damping enhancement of a pneumatic inflatable structure … · the damping enhancement was...

DAMPING ENHANCEMENT OF A PNEUMATIC INFLATABLE STRUCTURE

by

GABRIEL JUDD

DR. VLADIMIR VANTSEVICH, ADVISOR AND COMMITTEE CHAIR

DR. ROY KOOMULLIL

DR. DAVID LITTLEFIELD

DR. MUKUL VERMA

A THESIS

Submitted to the graduate faculty of The University of Alabama at Birmingham,

in partial fulfillment of the requirements for the degree of

Master of Science

BIRMINGHAM, ALABAMA

2014

ii

DAMPING ENHANCEMENT OF A PNEUMATIC INFLATABLE STRUCTURE

GABRIEL JUDD

MECHANICAL ENGINEERING

ABSTRACT

In vehicles with stiff or no suspension systems, the pneumatic tires play a greater

role in vibration control. The challenge is to find an approach that enhances vibratory

damping in the tires without increasing the power losses due to rolling resistance effects.

The goal of this thesis is to experimentally prove a novel concept of active damping

within the tire while maintaining the rolling resistance found in a typical pneumatic tire.

The pneumatic structure containing two chambers connected by orifices can

enhance vibration damping using the force induced when air flows through the orifices.

Passive damping is produced when a road disturbance and tire defection causes a

pressure increase in the main chamber of the structure. This pressure increase causes

airflow between the chambers and the passive damping force. Active damping in the tire

can be produced by varying the pressure gradient between the chambers to change the

damping force in response to the road conditions. Both passive and active damping

modes will produce vibration damping without increasing the rolling resistance of the

tire.

The damping enhancement was evaluated by testing the pneumatic structure that

simulates a pneumatic tire. The experiment was initially configured to measure the

damping ratio of the conventional tire design using a calibrated external excitation and

analyzing the decay of the vibration. The passive and active damping enhancement

modes were then subjected to the same test and analysis procedure. Results of the

iii

analysis show that the damping enhancement measurably decreased the time of the

vibratory oscillation. The damping ratio of the active damping enhancement showed an

improvement of 9.4% over the baseline damping ratio.

Keywords: active, passive, damping, pneumatic inflatable structure, orifice

iv

TABLE OF CONTENTS

ABSTRACT ......................................................................................................................... ii

LIST OF TABLES ............................................................................................................... v

LIST OF FIGURES ............................................................................................................. vi

LIST OF ABBREVIATIONS .............................................................................................. vii

CHAPTER 1 – INTRODUCTION ...................................................................................... 1

CHAPTER 2 – DAMPING ENHANCEMENT SYSTEM DESCRIPTION ...................... 9

CHAPTER 3 – DAMPING ENHANCEMENT SYSTEM PROCEDURE ......................... 19

CHAPTER 4 – RESULTS ................................................................................................... 22

CHAPTER 5 - CONCLUSION ........................................................................................... 31

CHAPTER 6 – FUTURE WORK ....................................................................................... 33

REFERENCES .................................................................................................................... 34

v

LIST OF TABLES

Table Page

2.1 System Components....................................................................................................... 13

2.2 Experiment Variable Summary...................................................................................... 14

4.1 Auxiliary Chamber Comparison .................................................................................... 22

4.2 20 kPa Results ................................................................................................................ 23

4.3 Experiment Calculations ................................................................................................ 24

4.4 Baseline Damping Ratio ................................................................................................ 24

4.5 Passive System Summary .............................................................................................. 26

4.6 Active System Summary................................................................................................ 28

4.7 Active and Passive System Comparison ........................................................................ 29

vi

LIST OF FIGURES

Figure Page

1.1 Self-damped Pneumatic Spring...................................................................................... 3

2.1 Damping System Schematic .......................................................................................... 10

2.2 Active Operation by Injecting Air into Main Chamber ................................................. 12

2.3 Active Operation by Extracting Air from Main Chamber ............................................. 12

2.4 Active Operation by Injecting Air into Auxiliary Chamber .......................................... 13

2.5 Active Operation by Extracting Air from Auxiliary Chamber ...................................... 13

2.6 Active Damping System Components ........................................................................... 14

2.7 Inflatable Structure Components ................................................................................... 15

2.8 Laser Displacement Sensor Diagram and Picture .......................................................... 16

2.9 LabVIEW Program ........................................................................................................ 18

3.1 Typical Displacement Results........................................................................................ 19

3.2 Logarithmic Decrement Calculations ............................................................................ 20

4.1 Baseline Damping Ratio Results ................................................................................... 25

4.2 Top Three Passive Configuration Comparison .............................................................. 27

4.3 System Comparison ....................................................................................................... 30

vii

LIST OF ABBREVIATIONS

kPa kilopascals

mm millimeters

psi pounds per square inch

1

CHAPTER 1

INTRODUCTION

The pneumatic tire is generally thought of as a mechanism for generating forces

to control a vehicle that behaves as a spring and interacts with the body of the vehicle. In

modern highway vehicles all the primary control and disturbance forces which are

applied to the vehicle, with the exception of aerodynamic forces, are generated in the tire-

road contact patch [1]. The tire, however, is also a dynamic system that affects the

transmission of vibrations to the vehicle and may interact with vehicle resonances [2].

