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Abdalslam Darafon1, Andrew Warkentin2 and Robert Bauer2. 1Faculty of ... E-mail: [email protected]; [email protected]; robert.bauer@dal.ca.
COMPARISON OF EXPERIMENTALLY MEASURED AND SIMULATED WORKPIECE AND GRINDING WHEEL TOPOGRAPHY USING A NEW DRESSING MODEL Abdalslam Darafon1 , Andrew Warkentin2 and Robert Bauer2 1 Faculty

of Engineering Technology, Houn University, Houn, Libya of Mechanical Engineering, Dalhousie University, Halifax, NS, Canada E-mail: [email protected]; [email protected]; [email protected]

2 Department

Received January 2015, Accepted May 2015 No. 15-CSME-04, E.I.C. Accession 3779

ABSTRACT This paper presents a new empirical model of the dressing process in grinding which is then incorporated into a 3D metal removal computer simulator to numerically predict the ground surface of a workpiece as well as the dressed surface of the grinding wheel. The proposed model superimposes a ductile cutting dressing model with a grain fracture model to numerically generate the resulting grinding wheel topography and workpiece surface. Grinding experiments were carried out using “fine”, “medium” and “coarse” dressing conditions to validate both the predicted wheel topography as well as the workpiece surface finish. For the grinding conditions used in this research, it was observed that the proposed dressing model is able to accurately predict the resulting workpiece surface finish for all dressing conditions tested. Furthermore, similar trends were observed between the predicted and experimentally-measured grinding wheel topographies when plotting the cutting edge density, average cutting edge width and average cutting edge spacing as a function of depth for all dressing conditions tested. Keywords: grinding; dressing model.

COMPARISON DE MESURES EXPÉRIMENTALES ET SIMULÉES DE LA TOPOGRAPHIE DE MEULE ET PIÈCE DE FABRICATION AVEC UN NOUVEAU MODÈLE DE DRESSAGE RÉSUMÉ Cet article présente un nouveau modèle empirique du processus de dressage lors du meulage qui est incorporé dans un simulateur informatique 3D d’enlèvement de métal pour prédire numériquement l’état de la surface rectifiée d’une pièce de fabrication ainsi que la surface de dressage de la meule. Le modèle proposé superpose un modèle de dressage de coupe ductile avec un modèle de cassure des grains pour générer numériquement la topographie de la meule et la surface rectifiée de la pièce de fabrication résultantes. Des expériences de dressage ont été faites utilisant des conditions de meulage “fine”, “medium” et “grossière” afin de valider la topographie de la meule prédite ainsi que le fini de surface de la pièce de fabrication. Pour les conditions de dressage utilisées dans cette recherche, il a été observé que le modèle de dressage proposé est capable de prédire avec précision le fini de surface de la pièce de fabrication résultant pour toutes les conditions de dressage testées. De plus, des tendances similaires ont été observées entre les topographies de la meule prédites et expérimentales en traçant la densité de l’arête tranchante, l’épaisseur moyenne de l’arête tranchante et l’espacement moyen de l’arête tranchante en fonction de la profondeur pour toutes les conditions de dressage testées. Mots-clés : meulage; modèle de dressage.

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1. INTRODUCTION Perhaps the most important characteristic of the grinding process is its ability to create smooth surfaces and tight tolerances on both flat and cylindrical surfaces as stated by Komanduri [1]. While different grinding process parameters, including grinding material, cutting depth and cutting speed, influence the cutting process, Malkin and Guo [2] as well as Verkerk [3] have pointed out that the performance of the grinding manufacturing process (as characterized by the resulting grinding forces, spindle power consumption, grinding zone temperatures and workpiece surface finish) is strongly influenced by the grinding wheel surface topography. Recently, Liu et al. [4] found that dressing had a greater role to play in modeling grinding wheel topography than grain shape. Researchers at the Dalhousie University Grinding Lab have been developing methods of measuring and modeling grinding wheel topography which is a key step in developing a mechanistic model of the grinding process. In this paper a new 2D empirical model of the dressing process is presented which is based on the dressing model proposed by Chen and Rowe [5]. This 2D empirical model is then applied to a 3D wheel model and incorporated into a 3D metal removal computer simulator to numerically generate the ground surface of a workpiece. This research is unique in that the resulting predicted surface topographies of not only the ground workpiece but also the dressed grinding wheel are compared to experimental measurements. 2. BACKGROUND Different procedures have been developed to dress grinding wheels. In single-point dressing, as illustrated on the right-hand side of Fig. 1, a single diamond tool travels across the surface of the grinding wheel with a cross-feed velocity νd and a dressing depth of cut ad as a grinding wheel of diameter ds rotates with tangential velocity νs . This kind of dressing motion is analogous to the turning operation on a lathe. The axial feed of the dressing tool per wheel revolution is called the dressing lead fd which can be calculated using the following equation: πds νd fd = . (1) νs The resulting dressing overlap ratio Ud can then be calculated as follows: Ud =

