Characterizing Edge Rounding In Vibratory Finishing. Shivinder S. Babbar

Transcription

1 Characterizing Edge Rounding In Vibratory Finishing Shivinder S. Babbar A thesis submitted in partial fulfilment of the requirements for the degree of BACHELOR OF APPLIED SCIENCE Supervisor: A.N. Sinclair Department of Mechanical and Industrial Engineering University of Toronto March, 28

2 Abstract Edge rounding is an important consequence of the vibratory finishing process. This thesis focused on characterizing the edge rounding process. In order to obtain the objectives of the study, five experiment runs were performed. 9 and 6 triangular samples were used to carry out the experiments in vertical, horizontal and free flow orientations. Each experiment run was performed for six time periods ranging from 15 minutes to 8 hours. After finishing, the sample profiles were recorded and their radius of curvature was calculated. Radius of curvature versus time graphs obtained from all experiment runs were then compared to two established studies to find a mathematical model that could be used to characterize the edge rounding process. The experimental results satisfied one of the pre-formulated models with reasonable accuracy. This model can now be used to enhance the overall efficiency of the edge rounding process. Supporting the strain hardening theory the thesis also provides an insight into the physical mechanism of the edge rounding process. Growth rate of the edge radius seemed to depend upon both the orientation of the samples and the geometry while the symmetry of the finished edge depended heavily upon the orientation of the samples. 1

3 Acknowledgements I would like to thank Professor Jan K. Spelt for his support, guidance and assistance in the preparation of this thesis. In addition, special thanks are due to Amir Mohejarani, whose familiarity with the subject of vibratory finishing was invaluable. Without the generous help of these individuals, this investigation would not have been possible. 2

4 Table of Contents 1. Background and Introduction Background of the vibratory finishing process Almen system as a tool to characterize the vibratory 7 finishing process 1.3 Objective and motivation Key assumptions Methodology Apparatus Experiment procedure Results and Discussion samples in horizontal orientation samples in vertical orientation Experiment samples in vertical orientation Experiment samples in vertical orientation Freely finished samples (9 ) Edge rounding comparison between 9 and 6 samples Edge rounding comparison between 9 constrained samples 33 and freely finished samples 3.8 Edge rounding comparison between 6 samples 36 and freely finished samples 3.9 Correlation of results with Ciampini s Almen strip study Correlation of results with Sofronas & Taraman s study The edge rounding mechanism and the repeatability of the 41 process 3.12 Sources of error Conclusion 53 References 45 Appendices 3

5 List of Figures Figure Page Fig Elastic-plastic boundary below contact zone Fig (a) Saturation curves obtained by the vibratory finisher for three types of Almen strips [3], (b) Expanded view of the data in (a) for low finishing durations Fig Saturation curves obtained from vibratory finisher simulator [3] for 617 µm strips (open symbols) and 779 µm strips (filled symbols). Impact velocities of.33 m/s (circles),.22m/s (squares) and.18 m/s (triangles) Fig Triangular aluminum sample (9 degree) Fig degree and 6 degree samples Fig Orientation of the sample with respect to the media Fig Constrained orientation of the sample in the sample holder Fig Manufacturing triangular samples Fig Sample holder Fig Minimum exposed height (h min ) of the sample to allow media contact on the side surfaces Fig Recording sample s profile Fig Profile recorded by the profilometer (thick black line) along with the polynomial of order six that fits it (thin red line) Fig Radius of curvature versus time for an aluminum sample processed by abrasive media Fig Edge of the finished aluminum sample Fig Edge profile after 135 minutes of finishing Fig Flow of media against the sample Fig Edge profiles for three finishing durations Figure Sample in the vertical orientation Fig Radius of curvature versus finishing duration

6 Fig Edge profiles for six finishing durations 24 Fig Radius of curvature versus finishing duration 25 Fig Edge profiles for six finishing durations 26 Fig Radius of curvature versus finishing time 27 Fig Edge profiles for six finishing durations 28 Fig Radius of curvature versus finishing duration 3 Fig Edge profiles for six finishing durations Fig Radius of curvature versus time for 9 degree samples and 6 degree samples Fig Variation in edge profiles for 9 and 6 degree samples Fig Radius of curvature versus time for 9 degree samples and freely finished samples Fig Variation in edge profiles for 9 degree samples and freely finished samples Fig Radius of curvature versus time for 6 degree samples and freely finished samples Fig Variation in edge profiles for 6 degree samples and freely finished samples Fig (a) David Ciampini s Almen strip study (91 kg of steel media and samples placed at 44 mm from the high wall) [3] (b) Current experimental results Fig (a) 9 degree constrained samples (b) 6 degree constrained samples (c) Freely finished samples

