper

Damping force

x2

x1

k

V

c1

Rod velocity




Experiment 119899 04399 04524 04148 03890 04240119888 47672 44224 44393 42680 44742

Simulation 119899 05410 05306 05245 05164 05281119888 44237 43968 43857 43827 43972








1198811198982

=1

1198982

int119905

0

[1198982119892 minus 119896 (119909


(11)



1and 119898




Axis


Model details

Moving wall

Stationary wall







Impact

800

400

600800

1000

600

400

200

00 1 2

00

200

5 10 20 3015 25 35

minus1

Time (ms)

Shoc

k ac

cele

ratio

n (m

s2)

Buffering

h200h400h600

h800h1000







1= int119860end119901119889119860 where




3= int119860rod120591rod119889119860 where


0 5 10 15 20 25 30

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

35

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(c)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(d)



VFr

z

120591pistion







3 forces on




00

150

300

450

5 10 15 20 25 30 35

Time (ms)

Dam

ping

forc

e (N

)

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(c)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(d)


2 dotted

line 1198913




















800800

0

0

0

0 10 20 30

1 2 3 4 5 6200

200

400

600600

400

Shoc

k ac

cele

ratio

n (m

s2)

Time (ms)

01m2

05m2

15m2

10m2

20m2



011198982 dashed line 05119898




2









0 1 2 3 4 5 6

800

0

200

400

600

0 10 20 30Time (ms)

800

0

200

600

400

Shoc

k ac

cele

ratio

n (m

s2)

01k 01c1 15k 15c105k 05c110k 10c1

20k 20c1





2 dashed-dotted


2

539e+004

246e+005

439e+005

631e+005

823e+005

102e+006

121e+006

178e+006

198e+006

140e+006

159e+006

minus110e+006

minus908e+005

minus715e+005

minus523e+005

minus331e+005

minus138e+005

(Pa)


000e+000

104e+000

913eminus001

783eminus001

652eminus001

117e+000

130e+000

143e+000

157e+000

196e+000

209e+000

170e+000

183e+000

130eminus001

261eminus001

391eminus001

522eminus001

(m sminus1)



468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)




7 Conclusions









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Axis


Model details

Moving wall

Stationary wall







Impact

800

400

600800

1000

600

400

200

00 1 2

00

200

5 10 20 3015 25 35

minus1

Time (ms)

Shoc

k ac

cele

ratio

n (m

s2)

Buffering

h200h400h600

h800h1000







1= int119860end119901119889119860 where




3= int119860rod120591rod119889119860 where


0 5 10 15 20 25 30

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

35

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(c)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(d)



VFr

z

120591pistion







3 forces on




00

150

300

450

5 10 15 20 25 30 35

Time (ms)

Dam

ping

forc

e (N

)

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(c)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(d)


2 dotted

line 1198913




















800800

0

0

0

0 10 20 30

1 2 3 4 5 6200

200

400

600600

400

Shoc

k ac

cele

ratio

n (m

s2)

Time (ms)

01m2

05m2

15m2

10m2

20m2



011198982 dashed line 05119898




2









0 1 2 3 4 5 6

800

0

200

400

600

0 10 20 30Time (ms)

800

0

200

600

400

Shoc

k ac

cele

ratio

n (m

s2)

01k 01c1 15k 15c105k 05c110k 10c1

20k 20c1





2 dashed-dotted


2

539e+004

246e+005

439e+005

631e+005

823e+005

102e+006

121e+006

178e+006

198e+006

140e+006

159e+006

minus110e+006

minus908e+005

minus715e+005

minus523e+005

minus331e+005

minus138e+005

(Pa)


000e+000

104e+000

913eminus001

783eminus001

652eminus001

117e+000

130e+000

143e+000

157e+000

196e+000

209e+000

170e+000

183e+000

130eminus001

261eminus001

391eminus001

522eminus001

(m sminus1)



468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)




7 Conclusions









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25 30

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

35

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(c)

0 5 10 15 20 25 30 35

Time (ms)

0

300

600

900

Shoc

k ac

cele

ratio

n (m

s2)


(d)