bd , fd

(2)

where the active width bd is the width of the dressing tool at the dressing depth of cut. The overlap ratio provides a good indication of the type of dressing operation. For example, a fine dressing operation typically has an overlap ratio between 6 and 9, while a coarse dressing operation has an overlap ratio approaching 1. Another common method of dressing is called diamond roll dressing. This dressing technique rotates a metal roll covered in diamonds, as illustrated on the left-hand side of Fig. 1, to “grind” the grinding wheel. One of the advantages of this kind of dressing approach is that it is quicker than single-point dressing – especially for complex wheel profiles as discussed by Lal and Shaw [6]. In diamond roll dressing, a grinding wheel with peripheral velocity νs is radially fed at velocity νi into the rotating diamond roll having peripheral velocity νr (which corresponds to a dressing depth per wheel revolution of ar ). The dressing ratio, which is the ratio of the dresser peripheral velocity to the wheel peripheral velocity, can be used to help characterize the diamond roll dressing operation. For example, when the dressing ratio is 1 (referred to as “crush” dressing), the bonding material in the area of the contact may fracture because of the resulting high compressive stresses. Malkin [7] and Shih [8] noted that crush dressing, therefore, can be used to maximize bond fracture and minimize grain fracture with the intent to minimize the effect of the dressing process on grain shape and distribution. 2

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Fig. 1. Illustration of rotary and single point dressing operations.

3. REVIEW OF DRESSING MODELS Doman et al. [9] carried out a review of grinding wheel topography models and, according to their survey, the dressing models proposed by Hegeman [10], Koshy et al. [11], Torrance and Badger [12] and Chen and Rowe [5] are the only grinding wheel computer models found in the literature that incorporate dressing effects. Hegeman [10] used the following stochastic periodic function to simulate the effects of dressing on the wheel surface z f r (x, y) = cos(ωˆ x x + αˆ x ) + cos(ωˆ y y + αˆ y ), (3) where ωˆ x , αˆ x , ωˆ y and αˆ x are random numbers. While this function generates a non-smooth surface of ellipsoidal grains, it does not take into account any physical dressing parameters. Koshy et al. [11] considered the dislodgement of the grains from the wheel surface which is caused by dressing; however, the grain fracture caused by dressing was not taken into consideration. Torrance and Badger [12] proposed a grinding wheel computer model that represented grain and bond fracture on the wheel surface due to dressing by a series of angled line segments whose slopes were stochastically distributed between a maximum and minimum value. In Chen and Rowe’s [5] dressing model, ductile cutting and grain fracture were considered separately. The resulting dressing traces responsible for ductile cutting, as well as a dressing fracture wave associated with grain fracture, were then removed from each abrasive grain on the surface of the grinding wheel model as shown in Fig. 2. Chen and Rowe [5] approximated the single-point dressing tool profile zd (x) by a parabola defined by the parabola’s height dh and width dw using dh zd (x) = 4 2 x2 . (4) dw Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 1, 2016

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Fig. 2. Dressing simulation by Chen and Rowe [5].

