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A Dissertation entitled Pneumatic Polishing- New Polishing Method focusing on the effect of Abrasive Grain Size on Surface Roughness of Stainless Steel by Ibrahim M. Basudan Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Engineering

________________________________________ Ioan Marinescu PhD, Committee Chair

________________________________________ Abdollah Afjeh PhD, Committee Member

________________________________________ Sarit Bhaduri PhD, Committee Member ________________________________________ Matthew Franchetti PhD, Committee Member ________________________________________ Daniel Georgiev PhD, Committee Member

________________________________________ Amanda Bryant-Friedrich, PhD, Dean College of Graduate Studies

The University of Toledo June 2017

Copyright 2017, Ibrahim Basudan This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

An Abstract of Pneumatic Polishing- New Polishing Method focusing on the effect of Abrasive Grain Size on Surface Roughness of Stainless Steel by Ibrahim Basudan Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Engineering The University of Toledo June 2017 A novel Pneumatic Polishing tool that utilizes the Magnetic Abrasive Polishing (MAP) technique is developed. This polishing tool shows a significant increase in the process efficiency as well as better surface roughness results. The design, fabrication and testing processes of the pneumatic polishing tool were done in house. In order to achieve the desired results one would need to understand the role of process parameters during the polishing process and study their effect on surface roughness. As a result of the study, an empirical model is proposed to predict the values of surface roughness and material removed based on experiments that were performed in a full factorial design, each factor at three levels. The parameters include pressure inside the rubber ball (8, 10, 12 psi), Al2O3 abrasive grain size (32, 16, 1 um), and polishing tool rotational speed (900, 1200, 1500 rpm). The workpieces are made of 304L HRAP stainless steel and were prepared to have a concave hemisphere with a 1.5 in diameter. Experiments were conducted on the Haas VF-2 VMC milling machine. The experimental results show a significant improve of surface roughness, up to 77% in one of the cases from 0.4043 down to 0.0913 um. The results show that as the pressure and rotational speed increase but grain size decreases then

the surface roughness improves until both pressure and speed reach the highest level (12 psi and 1500 rpm respectively). At this stage, it is shown that the surface quality deteriorates due to the decrease in load per grain caused by the fracture of large grains into smaller ones. Moreover, the low number of active grains engaged in cutting at high speed contribute to a lower process efficiency which leads to a lower surface finish quality.

To my father Mohammad, my brother Sameer, my nephew Sameer, and my dear son Yousuf.

Acknowledgements

I would like to express my gratitude to Professor Marinescu for his constant encouragement, direction, and support. I would like also to thank Todd Gearing of Master Chemical Corp, and Len Carravallah of Mitutoyo Michigan.

v

Table of Contents

Abstract .............................................................................................................................. iii Acknowledgements ..............................................................................................................v Table of Contents ............................................................................................................... vi List of Tables ................................................................................................................. viii List of Figures .................................................................................................................... ix List of Abbreviations ........................................................................................................ xii List of Symbols ................................................................................................................ xiii Chapter 1: Introduction ...................................................... Error! Bookmark not defined. 1.1 Steel ............................................................................................................................2 1.2 Abrasives ....................................................................................................................3 Chapter 2: Literature Review ............................................. Error! Bookmark not defined. Chapter 3: Research Objectives ......................................... Error! Bookmark not defined. Chapter 4: Research Methodologies .................................. Error! Bookmark not defined. 4.1 Design and Development of the Pneumatic Polishing Tool ....................................11 4.2 Magnetic Abrasive Polishing Technique .................................................................15 4.3 Abrasive cutting mechanism ....................................................................................16 4.4 Design of Experiments .............................................................................................18 Chapter 5: Significance ......................................................................................................20 Chapter 6: Experimental Work and Results.......................................................................21 6.1 Experiment Set-up ....................................................................................................21 6.2 Process Parameters Investigation .............................................................................22 6.3 First Experiment: Study of the effect of polishing process parameters on the surface roughness and material removal rate of hemispherical 304L Stainless Steel ................25 vi

6.3.1.1 Surface Roughness .........................................................................................28 6.3.1.2 Material Removal Rate ...................................................................................53 6.3.1.3 Comparison .....................................................................................................49 6.4 Second Experiment: Study of the effect of sub-micron abrasive grains and magnetic force on the surface finish of 304L Stainless Steel in Pneumatic Polishing ..................57 6.4.1 Introduction .......................................................................................................57 6.4.2 Methodology......................................................................................................59 6.4.3 Experimental Set-up ..........................................................................................63 6.4.4 Results ...............................................................................................................65 6.4.4.1 Analysis using the missing values ..................................................................67 6.4.4.2 Analysis using add a constant approach .........................................................72 6.4.4.3 Discussion .......................................................................................................75 Chapter 7: Discussion and Conclusions............................. Error! Bookmark not defined. Chapter 8: Model Validation .............................................................................................81 Chapter 9: Future Work .....................................................................................................85 References ..........................................................................................................................86

vii

List of Tables 6.1

Polishing Process Parameters Investigation Results ..............................................23

6.2

Design of Experiment-Factor levels ......................................................................25

6.3

Runs generated by Minitab ....................................................................................26

6.4

Experiment results .................................................................................................27

6.5

Surface Roughness comparison at different speeds ...............................................29

6.6

Surface Roughness comparison at different pressure levels ..................................30

6.7

Sum of Square deviation by the first and second order models .............................43

6.8

Sum of squared deviation by the three models ......................................................44

6.9

A run borrowed from table 6.1 ..............................................................................50

6.10

A run borrowed from table 6.4 ..............................................................................50

6.11

Material removal rate experimental results............................................................53

6.12

Factors to be studied ..............................................................................................57

6.13

Size comparison between the particles ..................................................................63

6.14

Minitab generated table of experimental runs showing factor levels ....................65

6.15

Surface roughness measurements ..........................................................................66

6.16

Data to be used for Analysis using the missing values method .............................67

6.17

Results using add a constant approach...................................................................72

8.1

Runs generated by Minitab using Tagouchi method .............................................81

8.2

Surface roughness values (actual vs. predicted by the models) .............................82

8.3

Error comparison ...................................................................................................83 viii

List of Figures

4-1

First Concept Design..............................................................................................11

4-2

First tool with several parts ....................................................................................12

4-3

Schematic of the final design .................................................................................13

4-4

Pneumatic Polishing Tool .....................................................................................13

4-5

Pneumatic Polishing Tool mounted on the milling machine .................................14

4-6

Workpiece shape design in 3D ..............................................................................15

4-7

Schematic and actual PPT showing the location of the magnets ...........................15

4-8

Schematic showing two and three body abrasion (Marinescu, 2007) ...................16

4-9

Cutting mechanism hypotheses..............................................................................17

6-1

Tool set-up before parameters investigation experiment .......................................22

6-2

Workpiece after machining ...................................................................................24

6-3

Three dimensional illustration of the results ..........................................................28

6-4

Variability in the results at different pressure and speed levels.............................29

6-5

Main effect plot generated by Minitab...................................................................31

6-6

Surface Roughness at 8, 10, and 12 psi .................................................................32

6-7

Contour plot of Surface Roughness (P and G).......................................................33

6-8

Contour plot of Surface Roughness (S and P) .......................................................34

6-9

Contour plot of Surface Roughness (S and G).......................................................34

6-10

Surface response plot of Ra at Grain size and Pressure .........................................35 ix

6-11

Surface response plot of Ra at Grain size and Speed.............................................36

6-12

Surface response plot of Ra at Pressure and Speed ...............................................36

6-13

Factors interaction plot .........................................................................................37

6-14

General Linear Model Analysis for the first experiment .......................................38

6-15

Residual plots for the first experiment ...................................................................39

6-16

Regression model and ANOVA generated by Minitab .........................................40

6-17

Regression model and ANOVA of the second order model generated by Minitab .........41

6-18

Comparison of % of Error generated by the first-order and the second-order models ...43

6-19

Regression model and ANOVA for the third model .............................................44

6-20

The difference in Error % generated by the three models .....................................45

6-21

New regression model with no data transformation ..............................................46

6-22

Normality assumptions are met, and no abnormality is found ..............................47

6-23

ANOVA of the SQRT Transformation model .......................................................48

6-24

This model (SQRT-Model) shows no sign of abnormality ...................................48

6-25

Natural Log transformation based model analysis.................................................49

6-26

Natural Log-Model residual plots ..........................................................................51

6-27

A surface texture generated by Zygo® NewView 5000 ........................................52

6-28

Surface profile generated by Mitutoyo® SV-C4500 .............................................54

6-29

3D view of the behavior of material removed ......................................................55

6-30

ANOVA, Normal Probability Plot and Residual plot for MRR ............................56

6-31

Main effect plot for MRR generated by Minitab ...................................................60

6-32

Schematic showing two- and three-body abrasion (Marinescu, 2007) ..................60

6-33

Cutting Mechanism during polishing with the use of magnets .............................61 x

6-34

Mechanism of polishing in this study ....................................................................62

6-35

Analysis of forces acting on the magnetic abrasive as described (Wang, 2017) ...64

6-36

Pneumatic Polishing Tool mounted on the milling machine .................................64

6-37

3D representation of the 304L Stainless Steel workpiece .....................................68

6-38

First Regression Analysis of the Surface Roughness results using missing data ..69

6-39

Normality and residual plots of Ra results using the missing data approach ........70

6-40

Regression Analysis using missing data with natural log data transformation .....71

6-41

Normality and Residual plots of Ra difference using Missing Values Approach .72

6-42

Comparison of the actual and predicted results of the % difference in Ra ............74

6-43

Regression analysis of the first transformed data - add a constant approach ........75

6-44

Normality assumption of the residual plots is satisfied .........................................76

6-45

Predicted values using models a and 3 against actual unchanged results ..............77

6-46

Factors influence on the surface roughness change ...............................................78

7-1

Grain Size effect on Ra ..........................................................................................79

7-2

Roughness improves as Grain size gets smaller ....................................................80

8-1

Models validation against the actual values of surface roughness ........................82

8-2

Error plot of the modes' predicted values of Ra .....................................................83

xi

List of Abbreviations

PPT.............................Pneumatic Polishing Tool MAP ...........................Magnetic Abrasive Polishing MAF ...........................Magnetic Abrasive Finishing

MRR...........................Material Removal Rate in ................................Inches um ..............................Micrometer nm ..............................Nanometer rpm .............................Revolution per minute psi ...............................Pounds per square inch min .............................Minutes

AISI ............................American Iron and Steel Institute PMMC........................Precision Micro-Machining Center

xii

List of Symbols

Ra ...............................Surface roughness P .................................Pressure G.................................Abrasive Grain size S .................................Polishing tool rotational speed C .................................Constant in the model α .................................Power of the first factor in the model β .................................Power of the second factor in the model γ ..................................Power of the third factor in the model Al2O3 ..........................Aluminum Oxide

xiii

Chapter 1

Introduction

Polishing process is one of final steps before a product is out to be used, as it helps attain the final shape, texture and surface quality of a product by removing machining traces or damaged sublayers. Conventionally though polishing process is carried out either manually or semiautomated, but in both cases it consumes a long time and requires highly skilled labor. This is clear in the case of free form surfaces, as the complex geometry can pose hurdles to achieve the final desired surface roughness in addition to the noticeable variability in surface quality due to labor’s skills. So realizing the current limitations to the process led to proposing a state of the art Pneumatic Polishing tool that uses pressurized air inside a rubber ball which can work with any workpiece shape and provide the desired surface finish. The tool is also equipped with a ceramic magnet rings as part of utilizing the Magnetic Abrasive Polishing (MAP) technique which has been proven to improve the polishing process efficiency as well as surface roughness according to Jae-Seob Kwak (2012) and Y. Wang et al (2017). The purpose of this study is to develop a novel automated Pneumatic Polishing tool technique that enhances the polishing process efficiency as well as generates surfaces with a nanoscale quality. It is known that precision machining plays a vital role in many industries as it provides better results in terms of process control, accuracy, efficiency and ultimately nanoscale 1

surface finish. Light industry, electronics, automotive, and any field that deals with accuracy can benefit from this project. Companies that look for a better efficiency in terms of quantity and quality of production in polishing such as polishing a mold engine for an automotive, or those which rely on devices that provide a level of sophistication and reliability such as medical devices or implants will all find this project beneficial as the results are promising.

