THE EFFECT OF SURFACE ROUGHNESS ON THE
PRECISION OF THE ENCAPSULATED FIXTURING SYSTEM
BY
WINSTON CHI HANG FAN
S.B., MECHANICAL
ENGINEERING,
1998
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
AUGUST2000
L
(110bey D004]
©2000 Massachusetts Institute of Technology
All rights reserved
Author:
Department of Mechanical Engineering
August 4, 2000
Certified by:
Sanjay E. Sarma
Assi stant Professor of Mechanical Engineering
Thesis Supervisor
Accepted by:
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
SEP 2 0 2000
LIBRARIES
Ain A. Sonin
Professor of Mechanical Engineering
C hiairman of the Graduate Thesis Committee
BARKER
The Effect of Surface Roughness on the Precision of the
Encapsulated Fixturing System
by
Winston Chi Hang Fan
Submitted to the Department of Mechanical Engineering
on August 4, 2000 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Mechanical Engineering
ABSTRACT
Fixturing systems seek to locate, secure, and support a workpiece while minimizing cost
and complexity. A novel method, the Encapsulated Fixturing System, is currently under
development at MIT. This concept encloses the workpiece within an encapsulation of a
low temperature alloy, such as tin-bismuth. The encapsulation provides a locating
reference and support for the workpiece. The surface topography of the encapsulation
has a potentially significant effect on the precision of the process. This study shows that
deformation at the asperity level is unlikely to have a significant impact on the precision
of the process. Additionally, this study shows that the desired surface finish can be
generated reliably if the proper encapsulation material, pressure, and mold surface finish
are selected. Experimental results indicate that eutectic alloy is superior to its noneutectic counterpart in the prevention of surface porosity. A molding pressure of at least
60 psi and a mold surface roughness of approximately 0.4 gm are recommended to
produce accurate and repeatable surfaces.
Thesis Supervisor: Sanjay E. Sarma
Title: Assistant Professor of Mechanical Engineering
2
Table of Contents
CHAPTER 1: INTRODUCTION.......................................................................
9
1.1.
Requirements of Fixturing Systems .........................................................
9
1.2.
Modular Fixturing Systems.....................................................................
11
1.3.
Universal Flexible Fixturing Systems.....................................................
12
Conformable Clamp Fixturing .......................................................
12
1.3.1.
1.4.
1.5.
1.3.2. Fluidized Bed Fixturing ..................................................................
1.3.3. Phase Change Fixturing ..................................................................
1.3.4. Efficacy of Universal Fixturing Systems ......................................
13
15
16
Encapsulated Fixturing System ..............................................................
16
1.4.1. 2D Milling Strategy.......................................................................
1.4.2. 2 D Milling Strategy...................................................................
1.4.3. 3D Milling Strategy.......................................................................
22
22
23
Current Status of the Encapsulation Fixturing System........................
23
CHAPTER 2: MOTIVATION AND BACKGROUND........................................25
2.1.
2.2.
CHAPTER
3.1.
Surface Properties.....................................................................................25
2.1.1. Types of Surface Irregularities.......................................................
2.1.2. Contact Interactions between Two Surfaces ..................................
26
27
The Effect of Surface Roughness on the Encapsulated Fixturing
Process.......................................................................................................
31
3:
THE EXPECTED DEFLECTION AT THE ASPERITY LEVEL........32
Theoretical Analysis.................................................................................
3.1.1.
3.1.2.
3.1.3.
3.2.
Surface Characterization ................................................................
Elastic Deflection using Hertzian Theory .......................................
Plastic Deformation of the Asperities .............................................
33
34
35
37
Experimental Apparatus and Procedure................................................38
3.2.1. Experimental Apparatus................................................................
3.2.2. Experimental Procedure ................................................................
3
38
39
3.3.
Surface Characteristics of Typical Machined Surfaces........................
3.4.
Discussion...................................................................................................41
40
CHAPTER 4: GENERATION OF SURFACE ROUGHNESS IN CASTING ............. 43
4.1.
4.2.
4.3.
Experimental Apparatus and Procedure..............................................
43
4.1.1. Experimental Apparatus................................................................
4.1.2. Experimental Procedure ................................................................
44
45
Experimental Results..............................................................................
46
4.2.1. Eutectic vs. Non Eutectic Tin-Bismuth Alloy................................
4.2.2. Pressure and Mold Surface Roughness ...........................................
47
48
Discussion...................................................................................................51
4.3.1. Effects of Eutectic vs. Non-Eutectic Alloy ....................................
4.3.2. Effects of Pressure..........................................................................
4.3.3. Effects of Mold Surface Roughness................................................
52
53
55
Process Limits for Encapsulation Molding............................................
56
CHAPTER 5: CONCLUSION AND FUTURE W ORK .......................................
58
4.4.
5.1.
Identification of Design and Process Parameters..................................
59
5.2.
Sensitivity Studies ....................................................................................
60
5.2.1.
5.2.2.
5.2.3.
5.2.4.
Clamping Load..............................................................................
Injection Pressure ...........................................................................
C ooling R ate...................................................................................
Scaling and Encapsulation Stability................................................
60
61
62
62
Design of the 3D Encapsulated Fixturing System.................................
63
5.3.
REFERENCES...............................................................................................64
4
List of Figures
Figure 1: Conformable clamp fixturing..........................................................................
13
Figure 2: Fluidized bed fixturing ..................................................................................
14
Figure 3: Phase change fixturing...................................................................................
15
Figure 4: Steps of the Encapsulated Fixturing System...................................................
18
Figure 5: Illustration of the three fundamental machining strategies: 2D, 2
D , an d 3D ..........................................................................................................................
Figure 6: In the 2
21
D milling strategy, the fixturing element obscures the
six th sid e ............................................................................................................................
23
Figure 7: A surface with form error, waviness, and roughness.....................................
26
Figure 8: Model of surfaces as flat, and in perfect contact ...........................................
27
Figure 9: Asperities reduce the real to nominal surface area ratio................................
28
Figure 10: Analytical Model - A perfectly flat rigid plate loaded against a
surface with the aggregate material and surface profile properties of the two
surface s..............................................................................................................................
29
Figure 11: Contact between a rough nominally flat surface and a rough surface
w ith d efects........................................................................................................................
30
Figure 12: Profilometer trace for a 0.4 gm surface, with no wavelength
filterin g ..............................................................................................................................
40
Figure 13: Mold used to produce experimental specimens...........................................
44
Figure 14: Specimen molded with non-eutectic alloy. The left specimen is
molded at atmospheric pressure. The right specimen is molded at 80 psi...................
47
Figure 15: Reflected roughness of the tin-bismuth specimen when molded
against an insert with 0.1 gm nominal roughness.........................................................
49
Figure 16: Reflected roughness of the tin-bismuth specimen when molded
against an insert with 0.4gm nominal roughness. ........................................................
49
Figure 17: Reflected roughness of the tin-bismuth specimen when molded
against an insert with 1.6gm nominal roughness. ........................................................
5
50
Figure 18: Reflected roughness of the tin-bismuth specimen when molded
against an insert with 3.2gm nominal roughness .........................................................
50
Figure 19: The peak to valley height of all the specimens and inserts..........................
51
Figure 20: Eutectic 0.1 gm specimens. The left specimen was molded at 80
psi. Note the smudged area due to the thin layer of oxide. The right specimen
was molded at 40 psi. The defects can clearly be seen in this example.......................
54
Figure 21: Presence of defects on specimens molded at 40 psi on the left and
atmospheric pressure on the right. The surface of the atmospheric specimen is
entirely covered by defects............................................................................................
55
Figure 22: The Encapsulated Fixturing System process window .................................
57
6
List of Tables
Table 1: Roughness, summit curvature, and deflection values of the surface
roughness standards.......................................................................................................
41
Table 2: Peak to valley depth for various surface roughness standards........................
42
Table 3 : Description of the surface roughness specimens ...........................................
46
7
Acknowledgements
I would like to take this opportunity to extend my thanks to some people without whose
help this thesis would not be possible:
+ To Professor Sanjay Sarma, whose advice and guidance have been invaluable.