Damping in the pneumatic tire is usually neglected in the analysis of vehicle

motion as it relates to ride quality. While tires do have some intrinsic damping capability,

the damping is maximized under static conditions and decreases with rolling speed and is

typically not analyzed in simulations of vehicle motion [3]. Damping in the tire is also

nonlinear, being a function of amplitude, but is small and is often neglected [4].

Pacejka’s widely used Magic Formula models do not even consider the damping

properties of pneumatic tires [5].

Despite the trend towards neglecting tire damping, the tires provide for an

additional mechanism to dampen vibratory disturbances in vehicles and should be

utilized to further enhance driver comfort and vehicle endurance. This damping potential

in the tires is extremely important in vehicles where traditional suspensions are absent.

2

Farm tractors, construction machinery, and some off-road military vehicles lack

suspensions and rely heavily on the tire to dampen terrain vibrations.

The medical effects of vibration on the human body have been studied for many

years and there are many frequency ranges that cause discomfort to the vehicle occupants

[6]. For a passenger car, the effect of vertical vibration on the seated person is clearly

the most relevant although horizontal vibration can become important on taller vehicles

such as trucks or sport utility vehicles. The vertical vibrations that seem the most

uncomfortable for the passenger fall in the range between 4 – 8 Hz for whole-body

vibration and 18 – 200 Hz for individual body part vibration [7]. Vibration, in addition to

vertical acceleration, is an important factor in determining rider fatigue and endurance.

The European Union issued a directive stating that extended exposure to vibration can

cause health and safety issues for workers. The directive highlighted disorders to the

muscular/bone structure, neurological and vascular systems and set out limits to protect

the workers from vibration and shock induced syndromes [8]. A vast majority of off-road

vehicles were found to exceed the exposure action value found in the directive [9]. Some

European heavy equipment manufacturers have begun to add full suspension systems to

their off-road vehicles to try to address the issue of vibration and its impact on driver and

cargo fatigue [10].

There are many mechanical systems designed to dampen vibratory excitations.

The suspension is what links the wheels to the vehicle body and allows for relative

motion. The wheels, through the suspension linkage, must propel, steer, and stop the

vehicle, and support the associated force [11]. There are single axle and independent

suspensions with a wide variety of springs and damper components employed [12]. The

3

challenge is find a damping system that can be utilized when one of the traditional,

proven systems is not feasible.

Bachrach and Rivin [13] analyzed a damped pneumatic spring in which the

damping effect is produced by transient pressure feedback from an auxiliary tank

connected by a capillary to the spring cylinder (Figure 1.1).

Figure 1.1 – Self-damped Pneumatic Spring

Note: From “ANALYSIS OF A DAMPED PNEUMATIC SPRING” by B. I.

Bachrach and E. Riven, 1983, Journal of Sound and Vibration, 86(2), p. 192.

Copyright 1983 by Elsevier. Reprinted with permission.

The paper attempts to show the effect of design parameters on spring stiffness,

damping, and frequency response for a single sided damped pneumatic spring. The

damping and stiffness was determined as a function of excitation frequency from the

complex stiffness. It was demonstrated that an auxiliary tank connected to the pneumatic

spring can provide a significant amount of damping and that the damping loss factor

depends only on the tank/cylinder volume ratio and that the capillary dimensions affect

only the frequency at which maximum damping occurs.

A tire/wheel system with two air chambers connected by an orifice or capillary

was examined in [14] to determine the potential for increasing tire damping to improve

4

ride quality. Traditionally, pneumatic tires were used primarily as a road interface with

little regard given to their damping abilities and tires have not played a large role in the

ride quality of passenger vehicles. Low damping in tires can cause a significant

resonance at the wheel hop frequency which can be partially dissipated by the main

suspension and partially transmitted to the passengers. The damping properties of tires

play a much greater role in vibration control for agricultural and off-road vehicles where

the tires act as the only suspension [15]. Many heavy, off-road vehicles are designed for

a low top speed and lack traditional suspension systems. In these cases, the tire is the

only damping mechanism available. Tires on these vehicles typically have low inflation

pressures to improve the tire damping, but large vibratory forces still are felt by the driver

when in rough terrain. Improved tire damping is generally associated with the hysteretic

behavior of the rubber and cord of the tire [16]. This improved damping comes at a cost

however, as the increased rolling resistance affects the efficiency of the tire.

