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Methodology for design of a vibration operated valve for abrasive viscous fluids
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Methodology for design of a vibration operated valve for abrasive viscous fluids
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Content
METHODOLOGY FOR DESIGN OF A VIBRATION
OPERATED VALVE
FOR ABRASIVE VISCOUS FLUIDS
by
Khashayar Behdinan
______________________________________________________________
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEM ENGINEERING)
May 2009
i
Copyright 2009 Khashayar Behdinan
Acknowledgments
I would like to express my appreciation and sincere thanks to my advisor,
Professor Behrokh Khoshnevis, for presenting me with the opportunity to work on a
novel project called Contour Crafting. His support, patience, encouragement, and
technical and editorial advice were essential to the completion of this dissertation and
have taught me how to be creative in academic research and in my life in general.
A special thank you to my dissertation committee member, Dr. Yong Chen,
for his constant guidance and encouragement. I also want to thank the other member
who served on my dissertation committee, Dr. Paul Rosenbloom, for his suggestions.
Also I thank Dr. Chiara F. Ferraris for giving me her useful information.
I am also thankful to my wife, Nooshin, my son, Pouya, and my daughter,
Farnaz, for their patience, encouragement, and emotional support. Finally, I am
extremely grateful to my parents for their ever-loving support, prayers, and
encouragement during my entire life. I dedicate this dissertation to them in
appreciation of their endless love and kindness.
ii
Table of Contents
Acknowledgments ii
List of Tables vii
List of Figures ix
Abstract xiii
Chapter One: Introduction 1
1.1 Introduction of the Problem 1
1.2 Previous Attempts at Controlling Viscous Flow 2
1.3 Purpose of the Study 6
1.4 Hypothesis 7
1.5 Research Contribution 7
1.6 Organization of the Dissertation 8
Chapter Two: Literature Review 9
2.1 Introduction 9
2.2 Viscous Flow inside Pipe 9
2.2.1 Newtonian Flow 9
2.2.2 Non-Newtonian Flow 10
2.3 Mobility of Fresh Concrete 11
2.3.1 The Flow of Concrete Along a Pipeline 12
2.3.2 Self-Consolidating Concrete 17
2.4 Behavior of Fresh Concrete During Vibration 18
2.5 Fundamental Mechanism of Vibration Valves 19
2.6 Power Ultrasonic 20
iii
2.7 Conclusion 23
Chapter Three: Research Methodology 24
3.1 Introduction 24
3.2 Experimental Research 25
3.2.1 Construction of a Valve Model 26
3.2.2 Measuring Static Friction 26
3.3 Factor Identification and Classification 28
3.4 Operational Range Determination 29
3.5 Ultrasonic Acoustic Vibration Generation 30
3.5.1 The Main Components in Ultrasonic Acoustic
Vibration Generation 30
3.5.2 Selecting Sandwich Transducers 32
3.5.3 Selecting the Booster 33
3.5.4 Selecting Ultrasonic Generators 35
3.6 Vibration Modes 36
3.7 Conducting Experiments 39
3.7.1 Static Friction Flow Stop Test 39
3.7.2 Measuring Flow with Vibration 41
3.7.3 Optimal Valve Shape 42
3.8 Analytical Research 44
3.8.1 Finite Element Analysis 44
3.9 Design Assumptions 48
3.10 Controlling Flow with Duty Cycle 49
3.11 Conclusion 49
iv
Chapter Four: Results 51
4.1 Design of Experiments and Result Analysis 51
4.2 Static Friction Response Surface Methodology 52
4.2.1 Backward Elimination 58
4.3 Measuring Flow with Vibration 63
4.3.1 Screening Test 65
4.3.2 Backward Elimination 66
4.4 Finite Element Analysis 70
4.4.1 Selecting Resonator Type 71
4.4.2 Auto Tuning Thickness 73
4.4.3 Auto Tuning Length 77
4.4.4 The FEM Analysis Problem 80
4.5 Controlling Flow with Duty Cycle 80
Chapter Five: Conclusion 83
5.1 Research Contribution 83
5.2 Research Methodology 83
5.3 Result Summary 85
5.4 Suggested Direction for Future Research 87
5.4.1 Improving Piezo Vibration Performance 87
5.4.2 Loading of Ultrasonic Transducers 88
5.4.3 Fluid Dynamic Analysis 91
5.4.4 Heat Transfer 91
Bibliography 93
v
Appendix A Fundamentals of Piezoelectric Vibrators 97
A.1 Ceramic Material 97
A.2 Modeling Ultrasonic Transducers 99
A.3 Modeling of the Horn 104
vi
List of Tables
Table 2.1. Proportion of Each Constituent Normally Used in Concrete 14
Table 3.1. Concrete Viscosity with Different Aggregate Size and
Water-to-Concrete Ratio 27
Table 3.2. Operating Range for the Experiment 29
Table 4.1. Range of Factors 52
Table 4.2. Design of Experiment Established 53
Table 4.3. Results of Static Friction Experiment 54
Table 4.4. Summary of Fit 55
Table 4.5. Analysis of Variance 55
Table 4.6. Lack of Fit 56
Table 4.7. Parameter Estimates 57
Table 4.8. Sorted Parameter Estimates 58
Table 4.9. Summary of Fit 59
Table 4.10. Analysis of Variance 59
Table 4.11. Lack of Fit 60
Table 4.12. Parameter Estimates 60
Table 4.13. Sorted Parameter Estimates 61
Table 4.14. Results of Vibration Experiment 64
Table 4.15. Summary of Fit 65
Table 4.16. Analysis of Variance 65
Table 4.17. Lack of Fit 65
Table 4.18. Sorted Parameter Estimates 66
vii
Table 4.19. Summary of Fit 66
Table 4.20. Analysis of Variance 67
Table 4.21. Lack of Fit 67
Table 4.22. Parameter Estimates 67
Table 4.23. Sorted Parameter Estimates 68
viii
List of Figures
Figure 1.1. A Pump Coupled with a DC Motor 2
Figure 1.2. A New Dosing Pump Coupled to its Driving DC Motor 3
Figure 1.3. Mechanical Parts of the Pinch Valve 4
Figure 1.4. Body of the Pinch Valve 4
Figure 1.5. Rupture of Latex Tube Due to Valve Failure and
Subsequent Pressure Accumulation 5
Figure 1.6. Mechanical Parts of the Cut-Off Valve 5
Figure 1.7. Result of Current Contour Crafting Machine using a Cut-
Off Valve 6
Figure 2.1. Model of Surfaces Along Flow Path 10
Figure 2.2. Shear Stress Versus Rate of Shear in Non-Newtonian
Fluids 11
Figure 2.3. Concrete Velocity Profile Along Pipe 13
Figure 2.4. Pressure to Overcome Friction 13
Figure 2.5. Different States of Pumping Concrete 15
Figure 2.6. Model of particles Along Flow Path 15
Figure 2.7. Model of Surfaces Along Flow Path 16
Figure 2.8. Model Particles Contact 16
Figure 2.9. Viscous Flow Frictional Resistance 18
Figure 2.10. Friction Force between Abrasive Particles 20
Figure 3.1. Research Methodology 24
Figure 3.2. Experimental Design Methodology 25
Figure 3.3. Model of Designed Valve 26
ix
Figure 3.4. Model of Valve Head 27
Figure 3.5. Schematic of Generator, Converter and Load 31
Figure 3.6. Sandwich Transducer 32
Figure 3.7. Sandwich Transducer Parts 33
Figure 3.8. Sample of a Booster 34
Figure 3.9. Different Types of Boosters 34
Figure 3.10. Vibration Amplification Diagram of a Step-Up Booster 35
Figure 3.11. Branson Ultrasonic Generator 36
Figure 3.12. Frequency Response of a Piezoelectric Transducer (Phase
and Impedance Z). 37
Figure 3.13. Frequency Response of a Piezoelectric Transducer (Phase
and Impedance Z). 38
Figure 3.14. Vibration Amplitude in μm between 10 and 40 kHz. 39
Figure 3.15. Picture of the Test Stand 40
Figure 3.16. Model of a Developed Valve Including Transducer,
Booster and Cover 42
Figure 3.17. Possible Shapes of Candidate Valve Designs 43
Figure 4.1. Residual by Row Plot 58
Figure 4.2. Actual by Predicted Plot 59
Figure 4.3. Residual by Row Plot 60
Figure 4.4. Prediction Profiler 61
Figure 4.5. Cube Plot 61
Figure 4.6. Normal Plot 62
Figure 4.7. Residual by Row Plot 68
Figure 4.8. Prediction Profiler 68
x
Figure 4.9. Normal Plot 69
Figure 4.10. Pareto Plot of Estimates 69
Figure 4.11. Cube Plot 69
Figure 4.12. Selecting Resonator Type 71
Figure 4.13. Selecting Tuning Mode 72
Figure 4.14. Frequency Selection 72
Figure 4.15. Size setting 73
Figure 4.16. Resonator Geometry (Half-Shape) 73
Figure 4.17. Resonator Geometry 74
Figure 4.18. Auto Tune Result 74
Figure 4.19. Amplitude Result 75
Figure 4.20. Stress Diagram 75
Figure 4.21. Cumulative Strain Energy 76
Figure 4.22. Cumulative Loss 76
Figure 4.23. Resonator Geometry (Half-Shape) 77
Figure 4.24. Result Amplitude 77
Figure 4.25. Auto Tune Result 78
Figure 4.26. Stress Diagram 78
Figure 4.27. Cumulative Strain Energy 79
Figure 4.28. Cumulative Loss 79
Figure 4.29. 80% Duty Cycle Graph 81
Figure 4.30. 60% Duty Cycle Graph 81
Figure 4.31. 40% Duty Cycle Graph 82
xi
Figure 4.32. Flow Versus Duty Cycle Graph 82
Figure A.1. Internal structure of a piezo ceramic material 97
Figure A.2. Polarization of Piezoelectric Materials 98
Figure A.3. Polarization of Piezoelectric Materials 98
Figure A.4. Polarization of Piezoelectric Materials 99
Figure A.5. The Piezoelectric Effect inside Different Bodies 99
Figure A.6. Piezoelectric Converter Dual, BVD Models 100
Figure A.7. BVD Piezoelectric Converter Models with Dissipative
Elements 101
Figure A.8. Simplified BVD Piezoelectric Converter Models 101
Figure A.9. BVD Piezoelectric Converter Models by Considering
External Load 102
Figure A.10. Alternative BVD Models of Loaded Piezoelectric
Converters with Block 103
Figure A.11. Schematic of the Equivalent Circuit of the Transducer
around Resonance 103
Figure A.12. Schematic of the Equivalent Circuit of the Transducer
with Added Horn 104
xii
xiii
Abstract
In this research, a new ultrasonic operated valve was analyzed, prototyped, and
tested for use in an abrasive viscous fluid application. The innovative valve concept is
based on controlling the friction of material by employing several friction elements
along the flow direction. Abrasive particles in the viscous fluid are stopped by the
force of friction when coming into contact with the friction elements. Friction is
neutralized by use of vibration to break away the abrasive particles from the friction
element surfaces. Several factors were considered in designing the piezoelectric valve.
Factor identification was done by conducting experiments and analyzing data. Some
important factors that affect the valve design were recognized to be back pressure, size
of friction blades along the direction of flow, density of material, viscosity, amplitude,
frequency of vibration, and proportion of particles in the mix. First, a method was
designed for measuring the friction coefficient of the given viscous materials. A
design of experiment approach was pursued in order to identify the significant
parameters. A piezoelectric transducer was used, which vibrated at the resonance
frequency of 20 kHz. FEM modeling was used at that stage to ensure that the
resonance frequency of the designed valve matched the resonance frequency of the
transducer and booster that provided vibration. In order to perform proportional flow
control, pulse width modulation was used to control the duty cycle of ultrasonic power
transferred to the valve. A study was performed to find the best vibration performance
for the parameters in the range of operation.
1 Chapter One: Introduction
1.1 Introduction of the Problem
Controlling the flow of abrasive viscous fluids has been a major problem,
especially when the fluid contains particles of different sizes. Problems include
clogging of material and cleaning of the valve after use. The challenge of this study,
therefore, was to design a vibration-operated valve that would provide steady, on-
demand flow for abrasive viscous fluids at the desired rates, based on the following
given information:
1. Required flow rate
2. Material friction characteristics
3. Desired back pressure
4. Pipe diameter, which affects the design of the starting section of the valve
5. Material density
The purpose of the research was to develop and test a methodology for design
of a novel valve based on high frequency vibration. This research was conducted in
an attempt to address a problem discovered while controlling material flow in a
contour crafting system. Since concrete was the material used in that system and there
was need to regulate flow, this study is also based on concrete, composed of cement,
1
water, and sand. The result of this study is applicable to all other types of viscous
fluids.
