Available online at www.sciencedirect.com Wear 264 (2008) 671–678 Characterization of vibratory finishing using the Almen system D. Ciampini a , M. Papini b,a , J.K. Spelt a,b,∗ a Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ont. M5S 3G8, Canada b Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ont. M5B 2K3, Canada Received 9 August 2006; received in revised form 4 April 2007; accepted 4 June 2007 Available online 19 July 2007 Abstract The Almen system was adapted to a vibratory finishing process to characterize the effect of varying process parameters for the purposes of process development and control. Saturation curves for two types of aluminum Almen strips were obtained by finishing at two distinct conditions using a tub type vibratory finisher and steel spherical media. Comparison with the normal contact forces and effective impact velocities, measured for both these conditions in a previous study [D. Ciampini, M. Papini, J.K. Spelt, Impact velocity measurement of media in a vibratory finisher, J. Mater. Process. Technol., 183 (2007) 347–357], provided insight into the mechanics of the vibratory finishing process. An electromagnetic apparatus was constructed to simulate the normal impacts in the vibratory finisher. It was found that surface-normal impacts at velocities comparable to the higher range in the vibratory finisher produced Almen saturation curves similar to those created in the vibratory finisher. This provided support for the modeling approximation of treating all contact events in a vibratory finisher as effective surface-normal impacts, and the accuracy of the effective impact velocity measurement employed in [D. Ciampini, M. Papini, J.K. Spelt, Impact velocity measurement of media in a vibratory finisher, J. Mater. Process. Technol., 183 (2007) 347–357]. © 2007 Elsevier B.V. All rights reserved. Keywords: Almen; Vibratory; Finishing; Shot-peening; Impact 1. Introduction Vibratory finishing is a widely used industrial process to modify the properties and microtopography of metal, ceramic, and plastic parts. It is used to polish metal and plastic components, to smooth the sharp edges of steel parts that have been cast or stamped, to harden and texture metals, and to clean surfaces by removing rust and other contaminants. Current industrial practice relies largely on experience and experimentation to optimize the process for new parts and materials. Several authors [2–4] have proposed correlations to predict erosion rates in vibratory finishing. In a typical configuration, a vibrating container fluidizes a bed of granular media creating a circulating bulk flow. A workpiece entrained in this flow is subject to the impacts of the vibrating media. The impact velocity of the vibrating media will control ∗ Corresponding author at: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ont. M5S 3G8, Canada. Tel.: +1 416 978 5435; fax: +1 416 978 7753. E-mail address: [email protected] (J.K. Spelt). 0043-1648/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2007.06.002 the impact force and hence the degree of plastic deformation and erosion of the workpiece surface. The Almen system is well established  as an effective standardized (i.e. SAE J442) means of characterizing the shot peening process. Standardized metal strips are clamped to a rigid support and subject to the shot peening stream. On release of the clamps, residual stresses created by plastic deformation cause the strips to curve. The degree of curvature and its rate of change are related to the process parameters. The “Almen intensity” is the ultimate strip arc height reached after a certain saturation time defined such that doubling the exposure time causes only a 10% increase in arc height . The Almen system has the advantage that it combines the effects of all the process parameters into one measurement allowing for the characterization and determination of the repeatability of the process. These process parameters include shot density, radius, velocity, impact frequency, impact coverage, elastic modulus, and yield stress, if the shot deforms plastically during impact. Baghbanan et al.  measured Almen strip curvature in a vibratory finisher as a function of lubrication, finishing duration, aluminum alloy, and finisher type. They measured the hardness 672 D. Ciampini et al. / Wear 264 (2008) 671–678 Fig. 1. Cross-section of the vibratory finisher showing direction of media circulation and resulting slope of the free surface. Dimensions in mm . of finished workpieces as a function of depth from the