Experimental investigation on the effect of wear flat inclination on the cutting response of a blunt tool in rock cutting

Abstract

A vast majority of experimental researches focuses on the cutting action of a sharp cutter, while there has been limited experimental work devoted to the study of the contact process at the wear flat-rock interface. The specific objective of this study is to determine the effect of the wear flat inclination angle ($\beta$) with respect to the cutter velocity vector ($\varvec{v}$) on both the contact stress ($\sigma$) and friction coefficient ($\mu$) mobilized at the wear flat-rock interface. An extensive and comprehensive set of cutting experiments was carried out on thirteen different sedimentary quarry rock samples using a state-of-the-art rock cutting equipment. A unique cutter holder was purposely designed and manufactured along with a precise experimental protocol implemented in order to change the back rake angle and therefore the inclination $\beta$ by steps of $0.10^{\circ }$. The experimental observations confirm the existence of three regimes of frictional contact (identified as elastic, elasto-plastic and plastic) for all rock samples. Further, the results suggest that the scaled contact stress is predominantly controlled by a dimensionless number $\eta =\frac{E^{*}\tan \beta }{q}$ with $E^{*}$ the plane strain elastic modulus and q the rock strength.

Appendices

Appendix A: Physical and mechanical properties of rock samples used for cutting tests

See Tables 8, 9 and 10.

Table 8 Physical and mechanical properties of rock samples used in this study [43]

Table 9 Standard deviation (SD) of porosity and permeability [43]

Table 10 Grain size distribution diameters and their standard deviations [43]

Appendix B: Procedures to determine the physical and mechanical proprietors of rock samples

A compression test machine (manufactured by Wykeham Farrance) was used to measure the uni-axial compressive strength (q), Young’s modulus (E), Poisson’s ratio ($\nu$), and density ($\rho$) of the rock samples used in this research. This machine is a displacement controlled machine which comprises of the main mechanical parts: a load frame, a load cell, two strain gauges for radial strain ($\epsilon _\mathrm{r}$) which have been manufactured by CSIRO, two compression platens, a control system, a gear box and two LVDTs (Linear variable displacement transducers) for axial strain ($\epsilon _\mathrm{a}$). The rock samples were cut into cylindrical shapes with length over diameter ratio of approximately 2.2. The rock sample was set up in the compression test machine with transducers in place to measure sample axial and radial deformations and axial load. Each core plug was tested unsaturated. Each sample was axially loaded under a constant average axial strain rate 0.5% giving a loading rate of 0.259 mm/min for both Bentheimer and Boise and 0.014 mm/min for all other rocks until the samples failed. The Young’s modulus (E) and Poisson’s ratio ($\nu$) were determined from the tangential slope of the curve of deviatoric stress versus average axial strain and the tangential slope of the curve of average radial strain versus average axial strain between 40 and 60% of the maximum deviatoric stress, respectively.

To measure the grain (or particle) size of the rock samples, the rock samples were crushed very gently in a mortar with a plastic pestle. An Ultrasonic Bath Cleaner was also used to ensure the grains were completely separated from each other. A Mastersizer 3000 laser diffraction particle size analyzer was used to measure the grain (particle) sizes. This machine can be used for both wet and dry particles by measuring the intensity of the light scattered as a laser beam passes through a dispersed particulate sample. Fig. 23 shows the granular distribution of some rock samples used for cutting experiments.

Fig. 23

Grain-size distribution of the rock samples

AP-608 Automated Porosimeter–Permeameter was used to measure the permeability and the porosity of the rock samples, see Fig. 24. This equipment measures porosity and permeability of cylindrical core samples using an inert gas (either helium or nitrogen). It uses the principle of gas expansion, as described by Boyle’s law. A known volume (reference cell volume) of gas, at a predetermined pressure, is isothermally expanded into a sample chamber. After expansion, the resulted equilibrium pressure is measured. This pressure depends on the volume of the sample chamber minus the rock grain volume, and then the porosity can be calculated. The rock permeability is also measured through the pulse decay method.

Fig. 24

AP-608 Automated Porosimeter–Permeameter

A Sanchez Technologies tri-axial rig was used to measure the internal friction angles of two rock samples (Tuffeau and Mountain Gold). This apparatus is able to reach 150 MPa confining pressure around cylindrical samples while the axial load is applied via a mobile piston. These two parameters are controlled separately using LabVIEW program during the experiment. The radial deformation is recorded via a Cantilever sensor (C-ring) that is fixed to the membrane via a screw and the axial deformation is recorded with 3 LVDTs. It is possible to add up to 20 sensors on 4 plans on the sample, inject fluid (oil, water) and heat the sample during the experiment. The magnitude of internal friction angle ($\varphi$) is obtained through the slope of tangential line to the Mohr circles at the confining pressures of 2, 2.5 and 5 MPa for Tuffeau limestone and 5, 10 and 15 MPa for Mountain Gold sandstone. The plots of shear stress as a function of normal stress are presented in Figs. 25 and 26.

Fig. 25

Plot of shear stress versus effective normal stress. Tests conducted on Mountain Gold sandstone

Fig. 26

Plot of shear stress versus effective normal stress. Tests conducted on Tuffeau limestone