1.2 Previous Attempts at Controlling Viscous Flow
In contour crafting research, where control of concrete flow is a strict
requirement, several attempts have been made to use available solutions or devise new
solutions for flow control. First, a relatively small, progressing cavity pump was
selected, which is shown in Figure 1.1. Such pumps, the larger version of which is
used as the main ground pump for concrete, provide a consistent flow rate
proportional to the shaft RPM. However, the flow pulsates as a result of the sequential
output of discrete volumes trapped in the helical cavities of the rubber stator. The
pump flow rate was controllable by controlling the speed of the large DC motor,
which drove a gear head, which drove the pump’s helical shaft in the tightly engaged
rubber rotor housing. The major problem with this pump was its excessively heavy
weight and its inability to pass a mixture that had sand content beyond even a small
proportion.
Figure 1.1. A Pump Coupled with a DC Motor
2
A new dosing device was then invented by Professor Khoshnevis in 2006.
This device was significantly smaller and lighter than the progressing cavity pump
system. This dosing device, shown in Figure 1.2, performed its function very
satisfactorily but the components used were not properly configured or dimensioned
for the intended duty loads and cycles. For example, the DC drive motor would
overheat and could not provide sufficient torque for very viscous concrete, and the
device was not designed for quick disassembly for cleaning. This dosing device
remains a practical and highly attractive option and is in the process of being
reconfigured by the research team for optimal performance.
Figure 1.2. A New Dosing Pump Coupled to its Driving DC Motor
The research team then considered the use of proportional valves with
feedback control. Subsequently, several valves were designed, fabricated and tested.
For example, a pinch valve concept (Figure 1.3) using a latex tube, was devised. It
was mechanically pinched by a blade that could reciprocate by means of a DC motor
3
connected to a worm gear. The valve operated somewhat satisfactorily but had the
occasional problem of segregation and clogging.
Figure 1.3. Mechanical Parts of the Pinch Valve
Figure 1.4. Body of the Pinch Valve
4
Figure 1.5. Rupture of Latex Tube Due to Valve Failure and Subsequent Pressure Accumulation
After testing the pinch valve, a new valve was designed as a cut-off valve. In
this valve, pinching was avoided and instead a blade was implemented in the valve to
obstruct the concrete flow. A schematic of this valve is shown in Figure 1.6.
Figure 1.6. Mechanical Parts of the Cut-Off Valve
This valve had problem of cleaning and blockage and it performed only as an
open- close valve. This valve was not able to regulate flow and sometime it could not
be fully closed due to obstacle of sand particles.
5
With presence of above problems one of the first successful dosed-depositions
for the contour crafting system employed a type of cut-off valve, and it is shown in
Figure 1.7.
Figure 1.7. Result of Current Contour Crafting Machine using a Cut-Off Valve
6
1.3 Purpose of the Study
Objective 1: The first purpose of this study is to devise a procedure for finding
an optimal valve design that will result in minimum valve size, minimum power
demand, and the ability to start and stop the flow of a viscous material while assuring
that the required flow rate is met.
20 KHz was the decided frequency of the vibration source and acts as a
constraint; besides the hardware design specifications, the required valve blade
material and surface condition, back pressure and vibration power were the outputs of
the design process.
Objective 2: The second purpose of this study was to accomplish flow control
by means of controlled duty cycle (i.e., the duration of vibration ON divided by
duration of vibration OFF) applied to the vibration power given to the valve designed
using the procedure used for Objective 1.
1.4 Hypothesis
In this research, the hypothesis is that the designed valve models will control
the flow of a given material with an accuracy of 90%. Based on the preliminary valve
design and experiments, it is anticipated that the designed valve will show a
reasonably accurate performance provided that systematic design and operation
processes are devised and followed.
1.5 Research Contribution
This thesis is the first extensive research in designing piezoelectric valves.
This research resulted in design and implementation of a novel valve that controls the
flow of viscous material using dynamic vibration generation, and eliminates the
problems of clogging and cleaning that attend the nature of those materials.
7
1.6 Organization of the Dissertation
Chapter1. This chapter includes an introduction to the high viscous flow
control problem, previous attempts at finding a solution, and also a brief description of
the new piezo-operated valve.
Chapter 2. This chapter reviews all fundamentals about viscous material flow
and the field of ultrasonic vibration generation.
Chapter 3. This chapter covers the research methodology used for conducting
this research in the three directions of developmental, experimental, and analytical
research. Also it includes factor identification and operating range determination.
Chapter 4. This section analyses the experimental results by doing regression
and factor elimination, statistical design of experiments, main, and interaction plots.
This chapter also includes the FEM analysis for valve shape optimization.
Chapter 5. The conclusion discusses the achieved results and areas of
enhancement, as well as providing recommendations for future practices.
Appendix A. This Part includes some information on fundamentals of
Piezoelectric vibrators and modeling ultrasonic transducers.
8
2 Chapter Two: Literature Review
2.1 Introduction
Using vibration to control the flow of material has been recently approached
by researchers. The study of viscous material flow control is related to several major
topics. This research studied literature in the fields of material behavior and high
frequency active vibration control. This research was performed with the intention of
improving material delivery in Contour Crafting and, since the study is focused on
concrete material, characteristics of concrete were also studied in this research.
2.2 Viscous Flow inside Pipe
2.2.1 Newtonian Flow
A Newtonian fluid is a fluid whose stress versus rate of strain curve is linear
and passes through the origin. The constant of proportionality is known as the
viscosity. Pipe flow is limited by a kind of liquid friction called viscosity. For
straight, parallel, and uniform flow, the shear stress, τ, between layers is proportional
to the velocity gradient, ∂u/ ∂y, in the direction perpendicular to the layers.
A simple equation to describe Newtonian fluid behavior is:
( 2-1)
9
Where:
τ is the shear stress exerted by the fluid [Pa]
μ is the fluid viscosity - a constant of proportionality [Pa·s]
is the velocity gradient perpendicular to the direction of shear [
]
Figure 2.1 shows a shear stress model for Newtonian fluid along a path.
Figure 2.1. Model of Surfaces Along Flow Path
Source: http://en.wikipedia.org/wiki/Viscous
2.2.2 Non-Newtonian Flow
A non-Newtonian fluid is a fluid in which the viscosity changes with the
applied strain rate and is not constant with respect to shear rate. As a result, non-
Newtonian fluids may not have a well-defined viscosity.
10
However, for a wide range of "fluid like" materials, either the viscosity is not
constant with respect to shear rate and or the flow behavior is not fully described.
Non-Newtonian flow curve is shown in Figure 2.2:
Figure 2.2. Shear Stress Versus Rate of Shear in Non-Newtonian Fluids
http://en.wikipedia.org/wiki/Non_Newtonian_fluid
Although the concept of viscosity is commonly used to characterize a material,
viscosity can be insufficient to describe the mechanical behavior of a substance,
particularly the non-Newtonian fluids.
2.3 Mobility of Fresh Concrete
Concrete is a suspension composed of a fluid phase and a solid phase. The
fluid phase is the cement paste and the sand is the solid phase.
In mixed concrete, particle assembly is composed of cohesion less particles
(aggregate grains) and cohesive particles (cement grains) surrounded by mixing water
membranes. In the static state, both particle groups are only subjected to the frictional
11
resistance, but in the moving state, only the former simultaneously bears the viscous
resistance together with the frictional resistance.
2.3.1 The Flow of Concrete Along a Pipeline
The flow of concrete along a pipeline may be visualized as a suspension of
variously sized aggregate and cement particles in water. Chiara F. Ferraris (2003)
showed that freshly mixed cement paste exhibits non-Newtonian fluid properties, in
that it has a yield point and a plastic viscosity which varies both with time under shear
and also shearing rate. The addition of aggregate to cement paste further removes
concrete flow properties from the Newtonian concept. When starting with new pipes
it must be remembered that the internal surface of these pipes will be relatively rough
compared with pipes that have been used for some time.
Loadwick (1970) discussed mobility of fresh concrete in terms of its viscosity,
cohesion, and internal resistance to shear. Roger D. Brown (1977) created a model to
relate state of concrete in the pipeline to the mixed components. He established a
pumping system to pump the concrete along a pipe and measured the mobility and
pumpability of fresh concrete. He observed that a concrete mixture with excessive
coarse aggregate results in a loss of cohesion and mobility. Base on his study,
aggregate particle shape and size distribution is important factors influencing the
rheology. Practical experiments with concrete exiting a pipeline show that it flows in
the form of a toothpaste-like "plug," separated from the pipe wall by a thin lubricating
layer.(Figure 2.3)
12
Figure 2.3. Concrete Velocity Profile Along Pipe
Source : Ede
Figure 2.4. Pressure to Overcome Friction
Source : Ede
Practice has shown that the pumpability of concrete depends on the proportions
and characteristics (coarseness or fineness) of the mixture. This means that the
cement content is of major importance and, in fact, concrete that lacks cement is not
consistently pumpable.(Figure 2.4)
13
Cement Aggregate Water
Fine Coarse
Volume proportion range 5- 16% 22-29% 42-54% 12-20%
Weight proportion range for
unit cement weight
1 0.7-2.4 1.3-4.6 0.4-0.7
Table 2.1. Proportion of Each Constituent Normally Used in Concrete
The movement of the concrete along the pipeline is resisted by the pipe itself.
This flow resistance consists of two components, being the hydraulic shearing of the
lubricating layer and solid friction of particles against the pipe wall. Figure 2.5 shows
that flow resistance will be low if the concrete is in hydraulic, i.e., saturated state.
However, if the permeability of the concrete at the pressure gradients applied by the
pump is such that water flows at an excessive rate down the pipeline, then the concrete
near the pump may become "dewatered." This "dewatering" could transform the
concrete from the saturated (hydraulic) state to the transitional or friction state, with a
corresponding dramatic increase in flow resistance. The pressures required to
maintain a given flow rate are dependent on the flow resistance. Both the permeability
and the flow resistance are functions of the mix proportions. Additionally, the
permeability is governed by the pressure gradient that is directly proportional to the
flow resistance (for a constant-diameter pipe).
The flow of concrete in a pipe will depend on a variety of factors including the
concrete viscosity, the yield stress, and the size distribution and shape of the coarse
14
aggregates. Modeling the flow of complex fluids like concrete presents a great
research challenge because of the necessity to account for the motion of the
aggregates.
Figure 2.5. Different States of Pumping Concrete
Source :F.Loadwick
Figure 2.6. Model of particles Along Flow Path
Source: http://ciks.cbt.nist.gov/~garbocz/scc_2003/node1.htm
15
The graphic below shows a snapshot of a simulation of the flow of concrete
between separate walls. In this example, forces are being applied in opposite
directions on parallel walls, placing the concrete under shear. Various colors are used
to represent rock particles of different sizes.
Figure 2.7. Model of Surfaces Along Flow Path
Source: http://www.nist.gov/public_affairs/techbeat/concrete.htm
Almost all particles make contact with adjacent particles. The particles that are
completely separate in the initial state will push aside the surrounding water, and also
come into contact with others when they move.
Figure 2.8. Model Particles Contact
Source: Murayama
16
According to Murayama (1991), the contact slant of particles is not generally
parallel to the maximum shear (MS) plane, and changes with the particle positions.
The contact between particles results in the inter-particle friction that is thought to
follow Coulomb’s solid friction law. Hence, whether the particles in fresh concrete
are stationary or moving, all the cement particles and all the aggregate particles are
subject to frictional resistance. A stationary cement particle is in approximate
equilibrium with attractive and repulsive forces from its surrounding particles.
However, when the cement particle moves, it also meets other types of resistance; the
interparticle force must first destroy the links of atoms or molecules on the particle
interfaces that contribute to the interparticle solid friction.
Depending on how the structure responds to an applied shear stress, one can
observe different types of macroscopic flow behavior such as yield stress behavior and
viscoelasticity.
2.3.2 Self-Consolidating Concrete
One form of concrete is self-consolidating concrete (SCC), which allows easy
movement of concrete around flow obstructions under its own weight without the use
of external vibration. However if there is a back pressure then the sand particles are
pushed around the wall and resist the motion. This form of concrete cannot be used in
contour crafting because it cannot hold its shape.
17
2.4 Behavior of Fresh Concrete During Vibration
Chiara F. Ferraris (1999) performed research into testing and modeling of
fresh concrete Rheology. Rheology is the science that deals with the flow of materials
and includes the deformation of hardened concrete.