+ To my family, for all their support.
+ To Ceani Guevara, for her help with experiments, proofreading, and many other
things.
+ To Elmer Lee for his help and knowledge this past year.
+ To everyone in the Rapid Autonomous Machining Laboratory, for making the
laboratory such a pleasant place.
I would like to dedicate this thesis to the memory of my grandfather, Wah Fan.
8
Chapter 1: Introduction
The goal of manufacturing is to produce products to the desired specifications at the
minimum cost, the maximum speed, and the best quality. These criteria are competitive
in nature, with improvement in one area usually possible only at the degradation of at
least one other factor. As may be expected, constant effort is made to achieve an optimal
balance for specific areas of manufacturing. One of these critical areas is fixturing.
Fixturing forms a critical link between the design and production of a part. The
requirements of a particular fixturing system have a direct impact on the cost, speed,
quality, and flexibility of the overall manufacturing process. This study evaluates the
feasibility of the Encapsulated Fixturing System, an alternative fixturing system currently
under development at MIT. In particular, this study focuses on the effect of surface
roughness on the precision of the Encapsulated Fixturing Process.
1.1.
Requirements of Fixturing Systems
Fixturing systems-or workholding systems, as they are also known-are evaluated in
terms of four functional requirements: deterministic workpiece location, locational
stability, total restraint, and clamping stability [Chou 89]. Deterministic workpiece
location means that the fixture should locate the workpiece precisely in order to ensure
accuracy in the machining process. Locational stability refers to the ability of the
workpiece to assume a stable resting position upon insertion into the fixture. Total
restraint signifies that the clamping force and geometry must be sufficient to secure the
workpiece against machining forces. Finally, clamping stability establishes that clamping
forces should not deform the workpiece from its desired geometry.
9
Unfortunately, satisfying these functional requirements is far from a simple task. Success
is limited to parts that are of a regular geometry. Even a slight increase in complexity
may result in a part that cannot be completely located, secured, and supported. In such
cases, the complexity of the fixture must increase dramatically to accommodate the part.
Even if the part can be successfully secured, there is no guarantee that the component can
be manufactured as desired, since the fixtures required to completely secure the part often
deny access to the machine tool. Thus, often the simplest fixturing method cannot be
used and more complex and expensive alternatives need to be pursued to locate, secure,
and support a part during the machining process.
Fixturing requirements must be balanced against the requirements of the manufacturing
process and the cost involved in reaching the goal. This tradeoff often curtails the ability
of the designer to create a desired part. Design engineers are told that they need to
consider the manufacturability of their design. Although this makes sense nowadays, it
would be much better if the manufacturing process could adapt to the designer's needs,
and not vice versa. Although improvements continue to be made in fixturing
technologies to minimize the restrictions that these systems place on the design to
production process, a great deal of distance remains to be covered.
The current fixturing technologies are categorized into modular fixtures and universal
flexible fixtures. Sections 1.2 and 1.3 describe these two categories.
10
1.2.
Modular Fixturing Systems
Modular fixturing systems are based on a set of standard elements such as clamps,
parallels, and v-blocks. These fixturing systems can be configured to secure a wide
variety of regular shapes. However, in spite of additions such as ball and socket
assemblies to clamping elements, modular fixtures are still limited in their ability to
properly locate, secure, and support workpiece geometries that are irregular in shape.
This places a severe constraint on the design process.
The time and manpower commitment required to design and set up modular fixturing
plans is quite large. The cost is further exacerbated by the need for a distinct fixture for
each machining operation. This means that the cost involved limits modular fixturing set
ups to mass manufacturing processes, where the cost can be amortized over large
component volumes and long production runs. In an attempt to improve the situation,
pallet-mounted fixturing systems have been introduced in recent years. These pallets
allow the fixtures and workpieces to be set up outside of the machine, and thus reduce
machine downtime. There have also been efforts to automate fixturing analysis and
layout [Asada 85, Chou 94]. These various developments have led to an evolution in
modular fixturing technology that brings about incremental improvements in quality and
speed. However, these advances do not address the limitations that such fixturing
systems place on the creativity of the designer.
11
1.3.
Universal Flexible Fixturing Systems
Universal flexible fixturing systems hold a variety of irregularly shaped parts during
manufacturing and assembly without the need for a unique fixturing plan for each part
shape. These flexible systems provide a number of advantages compared to modular
fixturing [Thompson 85]. First, universal flexible fixturing greatly reduces the time and
effort needed to design specific fixtures. Secondly, because a single fixture type is used,
there is no need for unique fixtures that become obsolete with the introduction of each
subsequent new design, as in the case of modular fixtures. This ability to reuse fixtures
helps reduce the cost required to store and maintain the fixtures. Finally, the use of
standardized fixtures greatly simplifies the programming of machining operations.
There are three types of universal flexible fixtures: conformable clamps, fluidized bed
and phase change. These types are discussed in Sections 1.3.1, 1.3.2, and 1.3.3
respectively. Section 1.3.4 compares the efficacy of the three types of universal flexible
fixtures.
1.3.1. Conformable Clamp Fixturing
Conformable clamps are universal flexible fixtures that can be adjusted to match the
profile of the workpiece. Figure 1 [Lee 99] displays an example of a conformable clamp.
12
Figure 1: Conformable clamp fixturing
A conformable clamp is subdivided into elements that can either slide linearly or pivot to
accommodate the part geometry. The workpiece is accurately aligned before the clamp is
actuated. The clamping assembly can then travel with the workpiece, maintaining its
locational accuracy throughout several machining operations, even if they are on separate
machines. The advantage of this system is that for large geometries, such as those of a
turbine blade, high locational accuracy can be maintained throughout the machining
process. However, the reliability of the system is at risk due to the large number of
moving parts. The presence of debris from the machining operation increases the risk of
machine failure. Furthermore, the debris also adds to the danger of improper part
location. Another concern is the ability of the clamp to secure a part with a compact
geometry, such as a sphere, and still provide sufficient access for the machining tool.
Finally, the rigid elements that form the conformable clamp do not provide much
damping against the effects of the machining forces.
1.3.2. Fluidized Bed Fixturing
Another type of universal flexible fixturing is the fluidized bed concept. This concept
secures and supports the part with particles that surround the workpiece.
13
Figure 2 [Lee 99] shows the cross section of a part held in place with fluidized bed
fixturing.
Figure 2: Fluidized bed fixturing
In order to place the part in a fluidized bed fixture, air is passed at a controlled rate
through a bed of particles. This causes the air-particulate mass to behave like a fluid.
The workpiece is then partially immersed into this fluid-like mixture. Upon the
subsequent removal of air from the system, often aided by the imposition of a vacuum or
a magnetic field, the particles are compacted into a solid mass. This solid mass secures
the workpiece. The fluidized bed system has many advantages. First, it is a very simple
design that can be operated reliably. Additionally, the cycle time is very short. Most
importantly, the fluidized bed can conform to and grip a variety of geometries. The
downside of the fluidized bed concept is fourfold. First, like the conformable clamps, the
fluidized bed system requires external metrology to determine the location and
orientation of the workpiece. In addition, care must be taken to ensure that the fixture
does not interfere with machine tool access. Furthermore, the force exerted by the
compacted material may be insufficient to secure the part against machining forces.
Finally, voids and inclusions can form inside the fluidized bed, which may allow the part
to shift.
14
1.3.3. Phase Change Fixturing
Figure 3 [Lee 99] depicts an example of phase change fixturing, the third type of
universal flexible fixturing systems.
Figure 3: Phase change fixturing
As its name suggests, this concept uses a phase change material to secure the workpiece.
The molten material, usually a plastic or a metallic alloy, conforms to the workpiece.
Once the fixturing material has solidified, it grips the workpiece securely. If the
solidification takes place in a regularly shaped die, this method provides an encapsulated
workpiece with a regular geometry. This regular geometry allows the encapsulated part
to be manipulated and secured easily. The solidified phase change material provides full
support for the workpiece and has excellent damping properties.