Given the dressing depth of cut ad , the resulting dressing tool trace zt (x) was determined using  Z   x , zt (x) = ad − zd x − fd fd

(5)

R

where x is the position across the grinding wheel face and the function ( ) is used to convert the number within the brackets into an integer value. A fracture wave consisting of a sine wave function having random frequency ω and random phase angle α was then added to Eq. (5) to account for the effects of grain fracture as follows: z(x) = zt (x) + h(sin(ωx + α) + 1), (6) where the random frequency ω was calculated using ω=

4(1 + δ )π f d + dw

(7)

and δ corresponds to a random value ranging between 0 and 1. The amplitude of the sine wave h in Eq. (6) represents the extent of the grain fracture and was expressed as h=k

AdgUd , fd

(8)

where k is an empirical constant which was found by Chen and Rowe [5] to be 0.25, and Adg is the intersection area of the tool with the grain as shown in Fig. 2. 4

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Fig. 3. Dressing tool profile.

4. PROPOSED DRESSING MODEL This paper further develops the concept of superimposing a ductile cutting trace and a fracture wave as originally proposed by Chen and Rowe [5], and the new dressing model is then added to the metal removal simulator developed by Darafon et al. [14] which can calculate chip geometry. In the proposed dressing model, the contours of the single-point dressing tool as well as the kinematics associated with ductile cutting have been modified. Single-point dressing tools are typically made by sintering a natural diamond onto a metal tool holder and typically do not have a symmetrical parabolic shape. Furthermore, as the dressing process continues, wear causes the dressing tool to change shape. Capturing the correct shape of the dressing tool is important when measuring the resulting workpiece surface roughness at the sub-micron level. As a result, for the dressing model proposed in the present work, the actual dressing tool profile was measured using a Nanovea PS50 non-contact optical profiler as shown in Fig. 3. Subsequently, a 6th order polynomial function was used to define the best fit to the measured dressing tool profile zd (x) = 2.7x6 + 0.03x5 − 2.7x4 + 0.02x3 − 1.7x2 ,

(9)

where x ranges between −0.5 and 0.5. The kinematics associated with dressing is analogous to the turning operation on a lathe whereby the dressing tool travels helically around the grinding wheel working surface. The pitch of the helical path of the dressing tool corresponds to the dressing lead fd ; however, Chen and Rowe’s dressing tool trace (represented by Eq. (5)) does not provide a helical path – rather it assumes circular paths around the wheel working surface. To prevent these circular grooves on the wheel from being imprinted onto the workpiece surface during the grinding process, Eq. (5) has been modified to provide a helical path for the dressing tool as      β   Z x + f d 2π β  , zt (x) = ad − zd x + fd − fd  (10) 2π fd Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 1, 2016

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where β is the angular position of an individual grain being dressed around the circumference of the grinding wheel. In the proposed model the fracture wave frequency ω increases as the instantaneous dressing depth hdg decreases because, referring to Fig. 2, a larger depth of cut will likely remove larger pieces from an abrasive grain. To achieve this increase in frequency, Eq. (7) was modified to incorporate the instantaneous dressing depth hdg as follows: ! π(1 + δ ) 1 ω= , (11) fd + dw hndg1 where the exponent n1 is an empirical model parameter. The fracture wave amplitude h was also modified to make it inversely proportional to Ud and directly proportional to the instantaneous depth of cut hdg . These modifications to Eq. (8) were made because, as the overlap ratio decreases and the dressing depth of cut increases, the workpiece surface roughness increases. The present authors hypothesize that this increase in roughness can be attributed to a rougher grinding wheel surface due to more grain fracture (corresponding to a larger value for h). The new relationship, therefore, takes the following form: hndg1 h = k n2 , (12) Ud where n1 is the same exponent used in Eq. (11) and n2 is a new empirical model parameter. A summary of the proposed changes to Chen and Rowe’s dressing model equations can be found in Table 1. The new dressing model was then used to numerically dress a 3D computer model of a grinding wheel. This model was then incorporated into a grinding metal removal simulator to predict the surface finish of a ground workpiece. As outlined in Eqs. (11) and (12), the new model has three fitted parameters: k, n1 and n2 . The values of these parameters were selected by comparing the simulated ground workpiece surface roughness with experimental roughness measurements. For the grinding conditions used in this research, it was found that values of 6.0, 0.5, and 1.3 for k, n1 and n2 , respectively, gave the best results. In the following sections the experimental apparatus and simulation techniques will be described. 5. EXPERIMENTAL APPARATUS Grinding experiments were carried out using a Blohm Planomat 408 CNC grinding machine with an aluminum oxide vitrified bond grinding wheel (WR-A-60-J5-V1) and 6.35 mm ×41.5 mm ×75 mm 1018 steel workpieces. For these experiments, the grinding wheel diameter was 354.1 mm, the grinding depth of cut was 0.03 mm, the cutting speed was 20 m/s and the workpiece speed was 0.03 m/s. Using a dressing depth of 0.02 mm, “coarse”, “medium” and “fine” single-point diamond dressing conditions were tested corresponding to dressing overlap ratios Ud of 1, 3 and 6, respectively. Before each single-point dressing operation, diamond roll dressing with a speed ratio of 1.1 and an infeed rate of 25.4 m/rev was initially used to create an “undressed” wheel. Surface topography measurements of the resulting ground workpieces were conducted using a Nanovea PS50 non-contact profiler to determine the surface roughness. In addition to measuring the workpiece surface finish, the surface topography of the grinding wheel was measured using a novel automated grinding wheel measuring system and wheel topography analysis technique developed by Darafon et al. [13]. This wheel measuring system is illustrated in Fig. 4 where a digital camera system mounted on an adjustable stage is used to take images of the wheel surface, while a white chromatic sensor measures the surface profile height (along the z-direction). A linear actuator and encoder are used to position the chromatic sensor along the axial (y) direction, and a friction wheel drive system used in conjunction with a wheel rotary encoder controls the angular position and velocity of a grinding wheel along the circumferential (x) direction. Grinding wheel topographical characteristics are 6