7 1. Background and Introduction: This section gives a brief overview of the vibratory finishing process and the Almen strip study. It also enlists the objectives of the thesis and any assumptions that were made. 1.1 Background of the vibratory finishing process This thesis focuses on characterizing the edge rounding process in vibratory finishing. Vibratory finishing is a popular mass finishing technique that is used to polish plastic and metallic objects, remove sharp and unwanted edges, enhance hardness and clean surfaces. Owing to the economy and consistency offered by automated finishing equipment, mass finishing of parts in batches has largely replaced manual finishing of individual components in manufacturing [1]. During vibratory finishing a work-piece is finished by the abrasive action of fluidized media in a vibratory chamber. The work-piece experiences a series of normal and tangential forces by coming in contact with the media. Contact forces in the vibratory finisher were measured by a number of researchers. Yabuki [2] concluded that the tangential impact forces are ten times less than the normal impact forces. In addition to material removal, the finishing action also results from the peening and ploughing action generated during the media contact [1]. In order to lubricate the media and keep the workpiece clean from debris, the finishing process is often performed in wet conditions. Significant parameters of the vibratory finishing process include the frequency and amplitude of vibrations, size, shape, mass and properties of media. The degree of erosion and plastic deformation of the workpiece is governed primarily by the impact velocity of the vibrating media [3]. 6

8 The type of media to be used depends upon the objective of the process (metal removal or surface finishing). Rough media with a high value of cutting factor are used where high material removal rate (MRR) is required whereas smooth media are primarily used for surface polishing [1]. 1.2 Almen system as a tool to characterize the vibratory finishing process The Almen system is now being employed to characterize the vibratory finishing process. It is already an established means of characterizing the shot peening process [4]. It consists of standardized metallic strips that are clamped to rigid supports and subjected to the peening agent. Residual stresses created by plastic deformation cause the strip to curve once the clamps are removed. The degree of curvature and its rate of change are governed by the process parameters such as shot density, radius, velocity, impact frequency, impact coverage, elastic modulus and yield strength [3]. The advantage of the Almen system lies in the fact that it allows characterization of the shot peening process via one measurement (arc height of the curved strip). When a shot strikes the surface of the workpiece an indentation is produced at the point of impact due to plastic yielding (Figure 1.2.1) [5]. As the deformed regions tend to expand, they are restrained by P deeper layers of metal that were not Elastic Plastic deformed by the shot impact. A uniform layer of plastic zone is Boundary Fig Elastic-plastic boundary below contact zone formed as more and more shots impact the surface. Since the 7

9 plastically deformed surface layer seeks to occupy more space, it is progressively compressed [5]. This layer with residual compressive stresses tends to close up surface defects and cracks and prevents premature failure. Even though the impact velocities are much smaller in vibratory finishing than in shot peening, the basic mechanism of compressive residual stress generation is the same in both cases. Baghbanan [6] measured Almen strip curvature in a vibratory finisher as a function of lubrication, finishing duration, aluminum alloy and finishing type. Hardness was measured as a function of depth from the finished surface. It was concluded that the location of maximum hardness moved from the surface to a depth of about 2µm with time [6]. The curvature of AA11-O, AA661-T6 and Cu11 strips was also found to increase consistently with the finishing duration. Ciampini [3] also subjected Almen strips to finishing in a tub style vibratory finisher to generate saturation curves at two of the contact conditions that were characterized previously in terms of effective impact velocity distributions. Impact conditions were correlated with changes in arc height (curvature) as a function of finishing time. Relationship between Almen strip curvature and normal impact velocity was also investigated by using a vibratory finishing simulator. In the simulator the Almen strip was finished via normal impacts only. The simulator comprised of an electromagnet-relay arrangement which repeatedly picked up and dropped steel balls on the Almen strip surface [3]. The results of finishing Almen strips in a vibratory finisher are shown in Figure below [3]. As the Almen strip arc height approached a saturated value the finishing time increased. Another striking feature of the graphs is that the rate of change of arc 8

10 height begins high but gradually reduces with time. This suggests that the majority of plastic deformation occurs early during finishing and it reduces subsequently as the workpiece strain hardens. Majority of the curves displayed in Figure also satisfied the exponential function used to characterize the Almen saturation curves generated from the shot peening data [3]. Fig (a) Saturation curves obtained by the vibratory finisher for three types of Almen strips [3], (b) Expanded view of the data in (a) for low finishing durations The saturation curves obtained from the vibratory finisher simulator (Figure 1.2.3) also exhibited similar characteristics as the ones shown in Figure The main differences between the curves generated from the finisher and the simulator are that curvature relaxation is more common in the simulator and the finishing durations are much longer in the simulator as well [3]. Longer finishing time in the simulator might be attributed to the fact that it ran with a frequency lower than that of the vibrator finisher (2 Hz versus 46 Hz). Also, media was observed to be more closely packed in the finisher than in the simulator [3]. In general the time required to attain maximum curvature reduced as the impact velocity increased. 9

11 The similarity between the two sets of data support the argument that normal impact velocity is a dominant parameter in vibratory finishing. It also points to the fact that, to a first order approximation, arc height is controlled primarily by the largest impact velocities [3]. Fig Saturation curves obtained from vibratory finisher simulator [3] for 617 µm strips (open symbols) and 779 µm strips (filled symbols). Impact velocities of.33 m/s (circles),.22m/s (squares) and.18 m/s (triangles) 1.3 Objective and motivation Up until now vibratory finishing has only been dealt empirically. This is primarily due to the unpredictable motion of the media. Also, the mechanics of media-workpiece contact is not yet understood comprehensively [2]. Due to a large number of governing parameters in the vibratory finishing process the trial and error approach is not only difficult but also very cumbersome. 1