1.1 Steel The production of steels and cast irons in the U.S alone exceeds 100 million tons annually, this is how much these to metal groups are used (Tlusty, 2000). Although that figure is old, it stills highlights the importance of steels in any industry. Therefore, the need for abundant resources of and variety of grades of steels are obvious. Iron ore makes the core substance in the process of making cast irons and steels, but they differ in the amount of carbon content. Steels usually contain up to 1.7% carbon, whereas carbon levels exceed that amount for the cast irons (Krar, 2011). Depending on the level of carbon also, steels are classified as carbon steels and alloy steels (Krar, 2011). There are three types of carbon steels: low-carbon steels (0.02% to 0.3% carbon by mass), medium-carbon steels (0.3% to 0.6% carbon), and high-carbon steels (up to 1.7% carbon). The alloy steels are therefore a combination of carbon steels with an addition of alloys that help achieve a certain application such as adding chromium to low-carbon steels to enhance its mechanical properties as well as making a film layer on the steel to resist corrosion (Marinescu et al, 2007). Alloy steels can be subcategorized based on the level of alloying elements (i.e., more or less than 5%) into high and low alloy steels (Tlusty, 2000). Therefore, Stainless Steel is then of the high alloy steels since the level of chromium exceeds that threshold. Stainless Steels are mainly used in the food, medical, petroleum, and chemical industries due to their hardness and corrosion

2

resistance, some though are designed to withstand high temperatures as in the aerospace industry (Marinescu et al, 2007). Moreover, the American Iron and Steel Institute (AISI) divides the stainless steels based on their microstructural families to three main types: Austenitic (AISI 200 and 300 series), Ferritic (AISI 400 series), and Martensitic (AISI 500 series) according to DeGarmo et al. Our workpiece is made of 304L (L denotes the low carbon content) Stainless Steel that falls into the austenitic type. Austenitic stainless steels are nonmagnetic, share the corrosion resistivity like other types of stainless steel, retain an outstanding formability due to its FCC crystal structure, and they tend to mechanically improve as a result of cold working (DeGramo et al, 1988). Another alloy that can improve the mechanical properties of austenitic stainless steels is addition of Ni as it is known to improve the hardness (Tlusty, 2000). Austenitic stainless steels are the most ductile, but can be susceptible to stress-corrosion cracks (Klpakjian, 2000). They are costly, so caution should be exercised when selecting the material to be used in the design and/or manufacturing processes.

1.2 Abrasives An abrasive is, according to DeGarmo et al, a hard material that can cut or abrade other substances. Abrasives can be found in the nature in the forms of emery, sandstones, corundum and diamond. They can also be manufactured such as aluminum oxides and synthetic diamond. Whenever there is a need to produce any part that requires a high level of accuracy and precision, finishing processes that utilize abrasive grains are of choice. Evidently the control of the shape and size of the natural abrasives can be a hard task to overcome, so the production of various abrasive grain sizes and shape have made it possible to study and research the field of precision engineering. 3

The cutting action of those abrasive is very fine, and thus produce a smooth surface with better quality (Kalpakjian, 2000). The hardness of abrasive grains makes the classification into conventional and super-abrasives where the latter are 10 to 100 times harder and more expensive (Marinescue et al, 2007). Aluminum oxides and Silicon Carbides are among the conventional abrasives, whereas Diamond, Cubic Boron Nitride are types of the Superabrasives all of which are synthetic (Marinescu et al, 2007). Before producing any type of synthetic abrasives, one needs to consider three main properties of abrasive grains: Hardness, Friability and attritious wear (Kalpakjian, 2000) (DeGarmo, 1988). High capability to resist penetration is desire, that’s hardness (DeGarmo, 1988). Attritious wear is low when the abrasive grains and the workpiece material are chemically inert with respect to each other. For instance Aluminum Oxides are chemically inert with iron, and they are used to machine iron and steels because of the low attritious wear than that of Silicon Carbides. Friability is beneficial in the finishing processes as they insure the generation of sharp edges for the abrasive grains which makes them self-sharpening particles (Kalpakjian, 2000).

Alumina was first discovered in 1893, it is known for its toughness when working on steels and irons, and it is estimated to have an average hardness of 2100 Knoop (DeGarmo, 1988). They are divided into two main groups: fused and unfused. Fused alumina can be found in three forms based on their friability (which is the ability of abrasive grains to fracture into smaller particles): dark (low), white (high), and monocrystalline. Unfused alumina or ceramic aluminum oxides are harder than fused alumina, the example of which is seeded gel (Kalpakjian, 2000). It is estimated that aluminum oxides make up to 75% of grinding wheels, which makes this type of abrasives the most important and commonly used (Krar, 2011). There are different levels of purity of the aluminum oxides depending on the application in which they are used; though as 4

the purity increases, the hardness and brittleness increase. 97.5% aluminum oxides are more brittle but not as tough as the regular aluminum oxides (94.5% pure) (Krar, 2011). Applications of the abrasives according to their grain sizes are (Krar, 2011): 

8 to 54 for rough grinding operations



54 to 400 for precision grinding processes



320 to 2000 for ultra precision processes

5

Chapter 2

Literature Review Striving for better surface roughness is very important in precision engineering, in this section a light will be shed on the history of what has been done and what has inspired coming up with this project. The main focus is on polishing and related contribution by authors from across the globe. Since the mid-eighties, many have tried to automate the polishing process, one particular field in which automation of the classical polishing was of a great importance has been the manufacturing of optics (D. Walker et al, 2003). The Stressed Lap developed by Steward Observatory was the first use a computer-controlled approach but at the time it was very expensive process (D. Walker et al, 2003). So as technology advances, it has become possible to design and make machines which are capable of controlling and monitoring the polishing process. This is clear as a fully automated grinding and polishing of aspheric optics was introduced by the collaboration of Zeeko® Ltd and the Optical Science Lab of London in the early 2000. Dr. Wlaker and co-workers developed a technique using a computer numerical control (CNC) to minimize polishing process time and improve surface quality, it is known as bonnet polishing (S. Zeng, L. Blunt, 2014). Moreover, Harbin Institute of Technology in China has made their own prototype and studied its potential applications, from which a roughness of about 0.931 nm was achieved when 6

a BK7 optical glass was polished (B. Gao, 2005)(B. Gao et al, 2004)(J. Song, Y. Yao, D. Xie, B. Gao, 2007). Other efforts using a computer controlled polishing system was developed by Yi et al (A. Yi, M. Hezlep, T. Pol, 2004), where the polishing head and the motor were monitored by an in line torque sensor that sends pressure readings feedback constantly in a process using a pinpolisher. Though it is fully automatic, but it still requires paying a close attention to the sensor accuracy as well as the limitation to working with sever asphericity (A. Yi, M. Hezlep, T. Pol, 2004). Additionally, Ryuh et al went as far as embedding the use of a robot that feeds off a polishing program generated by a PC in a robotic die polishing station (B. Ryuh, S. Park, G. Pennock, 2005). This workstation has shown success as a standalone polishing center, fully automated, and results showed surface roughness of a good quality as well as the ability to work with a variety of shapes. On the other hands though, it can only work on metals, any additional technologies such as the use of magnetic field will significantly alter the polishing tool design and ultimately the whole program that is generated by the PC. S. Ji et al presented a gasbag polishing technique used on free form molds, and reported good surface roughness values as low as 5 nm, the system was reported to be more efficient compared to the conventional polishing methods (S. Ji et al, 2006). The common principle used in most or all the above mentioned systems is their reliance on the flexible and compliant contact in order to generate better quality and smoother surface finish. However, as the project utilizes the use of magnetic field properties, some of the efforts that have been published are worthy of mentioning in the following paragraphs. Magnetic field assisted finishing technique has been an interesting study since it’s the first introduction by the Soviet Union (H.-J. Ruben, 1987). T. Mori et al discuss the mechanism that 7

governs the process of magnetic abrasive finishing the in his paper titled “Clarification of magnetic abrasive finishing mechanism”. In this paper a nonmagnetic stainless steel workpiece was polished by a magnetic abrasive brush, which was generated in the middle of a magnetic pole and the surface to be polished creating a normal force to push the abrasives to penetrate the workpiece surface and a tangential force to keep the abrasives from deviating away from the magnetic balance point. S. Ji et al presented a case of applying the Magnetic Abrasive Finishing (MAF) whereby the control of the working abrasive form and structure was studied, and it was reported that using the MAF in combination with gasbag polishing is a solution to the “incline effect” (S. Ji et al, 2010). J. Kwak introduced a new way of increasing the density of the magnetic flux, which is directly correlated to the contact force exerted by the abrasives on the workpiece, by installing permanent magnets under the workpiece and surface roughness readings for the AISI316 stainless steel (nonferrous) were shown to be improved (J. Kwak, 2012). Moreover, Singh, D.K., Jain, V.K., Raghuram, V., & Komanduri, R. have found that the magnetic force contribute to assist significantly in the formation of an abrasive brush that develops abrasion pressure which causes micro scratched in the surface being polished (2005).

8

Chapter 3

Research Objectives

The design and development of a pneumatic polishing tool that utilizes the flexible polishing theory and Magnetic Abrasive Polishing (MAP) technique is to be achieved in this project. This will include full control of all the parameters which govern the mechanism of polishing through the use of the milling machine at the high-bay area (Haas VF-2 VMC), and the polishing process will be performed on concave shaped 304L HRAP Stainless Steel. Based on the literature search, the techniques proposed within this project are found to be new. The following are to be expected at the end of this project; 

Full development of the Pneumatic Polishing tool that uses a MAP technique, mounted on a milling machine as a platform.



Analysis of the contact area between the Pneumatic Polishing tool and the workpiece surface.



Obtain a significant surface roughness value reduction and study the effect of several parameters that have a direct effect on results.



Optimize the polishing process parameters that will allow for an accurate prediction of final surface finish.



Study the effect of finer abrasive grains (nano-level) on the surface roughness. 9



Experimental study of the surface roughness of Stainless Steel with respect to different levels of magnetic force.

10

Chapter 4

Research Methodologies

4.1 Design and Development of the Pneumatic Polishing Tool

Simplicity and efficiency have been taken in consideration during the very first stages in the design process. Half spherical shape of the tool helps working on any complex surfaces, as the rubber is flexible enough to attain the shape of the workpieces yet maintaining other process parameters (pressure, cutting/contact area, speed...etc) which in fact enhances the process outcome in terms of surface roughness. The first proposed designs are shown in figure 4-1.

Figure 4-1 First concept designs

11

After examining the two designs, the selection was based on the ease of manufacturing the tool in house so design 2 was the choice. Finding the rubber end of the tool took a few stages; first an additive manufacturing method was utilized but this technology does not provide a sealed final product as the part shown in figure 4-2 below did not hold any air due to the lack of solidity. Then a piece of rubber used for a bicycle horn was utilized. The tool was made of steel in two pieces; rubber holder and a shaft to be screwed together.

Figure 4-2 First tool with several parts

This design though failed to keep air pressured in the rubber end. So some modifications were added in order to overcome the main issue of air leakage, and the final design is shown below. Though it looks very simple, this design is practical, easy to assemble and secures air pressure.

12

Figure 4-3 Schematic of the final design

Figure 4-1 Pneumatic Polishing Tool

The parts were then made and assembled, air was pumped, rubber was covered with a typical polishing cloth and the tool was mounted on a milling machine (Haas VF-2 VMC) located at the Precision Micro-Machining Center which allows for at least three degrees of freedom movement as seen in figures 4-4 and 4-5.

