non-linear finite element analysis of a shock absorber elastomer piston head

8/11/2019 Non-Linear Finite Element Analysis of a Shock Absorber Elastomer Piston Head

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Non-Linear Finite Element Analysis of a

Shock Absorber Elastomer Piston Head

by

Phillip Rodenbeck

CM267

in partial fulfillment of ME522 Advanced Finite Element Analysis course requirements

Phil,This is a very nice project report. I

only have one remaining question-- isthis a transient analysis or a quasi-

static analysis? What does the 2.5seconds correspond to? It is possiblethat I missed that explanation in the

text.Otherwise the report is wonderful.

L. O.

Project Report Grade: 98


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Table of Contents

Table of Nomenclature ................................................................................................................................. 2

Table of Figures ............................................................................................................................................. 3

Introduction .................................................................................................................................................. 4

Model ............................................................................................................................................................ 7

Theoretical Analysis .................................................................................................................................... 10

Finite Element Analysis ............................................................................................................................... 11

Results and Discussion ................................................................................................................................ 15

Theoretical Validation ............................................................................................................................. 15

Design Results ......................................................................................................................................... 17

Coarse Optimization ............................................................................................................................... 27

Conclusions ................................................................................................................................................. 32

Works Cited ................................................................................................................................................. 33


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Table of Nomenclature

Word Explanation

AVED Adaptive variable elastomer damping, a novel form of semi-active damping

which utilizes the compression and decompression of an elastomer to regulate

damping rates

Compression chamber The volume inside the shock absorber which has compressive work performed

on it during the compressive stroke of an excitation

Damper A mechanism which impedes the relative motion of one object to another

Damping ratio Indicates how rapidly a system will return to static equilibrium following an

excitation

Fluid channel An open pathway through which fluid can travel

Frequency ratio The ratio of a systems operating frequency to its natural frequency

Inner piston rod The rod which passes through the elastomer puck, is in contact with its interior

surface, and connects to the lower elastomer mounting plate

Natural frequency Is determined by a systems mass and stiffness, it represents the frequency at

which unforced vibrations travel in the systemOperating frequency Also known as forcing frequency, it is the frequency at which an excitation

drives a system

Passive damper A damper with a constant damping ratio

Piston head The cylindrical object within a damper that divides the compression and

rebound chambers and contains the fluid channels or valving through which

damping fluid passes

Rebound chamber The volume inside the shock absorber which has compressive work performed

on it during the rebound stroke of an excitation

Semi-active damper A damper which can vary its damping ratio

Shock body The tubular body of a shock absorber which defines the boundaries of the

compression and rebound chambers and houses the piston head which is ableto coaxially displace within it

Shock absorber See damper

Transmissibility The ratio of output force to input force, the input force being exerted on a

mass system and that mass system transmitting an output force onto another

system

Upper/lower

elastomer mounting

plate

The plates which sandwich the elastomer puck within the AVED shock absorber

and whose axial motion relative to one another places the elastomer into

either compressed or relaxed states

Upper/lower

mounting pins

The small pins extending from the upper and lower mounting plates and into

mounting pin holes present in the elastomer puck; as a result, the elastomer

cannot rotate on the mounting plates and the fluid channels which permeatethe mounting plates and the elastomer are kept aligned


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Table of Figures

Figure Title Page #

Figure 1. Transmissibility as a function of frequency ratio for various damping ratios 4

Figure 2. AVED elastomer geometry 5

Figure 3. AVED basic operation 6

Figure 4. Overall geometry of AVED shock and close-up of elastomer puck 7

Figure 5. Full and quarter models of Straight Hole Far/Far elastomer geometry 8

Figure 6. Initial test geometries of elastomer puck, all dimensions in inches 8

Figure 7. Prototype AVED shocks for bicycle front fork 9

Figure 8. Theoretical model of AVED puck compression 10

Figure 9. Design Modeler set-up 11

Table 1. Various material properties of Structural Steel from ANSYS Workbench 12.1 11

Figure 10. Stress-strain behavior of Neoprene Rubber under uniaxial loading from ANSYS

Workbench 12.1

12

Figure 11. Contact settings 12

Figure 12. Mesh controls and sample meshes 13

Figure 13. Shared displacement boundary conditions set-up 14

Figure 14. Shared loading set-up 15

Figure 15. Axial deformation of validation models: neoprene and steel 16

Table 2. Comparison of FEA axial deflection and theoretical axial deflection in steel and

neoprene validation models

17

Figure 16. FEA results for Straight HoleFar/Far puck geometry 18

Figure 17. FEA results for Straight HoleClose/Close puck geometry 19

Figure 18. FEA results for Straight HoleClose/Far puck geometry 20

Figure 19. FEA results for Straight HoleClose/Far with Round puck geometry 21

Figure 20. FEA results for 6 Spiral puck geometry 22

Figure 21. FEA results for 3 Spiral puck geometry 23

Figure 22. FEA results for Slot HoleMid/Mid puck geometry 24

Figure 23. FEA results for Slot HoleClose/Far puck geometry 25

Table 3. Summary table of initial elastomer puck design results 26

Figure 24. Geometry of roughly optimized AVED puck based on observations of performance

from initial designs

28

Figure 25. Commands to raise substep limit to 3000 29

Figure 26. Deformation, Equivalent Stress, and Gap FEA results for Optimized puck

geometry

30

Figure 27. Contact Pressure FEA results for Optimized puck geometry 30

Table 4. Performance results of optimized design compared to previous bests 31

Table 5. Performance results of optimized design compared to straight hole close/far 32


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Introduction

Shock absorbers or dampers are mechanisms which impede the relative motion of one object to

another. They are commonly used in applications requiring the minimization of vibrational amplitudes.

