James Pitts_Thesis_2014

1

Study on the Optimization and Process Modeling

of the Rotary Ultrasonic Machining of Zerodur

Glass-Ceramic

by

JAMES DANIEL PITTS

B.S. (University of California, Davis) 2012

THESIS

Submitted in partial satisfaction of the requirements for the degree of

MASTER OF SCIENCE

in

Mechanical and Aeronautical Engineering

in the

OFFICE OF GRADUATE STUDIES

of the

UNIVERSITY OF CALIFORNIA

DAVIS

Approved:

__________________________________

Kazuo Yamazaki (Chair)

__________________________________

Bahram Ravani

__________________________________

Masakazu Soshi

Committee in Charge

2014

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“Don't be too timid and squeamish about your actions. All life is an experiment. The

more experiments you make the better.” ― Ralph Waldo Emerson

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Abstract

Rotary ultrasonic machining (RUM), a hybrid process combining ultrasonic machining

and diamond grinding, was created to increase material removal rates for the fabrication

of hard and brittle workpieces. The objective of this research was to experimentally

derive empirical equations for the prediction of multiple machined surface roughness

parameters for helically pocketed rotary ultrasonic machined Zerodur glass-ceramic

workpieces by means of a systematic statistical experimental approach.

A Taguchi parametric screening design of experiments was employed to systematically

determine the RUM process parameters with the largest effect on mean surface

roughness. Next empirically determined equations for the seven common surface quality

metrics were developed via Box-Behnken surface response experimental trials. Validation

trials were conducted resulting in predicted and experimental surface roughness in

varying levels of agreement.

The reductions in cutting force and tool wear associated with RUM, reported by previous

researchers, was experimentally verified to also extended to helical pocketing of Zerodur

glass-ceramic.

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Dedication

This thesis is dedicated to my father Danny (1956-2003).

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Acknowledgements

I would like to acknowledge and express my sincere appreciation to the many colleagues,

professors, friends, and family members that have been instrumental in, not only this

research, but the completion of my graduate studies. Firstly, I would like to thank

Professor Kazuo Yamazaki, director of the UC Davis Intelligent Manufacturing and

Mechatronic Laboratory (IMS-M Lab), the Precision Manufacturing Center, and Machine

Tool Technologies Research Foundation (MTTRF) Berkeley Institute. Professor

Yamazaki’s tireless support has provided me with the overwhelming amount of resources

utilized throughout my undergraduate and graduate manufacturing activities.

Professors Bahram Ravani and Masakazu Soshi have given me, as committee members,

advisers, and instructors, countless insights that continue to be instrumental to my course

work, master’s research, and professional life as an engineer.

Dr. Masahiko Mori, whose unyielding support to machine tool education, research, and

development have provided me, and countless other young engineers, the opportunity to

fully realize and expand the capabilities of manufacturing technologies.

I would also like to thank the many past and present members of the UC Davis IMS-M

Lab.

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Table of Contents

Abstract .......................................................................................................................................... iii

Dedication ...................................................................................................................................... iv

Acknowledgements ......................................................................................................................... v

Table of Figures ............................................................................................................................ xii

1 Introduction ............................................................................................................................. 1

1.1 A Brief History of Hard and Brittle Machining .................................................................. 1

1.1.1 Hard and Brittle Material Removal: Birth of Tool Making ........................................ 1

1.1.2 Early Advanced Materials and Sharpening Methods .................................................. 3

1.1.3 Optics in Antiquity ...................................................................................................... 4

1.1.4 Quartz to Manufactured Glass .................................................................................... 5

1.1.5 Increased Accuracy; Automatic Production Methods ................................................. 6

1.1.6 From Perspicillium to Ganymede ............................................................................... 8

1.1.7 From Galileo to Hubble .............................................................................................. 9

1.2 Zerodur Glass-Ceramic ......................................................................................................11

1.2.1 Advanced Properties of Modern Materials ............................................................... 12

1.2.2 Engineering Applications of Zerodur ........................................................................ 12

1.3 Industrial Need for Improved Zerodur Machining ........................................................... 16

1.3.1 Rotary Ultrasonic Machining .................................................................................... 17

1.4 Research Objective ........................................................................................................... 17

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1.4.1 Benefits of This Research ......................................................................................... 18

1.5 Chapter Summary ............................................................................................................. 18

2 Fundamentals of Rotary Ultrasonic Machining .................................................................... 19

2.1 History; From USM to RUM ............................................................................................ 19

2.1.1 History of Ultrasonic Machining .............................................................................. 19

2.1.2 From USM to RUM .................................................................................................. 21

2.1.3 RUM Material Removal Mechanisms ...................................................................... 22

2.1.4 RUM Tooling ............................................................................................................ 25

2.2 Previous RUM Research ................................................................................................... 27

2.2.1 RUM Process Parameters ......................................................................................... 28

2.2.2 RUM Process Outcomes ........................................................................................... 30

2.3 Chapter 2 Summary .......................................................................................................... 31

3 Experimental Methodology .................................................................................................. 32

3.1 Research Overview ........................................................................................................... 32

3.2 Helical Pocketing .............................................................................................................. 33

3.3 Experimental Materials ..................................................................................................... 34

3.3.1 Statistical Modeling and Validation Stock Material ................................................. 36

3.4 Machine Tool and Ultrasonic Systems.............................................................................. 36

3.4.1 US20 Specifications .................................................................................................. 38

3.4.2 Actor® Ultrasonic Tool Holder ................................................................................ 38

3.4.3 Through Spindle Coolant .......................................................................................... 39

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3.5 Fixturing Methods ............................................................................................................. 40

3.5.1 Glass Fixturing Methods ........................................................................................... 43

3.5.2 Wax Fixture ............................................................................................................... 46

3.6 Surface Quality Measurement........................................................................................... 52

3.6.1 Parametric Screening Surface Measurement ............................................................ 52

3.6.2 Statistical Modeling Surface Measurement .............................................................. 52

3.7 Surface Profile Methodology ............................................................................................ 58

3.7.1 Surface Topological Calculation Metrics .................................................................. 62

3.8 Tooling .............................................................................................................................. 66

3.8.1 Tool Length Measurement Method ........................................................................... 67

3.8.2 Tool Dressing Method ............................................................................................... 68

3.9 Toolpath Creation and Strategy ........................................................................................ 70

3.9.1 Helical Pitch .............................................................................................................. 71

3.9.2 CAM Based Toolpath Creation ................................................................................. 75

3.9.3 Statistical Modeling Toolpath ................................................................................... 75

3.10 Ultrasonic Actuation Measurement............................................................................... 77

3.10.1 Ultrasonic Measurement System .......................................................................... 77

3.10.2 Ultrasonic Parametric Tuning ............................................................................... 79

3.11 Cutting Force Measurement .......................................................................................... 80

3.12 Statistical Methods ........................................................................................................ 83

3.12.1 Taguchi Parametric Screening DOE ..................................................................... 83

3.12.2 Box-Behnken Response Surface Modeling DOE ................................................. 84

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3.13 Chapter 3 Summary ...................................................................................................... 85

4 Study and evaluation of Results ............................................................................................ 86

4.1 Taguchi Design Type and Parameters ............................................................................... 86

4.1.1 Experimental Procedure ............................................................................................ 87

4.1.2 Parametric Modeling Results .................................................................................... 89

4.2 Box-Behnken Modeling DOE........................................................................................... 93

4.2.1 Experimental Procedure ............................................................................................ 94

4.2.2 Modeling DOE Experimental Results ...................................................................... 96

4.2.3 Box-Behnken Modeling DOE Conclusions .............................................................116

4.3 Validation Trials ...............................................................................................................116

4.3.1 Arithmetic Average (Ra) ..........................................................................................118

4.3.2 Root Mean Squared (Rq) .........................................................................................119

4.3.3 Mean Height of Profile Irregularities (Rc).............................................................. 120

4.3.4 Maximum Peak (Rp) ............................................................................................... 121

4.3.5 Maximum Valley Depth (Rv) .................................................................................. 122

4.3.6 Average Maximum Profiler Height (Rz) ................................................................ 123

4.3.7 Maximum Height of Profile (Rt) ............................................................................ 124

4.3.8 Validation Trial Summary ....................................................................................... 125

4.4 Tool Wear Experimental Trials ....................................................................................... 125

4.4.1 BK7 Tool Wear Trials ............................................................................................. 126

4.4.2 Zerodur Block Tool Wear Trials ............................................................................. 128

4.5 Ultrasonic Effect on Surface Quality .............................................................................. 130

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4.5.1 Ultrasonic Surface Quality Comparison Results .................................................... 130

4.6 Cutting Force Comparison .............................................................................................. 131

4.6.1 Cutting Force Comparison Results ......................................................................... 132

4.7 Chapter 4 Summary ........................................................................................................ 134

5 Conclusions and Suggested Future Work ........................................................................... 135

5.1 Thesis Overview ............................................................................................................. 135

5.2 Conclusions and Contributions ....................................................................................... 135

5.3 Recommendations for Future Work ................................................................................ 137

6 Reference and Appendices .................................................................................................. 139

Work Sited............................................................................................................................... 139

Appendix A: Sauer Application Interview .............................................................................. 146

6.1.1 Primary .................................................................................................................... 146

6.1.2 Process and Operations ........................................................................................... 147

6.1.3 Equipment ............................................................................................................... 148

6.1.4 Logistics .................................................................................................................. 148

Appendix B: Tool Length Measurement Method Validation Data ......................................... 149

Appendix C: Tool Dressing Method Validation Data ............................................................. 153

Appendix D: Taguchi and Box-Behnken DOE Matrices ........................................................ 156

Appendix E: Taguchi Parametric Screening Data ................................................................... 158

Appendix F: Box-Behnken Modeling DOE Data .................................................................. 159

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Appendix G: Validation Trial Experimental Data .................................................................. 161

Appendix H: Tool Wear Experimental Data ........................................................................... 164

Appendix I: Ultrasonic Frequency and Amplitude Measurement Trials ................................ 166

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Table of Figures

Figure 1: Impact-Based Lithic Reduction ....................................................................................... 2

Figure 2: Hertzian Cone crack in glass [4] ..................................................................................... 3

Figure 3: Piano-convex crystal lens. Archaeological Museum, Herakleion [7] ............................. 5

Figure 4: Proposed Method of Ancient Lens Fabrication ............................................................... 7

Figure 5: Mounted Objective Lens of Galileo’s Telescope ............................................................. 9

Figure 6: Southern Africa Large Telescope ...................................................................................11

Figure 7: Ultra-Lightweight Zerodur Optical Support; Schott AG ............................................... 14

Figure 8: Zerodur Gyroscope Housing, IMTS 2014 DMG MORI Ultrasonic Demo .................. 15

Figure 9: Schematic of USM Process ........................................................................................... 20

Figure 10: Initial RUM Prototype; Legge 1964 [35] .................................................................... 21

Figure 11: RUM Tool Actuation Diagram .................................................................................... 22

Figure 12: Example of Hammering in RUM ................................................................................ 23

Figure 13: Example of Abrasion in RUM ..................................................................................... 24

Figure 14: Schematic View of Coolant-Base Abrasive Follow .................................................... 25

Figure 15: Common RUM Tools .................................................................................................. 25

Figure 16: Electroplated Diamond Tools ...................................................................................... 27

Figure 17: Primary Experimental Fixturing CAD Rendering ...................................................... 32

Figure 18: Helical Milling Diagram ............................................................................................. 34

Figure 19: Zerodur Block.............................................................................................................. 35

Figure 20: BK7 Optical Glass Block ............................................................................................ 35

Figure 21: Experimental Workpiece, Zerodur Optical Blank ....................................................... 36

Figure 22: Sauer Ultrasonic 20 linear ........................................................................................... 37

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Figure 23: Actor Ultrasonic Toolholder ........................................................................................ 39

Figure 24: Actor Ultrasonic Toolholder Internal Coolant Input ................................................... 40

Figure 25: Zerodur Experimental Stock Material Fixturing Example .......................................... 40

Figure 26: Kistler 9257B Schematic [68] ..................................................................................... 41

Figure 27: Erowa Chuck; ER-029313 [69] ................................................................................... 42

Figure 28: Exploded View of Experimental Work Holding Assembly ......................................... 43

Figure 29: Gem Stone Dopping Wax Fixturing Example ............................................................. 44

Figure 30: Fixturing Wax and Heating Plate ................................................................................ 44

Figure 31: Stock Preperation Via Digital Oven ............................................................................ 45

Figure 32: Zerodur Stock Materials Preperation Via Digital Hotplate ......................................... 46

Figure 33: Experimental Fixture Schematic Drawing .................................................................. 46

Figure 34: Sodick AQ327L WEDM and Work Area .................................................................... 47

Figure 35: Sodick MC430L 3-Axis High Speed Machining Center ............................................. 48

Figure 36: First 12 Sandblasted Wax Fixtures .............................................................................. 49

Figure 37: Backside Milling Results............................................................................................. 50

Figure 38: Polished Results .......................................................................................................... 50

Figure 39: Centering Fixture Example ......................................................................................... 51

Figure 40: Centering Fixture Schematic ....................................................................................... 51

Figure 41: Surface Roughness Measurement System ................................................................... 52

Figure 42:Machined Surface Measurement System ..................................................................... 53

Figure 43: Typical Autofucus System [71] ................................................................................... 54

Figure 44: PAI Measurement Example ......................................................................................... 54

Figure 45: PAI System Diagram ................................................................................................... 55

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Figure 46: Mitaka MLP2 Measurement System ........................................................................... 56

Figure 47: Mitaka Measurement Fixture ...................................................................................... 57

Figure 48: Centering Macro Output, MMap ................................................................................. 58

Figure 49: Raw Surface Profile..................................................................................................... 59

Figure 50: Extracted Profile Section ............................................................................................. 60

Figure 51: Least Squares Leveled Section .................................................................................... 61

Figure 52: Measuremnt Identity Card ........................................................................................... 61

Figure 53: Calculated Surface Parameters ................................................................................... 62

Figure 54: Ra Example [74] .......................................................................................................... 63

Figure 55: Rq Example [74] ......................................................................................................... 63

Figure 56: Rc Example [74] .......................................................................................................... 64

Figure 57: Rp Example [74] ......................................................................................................... 64

Figure 58: Rv Example [74] ......................................................................................................... 65

Figure 59: Rz Example [74] .......................................................................................................... 65

Figure 60: Rt Example [74] .......................................................................................................... 66

Figure 61: Experimental Tools ...................................................................................................... 67

Figure 62: Renishaw NC4 Tx [75] ................................................................................................ 68

Figure 63: Manual Diamond Tool Dressing ................................................................................. 69

Figure 64: Custom Experimental Dressing Fixture ...................................................................... 69

Figure 65: Radius and Pitch of Helix; Adapted from [77] ............................................................ 71

Figure 66: Pilot Study Workpiece Setup and Pocketing Results .................................................. 72

Figure 67: Machined Result Inspection ........................................................................................ 73

Figure 68: Result of Excessive Helical Pitch ................................................................................ 73

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Figure 69: New 6mm D107 Diamond Endmill............................................................................. 74

Figure 70: Used 6mm D107 Diamond Endmill ............................................................................ 74

Figure 71: Pilot Study 2 Toolpath Organization ........................................................................... 75

Figure 72: Example Statistical Modeling NC Code ..................................................................... 76

Figure 73: Polytec NLV-2500 Laser Vibrometer .......................................................................... 77

Figure 74: System Working Principle Diagram [78] .................................................................... 78

Figure 75: Tool Amplitude and Frequency Measurement System ................................................ 78

Figure 76: Manual Ultrasonic Parameter Determination Method ................................................ 80

Figure 77: Kistler Cutting Force Measurement Setup .................................................................. 81

Figure 78: 9257B Force Measurement Convention [68] .............................................................. 82

Figure 79: Taguchi DOE Experimental Trial Flowchart ............................................................... 88

Figure 80: Parmtric Screnining Pockets, Sample 1 of 2 ............................................................... 88

Figure 81: Mean Effects Plot of Means ........................................................................................ 90

Figure 82: Interaction Plot of Means ............................................................................................ 91

Figure 83: Main Effects Plot of Standard Deviations ................................................................... 92

Figure 84: Interaction Plot of Standard Deviations ...................................................................... 93

Figure 85: Prepared Experimental Stock Materials ...................................................................... 95

Figure 86: Box-Behnken DOE Experimental Trial Flowchart ..................................................... 96

Figure 87: Experimentally Machined Zerodur Pockets ................................................................ 97

Figure 88: Main Effects Plot for Ra ............................................................................................ 100

Figure 89: Contour Plot of Ra ..................................................................................................... 100

Figure 90: Response Surface Plot Ra .......................................................................................... 101

Figure 91: Main Effects Plot for Rq ........................................................................................... 102

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Figure 92: Interactions Plot of Rq Predictive Model .................................................................. 102

Figure 93: Contour Plot of Rq .................................................................................................... 103

Figure 94: Response Surface Plot Rq: ........................................................................................ 103

Figure 95: Main Effects Plot for Rc ............................................................................................ 104

Figure 96: Interactions Plot of Rc Predictive Model .................................................................. 105

Figure 97: Contour Plot of Rc ..................................................................................................... 105

Figure 98: Response Surface Plot Rc .......................................................................................... 106

Figure 99: Main Effects Plot for Rp ........................................................................................... 107

Figure 100: Contour Plot of Rp .................................................................................................. 107

Figure 101: Response Surface Plot of Rp ................................................................................... 108

Figure 102: Main Effects Plot for Rv ......................................................................................... 109

Figure 103: Interactions Plot of Rv Predictive Model ................................................................ 109

Figure 104: Contour Plot of Rv ...................................................................................................110

Figure 105: Response Surface Plot Rv ........................................................................................110

Figure 106: Main Effects Plot for Rz ........................................................................................... 111

Figure 107: Interactions Plot of Rz Predictive Model .................................................................112

Figure 108: Contour Plot of Rv ...................................................................................................112

Figure 109: Response Surface Plot Rz.........................................................................................113

Figure 110: Main Effects Plot for Rt............................................................................................114

Figure 111: Interactions Plot of Rt Predictive Model ..................................................................114

Figure 112: Contour Plot of Rt ....................................................................................................115

Figure 113: Response Surface Plot Rt .........................................................................................115

Figure 114: Ra Validation Trial Results .......................................................................................118

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Figure 115: Rq Validation Trial Results .......................................................................................119

Figure 116: Rc Validation Trial Results ...................................................................................... 120

Figure 117: Rp Validation Trial Results ...................................................................................... 121

Figure 118: Rv Validation Trial Results ...................................................................................... 122

Figure 119: Rz Validation Trial Results ...................................................................................... 123

Figure 120: Rt Validation Trial Results ...................................................................................... 124

Figure 121: Compared Parametric Model Accuracy by Regime ................................................ 125

Figure 122: BK7 Tool Wear Experimental Trial Flowchart ........................................................ 126

Figure 123: Compared Tool Wear with Material Removal ......................................................... 128

Figure 124: Zerodur Tool Wear vs. Material Removal (US On/Off) .......................................... 129

Figure 125: Surface Roughness Parameters Compared (US On/Off) ........................................ 131

Figure 126: Zerodur Tool Wear Experimental Trial Flowchart .................................................. 132

Figure 127: Average Cutting Forces Compared .......................................................................... 133

Figure 128: Max Cutting Forces Compared ............................................................................... 133

Figure 129: Laser Measurement Trial Results Summary ........................................................... 150

Figure 130: Hieght Gage Trial Results Summary ....................................................................... 151

Figure 131: Tool Length Measurement Methods Compared ...................................................... 152

Figure 132: Tool Length Reduction With Dressing Operations ................................................. 154

Figure 133: Dressing Trial Results Summary ............................................................................. 154

Figure 134: Dressing Process Cycle Time .................................................................................. 155

Figure 135: Ultrasonic Amplitude with Frequency .................................................................... 167

Figure 136: Tool Amplitude with Frequency .............................................................................. 168

Figure 137: Average Tool Amplitude vs. Percent Amplitude ..................................................... 169

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Figure 138: easySONIC Gage Study Report .............................................................................. 170

1

1 Introduction

The following chapter provides an introduction to the history, materials, and applications

of hard and brittle machining. From this starting point the objectives and possible benefits

of this research are presented.

1.1 A Brief History of Hard and Brittle Machining

It is easy for a modern observer to discount the current state of technological

sophistication as isolated from those of antiquity, however, recent archeological

discoveries provide new insights into the origins of all current manufacturing processes

and advanced hard and brittle material applications. The following subsections are

provided to explain the essential benefits to the entirety of human existence made

possible by advanced materials and their applications.

1.1.1 Hard and Brittle Material Removal: Birth of Tool Making

Hard and brittle materials have been sought after and utilized throughout human history

due to their superior characteristics and abundance. For the overwhelming majority of

mankind’s existence, hard and brittle materials have been essential to survival [1].

Naturally occurring solid aggregates, mineraloids, and volcanic glasses served as the

starting points for all cutting and shaping processes as well as base work-piece materials.

Thus far, the oldest reliably dated examples of stone tools, known as the Odowan toolkit,

were created 2.6 million years ago [2], [3]. Current research has provided evidence of

early humanity’s astounding level of process complexity with respect to tool making and

item construction. Percussive and other pressure-based reduction techniques, commonly

2

referred to as knapping, served as an efficient means for shaping hard and brittle

materials.

Figure 1: Impact-Based Lithic Reduction

Knapping is a means of lithic reduction in which controlled fracturing of a hard and

brittle workpiece’s surface in order to remove unwanted material or to create usage

flakes. As seen in

Figure 1, the removed material, known as the flake, is extracted from the core material.