A method to increase tire damping with minimal impact on rolling resistance was

proposed in [17]. The method consisted of connecting a tire to an additional air chamber

via orifice or capillary. Tire deflections due to vibrations or rough terrain would cause

the pressure of the tire to increase relative to that of the air chamber. As a result, air

would move from the tire to the chamber through orifices which led to improved

vibration damping in the tire.

A linearized tire model was used to demonstrate the damping concept's potential

and the results were compared with a laboratory test using a conventional tire connected

to a surge tank. Numerical methods were used to determine the damping obtained using

a compliant auxiliary chamber that is integrated into the tire. The study indicates that for

5

vehicles without suspensions significant ride improvements are possible using

conventional tires with small compliant auxiliary chambers, and for vehicles with

suspensions, noticeable ride improvement could be achieved if new tire designs are

developed in which a greater portion of the tire stiffness is caused by deflection induced

pressure.

Rivin and Rayess [18] expanded this research and analyzed a damping

enhancement in which a typical vehicle tire would be partitioned into two chambers

interconnected by orifices. In the majority of vehicle designs, vibratory protection is

provided primarily by the spring and damper elements of a suspension system and the tire

is used to reduce vibratory input from small road imperfections. The performance range

of suspension systems is very broad. Passenger cars traditionally have a high

performance suspension with a low natural frequency to protect the cabin from direct

road inputs. Race cars or high speed passenger cars have stiff suspensions to improve

handling at high speeds and agricultural tractors usually do not have any suspension

system in order to enhance stability and reduce costs. Typical suspension systems try to

set the spring and damper parameters for optimal performance over a broad range of

vehicle speeds and road disturbances. This design method that optimizes performance

over a large range of excitation frequencies can cause resonance in the vibration damping

system. Rivin found that in traditional vibration protection systems, the suspension

subsystem and the tire subsystem have very different natural frequencies and are usually

weakly dynamically coupled [19]. As a result, high damping in the suspension

subsystem does not noticeably influence the low damping in the tires.

6

One method to improve tire damping is to change the structure of the tire such as

choosing a high damping rubber and/or cord. While this method would increase

damping, the modification would cause increased energy dissipation when the tire

undergoes cyclical deformation during rolling and result in increased fuel consumption

and tire temperatures. Because of these adverse fuel and temperature effects, tires are

typically designed to minimize energy dissipation which in turn deceases the tire

damping.

Using the Theory of Inventive Problem Solving (TRIZ) [20], the damping

enhancement of tires can be approached as a physical contradiction. The tire should have

high energy dissipation under vibratory conditions while it should have low energy

dissipation under rolling conditions. Further analysis of tire damping indicates that

rolling conditions do not change the volume or pressure of air in the tire while radial

vibration does impact the volume and pressure of the air. Therefore, if this pressure

change present during radial vibration can be harnessed, the damping of vibratory

motions of the tire could be enhanced without increasing rolling losses.

The enhancement study achieved damping by generating a flow of air through

calibrated capillaries under vibrational conditions. A tire was modified to divide the

cavity into two chambers connected by capillaries. When a bump or other force deflects

the modified tire, the pressure gradient across the chambers induces flow through the

capillaries. This capillary flow was shown to dissipate energy and improve damping of

vibrations.

In addition to automotive applications for this work, there are also nautical

applications that could use a two chambered pneumatic design. Fenders are pneumatic

7

structures that act as bumpers for marine vessels during docking and mooring. Fenders

are often on large boats or ships to protect them from collisions with other vessels, docks,

and rocks. Damage due to berthing operations can result in substantial financial and

operational penalties to ships and wharves. Even in a well-executed berthing, a large ship

possesses enormous kinetic energy that could seriously damage the berthing structure, the

ship itself and result in injury to people operating the vessel or working on the dock.

Fender systems are provided at a berth to absorb and dissipate the kinetic energy of the

berthing ship and to mitigate impact forces. The amount of energy absorbed and the

maximum impact force imparted are the primary criteria applied in accepted fender

design practices [21].

Ship fenders are a promising potential target for pneumatic damping methods

described in this thesis. The fenders are used in ship-to-shore and ship-to-ship mooring

operations and undergo cyclic compressions in response to the wind and wave forces

against the ship [22]. Rapid dissipation of the energy involved in a ship as it collides

with a stationary object like a dock could provide potential financial benefit through

protection of cargo on the ship and/or protection of the dock and workers on the dock

[23]. Furthermore, operational efficiency can be improved by designing more rapidly

responding ship fenders that allow cargo to be unloaded from large freighters during a

variety of sea conditions. Currently, many docks have to wait for ideal sea conditions, or

so called harbor tranquility, in order to keep from damaging cargo. Improving the

efficiency of bumpers could help to increase the number of available hours for removing

cargo and thus would increase overall efficiency by increasing harbor tranquility [24].