VFr

z

120591pistion







3 forces on




00

150

300

450

5 10 15 20 25 30 35

Time (ms)

Dam

ping

forc

e (N

)

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(c)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(d)


2 dotted

line 1198913




















800800

0

0

0

0 10 20 30

1 2 3 4 5 6200

200

400

600600

400

Shoc

k ac

cele

ratio

n (m

s2)

Time (ms)

01m2

05m2

15m2

10m2

20m2



011198982 dashed line 05119898




2









0 1 2 3 4 5 6

800

0

200

400

600

0 10 20 30Time (ms)

800

0

200

600

400

Shoc

k ac

cele

ratio

n (m

s2)

01k 01c1 15k 15c105k 05c110k 10c1

20k 20c1





2 dashed-dotted


2

539e+004

246e+005

439e+005

631e+005

823e+005

102e+006

121e+006

178e+006

198e+006

140e+006

159e+006

minus110e+006

minus908e+005

minus715e+005

minus523e+005

minus331e+005

minus138e+005

(Pa)


000e+000

104e+000

913eminus001

783eminus001

652eminus001

117e+000

130e+000

143e+000

157e+000

196e+000

209e+000

170e+000

183e+000

130eminus001

261eminus001

391eminus001

522eminus001

(m sminus1)



468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)




7 Conclusions









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00

150

300

450

5 10 15 20 25 30 35

Time (ms)

Dam

ping

forc

e (N

)

(a)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

(b)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(c)

0 5 10 15 20 25 30 35

Time (ms)

0

150

300

450

Dam

ping

forc

e (N

)

f1f2f3

(d)


2 dotted

line 1198913




















800800

0

0

0

0 10 20 30

1 2 3 4 5 6200

200

400

600600

400

Shoc

k ac

cele

ratio

n (m

s2)

Time (ms)

01m2

05m2

15m2

10m2

20m2



011198982 dashed line 05119898




2









0 1 2 3 4 5 6

800

0

200

400

600

0 10 20 30Time (ms)

800

0

200

600

400

Shoc

k ac

cele

ratio

n (m

s2)

01k 01c1 15k 15c105k 05c110k 10c1

20k 20c1





2 dashed-dotted


2

539e+004

246e+005

439e+005

631e+005

823e+005

102e+006

121e+006

178e+006

198e+006

140e+006

159e+006

minus110e+006

minus908e+005

minus715e+005

minus523e+005

minus331e+005

minus138e+005

(Pa)


000e+000

104e+000

913eminus001

783eminus001

652eminus001

117e+000

130e+000

143e+000

157e+000

196e+000

209e+000

170e+000

183e+000

130eminus001

261eminus001

391eminus001

522eminus001

(m sminus1)



468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)




7 Conclusions









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










800800

0

0

0

0 10 20 30

1 2 3 4 5 6200

200

400

600600

400

Shoc

k ac

cele

ratio

n (m

s2)

Time (ms)

01m2

05m2

15m2

10m2

20m2



011198982 dashed line 05119898




2









0 1 2 3 4 5 6

800

0

200

400

600

0 10 20 30Time (ms)

800

0

200

600

400

Shoc

k ac

cele

ratio

n (m

s2)

01k 01c1 15k 15c105k 05c110k 10c1

20k 20c1





2 dashed-dotted


2

539e+004

246e+005

439e+005

631e+005

823e+005

102e+006

121e+006

178e+006

198e+006

140e+006

159e+006

minus110e+006

minus908e+005

minus715e+005

minus523e+005

minus331e+005

minus138e+005

(Pa)


000e+000

104e+000

913eminus001

783eminus001

652eminus001

117e+000

130e+000

143e+000

157e+000

196e+000

209e+000

170e+000

183e+000

130eminus001

261eminus001

391eminus001

522eminus001

(m sminus1)



468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)




7 Conclusions









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










468e

+001

724e+001

980e

+001

124e+002

149e+002

175e+002

200e+002

226e+002

251e+002

277e+002

303e+002

405e+002

431e+002

328e+002

354e+002

379e+002

(Pa s)




7 Conclusions









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article investigation into the impact and

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