At low stresses, the material behaves as a solid of extremely high viscosity. As
stresses increase, concrete behavior gradually changes to that of a liquid.
Figure 2.9. Viscous Flow Frictional Resistance
Source: ACI
Ferraris (1999) states that flow is restricted by frictional, cohesive, and viscous
forces. Cohesion develops due to attractive surface forces between particles while
resistance is caused by the viscous flow of the matrix. When increasing the shear
18
stresses below the yield value, no flow occurs, and the concrete behaves like a solid.
At higher oscillating stresses, the bond strength between particles becomes insufficient
to prevent flow, and at the same time the viscosity gradually decreases. Concrete
mixture proportioning, therefore, indirectly takes into account that the viscosity of the
lubricating cement paste can be adjusted to the vibratory stress and its frequency. It
follows that with increased vibratory or consolidation pressure an increase in paste
viscosity is required, i.e., a decrease in the water-cement ratio and/or increased
frequency of vibration mixture proportioning. Concrete mixtures are proportioned to
provide the workability needed during construction and to assure that the hardened
concrete will have the required properties.
2.5 Fundamental Mechanism of Vibration Valves
Vibration valves work on the basis of friction between abrasive particles within
the fluid material and the inner walls of the flow conduit. Vibration valves, therefore,
work only for viscous materials that contain abrasive parts.
By applying back pressure to cause flow of the viscous fluid, abrasive particles
accumulate along the flow path due to their inter particle friction and dewatering.
Removing these particles needs vibration to allow the passage of material. Vibration
breaks the mechanical locking between particles and the walls of the conduit, and it
also breaks apart the interlock between particles.
Figure 2-10 shows the friction concept between particles and the conduit walls.
In this figure the friction caused by interlocking of abrasive particles and conduit
19
surface is magnified by the "bridging" phenomenon. The pressure of incoming
material against the middle particles of the arc formation causes the particles near the
conduit surface to be pushed against the surface, hence increasing friction. Vibration
of the conduit walls breaks away these mechanical locking, hence allowing the flow.
Figure 2.10. Friction Force between Abrasive Particles
2.6 Power Ultrasonic
The field of power ultrasonic technique, which represents an important field of
industrial electronics, has experienced very swift and dynamic development in the
recent two decades. As a result, systematic design and construction methods for new
ultrasonic devices have been developed. Applications in the field of power ultrasound
have extended into different branches and processes of many industries, including
mechanical, electrical, and chemical. Alongside new applications of ultrasound, ever
newer and more efficient sandwich transducers are being designed and developed, and
20
many scientific papers have been published presenting aspects of power ultrasonic
technique, especially different electromechanical models that represent optimal design
of ultrasonic transducers. Following are some examples of the related developments.
Strgio S. Miihlen designed a high-power ultrasonic transducer for renal
lithotripsy. The device consists of a concentrator (horn) associated with piezoelectric
PZT ceramic rings to obtain maximum power transfer to the kidney stones. The
transducer works at 31 kHz and the vibratory amplitude measured on the application
tip is 0.12 mm.
Shirley C. Tsai1, T. Kuan Tseng performed related work in high frequency
silicon-based ultrasonic nozzles. Such high frequency nozzles could produce 5 μm-
diameter drops that are useful for alveolar delivery of medicine and nanoparticle
synthesis.
Li Junhui, Tan Jianping did research into the characteristics of ultrasonic
vibration transmission and coupling in bonding technology. The transmitting models
of ultrasonic vibration in ultrasonic transducer and capillary have been given out by
utilizing the propagating mechanism of ultrasonic wave in elastic body. They showed
that ultrasonic vibration displacement (or velocity) and energy density increase with
decreasing section in the transmitting process.
21
Neppiras E A (1973) worked on the pre-stressed piezoelectric sandwich
transducer. Dion J L, Cornieles E, Galindo F and Kodjo extracted the model for
ultrasonic transducers with several piezoelectric elements and passive layers.
Shuyu L (2005) studied the load characteristics of high power sandwich
piezoelectric ultrasonics. Cardoni and M. Lucas also worked on optimization of the
vibration response of ultrasonic cutting systems.
One of the most-used methods in numerical design is Finite Element Method
(FEM). Lorenzo Parrini and Patrick M. Cunningham (2001) studied this method
based on an initial design estimate obtained with finite element method (FEM)
simulations.
According to a Lorenzo Parrini (2001) study on ultrasonic transducers,
stepwise reduction of size toward the tip results in increased vibration amplitude at the
end. The clamping point of the transducer should be placed in longitudinal nodes of
the ultrasonic field, where the amplitude is small, to minimize the loss of ultrasonic
energy into the mounting system. However, because an anti-node of the radial
ultrasonic field always occurs at these longitudinal nodes and the horn exhibits a
maximum of its radial displacement there, the loss of ultrasonic energy in the
mounting system can never be removed completely. The radial displacement is
generated based on the vibration in radial mode. The effect of radial vibration is an
important problem in high power ultrasonic design. The radial displacements come
from the 3D distribution of the ultrasonic displacements of the main longitudinal mode
22
itself. The radial displacements are intrinsic in any 3D longitudinal mode and will
propagate into the mounting flange of an ultrasonic transducer.
Generally, when the radial dimensions are much less than a quarter of the
longitudinal wavelength, the one-dimensional design theory could be applicable and
the errors between the measured and designed frequencies negligible.
Theoretical analysis shows that the elasticity method is simple, easy to
calculate, and especially suitable for the study of coupled vibrations. It is shown that
the calculated resonant frequencies according to the simple elasticity method provide
better approximation of the measured results than those from one-dimensional theory.
2.7 Conclusion
In this chapter, different studies defining non-Newtonian fluids and effect of
viscosity in fresh concrete flow were reviewed. Separate studies in the field of
ultrasonic vibration generation were also reviewed. The proposed research will need
to use a valid model for calculation of friction in order to characterize the energy of
the vibration needed to neutralize it.
23
24
3 Chapter Three: Research Methodology
3.1 Introduction
In order to achieve the desired method of design and fabrication of a
piezoelectric valve that is able to control the flow of material, considerable effort has
been put into developing the shape and structure of these valves. The key activities
fall into the categories of analytical research, experimental research, and
Figure 3.1.
developmental research (Figure 3.1)
Research Methodology
ories of activities all relate to one another. Sim These categ ultaneous
theoret ucted. ical study, experimental research, analysis, and modification were cond
After analysis of each experiment, a new set of experiments were proposed and
pursued.
25
3.2 Experimental Research
s that could potentially influence the
consolid
static friction tests and dynamic flow tests. The design methodology flow chart is
Figure 3.2. Experimental Design Methodology
Because of the many variable
ation of concrete, accurate and controlled measurements were made to prevent
crediting the wrong variable for some measured response. In order to do so,
experimental research was set up and many experiments were carried out. A Design
of Experiment (DOE) was performed to study the impact of blade distances on both
shown in Figure 3.2
26
3.2.1 Construction of a Valve Model
ew valve model was constructed. The
schema
The horn in our system ning
ring the friction coefficient of the given
viscous ose,
In order to begin the experiments, a n
tic of this valve is shown in Figure 3.3.
Figure 3.3. Model of Designed Valve
is th signed by machi e valve tip. The valve tip was de
several blades along the path of concrete (Figure 3.4).
3.2.2 Measuring Static Friction
A method was devised for measu
materials with the given planar valve blade surface. To achieve this purp
different valve with varying blade sizes were constructed as shown in Figure 3.4.
27
Figure 3.4. Model of Valve Head
In this research, both sed as sample materials.
Concrete mass-per-volume varies, and was calculated from a measured sample. The
fine aggregate used in this experiment consisted of different varieties including sand
and silica. There was also coarse aggregate in the mixed concrete, consisting of river
gravel or crushed stone. The range of sand grain size was up to 5 mm.
Ratio
sity
Pa’sec
clay and fresh concrete were u
Classification
Water/Concrete Plastic Visco
concrete gate with fine aggre 0.55 41.2
concrete with course aggregate 0.6 56.7
Table 3. Size and Water-to oncrete Ratio
ty,
the concrete was poured inside a cylindrical chamber rotating at constant speed. By
measuring the torque, the viscosity of the concrete was derived. Although the
measurement was not entirely accurate, it was accurate enough to allow estimation of
1. Concrete Viscosity with Different Aggregate -C
Friction is influenced by material viscosity. In order to measure the viscosi
28
the range of material viscosity for the experiment. This identifies the friction
coefficient used in our design procedure.
3.3 Factor Identification and Classification
ied factors required many runs.
Howev
ack
crete
ossible configuration, a proper design of experiment
r
Conducting detailed experiments for all identif
er, by eliminating less important factors, this research was conducted using
fewer runs with a subset of factors. Some of the factors estimated to affect our
response were:
• B pressure of concrete
ection of movement
of vibration
• Size of blades along the dir
• Distance between blades
• Amplitude and frequency
• Viscosity of concrete
• Amount of sand,
• Size of sand
• Density of con
• On_off duty cycle
In order to apply the best p
was established. The design variables were selected based on the most significant
variables affecting the outcome. These Design Variables (DVs) are independent
quantities that were varied in order to achieve an optimal design. Upper and lowe
limits were specified, to serve as "constraints" on the design variables. These limits
29
defined the range of variation for the DVs. State variables (SVs) are quantities that
constrain the design. These were also known as "dependent variables" and were
typically response quantities being functions of the design variables.
The objective function is the dependent variable that provides an overall
indicati is,
3.4 Operational Range Determination
erational range for each factor needed
to be de
arameter Min Operating Point Max
on of the valve performance. This function was in terms of the DVs, that
changing the values of the DVs changed the value of the objective function.
Before designing the experiments, the op
termined. For example, back pressure needed to be adjusted, concrete could
be made more viscous, and the sand size and proportion of sand in the mix could be
adjusted.
P
back pressure of concrete 10 psi 20 p 15 psi si
amplitude of vibration 20% 50% 100%
viscosity of concrete 6000 Cst Cst Cst 11000 16000
size of sand 2mm 3.5 mm 5mm
On_Off duty cycle 0% 50% 100%
density of concrete 2100 kg/m3 kg/m3 g/m3 2300 2500 k
Table 3.2. O for the E perating Range xperiment
Determination of the maximum and minimum values for each factor was based
on previous experience and a set of preliminary planned experiments. The preliminary
experiments were based on one-factor-at-a-time variation. However, this method may
unnecessarily eliminate part of the operational region for factor ranges.
3.5 Ultrasonic Acoustic Vibration Generation
The designed valve was connected to an ultrasonic converter via an interface.
The best operating frequency of the ultrasonic converter is normally found when the
maximum traveling-wave amplitude is reached and when a relatively stable oscillation
is established.
The best operating ultrasonic systems are those that produce very strong
mechanical oscillations or high and stable vibrating mechanical amplitudes, with
moderate electric output power from the ultrasonic power supply. The second
criterion is that thermal power dissipation of the total mechanical system, in
continuous operation with no additional system loading, be minimal.
After selecting the proper sandwich transducer, the booster was selected. The
booster contacts the valve head and delivers power to the load.
3.5.1 The Main Components in Ultrasonic Acoustic Vibration Generation
The main components in ultrasonic acoustic vibration generation are the
following:
30
A) Ultrasonic generator, being an electronic ultrasonic signal generator. The
converter, which is a device for generating vibration from an electrical signal, is
driven by a signal generator.
B) High power ultrasonic converter, which converts electricity into high
frequency mechanical vibration.
C) Booster, being a metal bar of, for example, aluminum or titanium, that
connects the ultrasonic transducer with an acoustic load, oscillating body, or resonator;
this can also boost the amplitude of input signal.
D) Acoustic load, which is the mechanical resonating body.
Figure 3.5. Schematic of Generator, Converter and Load
The acoustic load, which in our case is the designed valve, was driven by
incoming frequency and amplitude modulated pulse-train, causing it to begin
oscillating in one or more of its natural vibration modes or harmonics.
31
3.5.2 Selecting Sandwich Transducers
The transducer converts electricity into high frequency mechanical vibration.
The active elements are usually piezoelectric ceramics although magnetostrictive
materials are also used. Transducers are also called “converters.” Bolt-clamped
Langevin-type (sandwich) transducers are widely used as efficient vibratory sources in
various fields of industrial application of high-power ultrasonics. A transducer of this
type can steadily generate high-amplitude ultrasonic vibrations.