8

In ship-to-ship operations, the berthing energy of the two ships along with

weather conditions and fender size need to be carefully considered [25]. The use of ship

fenders during ship-to-ship moorings has become commonplace and is particularly

troublesome because the operation is typically conducted in open water and rough seas to

transfer goods or replenish a ship at sea [26]. The fender could be adapted to a two-

chambered design and the cyclic fender compression could be harnessed to generate

airflow between chambers and increase damping of the collision thereby resulting in safer

ship-to-ship moorings.

There are many applications that lack a viable method of vibration damping. In

applications such as vehicle tires and ship fenders, the pneumatic structure is already a

main component of the application. As such, redesigning the pneumatic structure to

utilize an airflow based damping enhancement could be much more cost effective than

developing alternative methods for vibration damping in these applications. Methods to

employ airflow to achieve passive damping have been studied, but there has been no

research in an active damping improvement. This thesis analyzes and evaluates the

damping characteristics of a pneumatic structure with active feedback and control of the

pressure difference between the chambers. The air pressure in the main chamber is

controlled in order to increase the damping force and quickly cause the decay of the

vibrations.

9

CHAPTER 2

DAMPING ENHANCEMENT SYSTEM DESCRIPTION

The results of the literature search showed that significant research has been

conducted regarding the passive damping effect of connecting two air chambers by a

capillary or orifice. This thesis will demonstrate an active damping enhancement that

augments the damping force based on the external excitations subjected to the pneumatic

structure or tire.

The damping enhancement has passive and active damping modes. The passive

damping force is generated when a road disturbance and tire deflection causes airflow

between the chambers. The passive damping force depends on the number and size of

orifices employed and the volume ratio of the chambers. The active damping system

operates by increasing or decreasing the pressure in air spring’s main chamber or

auxiliary chamber in response to an external force. This active response changes the

chamber pressure to induce a higher damping force than delivered by the passive system.

The damping enhancement experiments used a calibrated vertical force to induce

an initial displacement to initiate the vibratory oscillation. Force was applied to the top

surface of the air spring to set an initial displacement of 25 – 30 mm and then removed to

allow a free vibratory oscillation. The laser displacement sensor attached to the structure

was used to measure the amplitude and frequency of the vibration and a pressure sensor

was utilized to monitor chamber pressure.

10

The active damping enhancement system is illustrated in a schematic in Figure

2.1 below. The external force, F, causes a pressure increase that is measured with a

pressure sensor, P. The major system components are:

(1) air spring main chamber

(2) air spring auxiliary chamber

(3) orifices

(4) pressure modulating cylinder

(5) linear actuator

(6) laser displacement sensor

(7) pressure sensor

(8) three way airflow control valve

Figure 2.1 – Damping System Schematic

The pneumatic structure is partitioned into two chambers that are interconnected

by up to twelve orifices. The larger, main chamber comprises most of the air spring and

has a volume of 1.54 liters at 10 kilopascals (kPa) inflation pressure. The volume of the

air spring is dependent on the height and inflation pressure of the air spring as seen from

the manufacturer’s product data [27]. Two sizes of auxiliary chambers, 0.13 (Small) and

F

1

2

4 5

3

P

6 7

8

11

0.20 (Large) liters, were initially evaluated. Each orifice interface has a ¼” threaded hole

to allow for different orifice sizes to be tested. Orifice sizes of 1.2 millimeters (mm), 1.5

mm and 6.35mm were evaluated in this research.

When an external force is applied to the structure, a pressure differential is

generated between the chambers of the structure. This pressure differential precipitates a

flow of air between the chambers and induces a damping force that counteracts the

applied external force. The number and size of the orifices and the relative sizes of the

chambers can be varied to modulate the damping force. The tire inflation pressure was

varied between 10 – 70 kPa during the damping enhancement testing. The change in

inflation pressure affected the stiffness of the tire and also changed the volume ratio

between the main and auxiliary air chambers. Each of these variables had an impact on

the overall damping ratio. As inflation pressure increased, stiffness increased and

brought a reduction of the damping ratio. On the other hand, a higher the ratio of the

auxiliary to main chamber volumes resulted in improved damping performance.

There is the capability to have passive and active damping with this system.