12 The current study is a subset of the bigger and more comprehensive project which involves modeling of the entire vibratory finishing process. This thesis focuses on developing an analytical model to predict edge rounding in the vibratory finishing process because it is one of the most common techniques employed to perform edge rounding, edge removal and deburring on a mass scale. It is also important to study edge rounding because it constitutes the basic mechanism via which removal of sharp and nonuniform edges takes place in vibratory finishing. The primary objectives of modeling the edge rounding process are to: Optimize the process: The amount of edge radiusing provides a convenient means of characterizing the energy imparted to the specimen by the vibratory finishing system [6]. Modeling edge radiusing will not only help us understand the mechanics of the process but may also provide novel ways of enhancing the efficiency of the process and reducing the energy and time consumption. Enhance the repeatability of the process: Modeling the process will provide more control over the parameters involved and help us duplicate the process over an over again. Repeatability is an important factor because it is required to maintain consistency in products in an industrial setting. Correlate the Almen strip curvature study (performed by D. Ciampini [3]) with actual edge rounding in the vibratory finishing process: Almen strip arc height versus time graphs (Figure 1.2.2) will be compared to the radius of curvature of the edge versus time graph. If there is correlation between the two studies then the Almen strip study could be used to predict edge rounding. Almen saturation curves may also 11

13 be used to show how changes in process parameters affect edge rounding and finishing rate in general. Edge rounding Mechanism: The results of this thesis will also be used to deduce an edge rounding mechanism. Edge rounding occurs either due to wear or due to plastic deformation. The contributions of each mechanism to edge radiusing will be analyzed. 1.4 Key assumptions For the purposed of this study it is assumed that the contact between the media and the sample is Hertzian in nature. By Hertzian we mean that the contact pressure is non-singular [7]. Also, the contact between the edge and the media will be modeled as the contact between a cylinder and sphere. Only normal impacts will be considered in the analysis and the effects of friction will be neglected. 12

14 2. Methodology: Information regarding the experiment apparatus and the number and types of experiments conducted is presented in this section. The section also mentions the procedure in which the experiments were conducted and the method used to perform the analysis. 2.1 Apparatus Aluminum samples: Triangular aluminum bars of length 76.2 mm were used as the experiment samples. Figure illustrates a triangular sample with an edge angle of 9 degree. The samples were machined out of aluminum alloy 33. Edge that will undergo finishing 76.2 mm 15 mm 9 45 Fig Triangular aluminum Sample (9 degree) Triangular samples with edge angle of 6 degree were also used in the experiments. The two isosceles faces were milled to ensure that the edge of interest subtends an angle of 9 and 6 respectively. Figure on the next page shows both types of samples. Almen strips of length 76.2 mm and material aluminum 33 were used in Ciampini s study [3]. Therefore, in order to maintain consistency with his study, the length of the triangular bars was also maintained at 76.2 mm. 13

15 Fig degree and 6 degree samples Vibratory finisher and media: The experiments were conducted in a tub style vibratory finisher (Burr Bench 216, Brandon Industries, TX). The tub has a U-shaped cross section and is lined with urethane. Carbon steel balls were used to finish the experiment samples. The average diameter and mass of one steel ball is 6.3 mm and.29 g respectively. Sample holder: A sample holder was required to hold the triangular samples in the vibratory finisher in such a way that only the edge of the sample was exposed to the media at all times. Figure on the next page clearly illustrates this point. Another function of the sample holder was to hold the triangular samples in a constrained orientation as the Almen strips in Ciampini s study (Figure 2.1.4). Profilometer: A Taylor Hobson profilometer and the corresponding software was be used to measure and record the surface profile of the sample edge before and after finishing. 14

16 Edge exposed to media contact Fig Constrained orientation of the sample in the sample holder Fig Orientation of the sample with respect to the media 2.2 Experiment procedure Machining: The first step in this study was to machine the sample holder and the samples. As mentioned earlier the triangular samples of length 76.2 mm were machined from Al-33 alloy in order to maintain consistency with Ciampini s study. A triangular cross section was chosen in order to accommodate the design constraints imposed by the sample holder. Figure illustrates the schematics of sample preparation. Saw Milled square block Cut the block along one diagonal Fig Manufacturing triangular samples Isosceles triangular samples One of the most important parts of this thesis was to manufacture the sample holder. The functions of the sample holder were to hold the sample so that only one edge is exposed to finishing at all times. The sample holder was designed keeping the 15

17 geometrical constraint in mind. It was required that the shape, size and thickness of the sample holder was identical to Ciampini s Almen strip holder. This was an important consideration because the shape of the sample holder affects the flow of media around the sample to some extent. The holder was machined from aluminum 661. Figure presents different views of the sample holder. Detailed engineering drawings of the holder are presented in Appendix A. Fig Sample holder Finishing samples: Once the samples were prepared they were subjected to vibratory finishing in the same orientation for six time durations (15 minutes, 3 minutes, 1 hour, 2 hour, 4 hour and 8 hour). 91 kg of steel media was used and the samples were placed 44 mm from the high wall of the finisher (the wall against which the relative flow of the media is in the upward direction). Five experimental runs were performed i) 9 degree samples constrained in horizontal orientation, ii) 9 degree samples constrained in vertical orientation, iii) another run in which the 9 degree samples were held in the vertical orientation, iv) 6 degree samples constrained in vertical orientation and v) 9 degree samples finished freely in the finisher without any sample holder. 16

