Chipping and crushing mechanisms in orthogonal rock cutting

Highlights

• A new cutting theory is proposed to explain rock's cutting and chipping mechanisms

• Experimental data is presented in support of force and chip formation predictions.

• The predictions of force responses and rock failure behaviors agree with the tests.

• The theory provides insights into the optimization of rock cutting processes.

Abstract

The understanding of rock removal mechanisms, as one of the essential elements for advancing the cutting performance of polycrystalline diamond compact (PDC) cutters, is still incomplete. This paper is seeking to formulate a cutting theory to analytically explain how rock interacts with PDC cutters in a simple cutting configuration – linear cutting. In the proposed approach, a rock crushing zone is introduced at the rock-cutter interface beneath the cutter's rake face, namely the Tip Crushing Zone (TCZ), which, as a destruction kernel, is responsible for both the crushing and chipping phenomena occurring in the cutting process. The physical aspects of these two disparate chip formation mechanisms are discussed. Moreover, closed form expressions for the cutting and thrust forces are derived based on the equilibrium of moments and on the minimum chipping energy principle. To evaluate the force model, comprehensive linear rock cutting tests were conducted on a newly developed rock cutting facility. Both the chip formation phenomena and force responses are in good agreement with the newly proposed theory.

Introduction

Rock shearing is a cutting process in which a cutting tool is dragged against a rock formation along a certain trajectory to facilitate rock material removal. Different trajectories are used in different removal applications. For instance, in modern oil/gas well drilling processes, polycrystalline diamond compact (PDC) cutters advance along a spiral trajectory as shown in Fig. 1. The introduction of the shearing action into the process has highly improved the drilling efficiency in comparison to the traditional gouging and crushing actions [1]. On the other hand, the shearing action makes PDC cutters intrinsically sensitive to the material properties of the drilled rock formations. Catastrophic damage such as cutter delamination and chipping commonly exist in drilling of extremely hard and abrasive rock formations [2]. Therefore, a comprehensive understanding of the rock-cutter interactions in shearing is highly needed which, if obtained, could offer basic guidelines for improving the cutting performance of PDC cutters and preventing catastrophic damage of the cutters [3]. Such a complete knowledge, however, is still missing due to the complexity of the shearing action and the rock's material properties, such as its inhomogeneity, dilatancy, and pressure-dependent failure behavior [4], [5].

In light of the above, in this paper an attempt will be made to formulate a novel cutting theory which is aimed at explaining rock removal mechanisms from a physical point of view that is rooted in experimental observations and derive corresponding force prediction relationships. Before going into the theory, however, a literature review is given to overview the tremendous efforts done in rock cutting theories in the past and explain the rationale for the approach proposed in this paper.

Although rock removal mechanisms have been explained in various ways, there are two major failure modes widely considered to be involved in the cutting processes, i.e., the crushing and chipping modes. The crushing mode creates highly fractured and inelastically deformed rock, while the chipping mode initiates and propagates cracks to form big chips [6]. Although some researchers have proposed that rock fails in a single failure mode [7], [8], a crushing-chipping hybrid failure mode has been widely accepted. Fine particles and large chips were found to be alternatively produced in a series of linear cutting tests conducted in 1956 [9]. Later on, typical rock chips were found to include an apparent crushed and a powdery zone in another linear rock cutting test [10]. According to these facts, a crushed zone of rock, namely the destruction kernel, was proposed to initiate/induce the formation of chip segments in a continuous shearing process [6], [11], which can be referred to as the crushing-induced chipping mode. A similar rock failure mode was also mentioned in some other researchers’ work [12], [13], [14]. In the current work the crushing-induced chipping failure mode of rock failure will be adopted given the overwhelming experimental evidence in its favor. Further justification for this choice is given below.