Figure 3.6. Sandwich Transducer
A sandwich transducer includes:
1- Metallic base
2- Connection bolt
3- Dielectric insulator
4- First metallic electrode positioned between the resonance enhancing disc and the
piezoelectric crystal
5 - Piezoelectric crystal
6- Second metallic part
32
Figure 3.7. Sandwich Transducer Parts
Source: http://www.staplaultrasonics.com/c3-struc/struc3.htm
By applying a sine wave voltage to the piezoelectric ring, the thickness of the
piezoelectric rings is periodically changed. By this oscillation of the thickness of the
piezo, the transducer is vibrated into longitudinal and other oscillations.
The amplitude of the ultrasonic oscillations of the ultrasonic transducer is on
the order of 20 nm. The largest amplitude develops at the transducer tip at the
longitudinal resonance of the horn. The frequency to which the horn is excited is
determined by the shape of the horn and type of materials.
3.5.3 Selecting the Booster
In order to amplify mechanical vibration, a booster was used. The booster
adjusts the vibration output from the transducer and transfers the ultrasonic energy to
the horn. The booster also generally provides a method for mounting the ultrasonic
stack to a support structure.
33
Figure 3.8. Sample of a Booster
Different boosters exist for different applications, with varying properties that
could increase or reduce vibration amplitude. (Figure 3.9)
Figure 3.9. Different Types of Boosters
Source: http://www.staplaultrasonics.com/c3-struc/struc3.htm
34
The graph of a step-up booster is shown in Figure 3.10
Figure 3.10. Vibration Amplification Diagram of a Step-Up Booster
Source: http://www.staplaultrasonics.com/c3-struc/struc3.htm
In our application the transducer was selected at 3KW and generated enough
vibration to operate valve, so the booster was selected with 1:1 ratio and it acts as a
coupling between generator and horn. Also the mounting bracket was installed on the
booster so that it can be easily connected to fixture without transferring vibration to
machine body.
3.5.4 Selecting Ultrasonic Generators
The ultrasonic generator is the device that generates ultrasonic waves. The
ultrasonic waves could be frequency modulated by varying the output frequency of the
ultrasonic generator. The ultrasonic waves can be also amplitude modulated by
35
changing the amplitude of the generator output. A frequency modulated ultrasonic
wave could also be amplitude modulated. This is the most general case of "designer
waveform" for a single generator driving a single transducer array.
Resonance phenomena are caused by repeatedly pumping energy into a part at
a known resonance frequency of the part.
Figure 3.11. Branson Ultrasonic Generator
In order to operate a single piezoelectric converter in resonance, a generator
was needed that was factory-set, with a frequency window containing 20 kHz (e.g., 18
kHz to 22 kHz). Having a wider interval of carrier frequency range would not offer
additional benefit in our application, and only destroy, overload, or over-heat the
mechanical system by trying to drive it contrary to its acoustical nature.
3.6 Vibration Modes
Every elastic mechanical system, body, or resonator that can oscillate has
many vibrating modes as well as frequency harmonics and sub harmonics in the low
and ultrasonic frequency domains. Many of these vibrating modes can be coupled
acoustically and mechanically, while others would stay relatively independent.
36
Figure 3-12 show the diagram of the mechanical vibration mode of the
transducer. It was possible to simulate many of the mechanical vibration modes of the
new transducer by means of FEM simulations. FEM modeling enables the designers
to determine which vibration modes are present in a given frequency range and to
characterize accurately the corresponding displacement fields. In reality, only a few
of these calculated modes are excited with significant amplitude.
Figure 3.12. Frequency Response of a Piezoelectric Transducer (Phase and Impedance Z).
Source: MPI
By measuring the frequency response, we can see that, in addition to the main
longitudinal resonance frequencies fs and fp, a physical transducer possesses many
other secondary resonances that arise from other mechanical modes and mechanical
construction. An example of such a secondary resonance is schematically drawn in
Figure 3-13 with a dotted line (fx1, fx2).
37
Figure 3.13. Frequency Response of a Piezoelectric Transducer (Phase and Impedance Z).
Source: Lorenzo Parrini
The above figures allow us to identify the precise few modes that exhibit a
resonance and that are actually excited by the given forcing stress. At this point, it can
sometimes happen that more electrical physical resonances appear than those
exhibited by the simulated resonance curves. The simulations are only a rough
approximation of the geometry of the vibrating body. The real elastic constants are
not linear and neither are the dissipation coefficients.
The vibration amplitude at the tip of the transducer is calculated between 10
and 40 kHz. Two maxima are evident, which correspond to modes 6 and 15. These
two modes are the pure longitudinal vibration modes of the transducer between 10 and
40 kHz.
38
Figure 3.14. Vibration Amplitude in μm between 10 and 40 kHz.
Source: MPI
3.7 Conducting Experiments
3.7.1 Static Friction Flow Stop Test
Here, several valves, with the same number and size of blades specified in the
previous stage, were constructed. The valves differed with respect to inter-blade
distances. Then, for each valve, a set of experiments was conducted with different
materials and different back pressures. The data were input into a regression model
and an equation was derived to relate flow to friction surface, back pressure, and
material characteristics, including viscosity and density. By putting the flow equal to
zero, back pressure to maximum, and having a standard material, the required surface
to stop the flow in that condition was calculated.
39
In order to perform a static test, a test stand was built. By using a compressor,
back pressure was applied to two pneumatic cylinders. A one-inch diameter pipe was
filled with one foot of material, and back pressure was incrementally adjusted between
10 and 30 psi. Then the output volume was measured and, by measuring the time, the
amount of flow at each incremental back pressure was found. The test stand is shown
in Figure 3.15
Figure 3.15. Picture of the Test Stand
40
3.7.2 Measuring Flow with Vibration
Vibratory friction reduction for viscous materials, at its most basic, is achieved
by setting the particles into motion, thus eliminating the internal friction.
In order to do so, the vibration test was conducted for each valve in the
previously constructed set, with the vibration power set at a certain value. Then, for
each valve configuration, different back pressure values and different materials were
used. The desired flow rate was determined by the required back pressure, provided
that the total valve friction in the ON state was known. To estimate the ON state
friction, an initial estimate of the back pressure, the pressure of the material at the
outlet of the pipe, i.e., inlet of the valve was measured and used in the design process.
The results were put into a regression model and an equation was derived for the valve
when in operation. Then, by putting the maximum pressure and calculated friction
surface from the above, we could find the flow when the valve was in the ON state. If
the flow was in the desired range, then we followed the FEM analysis or the
procedure was started over again. If we wanted a greater flow rate, then we needed
greater back pressure. In that case, the surface required to stop the flow was greater
than the previous amount. This back pressure, which was identified experimentally in
the design of experiments, was implemented after the design and construction of the
valve.
41
Figure 3.16. Model of a Developed Valve Including Transducer, Booster and Cover
3.7.3 Optimal Valve Shape
The challenge was to determine the number, size, and distance between the
blades to be placed along the material flow path.The optimal valve shape was then
selected through a process that began with an arbitrary starting design configuration
that provided the requisite total blade surface area. A heuristic search procedure was
then employed to converge toward the optimal (smallest with desirable form factor)
design. Figure 3.16 shows some possible shapes of candidate valve designs.
The optimum valve shape is selected in such a way that maximum vibration
energy is transmitted to each surface and it guarantees that each surface receive
enough vibration to dispose material which is attached to its surface. Usually longer
size along the transducer axis or movement direction give better results and dissipation
of the energy is minimized. An example of optimize shape is the middle valve shown
in Figure 3.17. Also the valve should be design in such a way that minimum fatigue
occurs due to excess of vibration.
42
The distance between blades was decided to be greater than larger particle size.
Then the blades were designed in such a way that the total surface would equal the
result from the above section.
Figure 3.17. Possible Shapes of Candidate Valve Designs
43
The objective function in the optimization process was the total active
displacement (i.e., movement because of vibration) of blade surfaces in the direction
of flow. Other forms of vibration were considered dissipative vibrations that result in
power loss.
3.8 Analytical Research
FEM modeling was used at this stage to assure that the resonance frequency of
the designed valve would match that of the transducer-booster providing the vibration.
The FEM model also provided the total (integral) of all surface displacements as a
single number to be used as the response (i.e., objective function value for the given
design). In these designs, the minimum distance between the blades will be larger
than the largest expected aggregate size in the concrete.
3.8.1 Finite Element Analysis
In FEM, the resonator is simulated as a computer model. The computer
simulation model consists of a large number of small "elements" that represent the
shape of the valve. Each element can be described mathematically by a set of
equations. The solution to this set of equations yields a prediction of the resonator's
performance. FEM can analyze the natural frequencies at which the resonator vibrates
and the amplitudes and stresses associated with each of these frequencies. After the
performance has been predicted, the resonator's dimensions or materials can be
changed within the FEM model in order to improve the performance.
44
In order to achieve higher performance, the following should be considered: In
one-dimensional sandwich transducer design theory, it is assumed that the transducer
vibrates in longitudinal mode, and that radial vibration is negligible. This means that
the lateral dimension of a transducer needs to be much less, compared to its
longitudinal dimension. Due to the approximations in the FEM model, some other
vibration modes cannot be found numerically.
Various numerical methods have been used to study the frequency
characteristics and vibration modes for the coupled vibration of piezoelectric sandwich
ultrasonic transducers. Numerical models of high power ultrasonic systems are
usually based on FEM.
In order to perform finite element analysis, Computer Aided Resonator Design
(CARD) software was used. This software applied quantitative techniques to the
design of ultrasonic resonators that vibrate in a longitudinal mode. CARD provided
assistance in the design of resonators having low-to-moderate complexity.
With CARD, alternative resonator designs were quickly evaluated without
machining and testing. The effects of proposed resonator modifications were easily
determined. CARD is especially useful for designing low-stress resonators, resonators
with a specified gain, and resonators with a specified node location. Following items
were considered in FEM analysis (Source: Krell Engineering)
45
Geometry
The model geometry reasonably presented the actual designed valve.
Sometimes insignificant changes in geometry can dramatically affect the FEM
predictions of resonator performance. For example, changing the size of the valve to a
large lateral dimension can significantly affect the amplitudes and stresses although
the effect on resonant frequencies may be minor.
Material Property
FEM cannot correctly predict the valve performance unless the material
properties, such as Young's modulus, modulus of rigidity, Poisson's ratio, and density,
are known. For resonators with small lateral dimensions, the density and the modulus
of elasticity determine the resonant frequencies. For larger resonators, the resonant
frequencies are affected somewhat by Poisson's ratio. Depending on the resonator's
shape, the amplitude could also be significantly affected by Poisson's ratio.
For materials that are reasonably isotropic, only two elastic property values are
needed to completely characterize the material. These properties are relatively easy to
determine. For materials such as titanium and piezoelectric ceramics that are
orthotropic (i.e., the properties depend on the test direction), nine elastic property
values are needed for complete characterization. However, using averaged material
values (assuming that titanium is isotropic) usually gives reasonable results.
Where resonator frequencies are concerned, a small error in the material
properties is usually not critical since we will have allowance for some extra material
to tune.
46
Frequencies
Frequencies are the easiest and most accurate parameter to measure and verify.
However, note that FEM may predict more frequencies than can be measured in the
actual resonator. These extra FEM frequencies are often bending resonances or
resonances at a node that runs through the resonator's axis. Although such frequencies
are actually present in the resonator, they often cannot be easily excited by the
transducer and are therefore difficult to detect by frequency analyzer equipment. Such
FEM frequencies were incorrect and did not exist in the actual resonator.
Amplitudes
Amplitudes are relatively easy to verify, but care should be taken to assure that
the amplitudes and their locations were correctly measured. This was especially
important where the amplitude changed rapidly depending on the sophistication of the
amplitude measurement equipment. A 5% amplitude difference between the
measured values and the FEM values would not be unusual.
If the FEM frequencies or amplitudes have larger error than expected, this may
indicate improper modeling such as improper boundary conditions, inadequate mesh
refinement, incorrect material properties, or incorrect measurements.
Stress
Since experimental stress data is usually not available, stress usually cannot be
directly verified. However, the FEM stresses will not be correct if the FEM
47
amplitudes are not correct, since stress depends on the amplitude gradient. Even if the
FEM amplitudes are correct, the FEM stress may still be incorrect due to poor choice
of element sizes or geometry. Some FEM programs permit estimates of FEM stress
error and indicate where the mesh needs to be refined to reduce the error.
Accuracy
The error in current methods for modeling ultrasonic transducers is on the
order of 2-5% for frequency response and 5-10% for amplitude response. Although
this level of accuracy is acceptable in most structural applications, ultrasonic products
have an elevated sensitivity to accuracy. Amplitude accuracy of 5-10% may not be
enough to determine if the material is below the fatigue limit.