A shock absorber may be used to reduce the flapping motion of an airplane wing, the swaying of a

skyscraper, the noise generated by an air compressor, or the transmittance of vibrational forces into the

operator of an automobile. Most shock absorbers fall under the category of passive dampers,

meaning they have a constant damping ratio. Examining Figure 1 below, the disadvantages of a

constant damping ratio become evident.

Figure 1. Transmissibility as a function of frequency ratio for various damping ratios (Friedrich)

The transmissibility represents the magnitude of an output force relative to a corresponding input force.

In example, a bumpy road provides an input force to an automobiles shock absorber and the shock

absorber will transmit some of that force into the vehicle body and, ultimately, the vehicle operator.

The higher the transmissibility, the higher the force that will be transmitted into a vehicle operator,

causing them discomfort. Therefore, it is desirable to minimize transmissibility in most cases. The

transmissibility is graphed in Figure 1 as a function of the frequency ratio, which is the ratio of theoperating frequency of a system to its natural frequency. Each curve in Figure 1 shows the relationship

between the transmissibility and frequency ratio of a system for a particular damping ratio (). It can be

seen that prior to a frequency ratio of root 2, transmissibility is minimized by a high damping ratio.

However, aft of frequency ratio root 2, transmissibility is minimized by a small damping ratio. Because

of these fundamental vibrational dynamics, it is desirable for a vibrating system to be able to change its

damping ratio in order to minimize transmissibility across all possible operational frequencies.


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In the shock absorber industry, this need has led to the development of semi-active dampers with the

capability of varying their damping ratio in response to operating conditions. While several established

methods of semi-active damping exist, this project is concerned with a novel method known as adaptive

variable elastomer damping (AVED). Figure 2 presents a diagram of the critical elastomer geometry of

AVED and Figure 3 presents a diagram of the basic operational principles of AVED.

Figure 2. AVED elastomer geometry

lower elastomer

mounting plate

upper elastomer

mounting plate

fluid channel

shock body

inner wall

piston head


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Figure 3. AVED basic operation

The AVED damper piston head has three primary components: the upper mounting plate, the lower

mounting plate, and the elastomer puck or rubber disc which is sandwiched between them. The electric

motor is connected via a shaft to the lower mounting plate and can move the plate axially up and down

by means of a thread and nut connection. When the lower mounting plate is moved away from the

upper mounting plate, the elastomer goes into a relaxed position and allows for freer fluid flow around

its outer surface and through its fluid channels. Conversely, when the lower mounting plate is moved

toward the upper plate, the elastomer is compressed and its outer surface may contact the inner wall of

the shock body, resulting in a sharp damping increase through Coulomb friction. In this way, the AVED

damper is able to change its damping ratio from low to high states and vice versa.

The design of the elastomer component is critical. Not only is the elastomer chiefly responsible for

providing the semi-active damping functionality of the part, but it is also the component most

vulnerable to degradation. The elastomer will experience Coulomb friction, continual transitions from

compressed to uncompressed states, transient loading, low and high temperatures, and will need to be

able to reliably perform under all of these conditions for up to one million loading cycles (LORD, 2009).If the elastomer component does not have adequate life, then the entire AVED damper will be useless

for automotive application.

This project is intended as the initial stages of an optimization and lifing study of the AVED elastomer

puck. A field of initial puck designs will be tested in compression and will undergo contact with the

shock body inner wall. The analyses will be non-linear in terms of both the contact and the neoprene


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puck material. Any resulting high stresses or plastic deformation in the designs will be of particular

interest as these may be indicative of future failure sites under long term loading. Also of interest will

be the evenness of the elastomers contact with the wall (i.e. areany gaps present?), the pressure the

elastomer exerts on the wall, how quickly the elastomer comes into contact with the wall, and how

much deformation the elastomer experiences under the applied compressive load. For this project,

loading will be restricted to structural.

Model

AVED technology relies on the durability and consistency of the elastomer puck, which is the major

component of the sandwich style piston head, as seen in Figure 4.

Figure 4. Overall geometry of AVED shock and close-up of elastomer puck

The puck which is shown in Figure 4having spiral fluid channels each making a quarter turn in the

cylindrical elastomer bodywould require either full modeling or cyclic symmetry modeling in an FEA

analysis. Because of the non-linear material properties and non-linear contact which greatly increase

the computation time of the model, it is desirable to minimize elements through use of a quarter model.

Therefore, for this analysis, only elastomer designs which could be captured by a quarter model were

studied. Figure 5 presents such a design.