Generally, localized fractures created during the knapping process is initiated through the

use of an impacter or pressure-based hand tool possessing suitable levels of hardness and

fracture toughness.

Due to their razor-sharp cutting edges, flakes were initially removed from flint, chert, and

other conchoidal fracturing materials for use as simple cutting tools [2]. The exact

physical principle of conchoidal fracture is not fully described and therefore relies on

3

empirically determined norms. Conchoidal fracturing typically refers to the phenomenon

producing Hertzian cone cracks. First described by the German physicist Heinrich Rudolf

Hertz, as a result of his investigation of wave-front propagation through various media,

Hertzian cone cracks leave visible bulbs of percussion on the fracture plane by means of

a force propagated through a brittle,

Figure 2: Hertzian Cone crack in glass [4]

amorphous, or cryptocrystalline solid [5]. The applied force thereby enables full or partial

removal of the cone material, producing the structures seen in Figure 2.

Although highly effective for bulk material removal, early percussion-based shaping

technologies could not produce finely controlled cutting edges. Larger tools such as hand

axes were produced through the removal of successive exterior flakes in order to create a

core element possessing the required shape. Under prolonged usage the cutting edges of

these early axes would be removed by fracturing and the axe would either need to be re-

knapped or discarded.

1.1.2 Early Advanced Materials and Sharpening Methods

As seen in the modern manufacturing industry, early man sought out advanced materials

and processes in order to produce weapons, tooling, structures, and ornamental objects.

The limitations of flint and other widely available hard and brittle materials lead early

4

toolmakers to seek out more advanced cutting tool substrates and stock materials. One of

the most highly praised Stone Age materials was obsidian, a naturally occurring volcanic

glass formed when extrusive igneous rock is rapidly cooled to form a hard and brittle

material of amorphous structure.

Like standard stone tool base materials, obsidian fractures conchoidaly but with no

preferred planes of weakness and could therefore be readily shaped by well-established

knapping methods. Obsidian is still to this day highly prized for its ability take a highly

sharpened edge. Recent investigation into obsidian-based cutting has produced cutting

blades sharper than those possible with steel; however, edge sharpness cannot be retained

as well as steel blades. Early stone and glass tools required repeated sharpening.

Motivated by this need for the maintenance and repair of tool cutting edges, early tool

users established re-sharpening techniques. In its most simple form, early tool users could

simply rub their tools on gritty rocks in order to re-sharpen them. This basic form of

material removal can be considered early grinding [6]. Grinding is the commonly

accepted name for a machining process in which hard abrasive particles are utilized as the

cutting medium. As today, grinding techniques were heavily relied upon in the re-

sharpening of tooling and the production of finely polished hard and brittle objects.

1.1.3 Optics in Antiquity

The first lenses were created in the Near East or Eastern Mediterranean [7]. Recent

archeological findings have proven that at least 3,500 years ago the Minoan era occupants

of the Greek island of Crete possessed the ability to create basic magnification with

quartz optics. Two single crystal quarts lens measuring 15 and 8 mm in diameter and

dating to the Archaic Greek period were discovered during a 1983 excavation of a cave in

5

central Crete and are known as the Idaean Cave lenses. These lens are considered in

context with other lenses found in the Palace of Knossos dating from 1400 B.C. [8]. The

larger of the two, seen in Figure 3, has the ability to magnify clearly up to seven times.

Albeit with considerable distortion, magnification of up to twenty times is also possible.

The need for quality optics was not simply limited to magnification. So called burning-

glasses were produced to start fires with sun light by around 3500 B.C. [7].

Figure 3: Piano-convex crystal lens. Archaeological Museum, Herakleion [7]

These ancient lenses likely had far greater capabilities than demonstrated by the surviving

examples. Chemical analysis of the surrounding shows that chemical etching may have

diminished the surface quality of the lenses during their extended burial.

1.1.4 Quartz to Manufactured Glass

Today we think of glass as the natural material of choice for the production of optics but

this is not the case. With an index of refraction of 1.54, crystal quartz is a better material

6

for lenses than common glass at only 1.46. [8]. Quartz is an abundant mineral in the

Earth’s continental crust; however, naturally occurring high quality single crystals, large

enough to be fashioned into lenses are exceedingly difficult to find in quantities required

for any level of mass production. The scarcity of high quality crystal helped to motivate

the invention of glass manufacturing.

The earliest evidence of the manufacture of glass dates back to at least Egyptian times,

but it was 1st century A.D. Romans who first manufactured glass objects at a large

enough scale to enable the use of glass for common household items [7], [9]. In early

1854 archeological excavations, in the Roman city of Pompeii, uncovered a 65mm

diameter glass lens along with several polished stones it what was termed “The House of

the Engraver” [9]. It stands to reason that for trades responsible for the creation of small

and intricately featured products, in which many years of training and practice are

required to become a practicing master craftsman and instructor, would more than outlast

the normal time span of optimal human vision. The demand for precision and accuracy at

small scale in trades such as engraving and gem cutting are commonly agreed upon as a

source for the development of optical magnification solutions.

1.1.5 Increased Accuracy; Automatic Production Methods

The optical elements previously discussed possessed relatively good optical quality, and

provided evidence of the utilization of abrasive machining techniques dating back several

millennia. Although there is some evidence of primitive lathes being used during their

manufacture, these ancient lenses were still reliant on manual shaping methods in their

construction and therefore likely suffered from protracted production times, limited

repeatability, and low quality. Evidence of geometric deficiencies due to manual grinding

7

methods can be seen in the Idaean Cave lenses. Both lenses have what has been

interpreted as deep cutter marks on their perimeters. These errors in manufacture are in

part responsible for the reduction of totally clear magnification found above seven times.

The manufacture of early optical products required only simple machines. Turning is one

of the most basic machining processes in which material removal is achieved the use of a

stationary cutter acting upon a rotating workpiece. The origin of turning dates back to the

ancient Egyptians around 1300 BCE with the invention of the two-person lathe, as seen

in Figure 4.

Adapted From [10] Figure 4: Proposed Method of Ancient Lens Fabrication

S. Kalpakjian and S. R. Schmid, the authors of the authoritative paper in the subject,

describe the process early optics makers could have utilized to produce lens like those

found in the Idaean Cave as follows:

“An approximately shaped blank having the desired curvature is first mounted on

the end of the shaft with sealing wax. Using an abrasive medium on the surface of

the blank, the end of a round, hollow, cylindrical metal or wooden rod is held in

8

contact with the surface, continuously rotated about its axis, and moved over the

surface. An alternative method would be to rotate the tube rapidly with a bow

drill and rotate the axle slowly by hand. These methods generate perfectly

spherical surfaces if continued until the entire surface contacts the end of the

tube. [10]”

With these primary methods, device makers helped to empower great advancements in

science made during the European Renaissance, between the 14th and 17th centuries

throughout Europe.

1.1.6 From Perspicillium to Ganymede

In the summer of 1609, Galileo Galilei (1564-1642), the Italian physicist, astronomer,

mathematician, philosopher, and engineer visited Venice. Venice, and the neighboring

island of Murano was Galileo’s early source for polished optics [11], [12]. During his

time in Venice, Galileo became fascinated by the new invention of a Dutch spectacle-

maker by the name of Hans Lippershey [13]. Lippershey called his invention the

perspicillium which consisted of a tube capped at each end by polished glass lenses.

Galileo quickly recreated a perspicillium with ten times the magnification of

Lippershey’s device and renamed it the telescope.

Equipped with his telescope, Galileo went on to make some of the greatest discoveries in

observational astronomy. He is credited with the discovery of Jupiter’s moons, also

known as the Galilean moons: Io, Europa, Ganymede, and Calisto [11]. On display at the

Istituto e Museo di Storia della Scienza is one of Galileo’s original lens, as seen in Figure

9

5. The 38mm objective lens is now cracked, but it was used to make many observations

from 1609-1610.

Taken at the Istituto e Museo di Storia della Scienza Florence Italy 2012

Figure 5: Mounted Objective Lens of Galileo’s Telescope

1.1.7 From Galileo to Hubble

The telescope is often considered to be one of the prototypical scientific instruments[14].

It wasn’t until the invention of optical instruments, in the late European Renaissance, that

the fog of thousands of years of conjecture and dogma could begin to be cleared allowing

humankind’s understanding of the universe and its position in it to be realized.

Throughout countless iterative improvements, optical systems have continued to prove

their preeminent position as scientific instruments.

10

Humankind ceaselessly endeavors to expand its sight outward. This expansion of

capability has required the creation of ever increasing telescope sizes. A common saying

in astronomy is that size does matter. Galileo’s simple 38 mm objective lens has evolved

over the course of 400 plus years into truly gigantic segmented reflecting telescopes, the

largest of which measures 10.4 m in diameter. Magnification is often cited as a

telescope’s primary specification; however, as we attempt to observe objects farther and

fainter than ever before, telescope size continues to increase due to the fact that the larger

the telescope the greater the amount of light it can collect. In order to find ever distant

and fainter objects require the creation of larger and larger telescope mirrors. Like the

lens before them, modern telescope mirrors require ultra-precision hard and brittle

manufacturing techniques to achieve near flawless image creation.

Due to the fact the current mirror construction methods limit monolithic construction to

approximately 8 m in diameter, most large telescopes rely on multiple mirror segments

combined in such a way as to act as a single mirror surface [15]–[17].

11

Source: http://salt.camk.edu.pl/firstlight/salt9.jpg

Figure 6: Southern Africa Large Telescope

Figure 6 depicts the segmented main mirror of the 9.2 meter Southern Africa Large

Telescope (SALT). SALT consists of 91 identical hexagonal mirrors each of which

measure 1 meter in diameter. Manufactures of optical systems and the material sciences

have had to continually improve in order to produce the extreme size and precision of

modern telescopes and related systems.

1.2 Zerodur Glass-Ceramic

Zerodur glass-ceramic is a lithium aluminosilicate glass-ceramic developed by Schott AG

(Schott AG, Mainz, Germany) to have a remarkably low coefficient of expansion

(±0.007E−7/K). Composed of 70 to 78% high-quartz micro-crystallites from 30 to 50

(nm) in size, Zerodur has both an amorphous and a crystalline component [18]. When

subjected to heat, the quartz micro-crystals contract and the glass components expand

[16]. When the mixture of quartz, glass, and other minor components is carefully

http://en.wikipedia.org/wiki/Amorphous

http://en.wikipedia.org/wiki/Crystalline

12

balanced during production, thermal expansion can be finely tuned. By controlling

thermal effects at the materials level, the need for peripheral thermal control systems or

design considerations in significantly decreased

1.2.1 Advanced Properties of Modern Materials

Due to their superior materials properties such as customizable thermal coefficients of

expansion, chemical stability, high internal quality, high wear resistance under high

temperature, etc., advanced glass-ceramics are supplanting more traditional materials in

critical industrial, scientific, and aerospace applications [19]–[23]. Regrettably, the very

same superior characteristics that make advanced ceramics ideal for many advanced

applications often result in their relatively low machinability and therefore lead to

increased machining costs compared to more traditional engineering materials [22], [24]–

[26].

1.2.2 Engineering Applications of Zerodur

The extraordinary thermal expansion properties and ability to be produced in large

batches make Zerodur an ideal substrate material for a large number of extreme precision

optical and scientific instruments. This propensity for application is best summarized as

follows:

Most applications take advantage of the negligibly small coefficient of thermal

expansion and its homogeneity over the entire volume. This property provides for

stability in shape and volume if the piece is exposed to temperature changes and

temperature gradients. This behavior is a requirement, in particular, for mirror

13

substrates in precision reflective optics supports, frames, or scales and gauges.

[27]”

1.2.2.1 Telescope Mirror Substrates

For the more than 400 years since their invention, telescopes of ever increasing sizes and

capabilities continued to be created in an effort to see farther and clearer than humankind

has before [15]. Significant improvements in the material sciences and production fields

have enabled modern glasses and glass-ceramics to further enhance the scope and

performance of many devices in the optical, aerospace, and precision manufacturing

industries.

The object seen in Figure 7 is an optical support structure made of a single piece of

Zerodur approximately 1.2 meters in diameter. The unique design of this work piece is

due to the need for extremely light weight, and stiff structures. The process by which a

component’s mass is reduced to a minimum is referred to as light weighting. In this

process, the maximum amount of material is removed while maintaining structural

stability. This optimized structure requires an extensive amount of material to be

removed resulting in extended cycle times.

These protracted operations, in turn, result in extremely high operational costs for

manufacturers. Unfortunately, the very process of machining these delicate structures,

through the cutting forces generated, can cause critical fracture and therefore total loss of

the work piece. This fragility requires that process parameters be effectively managed to

14

mitigate the threat of critical fracture and reduce the occurrence of defects in brittle work

pieces [28].

Figure 7: Ultra-Lightweight Zerodur Optical Support; Schott AG

1.2.2.2 Aerospace Avionics

In many modern aerospace applications, gyroscopes are highly critical elements required

for the determination of a body’s inertial reference and therefore making precise position

measurements possible. Typically, to help ensure safe operation, the 3-D-position of an

air or spacecraft is determined through the use of a minimum of three gyroscopes.

Reliable pitch and yaw measurement is critical for safe flight, thus all modern aircraft

utilize gyroscope-based attitude indicators to provide highly accurate and precise

methods of orientation measurement. Although all planes are equipped with compasses,

gyroscope-based heading indicators provide a reliable means of measuring an aircraft’s

15

direction in situations such as acceleration or turning. Minute changes in a gyroscope

positioning can greatly affect its accuracy. The use of Zerodur as a base material helps to

minimize thermal expansion effects on gyroscope accuracy and precision.

Figure 8: Zerodur Gyroscope Housing, IMTS 2014 DMG MORI Ultrasonic Demo

Figure 8 is an example of a Zerodur gyroscope body created as a machining

demonstration by DMG MORI for the 2014 International Manufacturing Technology

Show (IMTS). With its near-zero coefficient of thermal expansion, Zerodur is uniquely

suited to outperform traditional materials in the “challenging demands with respect to

temperature and pressure resistance.”[29]

1.2.2.3 Semiconductor Fabrication

Modern semiconductor fabrication and the ever advancing computational capabilities it

enables, depends on the effective resolution of micro-lithographic processes. In micro-

lithographics the desired semiconductor structures are projected onto silicon wafers in

order to expose lithograph chemical reactions responsible for the construction of

16

microchip element constriction. Zerodur mirrors are routinely relied upon to produce

resolution capabilities of 500 line pairs per mm allowing resolution of line widths of

approximately 1µm [27]. This method has reached wide-spread utilization, as can be seen

at the Japanese camera companies Cannon and Nikon, where Zerodur-based micro-

lithographic systems are commonly relied upon.

1.3 Industrial Need for Improved Zerodur Machining

Glass ceramics have traditionally been machined using various grinding methods. For

extreme precision applications, basic grinding processes require excessive tool

maintenance and decreased material removal rates (MRR) to ensure dimensional

tolerance, reduce the occurrence of critical fracture, and optimize surface quality

resulting in relatively low productivity and protracted production times. Additionally,

basic grinding methods suffer from limited work piece complexities and therefore may

require multiple work piece setups and fixturing solutions. These limitations necessitate

larger capital, labor, and tooling costs, resulting in much greater overall machining costs.

The “cost of machining can be as high as 90% of the total cost” for many hard and brittle

high precision workpieces [30].

The limited machinability of many hard and brittle materials provide a powerful incentive

to the development of manufacturing processes that minimize production time and cost.

Casting and other net shaping techniques can be employed; however the lead time for

model and form creation limit process flexibility and require extensive capital

investments that may not be suitable for small batch manufacturing. Additionally, for

extreme precision components, net shaping methods often do not produce the required

17

surface quality or dimensional tolerance dictating the need for some level of finishing

operations.

1.3.1 Rotary Ultrasonic Machining

Rotary ultrasonic machining (RUM) is a hybrid machining process combining ultrasonic

machining (USM) with diamond impregnated grinding. When coupled with the dexterity

of modern 5-axis machining centers, RUM has recently matured into a robust and

effective method of producing complex machined features in materials that were

previously considered too costly to utilize.

RUM operational parameters like vibration frequency, amplitude, feed rate, and spindle

speed, have only recently been experimentally investigated and are, as of yet, not fully

understood. Thus far, there are only a limited amount of publications utilizing the most

recent RUM machines. The advanced capabilities of modern RUM machine tools further

compound the need for improved process knowledge. The application of RUM to provide

optimized surface quality and MRR is of primary concern throughout this research.

1.4 Research Objective

The objective of this research was to twofold:

Primary: experimentally derive empirical models for the prediction of machined surface

roughness parameters for RUM helically milled Zerodur glass-ceramic pockets by means

of a systematic statistical experimental approach.

Secondary: To experimentally investigate and quantify possible reductions in cutting

force and tool wear associated in the helical pocketing of Zerodur glass-ceramic.

18

1.4.1 Benefits of This Research

This work will provide effective RUM strategies to improve the machined surface quality

of Zerodur glass-ceramic workpieces while maintaining a high material removal rate.

Secondarily, this research will advise the design and implementation of future RUM

manufacturing operations in both industrial and academic settings. An expanded ability to

precisely predict and manipulate the surface roughness will allow for an expanded use of

RUM.

1.5 Chapter Summary

In order to develop a more comprehensive understanding of a manufacturing process, it is

often necessary to possess a more than cursory grasp of its history and founding

principles. The purpose of this chapter is to provide both the historical prospective and

contemporary requirements that make Zerodur glass ceramic components integral parts of

many extreme precision engineering applications.

The need for improved methods for the machining of Zerodur and other similar hard and

brittle materials was presented; the remaining sections of this chapter outlined the

objectives and benefits of this research.

19

2 Fundamentals of Rotary Ultrasonic Machining

2.1 History; From USM to RUM

This section provides a general overview of the hard and brittle machining techniques

that superseded the invention of RUM.

2.1.1 History of Ultrasonic Machining

Ultrasonic machining (USM) is an early method of shaping hard and brittle materials, and

is widely considered the most frequently used method [23], [31]. R. W. Wood and A. L.

Loomis are credited with the first work on high powered piezoelectric ultrasonic

oscillators in 1927 [26], [31]–[33]. First patented in 1945 by members of the Cavitron

Corporation, USM provided a means by which hard and brittle materials could be

machined into complex geometries not readily possible with conventional methods [34].

As seen in Figure 9, material is removed primarily by the hammering action of a high-

frequency, low-amplitude oscillating metallic tool in conjunction with abrasive slurry.

Typically suspended in an aqueous solution, abrasives are pumped between the tool and

workpiece, resulting in material removal by brittle fracture.

20

Figure 9: Schematic of USM Process

2.1.1.1 Review of USM Advantages and Disadvantages

The following subsection provides a general overview of the advantages and

disadvantages of USM utilization over traditional machining methods such as grinding

and drilling.

Advantages of USM

Complex freeform features in brittle materials can be machined with a single tool.

USM does not require workpiece conductivity.

No heat affected zones have been found resulting from USM.

No chemical or electrical change to a workpiece’s surface.

Disadvantages of USM

Low relative material removal rate.

High tool wear due to slurry and tool surface interaction.

USM is not suitable for deep hole creation; depth to diameter ratio is limited to about

3:1.

Diminished edge accuracies due to unwanted slurry-wall interaction.

21

2.1.2 From USM to RUM

RUM was initially invented in order to overcome the disadvantages of USM on the

machining of deep holes in uranium glasses and other hard and brittle materials. Percy

Legge of the Harwell U.K. Atomic Energy Authority developed the RUM process in

which no slurry is required [35]. Figure 10 is an image of Legge’s prototype machine.

One of the main motivations for the development of RUM was the mitigation of lengthy

process times in the creation of nuclear glasses utilized in the atomic energy sector [12],

[13]. Experimental results have shown that the machining rate obtained from RUM is

about 10 times higher than that from USM under similar conditions [19].

Figure 10: Initial RUM Prototype; Legge 1964 [35]

22

The invention of RUM enabled improved surface quality, hole accuracy, lower tool

pressures, and increased capability to machine deep holes [23], [31], [36], [37]. RUM is a

hybrid process combining USM-like tool vibration and diamond-impregnated tooling.

Tool vibration frequencies greater than 20 kHz, in conjunction with spindle rotation, are

typically utilized. Oscillation amplitudes are typically in the range of 5-10µm. Figure 11

illustrates the combination of axial ultrasonic and rotary movement present in RUM and

their respective zones of primary material removal.

Figure 11: RUM Tool Actuation Diagram

This nontraditional tool-movement presents a particular challenge for the development of

analytical material removal models and there is still no scientific consensus or complete

model.

2.1.3 RUM Material Removal Mechanisms

When combined with 5-axis machining centers, RUM enables a wide spectrum of

previously difficult-to-machine materials to be used in the creation of complex

workpieces. The RUM process is inherently complex due to the combination of multiple

23

simultaneous interactions between the tool, workpiece, removed material, and supplied

coolant. Previous research has shown that RUM possesses multiple forms of material

removal, each of which is described in the following subsections.

2.1.3.1 RUM Material Removal Mechanisms

To date there is no commonly agreed upon material removal mechanism model in which

brittle fracture, ductile, abrasive flow, and cavitation are included.

Brittle fractures are created on the workpiece at the axial face of tool, as a result of

repeated impact between a tool’s many abrasive grains and the machined surfaces. These

impacts result in Hertzian crack formations, as seen in Figure 12. Once subsurface cracks

have been created, any of the material removal processes are capable of dislodging the

resulting fracture material. The subsequent removal of material affected by impact-based

fracturing constitutes the primary form of material removal in both RUM and USM

processes.