Additionally, the phase change system generally provides for a more secure fixture than
the fluidized bed system. The phase change system can also encompass a wider variety
of geometries than the conformable clamps can. However, dies must be used to locate
and orient the part. Since a unique die is used to locate the workpiece for each setup, the
cost increases. Unfortunately, the phase change process is hardware intensive, and thus
15
expensive to implement. Thus, the phase change system is currently only used for highly
critical operations such as securing jet turbine blades for grinding operations.
1.3.4. Efficacy of Universal Fixturing Systems
Of the three universal flexible fixturing methods, the phase change material has the most
promise. As mentioned previously, the phase change material is capable of capturing a
larger range of workpieces than the conformable clamps. The phase change material also
provides the holding forces that the fluidized bed concept lacks. Finally, the phase
change process is superior to the other two processes due to the its ability to let the
machine tool access the part nearly at will. The stability of the phase change system
depends on the yield strength and Young's Modulus of the phase change material
[Lee 99]. The tool can cut through large portions of the material, also called
encapsulation, without degrading the encapsulation's workholding abilities. Because the
material is much softer than both the tool and the workpiece, no damage is likely to occur
to either component.
1.4.
Encapsulated Fixturing System
The Encapsulated Fixturing System currently under development at MIT seeks to exploit
the advantages of the phase change system. The objective is to take the phase change
system one step further so that the location and orientation of the workpiece can be
preserved across setups.
16
In the Encapsulated Fixturing Process, the workpiece is placed into a mold and
encapsulated with a low-temperature phase change material. The molding process
generates an encapsulated workpiece that is rectangular in nature. This encapsulated
workpiece can then be accurately located and secured in a simple fixture. Once secured
and located, machining can begin. Following each sequence of machining operations, the
encapsulated workpiece is placed back into the mold and restored to its original shape.
The encapsulated workpiece can then be placed back in the fixture until all of the features
have been machined. In this fashion, the workpiece can potentially be machined in any
direction without having to incur the time and resources required to design and assemble
a unique fixture for each machining operation. Figure 4 [Lee 99] pictorially describes the
steps of the Encapsulated Fixturing System.
17
START:
RAW STOCK(EMBEDDED)
ENCAPSULATOR
MACHINE
ORIENT
REFILL
SIDE 1
SIDE2
SIDE N
P*j
FINISH:
Figure 4: Steps of the Encapsulated Fixturing System
18
The Encapsulated Fixturing Process removes the need for a unique, locating die for each
machining operation. The part is located from the surface of the encapsulated workpiece.
The main disadvantage of this process is that it is difficult to incorporate stock with preexisting features, such as those from a cast piece, unless unique molds are developed that
use these features to locate the part during the initial encapsulation. Despite this
constraint, the process has the potential of greatly increasing the flexibility of the
designer. The ability of the encapsulated workpiece to locate, secure and support the part
throughout the machining process; the ability to access the workpiece from all sides; and
the ability to secure the part to the machining center with the use of a low-profile, vicelike clamp, frees the designer from much of the constraints imposed by the current
fixturing technology. This allows the designer to focus on exploiting the limits of the
manufacturing process. Another advantage of this process is the simple geometry of the
encapsulated workpiece, which makes automation possible. With the support of a
CAD/CAM system and robotic manipulators, the Encapsulated Fixturing Process can be
expanded into a universal automated fixturing system that is capable of autonomous
prototype or low volume production.
As mentioned, the Encapsulated Fixturing System has the potential to remove many of
the fixturing constraints placed on the design and production processes. However, in
order to achieve this goal, a great deal of hardware is necessary to perform the molding
operation. In many cases, the system's full capabilities may not be necessary for the
operations in question. Accordingly, to reduce cost, the system can be modified for three
different machining strategies: 2D, 2
'/2
D, and 3D milling. Sections 1.4.1, 1.4.2, and
19
1.4.3 provide a brief overview of these strategies. As one processes from the 2D milling
strategy to the 3D milling strategy, the complexity permitted in the machining operations
increases, but so does the complexity and cost of the encapsulation equipment. Figure 5
depicts this path.
20
3-D Milling
Access: All 6 sides
Locational datum: Molded Walls
Molding Tolerances: Tight
T --
1
2 1/2-D Milling
Access: Only 5 sides
Locational datum: External
Embedded Features
Molding Tolerances: Loose
~IZD
\
czEIIO
2-D Milling
Access: Only 2 opposite sides
Locational datum: External Frame
Molding Tolerances: Very Loose
Figure 5: Illustration of the three fundamental machining strategies:
2D, 2 D, and 3D
21
1.4.1. 2D Milling Strategy
2D milling is the simplest of the three machining strategies. In 2D milling, all features of
the part must be accessible from two parallel surfaces. The four remaining surfaces hold
the part, both during the encapsulation process and during machining. The mold design
is thus greatly simplified-it just needs to grip the part, and can use the part's features to
hold it. Additionally, and possibly more importantly, this mold greatly simplifies the
machining and restoration cycle since the whole structure can be transported from the
encapsulation machine to the milling machine. The surface finish of the encapsulated
workpiece is not critical for 2D milling, since the mold is used to hold the workpiece
during both machining and encapsulation restoration. Thus, the surface finish of the
encapsulated workpiece never really comes into play.
1.4.2. 2
D Milling Strategy
The second milling strategy, 2 1/2 D milling, allows the workpiece to be accessed from
five out of the six sides. In this method, the encapsulation serves only to secure and
support the workpiece. The location is carried out by a fixturing element embedded into
the encapsulation for the duration of the machining operation, as shown in Figure 6. This
fixturing element obscures the sixth side. In return, since the encapsulation surfaces do
not need to be precise, the mold and ancillary equipment can be of much lower
tolerances, complexity and, of course, cost.
22
I
Figure 6: In the 2
D milling strategy, the fixturing element obscures
the sixth side
1.4.3. 3D Milling Strategy
3D milling is Encapsulated Fixturing at its fullest potential. Since the sides of the
encapsulation locate the workpiece, both during machining and restoration, the mold
must be designed such that the surfaces are in precise alignment for the initial
encapsulation and the subsequent encapsulations. In addition, the location of the
workpiece must be tracked as the block is rotated during subsequent machining
operations. This machining strategy requires the most complex and precise equipment in
order to succeed, but is potentially the most rewarding in the amount of freedom that it
provides to the designer.
1.5.
Current Status of the Encapsulation Fixturing System.
Most of the research and development to date has focused on the 2 1/2 D machining
strategy. This strategy allows for a manageable degree of complexity while preliminary
technical hurdles are overcome. A 2 /2 D encapsulation machine was developed by
Elmer Lee under the supervision of Professor Sanjay E. Sarma at MIT. Now that most of
23
the initial technical hurdles have been overcome for the 2 /21D encapsulation strategy, the
3D machining strategy can be developed. As a preliminary to laying down the functional
requirements and designing an encapsulation system to validate the concept, a study must
be carried out to examine various factors that might affect the viability of the concept.
The 3D encapsulation system requires the encapsulation to locate the workpiece, in
addition to securing and supporting it. This locating function is done via the surface of
the encapsulation. Thus, the surface roughness of the encapsulated workpiece becomes
critical to the process.
24
Chapter 2: Motivation and Background
During 3D milling, the surfaces of the encapsulated workpiece are used to locate the part
with respect to the fixture. In order to achieve precise, repeatable placement, the surfaces
must retain their position and alignment during the life of the encapsulated fixture. Any
deformation and damage to the surface of the encapsulation can result in loss of
precision. Thus, it is important to consider the effects of surface properties on the
precision of the Encapsulated Fixturing Process. Section 2.1 provides a background on
the characterization and interactions of surfaces. Section 2.2 discusses potential avenues
through which surface properties can have an effect on the precision of the process.
2.1.
Surface Properties
When two solids interact with each other, the surfaces that come into contact are often
assumed to be topographically smooth. This means that during modeling and
calculations, the two surfaces are assumed to be in perfect, continuous contact. In reality,
however, perfect contact can only be achieved in a few, very carefully contrived
laboratory experiments [Johnson 85]. In most cases, surface irregularities restrict contact
of two surfaces to only a portion of the nominal contact area. Depending on the
manufacturing process that generated a surface and the environmental conditions that can
result in surface wear, the asperities or defects can be regularly or randomly distributed.