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Figure 5. Full and quarter models of Straight Hole Far/Far elastomer geometry

In total, nine different geometries of elastomer puck were tested8 initial geometries and one

optimized geometry based on observations made from the testingof the initial eight. All of these

designs were quarter models analyzed as two parts: a steel wall part and a neoprene puck part.

Additionally, a control model, having no holes in the elastomer puck, was used to validate the results of

the FEA analysis relative to theoretical equations before more complex models were introduced. The

control geometry, which has dimensions shared by all designs, is presented in Figure 6 along with the

unique dimensions of the various initial designs.

Figure 6. Initial test geometries of elastomer puck, all dimensions in inches


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Each of these models will be seen in greater detail in the subsequent results sections. The geometry of

the optimized model will also be presented later, as its geometry is the result of observations made

about the initial designs shown in Figure 6. For this analysis, the shock body wall was defined as

structural steel and the elastomer puck was defined as neoprene rubber. Structural steel is the most

commonly used material for shock absorber bodies, although usage of aluminum is on the rise and may

be investigated in future studies. The material from which to manufacture the AVED elastomer pucks is

still undecided. Further studies on the performance of several candidate materials are necessary.

Neoprene rubber was chosen for this study primarily due to the ready availability of material properties

in the ANSYS library and because neoprene rubber was used in prototype AVED shocks for a bicycle

front fork, as seen in Figure 7.

Figure 7. Prototype AVED shocks for bicycle front fork

Each puck design considered has a fluid channel running through its length and holes for mounting pins

which secure the elastomer from rotation on the upper and lower mounting plates. Compression of the

elastomers will be modeled by applying a force to their bottom surface while restraining the upper

surface from axial movement.

Neoprene Rubber


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Theoretical Analysis

The results of greatest interest in this analysis are the stresses and deformations which occur in the

elastomer after it has contacted the inner shock wall and then been further compressed, yielding a

condition where there are practically no gaps between the outer surface of the elastomer and the inner

surface of the shock wall. However, the non-linearity of the material and the contact make theoretical

validation of the stresses at this point rather difficult. Moreover, the geometries of the puck designs

with holes, slots, and spirals add a level of complexity to any theoretical calculation which is less than

convenient and not terribly useful. Accordingly, the system will be greatly simplified so that a

theoretical calculation can be made easily and the validity of the setup of the FEA models can be made.

Figure 8 presents the simplified model for theoretical analysis.

Figure 8. Theoretical model of AVED puck compression

The theoretical model consists of a 2D slice of the Control Geometry elastomer puck and wall system.

The puck is restrained from axial + y-direction displacement on its top surface and radial + x-direction

displacement on its right surface where it mounts to the inner piston rod. The puck is freely allowed to

displace in the radialx-direction until it contacts the fixed wall representing the shock body. Under

these conditions, the axial y-direction deformation of the puck prior to contact may be modeled by

Eq. 1.

where

: is the axial deformation of the puck

:is the force applied to the lower puck surface

is the length of the puck

is the base area or cross sectional area of the puck (uniform in this case)

is Youngs Modulus for the puck material

Equation 1 is well known for axial deformation. In using it, the true, quarter cylinder geometry of the

elastomer model is being neglected. For a material with a very high stiffness, such as steel, this

y

x


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discrepancy should not pose much of an issue and the theoretical result and FEA result should be

practically identical. However, a larger difference will result when the considered material is neoprene.

For this reason, the AVED puck will initially be set up in ANSYS as steel. If the results do not match well,

than a fundamental set-up error has occurred. After validating the basic FEA set-up with a steel puck,

the puck material will be changed to neoprene. Again, the resulting deformation will be compared to

the theoretical prediction with the expectancy of more error relative to the all steel analysis.

Finite Element Analysis

All of the models were built in Solid Edge V20, converted into .stp files, and imported into Static

Structural projects within ANSYS Workbench 12.1. Within Design Modeler, the geometry was slightly

modified before it was imported into ANSYS Mechanical. The imported bodies were added as Frozen

members, symmetrically Sliced by the YZ plane, and grouped into two independent parts, as shown in

Figure 9.

Figure 9. Design Modeler set-up

As expected, one part was composed of the two elastomer solids and the other was composed of the

two wall solids. The part was split in half to create vertices for the application of boundary conditions.

Two materials were used throughout the analysis, Structural Steel and Neoprene Rubber which are

part of the ANSYS material library. The shock wall was always defined as Structural Steel and the

Neoprene Rubber was always assigned to the AVED puck, except in the initial validation case with the

Control Geometry where the puck was set to Structural Steel as well. Some material properties of the

Structural Steel are presented in Table 1 and a stress-strain graph of the Neoprene Rubber under

uniaxial loading is presented in Figure 10.

Table 1. Various material properties of Structural Steel from ANSYS Workbench 12.1

Youngs Modulus (GPa) 200

Poissons Ratio 0.3

Density (kg/m3) 7850

expectation


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Figure 10. Stress-strain behavior of Neoprene Rubber under uniaxial loading from ANSYS Workbench

12.1

After applying these materials to the appropriate parts in ANSYS Mechanical, a Manual Contact Region

had to be set up under the Connections branch. The following settings shown in Figure 11 were then

applied.