18 In all the experiments in which the holder was employed to constrain the samples it was made sure that the exposed height of the sample was such that it allowed media contact on the side surfaces in the vicinity of the edge. This was required to imitate the actual finishing process in a more realistic manner (in actual processes when the work piece is allowed freely flow in the media, not only does the edge but also the surfaces around the edge experience impacts from the media). Figure shows a schematic which displays the media contact with the surface around the sample s edge. Steel ball r - h min r β β h min h sample Fig Minimum exposed height (h min ) of the sample to allow media contact on the side surfaces If the exposed height h is less than h min the steel balls will only contact the sample at the edge (as displayed by the red dotted line). From Figure h min = r * [1 sin(β)] where r is the steel ball radius (3.15 mm) and β is half the edge angle (45 and 3 for an edge angle of 9 and 6 respectively). h min was calculated to be.922 mm for 9 degree samples and mm for the 6 degree samples. All the experiments were performed with the exposed height, h of about 2-3 mm, satisfying the h min criteria. 17

19 Data recording: After stipulated durations of finishing, the samples were removed from the holder and their profile was recorded via a profilometer. Figure shows a typical stylus profilometer. Profilometer Specimen Finished edge Fig Recording sample s profile Once the profile of the edge was recorded, a polynomial of order six was traced on it. Figure shows such a profile and the associated polynomial..8 y =.165x x x x x x Y (mm) X (mm) Fig Profile recorded by the profilometer (thick black line) along with the polynomial of order six that fits it (thin red line) Once the polynomial was obtained, the curvature of the curve every 5 µm apart was calculated. Curvature, k of a two dimensional curve y = f(x) is given by k = y (x)/ [1+y (x) 2 ] 1.5. The radius of curvature at each of the points was calculated and the 18

20 minimum radius of curvature for the entire edge profile was obtained (radius of curvature r = 1/k). A new sample was then fixed in the holder and subjected to finishing for the next time slot. Again, the curvature and the minimum radius of curvature were calculated. After all the six experiment runs was performed a graph of minimum radius of curvature versus time was plotted. A similar graph for an aluminum specimen finished with abrasive media is shown in Figure Figure also shows the edge of the aluminum sample that was finished. Please note that Figure and are derived from a PhD student s study. radius (m m ) duration (h) Fig Radius of curvature versus time for an aluminum sample processed by abrasive media Fig Edge of the finished aluminum sample Analysis: The graph of the radius of curvature versus time was then analyzed and compared to the Ciampini s Almen strip saturation curves (Figure 1.2.2). Similarities and differences between the graphs were accounted for and deductions regarding the edge rounding mechanism were made. 19

21 3. Results and Discussion: This section lists the results of the experiments and discusses important features of the results. It also compares the results of this thesis to the results of Ciampini s Almen strip study [3] and Sofronas and Taraman s edge rounding study [8] samples in horizontal orientation An unsymmetrical edge profile was generated when the 9 degree triangular samples were finished in the horizontal orientation. The edge profile after 135 minutes of finishing is presented in Figure below. The blue line shows the actual edge profile whereas the dotted red curve indicates the desired symmetrical edge profile. When the sample is placed horizontally, only the leading edge experiences significant contact with the media while the trailing edge is relatively unaffected by the media. Thereby only the leading edge experiences finishing and plastic deformation. This unbalanced finishing gives rise to the unsymmetrical edge profile..6.4 Trailing edge (unfinished) Leading edge (finished).2 Y (mm) Direction of bulk media flow -.8 X (mm) Table Fig Edge Edge profile after after hours minutes of finishing of finishing 2

22 Figure illustrates the unsymmetrical finishing process clearly. The localized flow of media against the sample is in the upward direction. This type of flow causes the leading edge (marked in red) to experience majority of the media contact. Being in the wake region of the flow the trailing edge experiences contacts of lesser intensity. Therefore, the leading edge gets selectively finished and produces an unsymmetrical edge profile. This phenomenon was also consistent with finishing durations of 4 hours and 8 hours. Figure shows the edge profiles for the three Fig Flow of media against the sample finishing durations. All three profiles have an unsymmetrical edge as expected MIN 4 HR 8 HR Normalized Y (mm) Normalized X (mm) Fig Edge profiles for three finishing durations 21

23 The figure also illustrates an extrapolated profile of the initial (unfinished edge). The media had two significant effects on the edge profile. It plastically deformed the leading edge causing it to have a curvature and also pushed the tip of the sample, effectively rotating its trailing edge in the direction of bulk media flow. The microscopic rotation of the tip of the sample also contributed to generation of unsymmetrical edge profile. An unsymmetrical edge profile is undesirable for two primary reasons. Firstly, it increases the complexity of calculating a representative radius of curvature for the entire edge. Secondly, it does not emulate the edge profile resulting from finishing of loose samples. When a sample is finished freely (like in most industrial vibratory finishing processes) it experiences bulk finishing which causes it to have a symmetrical edge profile. Since the objective of this thesis is to characterize edge rounding in vibratory industrial finishing it is necessary to perform experiments that yield similar results to the actual processes. Keeping this in mind all the following experiments were conducted by constraining the samples in a vertical rather than a horizontal orientation (Figure 3.1.4). Figure Sample in the vertical orientation 22