These asperities and defects may affect part or all of the surface. Section 2.1.1 describes
the classification of surface irregularities depending on their properties. Section 2.1.2
describes the typical interactions between two surfaces in contact.
25
2.1.1. Types of Surface Irregularities
Depending on its characteristics, surface topography is generally divided into three
general categories: form error, waviness, and roughness [Tencor 96]. Form error refers to
gross deviations from a perfectly flat surface, such as a general concavity or convexity
across the surface. Waviness denotes deviations that consist of regular undulations
across the surface. Finally, roughness is characterized by numerous randomly shaped
undulations. Depending on the manufacturing process, these undulations can be small or
large, and can be regularly or randomly distributed. Figure 7 shows a surface with form
error, waviness, and roughness [Tencor 96].
Roughness
Form Error
Waviness
Figure 7: A surface with form error, waviness, and roughness
Clearly, form error and waviness denote gross deformations of the surface. Since the
Encapsulated Fixturing System aims to produce high accuracy parts, and since the 3D
machining strategy relies on the surface for precise location, neither form error nor
waviness can be tolerated in the 3D machining strategy. Fortunately, form error and
waviness usually occur due to the thermal expansion and contraction of the material
during encapsulation. Therefore, these errors are preventable through careful mold
26
design and proper selection of materials with the desired coefficient of thermal
expansion.
On the other hand, roughness is characterized by deformations on a much smaller scale
than either form error or waviness. Thus, it is not immediately evident whether
roughness affects the precision of the 3D machining strategy in the Encapsulated
Fixturing Process. In order to understand the effects of roughness on the system, it is
important to understand how the surface will interact with the mold and the fixture. This
understanding will also provide an insight into how to control or mitigate any undesirable
effects that roughness may have on the system.
2.1.2. Contact Interactions between Two Surfaces
Whenever two surfaces are in contact, with a load placed on them, the surfaces deform
elastically and then plastically depending on the load. The simplest model of this
deformation assumes that the surfaces are in perfect contact, as shown in Figure 8.
Figure 8: Model of surfaces as flat, and in perfect contact
In the case of two flat surfaces in perfect contact, the real to nominal area ratio is 1.0.
Thus, the applied load is distributed evenly along the entire surface. This means that the
entire surface deflects elastically and then plastically. The mean applied pressure
27
required for the formation of a fully plastic field is approximately three times that of the
yield strength [Ashby 92].
Unfortunately, this model does not consider the surface irregularities discussed in
Sections 2.1 and 2.1.1. These surface irregularities reduce the contact area between the
two surfaces. Thus, the real to nominal contact area ratio is less than 1. This decrease in
contact area affects the load bearing properties adversely since deformation under a load
is proportional to area. This means that the model of two perfectly flat surfaces
underestimates the deflections that the yielding surface undergoes. Since surface
deflection is essential to the precision of the universal encapsulating system, a more
accurate model needs to be developed.
The more advanced model cannot assume that both surfaces are flat. Thus, this more
advanced, and thus more complex, model considers the interaction between two rough,
nominally flat surfaces. Figure 9 shows this type of surface contact.
Figure 9: Asperities reduce the real to nominal surface area ratio
In frictionless contact of elastic solids, the contact stress depends only on the material
properties and the relative profile of their two surfaces. Thus, two such surfaces can be
28
modeled as a flat, rigid surface and a solid with the aggregate material and surface profile
properties of the two surfaces, as shown in Figure 10.
Figure 10: Analytical Model - A perfectly flat rigid plate loaded
against a surface with the aggregate material and surface profile
properties of the two surfaces.
For this model, the effective Young's Modulus is E*. The profile of the solid provides
the same undeformed gap described by a root mean square roughness o. Equations 1 and
2 define these parameters of the surface with the combined characteristics.
1
E
(1)
+
El
E2
V072
2
(2)
v, E, q, and a2 are the Poisson's Ratio, the Young's Modulus and root mean square
roughness for the respective surfaces.
In this case, as the load is applied, deformation begins at the micro, asperity level. The
asperities deflect elastically and then plastically. Only once the asperity deformations
reach their maximum level of deflection does the surface undergo bulk plastic
deformation. The deformation of the asperities may or may not be complete. The
29
deflection of the asperities will affect the precision of the process. The significance of
this problem remains to be determined.
In practice, it is difficult to produce surfaces that are nominally flat with no defects.
While defects do not have a significant effect in isolation, they take on a great deal of
significance in larger numbers. In this scenario, two rough, nominally flat plates are
brought into contact. On at least one of the two surfaces, there are a number of dimplelike defects. An example of this is shown in Figure 11.
Figure 11: Contact between a rough nominally flat surface and a
rough surface with defects.
Clearly, while the nominal contact area remains the same as that of a part without the
dimples, the real contact area is reduced by the area of the defects. Thus, the real to
nominal contact area ratio further decreases. This introduces an additional layer of
complexity to the problem. When the surfaces are brought together, the initial behavior
is very similar to the previous case concerning two nominally flat rough surfaces. The
asperities on the surface undergo elastic and then plastic deflection. Once maximum
asperity deflection has been achieved, the asperities transfer the load directly to the bulk
material. Unlike the previous scenario, the presence of defects on the surface prevent the
load from being distributed across the entire nominal area. This means that the load
30
bearing area of the block is reduced. Thus, the block can undergo bulk plastic
deformation earlier than predicted by the nominal contact area. The severity of this
deflection is dependent on the number and size of these defects. In this way, the random
nature of the defects greatly increases the uncertainty of the load required to induce bulk
plastic deformation of the block.
2.2.
The Effect of Surface Roughness on the Encapsulated Fixturing
Process
It is clear that both micro and macro surface irregularities have a large effect on the real
contact area and the load capability of a surface. The lower the load capability of a
surface, the higher the probability is that the surface will deform plastically. This means
that these surface irregularities can have a serious effect on the locational accuracy of
encapsulated parts during 3D machining. In order to determine how much of an effect
surface roughness has on the precision of the Encapsulated Fixturing Process, two
questions need to be answered. First, it is important to determine the deflection possible
at the asperity level and its effect on the precision of the process. Second, one must
determine if it is possible to produce a desired surface roughness accurately and with
great repeatability.
31
Chapter 3: The Expected Deflection at the Asperity Level
A workpiece, encapsulated or not, should be held in total restraint during machining.
This implies that the workpiece is rigidly secured to the machining fixture and that a
stable locational reference is established between the workpiece and the machine tool.
Ideally, such restraints are applied geometrically in all six degrees of freedom through
devices such as the walls of a vice. In practice, however, the use of geometrical
constraints in all six degrees of freedom is unusual because of two reasons. First, access
must be provided for the machine tool. Second, the complexity of the fixture in both
design and operation cannot usually be justified by the results. Thus, in one or more
degrees of freedom, parts are typically held by frictional, not geometrical, constraints.
These frictional loads are supplied through the actuation of the clamping system.
Given that the encapsulation is made of soft materials, such as tin-bismuth alloy, care
must be taken in the selection of the clamping load. The loads must be sufficient to retain
the piece, yet be low enough to avoid plastic deformation of the surfaces. Any plastic
deformation may result in the loss of locational information for the workpiece. The
problem is even more acute due to the possible growth of the error in three dimensions as
the part is rotated to present a new side for machining. Finally, there is concern that such
deformations will introduce errors during the restoration process, as slop in one or more
surfaces is introduced into the system.
The plastic deformation can take place on the asperity and the bulk level. The load
required to cause bulk plastic deformation could be determined directly. However, while
32
it is inevitable that asperities deflect and deform under a load, the significance of this
effect must be examined. In order to control the Encapsulating Fixturing Process, the
amount of elastic versus plastic deformation of the asperities has to be determined. In
addition, the maximum amount of deflection that can be achieved at the asperity level
must be determined. From the examination of these two factors, the potential of asperity
deformation to contribute significantly to the errors of the process was explored.
The theoretical analysis used to analyze the surface roughness is presented in Section 3.1.