Figure 12: Example of Hammering in RUM

24

As seen in Figure 13 and analogous to conventional diamond impregnated grinding,

abrasion is the secondary form of material removal found in RUM. Tool vibration has

been found to not produce significant MRR increases at the tool’s lateral face [30], [38].

Figure 13: Example of Abrasion in RUM

Through the superposition of hammering and abrasion, a hybrid removal process referred

to as extraction, has also been investigated [30].

Abrasive flow is a process in which abrasive particles, suspended in flowing fluid remove

surface material of a workpiece through a combination of impact and abrasion. Abrasive

flow is commonly considered a tertiary form of material removal and is enabled through

the use of high pressure through spindle coolant, as seen in

Figure 14. Due to the fact that the amount of material removed by abrasive flow is orders

of magnitude less than hammering or abrasive material removal, it is normally neglected.

Recent investigation has suggested that ultrasonic cavitation may provide an additional,

yet minimal, source of material removal [39]. To date there is no commonly agreed

upon material removal mechanism model in which brittle fracture, ductile, abrasive flow,

and cavitation are included.

25

Figure 14: Schematic View of Coolant-Base Abrasive Follow

2.1.4 RUM Tooling

The majority of tools utilized for RUM consist of abrasive particles suspended in a

bonding material similar in composition to those seen in typical grinding wheels. Any

number of tool geometries and compositions are possible. Hollow tools are required for

the use of through spindle coolant Figure 15 is a selection of common RUM tool sizes

and varieties.

Figure 15: Common RUM Tools

26

2.1.4.1 Tool Bond Material

The fundamental role of a tool’s bond material is to hold abrasive grains together and

therefore provides the structural integrity of the grinding tool. Although a solid diamond

tool could be ideal for many applications, the use of diamond abrasives in a binding

material allows users to independently control overall tool material properties. Desired

properties of the bond material include strength, toughness, hardness, porosity, and

temperature resistance. Three common bonding methods are metal, resin, and

electroplating.

2.1.4.1.1 Metal Bonded Tooling

Metal bonding is suggested for glass machining. Usually bronze is the common material

for diamond and Cubic Boron Nitride (CBN) abrasives.

2.1.4.1.2 Resin Bonded Tooling

Resin bonded tools are best suited for finishing operations due to their generally weaker

bond strength. By enabling tool bond fracture, under excessive loading, a workpiece’s

surface is less prone to be deeply abraded and thus a surface of high relative smoothness

is created. Resin bonded tools have been found to maintain lower relative operational

temperatures leading to a reduction in surface burn and other temperature-based surface

defects.

2.1.4.2 Electroplated

Electroplated tooling lacks the advantage of grain refreshment upon tool wear; however,

their overall cost is less. An example of an electroplated tool of this bond material may be

27

seen in Figure 16. A particular advantage of electroplating is the ability to easily produce

complex tool and abrasive geometries allowing for increased customization of tool

characteristics.

Figure 16: Electroplated Diamond Tools

2.2 Previous RUM Research

Publications referring to RUM first appeared in the mid 1960’s. Since then a number of

papers have been published on its various characteristics, parametric trends and

applications for a number of materials. The use of RUM has been investigated for the

machining of the following materials.

Alumina / Advanced Ceramics ; [21]–[23], [40], [41]

Glasses; [24], [25], [35], [42]–[48]

Graphite; [49]

Potassium Dihydrogen Phosphate; [50]

Magnesia Stabilized Zirconia; [30], [36], [38], [51]

Matrix Composites & CFPD; [52]–[56]

28

Silicon Nitride; [31]

Silicon Carbide; [37]

Zerodur; [57], [58]

2.2.1 RUM Process Parameters

2.2.1.1 Spindle Speed

Spindle speed is a critical controllable factor in any milling process; spindle speed was

investigated throughout multiple stages of this research. A review of relevant literature

revealed that many of the previous RUM researchers were limited by their respective

machine tools specifications, often spindle speeds limited to between 3,000 and 8,000

rpm. Higher rotational speed RUM machine tools have recently enabled increased MRR

and surface quality and therefore have been incorporated during this research.

Spindle speed’s influence in RUM outcomes is as follows:

Surface roughness decreases with increased spindle speed [38], [53] .

Edge chipping has been found to be reduced by increased spindle speed [40].

Spindle speed has been found to have significant effects on cutting forces such that

decreased cutting forces occur with increased spindle speed [21], [53], [59].

MRR increases when spindle speed is increased however not proportionally [19],

[23], [36], [54].

2.2.1.2 Feed Rate

Feed rate is of primary concern in parametric selection due to its effect on MRR, cutting

force and surface quality in the RUM process as follows:

Feed rate can be considered to have the greatest effect on RUM MRR [25]

MRR increases with increasing feed rate [21], [38], [54], [60].

29

Cutting forces increase with increased feed rate [21], [54], [60].

Surface roughness (Ra) decreases with increased feed rate [60].

2.2.1.3 Ultrasonic Amplitude

Axial tool actuation is the primary difference between traditional face grinding and RUM.

Therefore the ultrasonic amplitude has been investigated in previous research with results

as follows:

MRR has been found to increase up to a point with increasing amplitude [19], [22],

[23], [36].

Cutting forces have been found to slightly decreases with in increasing amplitude

[21], [46].

2.2.1.4 Ultrasonic Frequency

Typically frequencies around 18 to 25 kHz, ultrasonic frequency has been found to effect

multiple machining outcomes as follows:

MRR has been found to increase with increasing vibration frequency [19] [23].

Specific tool wear has been reported to increase with increasing frequency [23].

Surface roughness (Ra) increases with increasing frequency [23] [60].

2.2.1.5 Abrasive Grain Size / Type

As with traditional grinding, the grit size of a RUM tool affects process outcomes as

follows:

MRR has been found to increase with increasing abrasive grit size up to an optimum

value [19] [22] [23].

Surface roughness increases to a point, then decreases as grit size is increased [61]

[62] [63].

30

2.2.1.6 Coolant

RUM investigations have found that coolant type and pressure have only a limited effect

on machining outcomes [23], [25], [52].

2.2.2 RUM Process Outcomes

2.2.2.1 Cutting Force

Understanding the cutting forces in a machining operation is essential to mitigate possible

defects such as critical workpiece failure, distortion of fixturing, excessive tool wear, etc.

Major trends in RUM cutting forces are as follows:

RUM has been found to reduce cutting forces when compared to USM and diamond

grinding [21], [45]–[47], [54], [64], [65]

Cutting forces increase with increasing feed rate [21] [38].

MRR has been found to increase with increasing static force [22] [23].

2.2.2.2 Material Removal Rate

An understanding of and a prediction method for MRR are critical for the effective use of

available temporal and capital resources. The following trends for MRR of RUM are as

follows:

RUM has been found to enable greater MRR than USM and grinding [22] [23] [60].

2.2.2.3 Tool Wear

Effective tool usage is critical to ensure the efficient use of available resources. As of yet,

there has been little investigation on diamond impregnated tooling explicitly used for

RUM. The following trends have been found in previous investigations.

31

RUM has been found to produce less tool wear when compared to USM [25], [31],

[64]

RUM has been found to produce less tool wear when compared to grinding alone

[45].

2.3 Chapter 2 Summary

In this chapter the history of RUM has been reviewed. The deficiencies in USM and thus

the motivations for the invention of RUM have been presented along with the commonly

utilized tooling. The results of previous RUM investigations, found during literature

review, were presented. Many research papers have focused on the RUM of various hard-

to-machine materials however; there has been no investigation reported on the helical

pocketing of Zerodur glass ceramic.

32

3 Experimental Methodology

Experimental trials carried out for this research were conducted at both DMG MORI’s

ultrasonic headquarters in Stipshausen Germany and the MTTRF Berkeley Institute in

Berkeley California. The experimental systems used at each of these locations are

detailed in the following chapter and are directly referenced in each experimental

overview, for purposes of clarity, in Chapter 4.

3.1 Research Overview

This research was carried out on a vertical RUM machine tool, equipped with a variety of

systems and peripheral equipment capable of measuring the operational characteristics

and resultant outcomes of a large number of RUM experimental trials. Several custom

fixturing and support elements were fabricated in order to create the experimental system

detailed in this chapter. Figure 17 was created via SolidWorks 2013-14 for both

visualization and use in Computer Aided Manufacturing (CAM) based collision testing.

(Left) Close Up of Machining Area (Right) Overview of System

Figure 17: Primary Experimental Fixturing CAD Rendering

33

The cylinder in the center of the figure represents the Zerodur test material affixed to a

custom fixture designed to be mounted to a cutting force dynamometer, which is in turn

connected to the machine tool via a pneumatic chuck system by way of custom adapter.

Several other fixtures were created for dressing, stock material setup, and data collection

material alignment.

3.2 Helical Pocketing

In order to decrease the machining costs associated with hard and brittle materials, a high

level of MRR must be maintained. Impact-based material removal has been identified by

previous research to be the primary mode removal mechanism [19], [57], [66], [67] .

Impacting only occurs at the axial face of the tool and therefore traditional slotting and

side cutting operations do not benefit from ultrasonic oscillation. Helical milling enables

full engagement of the tool’s axial face and therefore enables full employment of impact-

based material removal. Unlike drilling, helical milling enables the creation of features

much larger than the diameter of the tool as is required in the light weighted Zerodur

optical components discussed previously.

In the helical milling process, a tool gradually moves in the axial direction with a helical

motion as it traverses around a circle, a seen in Figure 18. Helical milling has been seen

to improve RUM outcomes in hard and brittle material during extensive testing at Sauer

Ultrasonic. Additionally, the use of a helical approach helps to decrease the high initial

forces imparted on a tool on entry into the workpiece material. This practice is similar to

the use of ramp feeds in grinding operations.

34

Figure 18: Helical Milling Diagram

Multiple helical toolpaths can be combined to produce pockets of diameter greater than

that of the utilized tooling. A sequence of helical pocketing operations can be slowly

transformed into non-circular shapes in order to create pockets of nearly any shape. All

experimental trials conducted throughout this research consisted of helically milled

pockets in order to model and investigate this method of fabrication for Zerodur

workpieces.

3.3 Experimental Materials

As previously described in Section 1.2, Zerodur glass-ceramic is an ideal choice for

extreme precision application in several industrial and scientific fields because of its

unique characteristics. Due to the fact that there is only one producer and it requires a

complex production process, Zerodur is prohibitively expensive. In order to reduce the

excessive expenditure of available resources, BK7 optical glass was utilized during the

initial familiarization and parametric screening stages of this research. For purposes of

example, Figure 19 and Figure 20 are identical blocks of Zerodur and BK7 respectively,

35

measuring 150 x150 x75 (mm). The Zerodur block costs approximately $5,500 while the

BK7 costs only $300. BK7 is often relied upon as a prototyping substitute for Zerodur

components due to its significantly lower price and its similar RUM machinability. In

preliminary testing, BK7 was found to be more likely to exhibit edge chipping during

machining while producing less tool wear and thus provides a “worst case scenario” for

edge surfaces while minimizing tooling costs.

The physical similarity of these glasses can be seen in their common engineering

parameters, as seen in Table 1 and Table 2 provided by Schott AG. Whenever possible,

BK7 was used in the initial testing phases of each successive experimental trial in order

to ensure the efficient use of laboratory resources. Although lower in price, BK7’s

Figure 19: Zerodur Block Figure 20: BK7 Optical Glass Block

Table 1: Zerodur Physical Parameters

Density 2.53 g/cc

Modulus of Elasticity 90.3 GPa

Poisson’s Ratio 0.240

Knoop Hardness 620

Shear Modulus 34.0 Gpa

Coef. Thermal Expansion 0.007E−7/K

Table 2: BK7 Physical Parameters

Density 2.53 g/cc

Modulus of Elasticity 91.0 GPa

Poisson’s Ratio 0.208

Knoop Hardness 520

Shear Modulus 36.7 Gpa

Coef. Thermal Expansion 86E-7/K

36

3.3.1 Statistical Modeling and Validation Stock Material

Figure 21: Experimental Workpiece, Zerodur Optical Blank

Zerodur optic blanks, as seen in Figure 21, were utilized for Zerodur statistical modeling

and tool wear experimental trials. Polished optical blanks with, 5 (nm) Ra and ¼ λ, were

chosen in order to minimize the presence of surface defects prior to machining that could

have effected machining outcomes. By ensuring stock materials had minimal surface

defects, it could be assumed that all machined surface features were the result of the

experimental process alone.

3.4 Machine Tool and Ultrasonic Systems

A DMG MORI Ultrasonic 20 linear (US20) 5-axis machining center, as seen in Figure

22, was employed for each of the many experimental trials carried out during this

research. The US20 is capable of not only 5-axis RUM, but also High Speed Cutting

37

(HSC) operations and thus provided both fast and effective material removal in a wide

variety of both traditional and advanced materials.

Source: DMGMORI.com

Figure 22: Sauer Ultrasonic 20 linear

During my undergraduate and master’s work with the UC Davis IMS-M Laboratory, I

have been very fortunate to attend several international manufacturing symposia; namely,

IMTS 2010, 2012, 2014, and EMO 2013. Throughout extensive investigation during

these events, no other machining center or system was found to provide RUM capabilities

with the comparable speed, accuracy, and flexibility found in the US20 and other

members of the DMG MORI ultrasonic series of machines. As of the date of this thesis’

creation, there is no other fully integrated ultrasonic milling machine currently available

from any other manufacture. The DMG MORI Ultrasonic line of machines can thus be

considered the preeminent RUM machining solution commercially available at this time.

The capabilities of the US20 provided both benefits and challenges with respect to this

research. Clearly, the ability to machine an ever increasing variety of materials is an

38

excellent benefit, however, due to the system’s novelty there is little to no openly

available academic or industrial research available with respect to the helical pocketing of

Zerodur glass-ceramic to use as a basis of comparison for my research. This lack of

available material was a primary motivation for this research.

3.4.1 US20 Specifications

The US20’s specifications are listed as follows:

5-axis gantry construction

Integrated NC swivel rotary table

2g acceleration in X / Y / Z

X / Y / Z linear driven for little to no backlash

Small footprint; 3,5 m² (37.67 ft.2)

An actively cooled HSK-32/40 spindle.

High speed spindle, up to 42,000 rpm

High contour accuracy

Automated real time feed adaptation

3.4.2 Actor® Ultrasonic Tool Holder

The outward appearance of the US20, and other ultrasonic series equipped machines, is

indistinguishable from a traditional machine tool. The point of their differentiation is the

Actor® Ultrasonic tool holder system and associated frequency generation equipment

developed at DMG MORI’s ultrasonic headquarters in Stipshausen Germany. Ultrasonic

axial tool movements are produced through the application of piezoelectric oscillatory

actuators in the tool holder assembly. An on-machine waveform generator provides the

required drive signals to the tool holder. Through the use of inductive coils in both the

tool-spindle interface and tool holder assemblies, the waveform generator’s signal is

39

imparted to the oscillatory motor. Figure 23 provides the overall tool holder appearance.

The spindle-to-holder interface is a traditional HSK32 tool holding interface.

Figure 23: Actor Ultrasonic Toolholder

3.4.3 Through Spindle Coolant

Reductions in friction, cutting zone temperature, and process forces are often cited as

cutting fluids primary benefits [10]. Additionally, coolant helps to prevent tool jamming

during deep drilling operations. Whenever hollow tooling is feasible, coolant can be

supplied both internally through the cutting tool and externally by nozzles located on or

around a machine’s headstock. Figure 24 provides a view of the Actor® HSK32

ultrasonic tool holder’s through-spindle coolant interface.

40

Figure 24: Actor Ultrasonic Toolholder Internal Coolant Input

3.5 Fixturing Methods

Figure 25: Zerodur Experimental Stock Material Fixturing Example

41

A wax-based fixturing method, as seen in Figure 25, was used to affix experimental stock

material. In addition to the wax-based fixture plates, several other functional elements

were combined through the use of custom fixturing elements. Cutting force is a primary

indicator of proper workpiece loading and process performance. A Kistler 3-Componenet

9257B piezoelectric dynamometer (Kistler Instrument Corp, Amherst, NY, USA) formed

the main body of the experimental fixturing assembly. Many of the experimental system’s

components were designed or chosen to work around or in conjunction with the 9257B

due to its relatively large size compared to the US20’s machining envelope.

Figure 26: Kistler 9257B Schematic [68]

The second design constraint of the experimental fixturing system was the need to

interface with the Erowa ER-029313 pneumatic chuck system, a schematic of which may

be seen in Figure 27 (Erowa LTD, Büron, Switzerland). The Erowa chuck interface is the

42

primary work holding method for the US20. This system provides excellent repeatability

with minimal setup time.

In order to mount the 9257B to the US20’s Erowa chuck, a custom Kistler-to-Erowa

adapter plate was designed and fabricated. Made of polished 25.4 (mm) thick 303

stainless steel, the adapter plate provided a ridged support for the rest of the fixturing

assembly.

Figure 28 is an exploded view of the entire work holding assembly.

Figure 27: Erowa Chuck; ER-029313 [69]

43

Figure 28: Exploded View of Experimental Work Holding Assembly

3.5.1 Glass Fixturing Methods

Unlike traditional ductile materials, the use of compressive fixturing systems such as

vises or clamps can be detrimental to a hard and brittle material. Once a critical

compression or shear threshold has been reached, increased clamping forces will result in

critical fracture and therefore total loss of the workpiece in most situations. For this

reason, stock materials are affixed with waxes, glues, and vacuum systems.

The technique most often employed as an affixing method, and used throughout this

research, is that of adhering stock material with dopping wax. Unlike typical vise

fixturing, wax fixturing prevents stress loading of the part and therefore alleviates the

propagation of critical fractures that can result in total workpiece loss. This method uses

44

wax to affix the stock material to be shaped onto a rod known as a dop. This method is

commonly used by jewelers during the faceting process, as illustrated in Figure 29.

Source: http://gem-sphalerite.com/faceting-process

Figure 29: Gem Stone Dopping Wax Fixturing Example

Specialized equipment, not typically found in a traditional CNC machine shop, is

required for wax fixturing. A sample of the fixturing wax used throughout this research is

shown in Figure 30. Typically used for decorative seals, this wax provides excellent

adhesion in both wet and dry environments. The fixturing wax’s ability to withstand

cutting fluid is critical due to the requirement of high pressure cutting fluids during the

majority of RUM operations.

Figure 30: Fixturing Wax and Heating Plate

45

As seen in Figure 32, a digital heating plate is used to gradually heat up the stock material

and fixture plate to the melting point of the wax, 145°C in the case of the wax used for

this research. Once the workpiece material and fixture are up to temperature, wax is

applied to both the fixture and stock material. Next, these elements are combined and the

assembly is allowed to cool. Particular attention must be paid in order to prevent the

initiation of workpiece fracture due to non-uniform heat distribution. For many hard and

brittle materials, the heating and cooling rates must be very gradual in order to

significantly reduce the risk of crack formation. BK7 glass requires a heating / cooling

rate of 100°C per hour. A digitally controlled convection oven capable of programed

temperature sequences, as seen in Figure 31, was used to minimize the risk of stock

material loss. A digital heat plate, as seen in Figure 32, was used for all Zerodur trials.

Figure 31: Stock Preperation Via Digital Oven

46

Figure 32: Zerodur Stock Materials Preperation Via Digital Hotplate

3.5.2 Wax Fixture

In order to utilize wax fixturing, a series of custom 303 stainless steel fixtures were

designed and fabricated. A schematic and CAD rendering can be seen in Figure 33. Each

experimental fixture was designed to be used in a variety of configurations.

Figure 33: Experimental Fixture Schematic Drawing

47

Source: http://ims.engr.ucdavis.edu

Figure 34: Sodick AQ327L WEDM and Work Area

These connection points and their distribution served as major design criteria for any

applicable fixturing solution. Using M8 bolts, each fixture could be directly mounted to

the 9257B thus providing cutting force measurement capability while enabling relatively

little setup time for each of the many experimental trials required.

In order to allow wax to contact the mating surface of the stock material while ensuring a

flat and uniform profile, an array of plateaus and valleys were added to the fixture’s top

surfaces. These intricate mating surfaces are critical to ensuring a robust connection

between the stock material and the fixture by providing ample surface area for wax

adhesion. These features were created through the use of a 4-axis Wire Electronic

Discharge Machining (WEDM) process. A Sodick AQ327L 4-Axis Wire EDM was used

for the fabrication of all wax fixturing surfaces, (Sodick Co. LTD, Nakamachidai, Japan),

as seen in Figure 33. WEDM was chosen due to its ability to make precise and intricate

geometry of minimal corner radius. The intricately textured mounting structures seen in

48

the accompanying figures were created through the use of only two WEDM operations

separated by a 90 degree automatic index on the AQ327L’s rotary axis.

A Sodick MC430L 3-Axis milling center, as seen in Figure 35, was used to the mill

mounting holes required for connection to the Kistler 9257B. All toolpaths were created

in Esprit 2013, (DP Technologies Corp, Camarillo, CA, USA). These operations were

created separately and then combined in post processing. A total of 20 wax fixtures were

created for both the preliminary testing and final statistical screening, modeling, and

validation phases of this research.

Source: http://ims.engr.ucdavis.edu

Figure 35: Sodick MC430L 3-Axis High Speed Machining Center

3.5.2.1 Fixture Texturization

Once primary machining operations were completed, wax mounting surfaces were

texturized through the use of sandblasting. This texturization increases the bond strength

of dopping wax by creating an increased amount of surface area while simultaneously

eliminating any burs or other unwanted machining artifacts created during milling

operations that could have caused stock material misalignment. The results of

sandblasting may be seen in Figure 36.