Figure 11. Contact settings


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The Contact faces were defined as the two outer faces of the AVED puck, the Target faces were

defined as the two inner faces of the shock body wall, and the Type of contact was set to

Frictionless. Under Advanced, the Interface Treatment was set to Add Offset, No Ramping and

the Offset was set to zerothis step is of critical importance!The model will notsolve properly if the

setting Add Offset, No Ramping with zero Offset is not used. Lastly, the Time Step Controls were

set to Predict For Impact.

After defining the contact region, a mesh was applied to the geometry. Because of the non-linearity of

the model, keeping the element count low without being overly coarse in critical regions was necessary

to obtain reasonable solution times. It was also important to maintain as much symmetry as possible

between the two halves of the mesh. The need for mesh symmetry, mesh density in critical locations,

and a minimized element count led to the use of multiple meshing controls. Figure 12 presents a

screenshot of typical meshing controls and a few sample meshes.

Figure 12. Mesh controls and sample meshes

Patch Conforming Tetrahedron Method was used as well as Mapped Face Meshing on select faces. Edge

sizing and face sizing were also used to get more elements on faces of interest and reduce the elements

on less important faces such as the outer surface of the shock wall.

After achieving an appropriate mesh, boundary conditions were applied to the model. The

displacement boundary conditions are detailed in Figure 13.


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Figure 13. Shared displacement boundary conditions set-up

Boundary condition 1 prevents the elastomer from moving in the Z-direction (axial) because it is

restrained by the upper elastomer mount plate (reference Figure 4). Boundary condition 2 prevents the

ZY cut plane from displacing in the X-direction. Boundary condition 3 prevents the ZX cut plane from

displacing in the Y-direction. Boundary condition 4 represents the attachment of the inner elastomer

surface to the inner piston rod and prevents those faces from moving in either the X or Y direction.

Boundary condition 5 represents the presence of the upper and lower mount pins in the elastomer puck

and restrains the corresponding hole faces from displacement in the X or Y direction. Boundary

condition 6 fixes the outer wall of the shock body. Boundary condition 7 fixes three points on the

interface of the elastomer top surface and inner cylindrical surface (this boundary condition may be

unnecessary, but it seemed to reduce rigid body errors).

Additionally, two loading boundary conditions were applied to the models, as detailed in Figure 14.

1

2 3 4

5 6

7


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Figure 14. Shared loading set-up

A stepped force was applied to the bottom faces of the elastomer model, representative of the loading

which occurs when the lower elastomer mount plate is pulled axially upward by the electric motor. The

final magnitudes of the forces were determined through trial and error with the neoprene material.

The radial displacement of the neoprene relative to the applied force was adjusted until conditions

resembling the physical behavior were identified. Because it was desirable to know the amount of force

required to cause adequate radial displacement, the model was set up with an applied force condition

as opposed to an applied displacement condition. This knowledge of the force required for radial

displacement leading to a contact condition will be useful in later prototype building when specifying an

appropriate motor. The hydrostatic pressure applied to the model was representative of the elastomer

puck being immersed in 3 inches of water. No additional pressures were applied to the model; however,

in future studies, it may be of interest to observe the effect of pressurizing the damping fluid which the

piston assembly resides within.

Having specified the boundary conditions, the eight different initial designs for the AVED elastomer puck

were analyzed, compared, and a rough optimized geometry was further produced and tested.

Results and Discussion

Theoretical Validation

The first model to be tested was the Control Geometry, having no mount holes or fluid channels, with

both the AVED puck and the shock wall being set to Structural Steel material. Following this analysis,

Or youcould uthe forcreactiotool.


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the Control Geometry was again tested, except with Neoprene Rubber set as the puck material. The

deformation results of these two validation runs are presented in Figure 15.

Figure 15. Axial deformation of validation models: neoprene and steel

The neoprene model was loaded with the stepped axial force maxing at 5 N as previously depicted inFigure 14 whereas the steel model was loaded with 1000X those same force steps, maxing at 5000 N.

Both of the models were loaded with hydrostatic pressure and the aforementioned boundary

conditions, barring boundary condition 5 since the mounting pin holes have been excluded from these

validation models. Because the neoprene is non-linear, its stiffness had to be calculated instantaneously

in order to check the FEA result with a theoretical value. The neoprene was compressed to the point

just before initial contact with the wall and the strain was measured. With this strain, which was 0.10,

the stress at that exact point was determined in the ANSYS material data and a Youngs Modulus for that

instance was found to be 79,902 Pa. With this value, it was then possible to calculate a theoretical axial

deformation for the neoprene puck according to Equation 1. The results of the validation models in

comparison to theoretical axial deflection values are compared in Table 2.