finished surface (Fig. 1). As the finishing time increased, the location of the maximum hardness moved from the surface to a depth of approximately 20 m. The Almen strip curvatures for strips made of AA1100-O, AA6061-T6, and Cu10100, were found to increase consistently as function of time. It was also found that at any given time, Almen strips finished in the tub had more curvature than those finished in the bowl since the tub was more energetic. Baghbanan et al.  also measured Almen strip curvature in both the wet and dry finishing conditions. The curvatures were always greater in the wet condition than the dry. This was unexpected, since it had been shown that the dry condition corresponded to higher surface-normal contact forces. It was hypothesized that, in the wet condition, water could find its way between the Almen strip holding fixture and the Almen strip itself, causing an increase in the effective stiffness and thus an increase in the contact forces relative to the dry condition. This was supported by demonstrating that the curvature of an Almen strip increased when a layer of grease was sandwiched between the strip and the holding fixture. Consequently, Baghbanan et al.  recognized the need to provide a consistent boundary condition during finishing and suggested using a hot melt adhesive to attach Almen strips to the holding fixture during the finishing operation. These issues are more significant in vibratory finishing than in shot peening because of the much lower impact velocities. A number of investigators [7,8] measured contact forces in a vibratory finisher. Yabuki et al.  concluded that tangential impact forces are approximately 10 times less than normal forces. However, the measured contact forces were a function of the compliance of the sensors employed and hence were not necessarily representative of contact conditions against an arbitrary workpiece. Ciampini et al.  related the normal component of the measured contact forces in a vibratory finisher to the impact velocity using a piezo-electric transducer. This method provided a measure of the energy availability in the contacts that was independent of the sensor compliance. Consistent with Yabuki et al., contacts could be classified as being either impact or nonimpact events, depending on their duration. Both were expressed in terms of an ‘effective’ normal impact velocity. Although the piezo-electric sensor measured accurate impact velocities, it was of interest to explore further the potential of the Almen system to provide a simpler characterization of the impact conditions in vibratory finishing. The objective was to develop a tool to aid vibratory finishing process development and quality control. In the present study, aluminum Almen strips were finished using the same vibratory finisher and media as in , providing saturation curves at two of the contact conditions that were characterized previously in terms of effective impact velocity distributions. This provided a means of relating the impact conditions to the observed changes in Almen strip curvature as a function of finishing time. The Almen strips were designed specifically for vibratory finishing applications, and a novel vacuum Almen strip attachment system was used to provide a constant boundary condition for the Almen strips during finishing. The deflection of the Almen strips was measured using a novel gauge that applied a negligible force to the strips to provide an accurate measurement of the deflection. The relationship between normal impact velocity and Almen strip curvature saturation curves was also determined independently using an apparatus that simulated the impacts in the vibratory finisher. 2. Apparatus 2.1. Almen strips Almen strips 76.2 mm long and 19.05 mm wide were machined from aluminum 3003-H14 sheet, ensuring that they remained flat. Two sheet thicknesses were used: 635 m (0.025 ) nominal thickness strips with an actual mean thickness of 617 m with a standard deviation of 3.84 m, and 813 m (0.032 ) nominal thickness strips having an actual mean thickness of 779 m with a standard deviation of 9.76 m. The mean and standard deviations of Almen strip thickness were based on ten strips with three measurements per strip. The 617 m (0.025 ) thickness was chosen to be less than that found in shot peening Almen strip specifications in order to accentuate the arc heights resulting from the much lower impact velocities in vibratory finishing. Previous investigators have measured a small amount of anisotropy in aluminum sheet properties as