3.9 Design Assumptions
Some of the design assumptions are as follows:
• Mechanical components are assumed to vibrate longitudinally only. Hence,
it is assumed that the vibration is one-dimensional.
• The propagation medium of the waves is assumed to be homogeneous, and
that specific properties such as density, Young’s modulus, etc., are constant.
• The effect of elements such as bolts and electrodes on the system is
negligible.
• The transducer, the front and back materials and the piezoelectric cylinders
are of disc shape.
48
3.10 Controlling Flow with Duty Cycle
To achieve flow control, a PWM (pulse width modulation) approach was used.
The duty cycle of the pulse (i.e., the duration of vibration ON divided by duration of
vibration OFF) influenced the overall flow rate through the valve. The preference
here was to maximize the PWM frequency such that flow pulsation was minimized.
Given that the fluid has mass, which is subject to inertia, there was a limit on the
deceleration time of concrete due to the exerted friction force. At this stage, two
experimental activities were performed for each vibration power to identify:
a) The duty cycle curve to achieve flow rates from zero to the specified (desired)
maximum flow.
b) The curve relating the PWM maximum frequency to flow ranges.
The optimum duty cycle for each flow rate was the one that had the highest
frequency (to minimize flow pulsation). Material mass inertia would prevent stoppage
if the duration of OFF cycles were too short. In other words, if OFF cycles were long
enough, they would allow the material to reach the complete stop before the next start.
A programmable logic controller “PLC” was used at this stage to control the
frequency and duty cycle of the pulses to the generator.
3.11 Conclusion
In order to design a proper valve, several experiments were performed. First,
the viscosity of the materials was identified. Then a set of static pressure tests were
49
established and the flow equation relating to friction surface was derived. The
objective was to determine the size of the blades along the flow to provide the required
maximum flow rate and stop the flow within a specific back pressure. By changing
back pressure and desired material, the required surface to stop the flow was
calculated using response surface methodology. After performing the static test, a set
of dynamic tests were conducted by implementing the piezo vibration. The back
pressure was adjusted and flow at each pressure was determined. If the pressure and
flow were within range, then the proper valves were optimized using the finite element
model. The result of these experiments is shown in next chapter.
50
4 Chapter Four: Results
4.1 Design of Experiments and Result Analysis
Response Surface Methodology (RSM) is a set of statistical techniques used
for process design, development, improvement, and optimization (Meyers and
Montgomery, 1995).
Identifying and fitting model from experimental data to an appropriate
response surface model requires:
1. Statistical experimental design fundamentals
2. Regression modeling techniques
3. Optimization methods.
The integration of all above three methods to improve processes or products
has been popularly called response surface methodology.
Input variables for RSM are called independent variables and performance
measure of the product is called response. Usually the response function is unknown
and must be approximated.
In order to perform a response surface study a factorial design need to be
established. Factorial designs are widely used in experiments involving several factors
where it is necessary to investigate the joint effects of the factors on a response
variable. In response surface methodology the exact functional form of the true
response curves is unknown. In order to find the true response curve, regression
technique is applied to find the best matching polynomial function.
51
We performed the Design of Experiment using JMP program. By randomizing
the data, we achieved the following results as our screening test. The screening data
were selected around a current operating point.
4.2 Static Friction Response Surface Methodology
The maximum, minimum, and center point settings shown in Table 4.1 were
used for the first experiment that included 20 runs:
Parameter Name Min Ave Max Unit
A Back Pressure of Concrete 10 20 30 PSI
B Viscosity of Concrete 6000 11000 16000 C toke entis
C Concrete Density 2100 2300 2500
D Friction Surface 50 75 100
Table 4.1. Range of Factors
The selection of a suitable model prior to the experiment depends upon
available knowledge about which factors do and do not interact. For example size of
sand does not affect the flow properties. It affects only the distance between blades.
So the distance is assumed to be greater than maximum sand size.
A full factorial design for 4 parameters was established (4
=16 runs) and 2
additional center point runs.
52
A B C D
−−−− -1 -1 -1 -1
+ −−+ 1 -1 -1 1
+ −++ 1 -1 1 1
++ −+ 1 1 -1 1
−+++ -1 1 1 1
++ −− 1 1 -1 -1
+ −+ − 1 -1 1 -1
−−+ − -1 -1 1 -1
−−++ -1 -1 1 1
−++ − -1 1 1 -1
−+ −− -1 1 -1 -1
+++ − 1 1 1 -1
−+ −+ -1 1 -1 1
++++ 1 1 1 1
−−−+ -1 -1 -1 1
+ −−− 1 -1 -1 -1
0 0 0 0 0
0 0 0 0 0
Table 4.2. Design of Experiment Established
Main effects and alias list is shown below:
A,B,C,D,A*B, A*C,B*C,A*D,B*D,C*D
After running this designed experiment, the output flow was measured and is
included in Table 4.3.
53
Back
Pressure
PSI
Viscosity
Centistoke
Density
Friction Surface
Measured
Flow
−−−− 10 6000 131 50 1
+ −−+ 30 6000 131 100 2
+ −++ 30 6000 156 100 1.7
++ −+ 30 16000 131 100 0.6
−+++ 10 16000 156 100 0
++ −− 30 16000 131 50 1.1
+ −+ − 30 6000 156 50 2.7
−−+ − 10 6000 156 50 0.8
−−++ 10 6000 156 100 0.4
−++ − 10 16000 156 50 0.2
−+ −− 10 16000 131 50 0.2
+++ − 30 16000 156 50 0.9
−+ −+ 10 16000 131 100 0.1
++++ 30 16000 156 100 0.5
−−−+ 10 6000 131 100 0.5
+ −−− 30 6000 131 50 3.3
0 20 11000 144 75 0.7
0 20 11000 144 75 0.7
Table 4.3. Results of Static Friction Experiment
Main effects are considered to be: A,B,C,D. Interaction factors are the product
of main effects and second degree polynomial level and considered to be:
AB,AC,AD,BC,BD,CD,AA,BB,CC,DD
54
Response Y was calculated using JMP software. Table 4.4 shows a summary
of fit.
RSquare 0.995
RSquare Adj 0.985833
Root Mean Square Error 0.108012
Mean of Response 0.966667
Observations (or Sum Wgts) 18
Table 4.4. Summary of Fit
RSquare estimates the proportion of the variation in the response around the
mean that can be attributed to terms in the model rather than to random error. An
RSquare of 1 occurs when there is a perfect fit. Adjusted RSquare makes it more
comparable over models with different numbers of parameters by using the degrees of
freedom in its computation. Root mean square error estimates the standard deviation
of the random error. Mean of response is the overall mean of the response values.
Observations records the number of observations used in the fit. If there are no
missing values and no excluded rows, this is the same as the number of rows in the
data table.
Analysis of variance shows the total degree of freedom for model and error in
our design. (Table 4.5)
Source DF Sum of
Squares
Mean Square F Ratio
Model 11 13.930000 1.26636 108.5455
Error 6 0.070000 0.01167 Prob > F
C. Total 17 14.000000 <.0001
Table 4.5. Analysis of Variance
Degree of freedom “DF” records associated degrees of freedom for each
source of variation. The Model degrees of freedom is the number of parameters
55
(except for the intercept) used to fit the model. The Error DF is the difference between
the C. Total DF and the Model DF. The Error sum of square is the sum of squared
differences between the fitted values and the actual values. Mean Square is a sum of
squares divided by its associated degrees of freedom.Table 4.6 shows the sum of
square for errors due to lack of fit and pure error.
Source DF Sum of
Squares
Mean Square F Ratio
Lack of Fit 5 0.07000000 0.014000 .
Pure Error 1 0.00000000 0.000000 Prob > F
Total Error 6 0.07000000
Max RSq
1.0000
Table 4.6. Lack of Fit
F Ratio is the model mean square divided by the error mean square. It tests the
hypothesis that all the regression parameters (except the intercept) are zero. Prob>F is
the probability of obtaining a greater F-value by chance alone if the specified model
fits no better than the overall response mean. Significance probabilities of 0.05 or less
are often considered evidence that there is at least one significant regression factor in
the model. Table 4.7 shows the t ratio and probability for main factors and their
interaction, the intercept and coefficient values for each factor and their interaction is
calculated by JMP software. The standard error is also shown.
The Parameter Estimates table shows the estimates of the parameters in the
linear model and a t-test for the hypothesis that each parameter is zero. Simple
continuous regression has only one parameter. Models with complex classification
effects have a parameter for each anticipated degree of freedom
56
Term Estimate Std Error t Ratio Prob>|t|
Intercept 0.7 0.076376 9.17 <.0001
A 0.6 0.027003 22.22 <.0001
B -0.55 0.027003 -20.37 <.0001
C -0.1 0.027003 -3.70 0.0100
D -0.275 0.027003 -10.18 <.0001
A*B -0.275 0.027003 -10.18 <.0001
A*C -0.05 0.027003 -1.85 0.1135
B*C 0.05 0.027003 1.85 0.1135
A*D -0.125 0.027003 -4.63 0.0036
B*D 0.125 0.027003 4.63 0.0036
C*D 0.025 0.027003 0.93 0.3903
A*A Biased 0.3 0.081009 3.70 0.0100
B*B Zeroed 0 0 . .
C*C Zeroed 0 0 . .
D*D Zeroed 0 0 . .
Table 4.7. Parameter Estimates
Term names the estimated parameter. The first parameter is always the
intercept. Estimate lists the parameter estimates for each term. They are the
coefficients of the linear model found by least squares. Std Error is the standard error,
an estimate of the standard deviation of the distribution of the parameter estimate. It is
used to construct t-tests and confidence intervals for the parameter. t Ratio is a statistic
that tests whether the true parameter is zero. It is the ratio of the estimate to its
standard error and has a t-distribution under the hypothesis. Prob>|t| is the probability
of getting an even greater t-statistic (in absolute value), given the hypothesis that the
parameter is zero. This is the two-tailed test against the alternatives in each direction.
Probabilities less than 0.05 are often considered as significant evidence that the
parameter is not zero.
57
58
The residuals are plotted versus run order to evaluate independence of the error
variables (Figure 4.1) and it displays the residual values by the predicted values of Y.
we typically want to see the residual values scattered randomly about zero.
Figure 4.1. Residual by Row Plot
Term Estimate Std Error t Ratio Prob>|t|
A 0.6 0.027003 22.22 <.0001
B -0.55 0.027003 -20.37 <.0001
D -0.275 0.027003 -10.18 <.0001
A*B -0.275 0.027003 -10.18 <.0001
A*D -0.125 0.027003 -4.63 0.0036
B*D 0.125 0.027003 4.63 0.0036
A*A Biased 0.3 0.081009 3.70 0.0100
C -0.1 0.027003 -3.70 0.0100
A*C -0.05 0.027003 -1.85 0.1135
B*C 0.05 0.027003 1.85 0.1135
C*D 0.025 0.027003 0.93 0.3903
Table 4.8. Sorted Parameter Estimates
By analyzing the T Ratio and Prob. in table 4.8 we can figure out the most
significant factor which have Prob>|t| less than 0.1 .Preliminary analysis showed that
A,B,C,D,AB,AD,BD,AA were the most significant effects, considering the square terms.
4.2.1 Backward Elimination
In backwards selection, terms are entered into the model and then least significant
terms are removed until all the remaining terms are significant. By performing backward
elimination, we could fit a regression model that best describes our static friction response:
-0.10
0.00
0.10
Residual
0 5 10 15 20
Row Number
59
Figure 4.2. Actual by Predicted Plot
Figure 4.2 shows actual versus predicted plot and shows the program could
match an accurate fit to the model after performing backward elimination.
Summary of fit is shown in Table 4.9 and it represents a well fit regression
model:
RSquare 0.988571
RSquare Adj 0.978413
Root Mean Square Error 0.133333
Mean of Response 0.966667
Observations (or Sum Wgts) 18
Table 4.9. Summary of Fit
Analysis of variances is shown in Table 4-10. It is shown that there are 8
Degrees of freedom for the model which means that we have total 8 parameters in our
analysis.
Source DF Sum of
Squares
Mean Square F Ratio
Model 8 13.840000 1.73000 97.3125
Error 9 0.160000 0.01778 Prob > F
C. Total 17 14.000000 <.0001
Table 4.10. Analysis of Variance
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Y Actual
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Y Predicted P<.0001
RSq=0.99 RMSE=0.1333
60
Table 4.11 shows that there is a very small error due to lack of fit :
Source DF Sum of
Squares
Mean Square F Ratio
Lack of Fit 8 0.16000000 0.020000 .