24 3.2 9 samples in vertical orientation Experiment 1 Samples with edge angle of 9 degree were finished in constrained vertical orientation for six finishing durations. Figure shows the change in radius of curvature of the edge with respect to finishing time Radius of curvature (mm) Finishing duration (min) Fig Radius of curvature versus finishing duration The radius of curvature increases steeply with process duration for the first two hours of finishing. Subsequent finishing causes the radius of curvature to decrease in a steady manner. There is a drop of approximately 22% in the radius of curvature of the 8 hour sample as compared to the 2 hour sample. Such a large drop was unexpected and might be attributed to the sources of error discussed in section The steep slope of the graph during the initial part of the experiment shows that the majority of edge rounding occurs during the early part of the vibratory finishing process. As the work piece experiences impacts from the media it strain hardens and 23

25 resists subsequent plastic deformation. This is denoted by the reduction in radius of curvature of the 4 and 8 hour samples. The error bar for the 2 hour sample is largest amongst all the samples. This is because there was a large variation in the radius of curvature between the three samples for the 2 hour finishing time. Figure presents a superposition of the edge profiles for all six finishing durations. The dotted line indicates the original (unfinished edge). Normalized Y (mm) Slight bulge 15 MIN 3 MIN 1 HR 2 HR 4 HR 8 HR Normalized X (mm) Fig Edge profiles for six finishing durations In conjunction with Figure the radius of curvature increases from 15 minutes to 2 hours of finishing duration. This is represented by the decrease in curvature and decrease in maximum arc height of the edge profiles. In agreement with Figure the radius of curvature drops from the 2 hour point till the 8 hour point. A careful comparison between the unfinished profile and any finished profile indicates that the majority of edge rounding takes place due to plastic deformation rather than material removal. A slight bulge in all the samples indicates that as the media 24

26 impacts the sample there is redistribution of the material in the microscopic vicinity of the edge. This redistribution along with the plastic deformation generates the curvature in the finished samples samples in vertical orientation Experiment 2 Another run of experiments was conducted using the 9 degree samples constrained in vertical orientation. The results for the experiment are presented in Figure below Radius of curvature (mm) Finishing duration (min) Fig Radius of curvature versus finishing duration As expected the rate of change of radius of curvature with time is high in the initial part of the graph and gradually reduces as the time progresses. This observation regarding reduction in slope of the graph is once again supported by the strain hardening phenomenon. As the material strain hardens it resists deformation. 25

27 As compared to Figure in this case the radius of curvature does not decrease after a certain finishing duration. Rather, it increases throughout the experiment. This is expected because it is unlikely for the work piece to sharpen (reduction in radius of curvature) as finishing time in increased. Figure illustrates all the edge profiles generated in the experiment. The dotter black line indicates the extrapolated original (unfinished) edge profile. The graph is consistent with Figure As the finishing time increases the edge profile becomes less curved and reduces in height resulting in an increase in the radius of curvature MIN Normalized Y (mm) Bulge zone 3 MIN 1 HR 2 HR 4 HR 8 HR Normalized X (mm) Fig Edge profiles for six finishing durations A bulge or protruded zone such as in Figure is also evident in the above graph. It once again suggests the displacement of material around the edge in order to accommodate the change in radius of curvature. Since the bulge zone is not uniformly spread around the edge (for 1, 2 and 4 hour duration) it points to the fact that despite changing the orientation of the samples from horizontal to vertical there is still a presence of unsymmetrical finishing. The one sided bulge zone is significantly reduced in the 8 hour sample and it appears to be more 26

28 uniform. This indicates that the effects of unsymmetrical finishing are minimum when the work piece is finished for long duration in vertical orientation samples in vertical orientation To observe the effects of edge angle on edge rounding, a new set of experiments was performed using 6 degree triangular samples. The samples were finished in constrained vertical orientation for six finishing durations. Figure presents the results of the experiment Radius of curvature (mm) Finishing duration (min) Fig Radius of curvature versus finishing time The radius of curvature rises steeply from 15 minutes to 3 minutes of finishing. Following which there is a slight drop in the radius of curvature. This is unexpected as it is unlikely for the curvature of sample to increase during finishing. This anomaly might be attributed to the large error band associated with the 1 hour data point. A large error 27

29 band signifies large variation between the three profilometer measurements taken on the sample. If we ignore the 1 hour data point, the overall shape of the graph is promising. The slope in the initial part of the graph is steeper than the latter part of the graph, once again supporting the strain hardening theory. Figure provides an effective means of comparing the edge profiles after stipulated durations of finishing. The graph is in close agreement with Figure The curvature progressively decreases (i.e. radius of curvature progressively increases) with time. The edge profiles are also more symmetrical in this case..2 Original (unfinished) edge.15 Normalized Y (mm) MIN 3 MIN 1 HR 2 HR 4 HR 8 HR Normalized X (mm) Fig Edge profiles for six finishing durations 28