Passive damping is produced when an external force deforms the air spring and causes a

pressure increase in the main chamber. This deflection induced pressure rise results in a

pressure difference in the chambers and generates a stream of airflow through the orifices

connecting the chambers. This flow of air through the orifices generates a drag force that

dissipates vibratory energy and improves damping. Active damping can be achieved by

using a cylinder to increase the pressure differential between the chambers in response to

an external force which in turn will increase the damping force. The triggering of the

cylinder in the active system can be achieved by different means. The pressure

12

difference between the chambers could be controlled automatically in response to road

conditions or manually if rough terrain is anticipated. For testing purposes, the active

system was triggered manually at the outset of each damping test. The active system was

designed with a three way valve that is used to control how the pressure differential is

created between the main and auxiliary chambers. The air mass can be injected or

extracted from either the main or auxiliary chambers. The four sub-configurations tested

for the active system were:

A) Air Injection into Main Chamber

B) Air Extraction from Main Chamber

C) Air Injection into Auxiliary Chamber

D) Air Extraction from Auxiliary Chamber

Schematics illustrating the airflow path for each active sub-configuration can be

seen in Figures 2.2 – 2.5.

Figure 2.2 – Active Operation by Injecting Air into Main Chamber

Figure 2.3 – Active Operation by Extracting Air from Main Chamber

P

P

13

Figure 2.4 – Active Operation by Injecting Air into Auxiliary Chamber

Figure 2.5 – Active Operation by Extracting Air from Auxiliary Chamber

The pneumatic structure components chosen for the project are listed in Table 2.1

and an exploded view of the main components is shown in Figure 2.6.

Component Manufacturer Model Website

Air Spring Conti FS-120-9 CI http://213.164.133.30/catalog/ShowBalgPDF/FS%20120-

9%20CI.pdf

Air Cylinder Parker P1Q http://www.parker.com/literature/Literature%20Files/pneumatic/

Literature/Actuator-Cylinder/0960-E_P1Q.pdf

Linear Actuator Thomson PR2402 http://www.thomsonlinear.com/website/com/eng/products/actuat

ors/electrak_pro.php

Pressure Sensor Prosense PTD25 http://www.automationdirect.com/static/specs/prosensetransmitt

ers.pdf

Laser Sensor Keyence IL-065 http://www.keyence.com/products/sensor/laser/il/models/il-

065/index.jsp

Table 2.1 – System Components

P

P

14

Figure 2.6 – Active Damping System Components

Table 2.2 below summarizes the variables tested for each configuration. The

baseline, passive, and active systems were tested at four inflation pressures. All three

sizes of orifices and both auxiliary chambers sizes were evaluated for the active and

passive damping enhancement systems.

Auxiliary Chambers

Tested

Orifice

Diameters

Tested

Actuator

Employed?

Active System Pressure Variation

Method

Baseline None None No N/A

Passive 0.13 liters (Small)

0.20 liters (Large)

1.2mm

1.5mm

6.35mm

No N/A

Active 0.13 liters (Small)

0.20 liters (Large)

1.2mm

1.5mm

6.35mm

Yes

A) Inject into Main Chamber

B) Extract from Main Chamber

C) Inject into Auxiliary Chamber

D) Extract from Auxiliary Chamber

Table 2.2 – Experiment Variable Summary

15

The disassembled pneumatic structure with both auxiliary chambers can be seen

in Figure 2.7. The air spring main chamber is shown at top and auxiliary chambers at

bottom.

Figure 2.7 – Inflatable Structure Components

A laser displacement sensor was attached to the air spring to measure the

vibrational oscillation. The high resolution Keyence IL-065 laser sensor seen in Figure

2.8 measured the decay of the oscillation when the air spring was subjected to a one time

excitation force. Early experiments utilized a MEK M1L laser sensor that had a lower

resolution than the IL-065. The MEK resolution of 0.3mm led to inconsistent, inaccurate

measurements of the displacement for both the active and passive system because the

laser could not measure displacement at a fine enough level. The high resolution

Keyence IL-065, with a resolution of 2 μm, provided reliable and consistent

16

measurements across all experiments and provided more accurate results for the damping

ratio calculations.

Figure 2.8 – Laser Displacement Sensor Diagram and Picture

The data acquisition and control of the damping enhancement system was done

using National Instruments LabVIEW programming software. LabVIEW provides

flexible system monitoring to allow data to be collected in real time at varying collection

intervals. It is also user friendly and can be programmed to have drag and drop features

for regularly tested procedures to reduce the amount of time spent programming the

software and increase the amount of time spent conducting the experiment. Data

acquisition functions were constructed to measure and record the pressure and vertical

X

17

displacement of the air spring (Figure 2.9). The vertical displacement data was then

analyzed in Microsoft Excel and the damping ratio for each experiment was calculated.