Section 3.2 details the experiments used to determine the elastic deformation of
asperities. Section 3.3 shows the experimental results. Section 3.4 examines the asperity
deformation and its error contribution to the Encapsulated Fixturing Process.
3.1.
Theoretical Analysis
In order to gain an understanding of the effects of the surface roughness, one must be
able to characterize the surface in a meaningful way. Section 3.1.1 presents the
calculations used to extract information from a surface roughness trace. Section 3.1.2
presents the analysis on the elastic deformation of an asperity based on Hertzian theory.
This theory covers the behavior of the asperity up until the onset of yield. Section 3.1.3
presents information about the plastic deformation of asperities. The analysis for plastic
deformation is complex and beyond the scope of this thesis. For further information on
the subject, please refer to Whitehouse's Handbook of Surface Metrology.
33
3.1.1. Surface Characterization
The surface roughness of a specimen can be measured via a number of parameters using
a profilometer. The first parameter is the average roughness, or Ra. Equation 3 defines
this parameter.
I y Idx
Ra=
(3)
L f0
where L represents the sampling length, while y is the height of the profile measured
relative to a graphical centerline computed by the profilometer. x is the incremental
distance traversed by the profilometer along the sampling length.
Unfortunately, while the average roughness provides a sense of the scale of roughness
about the centerline, it is not a meaningful measure of roughness. A more useful
parameter is the root mean square average, Rq, which is defined in Equation 4.
Rq = - Y2dX
(4)
S0
Using the square of the profile height to calculate Rq provides an emphasis on the more
pronounced asperities on the surface.
For the purposes of determining the load and the corresponding deflection, it is necessary
to obtain some geometrical information about the asperities. However, the asperities vary
greatly in shape and are very hard to characterize. One approximation is to assume a
34
constant summit curvature, K. Equation 5 can be used to approximate the summit
curvature.
Zi4 - 2zi + zi_1
(5)
h2
where z is the height from the centerline computed by the profilometer. h is the sampling
interval, defined in Equation 6.
L
h =-N
(6)
Equation 7 shows how the root mean squared curvature, or,, is obtained from the summit
curvature.
1/ 2
Si=N
N j=1
The root mean square curvature can be used to approximate the radius of curvature and
used to calculate the asperity deflection [Johnson 85]. Section 3.1.2 describes this
process.
3.1.2. Elastic Deflection using Hertzian Theory
In order to determine the amount of deflection undergone by a surface at the onset of
yield, Hertzian theory for elastic contact between solids of revolution was examined.
Equation 8 defines the mean pressure.
16LE*2
2
P=-P=
3
2
9r3R
35
(8)
where Pm, Po, R, and L are the mean pressure, the maximum pressure, the radius of
curvature and the load respectively.
Rearranging and solving for L yields Equation 9.
3R2
L = (cP
(9)
M)j 4R
4E*
According to Hertzian theory, the deflection can be determined as shown in Equation 10
[Johnson 85].
1
(10)
(16RE*2
By substituting Equation 9 into Equation 10, a direct relationship between the deflection
and the radius of curvature of the asperity is developed. Equation 11 defines this
relationship.
3=-
9
g
16
2
Pm2R
E *2
(11)
Thus, the deflection is a direct function of the radius of curvature. Given that the mean
pressure at the formation of a fully plastic field is approximately three times that of the
yield strength [Ashby 92], Equation 11 can be written in terms of the yield strength as
shown in Equation 12.
81 ,r 2Y 2 R
S ' =-E'
16 E*2
36
(12)
3.1.3. Plastic Deformation of the Asperities
During the plastic deformation process, one would expect the asperities to flow
plastically, filling in the valleys, until perfect contact has been achieved. Thus, the
maximum deflection possible would be half that of the peak to valley depth. However,
beginning with Moore's work in 1948 [Moore 48], followed by others [Greenwood and
Rowe 65, Williamson and Hunt 72], researchers have noted that asperities persist even
under extremely high compressive loads. In some cases, researchers have been able to
measure pressures in compressive tests approaching six times the yield strength and the
asperities still exist [Uppal and Probert 72]. However, this work was carried out on a
single asperity, which may not be a representative result.
The mechanisms that allow asperities to persist under extremely high loads are not fully
understood. Work conducted by Childs supports the theory that the mechanisms can be
explained in terms of plasticity mechanics of asperity interactions [Childs 73]. Based on
experimentation and modeling, real to nominal contact area ratio was found to be a
function of the asperity size distribution. For asperities with a base width between 1 m
and 70Rm, The real to nominal contact area ratio is expected to be in the range of 0.56 to
0.65 or greater, with the lowest limit being 0.5. Perfect contact is unlikely to be achieved
when the clamping load is applied to the encapsulation surface. Therefore, the maximum
possible deflection of the asperities is less than half the peak to valley height postulated
above.
37
3.2.
Experimental Apparatus and Procedure
In order to use the equations in Sections 3.1.1 and 3.1.2, it is necessary to measure certain
surface characteristics. The surface roughness and the summit curvature can be obtained
experimentally through profilometry. Thus, an experiment was necessary to gather this
data for a range of surface roughness. The topographical data can be used to determine
the deflection of a tin-bismuth sample with the same surface characteristics. This
experiment was also used to validate the equipment and the methodology.
3.2.1. Experimental Apparatus
There are two types of instruments that can be used to measure surface roughness: optical
and stylus profilometers. Optical profilometers provide information about a surface by
interpreting the light reflected off the specimen surface. They provide a better resolution
than the stylus profilometer, but can only measure well-characterized surfaces. The
optical profilometer assumes that there are no irregularities such as pits, particles,
scratches, and surface contamination layers. This means that they are unsuitable for use
in manufacturing settings where such disturbances are present. On the other hand, stylus
profilometry requires that no assumptions be made about the sample. It uses a probe that
directly contacts a surface and follows height variations as a sample is moved. The
height variations are converted into electrical signals, thus producing a profile. The
resulting trace represents a cross-sectional view with high vertical and spatial resolution
Since the experimental specimens may have irregularities such as pits, particles,
scratches, and surface contamination, a stylus profilometer was selected for the
38
experiment. A KLA-Tencor P-10 Profilometer was used for measuring the specimens. A
stylus with a 2 gm radius tip was used throughout the measurements. The scanning
speed was set to 20 gm/sec and the sampling rate to 100 Hz. The stylus load was 6 mg.
The test surfaces were provided by electro-formed surface roughness comparison
standards with average roughness of 0.05gm, 0.1 gm, 0.2gm, 0.4gm, 0.8gm, and 1.6gm
respectively. The standards were manufactured by grinding and were taken from a
Fowler-Rubert Composite pocket set No. 52-720-000. The standards are calibrated to
within 10% of the stated nominal values. These standards were selected because most
molds of the type that are used in the Encapsulated Fixturing Process and other die
casting processes are usually machined and/or ground.
3.2.2. Experimental Procedure
The profilometer was first calibrated using a calibration block with a known step height.
Following calibration, each specimen was loaded into the device. A trace of
approximately 1000gm was recorded. The average and root mean square roughness were
calculated by the profilometer. The stylus was then shifted over to the next specimen and
the procedure repeated.
The trace data was entered into Matlab. The average and root mean square roughness
were calculated as a means of comparing the data with the KLA-Tencor values, and the
given values of the standards. The root mean squared curvature was also calculated as
39
-
shown in Equation 7. The curvature was then used to calculate the deflection at the yield
pressure as defined in Equation 12.
3.3.
Surface Characteristics of Typical Machined Surfaces
Figure 12 shows a typical profilometer trace of a surface roughness standard.
20000
(0
15000
E 10000
0
-I
5000
0
I
-5000
-V
-
-10000
-15000
-20000
Data Number
Figure 12: Profilometer trace for a 0.4 Rm surface, with no
wavelength filtering
Table 1 shows the nominal and the calculated values of the surface properties of these
surface roughness standards. The nominal roughness of each standard is shown in the
leftmost column. The average and root mean squared roughness calculated by the
profilometer and through Matlab are shown in the next four columns. This provides a
means of checking the accuracy of the Matlab calculations. From the data, the summit
curvature, r, and the elastic deflection, 8y, were calculated.
