Cutting and ploughing forces for small clearance angles of hexa-octahedron shaped diamond grains R. Transchel a, *, C. Leinenbach b , K. Wegener (2) a,c a Institute of Machine Tools and Manufacturing, Tannenstrasse 3, 8092 Zurich, ETH Zurich, Switzerland b Empa, Swiss Federal Laboratories for Material Science and Technology, U ¨ berlandstrasse 129, 8600 Du ¨bendorf, Switzerland c inspire AG for Mechatronic Production Systems and Manufacturing Technology, Technoparkstrasse 1, 8005 Zurich, Switzerland 1. Introduction Cutting operations with geometrically non-defined cutting edges are essential to manufacture a huge variety of mechanical components with the desired surface quality. Therefore, a comprehensive knowledge about the material removal process in particularly the engagement of single grains with the workpiece material is required in order to synthesise the entire removal process of grinding tools. The inaccessibility of the contact zone as well as its stochastic character regarding grain size, grain morphologies and distribution on the tool body complicates the analysis of such processes. This emphasises the demand for meaningful models in order to predict resulting process forces, surface quality and surface integrity. However, it is widely known that the actual cutting process of single grains is also accompanied by elastic and plastic deformation, which makes it even more difficult to gain detailed information about the exact material removal mechanism at the cutting edge. 2. State of art in kinematic modelling of single grain cutting The numerous research works about modelling and simulation techniques on grinding and single grain operations that were published in the past decades, were summarised by Brinksmeier et al. [1]. Early kinematic grinding models were presented by Kassen [2], Werner [3] and Lortz [4] focussing on the determination of statistical characteristic parameters of the abrasive layer of the grinding tool and the process. Inasaki [5] measured the topography of a grinding wheel with a profilometer and used such information for the kinematic interaction of the abrasive cutting edges and workpiece surface. Warnecke and Zitt [6] presented a software tool that is based on a 3D-model describing the kinematic engagement conditions of grinding tools and workpiece as well as a micro geometry of the abrasive grains. This kinematic model was enhanced and subsequently applied to the simulation of structured grinding tools by Aurich et al. [7]. Koshy et al. [8] simulated the surface roughness of the workpiece assuming the abrasive grains to be spherical bodies. Pinto et al. [9] presented a kinematic model for simulation of cylindrical external plunge grinding and modified three dimen- sional grain morphologies to a two dimensional projection area in cutting direction for simulating workpiece roughness and process forces. This modification enabled a reduction of computation time. Vargas [10] proved the applicability of this model for the linear kinematic of hone broaching operations and also introduced force models distinguishing between different grain orientation cases. Most of the previously mentioned model approaches are only assuming the mere material removal mechanism and therefore using the cross-sectional area, cf. Fig. 1a, to determine the resulting specific cutting forces k c as the ratio of the cutting force F c and the cross-sectional area A cu according to: k c ¼ F c A cu (1) Waldorf et al. [11,12] modelled ploughing in orthogonal machining processes in consideration of the cutting edge radii and negative rake angles by using the slip-line field theory. Park and Liang [13] presented a ploughing force model by estimating the plastic deformation of an indentation process. Malekian et al. CIRP Annals - Manufacturing Technology 63 (2014) 325–328 A R T I C L E I N F O Keywords: Modelling Grinding Ploughing A B S T R A C T Investigations on the cutting behaviour of hexa-octahedron diamonds outlined an enormous influence of the grains’ clearance angle on the material removal process. Small negative clearance angles lead to increased specific cutting forces, decreased cutting force ratios and micro-structural changes. This is caused by additional ploughing of the material. This paper presents a kinematic-phenomenological model predicting the specific forces that are caused by the ploughed material. Therefore, the theoretical value of the specific ploughed volume is introduced as characteristic parameter. Results are subsequently compared for different grain cutting situations to experimental data allowing a validation of the proposed model. ß 2014 CIRP. * Corresponding author. E-mail address: transchel@iwf.mavt.ethz.ch (R. Transchel). Contents lists available at ScienceDirect CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp http://dx.doi.org/10.1016/j.cirp.2014.03.030 0007-8506/ß 2014 CIRP.