30 There is a discrepancy between Figure and in regards to the radius of curvature after 1 hour of finishing. As per Figure the radius of curvature should increase (which is expected) but as per Figure the radius of curvature at 1 hour data point is less than the radius of curvature at 3 minutes data point. This disagreement might be due to the 6 degree polynomial equation used to characterize the edge profiles. It can be seen from Figure that the edge profile for 1 hour data has abrupt changes in slope (i.e. it is not perfectly rounded). A 6 degree polynomial equation will accurately trace each junction where the change in slope occurs. Such a junction is likely to have higher curvature (lower radius of curvature) than the overall curvature of the edge. Therefore, a 6 degree polynomial will underestimate the overall radius curvature of the edge. 3.5 Freely finished samples (9 ) In order to understand how well the constrained finishing processes (i.e. in which the samples were held in the holder) represent the actual finishing process, an experiment run was performed in which the 9 degree samples were freely finished inside the tub for stipulated duration of time. The results from the experiment are graphed in Figure on the next page. In conjunction with the strain hardening theory the rate of change of radius of curvature is high at the inception of the graph and gradually reduces in the latter part of the graph. As expected the radius of curvature also increases throughout the graph. A striking feature of Figure is the presence of large error bars. As mentioned in the methodology section of the thesis three profilometer recordings were performed on each finished sample. The central point on the above graph and the two corresponding 29

31 error bar points represent the radius of curvature calculated from the three profilometer recordings. Because the samples were freely finished the edge rounding effect was non uniform along the edge of the samples. This resulted in significant variations between the radii of curvature calculated from the three profilometer measurements Radius of curvature (mm) Finishing duration (min) Fig Radius of curvature versus finishing duration Figure on the next page illustrates the edge profiles for various finishing durations. It can be seen from the above graph that the overall shape of the edge changes from time to time (i.e. the point of minimum radius of curvature on the edge profile is sometimes to the right and sometimes to the left) and does not follow constant pattern. This might indicate that finishing samples freely leads to inconsistency in shape with respect to time (i.e. the general shape of the edge changes from time to time). This happens because during free finishing the sample randomly flows in the media. Its motion and orientation is unpredictable which leads to uncertainty in determining the 3

32 edge profile after a certain amount time. Please note that while the shape of the edge profile changes from time to time, for long finishing durations (8 hours) the edge profile generated is rather symmetrical. Normalized Y (mm) Unfinished edge 15 MIN 3 MIN 1 HR 2 HR 4 HR 8 HR Normalized X (mm) Fig Edge profiles for six finishing durations Other striking feature of the graph is that the radius of curvature of the 1 hour sample seems to be more than that of 2 and 4 hour samples. This feature is probably not represented in Figure because of the errors associated with using a 6 degree polynomial equation to trace the edge profile. However a decrease in radius of curvature from 1 hour sample to the 2 or 4 hour sample is unexpected and may be attributed to the sources of error discussed in section Edge rounding comparison between 9 and 6 samples A comparative study between the 9 degree and 6 degree samples was performed in order to understand the effects of sample geometry on edge rounding and its 31

33 propagation. Figure compares the growth radius of curvature for the two types of samples. (Please note that the data from section 3.3 was used for the 9 degree samples).23 Radius of curvature DEG 6 DEG Finishing duration (min) Fig Radius of curvature versus time for 9 degree samples and 6 degree samples The radius of curvature grows by 131% in the case of 9 degree samples while a growth of 112% was observed for the 6 degree samples. The initial slope of both the curves is approximately same but there is a significant difference in the slopes in the latter part of the graph. The rate of increase of radius of curvature is higher for the 9 degree samples in the latter part of the graph. As evident from Figure the radius of curvature is higher for the 9 degree samples, therefore the effective surface area of the tip is also higher for the 9 degree samples. With higher area, the number of shots striking the edge per unit time is also higher for the 9 degree samples. Therefore the radius of curvature grows at a higher rate for the 9 degree samples. The slower growth of the radius of curvature of the 6 degree samples in the latter part of the graph also suggests that strain hardening occurs at a higher rate in the 6 degree samples. 32

34 samples. Figure clearly illustrates the growth of radius of curvature for both types of DEG-15 MIN 9 DEG-8 HR 6 DEG-15 MIN 6 DEG-8HR Normalized Y (mm) Normalized X (mm) Fig Variation in edge profiles for 9 and 6 degree samples Both types of samples show signs of unsymmetrical edge rounding but the extent of unsymmetry is less for the 6 degree samples. This once again might be attributed to the smaller effective impact area of the 6 degree samples. When the area is small the deformation is likely to be concentrated resulting in more symmetry. 3.7 Edge rounding comparison between 9 constrained samples and freely finished samples In order to compare the effects of actual finishing versus constrained finishing Figure on the next page was prepared. It displays the change in radius of curvature for the 9 degree samples (constrained in the holder) and the free samples. (Please note that the data from section 3.3 was used for the 9 degree constrained samples) 33

35 .6.5 Radius of curvature (mm) DEG FREE Finishing duration (min) Fig Radius of curvature versus time for 9 degree samples and freely finished samples There was an increment of about 15% in the radius of curvature of the freely finished samples while the 9 degree samples had a growth of 131% for 8 hours of finishing. Another striking feature of the above graph is that the slope (i.e. the rate of change of radius of curvature) is higher for the freely finished samples for the majority of the time. The above two features suggest that the samples experience higher impact forces when they are finished freely without constraining them to a holder in one orientation. When the sample is allowed to finish freely, it flows with the media in the finisher. Owing to its kinetic energy the impacts with the media are amplified and edge rounding is enhanced. During finishing the sample goes to the bottom of the tub and comes back up periodically in a rolling manner. When the sample is at the bottom it is closest to the 34