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Table 1. Modifications to Chen and Rowe’s [5] dressing model equations.

Fig. 4. Grinding wheel measurement system.

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Fig. 5. Simulated and experimental profiles of the ground surfaces.

extracted from the resulting data using a combination of Nanovea’s Mountains 3D Analysis Software and LabView’s ImageStudio. 6. SIMULATION TECHNIQUES The 3D grinding wheel computer model used in the present work was developed by Darafon et al. [14] and consists of randomly-sized spherical grains that were distributed throughout the entire wheel volume such that none of the grains overlapped. The size and number of grains were determined from the wheel marking system. The new dressing model presented in Section 4 was applied to this 3D grinding wheel computer model with seven passes. For each pass, the dressing depth ad was increased by 0.02 mm and, in order to be consistent with the experiments, overlap ratios Ud of 1, 3 and 6 were used (corresponding to coarse, medium and fine dressing conditions, respectively). Subsequently, the dressed 3D grinding wheel computer model was incorporated into a 3D metal removal simulation developed by Darafon et al. [14] in order to numerically generate a ground workpiece surface. Simulations were conducted using a high-performance computing cluster called the Atlantic Computational Excellence Network (ACEnet). 8

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Fig. 6. FFT of simulated and experimentally-measured workpiece surfaces.

7. RESULTS AND DISCUSSION In this section the workpiece surface finish results will first be presented and then the topography of the simulated and actual grinding wheel will be examined. Figure 5 plots the simulated and experimentally-measured profiles of the ground workpiece surface for the different dressing conditions studied in this research, while Fig. 6 shows the results of a fast Fourier transform (FFT) applied to these profiles. It can be seen in Figs. 5 and 6 that, after dressing the grinding wheel model, the predicted workpiece surface profiles are remarkably similar in both amplitude and frequency Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 1, 2016

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Table 2. Experimental and simulated surface results.