a function of orientation relative to the rolling direction. Wu et al.  found that the yield stress of AA3104-H19 and AA5182-0 aluminum in the cross-rolling direction was approximately 3.5% less than in the rolling direction. Very similar results were recorded for AA5019A-O by Choi et al. , who demonstrated that annealing can make the crystallographic textures nearly isotropic and produce a slight reduction in yield stress anisotropy. In the present work, the Almen strips were cut so that the sheet rolling direction was normal to the long edge. D. Ciampini et al. / Wear 264 (2008) 671–678 673 The Almen strips were annealed at 413 ◦ C for 1.5 h to Otemper in order to relieve all the residual stresses in the samples from the manufacturing and machining processes. Comparisons with unannealed strips showed that such pre-existing residual stress can influence significantly the magnitude and variability of the measured arc heights. 2.2. Vibratory ﬁnisher and media The present measurements were conducted in the same tub finisher used in Ref.  (Burr Bench 2016, Brandon Industries, TX), having a U-shaped cross-section with a urethane chamber liner and inner dimensions of 400 mm (x-direction) × 210 mm (y-direction) × 400 mm (z-direction) (Fig. 1). The media used were carbon steel balls (ABCO, Abbott Ball Company Inc., West Hartford, Connecticut, USA) having an average diameter and mass of 6.3 mm (standard deviation, S.D. = ±0.005 mm) and 0.29 g (S.D. = ±0.02 g). 2.3. Vacuum almen strip holder Almen strips were finished in a fixed position using a vacuum holder as shown in Figs. 2 and 3. This ensured that the strip remained flat, providing a constant boundary condition, and hence impact forces, as residual stresses accumulated during finishing. The vacuum holder consisted of a hollow aluminium cylinder with a polished, recessed rectangle (20.6 mm × 76.7 mm × 0.5 mm) milled into the flat face and containing fourteen 0.5 mm diameter holes through to the vacuum chamber. Placing an Almen strip in the recess and evacuating the cylinder to approximately 3 kPa held the strip securely during finishing. To ensure repeatable flow conditions over the surface, the long direction of the Almen strip was always kept horizontal as shown in Fig. 3. The holder was attached to a stiff supporting column connected to an adjacent wall. Fig. 2. Schematic of Almen strip vacuum fixture immersed in tub finisher. Fig. 3. Photograph of Almen strip vacuum holder. The curvature of the Almen strips may be a function of the compliance of the holder and its support. By being very stiff, the present vacuum holder and its supports provided a well defined, reproducible boundary condition. A vacuum holder that was free to flow with the media would have the advantage of providing an average response for the tub, but it would introduce the complication of a compliance and relative impact velocity that varied with its shape (drag coefficient), size, and mass. 2.4. Arc-height gauge Traditional Almen gauges use a dial gauge to measure the deflection of the finished Almen strips (the “arc height”) at their mid-span over a span of 38 mm (1.5 ) while the strip rests on ball supports. The force exerted by a gauge would create a significant error with the relatively thin, flexible aluminum Almen strips used in the present experiments. It has been estimated that typical Almen gauges exert tip forces between 0.2 and 1.5 N during typical usage . Loads of this magnitude would result in midspan deflections (or arc-heights) of between 40 and 300 m for a 617 m thickness AA3003 Almen strip over a 63.5 mm (2.5 ) span, and between 20 and 150 m for a similar 779 m thick strip. Given that the actual maximum deflection, measured using the optical system described below, was 760–335 m, for the 617 and 779 m thick strips, respectively, it is clear that the forces exerted by a typical contact dial gauges are too high for the presently utilized thin strips. Furthermore, the error is a function of the material and thickness of the strip, thereby adding further complications when trying to compare results from different types of Almen strip. Consequently, an alternative approach was 674 D. Ciampini et al. / Wear 264 (2008) 671–678 Fig. 4. Schematic of arc-height gauge. developed using the apparatus shown in Fig. 4. The Almen strip rested on four steel ball bearings over a span of 63.5 mm. This larger span increased the measured deflection at the midspan and thereby the accuracy. With a strip in place, a microscope was used to view the back-lit tip of the micrometer probe as it was lowered to the Almen strip surface and stopped just as it made contact with a negligible load. Repeated measurements of arc height made in this manner were always within ±4 m of the mean measurement. 