40
Table 1: Roughness, summit curvature, and deflection values of the
surface roughness standards
Nominal
Ra (gm)
KLA-Tencor
Ra (jm)
RRMS (gm)
Ra (gm)
RRMS (jim)
'Ks
0.05
0.1
0.2
0.4
0.8
1.6
0.0473
0.079
0.233
0.353
0.673
1.383
0.057
0.096
0.235
0.441
0.620
2.055
0.074
0.140
0.297
0.553
0.789
2.636
37150
51920
58040
115580
112540
157000
3.4.
Discussion
0.060
0.106
0.278
0.442
0.837
1.747
Matlab calculations
(M
I
8
(jim)
0.0138
0.009855
0.008811
0.004428
0.004545
0.003258
The surface roughness given by the profilometer correlates quite well with the nominal
values. On the other hand, the Matlab values conformed well at the smaller roughness,
but diverged as the roughness approached 1.6gm. A major contribution to this variation
is probably the method of integration. The Matlab function trapz approximates the
integral by summing the trapezoidal areas underneath the curve. However, this
methodology is relatively crude and induces a lot of error, especially in ill-behaved
functions such as a profilometer trace. However, although the error may be as large as
25%, it is not significant given the extremely small scale of the geometry.
As expected, the amount of elastic deflection decreased as the surface roughness
increased. The elastic deflection decreased from 0.0138[tm to 0.00326jm as the surface
roughness increased from 0.05 m to 1.6jm. The asperities had negligible deflection
prior to the onset of yield, as expected due to the small surface area. This means that the
asperity deflection is largely plastic in nature. Some indication of the range of plastic
asperity deflection can be obtained from the maximum peak to valley distance. These
41
values, obtained from the KLA-Tencor Profilometer, are given in Table 2. The
calculated elastic deflection is provided as a source for comparison.
Table 2: Peak to valley depth for various surface roughness standards
Ra (gm)
0.05
0.1
0.2
0.4
0.8
1.6
6 (gm)
0.0138
0.009855
0.008811
0.004428
0.004545
0.003258
Peak to Valley Depth (gm)
0.397
0.753
1.528
3.167
4.239
9.680
Although the plastic deflection is expected to be less than half of the peak to valley
height, it is still at least an order of magnitude greater that the calculated elastic
deflection. Therefore, it can be assumed that plastic deformation of the asperities is
inevitable under any load. However, even given the maximum height of asperities and
assuming full crushing, the amount of error caused by the plastic deformation of the
asperities is unlikely to be significant in the Encapsulated Fixturing Process.
The above experimental analysis assumes that the tin-bismuth specimens mirror the mold
surface roughness perfectly. This is not necessarily true because the molding process
may create additional roughness from porosity and other heat or flow related defects.
Chapter 4 examines the factors that will have an impact on the generation of a desired
surface roughness on tin-bismuth specimens.
42
Chapter 4: Generation of Surface Roughness in Casting
The ability to generate a desired surface accurately and reliably is one of the critical
requirements of the 3D Encapsulated Fixturing Process. This process is affected by a
number of factors ranging from material to molding pressure. In this study, eutectic
tin-bismuth was compared against the non-eutectic form of the same alloy. In addition,
the effects of pressure and mold surface finish on the reflected surface of the tin-bismuth
specimens were examined. The aim of these experiments is to determine the process
requirements and parameters needed to generate a surface accurately and reliably. The
experimental results shows that good reflected surface finish can be produced if a
molding pressure of 60 psi or higher and a mold surface roughness of 0.4 gm or smaller
is used.
Section 4.1 presents the experimental apparatus and procedure. Section 4.2 shows the
experimental results. Theses results are discussed in Section 4.3. The conclusions that
can be drawn from the experiment are laid out in Section 4.4.
4.1.
Experimental Apparatus and Procedure
Very few of these questions about surface roughness can be answered by analysis alone.
Even for those that can be answered analytically, information about the geometry of the
surface roughness, such as the root mean square roughness and the surface curvature,
must be obtained experimentally from a profilometer trace. Thus, an experiment was
designed to obtain this information. Section 4.1.1 will review the experimental
apparatus. The experimental procedure will be reviewed in Section 4.1.2.
43
4.1.1. Experimental Apparatus
A mold was made to produce tin-bismuth specimens with varying surface roughness
across a range of pressures. Figure 13 is a picture of this mold.
Figure 13: Mold used to produce experimental specimens
The mold was made of aluminum. It consisted of three parts: body, bottom plate, and top
plate. The mold body held a quick release pressure fitting that was used to pressurize the
mold cavity during the specimen formation. To facilitate specimen removal, the mold
cavity was machined with a three degree tapered end mill. The bottom opening of the
cavity was approximately two square inches in size. The bottom plate of the mold was
designed to hold surface roughness standards from the Gar Electroforming M- 15 Surface
Roughness Standard Set. These standards allowed various mold surface finishes to be
44
tested without the expense of producing multiple molds. Removal of the top plate
allowed access to the mold cavity so that the molten metal could be poured into the mold.
The KLA-Tencor P-10 Profilometer was used to evaluate the surface of the specimens.
4.1.2. Experimental Procedure
The experimental procedure was divided in two parts: specimen production and
profilometry.
To produce each specimen, the appropriate surface roughness insert was cleaned and
placed into the bottom plate and secured to the mold body. The mold was heated to at
least 300 degrees Fahrenheit. Molten tin-bismuth alloy was then poured into the mold.
The top plate was then secured and the mold pressurized to the desired pressure. The
mold was then placed on a cooling block and cooled by low velocity forced air
convection. Once the mold was at approximately 100 degrees Fahrenheit, the top and
bottom plates were removed and the specimen was extracted from the mold. Prior to
producing another specimen, the mold was cleaned.
The specimens were produced at atmospheric pressure and 40 psi, 60 psi, and 80 psi
above atmospheric pressure. For each pressure level, surface roughness standards of
0.1gm, 0.4 pim, 1.6 pm, and 3.2 gm were used. The latter two mold inserts were divided
into three partitions, each of which is a replication of the surface as created by a different
45
manufacturing process. Table 3 is a listing of the samples and the process by which they
were produced.
Table 3 : Description of the surface roughness specimens
Nominal Surface
Roughness (gm)
0.1
0.4
1.6
Machining Process
Grind
Grind
Turn or Shape (Top)
Grind (Middle)
Mill with Periphery
(Bottom)
3.2
Turn or Shape (Top)
End or Face Mill (Middle)
Mill with Periphery
(Bottom)
Each specimen was then placed into the profilometer. Using the settings listed in Section
3.2.1, a 2000 ptm length was scanned. For the rougher specimens with larger features,
scan lengths of 5000 pm to 7000 pm were used. Three profilometry traces were taken
for each specimen. The average roughness, root-mean-squared roughness, and the peak
to valley height were recorded for each trace. The results for each criterion were then
averaged to obtain a value for the surface.
4.2.
Experimental Results
The experimental results showing the comparison between eutectic and non-eutectic alloy
are presented in Section 4.2.1. The effects of pressure and mold surface roughness are
presented in Sections 4.2.2.
46
4.2.1. Eutectic vs. Non Eutectic Tin-Bismuth Alloy
Phase transition properties of the tin-bismuth alloy were not initially considered to be a
factor in determining the surface roughness of the parts. Thus, when experiments were
initially carried out to produce mold surface roughness specimens at different pressures,
non-eutectic alloy was used. However, upon removal from the mold, a scarred pattern
covering 20% to 30% of the surface was discovered. This scarring can be seen in
Figure 14.
Figure 14: Specimen molded with non-eutectic alloy. The left
specimen is molded at atmospheric pressure. The right specimen is
molded at 80 psi.
The scarred pattern was approximately 100 gm deep and persisted in every molding,
regardless of the pressure or the mold surface roughness. This porosity seemed to be
restricted to the surface only. When the specimens were cut open, there was no evidence
of macroporosity anywhere other than the surface of the specimen. When eutectic alloy
was used instead, the scarring pattern disappeared.