The chipping of rock is an extremely complex fracture process whose fundamental mechanisms have been studied over the past five decades but a clear consensus has not yet emerged. Some researchers proposed that chipping is caused by tensile breakage [7], [8], [15], [16] while others believed that the influence of the shear stresses is the intrinsic reasons for chipping [6], [17], [18], [19], [20], [21]. Shear stresses have been found to significantly influence the continuous chip formation of metals because of their obvious plastic behavior. On the other hand, rocks are generally observed to fail more like other brittle materials with discontinuous chips. To this end, the current work will be based on the assumption that the tensile stresses govern the rock's chipping process.

Experimental observations of rock failure processes are still limited to the measurements of the chip size, the recording of chip formation at the macro-scale, and the acquisition of force signals. Among them, force data are the easiest to collect and, therefore, are commonly used to indicate the cutter's performance and evaluate the predictive accuracy of developed rock cutting theories. Many force models have been put forward to predict force responses in rock cutting processes since the 1950s. Some force models were built to relate force/energy data to cutting parameters by curve fitting or regression methods under certain physical assumptions such as linear dependence of the force on cutting depth and a constant friction coefficient [22], [23], [24], [25]. Such models, i.e., phenomenological models, could quickly provide accurate force predictions in a certain parameter range and, as such are quite popular in industrial-level applications. However, to some extent, they fail to explain the intrinsic mechanisms of force responses from a physical point of view.

To overcome the limitations of phenomenological models, other researchers attempted to build force models based on the complete stress distributions obtained from solid and fracture mechanics theories [12], [26], [27]. Due to the complex mathematical formulations, closed form solutions for such models are usually difficult to obtain. In many cases, numerical methods are, therefore, needed to solve the built models [28], [29], [30]. In response, simplified force models were developed to predict the rock's failure behavior by defining critical stress distributions [7], [17], [18], [31]. Such models, if properly built, could provide closed form expressions for the force responses with trustful physical meanings. The newly proposed theory and models presented in this paper fall into this category. The idea of such force models originates from Merchant's metal cutting model [32], [33] in which the critical shear stresses were assumed to follow a straight line in front of the tool tip. The model was later on modified with a Mohr-Coulomb failure criterion to provide more accurate force response predictions in rock cutting [17], [18], [34]. However, the assumption of a linear shear plane is not realistic under the conditions of the very limited shear-induced plastic deformations in rock cutting. To alleviate this problem, critical tensile stresses along a curved propagation path were proposed to determine the rock's chipping behavior [7], [27], [35]. This was done in accordance with the rock's tensile failure behavior in uniaxial compression tests and in correspondence to the big curved chips obtained in coal mining. However, the tiny powder-like chips observed in rock cutting tests could not be explained by such models. More recently, a crushing zone was included in the force models to be responsible for the formation of powder-like chips [29], [31] but the models failed to predict the force responses when the cutting tool orientation (i.e., the rake angle) was changed. A more detailed literature review of rock cutting theories can be found in the author's previous publications [4], [5].

In response to the above, this paper aims to develop a new cutting theory that is more closely in tune with the observed experimental evidence and rooted in realistic rock removal mechanisms in order to formulate more accurate force predictions. To achieve this goal, a crushing zone, namely the Tip Crushing Zone (TCZ) is defined right beneath the cutter's rake face with a specific stress distribution. The TCZ, as it will be shown, determines the formation of power-like chips in accordance with the experimental observance. A crack that is assumed to initiate at an arbitrary location on the boundary of the TCZ and propagates towards the free surface of the virgin rock will, in turn, explain the observed chipping failure of rock. The force responses are then derived based on the equilibrium of moments applied to the chip and the minimum chipping energy principle. A series of linear rock cutting tests conducted on a newly developed rock cutting facility will facilitate the calibration and feasibility assessment of the developed force model.

The organization of this paper is given as follows: Section 2 develops the above-mentioned new cutting theory, followed by an introduction of the newly developed testbed for the linear cutting of rock described in Section 3. Then, the cutting theory will be evaluated in Section 4, by comparing the force predictions with experimental measurements. Several characteristic parameters for this new theory will be discussed in Section 5, followed by the conclusions drawn in Section 6.