2.5. Vibratory ﬁnishing simulator In order to investigate the hypothesis that only the surfacenormal component of the impact velocity had an appreciable effect on the Almen strip curvature in the vibratory finisher; an apparatus was constructed to finish an Almen strip with only normal impacts of a specified velocity. This was accomplished by using an electromagnet to pick up then drop the steel media repeatedly onto the Almen strip surface while it was secured using the vacuum holder. The vacuum holder and support beam shown in Fig. 2 were rotated 90◦ such that the Almen strip surface faced upward (Fig. 5). A cage (25.4 mm × 82.55 mm) was constructed around the perimeter of the strip to contain the steel media while permitting the balls to make contact with every portion of the Almen strip surface. It was found that 33 steel balls provided enough free space to create randomized impact locations while finishing reasonably quickly. The electromagnet was placed on the upper rim of the cage so that its flat surface was parallel to, and at a fixed height above the Almen strip. A function generator supplying a square wave at 2 Hz was used to control a relay (Fig. 5) that cycled the electromagnet on and off. The frequency of 2 Hz was chosen to allow the balls enough time between drops to randomize their position and settle before they were picked up again. The diode in the circuit protected the contacts of the relay. The constant impact speed was determined by the ball drop height (i.e. the height of the cage). Several cages of varying height were constructed to provide different maximum impact velocities. The range of possible impact velocities using the different cage heights was 0.1–0.37 m/s because of limitations of the electromagnet’s strength. The speed at which a ball dropped from the electromagnet once it was turned off was measured using a high speed photographic apparatus. Several overlapping exposures of the ball were taken as it fell from the electromagnet, to determine if the impact speed was being affected by lingering magnetism of the magnet or magnetization of the balls. Fig. 6 demonstrates that there was no appreciable difference between the measured and predicted velocities. Nevertheless, to eliminate ball magnetization as a possible source of error, a new set of 33 balls was used for every new strip that was finished. Although the balls struck every part of a strip, impacts tended to occur more frequently in two parallel lengthwise rows due to an uneven distribution of the magnetic field strength. This was evident mostly in the appearance of the surface during the early stages of finishing and became much less noticeable for longer times. Since this effect was the same for all strips, it did not influence comparisons among strips. 3. Results and discussion 3.1. Vibratory ﬁnisher saturation curves Almen strips were finished at two of the vibratory finishing conditions that were characterized in  using an impact velocity probe. The first condition (91Sa) utilized 91 kg of steel Fig. 5. Schematic of vibratory finisher simulator. D. Ciampini et al. / Wear 264 (2008) 671–678 675 flux (ETotal ) were all greater for the 91Sa condition compared to the 112Sb condition. favg was calculated by dividing the number of contacts found in a force signal by the signal duration (T). ETotal was evaluated by summing the effective kinetic energy of each contact found in a force signal and dividing by the sensor contact area, Asensor , and the signal duration, T, i.e. 2 mavg N i=1 vi ETotal = (1) 2TAsensor Fig. 6. Velocity of dropping ball as a function displacement from its initial position: measured – open symbols representing four repeat experiments; predicted assuming gravitational acceleration – filled symbols. Fig. 7. Plan view of tub showing finishing locations “a” and “b”. Arrows indicate orientation of exposed surface normal of the Almen strip. High wall (HW) and low wall (LW) as shown in Fig. 1. Depth of finishing was 210 mm above bottom of tub in all cases. media at location and orientation “a”, and the second (112Sb) utilized 112 kg of steel media at position and orientation “b”, shown in Fig. 7. Ciampini et al.  found that the 91Sa condition corresponded to a more aggressive finishing condition than the 112Sb condition. This is evident in Table 1 which shows