13

Figure 4-5 Pneumatic Polishing Tool mounted on the Milling Machine

The testing experiment was designed to allow different rotating speeds, but fixing other factors such as pressure, depth of rubber contacting the workpiece surface all at time intervals of 5 minutes. Aluminum oxide -66 micron was used as an abrasive paste throughout the testing stages. The workpiece tested has a complex shape with concaves and a flat bottom made of stainless steel. During the testing operation, it was successfully found the pneumatic polishing tool is operational with no issues reported. Thus, the two main objectives of simplicity of design and process efficiency are met at this stage. The workpiece material is 304L HRAP stainless steel, with a hemisphere shape having a diameter of 76.20 mm as shown in the three dimensional drawings below.

Figure 4-6 The workpiece shape design in 3D

14

4.2 Magnetic Abrasive Polishing Technique

The use of the Magnetic Abrasive Polishing (MAP) in this project is of a vital role due to the promising results of such a technique in the literature. A pair of ceramic ring magnets are to be installed to the polishing tool holder as shown in figure 4-7, and their effect will be studied based on the ratio of iron powder mix with aluminum oxide abrasive paste. The magnetic field density calculations are provided based on the geometry of the polishing tool. The iron powder to be mixed with the aluminum oxide abrasive paste is simply an educational iron filings and will be mixed in the most effective weight ratio to ultimately give the best results. So the abrasive paste will be mixed with iron powder with an equal weight of 1 gram each.

Figure 4-2 Schematic and actual picture show the magnets location inside the tool

15

4.3 Abrasive cutting mechanism

Loose abrasive cutting effect mechanism; sliding or rolling, is of important theoretical value as it allows for a better understanding of how one could achieve better process efficiency and thus better results. The cutting forces exerted by the abrasive particles are investigated, and the material removal rate model then established based on Preston’s law. Factors affecting the polishing process are as follows; rotating speed, air pressure, dwell time, depth of cut, magnet density, grain size and workpiece material and shape. The experiment will then help show which factors are significant, and need further studies. Then an optimization process will be useful to define the best working process parameters that guarantee best polishing performance. The experiment is detailed in the next portion of this chapter. From the experimental results, one would be able to examine the theoretical model’s prediction accuracy. However, from the literature, there are a number of researchers who have investigated the process of polishing and revealed many hypotheses as to what exactly happens in the contact area between the polishing tool and the surface to be polished. Three of those hypotheses are utilized in this project; the mechanical abrasion (three-body abrasion) causing the cracks in the subsurface, plastic deformation caused by the frictional heat, and the interaction between slurry, workpiece material and the tool (in our case it’s the magnetic force) simplified in figures 4-8 & 4-9.

Figure 4-8 Schematic showing two- and three-body abrasion (Marinescu, 2007)

16

To be able to understand the mechanism of polishing, one would need to study the major factors that play important roles in the process. As Preston law lays out the relationship between the volume of material removed in a polishing process to pressure, velocity and a constant that represent any other material and abrasive properties. Here, we will take into consideration the two main factors (pressure and velocity) but will add to them studying the effect of abrasive size.

Figure 4-9 Cutting Mechanism hypotheses

17

The empirical model to be used in this study for the surface roughness is as following: 𝑅𝑎 = 𝐶 ∗ 𝑃𝛼 ∗ 𝐺𝛽 ∗ 𝑆 𝛾

(1)

Where Ra is surface roughness, C is a constant, P is air pressure inside the polishing tool, G is the abrasive grain size, and S is the polishing tool rotational speed. The powers α, β, γ are to be found experimentally.

4.4 Design of Experiments

The polishing process mainly depends on applied pressure, relative velocity and a constant that represent various parameters, according to Preston’s law. However due to the significant change in the tool geometry, tool material, abrasive applications type, and other factors, the study of a full factorial design will be utilized. The factors selected are the air pressure inside the rubber part of the tool, abrasive grain size, and polishing time at three levels each. Therefore, twenty seven samples are required for the experimental runs. The selection of the workpiece material has been agreed upon to be 304L HRAP stainless steel due to its wide range of usage in several industries. A new polishing cloth will be used for each run to avoid mixing the loose abrasive sizes which will skew the results. The use of ANOVA, regression, and the design of experiment tools included in the Minitab software will help with the analysis of the process procedure, results and conclusions. Another set of runs were considered to study the effect of finer grain sizes and the magnetic flux strength on the final surface roughness. This includes three levels of submicron sizes of water based alumina (Al2O3) at 500, 300, and 50 nm. The magnetic flux density was represented by the value of force at 0.84, 1.68, and 2.52 lbs. The experimental study and analysis of this experiment is done as per the request of the doctoral dissertation committee request. Another empirical model is therefore generated and examined. 18

The equipment to be utilized for these sets of experiments are; the Haas VF-2 VMC milling machine at the high bay area. But in order to measure both surface roughness and measure the diameter of the workpiece before and after polishing, Mitutoyo surface roughness/contour measuring devices SV-C3200 and SV-C4500 provided by Mitutoyo of Plymouth, MI office were utilized. The initial surface roughness and contour diameter were measured for all twenty seven samples before polishing.

19

Chapter 5

Significance

As of recent years, the polishing process is mainly done manually or at the very best semiautomatic. This however causes the process reliability to go down as it depends on labors’ skills. It also causes the process to be time consuming, in addition to variations in the outputs. It is important to unify the results across the board, by introducing a method through which machines are utilized, performance is enhanced, and thus surface finish is of a commercial use. This project introduces a new technique of polishing within which various proven technologies are combined in one unique tool. The use of pneumatic polishing along with the magnetic abrasive finishing techniques embedded in one device that shows a great potential is needed as never before. It ensures the safe use of no-contact finishing method for higher process efficiency, better surface finish, and it also conforms to the basic polishing laws. The design and fabrication of the novel pneumatic polishing tool is therefore realized and conducted. This project will help mitigate the limitations to the traditional polishing, which cannot work on complicated workpiece geometries. It will also develop a basis that help optimize the best conditions at which significantly better results in terms of surface roughness and material removal rate are obtained.

20

Chapter 6

Experimental Work and Results

6.1 Experiment Set-up

Once the design of the polishing tool has been done, the parts were fabricated using the lathe machine in the Precision Micro-Machining Center. In order to test the functionality of the polishing tool, air is pumped in the rubber, a polishing cloth is installed, and then the tool is mounted on the Haas milling machine to perform the test. The parameters for the test are as following: pressure inside the rubber is set at 7.5 psi, depth the rubber will be pressed onto the workpiece is at 0.125 in, time is fixed at 5 minutes, with various rotating speeds set at 100,200,300,400, and 500 rpm. The loose abrasives used are aluminum oxide with an average size of 66 micron in a paste form, and the workpiece is made of stainless steel with a concave shape as shown figure 6-1.

21

Figure 3-1 Tool setup before parameters investigation experiment

The test described above was successfully conducted without any air leakage issues. This has allowed for the next step which is investigating the polishing process parameters through a set of chosen factors at different levels such as air pressure inside the rubber, tool speed, depth of tool exerts on the workpiece, abrasive grain size, and time.

6.2 Process Parameters Investigation

A set of investigative runs have been conducted to further understand the polishing process factors influence, the setup and results are shown in the table below (table 6.1).

22

Table 6.1 Polishing Process Parameters Investigation Results

P (psi) 2 4 6 8 10 6 6 6 6 6

S (rpm) 1250 1250 1250 1250 1250 750 1000 1250 1500 1750

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250 1250

d (in) 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 1/32 " 2/32" 3/32" 4/32" 5/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32" 3/32"

G t Rainitial (micron) (min) (µm) Ra (µm) 16 15 0.45 0.21 0.23 0.19 0.16 16 15 0.41 0.21 0.23 0.21 0.28 16 15 0.38 0.16 0.19 0.14 0.24 16 15 0.41 0.27 0.24 0.25 0.26 16 15 0.45 0.3 0.26 0.25 0.21 16 15 0.49 0.23 0.21 0.15 0.28 16 15 0.48 0.3 0.14 0.14 0.24 16 15 0.48 0.29 0.25 0.24 0.17 16 15 0.48 0.24 0.18 0.22 0.24 16 15 0.46 0.14 0.27 0.21 0.26 16 16 16 16 16 66 32 16 6 1 mic 16 16 16 16 16

15 15 15 15 15 15 15 15 15 15 5 10 15 20 25

0.48 0.48 0.5 0.49 0.5 0.47 0.41 0.4 0.49 0.48 0.42 0.46 0.42 0.55 0.46

0.26 0.26 0.2 0.26 0.28 0.19 0.14 0.21 0.19 0.21 0.14 0.19 0.17 0.15 0.23

0.14 0.25 0.26 0.26 0.31 0.21 0.16 0.12 0.18 0.16 0.19 0.17 0.15 0.16 0.23

0.25 0.26 0.21 0.28 0.36 0.16 0.14 0.14 0.22 0.26 0.13 0.17 0.19 0.21 0.29

0.23 0.17 0.23 0.26 0.29 0.17 0.23 0.19 0.22 0.19 0.13 0.13 0.27

Ra mean (µm) 0.215 0.22 0.17 0.25 0.2675 0.2 0.18 0.2575 0.205 0.2225

The Difference % 52.22 46.34 55.26 39.02 40.56 59.18 62.50 46.35 57.29 51.63

0.1975 0.255 0.2325 0.265 0.315 0.1925 0.15 0.1475 0.1925 0.21 0.1625 0.175 0.165 0.1733333333 0.245

58.85 46.88 53.50 45.92 37.00 59.04 63.41 63.13 60.71 56.25 61.31 61.96 60.71 68.48 46.74

Five factors were considered; air pressure (psi), rotating speed (rpm), depth of rubber contact (in), abrasive grain size (micron), and dwell time (minutes) each factor at five different levels. The runs are designed to investigate one variable at a time, fixing the four others at the average value, for example to examine the effect of time then pressure is fixed at the average value between 2 and 10 psi (6 psi is then selected) and so on. The workpiece material is a one inch thick block made of stainless steel, divided into twenty five equal squares of about 1”X1”. The 23

workpiece surface went through a grinding process, roughness measurements were taken before and after the polishing process using the Pocket Surf® tool. Four different readings were taken, and the average is compared to the initial value as seen in the table. It is therefore noticed that there is a significant reduction in the surface roughness of about fifty percent across the entire runs. The good news about this investigative experiment is that it shows a significant reduction in the values of surface roughness, 50% reduction in an average throughout the experiment. The results show that as pressure, speed, depth increase the surface finish ends up rougher. But dwell time has almost no impact between 5 to 20 minutes. Pressure and velocity are chosen to be studied further due their importance throughout the history of polishing, i.e., main factors in Preston law, but the influence of grain size is to become the new factor to be added to our investigation. The workpiece material to be polished was bought from Alro® as two plates of 304L HRAP Stainless Steel plates with dimension 7 in wide, 24.5 in long and 1.75 in thick. The hemisphere shape was then machined using the same milling machine. The plates is then cut to smaller parts, each contains two concave shapes to be polished. Figure 11 shows a plate with 8 final shapes machined, before it is cut into four rectangular blocks each containing two of the hemispheres.

Figure 6-2 Workpiece after being machined to have the final shape

24

6.3 First Experiment: Study of the effect of polishing process parameters on the surface roughness and material removal rate of hemispherical 304L Stainless Steel Our design of experiment is a full factorial with three factors, each at three levels 33 as following:

Table 6.2 Design of Experiment-Factor levels

Factor Pressure (psi) Grain Size (um) Speed (rpm)

Level 8, 10, 12 32, 16, 1 900, 1200, 1500

Using Minitab software, the order of runs is generated randomly as shown in the table below, then the experiment is conducted accordingly.