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Table 2. Comparison of FEA axial deflection and theoretical axial deflection in steel and neoprene

validation models

Model FEA axial deflection

(mm)

Theoretical axial

deflection (mm)

% Difference

Steel Puck 0.0032 0.0035 8.6%Neoprene Puck 2.2 2.9 24.1%

Overall, the model appears to behave as expected. Correlation to theoretical axial loading is not perfect,

made clear by the U-shaped deformation bands exhibited by both the neoprene and steel models

toward the top of the model where boundary condition 1 is located. Were the models perfect cases of

axial loading, the deformation bands across the entire model would be flata condition which only

occurs toward the bottom of the pucks. Obviously, the main source of difference between the FEA

results and the theoretical results lies in the fact that the FEA quarter models have a rather non-

cylindrical geometry. Further errors can be attributed to the applied hydrostatic pressure and, in the

case of the neoprene elastomer, its non-linearity. Overall, though, these validation models do

communicate that the boundary conditions have been set up properly and the results, at least before

contact, are within reason.

Design Results

Having confirmed the behavior of the FEA model with a Control Geometry, the more complicated and

pertinent geometries may be tested. All of the presented results for the initial designs correlate to

~2.50 seconds into the simulation. At this time, the elastomers have already contacted the shock walls

and are strongly pushing against them. Moreover, the ANSYS simulations reached the default maximum

1000 substeps not far after the 2.50 second mark.

The results from the analysis of the straight holefar/far geometry are presented in Figure 16.

Is this a transient analysisin which time has realmeaning? Or a staticnonlinear analysis inwhich time is just amarker for the forceprofile? I think that thedefinition of something

(force vs. time?) ismissing.


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Figure 16. FEA results for Straight HoleFar/Far puck geometry

In the far/far geometry, the straight fluid channel and the mount pin holes are positioned very close to

the pucks outer surface which contacts the inner surface of the shock wall. The positioning of thesegeometric features, particularly the mounting pin holes, yield some interesting results. Examining the

equivalent stress, it can be seen that a large band of stress occurs on the outer edge of the puck

geometry in the region which runs parallel to the pin mount hole. This outer edge at the bottom of the

puck next to the pin hole seems to be getting pulled in by the pin hole due to the fact that X and Y

deformation are restrained on the inner pin hole surfacewhile all of the material around it is

expanding toward the inner shock wall. This condition leaves that particular portion of the shock wall in

a fair amount of tensiongenerating stresses roughly twice as great as the average throughout the

entirety of the elastomer. Looking at the contact gap between the outer puck wall and the inner shock

wall, it can be seen that at 2.5 seconds, the vast majority of the elastomer wall has engaged the shock in

contact, aside from those corner locations where the mounting pin holes are located. This pattern is

repeated when examining the contact pressure and important stress concentrations are exposed. The

inward pulling of the mount pin holes at the corners of the outer elastomer edge coupled with the

outward pushing of the middle portion of the edge creates an overall bowed shape. This bowed shape

existing on the outer elastomer edges of both cut planes yields high, localized stress concentrations in

the midsection. While a high contact pressure is desirable along the contact face, it is more desirable

that this pressure be uniform and any localization minimized. The localized stress concentrations, while


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not currently producing any plasticity, represent a future concern in terms of wearparticularly

because the stress concentrations occur on the outer elastomer surface which is exposed to the most

demanding wear conditions.

The results from the analysis of the straight holeclose/close geometry are presented in Figure 17.

Figure 17. FEA results for Straight HoleClose/Close puck geometry

The close/close geometry moves the fluid channel and the pin mount holes into a position much closer

to the inner edge of the elastomer puck where it mounts to the inner piston rod. This change greatly

alters the locations of the major stress concentrations in the elastomer relative to the far/far geometry.

In this geometry, the locations of highest stress are sandwiched between the upper and lower mounting

pin holes. If, over time, stress concentrations in the elastomer lead to permanent deformation, it wouldbe more acceptable for those stress concentrations to occur on the part interior, as they do for the

close/close case, as opposed to the exterior surface, seen in the far/far case. This distinction is made

because the functionality of the overall part is highly dependent on the integrity of the exterior puck

surface and how it interfaces with the inner shock wall. Looking at the gap and pressure contact

patterns, it can be seen that more of the elastomer is now coming in contact with the shock wall relative

to the far/far case. The gaps are greatly reduced and the areas of high stress, which still occur along the


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beltline of the elastomer and the cut-planes, are far more gradual. Where the far/far design had a

general contact pressure around 7,000 Pa and small areas of almost 18,000 Pa, the close/close design

exhibits a general contact pressure range of approximately 4,000 to 9,000 Pa. This higher level of

uniformity across the contact face will mean less wear in extended use.

The results from the analysis of the straight holeclose/far geometry are presented in Figure 18.

Figure 18. FEA results for Straight HoleClose/Far puck geometry

This geometry keeps the close position of the mounting pin holes but moves the fluid channel out to a

far position. In general, the results of this close/far setup are very similar to the close/close model,

indicating that the location of the fluid channel may not significantly impact results. The gap, maximum

equivalent stress, and maximum contact stress have all been slightly increased. Deformation and stress

patterns, however, remain near identical to the close/close configuration.

The results from the analysis of the straight holeclose/far with round geometry are presented in

Figure 19.