49

Figure 36: First 12 Sandblasted Wax Fixtures

3.5.2.2 Fixture Polishing

In order to ensure the highest possible fidelity in the measurement of cutting forces by the

Kistler 9257B, every attempt was made to eliminate gaps or other surface irregularities

between the mating surfaces of the dynamometer and each of the experimental wax

fixtures. Although prepared on a high accuracy milling machine, the back side of the

experimental fixtures, seen in Figure 37, could not be assumed to be perfectly smooth and

were lapped on a granite surface plate with a series of abrasive grit sizes until a highly

polished surface was obtained, as seen in Figure 38.

50

Figure 37: Backside Milling Results

Figure 38: Polished Results

3.5.2.3 Experimental Stock Centering Fixture

One drawback of using such a highly polished experimental stock material is the

propensity for stock material misalignment due to unwanted movement during the

fixturing process. This misalignment can occur while the fixturing wax is still in its liquid

phase. Thus experimental stock material alignment was accomplished through the use of

a precision centering fixture. This centering fixture was designed and fabricated, as seen

in Figure 39 and Figure 40, out of 6061 aluminum. The centering fixture provided

increased stock positioning repeatability resulting in a dramatic decrease in result

measurement setup time. A second custom alignment fixture was designed and fabricated

to facilitate a quick yet repeatable means of workpiece alignment during surface analysis

(see section 3.6.2.2 for a full description). All machining operations for the stock

alignment fixture were conducted on the US20.

51

Figure 39: Centering Fixture Example

Figure 40: Centering Fixture Schematic

52

3.6 Surface Quality Measurement

3.6.1 Parametric Screening Surface Measurement

As seen in Figure 41, the Mitutoyo SJ-400 (Mitutoyo Corp, Kanagawa, Japan) was used

to acquire surface roughness measurements. Although used for initial parametric

screening trials this system was located at DMG MORI Sauer’s Stipshausen location and

therefore was not available after primary parametric screening trials carried out at the

Machine Tool Technologies Research Foundation’s Berkeley Institute.

Figure 41: Surface Roughness Measurement System

3.6.2 Statistical Modeling Surface Measurement

A Mitaka MLP2 surface analyzer, (Mitaka Kohki Co, Tokyo, Japan), as seen in Figure

42, was the primary system of surface quality measurement used throughout this

research.

53

Source: http://www.mitakakohki.co.jp

Figure 42:Machined Surface Measurement System

The MLP2 is a Point Autofocus Instrument (PAI) that employs a non-contact surface

texture measurement method known as point autofocusing. By precisely measuring the

distance required to bring the PAI’s laser in focus the relative height of a surface feature

can be determined (ISO/CD 25178-605 2011). A diagram of this system and its major

components is shown in Figure 43. This process can be repeated as the object is moved

laterally via an X Y scanning stage in order to create either a linear or 3D profile of the

surface with high resolution and high accuracy. The point autofocusing has a wide

measuring range in high precision and is not influenced by color or reflection ratios of

workpiece surfaces [70]. Figure 43 is provided in order to better explain basic mechanics

of the autofocus method.

54

Figure 43: Typical Autofucus System [71]

Adapated From [71]

Figure 44: PAI Measurement Example

55

Several peripheral components are required to actuate and log the measurements made by

the autofocus system, as seen in Figure 45.

Figure 45: PAI System Diagram

To minimize the effect of vibrations and minor thermal fluctuation on measurement

accuracy, the MLP2’s measurement systems are located inside a separate measurement

chamber. Figure 46 depicts the measurement area of the MLP2 comprised of the optical

system, a vertical Z-axis, and horizontal X Y-axis scanning stage, and rotary table.

56

Figure 46: Mitaka MLP2 Measurement System

3.6.2.1 Mitaka MLP2 Specifications

Table 3 and

Table 4 provide the MLP2’s autofocus and scanning stage specifications respectively.

Table 3: Autofocus Sensor Specifications

Laser spot diameter 1μm (at 100X )

57

Power ≤ 1mw (Class 2)

Wavelength λ=635nm

Autofocus Repeatability σ＝0.015μm

Table 4: Scanning Stage

Axis Moving range Resolution X 120mm 10 (nm) Y 120mm 10 (nm) Z 130mm 10 (nm) AF (Autofocus) 40mm 1 (nm) AZ (Rotary Axis) 360° 0.0002°

3.6.2.2 Mitaka Measurement Custom Fixture

Mitaka MLP2 uses a small vise to affix samples. A specimen can be simply placed on this

vise for measurement; however, due to the large number of experimental trials conducted

throughout this research, an alignment fixture was designed and fabricated, as seen in

Figure 47. Based on the alignment fixture use during wax fixturing, this fixture enables

the repeatable placement of samples with little to no setup or adjustment required. In this

manner, the center positions of each machined pocket were automatically known and

required no adjustment of measurement start positions. In excess of 600 individual profile

measurements were made with the MLP2; the minimal of setup time per sample provided

by the alignment fixture greatly reduced the time required for data collection.

58

(Left) Fixture Mounted to Mitaka MLP2 (Right) Measurement Fixture Usage Example

Figure 47: Mitaka Measurement Fixture

3.7 Surface Profile Methodology

MitakaMap (MMap) is the MLP2’s proprietary interface software. MMap was used to

extract surface profiles, perform corrective mathematical operations, calculate multiple

surface parameters, and perform initial data analysis and evaluation. A set of

measurement operation sequence macros were created in MMap in order to minimize

systematic measurement errors through the use of a standardized process and to expedite

the data collection process. The following sequence of actions was performed for each of

the 750 plus gathered throughout the course of this research. Profile reports were

automatically generated, and numerical information was exported to a CSV file format

for use in Microsoft Excel.

59

Figure 48: Centering Macro Output, MMap

The center of the machined pocket is first located through the use of a centering macro

before surface measurement. MLP2 scans for abrupt changes in surface height within a

set threshold corresponding to the vertical walls of each pocket. The blue and red profiles

seen in Figure 48 represent the X and Y scans respectively of the centering process. From

this data a corrected center position is generated.

The point data generated by the MLP2 is combined to generate a raw surface profile, as

seen in Figure 49. Note the large increase in profile height at the beginning and end of the

measurement profile created as the laser beam approaches the vertical walls of the

machined pocket.

60

Figure 49: Raw Surface Profile

The measurement aberrations seen in the raw profile are eliminated by MMap’s profile

trimming function. Four percent of each profiles start and end portions were trimmed,

resulting in the profile seen in Figure 50.

Profile curve - OP01

0 1 2 3 4 5 6 7 8 9 10 mm

µm

-100

-50

0

50

100

150

61

Figure 50: Extracted Profile Section

As seen in Figure 51, each profile was leveled through the use of MMap’s least squares

leveling function in order to minimize any tilting in the X and Y planes. The use of

custom alignment fixtures in conjunction with least squares leveling dramatically reduce

sample setup time.

Profile curve - Extracted area (92%)

0 1 2 3 4 5 6 7 8 9 mm

µm

-50

-40

-30

-20

-10

0

10

20

30

40

62

Figure 51: Least Squares Leveled Section

Finally a measurement identity card, 9 surface parameters (ISO 4287), and other profile

statistics are presented in an operation report as seen in seen in Figure 52 and Figure 53,

respectively.

Figure 52: Measuremnt Identity Card

Profile curve - Leveled (Least squares method)

0 1 2 3 4 5 6 7 8 9 mm

µm

-50

-40

-30

-20

-10

0

10

20

30

40

Identity card

Name: OP01

Filename: C:\Users\MLP2\Desktop\BB_DOE_75_8.15\OP01.am2

Axis: X

Length: 10 mm

Size: 4002 points

Spacing: 2.5 µm

Offset: 35 mm

Axis: Z

Length: 201 µm

Z min: 34488 µm

Z max: 34689 µm

Size: 200510 digits

Spacing: 1 nm

63

Figure 53: Calculated Surface Parameters

3.7.1 Surface Topological Calculation Metrics

The following subsections provide a brief summary and the calculation methods

commonly used to calculate each of the roughness parameters considered throughout this

research. In the scope of this work, roughness is defined as the closely spaced, irregular

deviations on small scale, expressed in terms of its height, width, and distance along a

surface [10]. ISO 4287, the master standard for profile parameters in the ISO GPS

system, was used for all surface roughness measurements. An important distinction must

be made in order to mitigate confusion in the parametric definitions presented later in this

subsection:

Sampling Length: A fixed length sampled from the surface profile curve to find the

characteristics of the surface.

Evaluation Length: The characteristics of the profile curve are evaluated over a fixed

length that includes at least one sampling length. This length is called the evaluation

length. The evaluation length is set to five times the sampling length by ISO standards.

64

Much of the following information was adapted from the following sources: [71]–[74].

3.7.1.1 Arithmetic Average (Ra)

Ra is almost certainly the most widely employed measure of surface quality in

manufacturing. The influence of an irregularity on the measurement value becomes

extremely small, so that stable results can be obtained.

Figure 54: Ra Example [74]

𝑅𝑎 =1

𝑛∑|𝑦𝑖|

𝑛

𝑖=1

(1)

3.7.1.2 Root Mean Squared (Rq)

Rq, formally known as RMS, is defined as the line height in which an equal amount of

area is created by the roughness profile both above and below. Rq is mainly used in the

United States.

Figure 55: Rq Example [74]

𝑅𝑞 = √1

𝑛∑ 𝑦𝑖

2

𝑛

𝑖=1

(2)

65

3.7.1.3 Mean Height of Profile Irregularities (Rc)

Rc is the mean value of the profile element heights Zt within a sampling length. Rc is

often used to evaluate the “high-grade feel”, adhesion performance, and frictional force.

Figure 56: Rc Example [74]

𝑅𝑐 =1

𝑚∑ 𝑍𝑡𝑖

𝑚

𝑖=1

(3)

3.7.1.4 Maximum Peak (Rp)

Rp is simply the highest point of a surface’s profile. Rp is often used for the evaluation of

frictional force and electrical contact resistance.

Figure 57: Rp Example [74]

𝑅𝑝 = (𝑚𝑎𝑥𝑖)𝑦𝑖 (4)

66

3.7.1.5 Maximum Valley Depth (Rv)

The inverse of Rp, the maximum valley depth is the lowest point. Rv is often used to

evaluate a surface’s strength and resistance to corrosion.

Figure 58: Rv Example [74]

𝑅𝑣 = (𝑚𝑖𝑛𝑖)𝑦𝑖 (5)

3.7.1.6 Average Maximum Profiler Height (Rz)

Rz provides an estimate of the overall peak to valley magnitude of a surface and may

serve to predict the thickness of coating needed to completely cover and level a surface.

Rz is often used to evaluation the gloss, luster, surface strength, or surface treatability of

a surface.

Figure 59: Rz Example [74]

𝑅𝑧 = 𝑅𝑝 + 𝑅𝑣 (6)

67

3.7.1.7 Maximum Height of Profile (Rt)

Rt is the difference between the highest peak and lowest valley, and can be thought of as

the amount of material that must be removed to produce a smooth surface. Because Rt is

calculated over the entire measurement length, it can be considered stricter than the

standard Rz.

Figure 60: Rt Example [74]

𝑅𝑡 = 𝑅𝑝 − 𝑅𝑣 (7)

3.8 Tooling

6mm Effgen Type: SK-6/4-1-5-FT25-BZ104-6D107-C90 hollow endmill, (Günter

Effgen, GmbH, Idar Oberstein, Germany), as seen in Figure 61, was selected for all

experimental trials. This tool is suited for roughing operations and therefore suited for the

high MRR strategies being investigated throughout this research.

68

Figure 61: Experimental Tools

Table 5 provides the specifications of the experimental tools used during all Zerodur and

BK7 machining trials throughout this research.

Table 5: Experimental Tool Specifications

Diameter 6 (mm)

Skank Type / Length ER11 / 25

Id Number 141428

Fert Number 668878.01

System Certification ISO 9001

3.8.1 Tool Length Measurement Method

Tool wear measurements were collected through the use of an on machine Renishaw laser

tool setter (Renishaw plc, Wotton-under-Edge, U.K.), as seen in Figure 62. This system

was determined to have decreased variation compared to all other available methods for

this reearch. A detailed description of system validation and comparison trials can be

found in Appendix B.

69

Figure 62: Renishaw NC4 Tx [75]

3.8.2 Tool Dressing Method

During the tool making process irregularities in cutting surface quality, such as loosely

bonded diamond grains and geometric defects, can compromise the surface quality of

resulting workpieces. In order to remove these irregularities, the cutting surfaces of new

tools are dressed to prepare them for machining in a process similar to grinding wheel

dressing. During the dressing process a tool is plunged into a sharpening stone as seen in

Figure 63. In order to increase both safety and repeatability of the dressing process, while

decreasing total cycle time, the custom setup depicted in Figure 64 was designed and

fabricated. The use of this assembly provided increased safety and repeatability.

70

Figure 63: Manual Diamond Tool Dressing

(Left) Dressing Fixture Setup (Right) Example Dressing Operation

Figure 64: Custom Experimental Dressing Fixture

71

During primary experimental modeling trials, dressing operations were carried out prior

to all machining operations in a standardized fashion. Although this repeated dressing

significantly increased tool consumption, and therefore would not recommended for

normal non-experimental operations, frequent dressing helped to ensure that the tool’s

cutting surface was normalized for every machining operation thus providing machining

outcomes that are less biased by previous cutting operations. In order to assume that the

surface quality of an individual experimental trial was the result of its particular RUM

parameters, and not that of a previous test, dressing operations were needed to remove

any and all effected tooling surface prior to each experimental trial.

The effect of dressing on tool length was investigated experimentally prior to modeling

and validation trials. Length reduction resulting from dressing operations was found to be

highly linear with a regression coefficient near unity. All measurement data and statistical

comparisons can be found in Appendix C. Preliminary testing suggested that each

Zerodur pocketing trial would result in a tool length reduction of 1±0.5 µm. The mean

length reduction of a dressing operation was found to be 53.9±8.3 µm. At an order of

magnitude greater than the predicted experimental tool wear, the tested dressing process

was considered adequate for the purposes of this research. Additionally, dressing process

cycle times were recorded for experimental process planning purposes.

3.9 Toolpath Creation and Strategy

Once literature review, RUM familiarization, consultation with ultrasonic applications

engineers, and initial parametric bounding tests were completed, operational cutting

conditions were established. CAM was initially used to create experimental toolpaths;

however, in an effort to increase the level of control over the experimental machining

72

processes during the statistical modeling and validation portion of this research, custom

macro programing was utilized. The following sections detail the toolpath creation

process throughout the course of this research.

3.9.1 Helical Pitch

As seen in Figure 65, the displacement of a tool in the vertical (Z-axis) per revolution in

the lateral (X Y) plane is referred to as the helical pitch. A helix can be described

parametrically as follows, with r and h representing the radius and helical pitch

respectively:

Figure 65: Radius and Pitch of Helix; Adapted from [77]

𝑥 = −𝑟 sin(𝑡) (8)

𝑦 = −𝑟 cos(𝑡) (9)

𝑧 =ℎ𝑡

2𝜋 (10)

Increasing the helical pitch of a toolpath linearly increases the rate at which the tool is

feed into the material both at the lateral and axial tool faces. Altering helical pitch can

affect MRR, process forces, and overall cycle time of a helical pocketing operation. No

previous investigation of helical pocketing of glasses was found. This lack of previous

research necessitated the need for exploratory trials.

73

Several preliminary trials were conducted in order to determine the upper boundary of

helical pitch. As seen in Figure 66, a series of pockets, 10.5 (mm) diameter 2 (mm) in

depth, were machined in BK7 glass with the tools described in Section 3.8. A minimum

helical of 0.1 (mm) was chosen. In non-helical RUM cutting carried out during US20

familiarization, 0.1 (mm) depth of cut has been shown to be an effective and stable

roughing operation depth of cut and thus a starting point in the investigation of Zerodur

machining regimes capable of maximized MRR. Increasing helical pitch was tested until

tool failure occurred at 0.7 (mm/rev). Tool failure occurred in the form of tool shank

deformation. This result was an important indication of the robustness of the wax fixtures

discussed in Section 3.5.2 and used throughout the course of this research. Up to the

maximum achievable cutting loads, wax fixturing held. The Keyence VHX-2000 digital

microscope (Keyence, Osaka, Japan) was used to record the overall appearance of the

machined features, as seen in Figure 67. This excessive helical pitch resulted in the

excessive fracture of the pocket walls as seen in Figure 68.

Figure 66: Pilot Study Workpiece Setup and Pocketing Results

74

Figure 67: Machined Result Inspection

Figure 68: Result of Excessive Helical Pitch

75

Observations of tools were made both before and after cutting trials, as seen in Figure 69

and Figure 70. Note the deformation in to form of bands in the metallic binder seen in the

used tool. After consultation with an Effgen representative familiar with RUM of glass, it

was concluded that the observed alterations of the cutting surface are indicative of an

aggressive cutting process and is not to be considered negative.

(X200) (X50)

Figure 69: New 6mm D107 Diamond Endmill

(X200) (X50)

Figure 70: Used 6mm D107 Diamond Endmill

76

3.9.2 CAM Based Toolpath Creation

Esprit 2013 used to create toolpaths for both parametric bounding and statistical

parametric screening experimental trials. Figure 71 is an example of the first 20 statistical

parametric screening helical pocketing toolpaths.

Figure 71: Pilot Study 2 Toolpath Organization

3.9.3 Statistical Modeling Toolpath

In order obtain an increased level of control on the machining process; CAM was

replaced with direct NC code creation by way of manual G-code. An example toolpath

used during statistical modeling and validation trials is provided in Figure 72.

77

Figure 72: Example Statistical Modeling NC Code

78

3.10 Ultrasonic Actuation Measurement

With micron level tool displacement at frequencies up to 50 kHz, measurement of

ultrasonic tool actuation is particularly challenging. Although the US20’s controller

displays the ultrasonic frequency and percent amplitude, it is not clear if these readings

are direct measurements or only commanded values. In order to properly quantify RUM

process parameters, an external means of frequency and amplitude measurement was

utilized.

3.10.1 Ultrasonic Measurement System

A Polytec NLV-2500 laser vibrometer (Polytec, Yokohama, Japan), as seen in Figure 73,

was used to measure ultrasonic parameters.

Figure 73: Polytec NLV-2500 Laser Vibrometer

This system extracts the vibration frequency and amplitude of a surface via the Doppler

shift of the system’s laser source in as seen in Figure 74.

79

Figure 74: System Working Principle Diagram [78]

Unlike an accelerometer, a laser vibrometer is a non-contact method. Due to the fact that

altering the mass of a tool-holder assembly can alter its ultrasonic characteristics, the

NVL-2500 is ideal for this application. The relatively small size and ability to be

mounted via a magnetic gage block enable the NLV-2500’s OF-534 sensor head to be

quickly installed and removed from the US20’s machining area. An Agilent/HP 54503A 4

Channel 500 MHz Oscilloscope (Hewlett-Packard, Palo Alto, CA, USA), was used to

display the NLV-2500’s output. Both the NLV-2500 and 54503A are capable of

measurement rates at least an order of magnitude higher than the tool’s oscillation and

therefore ensure that no sampling errors were created per the Nyquist-Shannon sampling

theorem. Figure 75 provides an example of a typical ultrasonic measurement.

Figure 75: Tool Amplitude and Frequency Measurement System

80

Table 6 provides the NLV-2500’s primary specifications.

Table 6: Polytec NLV-2500 Specifications

Bandwidth 2.5 MHz

Digital Velocity 8, up to 10m/s

Displacement Resolution 15 pm

Laser Diameter 1.5 µm

3.10.2 Ultrasonic Parametric Tuning

Each tool and holder combination requires a particular ultrasonic driving frequency in

order to produce the maximum tool amplitude at a power low enough to prevent

overheating of the piezoelectric system. This ultrasonic parameter is determined by

sweeping through the available frequencies (20 – 50 kHz) until the optimal frequency

corresponding to the largest oscillation is determined. The following subsection describes

the frequency determination process in both manual and semi-automatic fashions.

3.10.2.1 Manual Method

With the waveform generator on, a piece of glass or thin metal is pressed to the non-

spinning tool, as seen in Figure 76. The operator sweeps through the frequency range in

order to find an appropriate magnitude capable of producing an audible vibration in the

test material. Once above a particular threshold the tool will begin to remove material

from the test material’s surface. Particular caution must be exercised when selecting an

ultrasonic parameter. Improper input power levels can produce excessive heat generation

inside the tool holder, producing adverse effects such as tool, workpiece, and tool holder

damage. The user must cautiously test the tool holder assembly for any unnecessary heat

generation. In the specific case of a Sauer US20 equipped with an HSK-32 ultrasonic tool

holder, a waveform generator output of approximately 12W is generally recommended

for the tools utilized throughout these particular experimental trials.

81

Figure 76: Manual Ultrasonic Parameter Determination Method

3.10.2.2 EasySONIC Semi-Automatic Method

In order to minimize the need for extensive frequency determination training, Sauer

developed the easySONIC system. The easySONIC system is an option, available for

most Sauer ultrasonic machines, capable of automatically finding and monitoring the

ultrasonic frequencies of the Actor® ultrasonic tool holder. Extensive testing and

familiarization was conducted on the easySONIC system, Polytec vibrometer, and

associated systems, the results of which are provided in Appendix I. The easySONIC

frequency determination system was used for all modeling and validation trials.