25

Table 6.3 Runs generated by Minitab

Std Order 2 19 12 26 14 22 16 1 4 7 13 11 10 8 23 3 5 6 21 17 18 15 27 20 25 24 9

RunOrder 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Pressure (psi) 8 12 10 12 10 12 10 8 8 8 10 10 10 8 12 8 8 8 12 10 10 10 12 12 12 12 8

Grain Size (micron) 32 32 32 1 16 16 1 32 16 1 16 32 32 1 16 32 16 16 32 1 1 16 1 32 1 16 1

Speed (rpm) 1200 900 1500 1200 1200 900 900 900 900 900 900 1200 900 1200 1200 1500 1200 1500 1500 1200 1500 1500 1500 1200 900 1500 1500

All twenty seven runs were conducted in one day, samples were then taken to the Mitutoyo office in Plymouth, MI for measurements. Surface roughness after polishing was measured for all samples along with the diameter which will help us calculate the volume of material removed during the polishing process. The results are shown in table 6.4.

26

Table 6.3 Experiment Results

StdOrder

RunOrder

Pressure (psi)

Grain (micron)

1

8

8

2

1

3

Size Speed (rpm)

Ra (um)

B

Ra (um)

A

32

900

0.3053

0.2169

28.96

8

32

1200

0.3043

0.1838

39.60

16

8

32

1500

0.3029

0.1543

49.06

4

9

8

16

900

0.3568

0.2337

34.50

5

17

8

16

1200

0.4154

0.1839

55.73

6

18

8

16

1500

0.4355

0.1594

63.40

7

10

8

1

900

0.34

0.0816

76.00

8

14

8

1

1200

0.3199

0.0944

70.49

9

27

8

1

1500

0.3959

0.1206

69.54

10

13

10

32

900

0.2534

0.1879

25.85

11

12

10

32

1200

0.337

0.2639

21.69

12

3

10

32

1500

0.4195

0.2497

40.48

13

11

10

16

900

0.3375

0.2084

38.25

14

5

10

16

1200

0.3271

0.1539

52.95

15

22

10

16

1500

0.3579

0.1011

71.75

16

7

10

1

900

0.3509

0.1078

69.28

17

20

10

1

1200

0.4307

0.1676

61.09

18

21

10

1

1500

0.4043

0.0913

77.42

19

2

12

32

900

0.3018

0.2098

30.48

20

24

12

32

1200

0.3745

0.2695

28.04

21

19

12

32

1500

0.3973

0.2326

41.45

22

6

12

16

900

0.2838

0.0781

72.48

23

15

12

16

1200

0.3797

0.1167

69.27

24

26

12

16

1500

0.3562

0.1519

57.36

25

25

12

1

900

0.394

0.092

76.65

26

4

12

1

1200

0.2859

0.1182

58.66

27

23

12

1

1500

0.3371

0.0891

73.57

ΔRa%

Ra B is the mean value of surface roughness before polishing while Ra A stands for the mean value of surface roughness measured after polishing. The last column indicates the percentage difference of surface roughness before and after polishing.

27

6.3.1 Surface Roughness 6.3.1.1 Surface roughness results analysis

Figure 6-3 Three Dimensional illustration of the experiment results

This graph shows how the surface roughness is influenced by the three chosen factors, one would notice the downward trend of the value of surface roughness as the grain size changes from 32 to 1 micron. It is known that as the grain size gets smaller, the overall function of cutting becomes more efficient. This can be explained as a result of the total number of active abrasives, as the smaller the size of the abrasives the higher the number of active abrasives engaged in the cutting process during polishing. This conclusion has been drawn by C.J. Evans et al (2003) when he studied the effect of granule effect on the material removed during polishing, this is also valid in the surface roughness model under study. When the lowest level of grain size was used, 1 micron, it is clear we get the best values of Ra, indicated by the orange and grey categories in the graph, but one would need to further examine the influence of the other factors within this region; this may help in locating the optimized factors that would produce the best results. It is assumed 28

that the smaller grains along with the iron particles added would have a better and a uniform cutting action due to the fact that 1 micron grains do not undergo any fracture during the polishing process. It is also assumed that in any given abrasive mixture, the smaller size grains may contain higher number of particles than larger ones which in turn achieve more efficient cutting process and better results.

Ra (um)

Ra at G 1 um 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

0.4307

0.3959 0.4043

0.394 0.34

0.3509

0.3371

0.3199

0.2859 0.1676

0.0816

0.1078

0.092

900

0.1182

0.0944

0.1206

1200

0.0913 0.0891

1500

Speed (rpm) Ra B (um) @ 8 psi

Ra A (um) @ 8 psi

Ra B (um) @10 psi

Ra A (um) @ 10 psi

Ra B (um) @ 12 psi

Ra A (um) @ 12 psi

Figure 6-4 Variability in results at different levels of pressure and speed

Table 6.5 Surface Roughness comparison at different speeds, but 1 micron grain size

Speed (rpm) 900

1200

1500

Ra A (um)-Average

0.0938

0.1267

0.1003

% difference in Ra

73.9762

63.4114

73.5081

29

Table 6.4 Surface Roughness comparison at different pressure levels, but a fixed 1 micron grain size

Pressure (psi) 8

10

12

Ra A (um)-Average

0.0989

0.1222

0.0998

% difference in Ra

73.9762

63.4114

73.5081

It seems hard to draw a conclusion as to whether the speed and pressure have a consistent influence on the surface finish, as seen in the graph above (figure 6-4). This is translated in the values of the powers in our model. But generally, it seems reasonable to suggest that working at medium speed and either low or high pressure would generate good results according to the mean value of Ra calculated at 8, 10, and 12 psi (0.0989, 0.1222, and 0.0998 um respectively). The three surface response graphs shown in figure 6-6 can be useful in defining the areas where factors have their best and worst influence. At 32 micron, the average value of surface roughness reaches 0.2187 um, however as the grain size changes to 16 um that value is reduced by roughly 30% down to 0.154122 um. This trend continues to occur as the third level of grain size is applied, with average value of final surface roughness of 0.106956 um. The factors main effect is shown graphically in figure 6-5, the lowest values of surface roughness are found to result from low pressure, low speed and the smallest grain size.

30

Main Effects Plot for Ra (um) Data Means

Pressure (psi)

Grain Size (um)

0.20

Mean

0.15

0.10 8

10 Speed (rpm)

12

900

1200

1500

1

16

0.20

0.15

0.10

Figure 6-5 Main effect plot generated by Minitab

31

32

Figure 6-6 3D representation of Ra at 8,10 &12 psi

32

One way to explore further is to use the contour plot, which will help reveal if the three factors have any potential relationship which affects the output. Below are some contour plots retrieved from Minitab, they certainly support the finding above (Grain size is the significant factor) as lower values of the surface roughness are shown in the plots where grain size is included. Another finding is that the possible interaction between pressure and grain size may have better results than any other interactions, as seen in the plots, better contour values are shown in figure 6-7 compared to figures 6-8 and 6-9. Surface Roughness 12 0.125

Pressure (psi)

11

10

0.150

0.175

0.200

0.225

9

8

5

10

15 20 Grit Size (micron)

25

30

Figure 6-7 Contour plot of Surface roughness under the influence of Grain Size and Pressure

33

Surface Roughness 12 0.175

Pressure (psi)

11

10

9

8 900

1000

1100

1200 Speed (rpm)

1300

1400

1500

Figure 4 Contour plot of Surface roughness under the influence of Speed and Pressure

Surface Roughness 1500

Speed (rpm)

1400 1300 1200

0.150

0.175

0.200

0.225

1100 1000 900

5

10

15 20 Grit Size (micron)

25

30

Figure 6-9 Contour plot of Surface roughness under the influence of Grain Size and Speed

34

Surface response plots provide almost the same findings, but in a clearer concept of the response surface, as can be seen in the three plots below. One would quickly notice the steep surface generated when pressure and grain size are studied (figure 6-10) compared with all other factor interactions in figures 6-11 and 6-12. This is also supported by the factors interaction plot in figure 6-13, as one would be able to make decisions which will optimize the final output. For instance, at a fine grain size, i.e., one micron, one would choose to set the pressure at 8 psi as this combination is shown to give better surface roughness. Also at 900 rpm, only the lowest grain size shows better results. However, at such speed, pressure needs to be set at 12 psi to produce a fine surface. So from the contour plots, one would neglect the speed effect and choose the optimum values of 1 micron for the grain size and 8 psi for the pressure. Surface Roughness

0.25 Ra (um)

0.20 0.15

12

0.10 10 0

10

20

Pressure (psi)

8

30

Grit Size (micron)

Figure 6-10 Surface response of Ra at Grain Size and Pressure

35

Surface Roughness

0.25 Ra (um)

0.20 0.15 1400

0.10 1200 0

10

Speed (rpm)

1000 20

30

Grit Size (micron)

Figure 6-11 Surface response of Ra at Grain Size and Speed

Surface Roughness

0.25 Ra (um)

0.20 0.15 1400

0.10 1200 8

10 Pressure (psi)

Speed (rpm)

1000 12

Figure 5 Surface response of Ra at Pressure and Speed

36

Interaction Plot for Ra (um) Data Means

1

16

32

900

1200

1500

0.20 P r essur e (psi)

0.15

Pressure (psi) 8 10 12

0.10

0.20 Gr ain Size (um)

0.15 0.10

Speed (r pm)

Figure 6 Factor Interaction Plot for Ra generated by Minitab

37

Grain Size (um) 1 16 32

6.3.1.2 The Surface roughness model

The results show that the final surface roughness of the workpiece underwent a significant improvement, we will examine the outcome in general at first but then we will shed more light on the major factor(s) considered. The Minitab output below represent the basic study of the polishing process considering the linear regressing analysis (figure 614). The results show that the grain size is significant, which further support our study. Both the normal probability and the residual graphs show no abnormal behavior in the data as can be seen in figure 6-15. General Linear Model: Ra (um) versus Pressure (ps, Grain Size (m, ... Factor Pressure (psi) Grain Size (micron) Speed (rpm)

Type fixed fixed fixed

Levels 3 3 3

Values 8, 10, 12 1, 16, 32 900, 1200, 1500

Analysis of Variance for Ra (um), using Adjusted SS for Tests Source DF Pressure (psi) 2 Grain Size (micron) 2 Speed (rpm) 2 Pressure (psi)*Grain Size (micron) 4 Pressure (psi)*Speed (rpm) 4 Grain Size (micron)*Speed (rpm) 4 Error 8 Total 26 S = 0.0380672

R-Sq = 87.75%

Seq SS 0.001696 0.056657 0.002354 0.013328 0.005589 0.003383 0.011593 0.094600

Adj SS 0.001696 0.056657 0.002354 0.013328 0.005589 0.003383 0.011593

Adj MS 0.000848 0.028329 0.001177 0.003332 0.001397 0.000846 0.001449

R-Sq(adj) = 60.17%

Figure 6-14 General Linear Model generated by Minitab

38

F 0.59 19.55 0.81 2.30 0.96 0.58

P 0.579 0.001 0.477 0.147 0.477 0.684

Residual Plots for Ra (um) Versus Fits 0.04

90

0.02

Residual

Percent

Normal Probability Plot 99

50 10 1

-0.050

-0.025

0.000 Residual

0.025

0.00 -0.02 -0.04 0.05

0.050

0.10

Histogram

Versus Order

0.02

3.6

Residual

Frequency

0.25

0.04

4.8

2.4 1.2 0.0

0.15 0.20 Fitted Value

-0.04

-0.02

0.00 Residual

0.02

0.04

0.00 -0.02 -0.04

2

4

6

8 10 12 14 16 18 20 22 24 26 Observation Order

Figure 6-15 Normal Probability, Histogram and Residual Plots of Surface roughness generated by Minitab

So in order to solve for the model proposed, the natural log was taken for all the terms and so the model will look like Log (Ra) = Log (C) + α Log (P) + β Log (G) + γ Log (S)

(2)

Plugging the converted data into Minitab, we get the first regression model as (3)

39

Regression Analysis: Log (Ra) versus log (P), log (G), log (S) The regression equation is Log (Ra) = - 0.729 - 0.201 log (P) + 0.184 log (G) - 0.021 log (S)

General Linear Model: Ra (um) versus Pressure (ps, Grain Size (m, ... Factor Pressure (psi) Grain Size (micron) Speed (rpm)

Type fixed fixed fixed

Levels 3 3 3

Values 8, 10, 12 1, 16, 32 900, 1200, 1500

Analysis of Variance for Ra (um), using Adjusted SS for Tests Source DF Pressure (psi) 2 Grain Size (micron) 2 Speed (rpm) 2 Error 20 Total 26 S = 0.0411663

Seq SS 0.001696 0.056657 0.002354 0.033893 0.094600

R-Sq = 64.17%

Adj SS 0.001696 0.056657 0.002354 0.033893

Adj MS 0.000848 0.028329 0.001177 0.001695

F 0.50 16.72 0.69

P 0.614 0.000 0.511

R-Sq(adj) = 53.42%

Analysis of Variance Source Regression Residual Error Total

DF 3 23 26

SS 0.39179 0.36593 0.75772

MS 0.13060 0.01591

F 8.21

P 0.001

Figure 6-16 Regression model and ANOVA generated by Minitab

From the above Minitab output, it is clear that there is a significant correlation between the abrasive grain size and the final surface roughness. The model proves that statement as the grain size is the only factor that is raised to a positive, yet small, exponent. One way to improve a regression model is to raise it to a higher order then examine the estimation of error. So here we will use the second order regression model, solve for the powers, then compare it to the first order model obtained from earlier.