47
4.2.2. Pressure and Mold Surface Roughness
The figures presented below show the reflected surface roughness as a function of
pressure and mold surface roughness. The data is presented for a range of pressures, with
the measured mold roughness as a reference. It should be noted that the defects begin
appearing in sizable numbers at 40 psi. The size and number of these defects introduces
a significant amount of error, since the defects are on the order of the maximum scanning
length of the profilometer. This error increases as the molding pressure decreases, since
the number and size of the defects increases. Nevertheless, the experimental 40 psi data
is included in the figures to provide a sense of the impact of defects on the surface
roughness. However, below 40 psi, the data is extrapolated, since the error would be too
great in the experimental measurements. In the figures, both the average and the root
mean squared roughness values are presented.
Figure 15 shows the reflected roughness of the tin-bismuth specimen when molded
against an insert with 0.1 gm nominal roughness.
48
12 10
0
T '
Roughness beyond
profilometer range
Mold R
---
Exp. Ra
-
8
-
-Mold Rq
Exp. Rq
E
5I
.C
6
4
2
a
0
20
60
40
80
Pressure (psi gauge)
Figure 15: Reflected roughness of the tin-bismuth specimen when
molded against an insert with 0.1gm nominal roughness.
Figure 16 presents the reflected roughness data for the insert with 0.4 gm nominal
roughness.
4.54-
Roughness beyond
--- Mold Rn
profifomneter range
--
3.5 -
'.
-
3
Exp. Rn
-Mold Rq
-u-Exp.Rq
2.5 -
.
-
21.5 10.5-
00
20
40
60
80
Pressure (psi gauge)
Figure 16: Reflected roughness of the tin-bismuth specimen when
molded against an insert with 0.4gm nominal roughness.
49
Figure 17 presents the reflected roughness data for the insert with 1.6 gm nominal
roughness.
12
Roughness beyond
10 -
proflometerrange
-
Exp. Ra
vi 8 7
a,
.)
Mold Ru
-
-
-Mold Rq
I-
Exp. Rq
6
4
2
0
0
20
60
40
Pressure (psi gauge)
80
Figure 17: Reflected roughness of the tin-bismuth specimen when
molded against an insert with 1.6gm nominal roughness.
Figure 18 presents the reflected roughness data for the insert with 3.2 [tm nominal
roughness.
14-
Roughness beyond
12
VP
C
0
E.
i
-
10,
a
------- Mold Ra
Exp. Ra
profflometer range
I-.
-
-
-Mold Rq
--
8-
Exp. Rq
6-
.C
420
0
20
40
Pressure (psi gauge)
60
80
Figure 18: Reflected roughness of the tin-bismuth specimen when
molded against an insert with 3.2Rm nominal roughness.
50
Figure 19 presents the peak to valley height, Rt, of all the specimens and inserts.
60
-
501
5S40
---x
Roughessbeyo
sh
#
50
profilonettr
range
-old
Ra=31.6
.-.--- Mold Ra=1.6
Nom. Ra =1.6
-Mold Ra=0.4
-aNomn. Ra =0.4
------- Mold Ra= 0. 1
SNomn. Ra =0.1
-
0
ES 30
Mold Ra= 3.2
Nomn. Ra =3.2
-
.2
-
620
0
10-
0
40
20
60
80
Pressure (psi gauge)
Figure 19: The peak to valley height of all the specimens and inserts.
4.3.
Discussion
As mentioned in 4.2.2, the data was extrapolated for pressures below 40 psi, due to the
large number of defects on these samples. Since the defects were larger than the
maximum profilometer trace, any experimental data obtained for the lower pressures
would not accurately represent the roughness of those specimens, excluding a 3D trace.
The equipment available at MIT is currently not capable of carrying out a 3D trace,
which may provide better information, and external laboratory testing would be very
costly and time consuming. The cost cannot be justified since it is evident that the
parameters that produced these specimens will cause precision errors, even without
further examination of the surface roughness.
51
4.3.1. Effects of Eutectic vs. Non-Eutectic Alloy
The initial hypothesis for the presence of the scarred pattern was that these defects were
due to the presence of contaminants or air bubbles. However, the scarred pattern
persisted in test runs where the mold was vibrated and where the molten tin-bismuth was
stirred in the mold. Thus, it is unlikely that these defects are due to the presence of
contaminants or air bubbles. When eutectic tin-bismuth was used instead, the scarring
disappeared. The current hypothesis is that the surface defects in the non-eutectic
specimens are due to macrosegregation.
Macrosegregation takes places during the phase transition in alloys, when the metal is in
a mushy state. As the alloy solidifies dendritically, there tends to be a transport effect via
convection of the interdendritic liquid in the mushy zone. The heavier solute tends
towards the bottom of the specimen. This can change the strength characteristics of the
encapsulation. It may also be responsible for the formation of the surface porosity that
has been noted. The disappearance of the porosity with the eutectic alloy can be
accounted for by the rapid transition between liquid and solid phases. Therefore, the
eutectic alloy does not have sufficient time to segregate during solidification [Kou 96].
The hypothesis that macrosegregation causes the scarring in the non-eutectic alloy is
tentative and will have to be confirmed by research and experimentation. An alternate
solution may be to vary the cooling rate of the non-eutectic specimen. If the cooling rate
is sufficiently high, the surface porosity may not have the opportunity to form.
52
4.3.2. Effects of Pressure
Based on profilometry data and visual examination of the specimens, pressure is the most
significant factor in determining the reflected surface roughness of the tin-bismuth
samples. At gauge pressures of 60 psi and above, the reflected surface roughness was
quite close to that of the mold inserts. Furthermore, the high pressure minimized both the
number and size of the defects. At 80 psi gauge pressure, there were no defects visible
on the 0.1 [Lm surface. On the 0.4 gm specimen, a small number of defects were detected.
These defects were approximately 750 gm wide and 4 gm deep. When the pressure was
decreased to 60 psi, the defects were only approximately 1500 gm wide and 10 gm deep.
Thus, even at 60 psi, the defects would have a negligible effect on the performance of the
surface. When the pressure dropped below 60 psi, however, the defects became
significant, as seen in Figure 20.
53
Figure 20: Eutectic 0.1 gm specimens. The left specimen was molded
at 80 psi. Note the smudged area due to the thin layer of oxide. The
right specimen was molded at 40 psi. The defects can clearly be seen
in this example.
Figure 20 shows two 0.1 gm specimens. The left specimen was molded at a gauge
pressure of 80 psi, while the right specimen was molded at a gauge pressure of 40 psi.
The smudged pattern seen on the surface of the high pressure specimen seems to be a thin
layer of oxide. Profilometer measurements showed that the oxide layer did not have an
impact on the surface roughness. For the 0.1 gm specimen molded at 40 psi, which is the
surface finish with the best result at that pressure level, the defects are approximately
4000 m wide and 25gm deep. These defects cover at least a third of the specimen
surface.
When one examines the 1.6gm and 3.2gm surfaces shown in Figure 21, the defects cover
the entire surface. This results in an uneven surface with very little load bearing area.
54
Since this may prove to be a significant source of error for the Encapsulated Fixturing
Process, it is recommended that the gauge pressure be set a no less than 60 psi.
Figure 21: Presence of defects on specimens molded at 40 psi on the
left and atmospheric pressure on the right. The surface of the
atmospheric specimen is entirely covered by defects.
4.3.3. Effects of Mold Surface Roughness
The mold surface roughness has less of an impact on the surface finish of the tin-bismuth
sample than the pressure. However, the experiments have shown that it does tend to have
an effect on the repeatability of a surface. This means that the deformation of the
asperities, as outlined in Chapter 4, have an effect-albeit small-on the precision of the
55
process. As shown in Figure 15 and Figure 16, the mold inserts with a lower surface
roughness tend to produce good results across the entire surface.
While a roughness of 0.1 gm is difficult to produce and maintain in practice, surface
roughness of approximately 0.4gm is within the process capability of machining and
grinding processes. This mold roughness, along with a high pressure, will produce a high
quality reflected surface finish, without incurring the cost and fragility of a mold with a
finer surface roughness.