On the left side of Figure 2.9 are LabVIEW’s data acquisition functions that

measure and collect signals from the displacement and pressure sensors. Both sensors

send analog voltage signals to LabVIEW, which converts the voltage to the desired unit

based on scaling parameters. The right side of Figure 2.9 has the outputs for the linear

actuator control. The manually triggered outputs switched a set of relays that controlled

both actuator extension and retraction. Box 1 below illustrates the part of the program

that acquires and conditions the pressure signal. The pressure sensor has an analog

output of 0 – 10 volts and a range of 0 – 30 pounds per square inch (psi). The first

numeric constant (0.04472) is a scaling factor to zero the output. The second constant (3)

is the factor to convert the voltage to pressure in psi and the final constant (6.894757)

converts the pressure from psi to kPa. The displacement sensor functions are found near

box 2. The displacement sensor has an analog output of 0 – 5 volts and a range of 50

mm. The first constant (3.96) is a scaling factor to zero the output and the second (10) is

a factor to convert the voltage output to displacement in millimeters. The final area of

interest is the analog outputs for the linear actuator near box 3. Each output is a 5 volt

analog output configured to trigger a relay that activates the linear actuator by user

command. One output closes a relay to send power to extend the actuator. The second

output closes a relay that triggers a double pole, double throw switch that reverses the

power connections and causes actuator retraction.

18

Figure 2.9 – LabVIEW Program

2

1

3

19

CHAPTER 3

DAMPING ENHANCEMENT SYSTEM PROCEDURE

The displacement data was acquired via LabVIEW and plotted in Excel to analyze

the oscillation and calculate the damping ratio (as seen in Figure 3.1). In order to

calculate the damping ratio, first the logarithmic decrement had to be determined from

the amplitudes of the oscillations.

Figure 3.1 – Typical Displacement Result

The logarithmic decrement is used to find the damping ratio of an underdamped

system in the time domain and is calculated by taking the natural log of the ratio of the

-30

-25

-20

-15

-10

-5

0

5

10

0.00 0.43 0.86 1.30 1.73 2.16

Dis

pla

cem

en

t (m

m)

Time (s)

20

amplitudes of any two successive peaks [28]. The logarithmic decrement ( ) was

calculated with the following equation [29].

(3.1)

where is the first amplitude of the oscillation, n is the number of periods used

in the calculation, and is final amplitude of the oscillation.

The logarithmic decrement was calculated four times for each test. Values were

calculated using three and four periods on both the upper and lower halves of the

oscillation as demonstrated in Figure 3.2.

Figure 3.2 – Logarithmic Decrement Calculations

The mean of these four values was calculated and then used to determine the damping

ratio ( for each test [30].

21

√

(3.2)

Three baseline, passive, and active system configurations were tested at each

inflation pressure setting. The baseline configuration tests were the first conducted. The

auxiliary chamber with orifices was removed and a benchmark damping ratio was

calculated for that pressure. The second configuration was the passive damping system.

These tests were conducted with varying sizes and numbers of orifices and initially both

auxiliary chambers to determine the passive system parameters that produced the best

damping ratio improvement. The passive system tests were conducted by using a force to

manually compress the air spring and then release to allow oscillation. Active system

experiments were then completed with different orifices combinations and chamber sizes.

The active system tests were performed similarly to the passive experiments, but in the

active system the pressure difference between the chambers was changed immediately

before the initial displacement. The air cylinder and linear actuator were employed to

add or remove a mass of air to either the main or auxiliary chambers. This added

pressure gradient enhanced the airflow through the orifices during the test and enhanced

the damping observed.

22

CHAPTER 4

DAMPING ENHANCEMENT SYSTEM RESULTS

The first experiments conducted were to determine a baseline damping ratio for

the system at inflation pressures of 65 and 70 kPa. The baseline damping with no orifice

flow was determined and the system experiments in Table 4.1 were then undertaken to

evaluate the two sizes of auxiliary chambers. Each experiment was evaluated by

calculating the percent change from baseline using the following equation [31].

(4.1)

where is the damping ratio of the experiment and is the baseline

damping ratio.

System

Configuration

Chamber

Size

Number of

Orifices

Orifice

Diameter Pressure

Damping

Ratio, %

change

Baseline None None N/A 65 kPa 0.083 N/A

Passive Small 12 1.5 mm 65 kPa 0.083 0%

Active Small 12 1.5 mm 65 kPa 0.083 0%

Passive Large 12 1.5 mm 65 kPa 0.084 1.2%


Active Large 12 1.5 mm 65 kPa 0.084 1.2%


Passive Small 12 1.5 mm 70 kPa 0.080 0%

Table 4.1 – Auxiliary Chamber Comparison

23

The initial tests at 65 and 70 kPa showed that there was no difference between the

baseline damping ratio and configurations with the small auxiliary chamber. Rivin found

in [12] that the damping loss factor was determined by the volume ratio of the main and

auxiliary chambers. With a main chamber volume of 2 liters [27] (at 65 kPa) and the

small auxiliary tank at 0.13 liters, the system volume ratio of 6.5% was found to be

ineffective. The large auxiliary chamber provided a system volume ratio of 10.0%

performed slightly better with a 1.2%. Since the small auxiliary chamber appeared

ineffective, the remainder of the tests was carried out using the large auxiliary chamber.