40

The second order regression model will follow the form written as 𝑦 = 𝛽0 + 𝛽1 𝑥1 + 𝛽2 𝑥2 + 𝛽3 𝑥3 + 𝛽11 𝑥12 + 𝛽22 𝑥22 + 𝛽33 𝑥32 + 𝜖

(4)

Solving for the second order regression model using Minitab, we get the following results; General Regression Analysis: Log (Ra) versus log (P), log (G), log (S) Regression Equation Log (Ra)

=

-52.7305 + 11.8036 log (P) - 0.228091 log (G) + 30.1115 log (S) 6.06476 log (P)*log (P) + 0.290293 log (G)*log (G) - 4.91903 log (S)*log (S)

Coefficients Term Constant log (P) log (G) log (S) log (P)*log (P) log (G)*log (G) log (S)*log (S)

Coef -52.7305 11.8036 -0.2281 30.1115 -6.0648 0.2903 -4.9190

SE Coef 37.4894 12.3167 0.2004 24.1746 6.2206 0.1391 3.9462

T -1.40654 0.95834 -1.13793 1.24559 -0.97495 2.08650 -1.24653

P 0.175 0.349 0.269 0.227 0.341 0.050 0.227

Summary of Model S = 0.116725 PRESS = 0.496623

R-Sq = 64.04% R-Sq(pred) = 34.46%

R-Sq(adj) = 53.25%

Analysis of Variance Source Regression log (P) log (G) log (S) log (P)*log (P) log (G)*log (G) log (S)*log (S) Error Total

DF 6 1 1 1 1 1 1 20 26

Seq SS 0.485228 0.005642 0.386048 0.000101 0.012951 0.059315 0.021171 0.272496 0.757724

Adj SS 0.485228 0.012513 0.017643 0.021139 0.012951 0.059315 0.021171 0.272496

Adj MS 0.0808714 0.0125132 0.0176426 0.0211387 0.0129508 0.0593151 0.0211708 0.0136248

F 5.93561 0.91841 1.29489 1.55149 0.95053 4.35347 1.55384

P 0.001084 0.349334 0.268598 0.227311 0.341230 0.049947 0.226972

Figure 6-17 Regression model and ANOVA of the second order model generated by Minitab

41

Therefore, the new second order model will look like the following −6.065

𝑅𝑎 = 1.86 ∗ 10−53 𝑃11.804 𝐺 −0.228 𝑆 30.112 𝑃𝐿𝑜𝑔(𝑃)

𝐺𝐿𝑜𝑔(𝐺)

0.2903

−4.919

𝑆𝐿𝑜𝑔(𝑆)

(5)

The model represented above, can predict the values at a better confidence but an analysis to the error resulted between the first and second order models is needed. So in this section we will perform a comparison between the two models.

Error 40 30 20

% Error

10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 -10 -20 -30 -40

Experiment Run Number % E - 1st Order

% E-2Nd order

Figure 7 Comparison of % of Error generated by the first-order and the second-order models

The error caused by the second order model seems to be of a lesser value compared with that caused by the first order model as can be noticed in figure 6-18. Accordingly, the value of the sum of squared deviation is less when obtaining values of surface roughness using the second order model as shown in the table below (Table 6.7).

42

Table 6.5 Sum of Squared deviation by first-order and second-order models

First Order 0.3659

Sum of Squared Deviation

Second Order 0.2725

The next step is now to examine the second order model using only the grain size squared in the model, then evaluate it and compare the obtained results to the rest. So the Minitab output looks like the following;

General Regression Analysis: Log (Ra) versus log (P), log (G), log (S) Regression Equation Log (Ra)

=

-0.716019 - 0.200751 log (P) - 0.228091 log (G) - 0.0212854 log (S) + 0.290293 log (G)*log (G)

Coefficients Term Constant log (P) log (G) log (S) log (G)*log (G)

Coef -0.716019 -0.200751 -0.228091 -0.021285 0.290293

SE Coef 0.830551 0.315508 0.202728 0.250191 0.140715

T -0.86210 -0.63628 -1.12511 -0.08508 2.06298

P 0.398 0.531 0.273 0.933 0.051

Summary of Model S = 0.118056 PRESS = 0.466793

R-Sq = 59.53% R-Sq(pred) = 38.40%

R-Sq(adj) = 52.18%

Analysis of Variance Source Regression log (P) log (G) log (S) log (G)*log (G) Error Total

DF 4 1 1 1 1 22 26

Seq SS 0.451107 0.005642 0.386048 0.000101 0.059315 0.306617 0.757724

Adj SS 0.451107 0.005642 0.017643 0.000101 0.059315 0.306617

Adj MS 0.112777 0.005642 0.017643 0.000101 0.059315 0.013937

Figure 6-18 Regression model and ANOVA for the third model

43

F 8.09181 0.40485 1.26587 0.00724 4.25590

P 0.000360 0.531159 0.272669 0.932970 0.051113

As can be noticed that the percentage of variability explained by the model represented by R-Squared in this case has a lower value than that of the second order model which contained all the terms, yet it is still better than the first order model. The empirical model will be as described by the equation below; 𝑅𝑎 = 0.192301 ∗ 𝑃−0.200751 ∗ 𝐺 −0.228091 ∗ 𝑆 −0.0212854 ∗ 𝐺𝐿𝑜𝑔(𝐺)

0.290293

(6)

This model actually shows comparable results to those generated by the second order-model with all terms as shown in the figure(6-19), but it produces a larger sum of squared deviation.

Error 40 30

% Error

20 10 0 -10

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

-20 -30 -40

Experiment Run Number % E - 1st Order

% E-2Nd order

% E - 2nd Oder 2

Figure 8 The difference in Error % generated by the three models

Table 6.6 Sum of squared deviation generated by the three models

Sum of Squared Deviation

First Order 0.3659 44

Second Order 0.2725

2nd-Order w/ G 0.30662

Equations 3 through 6 represent various forms of models that best fit the results, however all of them lack the power of prediction on one hand, and generate variabilities. The original straightforward form of a regression model is therefore shown in equation 7. This representation of the data is then transformed to test for better prediction and less variability as shown. Figures 6-20 and 6-21 show the same finding as before, that the abrasive grain size is the only significant factor and the model is moderate in its power at 60% but the S-statistic shows that the average deviation from the mean is low which means that the model can fit the data well. 𝑅𝑎 (𝑢𝑚) = 0.1353 − 0.00196 𝑃 + 0.00361 𝐺 − 0.000012 𝑆

(7)

Regression Analysis: Ra (um) versus Pressure (ps, Grit Size (m, Speed (rpm) Analysis of Variance Source Regression Pressure (psi) Grit Size (micron) Speed (rpm) Error Total

DF 3 1 1 1 23 26

Adj SS 0.056892 0.000278 0.056371 0.000243 0.037708 0.094600

Adj MS 0.018964 0.000278 0.056371 0.000243 0.001639

F-Value 11.57 0.17 34.38 0.15

P-Value 0.000 0.684 0.000 0.704

Model Summary S 0.0404905

R-sq 60.14%

R-sq(adj) 54.94%

R-sq(pred) 46.06%

Coefficients Term Constant Pressure (psi) Grit Size (micron) Speed (rpm)

Coef 0.1353 -0.00196 0.003610 -0.000012

SE Coef 0.0624 0.00477 0.000616 0.000032

T-Value 2.17 -0.41 5.86 -0.39

P-Value 0.041 0.684 0.000 0.704

VIF 1.00 1.00 1.00

Regression Equation Ra (um) = 0.1353 - 0.00196 Pressure (psi) + 0.003610 Grit Size (micron) - 0.000012 (rpm) FigureSpeed 6-20 New regression model with no data transformation

45

Figure 6-21 Normality assumptions are met, and no abnormality is found

46

Data transformation was used to examine the possibility of a better fit to the results by other models, and the resulted models are shown in equations 8 and 9. Both models (square root transformation and natural log transformation) are shown to have the same ANOVA with the abrasive grain size being the significant factor, figures 6-22 and 6-24 respectively. It can be noticed though that the average deviation from the mean values using the SQRT-model is smaller and thus better than that generated using the Nat-LogModel. Both also show normality assumptions being met with no abnormalities in the residual plots as shown in figures 6-23 and 6-25 respectively. Regression Analysis: Ra (um) versus Pressure (ps, Grit Size (m, Speed (rpm) Method Box-Cox transformation Rounded λ Estimated λ 90% CI for λ

0.5 0.335332 (-0.483168, 1.14783)

Analysis of Variance for Transformed Response Source DF Adj SS Adj MS Regression 3 0.090567 0.030189 Pressure (psi) 1 0.000841 0.000841 Grit Size (micron) 1 0.089497 0.089497 Speed (rpm) 1 0.000229 0.000229 Error 23 0.059475 0.002586 Total 26 0.150042 Model Summary for Transformed Response S 0.0508513

R-sq 60.36%

R-sq(adj) 55.19%

F-Value 11.67 0.33 34.61 0.09

P-Value 0.000 0.574 0.000 0.769

R-sq(pred) 46.40%

Coefficients for Transformed Response Term Constant Pressure (psi) Grit Size (micron) Speed (rpm)

Coef 0.3671 -0.00342 0.004548 -0.000012

SE Coef 0.0784 0.00599 0.000773 0.000040

T-Value 4.68 -0.57 5.88 -0.30

P-Value 0.000 0.574 0.000 0.769

VIF 1.00 1.00 1.00

Regression Equation Ra (um)^0.5 = 0.3671 - 0.00342 Pressure (psi) + 0.004548 Grit Size (micron) - 0.000012 Speed (rpm) Figure 6-22 ANOVA of the SQRT Transformation model

47

Figure 6-23 This model (SQRT-Model) shows no sign of abnormality

Regression Analysis: Ra (um) versus Pressure (ps, Grit Size (m, Speed (rpm) Method Box-Cox transformation λ = 0 Analysis of Variance for Transformed Response Source Regression Pressure (psi) Grit Size (micron) Speed (rpm) Error Total

DF 3 1 1 1 23 26

Adj SS 2.39773 0.03530 2.36018 0.00225 1.61965 4.01738

Adj MS 0.79924 0.03530 2.36018 0.00225 0.07042

F-Value 11.35 0.50 33.52 0.03

P-Value 0.000 0.486 0.000 0.860

Model Summary for Transformed Response S R-sq R-sq(adj) R-sq(pred) 0.265366 59.68% 54.43% 45.48% Coefficients for Transformed Response Term Coef SE Coef Constant -2.021 0.409 Pressure (psi) -0.0221 0.0313 Grit Size (micron) 0.02336 0.00403 Speed (rpm) -0.000037 0.000208

T-Value -4.94 -0.71 5.79 -0.18

P-Value 0.000 0.486 0.000 0.860

VIF 1.00 1.00 1.00

Regression Equation ln(Ra (um)) = -2.021 - 0.0221 Pressure (psi) + 0.02336 Grit Size (micron) - 0.000037 Figure 6-24Speed Natural(rpm) Log transformation based model analysis

48

Figure 6-25 Natural Log-Model residual plots

√𝑅𝑎 = 0.3671 − 0.00342 𝑃 + 0.004548 𝐺 − 0.000012 𝑆

(8)

ln 𝑅𝑎 = −2.021 − 0.0221 𝑃 + 0.02336 𝐺 − 0.000037 𝑆

(9)

6.3.1.3 Comparison

Now that we have established the a solid ground in the relationship between the polishing process output in terms of surface roughness and the main focus in this case which is the abrasive grain size, it would be beneficial to show how the proposed mechanism differ from conventional polishing. In doing so, we shall compare two set of runs; one from the process parameters investigation group where no MAP nor a complex 49

shape was used (represented by table 6.9), and another from the experimental runs where the magnets were installed, and the workpiece has a hemispheric shape (table 6.10).