that the recorded average contact frequency (favg ), maximum (vmax ) and average (vavg ) effective impact velocities and the total energy where N is the total number of contacts that occurred during T, and mavg and vi are the average media mass and effective impact velocity of the ith contact, respectively. Three types of Almen strips were finished at these two finishing conditions to generate the six saturation curves shown in Fig. 8. A new strip was used to determine the arc height for each finishing duration; i.e., strips were not finished again after their arc height was measured. Each data point in Fig. 8 corresponds to the average of five finished samples, and the error bars show the minimum and maximum arc heights. Significant variability was observed in the data from the vibratory finisher; the average standard deviation was 44 m for each set of five strips finished at the same condition. Table 2 gives the average and standard deviation for the five samples at each condition. The scatter was due to the randomness of the contact conditions, the variability of the Almen strip thickness, small changes in the strip positioning during finishing, and arc height measurement error. Fig. 8 shows that, for each of the three types of Almen strips, the arc height at any given finishing duration was always higher for the 91Sa condition than the 112Sb. This was expected, because the 91Sa condition generated much higher effective impact velocities as well as a higher contact frequency (Table 1). Almen strips at 91Sa thus experienced more plastic deformation per unit time than those at 112Sb. It is apparent from Fig. 8 that the thin (617 m) O-temper strips were the most sensitive to either finishing condition, showing the greatest change in arc height. This made them the better probes for characterizing the current vibratory finishing conditions. The arc heights of the thick (779 m) O-temper and the thin (617 m) H14-temper were similar. The thin H14-temper strips deflected to a lesser extent during the maximum finishing duration than the thin O-temper strips because they had a higher yield stress, 151 and 41 MPa, respectively. The arc height of each Almen strip approached a saturation value as finishing time increased (Fig. 8). In the case of the thin O-temper sheet, the arc height began to decrease after approximately 120 min at the 91Sa condition. A related finite element modeling study  has indicated that the compressive residual radial stress distribution is driven below the neutral axis by repeated impacts leading to a decrease in curvature. After a sin- Table 1 Finishing impact conditions measured using the impact velocity probe of  at locations “a” and “b” of Fig. 7 Condition Average contact frequency favg (Hz) Average effective impact velocity vavg (m/s) Max. effective impact velocity vmax (m/s) Total energy flux ETotal (W/m2 ) 91Sa 112Sb 462 224 0.014 0.011 0.378 0.163 12.8 3.13 676 D. Ciampini et al. / Wear 264 (2008) 671–678 Fig. 8. Saturation curves produced using two finishing conditions and three types of Almen strip (617 m thick 3003-O and 3003-H14; 779 m thick 3003-O). Fig. (b) shows an expanded view of the data of Fig. (a) at low finishing durations. Table 2 Average arc height and standard deviation (in brackets) of each set of five Almen strips finished in the vibratory finisher at the conditions in Fig. 8 Finishing duration (min) 0 1 2 5 15 60 120 Al 3003-O 617 m Al 3003-H14 617 m Al 3003-O 779 m 91Sa 112Sb 91Sa 112Sb 91Sa 112Sb 0 (57) 347 (32) 378 (34) 501 (38) 585 (56) 714 (46) 643 (29) 0 (38) 103 (34) 121 (57) 105 (36) 311 (54) 316 (73) 390 (67) 0 (63) 181 (67) 111 (56) 160 (43) 212 (74) 273 (46) 333 (61) 0 (59) 53 (62) 59 (38) 91 (33) 122 (57) 200 (40) 243 (65) 0 (4) 117 (29) 150 (65) 192 (26) 206 (23) 275 (42) 295 (40) 0 (13) 75 (20) 76 (16) 88 (21) 155 (41) 193 (30) 254 (43) gle 0.225 m/s impact the plastic depth was predicted to be about half of the strip thickness, however, after one hundred overlapping impacts, this depth has extended to more than 75% of the strip thickness, resulting in a decrease in the internal bending moment. It is to be expected that this would have occurred earliest at the most aggressive finishing condition (91Sa) and with the thin O-temper Almen strip which had the lowest yield strength. Almen saturation curves created from shot peening data are usually fit to exponential functions (Eq. (2)) in order to determine the Almen intensity . H(T ) = A(1 − exp(BT C )) + DT (2) where A, B, C, and D are parameters for the curve fit. Eq. (2) also provides