The next several experiments were carried out at an inflation pressure of 20 kPa.

The main chamber volume at this pressure was 1.67 liters [27], giving a system volume

ratio of 12.0%. The results in Table 4.2 showed a small damping improvement over the

65 and 70 kPa inflation pressures, but the improvement was still small at 2.2% so the

inflation pressure was reduced for the next group of experiments.

System

Configuration

Chamber

Size

Number of

Orifices

Orifice

Diameter Pressure

Damping

Ratio, %

change



Active Large 12 6.35 mm 20 kPa 0.092 0%

Active Large 12 1.5 mm 20 kPa 0.093 1.1%

Table 4.2 – 20 kPa Results

The next inflation pressure to be evaluated was 10 kPa. As before, the baseline

damping ratio was determined and then passive and active system configurations were

tested. The 10 kPa pressure setting provided good improvement in both the passive and

active configurations. The volume of the main chamber decreased to 1.54 liters so this

24

pressure coupled with the large auxiliary chamber produced a system volume ratio of

13.0%.

Multiple experiments were carried out on the baseline configuration with no

orifice flow. The damping ratio results were consistent and averaged to a value of 0.096

for the baseline damping ratio. A logarithmic decrement and damping ratio calculation

for one experiment can be seen in Table 4.3 below.

Top Half of

Oscillation

Bottom Half of

Oscillation

Logarithmic decrement, 3 Periods 0.612 0.614

Logarithmic decrement, 4 Periods 0.598 0.593

Damping Ratio, 3 Periods 0.097 0.097

Damping Ratio, 4 Periods 0.095 0.094

Average Damping Ratio 0.096

Table 4.3 – Experiment Calculations

The calculations above were made for every experiment and the results were

averaged to get an aggregate damping ratio for each configuration as seen for the baseline

configuration in Table 4.4 and Figure 4.1.

Damping Ratio, Baseline Experiment 1 0.096





Average Baseline Damping Ratio 0.096

Table 4.4 – Baseline Damping Ratio

25

Figure 4.1 – Baseline Damping Ratio Results

The passive system had five configurations tested that showed a damping

improvement over the baseline results with the best having a 5.2% improvement. The

most improved configurations had a mixture of 1.2 mm and 6.35 mm orifices (Table 4.5)

with an even split of six of each size resulting in the largest enhancement of the vibration

damping.

-5

-4

-3

-2

-1

0

1

2

3

4

5

0.00 0.86 1.73 2.59 3.46

Dis

pla

cem

ent

(mm

)

Time (s)

1, ζ=0.095

2, ζ=0.096

3, ζ=0.096

4, ζ=0.096

5, ζ=0.097

1 2 3 4 5

26

System

Configuration

Chamber

Size

Number of

Orifices

Orifice

Diameter Pressure

Damping

Ratio

%

change


Passive Large 6

6

1.2 mm

6.35 mm 10 kPa 0.097 1.0%

Passive Large 7

5

1.2 mm

6.35 mm 10 kPa 0.097 1.0%


Passive Large 6

6

1.5 mm

6.35 mm 10 kPa 0.101 5.2%

Passive Large 9

3

1.5 mm

6.35 mm 10 kPa 0.099 3.1%

Passive Large 5

7

1.5 mm

6.35 mm 10 kPa 0.096 0%

Passive Large 7

5

1.5 mm

6.35 mm 10 kPa 0.096 0%

Table 4.5 – Passive System Summary

The three passive configurations with the best damping improvement are

compared on Figure 4.2. The configuration with twelve 1.5 mm orifices is shown on the

left, the configuration with nine 1.5 mm and three 6.35 mm orifices is in the center, and

the configuration with six each of the 1.5 mm and 6.35 mm orifices is on the right. The

most improved passive configuration, with a damping ratio of 0.101 relative to the

baseline ratio of 0.096, enhanced the damping ratio by 0.005 for a 5.2% improvement

over baseline. An error analysis was completed on this passive configuration. The

maximum possible absolute error of the displacement measurement was 16 microns [32].

This absolute error of displacement was used to calculate the error of the damping ratios

using the following equation [31].

| | 4.2

27

where is the is the measured damping ratio and is the actual damping ratio.

The absolute error of the baseline damping ratio was 0.001 and the passive damping ratio

absolute error was 0.002, giving a total possible error 0.003 for the passive damping

improvement.

Figure 4.2 – Top Three Passive Configuration Comparison

The active system experiments at an inflation pressure of 10 kPa had a total of

twelve configurations that had a damping improvement over baseline. Two

configurations of the active system demonstrated the largest damping ratio improvement.