4.4.
Process Limits for Encapsulation Molding
From these experiments, it is clear that the eutectic nature of the tin-bismuth, the
pressure, and the mold surface roughness all have an impact on the surface roughness of
the encapsulation. Based on experimental results, a set of recommended parameters was
generated. Eutectic alloy is recommended for the encapsulation process. An
approximate process window has been generated in Figure 22 to show the tolerable
roughness as a function of the molding pressure.
56
-
3.5
-.-
U,
7
6.
Tolerable Roughnes s
(microns)
3-
0
2.5
-
2 a
1.5 -
Process
Incapable
Process
Capable
0
6.
i
0.5 -
w4
0
0
20
60
40
80
100
Molding Pressure (psi gauge)
Figure 22: The Encapsulated Fixturing System process window
Conservatively, the mold surface roughness should not exceed 0.4[tm. Finally, it is
important to maintain a molding gauge pressure of at least 60 psi in order to minimize the
presence and size of defects.
57
Chapter 5: Conclusion and Future Work
The Encapsulated Fixturing System has the potential to be a universal fixturing system
that can fully locate, secure and support a workpiece, while allowing a great deal of
access for the machine tool and flexibility for the designer. This study examined the
effects of surface roughness on the precision of the 3D Encapsulated Fixturing System.
The results from experimentation and analysis show that, with proper equipment design
and parameter settings, the sensitivity of the system can be minimized. With the use of
eutectic alloy, molding pressure above 60 psi, and a mold surface roughness that does not
exceed 0.4 gm, surface roughness will not be a significant source of error in the
Encapsulated Fixturing System.
Three main areas require future work. First, design and process parameters that may
have an impact on the quality and efficacy of the Encapsulated Fixturing System need to
be identified. Additionally, a series of sensitivity studies need to be carried out in order
to eliminate all factors with negligible impact on the process. For those factors that
remain a threat to the viability of the process, these analyses and experiments will
identify approaches that will minimize the process's sensitivity to these errors. Finally,
prototype systems need to be designed and built to prove the viability of the Encapsulated
Fixturing System.
Section 5.1 covers the identification of process parameters. Section 5.2 outlines the goal
of the sensitivity studies. Finally, Section 5.3 covers the work that needs to be done in
order to validate the Encapsulated Fixturing System.
58
5.1.
Identification of Design and Process Parameters
The proper functioning of the Encapsulated Fixturing System depends on a large number
of interdependent parameters. In order to optimize the design of the equipment and the
process, these parameters, along with their impact on each other, must be identified.
These factors can be identified through the examination of research into similar processes
such as die casting. In addition, experimental results from the 2
D apparatus will aid in
the determination of potential problems with the 3D equipment design. The set of design
and process parameters identified from this research will form the basis for the sensitivity
studies.
There are a number of design parameters that may have a critical effect on the precision
of the system that have come to the forefront during this thesis. These parameters are
focused on the design of the mold, gate plate and machining fixture. For the mold, the
mold surface properties must take into account the thermal properties of the
encapsulation material. The mold walls must be designed so that the reflected surface on
the encapsulation can provide accurate location and alignment. Care must be taken to
address not only the surface roughness, but also to minimize the presence of form error
and waviness. The gate plate must allow for sufficient flow in order to fill the mold
properly. This is especially important during the restoration process as only part of the
inlets can supply new encapsulation material to the machined areas. Finally, the
machining fixture is faced with a number of challenges. It must provide a rigid
connection between the machining center and the encapsulated workpiece. In addition,
precise alignment is required between the fixture and the axis of the machining center.
59
Finally, the fixture must provide sufficient clamping loads to restrain the workpiece
against machining forces without damaging the encapsulation.
In terms of process parameters, there are two main factors that seems to dominate the
process. First, there is the injection pressure. This factor directly affects the injection
velocity, the presence of porosity, and the ability to filled the mold completely. Second,
there is the temperature. The temperature determines the phase transition temperature
range. Additionally, the effect that the cooling rate has on the encapsulation must be
considered.
5.2.
Sensitivity Studies
Once the design and process parameters have been outlined, sensitivity studies are
required to determine the impact of each parameter on the system. These studies will
also aid in the development of strategies to minimize any negative impacts on the
precision of the process. Experiments to test the sensitivity of a number of factors are
outlined below.
5.2.1. Clamping Load
There are two main concerns that arise in determining the desired clamping load. First,
one must determine the load required to secure an encapsulated workpiece against
machining forces. Secondly, an experiment should be carried out to verify that the
analysis laid out in Chapter 3 regarding the significance of asperity deflection is correct.
The effect of the required clamping load on the encapsulation can also be determined.
60
With a tin-bismuth sample secured in a compression testing machine, the deflection as a
function of the load can be established. A profilometer trace will obtain the surface
properties prior to the experiment so that the expected deflection can be determined. For
high-resolution deflection measurements, optical measurement devices such as an optical
interferometer may be required.
5.2.2. Injection Pressure
For the apparatus used in the surface roughness study, static pressure was applied
following the pouring of the alloy into the mold. During the actual encapsulation
process, however, the alloy will be injected under pressure. The rate of change of the
pressure during the casting process will have a direct effect on the injection velocity and,
thus, on the ability to deliver a good quality encapsulation. While this effect may not be
evident in current process since the mold remains heated and pressurized for a long time
after injection, adverse effects may develop as the cooling rate is increased to shorten the
cycle time.
The study of pressure effects can begin with an analysis of the pressurized air supply and
the demands of the injection piston during injection. If the supply does not equal the
demand, the pressure towards the end of injection can decrease in a dramatic fashion.
The larger the mold and the more complex the flow path, the harder it will be to fill the
mold completely. If this is a concern, a pressure transducer may be used to record the
pressure transient in the compressed air line. A possible solution to the problem may be
61
to install an accumulator upstream of the injection piston to supply the demand during
injection.
5.2.3. Cooling Rate
Another factor that needs to be explored is that of the cooling rate. A high cooling rate is
desired to minimize the cycle time of the process. However, the rate of cooling will have
an impact on the microstructure of the encapsulation material. This may be expressed
through variations in the quality of the encapsulation. In addition to the cooling rate, the
direction of solidification may also play a role in the determining the defects present in
the encapsulation
The cooling rate and directional solidification can be tested with immersion baths and
cooling plates applied to a mold. By varying the coolant, be it water, air, or liquid
nitrogen, and the rate of convection, a range of cooling rates can be achieved.
Knowledge about the required cooling rate and direction will permit the optimization of
the encapsulation equipment and process.
5.2.4. Scaling and Encapsulation Stability
The experiments to date have been carried out on small sized samples. However, as one
begins to finalize the requirements of the equipment and process, scaling issues must be
addressed. In particular, it is important to demonstrate that a larger surface, more closely
approaching the six-inch cube envisioned for 3D milling prototype, can be generated
repeatedly to the desired specifications.
62
Also important is the stability of the encapsulation material following molding. Of
particular concern is any change in the dimensions of the encapsulation during the days
following the encapsulation process. If significant changes in dimensions are present,
mitigation strategies will have to be generated to maintain precision throughout the entire
machining process. This issue can be addressed through the molding of a tin-bismuth
specimen and measuring its dimensions at set intervals over several days.
5.3.
Design of the 3D Encapsulated Fixturing System
The study of these and other factors will aid in the definition of the process parameters
and functional requirements of the 3D Encapsulated Fixturing System. These
requirements will be critical in guiding the development of the mold, gate plate and
machining fixture. The understanding developed from the sensitivity studies will aid in
the optimization of the encapsulation process. Finally, the prototype equipment for the
3D Encapsulated Fixturing System must be manufactured and tested to prove the viability
of the new fixturing methodology.
This thesis has determined that surface roughness, with proper precautions, does not
degrade the precision of the Encapsulated Fixturing System in a significant manner.
Further studies are required before all the design and process parameters have been
identified and tested for their impact on system performance. The Encapsulated
Fixturing System has the potential to become a revolutionary universal fixturing system.
By proceeding through the steps outlined above, the viability of the concept can be
proven.
63
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