Table 6.7 A run borrowed from table 1

P (psi)

S (rpm)

d (in)

G

t (min)

(micron)

Ra

Ra final

%

initial

(µm)

difference

0.25

39.02

(µm) 8

1250

3/32

16

15

0.41

As the findings have shown before that the speed does not play a major role in influencing the surface roughness, the difference in speed within this comparison is not of a great concern. Therefore, it is clear that using the new proposed polishing tool and technique has reached to better results, i.e. Ra (mean value) at 0.1839 um, in a fraction of the time it took to obtain a surface that is not even comparable in roughness Ra at 0.25 um.

Table 6.8 A run borrowed from table 4

P (psi)

8

G (micron)

16

S (rpm)

1200

Ra before

Ra after

(µm)

(µm)

0.4154

0.1839

% difference

55.73

Visible comparison of the smoothness of the surface profile produced by both methods can easily be found in figures 6-26 and 6-27 below. Despite the geometry difference, one could argue that working on a flat surface could have produced better results, unfortunately it is not the case when using a tool that has a convex rubber nose as 50

that is shown to contribute negatively due to the dimple shape produced when the polishing tool rotates in a fixed location. On the other hand, when the tool rotates around the tool axis in addition to a negligible rotation around the workpiece axis, but that dimple effect is shown to be absent which in turn enhances the process efficiency and produce a better surface finish.

Figure 6-26 A surface texture generated by Zygo® NewView 5000

51

Figure 6-27 Surface profile generated by Mitutoyo® SV-C4500

52

6.3.2 Material Removal Rate 6.3.2.1 Results Analysis

Table 6.9 Material removal rate experimental results

Pressure StdOrder RunOrder (psi)

Grain (micron)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

32 32 32 16 16 16 1 1 1 32 32 32 16 16 16 1 1 1 32 32 32 16 16 16 1 1 1

8 1 16 9 17 18 10 14 27 13 12 3 11 5 22 7 20 21 2 24 19 6 15 26 25 4 23

8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10 12 12 12 12 12 12 12 12 12

Size Speed (rpm) 900 1200 1500 900 1200 1500 900 1200 1500 900 1200 1500 900 1200 1500 900 1200 1500 900 1200 1500 900 1200 1500 900 1200 1500

53

MRR (mm^3/min) 713.7953 751.0252 723.3063 719.887 694.9947 691.8825 729.4743 735.8855 667.7309 703.138 723.3467 729.4002 711.7595 713.7935 729.2234 737.8924 737.3755 729.4973 713.7639 715.5666 671.3102 673.1551 713.3481 723.9244 699.1521 713.403 719.9695

The results of the material removed during the polishing process are shown the table above. The last column was calculated though measurements of the diameter of the hemisphere before and after the polishing then the difference in volume was calculated in millimeter cube which then was divided by the process time. Unfortunately this section did not reveal so much about the relationship between the three factors and the material removed. Nevertheless, this section will shed some light on the results followed by a section dedicated to the model analysis.

760 740 720 700 680 660 640 620

12 32

32

900

1200

32 1500

10

16 900

16 1200

16 1500

1 900

1 1200

1

8

1500

Grain Size (um) and Speed (rpm) 620-640

640-660

660-680

680-700

700-720

720-740

740-760

Figure 6-28 Three dimensional view of the behavior of material removed under the influence of all three factors

The material removed during polishing did not seem to have been affected by the change in any of the three factors, which is hard to explain at this point as historically polishing has always been dependent on at least the pressure and speed. This finding proves that there is so much variability during the process. From ANOVA, one will be able to 54

Pressure (psi)

MRR (mm^3/min)

MRR (mm^3/min)

notice the lack of correlation between any of the factors studied and the response. In addition, the regression is only able to explain a very low percentage of the variability, Rsquared at 27.5%. Therefore, the model interprets that in a weak relationship represented in the equation below. 𝑀𝑅𝑅 = 780.4927 ∗ 𝑃−0.02856 ∗ 𝐺 −0.00237 ∗ 𝑆 −0.00264

(10)

General Regression Analysis: LOG (MRR) versus LOG (P), LOG (G), LOG (S) Regression Equation LOG (MRR) LOG(S)

=

2.89237 - 0.0285642 LOG (P) - 0.00236817 LOG (G) - 0.00264223

General Linear Model: MRR (mm^3/mi versus Pressure (ps, Grain Size (m, ... Factor Pressure (psi) Grain Size (micron) Speed (rpm)

Type fixed fixed fixed

Levels 3 3 3

Values 8, 10, 12 1, 16, 32 900, 1200, 1500

Analysis of Variance for MRR (mm^3/min), using Adjusted SS for Tests Source DF Pressure (psi) 2 Grain Size (micron) 2 Speed (rpm) 2 Error 20

S = 20.0404

Seq SS 1639.1 578.2 823.6 8032.3 Total

R-Sq = 27.46%

Adj SS 1639.1 578.2 823.6 8032.3

Adj MS F P 819.5 2.04 0.156 289.1 0.72 0.499 411.8 1.03 0.377 401.6 26 11073.2

R-Sq(adj) = 5.70%

Normal Probability Plot

Versus Fits

(response is MRR (mm^3/min))

(response is MRR (mm^3/min))

99

40 30

90

20

80

10

70

Residual

Percent

95

60 50 40 30

0 -10

20

-20

10

-30

5

-40

1

-50

-50

-25

0 Residual

25

50

690

700

710 720 Fitted Value

730

Figure 6-29 Regression mode, ANOVA, Normal Probability Plot and Residual plot for MRR

55

740

The main effect plots (figure 6-30) though show agreement with the knowledge in the polishing world, take for instance the pressure effect on the mean value of material removed; as the pressure increases it allows for a better cutting process by the abrasives up to a certain level at which the grains start to break into smaller pieces that leads to loss in load per grain, which eventually contribute to a less cutting action. The same argument can be applied to the speed influence on the material removed, but with the abrasive grain size it seems hard to explain the drop in the amount of material removed at 16 micron.

Main Effects Plot for MRR (mm^3/min) Data Means

Pressure (psi)

725

Grain Size (um)

720 715

Mean

710 705 8

10

12

1

16

Speed (rpm)

725 720 715 710 705 900

1200

1500

Figure 6-30 Main effect plot for MRR generated by Minitab

56

32

6.4 Second Experiment: Study of the effect of sub-micron abrasive grains and magnetic force on the surface finish of 304L Stainless Steel in Pneumatic Polishing

6.4.1 Introduction

As the need for finer surfaces of molds or medical devices is increasing, the finishing process undergoes a significant amount of research and investigation. In this study, a novel polishing device, previously made in-house, is used to study the influence of finer abrasive grain size on the surface roughness of non-magnetic Stainless Steel that has a concave shape. Three nanometer levels of Alumina (Al2O3) water-based abrasive slurry are used to form the magnetic abrasive with iron powder.

Another area of

investigation is to study the behavior of surface roughness against three different levels of magnetic strength. For the rest of the process parameters, the levels at which surface roughness values were optimized were considered, i.e. rotational speed at 1500 rpm, and air pressure inside the rubber part of the tool is kept at 12 psi. So the new set of parameters are shown in the table 12;

Table 6.10 Factors to be studied

Factor Grain Size (nm) Magnetic Force(lb)

Level 500, 300, 50 0.84, 1.68, 2.52

From the study done by T. Shinmura (1990), one could draw the conclusion that the magnetic field generates enough pressure exerted on the magnetic abrasives during the finishing process. And from the same study, the magnetic abrasives are formed by subjecting the abrasives and the iron powder particles to high pressure and temperature 57

then sinter the mixture. This mixture is then controlled and kept together by the use of magnetic forces inside the working zone. J-D Kim et al (1995) study was the pioneer to put the magnetic polishing technology to an actual use when they introduced the two stages polishing mechanism which was shown to have significantly improve the surface roughness of steel. A magnetic brush was formed that employs the use of generated pressure in the polishing zone by the permanent magnet which therefore pushes the abrasives to indent the workpiece surface. Surface roughness was improved from 0.64 um down to 0.008 um. Not until 2003 when T. Mori et al was the behavior of magnetic abrasives first studied and force analysis during a finishing process was introduced. In their study, it was found that the abrasive weight is proportional to the acting normal force. The magnetic abrasive polishing was characterized by two main clauses: a. the magnetic field generates normal and tangential forces that act on the magnetic abrasive and b. magnetic abrasive bundles are separated from each other. The range of magnetic forces was found to be 0 -20 N, which conforms to our selection of magnetic force levels. C-T Lin et al (2007) were able to study and optimize the weight of the magnetic abrasive when used to finish stainless steel specimen (SUS304) on a CNC machine. A correlation between the finishing forces and magnetic abrasive weight was found experimentally, and the optimum weight was found to be 2 grams. Another study on the finishing forces during Magnetic Abrasive Finishing (MAF) process was conducted and proved by Kanish T. et al (2017), where the relationship between the magnetic abrasive sizes (grit) was established. Stainless Steel (SS316L) was polished, and the forces acting on the magnetic abrasive were shown to be influenced by grit size of high order (1200 mesh). This motivates our study as to investigate the nano-level of Alumina and its influence on surface roughness. The recent 58

study done by Wang Y. et al (2017) explores the behavior of the components of the magnetic abrasive slurry (i.e., abrasives and iron particles) both theoretically and experimentally with respect to acting forces. The resultant force acting on both the abrasive and iron particles is found to be dependent on the nature of the workpiece undergoing the finishing process (magnetic or non-magnetic). More abrasive particles are shown to be engaged in the material removal during the finishing of a non-magnetic workpiece due to the influence of the resultant force acting on the particles. This conclusion will be a basis to the finer alumina that will be used in our study.

6.4.2 Methodology

Finishing process involves a combination of cutting actions as well as subsurface deformation, according to the principle of polishing described I. Marinescu et al (2007). The loose abrasive particles are either sliding or rolling during the polishing and lapping processes. Therefore, the mechanical action of those loose abrasive particles is noticed; as abrasion which causes subsurface micro-level cracks in the workpiece material, and the heat generated by the friction in the working zone which causes plastic deformation in that area, this is shown in figure 6-31. This cutting concept along with the utilization of the magnetic assisted finishing (MAF) is the backbone of this study.

59

Figure 6-31 Schematic showing two- and three-body abrasion [I. Marinescu]

The magnet is attached to the Pneumatic Polishing Tool from inside, and the magnetic field is generated in the working zone causing a magnetic field that acts on the magnetic abrasive (both alumina and iron powder) particles.