3.11 Cutting Force Measurement

Cutting forces were measured with a Kistler 9257B piezoelectric dynamometer (Kistler

Instrument Corp, Amherst, NY, USA), in order to quantitatively investigate the effect of

experimental process parameters on machining outcomes.

82

Figure 77: Kistler Cutting Force Measurement Setup

The overall experimental cutting force setup can be seen in Figure 77 and is comprised of

a 9257B 3-Component Piezoelectric Dynamometer, 3 Dual Mode Type 5010 Charge

Amplifier, Remote Control, Dell XPS 15C Interface PC, Kistler DynoWare 2825A1-2,

and a Kistler Type 5697A/D Converter. The 9257B is a 3-component (3-Axis)

dynamometer composed of four piezoelectric force sensors. Figure 78 provides the

system’s force direction conventions.

83

Figure 78: 9257B Force Measurement Convention [68]

Table 7 provides the 9257B’s specifications.

Table 7: Kistler 9257B Specifications

Measurement Range (kN) -5 to 5

Natural Frequency (kHz) 2.3 (X Y) 3.5 (Z)

Experimental Measurement Frequency (Hz) 1000

Kistler suggests that measurement frequencies be kept at less than 1/3 the natural

frequency of the dynamometer [79]. Because of this limitation, all force measurements

conducted throughout the course of this research are considered to be non-ultrasonic.

There is no commercially available cutting force dynamometer capable of measurement

frequencies in the ultrasonic range at the workpiece scale being investigated. With

sampling periods of 40 seconds and greater, for a minimum of 40,000 measurements,

combined with the cyclic nature of helical pocketing, all measurements were considered

to be taken at steady state.

84

3.12 Statistical Methods

For the purposes of this research, statistical Design of Experiments (DOE) methods were

employed to model the effect of RUM process parameters on the machined surface

quality resulting helically pocketed Zerodur glass-ceramic. Minitab 17 statistical analysis

software (Minitab Inc., State College, PA, USA), was used throughout this research for

DOE matrix creation, results analysis, and calculation of various test statistics.

3.12.1 Taguchi Parametric Screening DOE

A Taguchi parametric screening DOE methodology was employed to systematically

separate the vital few RUM process inputs from the trivial many. The Taguchi method

provides a method identifying variation in a process through robust design of

experiments. The Taguchi method was developed by Dr. Genichi Taguchi [80], [81].

Taguchi developed a method for designing experiments to investigate how different

parameters affect the mean and variance of a process performance characteristic that

defines how well the process is functioning [82], [83].

Through the course of literature review, it was determined that the majority of glass-

ceramic RUM experimentation has focused on core drilling. Drilling is a commonly

employed machining stratagy; however, this limited process, and the features it creates,

are of only limited use. For workpieces possesing curvature drilling is not utilized.

Pocketing was selected as the primary focus of my resarch due to its neccesity in the

majority of zerodur and other glass-ceramic workpieces, as discussed in Section 1.2.2.

The experiemtental determination of effective pocketing stratagies can also yield possible

insights into process parameter regimes beneficial for facing and freeform curvature

creation.

85

3.12.1.1 Parametric Screening Factor Selection

Experimental RUM process parameters were selected through literature review and

consultation with application engineers at Sauer Ultrasonic. Andreas Schwartz, the

applications manager at the Sauer Ultrasonic headquarters, and other Sauer personnel,

were asked a series of general and advanced questions regarding not only RUM operation

standards and findings, but also the needs of Sauer customer’s and ultrasonic

application’s department. The proceedings from this interview can be found in Appendix

A. The information gathered proved to be invaluable in guiding this research. A larger

numbers of RUM parameters were investigated than have appeared in previously

published research.

The experimental design developed by Taguchi involves several different combinations

of process variables, referred to as factors, affect the process being investigated. Instead

of having to test all possible combinations of factors individually, the Taguchi method

tests pairs of combinations. This allows for the collection of the necessary data to

determine which factors most affect product quality with a minimum amount of

experimentation, thus saving time and resources [58], [80], [83]. An example of the

dramatic reduction in trials enabled through the use of Taguchi orthogonal arrays.

3.12.2 Box-Behnken Response Surface Modeling DOE

Once the RUM processes parameters feedrate and spindle speeds were found to be have

the largest effect to pocket surface quality were determined through Taguchi parametric

screening, empirically determined equations for the seven most common surface quality

metrics were developed via a Box-Behnken DOE. Box-Behnken designs

are experimental designs for response surface methodology developed by George E. P.

http://en.wikipedia.org/wiki/Experimental_design

http://en.wikipedia.org/wiki/Response_surface_methodology

86

Box and Donald Behnken in 1960 [81], [84]. Response Surface Methodology (RSM) is

one of the most applied statistical modeling techniques for the process modeling [85],

[86]. Box-Behnken designs are commonly employed to [87]:

Model a relationship between the quantitative factors and their response

Determine controllable operating conditions that produce the "best" response

Find factor settings that satisfy process specifications

Identify new operating conditions that produce demonstrated improvement in

product quality over the quality achieved by current conditions.

An added benefit of the Box-Behnken method is that the most extreme conditions

corresponding to all high settings are never tested simultaneously. Factor level

magnitudes can therefore be selected in the widest range possible and enable modeling

over a wider range of values. The test results, referred to as responses, to each of the

many settings are tested independently throughout the experimental process. The design

matrix used for parametric screening can be found in

87

Table 41 of Appendix D. A total of five of these matrices were combined and randomized

to create the 75 total machining trials conducted, per suggested DOE practices [80].


The operating principles, configuration, and experimentally verified justifications for the

experimental setup used throughout all portion of this research were described. Once the

physical experimental apparatus was discussed, the statistical screening and modeling

techniques utilized throughout this research were presented.

88

4 Study and evaluation of Results

4.1 Taguchi Design Type and Parameters

A Taguchi L27 orthogonal array was to evaluate 7 RUM process factors at 3 different

magnitudes referred to as levels. The L27 design matrix used for parametric screening

trials is provided in Table 40 of Appendix D. Table 8 outlines the investigated parameters

as well as the levels at which they were evaluated during parametric screening trials.

Low, medium, and high factor levels are coded as 1, 2, and 3 respectively.

Table 8: Taguchi DOE Parameters

Parameter Units Low Med High

Ultrasonic Frequency kHz 20.9 23.5 28.1

Accuraccy Setting n/a Roughing Semi-Finishing Finishing

Feed Rate mm/min 500 1050 1600

Helical Pitch mm/rev 0.1 0.3 0.5

Spindle Speed rpm 10,000 25,000 40,000

Spring Passes interger 1 3 5

Coolant Pressure bar 10 20 30

Feedrate, helical pitch, and spindle speeds were determined through the testing process

described in Section 3.9.1. Once selected, the remaining experimental factor levels were

determined as follows:

Ultrasonic Frequency: The medium level of ultrasonic frequency was chosen such that

it provided the largest oscillation, with the low and high setting place at the boundary of

discernable oscillation, as determined through manual tuning. By this stage of

experimentation the easySONIC frequency determination option was not yet available.

Accuracy Settings: Helical milling requires the precise control of circular motions in

order to produce accurate pocket dimensions. As minimal previous helical RUM research

has been published, it was necessary to determine the effect of the US20’s Siemens 840D

89

Solutionline NC controllers setting on process outcomes. Three levels of accuracy are

available and therefore were selected for testing.

Spring Passes: Circular movements in the X Y plane are required at a pocket’s floor in

order to create a flat surface are associated with helical pocketing. Spring passes, past the

first, are non-cutting moves similar to a dwell. Ultrasonic dwelling has been found to

improve surface quality in glasses [24]. A minimum of 1 spring pass is require and

therefore is the lowest factor level with 5 chosen as the maximum level.

Coolant Pressure: The US20’s internal coolant supply ranges from 10 to 30 (bar) and

therefore were chosen as the low and high levels respectively, with medium set at 20

(bar).

4.1.1 Experimental Procedure

Six replications of the L27 were run for a total of 162 individual machining trials. The

run order of experimental trials was randomized per DOE good practices [84]. Detailed

descriptions of experimental setup employed for parametric screening trials can be found

in the following sections:

Section 3.1 Experimental Materials

Section 3.2 Machine Tool and Ultrasonic Systems

Section 3.3.2 Wax Fixture

Section 3.6.1 Surface Profile Methodology

Section 3.4.2.1 Parametric Screening Surface Measurement

Section 3.7.2 CAM Based Toolpath Creation

Figure 79 was created during process planning and clearly depicts the many steps carried

out during each of the experimental machining trials in the parametric screening DOE.

90

Figure 79: Taguchi DOE Experimental Trial Flowchart

One of two BK7 experimental stocks used for parametric screening can be seen in Figure

80.

Figure 80: Parmtric Screnining Pockets, Sample 1 of 2

91

4.1.2 Parametric Modeling Results

The 162 experimental pocket floors were measured three times and the average Ra,

Equation (1), was computed. A summary of the calculated Ra measurements is presented

in Table 9. Ra of 0.3 (µm) was considered as the minimum finished surface roughness

required. This value was average value required by several customer requirements.

Surface roughnesses under this threshold are normally achieved through the use of

finishing methods such as lapping and polishing methods.

Table 9: Pocket Floor Ra Values

Value Ra (µm)

Max 2.77

Avg. 1.23

Min 0.44

Table 10 provides the parametric hierarchy resulting from Minitab 17’s Taguchi analysis

in the form of a ranking and response delta. The response delta is the difference between

the maximum and minimum mean response (Ra) of each parameter, across each of the

three levels, associated with each RUM parameter.

Table 10: Response Table of Means

Table 11 was created in order to compare the relative magnitudes of each RUM

parameter’s effect on the mean pocket floor Ra. Encompassing 77.57%of the total delta,

feedrate and spindle speed were considered the main parameters affecting pocket floor

Ra.

92

Table 11: Mean Response Delta Ranking

Rank Parameter Delta %Delta

1 Feedrate 0.5722 46.80

2 Spindle Speed 0.3542 28.97

3 Frequency 0.0861 7.04

4 Spring Pass 0.0857 7.01

5 Coolant Pressure 0.0784 6.41

6 Accuracy Setting 0.0359 2.94

7 Helical Pitch 0.0101 0.83

The Main effects plot of response means, seen in Figure 81 and Figure 82, were created

in order to determine the effect of each parameters level on Ra. The deltas previously

discuss correspond to the slope each parameters plot when taken for low “1” to high “3”.

Figure 81: Mean Effects Plot of Means

93

Figure 82: Interaction Plot of Means

Feedrate and spindle speed have the most effect on surface Ra and increases as feedrate is

increased. Ra decreases with increasing spindle speed, increased ultrasonic frequency,

and increasing spring passes. Minor effect parameters may be quadratic in nature. The

general trends found in spindle speed, feedrate, ultrasonic frequency, and coolant pressure

conform to those discussed in Section 2.2. The effect of spring pass and accuracy

settings, on BK7 pocket floor surface roughness has not been published as of the writing

of this thesis.

Taguchi analysis methods were next applied to the investigation variation, in the form of

pocket floor Ra standard deviation, due to experimental factor levels, as seen in Table 12,

Table 13, Figure 83, and Figure 84.

94

Table 12: Response Table of Standard Deviations

Table 13: Responce Deltas Compared

Rank Parameter Delta %Delta

1 Feedrate 0.1377 11.26


3 Coolant Pressure 0.0798 6.53

4 Spring Pass 0.0705 5.77

5 Helical Pitch 0.0667 5.46


7 Frequency 0.0305 2.49

Figure 83: Main Effects Plot of Standard Deviations

95

Figure 84: Interaction Plot of Standard Deviations

The investigated factors found to produce the largest amount of variation in pocket floor

Ra were feedrate and accuracy setting. Variation was found to increase with increasing

feedrate and spring passes. Variation was found to decrease with increasing accuracy

setting. Again variation in multiple minor effect show possible quadratic trends.

4.2 Box-Behnken Modeling DOE

Table 14 outlines the investigated parameters as well as the levels at which they were

evaluated during modeling trials. Ultrasonic amplitude, although not investigated during

parametric screening trials due to a lack of effect measurement capabilities, was added.

This addition enabled the direct comparison of both ultrasonic on and off helical milling.

The 15 run Box-Behnken design matrix used can be found in Table 41 of Appendix D.

96

Table 14: Box-Behnken DOE Parameters

Parameter Units Low Med High

Percent Ultrasonic Amplitude % 0 50 100

Feed Rate mm/min 500 1000 1500

Spindle Speed rpm 10,000 25,000 40,000

Motivated by the high relative cost of Zerodur, the total number of experimental

parameters was reduced to three in order to decrease the total number of experimental

trials required. The results of Taguchi parametric screening were employed to select

appropriate levels parameters levels for those factors not being included in the modeling

process and are seen in Table 15. Ultrasonic frequency was determined as described in

Section 3.10.2.

Table 15: Modeling DOE Static Parameter Values

Parameter Setting Relative Level

Accuracy Setting Finishing High

Helical Pitch 0.3 (mm) Med

Coolant Pressure 20 (bar) High

Spring Passes 5 High

4.2.1 Experimental Procedure

Five replications of a 15 run Box-Behnken, 3 factor, 3 level DOE were run for a total of

75 individual machining runs. The run order of experimental trials was randomized per

DOE good practices. Detailed descriptions of each element of the experimental setup

employed can be found in the following sections:



Section 3.4.2.5 Mitaka Measurement Custom Fixture

Section 3.6.1 Surface Topological Calculation Metrics

Section 3.6.3 Tool Dressing Method

97

Section 3.7 Tooling

Section 3.7.2 Tool Length Measurement Method

Section 3.5.1.1 - 3.5.1.9 Surface Topological Calculation Metrics

Section 3.8.1 Ultrasonic Measurement System

This phase of test utilized multiple Zerodur optical blanks and therefore the following

expanded controls were instituted during this portion of experimental trials in order to

further increase the mitigation of experimental errors due to improper experimental of

methods:

All optical blanks, as seen in Figure 85, were affixed at the same time.

An equal portion, by weight, of dopping wax was applied to each.

A digital oven was used to cool all stocks together at the same rate.

Figure 85: Prepared Experimental Stock Materials

The flowchart seen in Figure 86 was created during process planning and clearly depicts

the many steps carried out during the experimental process. A clear departure from the

98

Taguchi parametric screening procedure described in Section 3.12.1 can be seen in the

addition of the tool dressing procedures in order to ensure that the tool’s cutting surface is

normalized for every machining operation thus providing machining outcomes that are

less biased by previous cutting operations..

Figure 86: Box-Behnken DOE Experimental Trial Flowchart

4.2.2 Modeling DOE Experimental Results

Upon the completion of experimental machining trials, as seen in Figure 87, each of the

75 pocket floors was measured, as described in Appendix F. Prior to measurement, all

samples were meticulously cleaned to remove any cutting fluid or debris that may alter

the results of measurement with acetone and compressed nitrogen. A summary of the

calculated surface roughness parameters described by Equations (1) through (7) are

presented in Table 16.

99

Table 16: Pocket Floor Surface Roughness Parameter Values

Ra (µm) Rq (µm) Rc (µm) Rp (µm) Rv (µm) Rz (µm) Rt (µm)

Max 3.561 8.456 18.64 28.327 30.021 55.994 135.964

Avg. 2.369 4.756 10.698 14.176 16.726 30.902 61.082

Min 1.495 2.503 5.795 6.101 8.851 15.265 23.04

Figure 87: Experimentally Machined Zerodur Pockets

4.2.2.1 Model Creation and Analysis Overview

Response Surface Regression Analysis (RSRA), carried out in Minitab 17, was used to

derive empirical equations for each of the experimental surface roughness parameters.

The stepwise regression method was implemented in model variable selection in order to

reduce the inclusion of non-significant terms resulting in over fitted models. Coefficients

of Regression (COR) are an important set of outputs created during the RSRA process. A

summary of these outputs, taken from Minitab’s instructions, is as follows:

100

S: is measured in the units of the response variable and represents the standard

distance that data values fall from the regression line.

R2: Describes the amount of variation in the observed response values that is

explained by the predictors. It

R2 (adj): Adjusted R

2 is a modified R

2 that has been adjusted for the number of terms

in the model. If you include unnecessary terms, R2 can be artificially high.

R2 (pred): Predicted R

2 is a measure of how well the model predicts the response for

new observations. Large differences between Predicted R2 and the other two R2

statistics can indicate that the model is overfit.

As part of the RSRA process, outliers are identified by the Dixon’s test in Minitab 17.

Outliers can strongly influence the result of any statistical analysis performed on a data

set. An iterative process was carried out in which, once identified by the Dixon’s test

method, outliers were removed and RSRA was ran again. The resultant changes in model

COR were interpreted in order to provide a quantitative method of model evaluation.

Although effective, this method can lead to the accumulation of error due to a lack of

usable experimental data as the total number of points is reduced. This process was

carried out a minimal number of times and no more than five outliers, 6.67% of total

source data were removed.

Visualization methods were extensively used to during the analysis process in order to

enable more functional interpretation of the prediction model. The following visualization

methods were utilized:

Mean Effects Plot: Plot slopes represent the relative magnitude of the effects.

Contour Plot: Response variables of two continuous variables based on the model

equation while any additional variables are held constant.

101

Surface Plot: 3D version of a contour plot enables increased visualization of continuous

variables.

The following subsections provide the results of RSRA and associated visualization

methods for each of the nine surface roughness parameters. All surface roughness

parameter equations are uncoded factors.

4.2.2.2 Arithmetic Average (Ra)

Table 17 and Equation (11) are the results of iterative Ra RSRA.

Table 17: COR Description of Ra Prediction Model

S 0.29632

R2 65.28%

R2 (adj) 63.27%

R2 (pred) 60.44%

𝑅𝑎 = 2.620 + 0.000550 Feed − 0.000059 RPM + 0.003898 Amp (11)

4.2.2.2.1 Main Effects and Interactions, Ra

The main effects plot of response means, seen in Figure 88, was created in order to

determine the effect of each parameters level on Ra. Mean Ra is seen to decease with

increasing spindle speed nearly linearly. The curvature seen in spindle speed is evident

due to the use of quadratic modeling capabilities of the Box-Behnken method. Both

feedrate and amplitude were found to increase mean Ra. These findings are consistent

with previously RUM published research.

With p-values much greater than 0.05, no statistically significant interactions were found

to affect Ra, within the range of experimental trials.

102

Figure 88: Main Effects Plot for Ra

4.2.2.2.2 Visualization of Predicted Ra Model

Contour and surface plots of the Ra prediction model were created as seen in Figure 89

and Figure 90.

Figure 89: Contour Plot of Ra

15001000500

2.9

2.8

2.7

2.6

2.5

2.4

2.3

2.2

2.1

2.0

350002500015000 100500

Feed

Mean

of

Ra

RPM Amp

Main Effects Plot for RaFitted Means

Feed 1000

RPM 25000

Amp 50

Hold Values

RPM*Feed

150012501000750500

40000

30000

20000

10000

Amp*Feed

150012501000750500

100

75

50

25

0

Amp*RPM

40000300002000010000

100

75

50

25

0

>

–

–

–

–

–

–

< 1.8

1.8 2.0

2.0 2.2

2.2 2.4

2.4 2.6

2.6 2.8

2.8 3.0

3.0

Ra

Contour Plots of Ra

103

Figure 90: Response Surface Plot Ra

4.2.2.3 Root Mean Squared (Rq)

Table 18 and Equation (12) are the results of iterative Rq RSRA.

Table 18: COR Description of Rq Prediction Model

S 0.754937

R2 72.16%

R2 (adj) 69.60%

R2 (pred) 66.30%

𝑅𝑞 = 4.557 + 0.002607 𝐹𝑒𝑒𝑑 − 0.000126 𝑅𝑃𝑀 + 0.00994 𝐴𝑚𝑝 (12)

4.2.2.3.1 Main Effects and Interactions, Rq

The nonlinear mean effect of spindle speed was detected in the Rq prediction model

along with the tendency of increased Rq with either increased feedrate or amplitude, as

seen in Figure 91. Minor interaction between feedrate and spindle speed were found, as

seen in Figure 92. With increasing feedrate mean Rq was found to also increase with

differing rates, depending on spindle speed magnitude.

Feed 1000

RPM 25000

Amp 50

Hold Values

500

1 000

051

.2 0

2.4

2 8.

3.2

25000

15000

005

350 00

3.2

aR

deeF

MPR05 0

0001

051

.002

52.2

02.5

5.2 7

50

0050

001

5.2 7

aR

deeF

pmA

02.

51 0 00

50002

00053

02.

2.4

2.8

3.2

05

0

001

3.2

aR

MPR

pmA

aR fo stolP ecafruS

104

Figure 91: Main Effects Plot for Rq

Figure 92: Interactions Plot of Rq Predictive Model

15001000500

6.0

5.5

5.0

4.5

4.0

350002500015000 100500

Feed

Mean

of

Rq

RPM Amp

Main Effects Plot for RqFitted Means

105

4.2.2.3.2 Visualization of Predicted Rq Model

Contour and surface plots of the Rq prediction model were created as seen in Figure 93

and Figure 94.

Figure 93: Contour Plot of Rq

Figure 94: Response Surface Plot Rq:

Feed 1000

RPM 25000

Amp 50

Hold Values

RPM*Feed

150012501000750500

40000

30000

20000

10000

Amp*Feed

150012501000750500

100

75

50

25

0

Amp*RPM

40000300002000010000

100

75

50

25

0

>

–

–

–

< 4

4 5

5 6

6 7

7

Rq

Contour Plots of Rq

Feed 1000

RPM 25000

Amp 50

Hold Values

25 000

35000

51 00

0051 0

25 000

500

4

001 0

5

6

7

qR

deeF

MPR50

1500100

0

50

3500

4

0001

4

5

6

qR

deeF

pmA

05

350001

0

05

3

4

00051052 00

0500

4

5

6

qR

MPR

pmA

qR fo stolP ecafruS

106

4.2.2.4 Mean Height of Profile Irregularities (Rc)

Table 19 and Equation (13) are the results of iterative Rc RSRA.