Pure Error 1 0.00000000 0.000000 Prob > F
Total Error 9 0.16000000
Max RSq
1.0000
Table 4.11. Lack of Fit
Table 4.12 shows parameter estimates and coefficient for each factor and their
interactions. The probability>|t| is less than 0.05 for all parameter estimate and
represent a very well fit model.
Term Estimate Std Error t Ratio Prob>|t|
Intercept 0.7 0.094281 7.42 <.0001
A 0.6 0.033333 18.00 <.0001
B -0.55 0.033333 -16.50 <.0001
C -0.1 0.033333 -3.00 0.0150
D -0.275 0.033333 -8.25 <.0001
A*B -0.275 0.033333 -8.25 <.0001
A*D -0.125 0.033333 -3.75 0.0046
B*D 0.125 0.033333 3.75 0.0046
A*A 0.3 0.1 3.00 0.0150
Table 4.12. Parameter Estimates
Residuals are plot by row number in Figure 4.3 and since they have a random
pattern so the model is accurately fit the data. Parameter estimates are sorted and
shown in Table 4.13:
Figure 4.3. Residual by Row Plot
-0.2
0.0
0.2
Residual
0 5 10 15 20
Row Number
61
Term Estimate Std Error t Ratio t Ratio Prob>|t|
A 0.6 0.033333 18.00
<.0001
B -0.55 0.033333 -16.50
<.0001
D -0.275 0.033333 -8.25
<.0001
A*B -0.275 0.033333 -8.25
<.0001
A*D -0.125 0.033333 -3.75
0.0046
B*D 0.125 0.033333 3.75
0.0046
A*A 0.3 0.1 3.00
0.0150
C -0.1 0.033333 -3.00
0.0150
Table 4.13. Sorted Parameter Estimates
Prediction profiles are especially useful in multiple-response models to help
judge which factor values can optimize a complex set of criteria. Prediction profiler
shown in Figure 4.4 and cube plot Figure 4.5 represent the interaction of each
parameter. As seen in the figures the main effect A and its second degree are
significant factors.
Figure 4.4. Prediction Profiler
Figure 4.5. Cube Plot
-0.5
0.5
1.5
2.5
3.5
Y
0.7
±0.213278
0 0.5 1
Desirability
0.323132
-1
-0.5
0
0.5
1
0
A
-1
-0.5
0
0.5
1
0
B
-1
-0.5
0
0.5
1
0
C
-1
-0.5
0
0.5
1
0
D
0
0.25
0.5
0.75
1
Desirability
1.05 3.05
0.25 1.15
0.85 2.85
0.05 0.95
A -1 1
B1 -1
C
-1
1
D=-1
0.5 2
0.2 0.6
0.3 1.8
-1e-16 0.4
A -1 1
B1 -1
C
-1
1
D=1
62
The Normal Plot (Figure 4.6) displays the parameter estimates population table
and shows a normal plot of these parameter estimates .Blue line is Lenth's PSE, from
the estimates population and red line is RMSE, Root Mean Squared Error from the
residual. Since the distance to PSE line is minimal so we have a very accurate fit to
our model.
Figure 4.6. Normal Plot
The derived model is:
0.7 0.6 .55 .1 0.275 0.275 0.125 0.125 . 0 3
( 4-1)
Where p is the operation pressure and
( 4-2)
Where μ is the operation viscosity and
-20
-15
-10
-5
0
5
10
15
20
t Ratio
A
B
C
D A*B
A*D
B*D
A*A
-3 -2 -1 0 1 2 3
Normal Quantile
Where ρ is the operation density and
( 4-3)
Where A is the friction surface and
( 4-4)
And Y is the result output flow
For a given pressure of P = 20 psi and, µ 15000 centistock , ρ= 156
I
the
minim m friction surface to stop the flow is calculated to be : u
A=91
63
4.3 Measuring Flow with Vibration
Fresh concrete has mechanical properties like a solid at low applied dynamic
stresses; it has mass, damping, and stiffness characteristics. At higher stress levels,
above a critical level of vibration, its mechanical properties are similar to a liquid, in
that the resistance to movement is only a function of mass. It was observed that the
fresh concrete appeared to become liquid at the point of the impedance breakdown.
Fresh concrete does not have a resonant frequency before breakdown, because the
damping is too high. There is minimum impedance for each mixture of fresh concrete,
but the frequency at which the impedance is at a minimum is a function of the mixture.
The impedance minimum is neither sharp nor consequential.
A full factorial design for 4 parameters was established (4
=16 runs) and 2
additional center point runs. The range of experiment was set like the static flow test
mentioned in section 4.2.
In this series of test the vibration was used to reduce the friction of the material
with surface and hence resulted in flow rate increase. The measurements revealed that
the force required to cause the static concrete to break down in impedance was much
higher than that needed to maintain motion after breakdown had occurred. The result
of these experiments is shown in Table 4.14.
Back Pressure
PSI
Viscosity
Centistoke
Density
ft
Friction Surface
Measured
Flow
−−−− 10 6000 131 50 2.2
+ −−+ 30 6000 131 100 7.6
+ −++ 30 6000 156 100 6.4
++ −+ 30 16000 131 100 2.6
−+++ 10 16000 156 100 0.4
++ −− 30 16000 131 50 2.6
+ −+ − 30 6000 156 50 6.4
−−+ − 10 6000 156 50 1.8
−−++ 10 6000 156 100 1.8
−++ − 10 16000 156 50 0.4
−+ −− 10 16000 131 50 0.5
+++ − 30 16000 156 50 2.1
−+ −+ 10 16000 131 100 0.5
++++ 30 16000 156 100 2.1
−−−+ 10 6000 131 100 2.2
+ −−− 30 6000 131 50 7.7
0 20 11000 144 75 2.2
0 20 11000 144 75 2.2
Table 4.14. Results of Vibration Experiment
64
4.3.1 Screening Test
In order to analyze the most significant factor, a screening test was performed
using the data in Table 4-14. Summary of fit is shown in Table 4.15.It is seen that
RSquare is near to 1 which means there is a good fit to the model. And also root Mean
square error is around 0.9 with maximum 18 observation.
RSquare 0.999466
RSquare Adj 0.998487
Root Mean Square Error 0.094097
Mean of Response 2.872222
Observations (or Sum Wgts) 18
Table 4.15. Summary of Fit
The result of the screening test is presented in Table 4.16. The prob>F is less
than 0.0001 which means the model regression is a perfect fit.
Source DF Sum of
Squares
Mean Square F Ratio
Model 11 99.422986 9.03845 1020.814
Error 6 0.053125 0.00885 Prob > F
C. Total 17 99.476111 <.0001
Table 4.16. Analysis of Variance
Sum of squares errors for each source of error including lack of fit and pure
error is shown in following tables. Since those numbers are small they can be ignored
in the model evaluation:
Source DF Sum of
Squares
Mean Square F Ratio
Lack of Fit 5 0.05312500 0.010625 .
Pure Error 1 0.00000000 0.000000 Prob > F
Total Error 6 0.05312500 .
Max RSq
1.0000
Table 4.17. Lack of Fit
65
Parameter estimate for each factor and their interaction is calculated by JMP
software are sorted and shown in Table 4.18.
Term Estimate Std Error t Ratio Prob>|t|
A 1.73125 0.023524 73.59 <.0001
B -1.55625 0.023524 -66.16 <.0001
A*B -0.78125 0.023524 -33.21 <.0001
C -0.28125 0.023524 -11.96 <.0001
A*A Biased 0.75625 0.070572 10.72 <.0001
A*C -0.15625 0.023524 -6.64 0.0006
B*C 0.13125 0.023524 5.58 0.0014
D -0.00625 0.023524 -0.27 0.7994
B*D 0.00625 0.023524 0.27 0.7994
C*D 0.00625 0.023524 0.27 0.7994
A*D -0.00625 0.023524 -0.27 0.7994
Table 4.18. Sorted Parameter Estimates
From above table it is shown that that factor A, B, AB, C, AA, AC, BC are the
most significant effects, considering the square terms, since Prop>|t| is greater than 0.1
for those factors. It is observed that the friction surface “effect D” has no effect in this
test.
4.3.2 Backward Elimination
By performing backward elimination, we could fit a regression model that best
describes our friction response due to vibration. Again the Rsquare is near to 1 and
shows a perfect regression. Also Root mean square error is near zero which is a good
sign for accurate fit.
RSquare 0.999441
RSquare Adj 0.999049
Root Mean Square Error 0.074582
Mean of Response 2.872222
Observations (or Sum Wgts) 18
Table 4.19. Summary of Fit
66
Analysis of variances is shown in Table 4.20, F ratio is high enough to
represent a well fit regression model.
Source DF Sum of
Squares
Mean Square F Ratio
Model 7 99.420486 14.2029 2553.335
Error 10 0.055625 0.0056 Prob > F
C. Total 17 99.476111 <.0001
Table 4.20. Analysis of Variance
Sum of square of errors due to lack of fit and pure error are calculated by JMP
software as shown in Table 4.21 and they are negligible.
Source DF Sum of
Squares
Mean Square F Ratio
Lack of Fit 1 0.05062500 0.050625 91.1250
Pure Error 9 0.00500000 0.000556 Prob > F
Total Error 10 0.05562500 <.0001
Max RSq
0.9999
Table 4.21. Lack of Fit
Table 4.22 shows all parameter estimates. Since prob>|t| is in order of .0001
so all the effects A, B, C, AB, AC, BC, AA are important factors in flow test with
activating of vibration .It is shown that friction surface are eliminated from the
equation for flow calculation.
Term Estimate Std Error t Ratio Prob>|t|
Intercept 2.2 0.052738 41.72 <.0001
A 1.73125 0.018646 92.85 <.0001
B -1.55625 0.018646 -83.46 <.0001
C -0.28125 0.018646 -15.08 <.0001
A*B -0.78125 0.018646 -41.90 <.0001
A*C -0.15625 0.018646 -8.38 <.0001
B*C 0.13125 0.018646 7.04 <.0001
A*A 0.75625 0.055937 13.52 <.0001
Table 4.22. Parameter Estimates
67
68
Residuals are randomly distributed in the fitted model and hence derived
equation can appropriately represent the model with active vibration.(Figure 4.7)
Figure 4.7. Residual by Row Plot
The effects are sorted base on their ratio in Table 4.23. The Pareto plot in
Figure 4.10 also represent those effects.
Term Estimate Std Error t Ratio Prob>|t|
A 1.73125 0.018646 92.85 <.0001
B -1.55625 0.018646 -83.46 <.0001
A*B -0.78125 0.018646 -41.90 <.0001
C -0.28125 0.018646 -15.08 <.0001
A*A 0.75625 0.055937 13.52 <.0001
A*C -0.15625 0.018646 -8.38 <.0001
B*C 0.13125 0.018646 7.04 <.0001
Table 4.23. Sorted Parameter Estimates
Prediction profiler is drawn on Figure 4.8 and it shows that term A has second
order relationship to model Y.
Figure 4.8. Prediction Profiler
-0.05
0.00
0.05
0.10
Residual
0 5 10 15 20
Row Number
0
2
4
6
8
Y
2.2
±0.117507
0 0.25 0.5 0.75 1
Desirability
0.30161
-1
-0.5
0
0.5
1
0
A
-1
-0.5
0
0.5
1
0
B
-1
-0.5
0
0.5
1
0
C
0
0.25
0.5
0.75
1
Desirability
69
The normal plot in Figure 4.9 shows that most effects are along the normal
quantile line.
Figure 4.9. Normal Plot
The Pareto Plot selection gives plots of orthogonal estimates showing their
composition relative to the sum of the absolute values. We can estimate the most
important factor from following figure to be A, B and their interaction AB.
Figure 4.10. Pareto Plot of Estimates
Figure 4.11. Cube Plot
-100
-50
0
50
100
t Ratio
A
B
C
A*B
A*C
B*C
A*A
-3 -2 -1 0 1 2 3
Normal Quantile
A
B
A*B
C
A*A
A*C
B*C
Term
92.85061
-83.46499
-41.90010
-15.08403
13.51976
-8.38002
7.03922
t Ratio
2.25625 7.59375
0.44375 2.65625
1.74375 6.45625
0.45625 2.04375
A -1 1
B1 -1
C
-1
1
Cube plot shows the relationship between parameter A, B, C. From the
param ate table we can drive eter estim the model as bellow:
2.2 1.731 1.55 .28 0.78 0.15 0.13 0.75
And Y is the resultant output flow.