Figure 9 Cutting Mechanism during polishing with the use of magnets

From previous investigation such as the one done by Wang Y. et al (2017), the forces acting on the magnetic abrasive particles are found to be magnetic force and gravity force as shown in figure 6-33. 60

Figure 6-33 Mechanism of polishing in this study-Using mechanical and magnetic hypotheses

The forces influencing the behavior of the abrasive particles are shown to have two components Fm and Fg; that is a magnetic force and the gravity force (figure 6-34). The resultant force is Fres-Abr and it is always negative in direction with respect to the magnetic field (equation 13). This means that the forces are exerted on the abrasive particles to push them towards the surface to be finished. Forces that are acting on the iron powder particles are of the same types, but with an opposite influence. The resultant force on the iron powder is positive in our case as the workpiece material is nonmagnetic, which makes the direction of the magnetic force upward towards the magnet (refer to equation 15). This though is highly influenced by the mass ratio of the magnetic abrasive components. The finer the alumina, and since the iron powder size is fixed and the weight ratio is fixed, the higher the magnetic force acting on the iron powder.

61

Figure 6-34 Analysis of forces acting on the magnetic abrasive as described by Wang Y et al (2017)

From the analysis provided in figure 44, one can easily find the force components as following: Forces acting on the Abrasive Particles: 𝐹𝑎𝑏𝑟,𝑥 = −𝐹𝑚 cos 𝜃

(11)

𝐹𝑎𝑏𝑟,𝑦 = −𝐹𝑚 𝑆𝑖𝑛 𝜃 − 𝐹𝑔

(12)

𝐹𝑟𝑒𝑠,𝑎𝑏𝑟 = 𝐹𝑎𝑏𝑟,𝑥 + 𝐹𝑎𝑏𝑟,𝑦

(13)

Forces acting on the Iron Powder Particles: 𝐹𝑦 = 𝐹𝑚 − 𝐹𝑔

(14)

𝐹𝑟𝑒𝑠,𝑖𝑟𝑜𝑛 = 𝐹𝑚 − 𝐹𝑔

(15)

The forces on the x-direction acting on the iron powder are assumed to be neglected since the influence of forces in the y-direction is significant with respect to the overall behavior of the particles during the process. In this study, the size comparison between the particles of iron powder and that of the alumina is shown in table 6.13 where it is noticed that the iron powder is larger than all 62

the three levels of the alumina. This is sought after in hope it will not only cluster the magnetic abrasive in the working zone but also to give a bit of free space to the abrasives to cut and itch the workpiece surface.

Table 6.11 Size comparison between the particles

Particle Type Iron Powder Alumina Ratio

Size (nanometer) 2500 2500 2500 500 300 50 1:05 1:08 1:50

6.4.3 Experimental Set-up

The Pneumatic Polishing Tool (PPT) is mounted on a milling machine (Haas VF-2 VMC), 304L Stainless Steel workpiece is to be polished and is shown in figures 45 and 46. The design of experiment is a full factorial with two factors, three level each (23) that comprises nine runs as shown in table 14. Workpiece material is 304L stainless steel with a concave shape of a diameter of 72 mm as shown in figure 6-36. Surface roughness values before and after polishing are measured using a device provided by Mitutoyo (SV-3200) in Plymouth, MI. The weight ratio of alumina to the iron powder was 1gram to 1 gram.

63

Figure 6-35 Pneumatic Polishing Tool mounted on the milling machine

Figure 6-36 3D representation of the 304L Stainless Steel workpiece

The Minitab generated table of runs combination is shown in table 6.14, where randomized run order is to be followed during the experiment to protect the randomization assumption.

64

Table 6.12 Minitab generated table of experimental runs showing the factor levels

StdOrder 7 8 1 9 2 3 4 6 5

RunOrder 1 2 3 4 5 6 7 8 9

PtType 1 1 1 1 1 1 1 1 1

Blocks 1 1 1 1 1 1 1 1 1

G 50 50 500 50 500 500 300 300 300

F 0.84 1.68 0.84 2.52 1.68 2.52 0.84 2.52 1.68

6.4.4 Results

Some unforeseen obstacles were encountered during the experiment which resulted in deflation of the rubber part due to heat generated in the polishing area. Process modifications were needed as more than one run had the undergone the same heat issue. This is explained by the usage of water based slurry compared with the previous type which is oil based alumina polishing paste. Therefore, speed was reduced to 1200 rpm, pressure was reduced to 10 psi (first experiment shows good results at these levels), and most importantly the polishing time was reduced to 2.5 minutes. Once the runs are conducted, samples are taken again to the Mitutoyo branch in Plymouth, MI for surface roughness measurements. Surface roughness measurements are taken three times and the average value is then calculated and used in the analysis, results are shown in table 6.15 as following;

65

Table 6.13 Surface roughness measurements

StdOrder 1 2 3 4 5 6 7 8 9

Grain Size (nm) 500 500 500 300 300 300 50 50 50

Magnet Force (lb) 0.84 1.68 2.52 0.84 1.68 2.52 0.84 1.68 2.52

Ra before Ra (um) (um) 0.124357 0.1539 0.182453 0.1879 0.17854 0.2169 0.22143 0.2337 0.21323 0.2639 0.09078 0.0816 0.23487 0.2497 0.149447 0.1182 0.124443 0.0781

% Difference (um) 19.20 2.90 17.69 5.25 19.20 -11.25 5.94 -26.44 -59.34

First look at the results in the table reveals improvement in surface roughness, but there seem to be cases where the change is negative which suggests the surface has become rougher than before polishing. A further analysis will follow such as ANOVA, and the empirical model will be presented afterwards. But in order to study the results, one would put some effort in avoiding the negative values and that is possible in two ways; either by adding a constant (a) so that the least negative value becomes a very small number, say 0.01, or by using the missing values (any negative value will be omitted) as recommended by Rick Wicklin in his article (2011).

66

6.4.4.1 Analysis using the missing values

In this case as mentioned previously, we omit the negative values in the percentage difference in the overall surface roughness values as shown in table 6.16.

Table 6.14 Data to be used for Analysis using the missing values method

StdOrder 1 2 3 4 5 6 7 8 9

Grain Size (nm) 500 500 500 300 300 300 50 50 50

Magnet Force (lb) 0.84 1.68 2.52 0.84 1.68 2.52 0.84 1.68 2.52

Ra before Ra (um) (um) 0.124357 0.1539 0.182453 0.1879 0.17854 0.2169 0.22143 0.2337 0.21323 0.2639 0.09078 0.0816 0.23487 0.2497 0.149447 0.1182 0.124443 0.0781

% Difference (um) 19.20 2.90 17.69 5.25 19.20 0.0 5.94 0.0 0.0

The regression model generated by Minitab is represented by equation (16) and the ANOVA analysis shown in figure 6-37. It is noticed that neither factor has a significant influence on the results, but this might be related to the method used in analyzing the negative values of the surface roughness. Equation 16 shows that the percentage difference in the final surface roughness is slightly proportional to the abrasive size but inversely proportional to the magnetic force. This is expected as the material removed by larger grains is more than that removed by much finer ones. One should notice that in our case the larger the percentage difference in the surface roughness, the smoother the surface. On the other hand, the magnetic force is shown to have a negative influence on the surface roughness. This part will be explained in a later section with the discussion and conclusions. Form the Minitab output in the same figure, one could also notice that the 67

model generated is weak, and there is so much variability that cannot be explained. Nevertheless, data are showing an acceptable normality behavior and the residual versus fitted values are not showing any abnormality as shown in figure 6-38.

𝑅𝑎(% 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒) = 4.93

𝐺 0.025

(16)

𝐹2.52

Regression Analysis: Ra (% diff) versus Grain Size (nm), Magnet Force (lb) Analysis of Variance Source Value Regression 0.238 Grain Size (nm) 0.123 Magnet Force (lb) 0.526 Error Total

DF

Seq SS

Contribution

Adj SS

Adj MS

F-Value

2

218.27

38.02%

218.27

109.14

1.84

1

191.40

33.34%

191.40

191.40

3.23

1

26.87

4.68%

26.87

26.87

0.45

6 8

355.76 574.03

61.98% 100.00%

355.76

59.29

Model Summary S 7.70018

R-sq 38.02%

R-sq(adj) 17.37%

PRESS 670.943

R-sq(pred) 0.00%

Coefficients Term VIF Constant Grain Size (nm) 1.00 Magnet Force (lb) 1.00

Coef

SE Coef

90% CI

4.93 0.0251

7.86 0.0139

( -10.33, 20.20) (-0.0020, 0.0521)

-2.52

3.74

(

-9.79,

4.75)

T-Value

P-Value

0.63 1.80

0.553 0.123

-0.67

0.526

Regression Equation Ra (% diff) = 4.93 + 0.0251 Grain Size (nm) - 2.52 Magnet Force (lb) Figure 6-37 First Regression Analysis of the Surface Roughness results using missing data

68

P-

Figure 6-38 Normality and residual plots of the surface roughness results using the missing data approach

Therefore, data transformation using the natural logarithm has been utilized and the new model is represented by equation 17. The new model is able to surpass the capability of the first one at a much higher confidence as shown in the regression analysis output (figure 6-39). 𝑅𝑎 (% 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒) = 2.69

𝐺 0.014

(17)

𝐹3.44

69

A comparison will be performed to show if this transformation has actually helped represent the result data in a more clear way. Equations 16 and 17 share the interpretation of the type of correlations between surface roughness difference and both of the studied factors (abrasive gran size and magnetic force). But the difference is in the value of the constant and the powers of both factors. Equation 17 shows a better model in terms of prediction accuracy though, that is the model is capable of explaining the process at a higher confidence level as seen in figure 6-39. Regression Analysis: Ra (% diff) versus Grain Size (nm), Magnet Force (lb) Analysis of Variance for Transformed Response Source DF Seq SS Value Regression 2 109.68 Grain Size (nm) 1 59.58 Magnet Force (lb)1 50.10 Error 6 60.10 Total 8 169.78

Contribution 64.60% 35.09% 29.51% 35.40% 100.00%

Adj SS 109.68 59.58 50.10 60.10

Adj MS

F-Value

54.84 59.58 50.10 10.02

5.47 5.95 5.00

P0.044 0.051 0.067

Model Summary for Transformed Response S 3.16489

R-sq R-sq(adj) 64.60% 52.80%

PRESS 140.882

R-sq(pred) 17.02%

Coefficients for Transformed Response Term Constant Grain Size (nm) Magnet Force (lb)

Coef SE Coef 90% CI T-Value P-Value 0.99 3.23 ( -5.28, 7.27) 0.31 0.769 0.01398 0.00573 (0.00284, 0.02511) 2.44 0.051 -3.44 1.54 ( -6.43, -0.45) -2.24 0.067

VIF 1.00 1.00

Regression Equation ln(Ra (% diff)) = 0.99 + 0.01398 Grain Size (nm) - 3.44 Magnet Force (lb)

Figure 6-39 Regression Analysis using missing data with natural log data transformation

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Both abrasives grain size and magnetic force are shown to be marginally significant at a 90% confidence interval, with a higher contribution percentage to the abrasive grain size. The transformed regression model is at about 65 % strength, almost double that of the first model in equation 16.

Figure 6-40 Normality and Residual plots of the Surface Roughness difference using the transformed data (Missing Values Approach)

A quick comparison of the models generated using the missing values approach are shown in figure 6-41 against the actual values of the percentage difference in surface roughness. It is clear that the natural logarithmic transformation to the data was helpful in reducing the large variations in the results as seen in the figure, even though one might argue the models are more conservative in predicting the values. One should keep in mind that it is desired to achieve a better roughness which is indicated by a higher positive 71

percentage difference in our study. Therefore, another look at the models obtained here in comparison to the model obtained by the other approach is necessary.

% Difference in Surface Roughness (Missing Values Approach)

25.00 20.00

%

15.00 10.00 5.00 0.00 1

2

3

4

-5.00 % Difference Actual

5

6

7

Run Standard Order

Model 1

8

9

Model 2

Figure 6-41 Comparison of the actual and predicted results of the % difference in Surface Roughness

6.4.4.2 Analysis using add a constant approach

In this case, a constant “a” will be added to the actual results so that the minimum value is so small but is not a zero (0.01). The new results are shown in table 6.17, and the analysis is done using Minitab to find the models.