One configuration utilized twelve 1.2 mm orifices and the other twelve 1.5 mm orifices.

Both configurations achieved their results by extracting air from the main chamber to

-5

-4

-3

-2

-1

0

1

2

3

4

5

0.00 0.43 0.86 1.30 1.73 2.16 2.59

Dis

pla

cem

ent

(mm

)

Time (s)

1, ζ=0.098

2, ζ=0.099

3, ζ=0.101

1 2 3

28

precipitate the damping enhancing orifice flow (sub-configuration B) and improved the

damping ratio by 0.009 or 9.4% over baseline. Equation 4.2 was used to calculate

absolute error of the active system damping ratio improvement. With a baseline damping

ratio error of 0.001 and active system error of 0.002, the total absolute error was again

0.003. The active system results can be found in Table 4.6.

System

Configuration

Sub-

Configuration

Number

of

Orifices

Orifice

Diameter Pressure

Damping

Ratio

%

change


Active A 6

6

1.5 mm

6.35 mm 10 kPa 0.096 0%

Active A 12 6.35 mm 10 kPa 0.098 2.1%

Active B 3

9

1.2 mm

1.5 mm 10 kPa 0.102 6.3%

Active B 6

6

1.5 mm

6.35 mm 10 kPa 0.103 7.3%

Active B 9

3

1.5 mm

6.35 mm 10 kPa 0.104 8.3%

Active B 12 1.5 mm 10 kPa 0.105 9.4%

Active B 12 1.2 mm 10 kPa 0.105 9.4%

Active B 6 1.2 mm 10 kPa 0.100 4.2%

Active B 9 1.2 mm 10 kPa 0.102 6.3%

Active B 9

3

1.2 mm

1.5 mm 10 kPa 0.102 6.3%

Active B 6

6

1.2 mm

1.5 mm 10 kPa 0.102 6.3%

Active C 12 1.2 mm 10 kPa 0.102 6.3%

Active D 12 1.2 mm 10 kPa 0.102 6.3%

Table 4.6 – Active System Summary

29

A summary of the baseline and best case configurations for the passive and active

systems can be found in Table 4.7 and Figure 4.3.

Active Passive Baseline

Damping Ratio, Experiment 1 0.105 0.100 0.096





Average Damping Ratio 0.105 0.101 0.096

% change 9.4% 5.2%

Damping Ratio Improvement

Absolute Error 0.003 0.003

Table 4.7 – Active and Passive System Comparison

30

Figure 4.3 – System Comparison

-5

-4

-3

-2

-1

0

1

2

3

4

5

0.00 0.86 1.73 2.59

Dis

pla

cem

ent

(mm

)

Time (s)

1, Baseline

ζ=0.096

2, Passive

ζ=0.101

3, Active

ζ=0.105

1 3 2

31

CHAPTER 5

CONCLUSION

This thesis presents experimental research results of a novel damping

enhancement method that utilizes airflow between two chambers of the pneumatic

structure to produce a damping force. Experiments were designed to test both an active

and passive enhancement system and measurements were taken to calculate the damping

ratio for each.

Both systems showed significant improvement in the damping ratio over the

undamped system. The passive system, which used only the pneumatic structure

deflection induced pressure gradient, provided a damping ratio improvement of 0.005 or

5.2% over baseline with absolute error of 0.003. The active system, which augmented

the deflection based pressure difference by removing air from the main chamber,

demonstrated a damping ratio improvement of 0.009 or 9.4% with an absolute error of

0.003. The active system produced an 80% improvement in damping ratio compared to

the passive enhancement system, but the variable configurations that produced the

maximum damping improvement were different for the passive and active systems. The

passive system showed the most improvement with six 1.5 mm orifices and six 6.35 mm

orifices utilized. The active configurations with the highest damping ratio improvement

had twelve of either the 1.2 mm or 1.5 mm orifices installed between the chambers.

32

The results of the experiments and analysis demonstrated the damping

enhancement capability of a two-chambered pneumatic structure with airflow between

the chambers. The passive system showed stable improvement and the active system

produced the largest change in damping ratio with the large pressure difference between

the chambers.

33

CHAPTER 6

FUTURE WORK

With the airflow based damping concept proven, further work is needed to

optimize the damping enhancement. A mathematical model developed to correlate the

configuration parameters to a damping force would allow for optimization of variables

such as orifice size and number, auxiliary/main chamber volume ratio, and inflation

pressure.

Once a mathematical model allows for the system parameter optimization, a

control strategy should be developed to allow for autonomous active damping system

operation. Whereas the active system was triggered manually during testing, system

operation can be made automatic and be triggered by road disturbances as registered by

the pressure sensor measuring inflation pressure.

.

34

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