content to the experimentally-measured workpiece surface profiles – for all dressing conditions tested. For example, for a dressing overlap ratio of 1, the amplitudes of the simulated and experimental profiles were 8.9 and 7.2 µm, respectively, the number of peaks per mm along the profile was 39.5 and 37 peaks/mm respectively, and the average surface roughness Ra was 1.1 and 0.97 µm, respectively. Reasonable agreement between simulated and experimental workpiece surface topographies were also observed for an overlap ratio of 3 and 6, as summarized in Table 2. This table also highlights the importance of applying a dressing model to the 3D grinding wheel computer model since, as shown in the right-most column, the workpiece surface topography predictions from an undressed grinding wheel computer model do not match the experimental results. It is interesting to note in Table 2 that, although the differences between the simulated and experimental surface roughness, frequency and maximum amplitude are, for the most part, relatively small, the simulator consistently over predicts these workpiece surface characteristics. The reason for the over prediction of these characteristics is likely because the simulator is based on a kinematic analysis and does not take into account factors such as plowing or rubbing phenomena that occur as the abrasive grains interact with the wheel. These real-life phenomena would likely have the tendency to “smooth” the resulting workpiece surface thereby causing the actual measured roughness, frequency and maximum amplitude values to be lower than that predicted by the simulator. The previous results demonstrate that the proposed dressing model can be used to predict the workpiece surface finish for a wide range of dressing conditions. Also very important (but overlooked in the literature) is how well the proposed dressing model can predict the surface topography of a grinding wheel. To examine the wheel topography, 5×10 mm areas of the simulated grinding wheel were compared to 5×10 mm patches on the actual grinding wheel. For clarity, smaller areas are shown in the illustrative figures (Figs. 7 and 8) while the full areas were used to calculate aggregate data. Figure 7 shows 2 × 2 mm patches of the simulated and measured surface topographies of the 3D grinding wheel before dressing as well as for the fine, medium and coarse dressing conditions, while Fig. 8 shows corresponding cross sections perpendicular to the feed direction. Note that the vertical direction has been magnified to emphasize the grain heights while the uppermost parts of the cutting edges are displayed as white. It is clear from Figs. 7 and 8 that, although the overall shape of the grains are very different, their sizes are roughly similar. In addition, as shown in Figs. 8b–d, f–h the small features left on the grain surface by the dressing process are similar in size, shape and distribution. The authors believe that, as evidenced by Liu et al. [4], the similarity of these features on the grains is responsible for the similarity of the workpiece 10

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Fig. 7. Representative samples of the simulated and measured grinding wheel topography: (a) simulated with no dressing, (b) simulated with Ud = 1, (c) simulated with Ud = 3, (d) simulated with Ud = 6, (e) measured with no dressing, (f) measured with Ud = 1, (g) measured with Ud = 3, (h) measured with Ud = 6.

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Fig. 8. Representative simulated and measure profiles across the grinding wheel: (a) simulated with no dressing, (b) simulated with Ud = 1, (c) simulated with Ud = 3, (d) simulated with Ud = 6, (e) measured with no dressing, (f) measured with Ud = 1, (g) measured with Ud = 3, (h) measured with Ud = 6.

surface finish profiles. It is also evident that, as the overlap ratio increases, there are more and larger cutting edges on both the simulated and measured grinding wheel. To further examine the effect of overlap ratio on the simulated grinding wheel topography, cross-sections of a single grain on the grinding wheel computer model have been plotted. Figures 9a and b show the effect of changing the overlap ratio on the fracture surface of a single grain. It can be seen in these figures that, as the overlap ratio gets larger, the number of fractures and the amplitude of the fractures decrease. Intuitively this observation makes senses because a larger overlap ratio will result in a smoother workpiece and so it should also result in a smoother surface on the abrasive grains. The effect of changing the dressing depth on the fracture surface of a single grain is shown in Figs. 9c and d. These figures show that, as the dressing depth of cut increases, the area of removed grain rapidly increases along with the size of the grain fractures. In order to quantify the surface topography in terms of cutting edge density, average cutting edge width and average cutting edge spacing, the “blob” analysis proposed by Darafon et al. [14] and described with the aid of Fig. 10 was used. A “blob” is a group of connected pixels that share the same intensity (height in this case). In blob analysis, the 3D surface topography of the wheel is sliced by a cutting plane at different threshold depths producing a “blob diagram’ at each depth. Each threshold depth is akin to the instantaneous uncut chip thickness. The blob diagram is then converted into a binary image enabling the size, shape and distribution of the cutting edges at a particular threshold depth to be assessed using standard techniques available in image processing software like LabView’s ImageStudio. Figure 11 plots the resulting simulated and experimentally-measured cutting edge density, average cutting edge width and average cutting edge spacing versus depth below the wheel surface for the different dressing 12