For a given pressure P = 20 PSI and µ 15000 centistock and ρ = 156
and friction
surface A 1 , the calculated flow is: =9
Y=1.62
If the above flow rate is greater than the desired value, then the valve design is
proper. If more flow needed, then steps one and two must be repeated with higher
pressure.
4.4 Finite Element Analysis
In order to perform finite element analysis, a software package called CARD
was used. This software automatically tunes the horn to the desired frequency by
adjusting the resonator dimensions. The adjustable dimensions include the length,
thickness or diameter, and location of a transition radius. In addition, CARD can
automatically adjust the gain and minimize the stress.
CARD calculates numerous acoustic parameters, including tuned length, tuned
frequency, gain, node location, maximum stress, stored energy, loss, overall quality
factor, and weight. When calculating the stress, CARD considers the effect of stress
concentrations at the radii and slot ends. CARD graphically displays the calculated
70
amplitude, stress, and strain-loss distributions at each point along the length of the
resonator. Analysis results can be viewed, printed, and saved to a file.
4.4.1 Selecting Resonator Type
In order to perform a FEM analysis, first a resonator type is selected as
rectangular block with slot.
Figure 4.12. Selecting Resonator Type
CARD operates in either of two modes:
Auto-tuning: If the resonator frequency is specified, then CARD will automatically
change the dimensions of a user-specified resonator surface until the specified
frequency is achieved. CARD can adjust a length dimension, a thickness dimension,
or the location of a radius or step. While the resonator is being tuned, the gain can be
automatically adjusted to a desired value. The stress can also be minimized
automatically.
Manual tuning: If all of the resonator dimensions are specified, then CARD will
calculate the resonant frequency. If desired, the resonator dimensions can then be
manually adjusted to change the frequency. Auto-tuning is used most often. Manual
tuning is used to adjust certain surfaces where auto-tuning is not appropriate
71
Figure 4.13. Selecting Tuning Mode
The resonator vibration frequency is set at 20 kHz . Amplitude output of the
resonator is set to be about 1 micron. A green booster was used, which was a 1:1
converter. Temperatures are set to ambient temperature.(Figure 4.14)
Figure 4.14. Frequency Selection
The dimension of the horn is set to match the friction surface calculated from
the above design of experiments analysis. A 50mm valve width is arbitrarily chosen.
A slot width of 5 mm, which is greater than maximum sand size, is chosen. The
length of the horn is set at 100 mm, with 5mm rear and front web length. The total
number of slots is set at 6. The total required friction area is about A=93
which is
about 60,000
. Assuming 12 total surface areas, each surface would be about
5000
. We started with dimension 50mm * 100mm.
72
4.4.2 Auto Tuning Thickness
As shown here, horn width is assumed to be 50mm, the slot length to be
100mm, and number of slots 6.
Figure 4.15. Size setting
Figure 4.16 show Geometry for half of the horn shape. As seen in the figure
there are total 3 slot in half part of the horn and totally there exist 6 slot with slot width
5mm.
Figure 4.16. Resonator Geometry (Half-Shape)
After performing auto tuning for thickness, the result is calculated after two
iteration and the results are shown in Figure 4-17.
73
Figure 4.17. Resonator Geometry
The result of auto tuning is presented in Figure 4.18. As seen in the result table
the tuning surface thickness is decreased from 60mm to 50.2 mm to match the
frequency criteria. Total strain energy and power dissipated is calculated during this
process.
Figure 4.18. Auto Tune Result
74
As shown in Figure 4.19 ,CARD software tuned the width for specific given
dimension to be about 50.2 mm. Figure 4-20 shows the amplitude result of the horn
due to vibration.
Figure 4.19. Amplitude Result
As it is shown in Figure 4.19 the maximum vibration occurs in valve tip.
Figure 4-20 shows the stress diagram of the horn due to vibration. The maximum
stress occurs in the middle of the valve and that is the point where maximum fatigue
exists. There is a change of stress value in the notch where the slot starts and ends
inside the horn.
Figure 4.20. Stress Diagram
75
Figure 4-21 shows the diagram of cumulative strain energy. The maximum
strain energy occurs at the tip of the valve.
Figure 4.21. Cumulative Strain Energy
Figure 4-22 shows the diagram of cumulative loss. As shown in the figure the
loss is low enough to avoid associated problems
Figure 4.22. Cumulative Loss
76
4.4.3 Auto Tuning Length
The CARD program can also tune the resonator length. In this case, the valve
thickness is set to a fixed value. The program ran several iterations and found the
desired length at which the resonance frequency matches 20 kHz. Figure 4.23 shows
the horn geometry. Result amplitude is shown in Figure 4.24. After several
calculations, the tuned length was calculated to be 115.7mm.
Figure 4.23. Resonator Geometry (Half-Shape)
Figure 4.24. Result Amplitude
77
As shown in Figure 4.24 maximum amplitude occurs at the end of the horn.
The result summery is shown in Figure 4.25. Resonator gain is 1 and the frequency is
20 kHz to match the piezo resonance frequency. The tuned length is 115.7 after two
iteration and it shows that the program has increased the length from 110 mm to 115.7
mm to match its frequency criteria.
Figure 4.25. Auto Tune Result
Figure 4-26 shows the stress diagram. The stress directly relates to amplitude
gradient. The maximum stress occurs at the middle of the valve. Again at the corner of
slots there is a change in stress and possibility of fatigue at that point exists.
Figure 4.26. Stress Diagram
78
Figure 4-27 shows the cumulative strain energy diagram. Maximum strain
energy is transmitted in the valve tip. Maximum energy occurs at the valve tip and that
is the reason for having maximum displacement there.
Figure 4.27. Cumulative Strain Energy
Figure 4-28 shows the cumulative loss diagram. Maximum energy loss is
occurred in the valve tip. The amount of loss is small enough to prevent heating in the
element.
Figure 4.28. Cumulative Loss
79
4.4.4 The FEM Analysis Problem
The problems we may face during FEM analysis of the horn shape are as
follows:
• Loss effects are very difficult to predict with FEM models.
• Predicting relative motion between piezoelectric material and driver materials
is difficult.
• Predicting relative motion at bolted interfaces requires a nonlinear analysis,
which increases the complexity of the model.
4.5 Controlling Flow with Duty Cycle
Pulse width modulation (PWM) was used to control average flow by varying
the valve duty cycle on a frequency to match the flow requirement.
The On and Off state was controlled within a program inside a PLC. The
following duty cycle was applied to control the flow of material. Using an 80% duty
cycle every 10 seconds, the signal was on for the first eight seconds and off for the
next two. The signal was connected to the generator input. It was observed that there
was about 2 second lag before the piezo became active. The volume of output
material was measured at this rate and the result was recorded. The flow rate was
about 1.3 gal/min. Figure 4.29 shows the 80% duty cycle pulse which was applied to
generator during the test.
80
Figure 4.29. 80% Duty Cycle Graph
The duty cycle was then set to 60 %, so that every 10 seconds the signal was
on for the first six seconds and off for the next four, as shown in Figure 4.30. It was
observed that the flow was reduced to1.1 gal/min , but it was not reduced linearly.
Finally, the duty cycle was reduced to 40% and the measured flow was about 0.8
gal/min.
Figure 4.30. 60% Duty Cycle Graph
81
Figure 4.31. 40% Duty Cycle Graph
The result of the change in duty cycle versus flow is shown in Figure 4.32.
Flow control with duty cycle mostly relates to the generator response, and since it
takes about two seconds for the generator to start, any duty cycle with a yet lower On
state did not measurably affect flow rate.
Figure 4.32. Flow Versus Duty Cycle Graph
As shown in above figure output flow has linear relationship with duty cycle.
The slope of the chart in lower duty cycle is different from the higher duty cycle and
the reason is mostly related to generator response in lower duty cycle. By using more
responsive generator accuracy is increased and the curve can become more linear.
82
5 Chapter Five: Conclusion
5.1 Research Contribution
Until now, there has been lack of knowledge and technique to control a critical
flow when a material has higher viscosity. Recently, small steps have been taken to
develop a valve that could overcome the stickiness and friction of viscous material.
The present study has developed an innovative approach to the issue. The main
contributions of this research are listed below:
1- In this dissertation, the feasibility of a novel piezoelectric valve was
demonstrated, with successful application to contour crafting technology.
2- This research developed a methodology for design and implementation of
such valves in instances where material properties and test configuration are not
known ahead of time.
3- The devised method enables dynamic control of the friction for materials
with different surfaces using piezoelectric elements. This research investigation used
both experimentation and analysis to explore and address these issues properly.
5.2 Research Methodology
To develop this valve, a set of experiments was designed to characterize the
properties of the material that would be controlled in this system. These properties
were mainly density and viscosity. Size of the aggregate plays a small role in the
material characteristics; here, it was considered a factor defining blade separation
distance.
83
The devised methodology included two sets of experiments. The first set was
a static friction test. In this experiment, a range of pressures was applied to material,
and the passage of flow was measured without blade vibration. All of the data were
inserted into a regression model, and an equation was derived to characterize the flow
properties resulting from change in material characteristics and back pressure. In the
above test, friction surface was also a variable. Changing it affected the material
delivery. The next set of experiments was the same as above, except that vibration
was active. In this case, the flow was greater because the friction surface was
neutralized by the piezo element vibration. By deriving the above equation using this
methodology, we were able to determine the configuration of our desired valve. The
back pressure and viscosity capable of stopping the material were identified using the
static friction equation. By substituting those values into the second set of equations,
we were able to identify the maximum flow that could be passed through the designed
valve.
If the flow did not meet our expectation, we repeated the calculation using
different parameters, and did this iteratively until desirable values were achieved.
After calculation of the friction, heuristic method was used to design valve shapes
within the given parameters, and an optimized valve shape was selected. We had
established that the designed valve and the piezo element would need to vibrate at
same resonant frequency. In order to match frequencies, a finite element study was
used to optimize the length and thickness of the designed valve. In testing, a series of
pulses with different duty cycles was applied to a generator, with material flow
84
measured and recorded at each change in duty cycle. These results allowed us to draw
conclusions about optimal valve shape and duty cycle for the material.
5.3 Result Summary
The results demonstrate that this innovative approach to viscous flow control
technology has the potential to revolutionize viscous material delivery in areas of
industrial flow control that require the accurate dosing of granular, powdered
materials, with or without aggregates. An obvious beneficial application would be in
the food industry, or for rapid prototyping witch needs accurate powder-based delivery
processes.
Controlling flow of viscous material that has abrasive part is very hard to
achieve due to the dewatering and clogging problem. Dewatering caused by
accumulation of abrasive particles inside the pipe or along flow path. Removing those
particles need vibration to allow passage of material and smoothing the flow. The
above problem is the major reason that the use of vibration operated valve is
beneficiary to avoid accumulation of abrasive particles inside the valve.
The suggested ultrasonic valve concept has high reliability and almost it is
maintenance free with comparison to other valves. Since this valve has no moving
part it has higher durability as well. Cleaning for the ultrasonic valve is of major
benefits which rank this valve higher among the other type of valve made to perform
the same action. The component used to operate this valve including transducer and
generator have high cost but by considering flawless operation and mass production of
85
the valve in near future the cost can be extremely reduced. Accuracy of the valve
depends on the generator response time and it depends upon how fast the generator
can start and shut down the vibration elements. The respond time of valve depends on
quality of the piezo element and signal generators. By using an efficient and
responsive generator, controlling duty cycle on the valve can be performed more
accurate and hence the vale can control the flow of material with higher resolution.
By using the methodology given in this dissertation the time to manufacture
such valve is extremely decreased and fabrication of these valves can be done easier
and such valves can be made faster for different application with different material and
flow rate requirement. The maximum achieved flow rate for Contour Crafting
application was calculated before designing the valve and it was about 1 Gal/sec for
making a wall with thickness 1 inch and speed 1 ft/Sec and the flow requirement was
met within the fabricated valve.
Results from research explained in this thesis indicate a very promising future
for ultrasonic valves. Ultrasonic valves will be a strong competitive process for
controlling flow in viscous abrasive fluids. Functional models can be readily built,
and they can be applied to control the flow of varied materials with high accuracy,
speed, and low cost. However, many issues related to the ultrasonic valve still need
further study and investigation.
86
5.4 Suggested Direction for Future Research
The multidisciplinary nature of the concept of viscous flow control with
vibration opens a wide variety of areas for future work.
The main considerations in designing an efficient valve include the following:
1- Devising a method for accurate flow rate control and more responsive duty cycle
pulse generation.
2- Best tuning the valve by FEM method.