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Figure 19. FEA results for Straight HoleClose/Far with Round puck geometry

This geometry is identical to the previous close/far geometry except now a 0.25 inch round has been

applied to the inner edge of the mounting pin holes. While results along the contact interface remain

relatively unchanged, the addition of the round greatly impacted the equivalent stress of the overall

elastomer. Rather than gathering in the midsection of the elastomer below the upper mounting pin

holes, the stress concentrations have clearly moved into the rounded edges along the base of the upper

mounting pin holes. Not only have the stress concentrations changed geometrical location, but they

have grown in magnitude from approximately 20,000 Pa to 50,000 Pa relative to the close/far geometry

without any rounding. This result was unexpected as, generally, adding rounds will reduce observed

stresses. It is possible that the way in which boundary condition 1 and boundary condition 5 interact

with the rounds causes an abnormally large stress.

The results from the analysis of the 6 spiral geometry are presented in Figure 20.

This could be a mesh

effect due to the

increased meshresolution used torepresent the roundedholes.


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Figure 20. FEA results for 6 Spiral puck geometry

The idea behind the spiral fluid pathway was to create a type of fluid spring within the elastomer that

would not only transmit damping fluid from the compression chamber to the rebound chamber of theshock, but would also help the elastomer spring back to its natural state after being released from a

compressive state. Unfortunately, large deformations and stresses occurred in the lower inlet area of

the elastomer where the material thickness is thin. While no plastic deformation occurred, the

deformation and stress concentrations affecting the fluid channel are not good for the health of the part

or the quality of damping it would produce. The deformation behavior observed would most likely lead

to a blocked or pinched fluid channel, severely impairing the performance of the AVED system. This

spiral design may require a stiffer puck material or pressurization of the damping fluid before it can work

properly. Future studies will examine these possibilities.

The results from the analysis of the 3 spiral geometry are presented in Figure 21.


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Figure 21. FEA results for 3 Spiral puck geometry

The idea behind the 3 spiral design was the same as the 6 spiral designto create a feature which

doubled as a fluid pathway and a restoring spring. The 6 spiral design failed partially due to the thinnessof the elastomer near the base orifice. The 3 spiral design, having a less aggressive pitch, addresses this

issue. However, the spiral inlet orifice still experiences undesirable deformation and stress in a similar

manner to the 6 spiral design. For this reason, it does not appear to be a viable geometry candidate, at

least with neoprene rubber as the puck material.

The results from the analysis of the slot holemid/mid puck geometry are presented in Figure 22.


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Figure 22. FEA results for Slot HoleMid/Mid puck geometry

The slot holemid/mid geometry replaces the circular profile of previous fluid channels with a slot-typeprofile that lies along an arc concentric to the elastomer puck and has a constant width equivalent to the

diameter of the straight holes used in the aforementioned designs. The observed gap pattern for the

slot hole set-up is very similar in appearance to the straight hole designs. The contact pressure pattern,

however, is a bit different. There is clearly a low pressure zone between the right and left sides of the

model. This center ridge of lower pressure was not as prevalent in the straight hole geometries which

all exhibited higher levels of pressure across the entire beltline of the contact surface. The equivalent

stress in this model is higher than in the straight hole designs (barring the close/far w/rounds model)

and appears to gather in a different location. Several high stress spots pop up on the surfaces of the

upper mounting pin holes as opposed to gathering beneath them as observed in the straight hole

designs. However, there is less concern about stress concentrations appearing on the mounting pincontact surfaces than there was for stress concentrations appearing on the contact surface of the

elastomer outer wallwhich occurred in the straight hole far/far geometry. On the mounting pin

surfaces, the only concern is maintaining contact with the mounting pinsit is not necessary that they

readily compress and decompress without issue. Higher stresses on the mounting pin contact surface

may be an even more advantageous location than the interior middle locations seen in the close/close

and close/far straight hole designs. The interior middle region of the elastomer needs to be able to


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deform and revert a significant amount without inducing any permanent damage. Comparatively, the

mounting pin contact surfaces should not deform at all. Therefore placing high stress in these locations

may be better for the long term health of the part.

The results from the analysis of the slot holeclose/far puck geometry are presented in Figure 23.

Figure 23. FEA results for Slot HoleClose/Far puck geometry

Examining the results of the slot hole close/far puck geometry, a few things become immediately

apparent. First of all, the observed gaps, although asymmetric, are greatly minimized. For all intents

and purposes, the outer surface of the puck is in full contact with the inner wall at 2.5 seconds into the

loading. Contrasting this result with the gaps observed in other designs, such as the Straight Hole

Far/Far design, really showcases how much of an improvement this contact condition is. The reduced

gap can be related to the close position of the mounting pin holes and the much larger deformation,

which is nearly a full millimeter greater than all of the straight hole designs. The more the puck is

pushed upward, the more it will push outward, and greater levels of contact can then occur. The

obvious negative result appearing in this analysis is the large stress concentration which appears on the

horizontal face of the right upper mounting pin hole. It is difficult to ascertain whether or not the

presence of this stress concentration is a physical result or not. Because the concentration does not


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appear on the left upper mounting pin face and because there is clearly some degree of mesh

asymmetry in the model (seen in the gap pattern) I am inclined to say it is not a real result. The

remainder of the model is at a relatively low stress level and this small area is the only location to exhibit

such high stress. Still, the presence of the concentration does raise some concerns in regard to the

robustness of the puck design. When the puck is physically manufactured, it will of course be imperfect

as the mesh applied to the model is also imperfect. If a small degree of imperfection is enough to

generate such a large stress concentration, than investigation of a design which is less sensitive to minor

geometric changes may be necessary. Still, the observed 50,000 Pa does not elicit any plastic

deformation in the elastomer member, so it may be acceptable to allow such a stress to occur.