a good fit for saturation curves created by the vibratory finishing of Almen strips (Fig. 9). The arc height H, and finishing duration T, that satisfy Eq. (3) are called the “Almen intensity” and “saturation time”, Fig. 9. Exponential curve fits (Eq. (2)) through vibratory finisher saturations curves of the O-temper strips. D. Ciampini et al. / Wear 264 (2008) 671–678 677 Table 3 “Almen intensity” and “saturation time” obtained using Eqs. (2) and (3) with values of parameters A and B given in the table and with C = 1 and D = 0 Condition A (m) B Almen intensity (m) Saturation time (min) AA3003-O 617 m 91Sa AA3003-O 617 m 112Sb AA3003-O 779 m 91Sa AA3003-O 779 m 112Sb AA3003-H14 617 m 91Sa AA3003-H14 617 m 112Sb 627 354 253 217 266 219 0.533 0.122 0.442 0.117 0.329 0.078 564 278 178 147 179 192 4 19 5 20 7 29 respectively . H(2T ) − H(T ) = 0.1 · H(T ) (3) There is no solution to Eq. (3) for the 617 m thick Almen strip finished under the 91Sa condition because of the maximum observed in the arc height (Fig. 9). However, when the data are approximated by Eq. (2) using C = 1 and D = 0, a solution can be found. Table 3 lists the Almen intensities and saturation times defined in this way for the data of Fig. 9 and for the AA3003-H14 strips. These parameters reflect the magnitude and frequency of the impact forces in the vibratory finisher at locations “a” and “b” with the two different media loads (91 and 112 kg). 3.2. Vibratory ﬁnishing simulator saturation curves The 617 m O-temper strips were finished in the vibratory finishing simulator set to produce impact velocities of 0.18, 0.22, and 0.33 m/s, representative of the higher end of the effective velocity distributions measured for the 91Sa and 112Sb conditions. In addition, the 779 m O-temper strip was finished at 0.22 m/s. Note that only the first impact of each drop cycle occurred at one of these target velocities; secondary impacts due to the bouncing of the media had much lower velocities. For example, a preliminary dynamic finite element analysis showed that a 0.22 m/s initial impacts had a second bounce impact velocity between 0.075 and 0.15 m/s, depending on the surface hardness. Assuming a typical aluminum coefficient of restitution of 0.5, the impact velocity after the first bounce will be half of the initial velocity. The saturation curves created by the simulator (Fig. 10) are similar to those resulting from the vibratory finisher (Fig. 8), reaching comparable maximum arc heights; i.e., 648 and 714 m for the simulator and finisher, respectively. The principal differences between the curves from the simulator and those from the vibratory finisher are that curvature relaxation is more common in the simulator and the finishing durations are much longer than in the finisher. Fig. 10 shows that the maximum curvature in the simulator was seen at approximately 300–500 min at 0.22 m/s, or 2.5–4 times later than in the vibratory finisher. At 0.33 m/s, the curvature reached a maximum even more quickly in the simulator at; i.e., between 150 and 300 min or 1.25–2.5 times later than in the vibratory finisher. In general, the time to reach the maximum Almen curvature decreased as the impact velocity increased. As mentioned previously, the strip curvature begins to decrease at some point corresponding to the movement of the plastic zone below the neutral axis of the strip as a result of the cumulative deformation from many impacts. A related finite element modeling study  has confirmed this hypothesis. Higher impact velocities create larger individual plastic zones, thereby reducing the number of impacts required to reach this point where the curvature begins to decrease. The longer finishing times seen in the simulator were expected since the operating frequency of the vibratory finisher was approximately 46 Hz compared with only 2 Hz in the simulator. Assuming that both the simulator and vibratory finisher had a close-packed arrangement of media and created the same impact velocity distribution, the simulator would have been expected to finish approximately 23 times slower. In reality, the media in the vibratory finisher was more closely packed than in the simulator, and therefore the vibratory finisher caused more impacts each cycle. Taking this into account, the simulator would have been expected to finish 28 times slower than the finisher. However, these packing and frequency effects were counteracted somewhat by the higher impact velocities in the simulator which were representative of maximum values in the finisher (Table 1). The similarity of the Almen curves in the simulator and the vibratory finisher supports the hypothesis that the normal media velocity component is dominant . It also indicates that, to a first order approximation, arc height is controlled by the largest impact velocities in vibratory finishing, with the more numerous Fig. 10. Vibratory finisher simulator saturation curves for 617 m strips (open symbols) and 779 m strips (filled symbols). Impact velocities of 0.33 m/s (circles), 0.22 m/s (squares), and 0.18 m/s (triangles). 