36 motor (media close to the motor vibrates more vigorously) and also experiences higher pressure from top due to the weight of the overlying media (higher pressure from top enhances the impact forces). This rolling phenomenon also enhances the rate of finishing in freely finishing samples. Figure compares the edge profiles for 15 minutes and 8 hours of finishing time for the two types of samples. The dotted line indicates the extrapolated profile of the original (unfinished) sample. Normalized Y (mm) Bulge zone 9 DEG-15 MIN 9 DEG-8 HR FREE-15 MIN FREE-8 HR Normalized X (mm) Fig Variation in edge profiles for 9 degree samples and freely finished samples Figure clearly illustrates that edge rounding is more symmetrical in the freely finished samples. There is no bulge zone present in the profiles of the freely finished samples. This suggests that finishing the samples freely in the finisher results in more balanced finishing because the sample experiences same net impact forces all along the vicinity of the edge. 35

37 3.8 Edge rounding comparison between 6 samples and freely finished samples The results of the 6 degree samples (constrained in the holder) were compared to the results of the freely finished samples to confirm the deductions made in section 3.7 above. Figure compares the growth of radius of curvature for the two types of samples Radius of curvature (mm) DEG FREE Finishing duration (min) Fig Radius of curvature versus time for 6 degree samples and freely finished samples As calculated earlier the radius of curvature grows by 15% for the freely finished samples, where as the corresponding growth is of only 112% for the constrained samples of edge angle 6 degree. Both the radius growth and the growth rate are higher for the freely finished samples. This confirms our previously made deduction that regardless of the sample geometry the edge rounding is highly pronounced when the samples are 36

38 allowed to finish freely. As mentioned in section 3.7 the reasons behind this include higher impact forces generated due to the kinetic energy of the sample and the effects of the rolling motion of the sample. Figure presents the edge profiles for the two types of samples after 15 minutes and 8 hours of finishing. Once again the edge rounding for long finishing duration seems to be more symmetrical for the freely finished samples due to the reasons mentioned in section DEG-15 MIN 6 DEG-8 HR FREE-15 MIN FREE-8 HR Normalized Y (mm) Normalized X (mm) Fig Variation in edge profiles for 6 degree samples and freely finished samples 3.9 Correlation of results with Ciampini s Almen strip study One of the primary objectives of the thesis was to check whether there is any correlation between Ciampini s Almen strip study and the edge rounding results obtained from the experiments. Figure shows the arc height versus time graph (Ciampini s study [3]) for three types of aluminum sheet samples, and the radius of curvature of the edge versus time graph. Please note that the experiments for this thesis were performed 37

39 under the same physical conditions as Ciampini s experiments (same media mass, media type and sample holder position). 8 AL 33 - O (617) AL 33 - H14 (617) AL 33 - O DEG CONSTRAINED 6 DEG CONSTRAINED 9 DEG FREE 7.5 Arc height (micron) Radius of curvature (mm) Time (min) (a) (a) Time (min) (b) (b) Fig (a) David Ciampini s Almen strip study (91 kg of steel media and samples placed at 44 mm from the high wall) [3] (b) Current experimental results The above figure illustrates that there is similarity between the two studies. Even though the blue curve (Al-33 O (617)) in Ciampini s study is an anomaly, the other two curves exhibit promising correlation with the experimental results of the current thesis. In both the graphs the initial slopes of the graphs are higher than the latter slopes. This illustrates how the strain hardening theory is equally applicable to both the studies. As the sample gets finished, it undergoes cold working and resists further deformation. An important point to note between the two graphs is the time scale. The time scale over which most of the finishing occurs is significantly less for the Almen strips. This is because the net area which was subjected to contact with the media is much 38

40 higher for the Almen strips (on the other hand for triangular samples the net area is only the area in the vicinity of the edge). Since the impact area is higher the number of contacts per unit time will also be more. More impacts per units time in turn accelerate the finishing process. Figure also shows that the transition in slope from a high value to a low value is sudden for the Almen strips and relatively gradual for the triangular samples. This is because a significantly large amount of the finishing occurs during the early time periods for the Almen strip. As the net impact area is higher for the Almen strips, even a short time span is sufficient to cause apparent changes in the arc height. Because of this the Almen strips strain harden faster and exhibit a sudden drop in slope (rate of change of arc height). On the other hand the net impact area is much smaller for the triangular samples and therefore longer initial time span is required to cause significant changes in the edge radius. As a result strain hardening occurs at a slower rate which translates into gradual changes in slope (rate of change of edge radius). Therefore Ciampini s study cannot accurately predict the edge rounding phenomenon because there is a lack of agreement between the two studies as far as the time scale and the onset of strain hardening is concerned. 3.1 Correlation of results with Sofronas & Taraman s study Sofronas and Taraman investigated the simultaneous effect of media size, process time and vibration frequency on sample edge radius [8]. Response surface methodology was used for model development. 39