Having calculated results at 2.5 seconds for all of the initial designs, the performance of each design can

be compared to its counterparts in Table 3. By looking at the performance of one design relative to

others, hopefully some trends may be observed that will assist in the development of a further

optimized design. The contact related results for the spiral designs were not calculated because the

designs were considered unviable after observing their deformation behavior.

Table 3. Summary table of initial elastomer puck design results

Design Desired Control

(no

hole)

Straight

Close/

Close

Straight

Far/Far

Straight

Close/Far

Straight

Close/Far

w/ Round

Slot

Mid/Mid

Slot

Close/Far

Eval Time (s) N/A 2.4 2.5008 2.5008 2.5011 2.5006 2.5008 2.5008

Total

Deformation

(mm)

elastic 2.4 2.7 2.6 2.7 2.7 3.3 3.4

Equivalent

Stress (Pa)

#3 Low 8,517 18,978 21,629 19,639 50,616 26,495 54,436

Contact

Pressure (Pa)

#4 High 5,682 9,029 17,822 9,988 8,562 12,732 9,458

~ Contact

Pressure (Pa)

#1 Low 1,000 5,000 11,000 6,000 6,500 11,000 7,500

Gap (mm) #2 Low 0 0.083 0.59 0.013 0.081 0.28 0.0017

Time to

Touch (s)

#5 Low 1.63 1.36 1.27 1.38 1.35 0.754 0.49


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In the Desired column, I have noted whether or not it is beneficial for the values of a particular

characteristic to be Low or High and then assigned them a ranking number to signify their

importance to the puck design. The range of pressures on the contact surface and the magnitude of the

gaps present on the contact surface receive the highest importance as these parameters are most

related to the quality of the contact experienced between the elastomer and the shock wall. Contact

which has low variations in its pressure distribution and very small gaps will result in less wear on the

part over time. The presence of large gapsmeaning only certain portions of the elastomer are

touching the wallor large variations in pressure across the contact surface is indicative of the

elastomer experiencing magnified and uneven wear. The best condition for the contact surface in terms

of reducing wear over time is uniform pressure and gapless contact. The next parameter of highest

concern was the equivalent stress occurring in the part. Keeping the stress low throughout the part

should translate to a longer part life. The last parameters to consider in gauging the performance of the

different puck geometries are the contact pressure and the elapsed time before the elastomer first

touches the shock wall. A higher contact pressure (while still being uniform) is desirable as this will

increase the upper level of attainable damping. A low time to touch is desirable so that the damper can

react quickly to inputs while in operation.

For each performance category, the best result and the worst result for the initial design field has been

colored either green or red, respectively. Comparing the results, it can be seen that the straight hole

close/close configuration produced the best results in terms of contact pressure range and equivalent

stress while the slot hole close/far configuration performed the best in terms of gap and time to touch.

More generally, it seemed that different positions of the mounting pin holes and different fluid channel

geometries produced distinguishable effects. Those designs which utilized a close position for the

mounting pin holes exhibited a more uniform pressure distribution across the contact surface and much

smaller gaps. Because these two traits really define the quality of contact and were ranked the most

importantit seems that positioning the mounting pin holes in a closelocation is essential to betterpart performance. Whether or not the geometry was a straight hole or a slot also had a large effect on

the results. Straight hole geometries produced the lowest equivalent stresses while slot geometries

performed best in time to touch. Lastly, it appeared that when the fluid channel (straight hole or slot

hole) was in the far position, the time to touch was reduced.

Coarse Optimization

Having made these observations, a coarse or eyeball optimization was performed. The two most

promising designsstraight hole close/close and slot hole close/farwere merged together to create

an optimized design. The optimized design incorporates close position pin mounting holes and a

sector-type fluid channel which is essentially a joining of the straight hole close/close fluid channel with

the slot hole close/far fluid channel. Ideally, this new fluid channel will allow for the elastomer to

quickly contact the surface of the inner shock body while also lowering equivalent stress levels. The

geometry of this optimized design is presented in Figure 24.


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Figure 24. Geometry of roughly optimized AVED puck based on observations of performance from initial

designs

Again, this eyeball optimized design has its sector-type fluid channel positioned more closely to the

outer puck surface and its mounting pin holes moved further radially inward. The optimized geometry

was then subject to the same boundary conditions as previous models and its structural properties wereanalyzed. However, it was discovered after the first run that the model was reaching its default substep

results limit of 1000 well before the desired analysis time of 2.5 seconds. To remedy this issue, the

following Commands lines shown in Figure 25were inserted into the ANSYS Mechanical set-up and

the substep limit was raised to 3000.