678 D. Ciampini et al. / Wear 264 (2008) 671–678 lower velocities playing a relatively small role. This is consistent with the approach taken in the analytical shot peening curvature model of Hill . Almen saturation curves in vibratory finishing may be used to show how changes in a process affect the finishing rate or the aggressiveness of the process. 4. Conclusion Acknowledgment The Almen system was adapted to vibratory finishing to quantify the effect of varying process parameters on the aggressiveness of the process. Saturation curves at two distinct operating conditions in a tub type vibratory finisher with steel spherical media were similar in form to those seen in shotpeening. More aggressive finishing conditions, characterized by greater impact velocities, caused more plastic deformation and resulted in more Almen strip deflection in less finishing time. This supported the role of the Almen strip as a probe to characterize the aggressiveness of a vibratory finishing system in either process development or control. Certain elements of the usual shot peening Almen system were modified to reflect the much lower impact velocities found in most vibratory finishers. Relatively thin AA3003 O-temper Almen strips (617 m) displayed the greatest change in arc height, making them more sensitive probes than the thicker (779 m) Almen strips. However, these thinner strips showed no saturation point in the arc height and instead the arc height decreased after reaching a maximum when subjected to the most aggressive finishing conditions encountered in the present study. The time to reach this maximum may be used as a characteristic of the impact conditions within a vibratory finishing system. Nevertheless, the generation of a traditional Almen curve displaying a well-defined saturation requires the selection of a strip having sufficient thickness given the impact conditions within the finisher under study. An apparatus was constructed that showed that normal impacts alone produce saturation curves similar to those created in the vibratory finisher when impact velocities are comparable in magnitude. This provided support for normal impacts as the dominant mechanism of finishing. The research was supported by the Natural Sciences and Engineering Research Council of Canada. References  D. Ciampini, M. Papini, J.K. Spelt, Impact velocity measurement of media in a vibratory finisher, J. Mater. Process. Technol. 183 (2007) 347– 357.  J. Domblesky, V. Cariapa, R. Evans, Investigation of vibratory bowl finishing, Int. J. Prod. Res. 41 (2003) 3943–3953.  J. Domblesky, R. Evans, V. Cariapa, Material removal model for vibratory finishing, Int. J. Prod. Res. 42 (2004) 1029–1041.  F. Hashimoto, Modelling and optimization of vibratory finishing process, Cirp Annals 45 (1996) 303–306.  W. Cao, R. Fathallah, L. Castex, Correlation of Almen arc height with residual stresses in shot peening process, Mater. Sci. Technol. 11 (9) (1995) 967–973.  M.R. Baghbanan, A. Yabuki, R.S. Timsit, J.K. Spelt, Tribological behavior of aluminum alloys in a vibratory finishing process, Wear 255 (2003) 1369–1379.  S. Wang, R.S. Timsit, J.K. Spelt, Experimental investigation of vibratory finishing of aluminium, Wear 243 (2000) 147–156.  A. Yabuki, M.R. Baghbanan, J.K. Spelt, Contact forces and mechanisms in a vibratory finisher, Wear 252 (2002) 635–643.  P.D. Wu, M. Jain, J. Savoie, S.R. MacEwen, P. Tugcu, K.W. Neale, Evaluation of anisotropic yield functions for aluminum sheets, Int. J. Plasticity 19 (2003) 121–138.  S.H. Choi, J.C. Brem, F. Barlat, K.H. Oh, Macroscopic anisotropy in AA5019A sheets, Acta Mater. 48 (2000) 1853–1863.  J. Champaigne, Almen gage accuracy, Shot Peener 6 (3) (1992) 14–16.  D. Ciampini, M. Papini, J.K. Spelt, Modeling the development of residual stress in vibratory finishing, submitted for publication.  D. Kirk, Computer-based saturation curve analysis, Shot Peener 19 (4) (2005) 16–21.  D.A. Hill, R.B. Waterhouse, B. Noble, An analysis of shot peening, J. Strain Anal. 18 (1983) 96–106.