Table 19: COR Description of Rc Prediction Model

S 1.87208

R2 62.90%

R2 (adj) 60.21%

R2 (pred) 56.16%

𝑅𝑐 = 10.41 + 0.00532 𝐹𝑒𝑒𝑑 − 0.000255 𝑅𝑃𝑀 + 0.02005 𝐴𝑚𝑝 (13)

4.2.2.4.1 Main Effects and Interactions, Rc

The nonlinear mean effect of spindle speed was detected in the Rc prediction model

along with the tendency of increased Rc with either increased feedrate or amplitude, as

seen in Figure 95. Minor interaction between feedrate and were determined to be

statistically significant, as seen in Figure 96; however within the ranges tested in this

modeling are not considered to have a significant effect to mean response effects.

Figure 95: Main Effects Plot for Rc

15001000500

14

13

12

11

10

9

8

350002500015000 100500

Feed

Mean

of

Rc

RPM Amp

Main Effects Plot for RcFitted Means

107

Figure 96: Interactions Plot of Rc Predictive Model

4.2.2.4.2 Visualization of Predicted Rc Model

Contour and surface plots of the Rc prediction model were created as seen in Figure 97

and Figure 98.

Figure 97: Contour Plot of Rc

Feed 1000

RPM 25000

Amp 50

Hold Values

RPM*Feed

150012501000750500

40000

30000

20000

10000

Amp*Feed

150012501000750500

100

75

50

25

0

Amp*RPM

40000300002000010000

100

75

50

25

0

>

–

–

–

< 8

8 10

10 12

12 14

14

Rc

Contour Plots of Rc

108

Figure 98: Response Surface Plot Rc

4.2.2.5 Maximum Peak (Rp)

Table 20 and Equation (14) are the results of iterative Rp RSRA.

Table 20: COR Description of Rp Prediction Model

S 2.36902

R2 59.70%

R2 (adj) 53.76%

R2 (pred) 45.51%

𝑅𝑝 = 17.79 + 0.004289 𝐹𝑒𝑒𝑑 − 0.000608 𝑅𝑃𝑀 + 0.02607 𝐴𝑚𝑝 (14)

4.2.2.5.1 Main Effects, Rp

The greater relative nonlinearity in the mean effect of spindle speed was detected in the

Rp prediction model with respect to previous roughness parameters. Again the tendency

of increased Rp with either increased feedrate or amplitude, as seen in Figure 99. No

statistically significant interactions were found to affect Rp, within the range of

experimental trials.

Feed 1000

RPM 25000

Amp 50

Hold Values

50001 00

8

12

25000

15000

0051

50003

25000

61

cR

MPR

deeF

0050001

8

01

50

00015

1 00

50

21

cR

pmA

deeF

1500025000

53 0

8

01

21

50

0000

001

50

21

14

cR

pmA

MPR

cR fo stolP ecafruS

109

Figure 99: Main Effects Plot for Rp

4.2.2.5.2 Visualization of Predicted Rp Model

Contour and surface plots of the Rp prediction model were created as seen in Figure 100

and Figure 101.

Figure 100: Contour Plot of Rp

15001000500

19

18

17

16

15

14

13

12

11

350002500015000 100500

Feed

Mean

of

Rp

RPM Amp

Main Effects Plot for RpFitted Means

Feed 1000

RPM 25000

Amp 50

Hold Values

RPM*Feed

150012501000750500

40000

30000

20000

10000

Amp*Feed

150012501000750500

100

75

50

25

0

Amp*RPM

40000300002000010000

100

75

50

25

0

>

–

–

–

–

–

< 10

10 12

12 14

14 16

16 18

18 20

20

Rp

Contour Plots of Rp

110

Figure 101: Response Surface Plot of Rp

4.2.2.6 Maximum Valley Depth (Rv)

Table 21 and Equation (15) are the results of iterative Rv RSRA.

Table 21: COR Description of Rv Prediction Model

S 2.5873

R2 69.73%

R2 (adj) 66.94%

R2 (pred) 62.66%

𝑅𝑣 = 10.77 + 0.01816 𝐹𝑒𝑒𝑑 − 0.000406 𝑅𝑃𝑀 + 0.03298 𝐴𝑚𝑝

− 0.000004 𝐹𝑒𝑒𝑑 ∗ 𝐹𝑒𝑒𝑑 (15)

4.2.2.6.1 Main Effects and Interactions, Rv

Nonlinearity in both feedrate and spindle speed were mean effect were detected Rv

prediction model, as seen in Figure 102. Minor interaction between feedrate and were

determined to be statistically significant, as seen in Figure 103. Differing in their

curvature from previous parameters, interaction was not considered to have a significant

effect on mean response effects, within the ranges tested in this modeling.

Feed 1000

RPM 25000

Amp 50

Hold Values

0500001

01

15

25000

0051 0

0051

053 00

25000

02

pR

MPR

deeF

5000001

01

21

14

05

00051

100

05

14

61

pR

pmA

deeF

010.

51 00000052

053

010.

5.21

15.0

50

0000

001

50

5.71

pR

pmA

MPR

pR fo stolP ecafruS

111

Figure 102: Main Effects Plot for Rv

Figure 103: Interactions Plot of Rv Predictive Model

4.2.2.6.2 Visualization of Predicted Rv Model

Contour and surface plots of the Rv prediction model were created as seen in Figure 104

and Figure 105.

15001000500

21

20

19

18

17

16

15

14

13

12

350002500015000 100500

Feed

Mean

of

Rv

RPM Amp

Main Effects Plot for RvFitted Means

112

Figure 104: Contour Plot of Rv

Figure 105: Response Surface Plot Rv

Feed 1000

RPM 25000

Amp 50

Hold Values

RPM*Feed

150012501000750500

40000

30000

20000

10000

Amp*Feed

150012501000750500

100

75

50

25

0

Amp*RPM

40000300002000010000

100

75

50

25

0

>

–

–

–

–

–

–

< 12

12 14

14 16

16 18

18 20

20 22

22 24

24

Rv

Contour Plots of Rv

Feed 1000

RPM 25000

Amp 50

Hold Values

005

0001

51 00

10005

51

20

053 00

02500

00 051

053 00

25

vR

deeFMPR

05 0

0001

0051

0105 0

51

50

0

100

02

vR

deeFpmA

15000

2 0500

35000

12

16

20

50

0

001

24

vR

MPRpmA

vR fo stolP ecafruS

113

4.2.2.7 Average Maximum Profiler Height (Rz)

Table 22 and Equation (16) are the results of iterative Rz RSRA.

Table 22: COR Description of Rz Prediction Model

S 4.43312

R2 72.80%

R2 (adj) 70.21%

R2 (pred) 66.71%

𝑅𝑧 = 16.78 + 0.0375 Feed − 0.000702 RPM + 0.0701 Amp

− 0.000009 Feed ∗ Feed (16)

4.2.2.7.1 Main Effects and Interactions, Rz

Nonlinearity in both feedrate and spindle speed were mean effect were detected Rz

prediction model, as seen in Figure 106. Minor nonlinearly interaction, seen in Figure

107, was not considered to have a significant effect on mean response effects, within the

ranges tested in this modeling.

Figure 106: Main Effects Plot for Rz

15001000500

40

35

30

25

350002500015000 100500

Feed

Mean

of

Rz

RPM Amp

Main Effects Plot for RzFitted Means

114

Figure 107: Interactions Plot of Rz Predictive Model

4.2.2.7.2 Visualization of Predicted Rz Model

Contour and surface plots of the Rz prediction model were created as seen in Figure 108

and Figure 109.

Figure 108: Contour Plot of Rv

Feed 1000

RPM 25000

Amp 50

Hold Values

RPM*Feed

150012501000750500

40000

30000

20000

10000

Amp*Feed

150012501000750500

100

75

50

25

0

Amp*RPM

40000300002000010000

100

75

50

25

0

>

–

–

–

–

–

< 20

20 25

25 30

30 35

35 40

40 45

45

Rz

Contour Plots of Rz

115

Figure 109: Response Surface Plot Rz

4.2.2.8 Maximum Height of Profile (Rt)

Table 23and Equation (17) are the results of iterative Rt RSRA.

Table 23: COR Description of Rt Prediction Model

S 18.8792

R2 41.16%

R2 (adj) 36.89%

R2 (pred) 28.79%

𝑅𝑡 = 62.9 + 0.0377 Feed − 0.00255 RPM + 0.1773 Amp − 0.000001 Feed

∗ RPM (17)

Feed 1000

RPM 25000

Amp 50

Hold Values

02

0050001

30

40

00051

0150

35000

00052

zR

MPR

deeF

20

005001 0

20

52

30

35

0

0051

010

05

010

zR

pmA

deeF

25

1 050025000

3

25

30

53

40

0 053 00

001

50

001

zR

pmA

MPR

zR fo stolP ecafruS

116

4.2.2.8.1 Main Effects and Interactions, Rt

Nonlinearity was detected in spindle speed mean effect were in Rt prediction model, as

seen in Figure 110.

Figure 110: Main Effects Plot for Rt

Figure 111: Interactions Plot of Rt Predictive Model

15001000500

85

80

75

70

65

60

55

50

45

350002500015000 100500

Feed

Mean

of

Rt

RPM Amp

Main Effects Plot for RtFitted Means

117

4.2.2.8.2 Visualization of Predicted Rt Model

Contour and surface plots of the Rt prediction model were created as seen in Figure 112

and Figure 113.

Figure 112: Contour Plot of Rt

Figure 113: Response Surface Plot Rt

Feed 1000

RPM 25000

Amp 50

Hold Values

RPM*Feed

150012501000750500

40000

30000

20000

10000

Amp*Feed

150012501000750500

100

75

50

25

0

Amp*RPM

40000300002000010000

100

75

50

25

0

>

–

–

–

–

–

< 40

40 50

50 60

60 70

70 80

80 90

90

Rt

Contour Plots of Rt

Feed 1000

RPM 25000

Amp 50

Hold Values

04

005

06

1000

06

80

100

15000

0051

00503

02 050

00503

tR

deeF

MPR

04

500

05

01 00

0560

70

1500

0

05

001

tR

deeF

pmA

40

50001

06

25000

06

08

003500

0

50

001

tR

MPR

pmA

tR fo stolP ecafruS

118

4.2.3 Box-Behnken Modeling DOE Conclusions

The majority of roughness parameters investigated possessed the following

characteristics:

Increased spindle speed results in decreased mean surface roughness. Varying levels

of nonlinearity were found at the upper extremes for many parameters.

As feedrate is increased, mean surface roughness parameters generally increased

linearly. The notable exceptions were; Rv and Rz with curvature seen at their upper

boundaries.

As ultrasonic amplitude increased, surface parameter magnitudes generally increased.

Interactions between feedrate and spindle speed were found to be statistically

significant in multiple regression models although no significant trend in overall

model performance was detected across groups.

These findings are consistent with previously published research on RUM with respect to

Ra. A general point of departure from the bulk of published work is the decrease in

surface roughness parameters with the inclusion of ultrasonic amplitude and the

investigation of a variety of surface roughness parameters other than Ra.

4.3 Validation Trials

Machining trials were carried out in order to validate the surface parametric models

created during the Box-Behnken modeling trials. Three machining regimes were chosen,

two within the boundaries of the Box-Behnken DOE space and one outside in a region

more aggressive, as seen in Table 24.

Table 24: Validation Trial Experimental Parameters

Parameter Units Low AB Med BC High / E

Feedrate (mm/min) 500 750 1000 1250 1500

Spindle Speed (rpm) 10000 17500 25000 32500 40000

Ultrasonic Amplitude (%) 0 25 50 75 100

119

As discussed in Section 4.2, high settings were not tested simultaneously during

modeling trials; however, as the aim of this research is the creation and modeling of

RUM parameters of high MRR capability, this group of all high settings, referred from

now on as E, were selected. The use of E settings also enables the investigation each

model’s ability to predicted roughness parameters outside the upper boundaries of

derivation trials.

Particular attention was paid to carry out both machining trials and data collection in a

manner as similar to modeling DOE procedures as possible. A total of 30 trials were

conducted at each setting. The sample size of each machining regime was such that the

normality assumptions of the inferential statistics methods employed are satisfied. 95%

confidence intervals were calculated for both predicted and empirical values and serve as

the intervals used for the following figures. The following subsections provide the results

of validation trials for each of the nine surface roughness parameters investigated,

followed by a summarization of the results in Section 4.3.8.

120

4.3.1 Arithmetic Average (Ra)

The predicted, actual, and percent differences for Ra are presented in Figure 114 and

Table 25.

Figure 114: Ra Validation Trial Results

Table 25: Predicted and Experimental Values of Ra

Setting Predicted Actual % Diff

AB 2.287 1.913 16.370

BC 2.345 1.833 21.832

E 2.482 2.150 13.357

2.287 2.345

2.482

1.913 1.833 1.861

1.000

1.500

2.000

2.500

3.000

AB BC E

Ra

µm

Predicted and Actual Ra Compared

Predicted Actual

121

4.3.2 Root Mean Squared (Rq)

The predicted, actual, and percent differences for Rq are presented in Figure 115 and

Table 26.

Figure 115: Rq Validation Trial Results

Table 26: Predicted and Experimental Values of Rq


AB 4.514 3.779 16.288

BC 4.558 3.591 21.218

E 4.639 4.578 1.317

4.514 4.558 4.639

3.779 3.591

4.578

1.000

2.000

3.000

4.000

5.000

6.000

7.000

AB BC E

Rq

µm

Predicted and Actual Rq Compared

Predicted Actual

122

4.3.3 Mean Height of Profile Irregularities (Rc)

The predicted, actual, and percent difference for Rc are presented in Figure 116 and Table

27.

Figure 116: Rc Validation Trial Results

Table 27: Predicted and Experimental Values of Rc


AB 10.317 8.729 15.396

BC 10.275 8.108 21.087

E 10.332 10.526 -1.878

10.317 10.275 10.332

8.729 8.108

10.526

3

5

7

9

11

13

15

AB BC E

Rc

µm

Predicted and Actual Rc Compared

Predicted Actual

123

4.3.4 Maximum Peak (Rp)

The predicted, actual, and percent differences for Rp are presented in Figure 117 and

Table 28.

Figure 117: Rp Validation Trial Results

Table 28: Predicted and Experimental Values of Rp


AB 13.487 9.815 27.223

BC 13.842 8.346 39.702

E 15.374 12.265 20.223

13.487 13.842

15.374

9.815

8.346

12.265

0

5

10

15

20

25

AB BC E

Rp

µm

Predicted and Actual Rp Compared

Predicted Actual

124

4.3.5 Maximum Valley Depth (Rv)

The predicted, actual, and percent differences for Rv are presented in Figure 118 and

Table 29.

Figure 118: Rv Validation Trial Results

Table 29: Predicted and Experimental Values of Rv


AB 15.559 13.320 14.389

BC 16.286 12.498 23.257

E 16.020 15.649 2.313

15.559 16.286 16.020

13.320 12.498

15.649

0.000

5.000

10.000

15.000

20.000

25.000

AB BC E

µm

Predicted and Actual Rv Compared

Predicted Actual

125

4.3.6 Average Maximum Profiler Height (Rz)

The predicted, actual, and percent differences for Rz are presented in Figure 119 and

Table 30.

Figure 119: Rz Validation Trial Results

Table 30: Predicted and Experimental Values of Rz


AB 28.416 23.135 18.585

BC 30.606 20.845 31.893

E 30.098 27.914 7.258

.

28.416

30.606 30.098

23.135

20.845

27.914

10

15

20

25

30

35

40

45

AB BC E

Rz

µm

Predicted and Actual Rz Compared

Predicted Actual

126

4.3.7 Maximum Height of Profile (Rt)

The predicted, actual, and percent difference for Rt are presented in Figure 120 and Table

31

Figure 120: Rt Validation Trial Results

Table 31: Predicted and Experimental Values of Rt


AB 54.894 45.338 17.409

BC 57.973 39.281 32.243

E 63.051 53.498 15.151

54.894 57.973

63.051

45.338

39.281

53.498

0

20

40

60

80

100

AB BC E

Rt

µm

Predicted and Actual Rt Compared

Predicted Actual

127

4.3.8 Validation Trial Summary

A surprising trend was found as a result of validation trials. E, the most aggressive regime

was found to be best described by the RSRA modeling process, with respect to percent

difference form actual and predicted values, as seen in Figure 121. All models in E

exhibit reduced deviation between theoretical and actual values.

Figure 121: Compared Parametric Model Accuracy by Regime

4.4 Tool Wear Experimental Trials

Three tool wear experimental studies were conducted to determine the wear rate of the

metal bonded diamond impregnated tooling used throughout this research. For the

purposes of this research, tool wear is defined as the overall reduction of tool length and

is attributed to diamond grain fracture involving the removal of abrasive fragments by

fracture within the grain and bond fracture [37].

0

5

10

15

20

25

30

35

40

RaRqRcRpRvRzRt

Per

cen

t D

iffe

ren

ce

Compared Parameter Accuracy by Regime

AB BC E

128

Figure 122 was created during process planning and clearly depicts the many procedures

carried out during each experimental machining trial. This general process plan was used

for all three tool wear investigations covered throughout this section.

Figure 122: BK7 Tool Wear Experimental Trial Flowchart

4.4.1 BK7 Tool Wear Trials

Due to the expense of Zerodur optical blanks, initial tool wear trials were conducted in

BK7 glass. In a manner similar to that of parametric screening trials, BK7 glass was

helically milled in order to determine the tool wear rates associated with various cutting

conditions. This stage of tool wear investigation focused on the determination of tool

wear rates associated with the cutting condition to be employed during Box-Behnken

modeling trials. This work both informed process planning and tooling procurement

requirements. In order to simulate the range of tool wear rates associated with modeling

trials, the most and least aggressive cutting conditions were assumed to be associated

with the highest and lowest rates of tool wear, respectively, as seen in Table 32.

129

Table 32: BK7 Tool Wear Parameters

Parameter Units Low High

Percent Ultrasonic Amplitude % 0 100

Spindle Speed rpm 10,000 40,000

Feed Rate mm/min 500 1500

A series of ten pockets were helically milled. Three tool length measurements were made

and average tool wear was calculated. A total of 100 pockets were machined per cutting

regime. Detailed descriptions of each element of the experimental setup can be found in

the following sections:


Section 3.2 Machine Tool and Ultrasonic Systems


Section 3.7 Tooling

Section 3.7.2 Tool Length Measurement

Section 3.9 Ultrasonic Measurement System

4.4.1.1 BK7 Tool Wear Results

The rates of tool wear per unit material removed were compared in order to quantitatively

compare each regime’s tool wear rate and are shown in Figure 123 and Table 33.

Table 33: Compared Tool Wear Per Material Removal, BK7

High (mm/cm3) Low (mm/cm

3) %Diff

-0.0231 -0.0195 15.58

130

Figure 123: Compared Tool Wear with Material Removal

Estimation of the average expected low range tool wear expected per Box-Behnken DOE

pocket was only 2.56 (µm). Due to the limited pocket depth possible when using Zerodur

optical it was determined the tool wear measurement during modeling trials would not

yield a signal to noise ratio of adequate magnitude to ensure a statistically significant

source of data. This finding motivated the need to conduct Zerodur tool wear trials on a

larger block Zerodur and not optical blanks.

4.4.2 Zerodur Block Tool Wear Trials

Through the use of a large Zerodur block, seen in Figure 19, pocket depths and the total

number pockets were significantly increased allowing for a larger signal to noise ratio

with respect to tool wear magnitudes and therefore enabling increased sensitivity to tool

wear. In order to investigate ultrasonic oscillation’s effect on tool wear rate, all cutting

y = -0.00195x + 1.08649

R² = 0.94114

y = -0.00231x + 1.04897

R² = 0.97986

0.5

0.6

0.7

0.8

0.9

1.0

0 50 100 150 200 250

To

ol

Len

gth

Red

uct

ion

(m

m)

Material Removed (cm^3)

BK7 Tool Wear Compared

Low Range High Range

131

condition parameters, other than percent ultrasonic amplitude, were held constant, as seen

in Table 34.

Table 34: Zerodur Block Tool Wear Trial Parameters

Parameter Units Low High




Zerodur block trials were conducted with the same setup and procedures used Section

4.4.1. A total 100 pockets were machined in each regime, the results of which are shown

in Table 35 Figure 124. A reduction in tool wear was found through the use of ultrasonic

actuation. This result is in agreement with previous research’s work on RUM of hard and

brittle materials.

Table 35: Zerodur Block Tool Wear Results Compared

Unit US On US Off %Diff

(mm/cm3) 0.0012 0.0013 8.33

Figure 124: Zerodur Tool Wear vs. Material Removal (US On/Off)

y = -0.0012x + 1.0304

R² = 0.9934 y = -0.0013x + 1.0273

R² = 0.9797

0.70

0.75

0.80

0.85

0.90

0.95

1.00

20 40 60 80 100 120 140 160 180 200 220

To

ol

Len

gth

Red

uct

ion

(m

m)

Material Removed (cm3)

Normalized Tool Wear v.s. MR (US On/Off)

US On US Off

132

4.5 Ultrasonic Effect on Surface Quality

The following experimental trials were conducted to inform modeling DOE trials and to

isolate, investigate, and quantify the possible effects of ultrasonic oscillation on various

helical pocketing outcomes, a series of trials of were conducted both with and without

ultrasonic oscillation. All cutting condition parameters, other than percent ultrasonic

amplitude, were held constant, as seen in Table 36.

