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Geometric Modeling of Engineered Abrasive Processes Andres L Rochester Institute of Technology RIT Scholar Works Articles 2005 Geometric Modeling of Engineered Abrasive Processes Andres L. Carrano Rochester Institute of Technology James B. Taylor Rochester Institute of Technology Follow this and additional works at: http://scholarworks.rit.edu/article Recommended Citation Carrano AL, Taylor JB. Geometric modeling of engineered abrasive processes. J Manuf Process 2005;7(1):17–27. https://doi.org/ 10.1016/S1526-6125(05)70078-5 This Article is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Articles by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. *Geometric Modeling of Engineered Abrasive Processes* Carrano, Andres L Abstract One of the common issues that arises in abrasive machining is the inconsistency of the surface roughness within the same batch and under identical machining conditions. Recent advances in engineered abrasives have allowed replacement of the random arrangement of minerals on conventional belts with precisely shaped structures uniformly cast directly onto a backing material. This allows for abrasive belts that are more deterministic in shape, size, distribution, orientation, and composition. A computer model based on known tooling geometry was developed to approximate the asymptotic surface profile that was achievable under specific loading conditions. Outputs included the theoretical surface parameters, R^sub q^, R^sub a^, R^sub v^, R^sub p^, R^sub t^, and R^sub sk^. Experimental validation was performed with a custom-made abrader apparatus and using engineered abrasives on highly polished aluminum samples. Interferometric microscopy was used in assessing the surface roughness. Results include the individual effects of pyramid base width, pyramid height, attack angle, and indentation depth on the surface descriptors. Introduction Some abrasives occur in nature (flint, garnet, etc.), and some are man-made (aluminum oxide, silicon carbide, zirconia, CBN, and so on). Until now, most coated abrasive tools have consisted of single or multiple layers of oriented grits of approximately the same size that are attached to a substrate. The size of the particles used on coated abrasives is established by sifting the crushed grits through screens of standard mesh (NBS), by sedimentation, or by air flotation. The application of the abrasive grits to the belt backing is either achieved through gravity or electrode-induced polarization. This traditional manufacturing practice, however, yields an abrasive belt that presents variations in grit size, shape, distribution, and orientation. Moreover, the geometry of the cutting grits changes from particle to particle, making it impossible to know, for instance, the rake or attack angle for any given grit or cut. The task of modeling the interaction of the grit and the surface of the part in an abrasive machining process has been attempted in several ways by previous researchers (Torrance 1987; Bahin 1987; Lin et al. 1996a, 1996b; Li and Liao 1997; Abede and Appl 1988; Dornfeld 1981; Buttery and Hamed 1977, 1978). The random size, shape, and relative placement of abrasive particles on the sandpaper has always presented a difficult problem to attack from a process modeling standpoint. Using statistical distributions of particle size and making assumptions about particle shape and relative placement on the substrate have allowed some researchers to estimate overall process results based on process parameters (Torrance 1987; Li and Liao 1997). This method, which is probabilistic in nature rather than deterministic, has typically served as a basis for a correlation of predicted and actual results. Another common approach to abrasive process modeling has been the single-grit approach (Abede and Appl 1988; Dornfeld 1981; Buttery and Hamed 1977; Lin et al. 1996b). This method seeks to deterministically model the interaction of a single abrasive grit and the surface of the part. Major contributions to the literature have been made via this modeling method especially with regard to the ploughing phenomenon and elastic/plastic effects (Abede and Appl 1988; Dornfeld 1981; Lin et al. 1996b; Buttery and Hamed 1978). The major shortcoming of this method is the lack of interaction of the multiple abrasive grits on the surface of the part. The actual abrasive process is the sum total of many single abrasive grits of different sizes and shapes and their effect on the surface. Recent advances in manufacturing processes have allowed replacement of the random arrangement of minerals on conventional belts by a patented technology called microreplication. The technology is a spin-off of work that was originally used in the manufacturing of reflectors. Since the original development by 3M, other companies have also produced their own engineered abrasives in similar manners (Mason 1999; Norton 2000). To date, engineered abrasives have been targeted at the much larger metals market, but interest has been shown from the wood and composites markets. As defined by 3 M (1997), microreplication is the science of creating small, precisely shaped, three-dimensional structures and reproducing them on a variety of surfaces. The belt's surface, in this case, consists of pyramidal structures containing micron-graded minerals that are uniformly applied to a backing material (see Figure 1). This development has been around for several years, but it was not until recently that commercial fabrication of belts became feasible. This new genre of abrasive tools is usually referred to as engineered or structured abrasives. They consist of abrasive belts that are more deterministic than the traditional counterpart: the shape, size, distribution, and orientation of the cutting grits are known and controlled. This provides a very even distribution of mineral and yields a more consistent rate of cut and surface finish. The motivation for pursuing such abrasives lies in the idea that, by removing variation in the grit geometry, it is possible to remove variation in the finish quality. However, a better understanding of the impact of the individual geometric features of the abrasive on the surface roughness is required as a basis for proposing an optimized geometry and for assessing the degree of performance improvement. It is believed that the future of abrasive-based machining is in microengineered belt patterns and that further job-based customization of these patterns will be a future step. Optimization of the resultant workpiece surface and machining parameters will also be possible. The main objective of this research was to develop and validate a 3-D computer-based model that would help in understanding the impact of the individual geometric features of the grit on the surface roughness of the workpiece. To date, most geometric models of abrasive processes have been developed based on a single-grit tooling supposition (Abede and Appl 1988; Dornfeld 1981; Buttery and Hamed 1977; Lin et al. 1996b; Oxley 1997), thus neglecting interactions between grits (multiple-pass effect), or consisted of theoretical approximations due to unknown geometry (Torrance 1987; Li and Liao 1997, Mulhearn and Samuels 1962). These are assumptions that simplify the models but also make them somewhat unrealistic and provide no basis for optimization. The model developed here was based on a pyramid-shaped abrasive grit, incorporated the effect of multiple passes, and was validated on commercially available products. Other literature relevant to abrasive process modeling is included for reference (Gahlin and Jacobson 1999; Komanduri 1971; Larsen-Badse 1968; Sin, Sada, and Suh 1979). Once the model was developed and validated, a second objective was to search for a better understanding of the individual geometric features and their impact on the final quality. Three main parameters were investigated: the attack angle of the belt, the pyramid width, and the pyramid height. These are the features that could potentially be changed during the manufacture of this abrasive. The other inputs to the model were: the amount of indentation (a function of the load applied), the sampling resolution (a function of the instrumentation), the number of grits/row, and the number of rows. Notice that some of these are artificial variables that arise because of the finite nature of the model (such as the number of grits and number of rows in the abrasive matrix) or variables that are not under control by the abrasive manufacturer (amount of grit indentation). Methodology The basic idea is to develop a geometric computer model that would parametrically represent the tooling and workpiece, as well as to calculate the surface descriptors that result from the interaction between these. A matrix with several grits per row and several rows, one after the other, was generated in a computer program. Because this abrasive tooling allows for perfectly known geometry, it is then possible to define the geometry as a function of base width and height of the pyramid. Rake and attack angle can be calculated from the design geometry but are also a function of the width and height. By knowing the pyramid orientation with respect to the feed direction, the offset between rows and columns of pyramids, and the depth of indentation into the workpiece (as a function of the applied pressure), it was possible to approximate the resultant 2-D surface profile after n rows of grits have performed a cut. The model assumed that the entire
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