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Fig. 9. Dressing simulation of a single grain (a) Ud = 1, (b) Ud = 6, (c) ad = 0.02 mm and (d) ad = 0.02 mm.

conditions studied in this research. The details of extracting these quantities from wheel topography data can be found in the work of Darafon et al. [14]. It should be noted that, in Fig. 11, a depth of zero refers to the outermost cutting edge on the grinding wheel’s periphery. Furthermore, in this figure the “crushed wheel” results refer to the diamond roll dressing condition having a speed ratio of 1.1 which was used to create an “undressed” wheel, while the “undressed model” results refer to the initial 3D grinding wheel model before the new dressing model was applied. As can be seen in Fig. 11, the cutting edge density, average cutting edge width and average cutting edge spacing for both the “crushed wheel” (experimental) and “undressed model” (simulation) follow similar behaviors in that the cutting edge density and average width gradually increase with depth while the average spacing decreases with depth in an exponential fashion. Furthermore, Fig. 11 shows that the simulated coarse, medium and fine dressing operations appear to condition the 3D grinding wheel computer model so that the resulting predicted and experimentally-measured cutting edge density, average cutting edge width and average cutting edge spacing curves exhibit similar trends. While the predicted and experimentally-measured wheel topography results shown in Fig. 11 generally follow similar trends, it is evident that there are significant differences in the results. There are likely two reasons for these discrepancies. First, the grinding wheel model only models the grain – it does not include any bond material or swarf that may exist between the grains, while the wheel topography measurements used to validate the wheel model does include the bond material and swarf (because a good method for exTransactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 1, 2016

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Fig. 10. Illustration of blob analysis.

perimentally distinguishing between bond and grit does not currently exist). Second, the proposed dressing model is only 2D and does not account for grain pullout during dressing. Malkin and Cook [15] examined fractured abrasive grains which were produced by a dressing operation and concluded that the dressing process produces fragments of the abrasive grains and can dislodge the whole abrasive from the grinding wheel surface. Thus, the abrasive material is mostly removed by brittle fracture to a depth greater than the dressing depth, rather than ductile cutting. This dislodgement of abrasive grains from the grinding wheel surface is caused by the fracture of bond material which is used to hold the abrasive grains in the grinding wheel. Furthermore, Pande and Lal [16] proposed that, as the dressing depth increases or the dressing lead decreases, the bond fracture increases – trends which could be added to the proposed dressing model in the future to further improve the results. These observations can be seen in Fig. 12 in which profiles through the 3D topographic data are shown in the feed direction. In the simulated grinding wheel, the tops of the dressed wheel appear relatively flat in the feed direction while in the experimental measurements the tops of the grains are relatively smaller and sharper in the feed direction suggesting that grain and bond fracture may have occurred. 8. CONCLUSIONS Incremental improvements were made to Chen and Rowe’s [5] dressing model to improve the way in which the modeling parameters were calculated. This 2D dressing model was then applied to a 3D grinding wheel computer model as a stepping stone towards developing a 3D dressing model. This grinding wheel computer model was then incorporated into a 3D kinematic metal removal computer simulator to numerically generate the ground surface of a workpiece. The most important contributions of this work stem from the comparison of the resulting predicted wheel and workpiece surface topographies with experimental data. In particular, reasonable agreement was observed when comparing numerically-predicted and experimentally14

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Fig. 11. Simulated and experimental cutting edge density, average cutting edge width and average cutting edge spacing versus depth.

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Fig. 12. Representative simulated (a) and measured (b) profiles along the grinding wheel circumference for Ud = 6.

measured workpiece surface roughness for coarse, medium and fine dressing conditions. When comparing the corresponding simulated and experimentally-measured grinding wheel topographies, it was observed that the cutting edge density, average cutting edge width and average cutting edge spacing follow similar trends; however, it is evident that more research is needed to further develop grinding simulators that can more accurately generate the surface characteristics of the grinding wheel while, at the same time, accurately predict the resulting workpiece surface finish. ACKNOWLEDGMENTS The authors would like to thank The Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Foundation for Innovation (CFI) for their financial support of this research. REFERENCES 1. 2. 3. 4. 5. 6. 7.

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