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Figure 25. Commands to raise substeplimit to 3000

With this alteration, the simulation was able to solve to the desired time. The results from the analysis

of the Optimized puck geometry are presented in Figures 26 and 27.


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Figure 26. Deformation, Equivalent Stress, and Contact Pressure FEA results for Optimized puck

geometry

Figure 27. Gap FEA results for Optimized puck geometry

Gap = 0.019 mm


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The sector fluid channel appears to behave most similarly to the slot fluid channel. Its contact pressure

still retains a low pressure ridge down the spine of the elastomer, although it is significantly less

pronounced than in the slot geometries and the uniformity of the pressure seems to have improved.

Also, the equivalent stress within the elastomer exhibits the same patterns as were seen in the slot

geometries. Low pressure regions occur on the outer edges of the mounting pin holes, stress

concentration(s) appear on the horizontal mounting pin hole face, and the middle region between the

upper and lower pin mounting holes shows slightly higher stresses than the majority of the part. To gain

a better understanding of what improvements or detriments were made by the coarse optimization,

the performance figures of the sector hole design are presented in Table 4 along with the original bests.

Table 4. Performance results of optimized design compared to previous bests

Design Desired Straight Hole

Close/Close

Slot

Close/Far

Compiled

Best

Optimized

Eval Time (s) N/A 2.5008 2.5008 ~2.5 2.5008

Total Deformation

(mm)

elastic 2.7 3.4 3.4 3.3

Equivalent Stress (Pa) #3 Low 18,978 54,436 18978 38,632

Contact Pressure (Pa) #4 High 9,029 9,458 17822 8,884

Contact Pressure (Pa) #1 Low 5,000 7,500 5000 7,000

Gap (mm) #2 Low 0.082 0.0017 0.0017 0.019

Time to Touch (s) #5 Low 1.36 0.49 0.49 0.921

The red tinted cells in Table 4 indicate the areas in which the two initial designs, straight hole close/close

and slot hole close/far, did the poorest. If those highlighted values are then compared to the results

produced by the optimized puck, it can be seen that the optimizedpuck performed better in each

case. However, examining the parameters in which the previous designs did well, it can be seen that the

optimized design offered less desirable results. The equivalent stress and contact pressure range forthe optimized design are worse than the straight hole close/close design. Likewise, the gap and time

to touch for the optimized design are worse than they were in the slot close/far design. Essentially,

these results communicate that the optimized sector-type geometry offers a middle ground of

performance between the straight hole close/close design and the slot hole close/far. While this is a

valuable result, it is worth noting that there was an initial design which produced similar performance

characteristics to the optimized design, as seen in Table 5.


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Table 5. Performance results of optimized design compared to straight hole close/far

Design Desired Straight Hole Close/Far Optimized

Eval Time (s) N/A 2.5011 2.5008

Total Deformation (mm) elastic 2.6908 3.34

Equivalent Stress (Pa) #3 Low 19,639 38,632

Contact Pressure (Pa) #4 High 9,988 8,884

Contact Pressure (Pa) #1 Low 6,000 7,000

Gap (mm) #2 Low .013 .019

Time to Touch (s) #5 Low 1.3758 .92151

Both of these geometries offer a good blend of performance while not outright leading in any category.

However, the initial design of the straight hole close/far offers a more advantageous middle ground than

the optimized design. Based on these results, it seems the straight hole close/far geometry is

currently the most balanced design and probably a good place to begin for future, more refined

optimization of the part.

Conclusions

From this finite element study, a number of important conclusions and directions for future work have

been reached.

First of all, eyeball optimization is not going to be sufficient for this part. The number of important

parameters and the complex ways in which they influence each other will require refined methods.

Future work in optimization will be necessary in order to tailor an algorithm to improve the performance

of the elastomer puck component.

While most of the geometrical changes made in this study resulted in better performance in someaspects and worse performance in others, the close positioning of the mounting pin holes seemed to

be ubiquitously advantageous. If the mounting pin holes remain the mechanism by which to secure the

elastomer, they will be built at a close location.

More modeling and finite element testing is required. This study analyzed a very general, initial design

field, but several other modifications can be made to the puck geometry in order to hopefully lessen

some of the observed trade-offs. One such modification is a tapered puck design so that contact with


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the shock wall as the puck is compressed will be more uniform as opposed to starting at the bottom

center and moving upward and outward.

Works Cited

Friedrich, D. C. (n.d.). Transmissibility Plot for a Damped Spring-Mass System.Retrieved May 15, 2011,

from Precision Micromanufacturing Processes Applied to Miniaturization Technologies:

http://www.me.mtu.edu/~microweb/GRAPH/Intro/TRANS.JPG

LORD. (2009, January 13). LORD MR Shock Durability Exceeds HMMWV Passive Damper Spec by Factor of

Four.Retrieved May 19, 2011, from LORD Corporation: http://www.lord.com/News-

Center/News-Stories/LORD-MR-Shock-Durability-Exceeds-HMMWV-Passive-Damper-Spec-by-

Factor-of-Four.xml

non-linear finite element analysis of a shock absorber elastomer piston head

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