Table 36: Zerodur Cutting Force Trial Parameters

Parameter Units US Off US On




30 ultrasonic and non-ultrasonic experimental trials were conducted using the

experimental setup and procedures utilized for Box-Behnken Modeling DOE, seen in

Section 4.2.

4.5.1 Ultrasonic Surface Quality Comparison Results

The use of ultrasonic oscillation was found to increase the mean magnitudes of overall

measured surface roughness parameters, as seen in Figure 125. Error bars created for

each mean value were based on the standard deviation of each respective quantity.

Ultrasonic oscillation in normally cited as improving surface quality in the literature;

however, as this is the first work focused on the helical pocketing of Zerodur. When

compared to drilling and side cutting operations previously studied, helical pocketing

should be considered an initial roughing strategy meant to be followed by finishing,

lapping, and polishing operations per surface quality requirements. In general practice by

ultrasonic applications engineers, ultrasonic oscillation is turned off during the finishing

of hard and brittle materials.

133

Figure 125: Surface Roughness Parameters Compared (US On/Off)

4.6 Cutting Force Comparison

Cutting force is of primary concern to the successful machining of hard and brittle

materials. The repeatability of extreme precision machined features is greatly influenced

by the cutting force variation [65]. With the use of ultrasonic oscillation, reduction in

cutting forces has been reported in previous research; however, no published work on

cutting forces of helical RUM pocketing of Zerodur has been found.

The experimental setup and procedures used in Section 4.5 and the force measurement

system described in Section 3.11 were used in conjunction throughout this portion of

experimental trials. Due to critical fault the Kistler 9257B cutting force measurement

system, only lateral forces were investigated throughout this investigation. Minitab 17

was used to analyze and interpret the results of all 60 cutting force trials utilized each

comprised of a total of 33,000 force measurements per axis, per cutting operation. Figure

Ra (µm) Rq (µm) Rc (µm) Rp (µm) Rv (µm) Rz (µm) Rt (µm)

US On 2.075 3.757 8.439 10.332 14.103 18.868 51.103

US Off 1.955 3.469 7.889 9.434 12.754 16.687 45.328

% Diff 5.758 7.672 6.520 8.695 9.565 11.560 11.299

0

10

20

30

40

50

60

70Compared Surface Roughness Parameter

US On US Off

134

126 was created during process planning and clearly depicts the many steps carried out

during each cutting force experimental machining trial.

Figure 126: Zerodur Tool Wear Experimental Trial Flowchart

4.6.1 Cutting Force Comparison Results

Ultrasonic oscillation was found to decrease both maximum and average lateral helical

pocketing process forces, as seen in Table 37, Figure 127, and Figure 128. The errors bars

in these graphs are based on the standard deviations of each respective quantity. The

observed reduction of cutting forces seen in these trials is in agreement with previously

published research on non-helical milling and helps to substantiate the effectiveness of its

use in workpieces susceptible to critical fracture due to excessive cutting forces.

Table 37: Cutting Force Comparison Results

US Off US On % Diff

RMS 21.3301 16.3013 23.58

Max 50.4123 32.6051 35.32

135

Figure 127: Average Cutting Forces Compared

Figure 128: Max Cutting Forces Compared

16.301 21.330

0

5

10

15

20

25

La

tera

l R

MS

Cu

ttin

g F

orc

s (N

)

Average Cutting Forces Compared

US On US Off

32.605 50.412

0

10

20

30

40

50

60

Ma

x L

ate

ra

l C

utt

ing

Fo

rce

(N)

Max Cutting Forces Compared

US On US Off

136


A Taguchi orthogonal array was employed to determine the relative effect on pocket floor

surface roughness parameters resulting from RUM helically milled Zerodur. The process

parameters found to have the largest effect on surface quality were investigated through

the use of a Box-Behnken modeling DOE. Validation trials were conducted in order to

evaluate each model’s accuracy in the prediction of surface roughness parameters.

Ultrasonic’s effect on the cutting forces and tool wear rates associated with Zerodur

helical pocketing were investigated.

137

5 Conclusions and Suggested Future Work

5.1 Thesis Overview

This thesis presents a series of statistical models capable of predicting multiple surface

roughness parameters in the helical pocketing of Zerodur by means of RUM. A brief

history of hard and brittle material shaping and previous RUM research was presented in

Chapters 1 and 2. Chapter 3 described the experimental methods used throughout

physical machining, the justification of their use. The results of parametric screening,

statistical modeling, model validation, tool wear, and cutting force comparison

experimental trials were presented in Chapter 4. The following sections summarize the

results of this research and provide recommendations for possible opportunities of future

RUM research.

5.2 Conclusions and Contributions

The motivation for the development of predictive models for the pocket floor surface

roughness parameters of helically milled Zerodur arose due to the enormous cost and

time involved in resorting to trial-and-error methods in the determination of optimum

RUM conditions. The contributions and conclusions from Chapter 4 are listed as follows:

1. With respect to the effectiveness and appropriate setting of RUM helical milling

parameter for minimization of mean pocket floor Ra.

Feedrate and spindle speed have the most effect on surface Ra

Ra increases as feedrate is increased

Ra decreases with increasing spindle speed

Ra decreases with increased ultrasonic frequency

Ra decreases with increasing spring passes

138

Minor effect parameters may be quadratic in nature

2. With respect to the effectiveness and appropriate setting of RUM helical milling

parameter for the minimization of pocket floor Ra variation.

Feedrate and accuracy setting have the most effect on process variation

Variation increases with increasing feedrate and spring passes

Variation decreases with increasing controller accuracy setting

3. With respect to pocket floor surface roughness parameters investigated, the following

characteristics were experimentally determined:

Increased spindle speed results in decreased mean surface roughness. Varying levels

of nonlinearity were found at the upper extremes for many parameters.

As feedrate is increased, mean surface roughness parameters generally increased

linearly. The notable exceptions were; Rv and Rz with curvature seen at their upper

boundaries.

As ultrasonic amplitude increased, surface parameter magnitudes generally increased.

Interactions between feedrate and spindle speed were found to be statistically

significant in multiple regression models although no significant trend in overall

model performance was detected across groups.

4. With respect to the predictive capability of the empirically determined surface

roughness parameter equations.

The most aggressive RUM process regime was found to be best described by the

RSRA modeling process with respect to percent difference form actual and predicted

values. This result may be an indication that the experimental variable ranges used for

parametric screening and prediction modeling may have been too narrow in

magnitude.

5. With respect to the effect of ultrasonic oscillation on overall pocket surface quality.

139

The surface roughness parameters for helically pocketed Zerodur are generally

increased in magnitude through the use of ultrasonic oscillation.

When compared to drilling and side cutting operations previously studied, helical

pocketing should be considered an initial roughing strategy meant to be followed by

finishing, lapping, and polishing operations per surface quality requirements.

6. With respect to lateral cutting forces during helical pocketing of Zerodur

The lateral cutting forces associate with helical pocketing can be decreased through

the implementation of ultrasonic oscillation.

The observed reduction of cutting forces seen in these trials is in agreement with

previously published research on non-helical milling and helps to substantiate the

effectiveness of its use in workpieces susceptible to critical fracture due to excessive

cutting forces.

5.3 Recommendations for Future Work

The following areas of investigation would help to advise the design and implementation

of future RUM manufacturing operations in both industrial and academic settings. An

expanded ability to precisely predict and manipulate RUM process outcomes could allow

for an expanded use of RUM utilization.

There are several hard and brittle materials that suffer from low relative machinability

and that would therefore benefit from experimental investigations like those

conducted throughout this research. A brief example of materials that could benefit

from increased RUM process investigation includes carbon matrix composites

(CMC), ultra-fine grain tungsten carbide, silicon carbide, and metallic foams.

Similar investigations into facing and freeform geometric creation would enable an

increased understanding of the RUM process in the context of workpieces of high

overall complexity.

140

An expansion of experimental variable ranges could be included in future parametric

screening and prediction modeling trials to investigate possible improvements to

model accuracies.

Tooling parameters such as bond type, abrasive type, abrasive size, concentrations,

etc. need to be investigated with respect to helical RUM milling.

An increased investigation in to multiple forms of tool wear attributed to RUM the

RUM process, for example the tendency for axial and lateral face boundary rounding

under non-plunge type cutting movements.

141

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Appendix A: Sauer Application Interview

In order to asses both ultrasonic customer needs and possible areas of interest for future

research, the following questions were asked to the Sauer Ultrasonic Applications

manager, Andreas Schwarz during the summer of 2013 during my second ultrasonic

internship at the DMG MORI Sauer Ultrasonic Headquarters in Stipshausen Germany.

6.1.1 Primary

1. What would you have application engineers investigate if budget and time was not an

issue?

Parametric studies

Tool variation

On-machine polishing

Deep hole boring straightness

MRR studies per material

2. What type of glass material is most often requested by customers?

Zerodur

3. Is MRR or surface roughness more often requested by customer?

Surface roughness is priority

4. In what form is a customer’s specification for MRR?

Time/part

5. What is the average requirement for MRR?

Time/part

6. Which is the most typical customer requirement unit for Surface Roughness (Ra or

RMS)

Ra normally, but does very depending of the country

7. What is the most typical level of requested Surface Roughness?

They want to see the best initially, but normally depends on the part,

typically Ra 0.2 (µm) and less

8. What is the best Surface Roughness obtained on a glass project?

Flat glass Ra=0.15≈0.2

9. Which is the most typical customer requirement unit for Tool wear? (mm wear /

volume removed)

Workpieces per tool for customer wants. Hours cutting, life time.

10. What is the most typical customer requirement for Tool wear?

minimal

149

11. What is the typical Tool wear obtained on a glass project?

Low in glass relative to other materials

12. What is the minimum Tool wear obtained on a glass project?

n/a

6.1.2 Process and Operations

13. What would be the normal operational sequence for a Zerodur mirror support like the

one often shown in marketing info?

1. Outer Dia 2. Pockets, helix w/ biggest tool possible, helical finish. 3.

Convex and concave mirror sides, then off to polishing.

14. Like traditional milling, are roughing, semi-finishing, and finishing operations

typically ran?

Semi then finishing

15. Is the EasySONIC option popular with customers, If yes/no why so?

Not yet, still too new, costs?

16. Helical interpolation normally created in Siemens 840D, CAM / Excel, other?

CAM powermill Dell CAM, Simetron

17. Are post-helical spring passes normally used, if so how and how many?

Yes, 1 Schmidt, but depends on application. For flat bottom no more than 1

needed.

18. Have there been any testing / previous customer parts in which a ratio of lateral to

vertical feed rates was found to improve machining outcomes?

Only small pitch so minimal z feed.

19. Diamond concentration; are there similar tools available to verify the diminished need

for varied diamond concentration?

Only can find in testing

Re-sharpening, then good

Not re-sharpening, bad results, until you get sharpening.

Look at, even when you get the right time or Ra, you can change conditions

and gain size (D)

*Look at G-factor for tool wear, 1:200 bad 1:20000 good, set TW to 1

19A) slotted tooling, helps to prevent hydroplaning. No research as of yet.

20. Have any tests been conducted on Climb vs. Conventional?

No, changing direction could make unstable grains. Grains get supported

on the none-cutting side and exposed on the cutting side. If you change, the

grain can be easily removed.

21. Optimized usage of ultrasonic actuation (UA) to prevent negative result outcomes for

example:

a. No Initial UA during material entry to prevent edge chipping

Yes, US off for threw hole exit.

150

b. No UA during spring passes.

yes

6.1.3 Equipment

22. What are the certified accuracies for the Renishaw laser tool measurement system for:

23. Length ± ≈4(µm)

Radius / Diameter ± ≈4(µm)

24. D107 parameters range safe for D35

no

25. What is the method for recording spindle force, torque, and other data on the US20?

Nope

26. What are the verifiable of their systems accuracies?

n/a

27. What data logging capabilities does the ULTRASONIC 20 linear have for these

outputs?

n/a

28. What wax types do you suggest to customers?

Data sheet with the 3 waxes.

29. Has any study been ran on the Pro & Cons of different wax types for different

applications?

No. some waxes dissolve or are not suited for prolonged rest periods

between machining.

6.1.4 Logistics

30. Wax order needed for CA, is there a local supplier I can visit while here?

Idar Oberstien, Kruel

151

Appendix B: Tool Length Measurement Method Validation Data

Table 38: Tool Length Measurement Method Comparison Data

Trial Total Time (sec) Laser (mm) Height Gage (mm)

1 198 130.845 130.827

2 26 130.843 130.847

3 24 130.842 130.857

4 44 130.842 130.849

5 123 130.842 130.842

6 27 130.842 130.848

7 119 130.843 130.850

8 24 130.844 130.847

9 28 130.843 130.848

10 112 130.842 130.847

11 59 130.843 130.840

12 115 130.843 130.845

13 26 130.843 130.849

14 24 130.844 130.837

15 200 130.844 130.845

16 25 130.844 130.845

17 82 130.845 130.849

18 61 130.844 130.844

19 27 130.844 130.848

20 25 130.844 130.843

21 57 130.843 130.845

22 112 130.844 130.845

23 24 130.845 130.849

24 168 130.844 130.845

25 58 130.844 130.849

26 17 130.841 130.842

27 32 130.844 130.845

28 153 130.844 130.846

29 25 130.843 130.847

30 35 130.843 130.847

31 31 130.843 130.850

32 68 130.844 130.851

33 24 130.843 130.851

34 31 130.845 130.845

35 63 130.843 130.850

36 410 130.846 130.850

37 28 130.843 130.849

38 26 130.844 130.849

39 98 130.842 130.852

40 69 130.843 130.844

152

Figure 129: Laser Measurement Trial Results Summary

153

Figure 130: Hieght Gage Trial Results Summary

154

Figure 131: Tool Length Measurement Methods Compared

130.835

130.840

130.845

130.850

130.855

130.860

1 11 21 31

To

ol

Len

gth

(m

m)

Trial Number

Compared Tool Length Measurement Methods

Laser (mm) Height Gage (mm)

155

Appendix C: Tool Dressing Method Validation Data

Table 39: Tool Dressing Investigation Data

Trial Tool Length (mm) Difference (mm)

133.891

1 133.834 0.057

2 133.743 0.091

3 133.673 0.070

4 133.627 0.046

5 133.528 0.099

6 133.476 0.052

7 133.460 0.016

8 133.422 0.038

9 133.352 0.070

10 133.269 0.083

11 133.209 0.060

12 133.161 0.048

13 133.112 0.049

14 133.049 0.063

15 133.016 0.033

16 132.956 0.060

17 132.929 0.027

18 132.865 0.064

19 132.824 0.041

20 132.724 0.100

21 132.677 0.047

22 132.654 0.023

23 132.638 0.016

24 132.586 0.052

25 132.554 0.032

26 132.523 0.031

27 132.444 0.079

28 132.384 0.060

29 132.321 0.063

30 132.275 0.046

156

Figure 132: Tool Length Reduction With Dressing Operations

Figure 133: Dressing Trial Results Summary

y = -0.0517x + 133.81

R² = 0.9954

132

132

132

133

133

133

133

133

134

134

134

0 5 10 15 20 25 30

To

ol

Len

gth

Experimetnal Dressing Trials

Tool Length v.s. Dressing Operations

157

Figure 134: Dressing Process Cycle Time

120

122

124

126

128

130

132

134

136

0 5 10 15 20 25 30

Tim

e (s

ec)

Trial Number

DOE Dressing Macro Cycle Time

158

Appendix D: Taguchi and Box-Behnken DOE Matrices

Table 40: Taguchi Coded DOE Matrix

R

un

Ultrasonic

Frequency

Accuracy

Setting

Feed

Rate

Helical

Pitch

Spindle

Speed

Spring

Passes

Coolant

Pressure

1 1 1 1 1 1 1 1

2 1 1 1 1 2 2 2

3 1 1 1 1 3 3 3

4 1 2 2 2 1 1 1

5 1 2 2 2 2 2 2

6 1 2 2 2 3 3 3

7 1 3 3 3 1 1 1

8 1 3 3 3 2 2 2

9 1 3 3 3 3 3 3

10 2 1 2 3 1 2 3

11 2 1 2 3 2 3 1

12 2 1 2 3 3 1 2

13 2 2 3 1 1 2 3

14 2 2 3 1 2 3 1

15 2 2 3 1 3 1 2

16 2 3 1 2 1 2 3

17 2 3 1 2 2 3 1

18 2 3 1 2 3 1 2

19 3 1 3 2 1 3 2

20 3 1 3 2 2 1 3

21 3 1 3 2 3 2 1

22 3 2 1 3 1 3 2

23 3 2 1 3 2 1 3

24 3 2 1 3 3 2 1

25 3 3 2 1 1 3 2

26 3 3 2 1 2 1 3

27 3 3 2 1 3 2 1

159

Table 41: Box-Behnken Coded DOE Matrix

StdOrder Feed RPM Amp

1 1 1 2

2 3 1 2

3 1 3 2

4 3 3 2

5 1 2 1

6 3 2 1

7 1 2 3

8 3 2 3

9 2 1 1

10 2 3 1

11 2 1 3

12 2 3 3

13 2 2 2

14 2 2 2

15 2 2 2

160

Appendix E: Taguchi Parametric Screening Data

Table 42: Taguchi Parametric Screening Data

Run Ra Run Ra Run Ra Run Ra Run Ra Run Ra

1 0.91 28 1.95 55 1.17 82 1.81 109 0.76 136 0.74

2 0.82 29 1.24 56 1.69 83 1.24 110 0.47 137 0.68

3 0.99 30 1.06 57 0.81 84 0.78 111 0.63 138 0.52

4 1.57 31 1.60 58 2.10 85 1.79 112 1.07 139 1.16

5 1.81 32 1.14 59 1.65 86 1.40 113 0.65 140 0.93

6 0.92 33 1.91 60 1.04 87 1.03 114 0.62 141 0.57

7 1.67 34 2.14 61 2.14 88 1.88 115 1.48 142 1.31

8 2.25 35 1.97 62 1.78 89 2.08 116 1.01 143 1.20

9 1.07 36 2.12 63 1.64 90 1.19 117 0.71 144 1.11

10 1.21 37 2.00 64 1.18 91 1.75 118 0.96 145 0.73

11 1.06 38 2.39 65 0.98 92 1.90 119 0.80 146 0.60

12 1.44 39 0.94 66 1.61 93 1.21 120 0.61 147 0.82

13 1.69 40 2.77 67 1.56 94 1.66 121 1.36 148 1.19

14 1.23 41 1.76 68 1.89 95 1.42 122 0.84 149 0.72

15 1.80 42 1.42 69 1.75 96 1.89 123 0.76 150 0.81

16 1.34 43 1.08 70 1.11 97 1.27 124 0.49 151 0.67

17 0.88 44 1.71 71 0.78 98 0.81 125 0.64 152 0.46

18 0.71 45 1.05 72 1.24 99 1.40 126 0.58 153 0.60

19 1.38 46 2.20 73 2.17 100 2.34 127 1.11 154 1.87

20 1.33 47 2.68 74 2.13 101 2.01 128 0.84 155 1.02

21 0.98 48 2.25 75 1.04 102 1.07 129 0.72 156 0.82

22 0.95 49 1.91 76 1.61 103 0.76 130 0.70 157 0.57

23 0.70 50 1.11 77 1.58 104 0.57 131 0.64 158 1.01

24 1.06 51 0.90 78 0.99 105 0.44 132 0.45 159 0.46

25 1.61 52 2.16 79 1.75 106 0.65 133 0.79 160 1.78

26 1.02 53 1.23 80 1.24 107 0.95 134 0.97 161 0.92

27 1.45 54 1.70 81 1.29 108 0.63 135 1.12 162 0.74

161

Appendix F: Box-Behnken Modeling DOE Data

Table 43: Box-Behnken Modeling Data (1 of 2)