Table 6.15 Results using add a constant approach

StdOrder 1 2 3 4 5 6 7 8 9

Grain Size (nm) 500 500 500 300 300 300 50 50 50

Magnet Force (lb) 0.84 1.68 2.52 0.84 1.68 2.52 0.84 1.68 2.52

Ra (um) 0.124357 0.182453 0.17854 0.22143 0.21323 0.09078 0.23487 0.149447 0.124443 72

Ra before (um) 0.1539 0.1879 0.2169 0.2337 0.2639 0.0816 0.2497 0.1182 0.0781

% Difference Actual 78.55 62.25 77.04 64.60 78.55 48.10 65.29 32.91 0.01

In this section we treated the data using the addition of constant “a = 59.35” to all the actual values of the percentage difference in surface roughness, analyzed them using ANOVA and found the regression model as seen in figure 6-42. Abrasive grain size contributes to almost half of the influence on the overall results, which is yet the same conclusion from the first study. The magnetic force, though it is not highly significant, might play a role if tested in an interaction effect. Therefore, the first model of the second approach is shown in equation 18 before adjusting for the constant “a” and in equation 19 after the adjustment. (𝑅𝑎 + 𝑎) = 58.6 𝑅𝑎 = −0.75

𝐺 0.0901

(18)

𝐹16.53

𝐺 0.0901

(19)

𝐹16.53

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Regression Analysis: Ra+a (%Diff) versus Grain Size (nm), Magnet Force (lb) Analysis of Variance Source DF Value Regression 2 Grain Size (nm) 1 Magnet Force (lb)1 Error 6 Total 8

Seq SS

Contribution

3630 2474 1156 1758 5387

67.37% 45.91% 21.46% 32.63% 100.00%

Adj SS 3630 2474 1156 1758

Adj MS

F-Value

1814.9 2473.6 1156.2 293.0

P-

6.20 8.44 3.95

0.035 0.027 0.094

Model Summary S 17.1158

R-sq 67.37%

R-sq(adj) PRESS 56.50% 4548.20

R-sq(pred) 15.58%

Coefficients Term Constant Grain Size (nm) Magnet Force (lb)

Coef 58.6 0.0901 -16.53

SE Coef 17.5 0.0310 8.32

90% CI ( 24.7, 92.5) (0.0298, 0.1503) (-32.69, -0.36)

T-Value 3.36 2.91 -1.99

P-Value 0.015 0.027 0.094

VIF 1.00 1.00

Regression Equation Ra+a (%Diff) = 58.6 + 0.0901 Grain Size (nm) - 16.53 Magnet Force (lb)

Figure 6-42 Regression analysis of the first transformed data using the add a constant approach

This new model (equation 19), is shown to have a better R-square value (at 67.37%) compared to either model obtained in the previous section (i.e., equations 16 and 17). The residual plots are shown in figure 6-43, normality assumption is met.

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Figure 6-43 Normality assumption of the residual plots is satisfied

6.4.4.3 Discussion

As this study is looking for better results in terms of lower values of surface roughness, it becomes important to find those conditions at which a model predicts values that are desired. The previous sections were a representation of the effort through which one is able to identify the potential correlations that govern the variables within a model. Now that a few models are obtained, a comparison between those models is necessary in order to choose the one that is capable of describing the finishing process at high level of confidence. Figure 6-44 shows a comparison between the first model (equation 16, using the missing values approach) and the third model using the absolute value (equation 19, using the ass a constant approach) against the actual data (unchanged). 75

Models Comparision against actual values

% Difference in Surface Roughness

40.00 20.00 0.00 1

2

3

4

5

6

7

8

9

-20.00 -40.00 -60.00 -80.00

Run Standard Order % Difference (Acutal)

Model 2

|model 3|

Figure 6-44 Predicted values using models a and 3 against actual unchanged results

One reason why the absolute value of model 3 was chosen is because this model is capable of showing comparable results to those obtained from the experiment as seen in figure 6-44. Therefore, the model that best describes this experimental study is shown in equation 20. 𝐺 0.09

𝑅𝑎 (% 𝐷𝑖𝑓𝑓) = |−0.75 ∗ 𝐹16.5 |

(20)

The effect of the abrasive grain size and the magnetic force on the mean value of the percentage difference in surface roughness is shown in figure 6-45, one can easily see the matching correlation from the graph compared to the model in equation 20. As has been seen before the effect of the alumina size is almost predictable, i.e. the larger the grain size the higher the difference in the roughness but one cannot conclude to a better surface quality as the difference could be negative which an indication of a rougher surface. On the other hand, the magnetic force effect shows an interesting correlation; the stronger the force, the less the difference becomes. This can be explained as following; at a high level 76

of magnetic strength and smaller abrasive grain size, the iron powder particles are pulled with a higher strength leaving behind the finer abrasives which are either trapped in the large grooves (as seen in figure 6-46) or the resultant force on the abrasive grains are high enough to cause deeper itching and cutting but not uniform. Main Effects Plot for Ra+a (%Diff) Fitted Means

Grain Size (nm)

120

Magnet Force (lb)

Mean of Ra+a (%Diff)

100

80

60

40

20

0 0

120

240

360

480

1.0

1.5

2.0

2.5

Figure 6-45 Factors influence on the surface roughness change

The experimental results show that the surface gets rougher at 50 nanometer grain size of the alumina, and that is the case where the magnetic force is at a high level too. This negative effect of the polishing process (or factors) is due to the reasons mentioned earlier; the groove effect and the pulling force of iron particles. Figure 50 shows the surface profile after polishing in that case (G 50 nm and F 2.52 lb), one can easily notice the deep grooves (multifold in size compared to 50 nm grains) generated on the surface being polished which acts as a trap to those fine grains. Moreover, as we know that the action of the abrasives is either rolling or sliding in a finishing process but in this case they lack the force that is 77

capable of returning the particles back to the cutting action due to the magnetic force (which is acting in the negative y-direction).

Figure 6-46 Surface profile at G 50 (nm) and F 2.52 (lb)

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Chapter 7

Discussion and Conclusions

In this project, we are able to make a novel yet simple pneumatic polishing tool that utilizes magnetic abrasive polishing concept. The tool has been successfully tested, and the results obtained are promising. The surface roughness is shown to have improved significantly, compared to conventional polishing, it is believed to be attributed to the cutting mechanisms that the grain size has a strong correlation to the output in polishing as seen in figures 7-1 and 7-2 which is agreed upon generally. Main Effects Plot for Ra (um) Data Means

0.22 0.20

Mean

0.18 0.16 0.14 0.12 0.10 1

16 Grain Size (um)

Figure 7-1 Grain Size effect on Ra

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32

Surface Roughness at different levels of Grain Sizes Ra (um)

0.3 0.2 0.1 0 32

16

1 Grain Size

Figure 7-2 Roughness improves as Grain size gets smaller

In the second part of this project, an investigation of the influence of nano-level abrasive grain size and magnetic field strength was experimentally conducted on the same workpiece material (304L Stainless Steel). A model that correlates the relationship between the surface roughness difference (percentage) and both of the studied factors was established. It was again found that the abrasive grain size plays a significant role in the polishing process, though at the smallest size the effect was found to be inversed due to the large grooves generated in the surface, and the large pulling force acting on the iron particles. There is a limit to applying the model proposed in the second part; that is it should not be used at finer abrasive grains less than 300 nanometer.

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Chapter 8

Model Validation

In this project, two experimental studies were conducted and the resulted models are to be verified in this section. In the first study, the effect of three main factors namely pressure in the rubber tip of the PPT, abrasive grain size, and tool rotational speed were considered. Now to validate the model(s), we chose values to those factors such that they are (1) available, and (2) reasonable and within the normal range. So the new set of runs is shown in table 8.1, following a Taguchi method.

Table 16.1 Runs generated using Taguchi method

Validation using Taguchi- 3^2 P (psi) G (micron) S (rpm) 9 66 1000 9 6 1300 11 66 1300 11 6 1000

The runs were all conducted on the same milling machine, in one day, and followed the same procedure. Workpieces were taken for measurements at the Mitutoyo new show room in Novi, MI, and the results are shown in table 8.2.

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Table 8.2 Surface roughness values (actual vs. predicted by the models)

After Before (Actual) Model1 Ra Ra S (rpm) (um) Ra (um) (um) 1000 0.1167 0.1429 0.34392 1300 0.1543 0.0697 0.12372 1300 0.1839 0.137 0.3364 1000 0.1594 0.0991 0.1234

Validation using Taguchi- 3^2 P (psi) 9 9 11 11

G (micron) 66 6 66 6

Model2 Model3 Ra Ra (um) (um) 0.38999 0.4891 0.12111 0.1191 0.3771 0.46281 0.11886 0.11522

One way to investigate the models’ adequacy in predicting the values of the surface roughness is to plot the results and examine the differences. This is shown in figure 8-1, as can be seen that the original regression model shows a good estimation of the values at low level of abrasive grain size (6 micron). In fact all the models provide a good estimation at those points, but both the square root and natural log models fail to rise to the challenge when the abrasive grain size goes to 66 microns.

Surface Roughness (um)

0.7

Models Validation against acutal values of Surface Rougness

0.6 0.5 0.4 0.3 0.2 0.1 0 1

2

Validation run order 3

Ra (um) Actual values Natural Log Transformation Model

4

No Data Transformation Model SQRT Transformation Model

Figure 10 Models validation against the actual values of surface roughness

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Another useful method of comparing the adequacy of the models, is to calculate and plot the error associated with the values using each model. This comparison is shown in table 8.3 and the plot is shown in figure 8-2.

Table 8.3 Error comparison

After Before (Acutal) Model1 Ra Ra (um) Ra (um) (um) 0.1167 0.1429 0.34392 0.1543 0.0697 0.12372 0.1839 0.137 0.3364 0.1594 0.0991 0.1234

% Error 1 58.45 43.66 59.27 19.69

Model2 Ra (um) 0.38999 0.12111 0.3771 0.11886

% Error 2 63.36 42.45 63.67 16.63

Model3 Ra (um) 0.4891 0.1191 0.46281 0.11522

% Error 3 70.78 41.47 70.4 13.99

Comparison between Error generated by several models 80

Percentage of Error

70 60 50 40 30 20 10 0 1

2

Error-No Data Transformation Model

Validation run order 3 Error-SQRT Model

4 Error-Natural Log Model

Figure 8-2 Error plot of the modes' predicted values of Ra

One could argue that there is so much variability that the models are not able to explain, which is true, but it is due to the weakness of the models as they have only the abrasive grain size to be the only influential factor in the study. Furthermore, since the 83

value of the abrasive grain size at 66 microns is so large compared to only 6 microns, the effect of such a large range is obvious in the values predicted and the large variation from one run to another. Because of this we will focus on runs 2 and 4 (at the G value of 6 microns). Model 3 (which is based on the natural logarithmic transformation of the data) shows to have the smallest value of error generated at G value of 6 microns, but then the error is so large at 66 microns compared to the other models. Therefore, the simple regression model (model 1) generates an acceptable error given the weakness of the model. In regards to the second study that involved the nano-level of the abrasives and the magnetic force, unfortunately validation runs to the models were not conducted due to some complications; lack of abrasive sizes in the range of 50 to 500 nanometers, and the lack of availability of certain levels of magnetic force.

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Chapter 9

Future Work

There are some areas to be investigated further; a study can be conducted to evaluate the effect of the type of slurry used in the finishing process, and another can focus on the preparation of the magnetic abrasive (i.e. sintered compound, different shape and size of the iron powder particles). One area is using different material (depending on the final application) which can lead to a study of the effect of magnetic forces on a magnetic versus non-magnetic workpiece material in pneumatic polishing. Another future work may focus on the tribology of the abrasive grains and the effect of the polishing process on it. This may be done by taking the polishing cloths under a microscope to investigate and draw conclusions.

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