On the mechanics of the grinding process. Stochastic
nature of the grinding process
Zhen Bing Hou, Ranga Komanduri.
School of Mechanical and Aerospace Engineering, Oklahoma State University,USA.
1 Introduction
Grinding, in general, is a very complex material removal operation involving cutting as well as plowing and rubbing between the abrasive grains and theworkmaterial [1,2]. Shaw [1] classified the grinding processinto two categories, namely, form and finish grinding (FFG) and stock removal grinding (SRG). The primary objective in FFG is to obtain the required form, finish,and accuracy while the primary objective in SRG is toobtain high removal rate. The wheels are periodically dressed, conditioned, and trued to maintain sharp cutting edges, to remove metal build-up on the grains or loading of the wheel (metallic chips occupying in the void space between the grains), and to maintain roundness of the wheel.
Finish grinding and cut-off operations come under the same category of grinding, there are several differences between them. In the cut-off operation, the wheel speed is generally 2–5 times higher than in conventional finish grinding. In the surface grinding, the workpiece reciprocates at a given depth of cut while in the cut-off operation the wheel is fed continuously into the workpiece at a given feed rate. The chip thickness as well as the length of contact (or length of chip) are generally an order of magnitude larger in the cut-off operation than in fine grinding. Consequently, the removal rate is significantly higher in the cut-off operation.
Also, the cut-off operation is generally conducted dry (or in air) as water tends to deteriorate the resin and reduce the life of the cut-off wheel, whereas a coolant is invariably used in finish grinding to dissipate the heat generated and to protect the workpiece from “grinding burn.”
In FFG and SRG operations, both attritious wear and microchipping wear of the abrasive grains take place. However, in the cut-off operation, additional wear occurs due to dislodgment of the whole abrasive grains from the wheel as a result of (a) thermal softening of the resin binder mechanical erosion of the resin binder by the flowing chip, and mechanical removal of bond material due to the pressure developed in the voids by the chips due to insufficient volume. In modeling these processes, these and other issues that affect the performance of the grinding wheel have to be considered carefully.
2 Brief review of literature on FFG and SRG
The mechanics of the grinding process (both FFG and SRG) was investigated extensively by many researchers. Pioneering work on this topic commenced in the early 1950s by Prof. Milton Shaw and his associates. For example, Marshall and Shaw [3] investigated the variation of grinding forces in dry surface grinding under different grinding conditions. They determined the number of contacting grains per unit area for the first time. They offered an explanation for the increase in the specific energy with decreasing chip thickness on the basis of size effect. It is now widely accepted that there are other explanations for this difference, including the factthat most abrasive grains present on average a large negative rake angle and there is considerable rubbing between the abrasive grains and the workpiece due to attritious wear of the abrasive grains.
Outwater and Shaw [5] investigated the surface temperatures generated in fine grinding and reported temperatures as high as 1163 °C (2125 °F) based on both experimental and analytical work. Reichenbach et al. [6] investigated the role
of chip thickness in grinding, while Mayer and Shaw [7] investigated the temperature in grinding experimentally. This work initiated a flurry of research activities in
grinding since then. Subsequently, Baker and Merchant [8] investigated the basic mechanics of grinding.
Most researchers considered the grinding process akin to milling process but on a microscale. They considered the cutting and thrust forces to be solely due to cutting and neglected the frictional rubbing forces on the clearance face of the grains. To account for the apparent anomalies between conventional machining and grinding, Hahn [9–11] introduced the rubbing grain hypothesis wherein rubbing forces on the clearance face of the abrasive grain play a major role compared to the forces due to cutting. Part of the justification for this is based on the ratio of tangential to normal forces in grinding. In grinding, this is typically in the range of 0.3–0.5, which is characteristic of a sliding friction process. Subsequently, Komanduri [12] reported an experimental investigation to simulate grinding using high negative rake angles in conventional cutting and showed the similarities between grinding and machining with high negative rake tools. In fact, the large negative rake angles presented by the abrasive grains in grinding can produce this ratio however, such an analysis is far simpler to analyze than the combination of cutting and rubbing as the number of cutting grains.
In this investigation, Hahn’s [9–11] approach is used in the analysis of the grinding process. It will be shown that based on statistical analysis of the abrasive grains on the grinding wheel surface in both FFG and SRG, not all grains participate in the cutting action; instead a majority of the grains merely rub due to insufficient depth of cut imposed on these individual grains and even smaller number of grains participate in the actual cutting process.
Other major contributors on the mechanics of fine grinding include Malkin, Rowe and Wetton, Opitz, Snoeys, Nakayama, Lavine to name some. In 1972, an International Grinding Conference [22] was held at Carnegie-Mellon University in Pittsburgh where leaders across the world in this field participated. The proceedings of this conference is a good source of reference material in grinding, for both FFG and SRG.
In the SRG area, especially in the cut-off operation, much of the research work was conducted in the late 1960s at Carnegie-Mellon University under the direction of Prof. Shaw and supported by the Grinding Wheel Institute and the Abrasive Grain Association.
Shaw investigated the mechanics of the abrasive cut-off operation in considerable detail. As part of that group investigated the thermal aspects of abrasive cut-off operation. Shaw also reported a method of rating cut-off wheels based not on conventional parameters, such as the grain size, grade (hardness), and structure number but on the basis of effective number of cutting points per unit area on the wheel, the void space between successive grains, the chip flexibility parameter, and the down-feed rate corresponding to a grinding ratio of unity. These studies at CMU have enabled the determination of the optimum cut-off grinding conditions, improvement of the efficiency of the operation, increase in the life of the cutoff wheel, and improvement of the surface integrity of the workpiece used.
Since, material removal in the grinding process involves cutting, plowing, and sliding, it is necessary to determine the contributions of actual cutting versus the other processes on a statistical basis. For that, it is necessary to determine the number of abrasive grains in actual contact per unit area on the wheel, the number of actual cutting grains per unit area, minimum diameter of the contacting and cutting grains, and the average chip volume under different grinding conditions. Since the grinding process is stochastic in nature, in this investigation, the grinding operation is analyzed using the probability statistics.
The number of contacting points in a grinding wheel plays an important role both on the mechanics and thermal aspects of grinding. Not all abrasive grains on the surface of a grinding wheel participate in the grinding process. Some may cut, others may rub or plough, and a large number may not be participating in the grinding process at all. This depends on the grinding wheel specifications (abrasive type and grain size as well as the bond, hardness, and structure of the wheel), as well as the grinding conditions (wheel speed, work speed, depth of cut, forces, grinding fluid, etc.) used, and the stiffness and accuracy of the machine tool.
Backer et al. [4] for the first time estimated the number of apparent contact points by rolling the grinding wheel under its own weight on a soot covered glass plate.
Brecker and Shaw developed a dynamic method to determine the effective number of cutting points on the surface of a grinding wheel. It employs a thin workpiece mounted on a special piezoelectric dynamometer of very high natural frequency of response to measure the instantaneous forces. The workpiece is so thin that only one grain is assumed to be in contact at a given time.
References
1. M.C. Shaw, Principles of Abrasive Processes, Oxford University Press, Oxford, UK, 1996.
2. M.C. Shaw, Fundamentals of the grinding process, in: M.C. Shaw (Ed.), Proceedings of the International Grinding Conference, Carnegie Press, Pittsburgh, PA, 1972, pp. 220-258.