Run Ra Rp Rv Rz Rc Rt Rq

1 3.2303 19.4967 26.1833 45.6800 16.3727 103.3015 7.0095

2 2.3717 14.2319 16.7974 31.0293 10.5983 55.3355 4.8360

3 1.8177 9.6321 10.8101 20.4423 7.5991 35.0755 3.3127

4 1.6702 9.1888 10.3901 19.5789 6.9827 34.5905 3.0552

5 2.7931 17.0636 21.8505 38.9141 13.4947 80.3005 6.0327

6 3.5049 27.5828 28.4109 55.9937 18.6401 104.5800 8.4560

7 1.7209 9.6031 9.6162 19.2194 7.1083 30.9945 3.0422

8 2.1043 12.1203 14.5724 26.6928 9.4426 47.0770 4.1514

9 2.7375 17.0407 17.3703 34.4111 12.3785 59.7435 5.4316

10 2.1279 12.5953 15.0057 27.6010 9.2799 54.8025 4.0052

11 2.3905 14.4954 15.4739 29.9693 10.4239 73.4085 4.4807

12 2.1036 11.7324 14.1786 25.9110 9.0640 39.3970 3.8902

13 1.6650 9.3779 10.9065 20.2844 6.7451 38.5340 2.9194

14 2.3863 14.7408 14.7086 29.4495 10.7758 45.9410 4.4652

15 2.6911 15.1033 19.7987 34.9020 12.7218 90.5185 5.4437

16 2.3215 15.9815 17.8098 33.7913 10.4818 74.4975 4.9588

17 1.7739 8.7430 12.5514 21.2944 7.1579 34.3825 3.1903

18 2.2434 13.2025 14.4903 27.6928 9.3059 54.5630 4.2323

19 3.1954 17.8512 24.6212 42.4724 15.1318 81.2645 6.7535

20 1.8452 10.1326 12.8817 23.0143 7.5778 42.7675 3.2998

21 2.8527 17.6945 19.3348 37.0293 13.2596 60.5995 5.8264

22 2.6073 15.9601 18.7215 34.6817 11.7055 73.5435 5.3437

23 2.2631 13.7913 14.5198 28.3111 9.2675 48.8800 4.1985

24 2.6082 15.0659 22.6146 37.6805 12.4900 84.2005 6.1969

25 2.0121 9.1878 15.0406 24.2285 8.4467 52.4565 3.6580

26 2.0706 12.4517 15.7470 28.1988 9.1200 63.1585 4.2745

27 2.3500 13.7189 14.1259 27.8448 9.7926 50.7125 4.6334

28 2.1430 13.1408 13.7591 26.9000 9.5737 53.7335 4.1376

29 2.2692 12.8599 15.6381 28.4980 10.3771 47.7235 4.4845

30 2.4253 13.6002 16.7681 30.3683 11.0534 53.2350 4.7342

31 2.9400 20.2193 19.6063 39.8256 14.5666 77.3265 6.3442

32 1.5577 6.4138 8.8508 15.2646 5.9853 23.0400 2.5031

33 2.0071 10.5821 12.4263 23.0085 8.7745 41.6385 3.6901

34 2.1708 11.8182 17.4682 29.2864 9.5730 56.1395 4.1907

35 3.1353 19.2250 30.0210 49.2460 16.0045 130.1830 7.7345

36 1.9833 14.8987 13.3937 28.2924 8.2377 61.9245 4.3438

37 3.0535 22.8179 22.0748 44.8928 15.2267 116.3195 6.8451

162

Table 44: : Box-Behnken Modeling Data (2 of 2)


38 2.3510 13.3941 16.3751 29.7692 11.2752 70.4115 4.6202

39 2.3269 13.4031 18.5378 31.9409 10.0974 77.9585 4.6031

40 2.8071 19.5300 18.0137 37.5437 13.9189 61.1170 5.8231

41 2.4004 15.3499 20.0325 35.3824 10.8510 84.7455 4.7034

42 2.0661 19.0393 14.8640 33.9033 9.2217 126.3990 4.7591

43 1.8288 9.7591 13.3417 23.1008 7.3402 48.1720 3.3720

44 2.0686 10.7878 14.5409 25.3288 8.5840 51.2685 4.0158

45 2.1710 14.2326 14.8318 29.0644 9.5257 56.4980 4.0869

46 3.0863 21.2678 23.6672 44.9350 15.4763 84.9855 7.0608

47 2.7348 14.9553 20.3623 35.3176 12.0719 63.9545 5.4180

48 1.8208 9.7963 10.0341 19.8304 7.4623 49.5075 3.0064

49 1.9603 11.0777 12.5991 23.6768 8.7572 47.1940 3.6999

50 3.0391 18.5356 29.2836 47.8192 15.1625 135.9640 7.7312

51 3.5610 28.3266 23.8204 52.1471 17.8747 102.1950 7.9879

52 2.1702 12.5290 14.3874 26.9165 10.0343 55.2290 4.1156

53 1.8550 9.5761 10.5360 20.1121 7.4240 33.0690 3.1524

54 2.8532 17.2568 20.4620 37.7189 12.9253 58.0265 5.7140

55 2.8348 17.6816 21.7641 39.4457 13.7060 84.9225 6.2899

56 2.6913 14.8591 17.3899 32.2491 12.3574 48.9360 5.3353

57 1.7291 8.6343 10.4193 19.0536 6.7108 31.4315 2.8755

58 2.6469 14.1977 19.3477 33.5454 12.2296 60.6010 5.4173

59 2.2502 14.1528 17.5535 31.7064 10.2503 57.4365 4.5001

60 1.7619 10.0151 11.3078 21.3229 7.2022 49.3565 3.2012

61 2.4602 14.3487 17.2443 31.5930 11.5029 51.3400 4.9485

62 2.7742 16.0228 17.2714 33.2942 12.4625 49.3625 5.6004

63 2.8160 16.3299 19.6608 35.9908 12.4584 66.7920 5.5067

64 1.9088 8.8893 14.4413 23.3306 7.3222 43.7580 3.4569

65 1.6812 9.1252 11.1187 20.2439 6.2396 42.4455 2.9515

66 2.5784 14.6278 17.1058 31.7336 11.6739 53.8340 5.0360

67 3.2311 19.3398 24.1184 43.4583 16.1028 76.5600 6.9399

68 1.4953 6.1010 9.4116 15.5126 5.7953 28.9920 2.5058

69 2.2965 13.6780 14.4471 28.1251 10.8514 44.1400 4.3539

70 2.0166 11.6569 13.1434 24.8003 8.5630 43.2740 3.6163

71 2.9906 18.0448 19.6864 37.7312 13.6103 59.0105 6.1348

72 2.1301 12.1925 14.2120 26.4045 9.0205 40.2450 3.8660

73 2.8228 16.3848 21.3987 37.7836 13.3433 71.5450 5.8577

74 2.1988 12.6539 15.4881 28.1420 9.5877 45.6780 4.2618

75 2.1199 12.0829 13.6741 25.7570 8.6414 48.9400 4.0582

163

Appendix G: Validation Trial Experimental Data

Table 45: AB Model Validation Trial Data

Run Ra Rp Rv Rz Rc Rt Ra Rq

1 1.9113 12.1357 12.1609 24.2966 8.84911 41.5395 2.76149 3.71797

2 1.85651 9.06418 13.951 23.0152 8.19755 41.4255 2.65797 3.57055

3 2.01088 12.7054 13.3267 26.0321 9.37119 47.351 3.02134 4.02824

4 2.22476 12.5187 15.684 28.2027 10.5304 54.8395 3.43291 4.56035

5 1.83906 9.40864 11.8825 21.2911 7.79891 41.167 2.67017 3.50727

6 1.98951 10.9972 11.854 22.8513 8.97909 44.2455 2.80744 3.68588

7 2.14372 12.3941 14.8083 27.2024 10.3599 48.0055 3.23356 4.27192

8 1.91828 11.029 12.7438 23.7728 8.90389 39.8735 2.87793 3.81449

9 2.31759 15.0265 16.9487 31.9752 11.5659 66.2435 3.60574 4.86298

10 1.68288 9.45731 12.2181 21.6755 7.50196 40.3375 2.48492 3.34587

11 1.89076 10.4801 11.7629 22.243 8.30694 35.181 2.76408 3.65217

12 2.24397 11.9934 18.256 30.2494 11.1332 63.967 3.82506 5.06215

13 1.71912 7.15274 10.7716 17.9244 7.29334 39.3505 2.62426 3.43279

14 1.76648 8.45318 12.1628 20.616 7.36695 44.6895 2.50137 3.35848

15 1.87823 7.44076 15.1036 22.5444 8.1788 40.689 2.72478 3.66907

16 1.7343 7.64459 14.3697 22.0143 7.58786 43.0295 2.51457 3.46125

17 1.93213 8.53641 15.7043 24.2407 9.14935 47.1695 2.91056 3.93825

18 1.7608 7.85979 15.136 22.9958 7.47395 66.7985 2.5662 3.60173

19 2.28824 11.7118 17.6105 29.3224 11.0761 52.887 3.71544 4.94166

20 1.67734 7.09643 11.013 18.1095 7.23206 31.565 2.46863 3.13832

21 1.63192 6.60548 10.227 16.8325 7.01731 28.7095 2.26634 2.89851

22 1.61978 6.47798 10.5695 17.0475 7.29698 26.5035 2.22421 2.87637

23 2.20632 10.5504 14.9185 25.469 10.1249 63.289 3.39038 4.38055

24 1.85892 7.90803 11.951 19.859 8.38882 29.2565 2.79596 3.57626

25 1.97191 10.2786 12.7571 23.0357 10.0555 53.86 2.84913 3.68908

26 1.82437 8.12817 12.0305 20.1587 7.9549 39.332 2.61428 3.38398

27 1.71269 7.12741 10.8434 17.9708 7.4851 34.8485 2.50019 3.22727

28 2.27881 15.2202 15.3762 30.5964 10.7911 78.9275 3.59747 4.81339

29 1.60597 8.49343 9.24942 17.7429 7.17636 25.8635 2.38338 3.04973

30 1.88159 10.5614 14.2113 24.7727 8.70691 49.1965 2.85495 3.84402

164

Table 46: BC Model Validation Trial Data


1 2.0458 9.5158 11.8582 21.3740 9.0448 42.6550 3.90228

2 1.7671 8.0595 16.4931 24.5526 8.4920 64.5670 4.06425

3 1.8181 9.4630 12.0134 21.4765 8.1135 36.2925 3.629

4 1.6595 6.9270 12.3188 19.2458 7.2120 34.7360 3.17781

5 2.1400 11.1803 13.1196 24.3000 9.8181 51.9165 4.19777

6 1.7528 9.6267 9.8283 19.4550 7.5181 37.9740 3.52889

7 2.2247 12.3314 14.4081 26.7395 11.0348 46.3315 4.45962

8 3.1843 20.6379 26.9507 47.5886 17.7071 97.5530 7.99077

9 1.8554 9.0195 12.0882 21.1077 8.2294 45.9380 3.92961

10 1.6252 6.1492 8.7747 14.9239 6.6686 19.2145 2.84455

11 1.7478 9.1605 12.3526 21.5131 8.0220 39.0670 3.44725

12 1.8491 8.2850 11.9601 20.2451 7.9231 40.1190 3.54685

13 1.6960 7.1661 10.9424 18.1085 7.1743 26.3455 3.08387

14 1.5921 6.0252 10.2847 16.3099 6.8890 31.7595 2.96423

15 1.8072 9.1275 11.9768 21.1043 7.3841 52.5125 3.40959

16 1.7447 7.4329 11.6086 19.0416 7.1024 30.0680 3.25563

17 1.6642 6.5350 10.7823 17.3174 6.8842 28.3590 2.95765

18 1.7550 6.3691 10.4798 16.8489 6.9791 26.3105 3.10304

19 1.7468 7.1312 11.7957 18.9270 7.2220 33.1640 3.2102

20 1.6819 6.3055 9.4389 15.7445 6.7975 28.9015 2.85388

21 1.7526 8.5428 11.5093 20.0521 7.3052 39.8135 3.31805

22 1.7669 6.2306 14.6155 20.8462 7.7037 39.9655 3.38686

23 1.7780 8.0252 13.1360 21.1612 7.6514 38.3220 3.38231

24 1.6361 6.7615 9.8112 16.5727 6.6934 28.4320 2.78907

25 1.6511 7.0326 10.1965 17.2291 6.7213 27.9845 3.18808

26 1.8159 7.7855 14.5229 22.3084 8.5191 50.9740 3.89361

27 1.7753 8.4662 10.9061 19.3724 7.8429 31.4105 3.48976

28 1.8014 7.0164 13.3588 20.3752 8.7372 35.3735 3.63257

29 1.8310 7.1967 11.7171 18.9138 7.4900 37.1795 3.31887

30 1.8284 6.8798 15.7011 22.5809 8.3647 35.1805 3.7785

165

Table 47: E Model Validation Trial Data


1 1.9507 12.3476 13.6022 25.9499 9.6352 51.7830 4.1633

2 2.1568 8.2321 15.4212 23.6533 9.0134 46.6075 3.9512

3 2.2331 9.5538 16.6126 26.1664 9.8868 50.5670 4.4694

4 2.2973 11.3566 17.3881 28.7447 9.6780 62.2010 4.4555

5 1.7982 10.3729 13.2128 23.5857 8.2821 47.1910 3.6596

6 1.7914 8.3590 12.3269 20.6860 7.5273 39.4035 3.4487

7 2.0852 12.0580 17.3996 29.4577 10.9665 66.5440 5.0226

8 1.7477 8.7763 10.5063 19.2827 7.2804 36.7290 3.1728

9 1.7159 8.9695 13.5547 22.5242 8.3976 36.9195 3.6612

10 1.7601 10.0566 12.9599 23.0165 8.0859 50.4770 3.8638

11 2.1283 13.4403 13.6539 27.0943 10.2361 54.7535 4.2935

12 2.1921 12.8827 17.5873 30.4700 11.0867 51.7025 4.9074

13 2.1367 14.3348 16.5670 30.9019 10.6759 50.4155 4.6358

14 2.8972 17.8739 25.1511 43.0250 17.0177 82.1410 7.1861

15 2.2739 13.7113 16.2474 29.9587 12.0871 45.5480 4.8980

16 2.2975 12.6320 16.4686 29.1007 10.9638 40.2620 4.6855

17 2.1939 12.3456 17.6334 29.9790 10.7688 55.9925 4.7093

18 2.6411 17.1410 16.8738 34.0148 13.4860 60.3090 5.4187

19 2.7945 17.6567 20.4217 38.0784 14.9640 91.3335 6.2190

20 2.0349 12.2811 14.2088 26.4899 9.9799 60.1275 4.6400

21 2.2538 12.9687 13.2913 26.2600 10.9299 45.2330 4.5050

22 1.8198 8.1003 11.5594 19.6597 7.9383 30.1035 3.5083

23 1.7530 7.5418 11.4141 18.9559 7.9228 36.8525 3.4827

24 2.0029 9.7339 14.7913 24.5252 9.9760 40.2460 4.4606

25 2.3593 14.3253 17.5905 31.9158 12.3889 62.0185 5.1534

26 2.0049 12.0090 17.6017 29.6107 10.6337 63.1355 4.9258

27 2.2865 13.8283 16.6707 30.4990 11.1774 56.4755 4.9715

28 2.3206 15.2080 16.5566 31.7646 11.4176 66.9640 5.0192

29 2.3476 16.9381 16.7454 33.6835 11.8898 73.1305 5.1898

30 2.2387 12.9180 15.4481 28.3661 11.4790 49.7865 4.6639

166

Appendix H: Tool Wear Experimental Data

The Renishaw system and a machinist’s height gage were evaluated through the use of

experimental trials of 40 trials of each method were conducted through the use of custom

designed macros in order to mitigate experimental errors due to non-standardized

procedures. The sample size of this study was such that normality assumptions of the

inferential statistics methods employed are satisfied. Excel 2013 and Minitab 17

statistical analysis software, (Minitab Inc., State College, PA, USA), were used to analyze

the results of this trial. The laser based method was found to possess a significantly

decreased variance, as can be seen in Table 48.

Table 48: Calculated Trial Results

Laser (mm) Height Gage (mm)

Max 130.846 130.857

Avg. 130.843 130.847

Min 130.841 130.827

StdDev. 0.0010 0.0047

Table 49:BK7 Tool Wear Data (Low)

Pocket # MR (cm3) Tool ΔL (mm)

10 21.561 0.009

20 43.121 0.027

30 64.682 0.036

40 86.242 0.022

50 107.803 0.031

60 129.364 0.039

70 150.924 0.101

80 172.485 0.055

90 194.045 0.051

100 215.606 0.057

Table 50: BK7 Tool Wear Data (High)


10 21.561 0.028

20 43.121 0.080

30 64.682 0.044

40 86.242 0.030

50 107.803 0.095

60 129.364 0.054

70 150.924 0.042

80 172.485 0.013

90 194.045 0.033

100 215.606 0.042

167

Table 51: Zerodur Tool Wear Data (US On)


10 22.126 0.005

20 44.252 0.021

30 66.379 0.028

40 88.505 0.020

50 110.631 0.023

60 132.757 0.027

70 154.883 0.027

80 177.010 0.039

90 199.136 0.032

100 221.262 0.023

Table 52: Zerodur Tool Wear Data (US On)


0 22.126 0.005

20 44.252 0.014

30 66.379 0.022

40 88.505 0.066

50 110.631 0.021

60 132.757 0.006

70 154.883 0.053

80 177.010 0.010

90 199.136 0.031

100 221.262 0.023

168

Appendix I: Ultrasonic Frequency and Amplitude Measurement

Trials

Extensive testing and familiarization was conducted with the easySONIC system, Polytec

vibrometer, and associated systems before a systematic evaluation process was begun. A

Type 1 Gage Study was chosen to validate the easySONIC’s capability to determine the

appropriate ultrasonic frequency and amplitude, within a reasonable accuracy with

minimal variation. In this Type 1 Gage Study, measurements of the resulted frequency

value determined by the easySONIC system were recorded by one operator and analyzed

to estimate the level of variation in the system, the system’s repeatability, and the

accuracy of measurements.

The data seen in Figure 135 are the result of successive easySONIC measurements of a

6mm hollow diamond impregnated endmill like those used for all experimental trials.

Amplitude settings of both 50 and 100 percent were tested in order to replicate

experimental conditions. Tool amplitudes clearly cluster in regions per their supplied

percent amplitude.

169

Figure 135: Ultrasonic Amplitude with Frequency

The largest variation in observed values was seen in the 50% regime with a maximum

difference of 0.4012 (µm) in a range of less than 1 kHz. In order to place this variation in

the perspective of typical operation, a sweep of the possible ultrasonic frequencies and

their corresponding amplitudes was run using the Polytec vibrometer, the results of which

can be seen in Figure 136 below. The first three peaks of resonance corresponding with

the positions of maximum tool amplitude can be clearly seen. For purposes of reference

value development, a requirement for gage testing, 1 kHz was selected as an acceptable

tolerance of frequency measurement. Validation trials were conducted at differences of 1

kHz with no appreciable difference in resultant surface quality or effect on tooling.

Due to the lack of any available reference standards for this system, both conservative

and lenient values were tested to ensure the validity of this assumption. Preliminary

cutting tests revealed no observable difference in surface quality or tool wear and

therefore this value was selected as the tolerance threshold for gage testing.

2.3000

2.5000

2.7000

2.9000

3.1000

3.3000

3.5000

23.300 23.350 23.400 23.450 23.500 23.550

To

ol

Am

pli

tud

e (µ

m)

Ultrasonic Frequency (kHz)

Ultrasonic Amplitude with Frequency

100%

50%

170

Figure 136: Tool Amplitude with Frequency

In order to ensure that the selected percent amplitudes would produce tool actuation that

was free of any unforeseen distortions or limitations, several measurements were carried

out for each of the 10 possible percent amplitude settings. A total of 30 actual tool

amplitude measurements were made with the Polytec vibrometer at each amplitude

setting, the results of which can be seen in Figure 137. The increasing percent amplitude

is logarithmic, justified by the relatively high coefficient of determination (R2). Once a

better understanding of easySONIC’s operational characteristics had been established,

gage testing was conducted.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

10000 15000 20000 25000 30000 35000 40000 45000 50000

Exp

erim

enta

l T

oo

l A

mp

litu

de

(µm

)

Programed Frequency (kHz)

Tool Amplitude With Frequency

171

Figure 137: Average Tool Amplitude vs. Percent Amplitude

6.2.1.1 Type 1 Gage Testing of easySONIC Measurement

The purpose of a Type 1 gage test is to assess the variation in measurement data due to

the measurement system itself. In this case, since the easySONIC system was used to

determine the ultrasonic frequency of experimental trials, the validity of experimental

results was incumbent on properly quantifying and mitigating sources of uncertainty

wherever possible.

A total of 40 easySONIC measurements were completed to generate data for gage testing.

The sample size of this study is such that normality assumptions of the inferential

statistics methods employed are satisfied. With the collected frequency measurement

data, a Type 1 Gage Study report was created with Minitab 17, the results of which are

shown Figure 138. Per method standards, the green Reference line represents the median

y = 1.0388ln(x) - 1.5785 R² = 0.9768

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

10 20 30 40 50 60 70 80 90 100

To

ol

Am

pli

tud

e (µ

m)

Percent Amplitude

Average Tool Amplitude v.s. Percent Amplitude

172

sample value reference line. The red tolerance lines above and below the reference line

represent the allowable standard tolerance of 10% in either direction.

Figure 138: easySONIC Gage Study Report

The results of this study are summarized as follows:

The system does present a positive bias of 0.0549 kHz. This is most evident by the

number of observations above the upper reference tolerance.

With a p-value of 0.0001 the bias in the system is considered statistically significant

and therefore not attributed to random occurring error.

Common practices dictate that the %Variance (Repeatability) and %Variance

(Repeatable and Bias) should be fewer than 10% thus the repeatability of this

measurement within the defined tolerance is not satisfactory.

The trend of decreasing bias with increasing observation number may have been

attributed to heating in the tool holder due to operation.

For the above reasons easySONIC frequency detection was not utilized for each of the

experimental trials.

Reference 23.3386

Mean 23.393500

StDev 0.0345335

6 × StDev (SV) 0.2072011

Tolerance (Tol) 1

Basic Statistics

Bias 0.054900

T 10.0545230

PValue 0.000

(Test Bias = 0)

Bias

Cg 0.97

Cgk 0.44

Capability

%Var(Repeatability) 20.72%

%Var(Repeatability and Bias) 45.94%

Gage name:

Date of study:

Reported by:

Tolerance: 1

Misc:

37332925211713951

23.45

23.40

23.35

23.30

23.25

Observation

Fre

q @

50

% (

kH

z)

Ref

Ref + 0.10 × Tol

Ref - 0.10 × Tol

Run Chart of Freq @ 50% (kHz)

Type 1 Gage Study for Freq @ 50% (kHz)

James Pitts_Thesis_2014

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