3- Defining efficient equivalent circuits for piezoelectric converters in series or
parallel resonance. This includes characterization and optimization for efficient
response of the valve. The resonance harmony should be obtained by optimal design.
4- Establishing the mechanical model of piezoelectric converter.
5- Improving response time and optimal power transfer of piezoelectric to converter
when operating in series or parallel resonance.
5.4.1 Improving Piezo Vibration Performance
In order to improve the performance of the valve and ultrasonic system, the
following considerations should be met:
1: In order to have an efficient system, Titanium would be a better material
choice for the new transducer device body. Ti is half as heavy as steel and possesses a
mechanical quality factor 20 time higher than steel. In addition, the tensile strength of
Ti is higher than that of steel or aluminum, and its elastic limit is three times higher
than that of aluminum or steel. The highest ultrasonic vibration amplitudes could
87
therefore be attained only with Ti horns. Moreover, the thermal expansion coefficient
of Ti is lower than that of steel or aluminum, which is very favorable to reducing the
thermal drift exhibited by the valve.
2: The new valve should be designed in one body form, meaning without
interfaces or bonds between the clamping end and the piezo. In this way, the
ultrasonic energy losses and reflections can be kept low and controlled.
3: The new valve will need to be solid, to allow a higher stored mechanical
energy and, consequently, allow a higher reproducibility of the oscillations to be
achieved.
4: The new transducer and horn will need to be symmetrical with reference to
the horizontal plane, which would eliminate the parasitic transversal vibration
components along the vertical direction.
5: The ultrasonic amplifier of the new horn will need to be a stepped cylinder.
The stepped cylinder would permit the highest ultrasonic amplification.
6: The capillary clamping system of the new transducer will be innovative and
symmetrical, not only with respect to the distribution of mass, but also with regard to
the distribution of stresses in the ultrasonic field. The transducer will be absolutely
insensitive to the clamping variations. Thus no ultrasonic coupling should occur
between the transducer and the valve.
5.4.2 Loading of Ultrasonic Transducers
In order to control load correctly, we need to perform real time and fast
automatic resonance control and tuning of the ultrasonic transducers’ energy. In our
88
application, the load is concrete, which enters the spaces between the valve blades.
The characteristics of concrete may vary. Therefore, the load should be categorically
defined. Also, a mechanism is required to control the power to the tip of the valve
when it is in operation. In our application, the power is transferred to the load in
relatively short time intervals, going to a full-load situation, which causes rapid
variation of all of the parameters of the ultrasonic system. In a no-load or low-power
application, the ultrasonic system typically behaves as a linear system. However, in
high-power operation, the system becomes increasingly non-linear. This is because
when the load varies, the ultrasonic system needs to continuously adapt its frequency
with respect to load variation. Without load, the system can run at a fixed frequency.
Therefore, a very accurate and fast generator is necessary in order to tune and
track the frequency. In our valve, mechanical loading of the transducer meant filling
the valve tip with concrete. All mechanical parameters with respect to the contact area
during energy transfer are important, and include, among other things, contact surface,
pressure, velocity, temperature, density, mechanical impedance, and mechanical load.
In fact, impedance-phase-frequency characteristics of our transducer will not be the
same when the transducer is driven at higher voltages. Also, impedance-phase-
frequency characteristics of our transducer are dependent on the transducer’s operating
temperature, and on its mechanical loading.
A piezoelectric transducer is both a source of ultrasonic vibrations and a
receiver of vibrations from its environment. As it creates vibrations, the transducer is
89
receiving its own reflected vibrations as well as varying mechanical excitation from its
loading environment. We should measure the RMS (Root Mean Square) active and
reactive power in a very wide frequency band in order to be sure of what is really
happening.
According to MPI ultrasonic reference in high power electronics, when driving
complex impedance in resonance, a PLL (Phase Locked Loop) is related to a power
control where load voltage and current have the same frequency. In order to maximize
the active load power, we make zero phase difference between the current and voltage
signals controlling the driving voltage frequency.
In modern power electronics, we use switch-mode operating control for power
regulation. In the case of R/L/C resonant circuits and electrical loads, current always
has a sinusoidal shape.
In ultrasonic technology, the transducers and connected elements are designed
to satisfy precise resonant conditions. In this research, to achieve maximum
efficiency, all oscillating elements must be tuned to operate at the same resonant
frequency.
If the frequency of the applied voltage does not coincide with the resonance
frequency of the system, the total impedance of the circuit is high and the resulting
current is of very small amplitude. When the driving frequency of the generator
matches the resonance frequency, the impedance of the ultrasonic system reduces
90
drastically. The drop in the voltage can be observed through the oscilloscope, and the
driving frequency is monitored by the frequency meter.
Sweeping and fast sweeping are additional modulation techniques added to the
fixed-frequency carrier signal. In other words, we start with a fixed-frequency signal
adjusted to the system resonance (example: 21.3 kHz) to work as a primary signal
carrier (or central operating frequency). Then, by using one of the following methods,
the driver makes complex modulations to cause shifting and sweeping of the primary
fixed-frequency signal. This provides many benefits including reduced or eliminated
standing waves, and better ultrasonic stimulation of large and arbitrary shaped
mechanical systems.
5.4.3 Fluid Dynamic Analysis
Fluid dynamic analysis using FEM is possible for most fluids, but due to the
complexity of concrete, a limited amount of related work is reported.
5.4.4 Heat Transfer
The mechanical vibration of the valve tip causes heating. On the other hand,
as the transducer is excited by high voltage, the dielectric loss in the ferroelectric
material could be another source of heating. These losses should be taken into
consideration for the design, as the temperature influences the transducer’s
performance. The temperature even determines the operational limit as the
ferroelectric material used must be operated at the temperature below the Curie point.
The stress due to the heat may also cause damage.
91
Heat generation in ultrasonic transducers is due to internal loss and results in
high temperature and low efficiency. High temperature not only changes the
transducer’s characteristics, but also degrades the strength of the materials used.
Depolarization may even occur in the electrostrictive element when the temperature
exceeds the Curie point. The heat design in the steady-state operation implies that the
temperature distribution must be within that of the safety range of the materials. For
the intense operation in pulsed-mode, the temperature distribution causes thermal
stress that must also be taken into account. In our present model, two inner heat
sources are considered in the ultrasonic vibrators; one is vibratory loss due to the
structural damping of the elastic materials used, and the other is dielectric loss.
Temperature rise causes the following effects:
1) Change of the elastic modulus
2) Dimensional change due to thermal expansion
3) Change of the mass density
92
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96
Appendix A
Appendix A Fundamentals of Piezoelectric Vibrators
A.1 Ceramic Material
Ceramic materials such as Barium Titanate are characterized as being
ferroelectric because the crystal domains of the material may be polarized through the
application of a large electric field, and a residual polarization will remain in the
material when the field is detached. These materials, when polarized, show
piezoelectric properties. However, materials such as barium Titanate have relatively
low Curie temperatures and become depolarized and lose their piezoelectric properties
at lower temperatures. The Curie temperature of Barium Titanate varies between
120°C and 130°C. Because these materials are heated by ultrasonic energy when an
alternating voltage is applied, it is better to use ceramic materials, which have high
Curie temperatures in ultrasonic transducers.
Figure A.1. Internal structure of a piezo ceramic material
http://www.trstechnologies.com/Materials/piezoceramics.php
97
In order to achieve a better result, a new ceramic material, like lead Titanate
Zirconate, commonly referred to as PZT, should be selected. This material has a Curie
temperature of 300 °C. It can therefore handle much higher power than previous
ceramic transducer materials. Consequently, it is desirable for use in ultrasonic
transducers used in applications attended by higher ambient temperatures. Examples
of high-temperature applications include ultrasonic welding and cleaning. Lead
Titanate Zirconate is, however, considerably more expensive than prior materials, such
as Barium Titanate, and this cost has in the past limited the use of PZT in ultrasonic
transducers. The energy generated in piezoelectric materials is conducted to the
interface where the horn is usually attached.
Figure A.2. Polarization of Piezoelectric Materials
Figure A.3. Polarization of Piezoelectric Materials
http://www.staplaultrasonics.com/c3-struc/struc3.htm
98
Figure A.4. Polarization of Piezoelectric Materials
http://www.staplaultrasonics.com/c3-struc/struc3.htm
Figure A.5. The Piezoelectric Effect inside Different Bodies
99
A.2 Modeling Ultrasonic Transducers
The main form of model for piezoelectric converter, the BVD model
(Butterworth-Van Dyke, dual-circuits model), is presented in Figure A.6. ( Source
MPI Ultrasonic )This model is useful for isolated coupled series and parallel
resonances that are not loaded. In fact, Figure A.6 presents simple models that are
applicable for relatively high mechanical quality factor piezoelectric converters, where
thermal dissipative elements in piezoceramics could be neglected. In this model, C
and C
are the clamped, static capacitance of piezoceramics, C1,C2 and L1,L2 are
motional mass and stiffness elements of the converter’s mechanical oscillating
circuit.
and are due to the mechanical circuit and come from converter joint loss,
planar friction loss between piezoceramics and metal parts, mounting elements loss,
and material hysteresis-related loss.
Figure A.6. Piezoelectric Converter Dual, BVD Models
Source: MPI
100
For more general models, where the effects of dissipative dielectric loss are not
negligible, the model is presented in the following Figure
Figure A.7. BVD Piezoelectric Converter Models with Dissipative Elements
Source: MPI
By considering the electrical equivalent model, the models from Figure A.7
can be schematically simplified as follows:
Figure A.8. Simplified BVD Piezoelectric Converter Models
Source: MPI
101
The influence of an external acoustic load on the converter modeling is
presented in Figure A.9 by introducing loading resistances
,
as the closest and
very much simplified equivalent of the real converter loading.
Figure A.9. BVD Piezoelectric Converter Models by Considering External Load
Source: MPI
The motional current
and motional voltage
are the most important
mechanical-output power amplitude controlling parameters of piezoelectric converters
in series and parallel resonance. Therefore, when the converter is operating in series
resonance, in order to control its output power and/or amplitude, we should control its
motional current and in the condition of parallel resonance, output power and/or
amplitude are directly proportional to the motional voltage um. More precisely, when
we compare two operating systems of the same converter, when the converters
produce the same output power, the converter that works in a series circuit can deliver
more force and at lower speed, and when operating in parallel resonance it is able to
deliver high output velocity and relatively low force.
102
Figure A.10. Alternative BVD Models of Loaded Piezoelectric Converters with Block
Source: MPI
Separation of purely electrical and purely mechanical elements
Figure A.11. Schematic of the Equivalent Circuit of the Transducer around Resonance
Source: MPI
103
A.3 Modeling of the Horn
In order for the horn to work properly, it should have almost the same resonant
frequency as the converter. We can add new equivalent circuit model representing an
added horn. The added horn represents one mechanical structure that can be replaced
by an equivalent electrical circuit.
Sometimes an added horn with complex shapes can create new resonant
frequencies. The internal losses of added horns are not neglected, since we can find
dissipative elements in added-horn-related resonant circuits.(Figure A.12)
Figure A.12. Schematic of the Equivalent Circuit of the Transducer with Added Horn
Source: MPI
104
Abstract (if available)
Abstract
In this research, a new ultrasonic operated valve was analyzed, prototyped, and tested for use in an abrasive viscous fluid application. The innovative valve concept is based on controlling the friction of material by employing several friction elements along the flow direction. Abrasive particles in the viscous fluid are stopped by the force of friction when coming into contact with the friction elements. Friction is neutralized by use of vibration to break away the abrasive particles from the friction element surfaces. Several factors were considered in designing the piezoelectric valve. Factor identification was done by conducting experiments and analyzing data. Some important factors that affect the valve design were recognized to be back pressure, size of friction blades along the direction of flow, density of material, viscosity, amplitude, frequency of vibration, and proportion of particles in the mix. First, a method was designed for measuring the friction coefficient of the given viscous materials. A design of experiment approach was pursued in order to identify the significant parameters. A piezoelectric transducer was used, which vibrated at the resonance frequency of 20 kHz. FEM modeling was used at that stage to ensure that the resonance frequency of the designed valve matched the resonance frequency of the transducer and booster that provided vibration. In order to perform proportional flow control, pulse width modulation was used to control the duty cycle of ultrasonic power transferred to the valve. A study was performed to find the best vibration performance for the parameters in the range of operation.
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Creator
Behdinan, Khashayar
(author)
Core Title
Methodology for design of a vibration operated valve for abrasive viscous fluids
School
Viterbi School of Engineering
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Doctor of Philosophy
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Industrial and Systems Engineering
Publication Date
04/27/2009
Defense Date
03/18/2009
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