International Journal of Machine Tools and Manufacture
An investigation into the mechanics of cutting using data from orthogonally cutting Nylon 66
Introduction
The idea that during a cutting process the chip is formed by intense shear along a well-defined plane is well established and was reported as early as 1881 [1]. Piispanen [2] later proposed a theory representing cutting as a shearing process along the shear plane consisting of infinitely thin lamella, often referred to as the deck of cards theory. Merchant [3], [4] also proposed a shear plane theory and developed a force equilibrium circle. Much of the research that followed was based on the Merchant's shear plane theory. However, both Piispanen and Merchant neglected the work of material separation. Merchant acknowledged that energy was required to separate the material, but dismissed it as insignificant compared to the energies expended in shear and friction. Although Merchant's theory was developed for the cutting of metals the same chip formation process can be found when cutting polymers and other materials. There are more chip classifications when cutting polymers than found when cutting metals; however, if the chips are produced in shear along a shear plane, Merchant's theory is applicable to the process [5]. The selection of Nylon 66 for this study was to enable a large range of rake angles to be investigated, which would not have been possible if cutting metal.
Many researchers have shown that the cutting force versus depth of cut plots, when regressed to zero depth of cut, produce positive force intercepts [6], [7]. Possible causes of this positive intercept are said to be the rubbing of the tool clearance face on the work piece [8], tool bluntness [9] or material separation [10]. Investigations using cutting tools with known nose radii have shown that when regressed to zero radius, i.e., perfectly sharp, a positive intercept is still found [11]. A study of ‘parasitic’ forces in cutting, which refers to both rubbing on the clearance face and tool bluntness, concluded that the positive force intercept could not be explained only in terms of rubbing and bluntness [12].
Recently [13] it has been shown that the inclusion of significant work of separation in a model of cutting explains many of the shortcomings of traditional plasticity and friction models, such as Merchant's. For instance the inclination of the primary shear plane is predicted to depend on the toughness/strength ratio of the workpiece and the theory also predicts a positive force intercept even when rubbing and bluntness are negligible. This theory has been investigated while cutting copper and good agreement was found [14]. The inclusion of fracture toughness may seem a peculiar parameter to use in steady-state cutting without visible cracks, but separation at the tool tip is required to permit shear band plastic flow, and the point is that a very short crack (the width of the primary shear band) keeps pace with the tool tip. Of course, with appropriate depths of cut and tool rake angles, cracks can be seen propagating ahead of the tool [15], but these depths of cut and tool angles are not generally investigated as they are not favourable for good surface finish or control of dimensional tolerances. Modelling of this type is possible, but is not relevant to steady-state cutting.
It should be noted that finite element models of cutting require computational ‘fixes’ to enable simulation of the cutting process. Separation criteria or re-meshing are typical fixes introduced into the models, as these enable the material to separate. Without the introduction of a separation criterion or re-meshing, the simulation models an indentation process, not cutting.
Many manufacturing processes rely on relatively small depths of cut. The increasing use of micro and nano technologies now requires cutting depths down to nanometre levels [16]. When cutting involves small depths of cut, the energy required to separate the material becomes more significant, yet traditional theories ignore this energy.
This paper investigates, using orthogonal cutting tests on Nylon 66, the validity of the existing cutting theories. Comparison is made between values of shear plane angle obtained from existing theories and experimental values. It will be shown that a better correlation is found with the inclusion of separation energy as proposed by Atkins [13], who related the fracture toughness to the separation energy. It is proposed that the fracture toughness parameter is a function of tool rake angle and is a mixture of tensile and shear modes of fracture, termed ‘mixed mode fracture’.
Section snippets
Experimental materials and method
An instrumented sledge microtome was used to cut the samples as shown in Fig. 1. Microtomes are generally used to cut thin sections of biological materials for microscopic examination; however, they have been used in previous research into cutting mechanics [17], [18]. The model used in this study comprised a fixed blade and a moving sledge to which the sample was attached. The blade holder of the microtome was modified to enable the blade to be rotated and clamped at the required rake angles.
Analysis
From each experimental cut a plot of both the cutting and the normal forces was produced for the duration of the cut, a typical example is shown in Fig. 2. The steady-state cutting value for each cut was taken as the average for the steady plateau, i.e., the initiation and end of the cutting process were not considered. Using Merchant's force equilibrium circle (Fig. 4), the tool forces S (along the rake face) and N (normal to tool rake face) were obtained from resolution:
Shear plane
The prediction of shear plane angles, when compared to experimental values (Fig. 5) showed that at higher rake angles Merchant's predictions were lower than experimental values, while Lee and Shaffer's tended to be higher. The values predicted by Atkins’ theory tended to be in far better agreement with the experimental values. At lower and negative rake angles all were in good agreement at greater depths of cut, but the values predicted by Lee and Shaffer tended to be lower at the smaller
Conclusion
It has been shown that the separation energy can be a significant proportion of the total cutting energy, especially for smaller depths of cut. This will be important in modern manufacturing processes employing micro and nano technologies. Conventional cutting theories ignore separation energy and as such underestimate the force and power requirements of cutting.
It has also been shown that a fracture toughness term included in Atkins’ theory seems to be more appropriately represented as a mixed
Acknowledgements
The author would like to express his gratitude to the EPSRC for the funding of this project and to Prof. Atkins for his invaluable advice and guidance. Thanks are also due to Prof. Chaplin, Prof. Williams and Dr. Peak for their assistance with this article.
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