41 .3.25 R =.5*T.26 After performing a series of experiments they formulated the edge Radius of curvature (mm) Radius of curvature SOFRONAS & TARAMAN EMPIRICAL EQUATION Time (min) R =.2*T SOFRONAS & TARAMAN.1 EMPIRICAL EQUATION Time (min) Experiment results Experiment results (a) (b) rounding process as per the following equation: R = 4.8*1-11 *T.25 M.79 F 2.43 where R is edge radius (in), T is process time, M is media size and F is process frequency. The media size and process frequency remained constant for all the experiments therefore, for the purpose of this thesis the above mentioned equation can be modifies as R = a*t.25 where a is a constant. Matlab was used to fit a curve Radius of curvature (mm) R =.9*T Time (min) Experiment results SOFRONAS & TARAMAN EMPIRICAL EQUATION (c) Fig (a) 9 degree constrained samples (b) 6 degree constrained samples (c) Freely finished samples of the form R = a*t b to all the radius of curvature versus time graphs. The constant b is of most importance. If it is close to.25 then it will not only increase confidence in our results but also provide us with a tool to achieve process optimization. Figure shows all the three graphs along with the fitted curves and the corresponding 4

42 equations. There is promising agreement between the fitted curves and the equation R = a*t b. The value of b is very close to.25 for the 9 degree samples and the freely finished samples (.26 and.27 respectively). Even though b for the 6 degree samples is.214 it is still in reasonable proximity to.25. Therefore Sofronas and Taraman s model could be applied to study and optimize the edge rounding process effectively. The equation derived by them could be used to determine the optimal levels of processing time, media size and process frequency The edge rounding mechanism and repeatability of the process After examining all the edge profile graphs (Figures 3.2.2, 3.3.2, and 3.5.2) it can be seen that plastic deformation contributed to the majority of the edge rounding process for the aluminum samples. Material removal played insignificant role in the generation and growth of the edge radius. As the media impacted the edge it was plastically deformed resulting in edge rounding. As the duration of finishing increased the samples strain hardened and resisted edge radius growth. As far as repeatability of the process is concerned, Sofronas and Taraman s equation can be applied to tune the process parameters in order to obtain a certain amount of edge radius. Repeatability is difficult to maintain owing to the large number of governing parameters of the vibratory finishing process Sources of error Sources of error were found to be present in the sample preparation and the experiment stages. 41

43 The main source of error in the sample preparation stage was associated with machining of the samples. As the samples were manufactured in batches it was difficult to maintain accurate consistency. Surface defects also arise during machining operations and become prime sources of errors. To reduce the errors associated with sample preparation all the samples were polish with a grinder to remove any possible surface defects. Slipping of the motor belt (of the vibratory finisher) and overheating of the media were the major sources of error in the experiment stage. Slipping of the motor belt alters the frequency of the finisher and introduces process inconsistencies. To prevent the above problem jets of compressed air were used to cool both the motor belt and the media. 42

44 4. Conclusion: The results of the experiments reveal that finishing a sample in a horizontal orientation causes unsymmetrical edge rounding. This is because the leading edge experience impacts of higher energy than the trailing edge. Even after the orientation of samples was changed from horizontal to vertical there was a presence of slight unsymmetrical edge rounding. The edge rounding became more symmetrical for longer durations of time when the samples were allowed to freely flow in the media. As far as growth rate of the edge radius is concerned, the freely finished samples exhibited the highest growth rate. The radius grew by approximately 15% for the free samples. This intense growth in radius of curvature was attributed to the higher impact velocities encountered by the sample when it was allowed to finish freely. The experimental results of this thesis did not completely agree with Ciampini s Almen strip study. The major difference between the two studies lied in the onset of strain hardening and time scale over which the entire finishing process took place. Almen strips showed consequences of finishing relatively earlier than the triangular samples. However there was a promising match between the experimental results and Sofronas and Taraman s model. Their model could be applied to edge rounding to enhance the optimization of the process. The edge profile graphs also indicated that the majority of edge rounding occurred due to plastic deformation rather than material removal. Lastly, the accuracy of the experiments could be increased by making sure that the motor belt does not slip and the media is prevented from being overheated. 43

45 The thesis achieved its objective by providing an empirical model that characterized the edge rounding process (derived from Sofronas and Taraman model) and by correlating the Almen strip study with the current experimental results. 44

46 References [1] J. Domblesky, V. Cariapa and R. Evans, Investigation of vibratory bowl finishing, International Journal of Production Research 41 (23) pp [2] A. Yabuki, M.R. Baghbanan, J.K. Spelt, Contact forces and mechanisms in a vibratory finisher, Wear 252 (22) pp [3] D. Ciampini, M. Papini, J.K. Spelt, Characterization of vibratory finishing using the Almen system, Wear 264 (28) pp [4] W.Cao, R.Fathallah, L.Castex, Correlation of Almen arc height with Residual stresses in shotpeening process, Mater.Sci.Technol. 11(9) (1995) pp [5] Y.F. Al-Obaid, A rudimentary analysis of improving fatigue life of metals by shot peening, J. Appl. Mech. 57 (199), pp [6] M.R. Baghbanan, A. Yabuki, R.S. Timsit, J.K. Spelt, Tribological behaviour of aluminum alloys in a vibratory finishing process, Wear 225 (23) pp [7] D.A. Hills and D. Nowell, Mechanics of Fretting Fatigue, Kluwer Academic Publ., Dordrecht 1994, ISBN [8] A. Sofronas and S. Taraman, Model development and optimization of vibratory finishing process, International Journal of Production Research 17 (1979), pp

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