CUTTING THEORY FOR
EVERYONE
SHORT DESCRIPTION
By Viktor P. Astakhov
Definition of metal cutting
The process of metal cutting is defined as a forming process, which
takes place in the components of the cutting system that are so
arranged that the external energy applied to the cutting system
causes the purposeful fracture of the layer being removed. This
fracture occurs due to the combined stress including the continuously
changing bending stress causing a cyclic nature of this process. The
most important property in metal cutting studies is the system time.
The system time was introduced as a new variable in the analysis of
the metal cutting system and it was conclusively proven that the
relevant properties of the cutting system’s components are time
dependent. The dynamic interactions of these components take place
in the cutting process, causing a cyclic nature of this process.
Consequences
It follows from this definition that, considered together (the system
approach), the following features distinguish metal cutting among
other closely related manufacturing processes and operations:
1. Bending moment. The bending moment forms the combined
stress in the deformation zone that significantly reduces the
resistance of the work material to cutting. As a result, metal
cutting is the most energy efficient material removal process
(energy per removed volume accounting for the achieved
accuracy) compare to other closely related operations.
2. Purposeful (micro)fracture of the layer being removed under
combined stress. The fracture occurs in each successive
cycle of chip formation. Although not recognized by the
prevailing notion in the metal cutting theory, computational
fracture is a part of modern FEM. As such, a great number of
separation criteria have been used based on the critical
distance, normal failure stress, strain energy, strain energy
density, etc. To achieve a reliable FEM simulation, and thus
produce reasonable results, the separation criterion must be a
sound criterion based on physics of fracture rather than on
computation conveniences. Moreover, the energy associated
with the formation of new surfaces should also be accounted
for.
3. Stress singularity at the cutting edge. The maximum combined stress
does not act at the cutting edge compared to other closely related
forming operations. Rather, a (micro) crack forms in front of the cutting
edge. As a result, when the cutting system is rigid and the cutting tool is
made and run properly, the wear occurs at a certain distance from the
cutting edge that allows maintaining the accuracy of machining over the
entire time of tool life.
4. Cyclical nature. Metal cutting is inherently a cyclic process. As such, a
single chip fragment forms in each chip formation cycle. As a result,
considered at the appropriate magnification, the chip structure is not
uniform. Rather, it consists of chip fragments and connectors. The
frequency of the chip formation process (known also as the chip
segmentation frequency) primarily depends on the cutting speed and
on the work material. The cutting feed and the depth of cut (>1 mm)
have very small influence on this frequency.
Basic Laws of Metal Cutting
(Ignorantia juris non excusat - Ignorance is not an excuse)
The basic laws in any branch of applied science establish its foundation and
underlying principles. For example, the laws of thermodynamics are amongst
the simplest, most elegant, and most impressive products of modern science.
Most physical laws are designed to explain processes which humans
experience in nature. The laws of thermodynamics on the other hand, were
developed to explain the absence of perpetual motion (a human concept) in
nature. The best and the most general way to establish such laws is to consider
the energy flow and transformation in a technical system distinguished by a
given science because only system considerations result in physics-based and
sound laws.
As the above-provided definition of the metal cutting process is system based,
the second law of metal cutting (the Astakhov’s law) a.k.a. the deformation law
is formulated as
Plastic deformation of the layer being removed in its
transformation into the chip is the greatest nuisance in metal
cutting, i.e., while it is needed to accomplish the process, it does
not add any value to the finished part. Therefore, being by far the
greatest part of the total energy required by the cutting system,
this energy must be considered as a waste which should be
minimized to achieve higher process efficiency.
The greater the energy of plastic deformation, the lower the tool life, quality of
the machined surface, and process efficiency. Therefore, the prime objective of
the cutting process design is to reduce this energy to its lowest possible
minimum by the proper selection of the tool geometry, tool material, machining
regime, coolant, and other design and process parameters.
Simple and accurate method to assess the amount of plastic deformation in
metal cutting has been developed and verified by the author that allows
optimization of the metal cutting process and tool design even at the shop floor
level.
The first metal-cutting law (Makarow’s law) formulated by Astakhov in the
following form
For a given combination of the tool and work materials, there is the
cutting temperature, referred to as the optimal cutting temperature
θopt, at which the combination of minimum tool wear rate, minimum
stabilized cutting force, and highest quality of the machined
surface, is achieved. This temperature is invariant to the way it has
been achieved (whether the workpiece was cooled, pre-heated,
etc)
The Makarow’s law, established initially for longitudinal turning of various work
materials, was then experimentally proven for various machining operations.
Therefore, the optimum cutting temperature for a given combination “work
material-tool material” should be established and used as the only criterion for
the suitability of this particular tool material for this particular work material. This
temperature is a physical property and thus does not depend on the intrinsic
details of tool design and geometry as well as on the parameters of a particular
test setup.
For cutting tools with various combinations of cutting geometry parameters as
the rake, flank, inclination, tool cutting edge angles, nose and cutting edge radii,
etc. – the optimal cutting temperature corresponds to the points of minimum on
the curves representing the dependence of tool wear rate on the cutting speed
while the optimal cutting speed corresponding to each and every particular case
varies in a wide range. The minimum tool wear rate is achieved at the same
optimal temperature in dry cutting and in cutting with various cutting fluids
(media) using various methods of cutting fluid supply. The optimal cutting
temperature is the same for various combinations of the temperature of the
preheated workpiece and uncut chip thicknesses. If the structure and/or
hardness of the work material are changed, the optimal cutting speed is
changed correspondingly, but the optimal temperature, remains the same.
Therefore, the optimal cutting temperature depends upon only the compositions
of the tool and work materials, so it can be determined once, and then used to
optimize various cutting processes where the same combination of tool/work
materials is used. This temperature does not depend on the type of cutting
operation, tool geometry, parameters of machining regime, particular type and
method of application of the cutting fluid, etc.
Machining at optimal cutting temperature results not only in the minimum tool
wear rate but also leads to obtaining the minimum cutting force and smallest
roughness of the machined surface.
Literature to read
Astakhov, V.P., Geometry of Single-Point Turning Tools and Drills:
Fundamentals and Practical Applications, Springer-Verlag: London 2010.
Astakhov, V.P., Metal Cutting: System Outlook of Research and Application
Aspects. Chapter in book “Metal Cutting: Research Advances,” Editor J.P.
Davim, NOVA SCIENCE PUBLISHERS,INC, 2010, PP. 1-1-36.
Astakhov, V.P., Tribology of Metal Cutting, Elsevier: London, 2006.
Komarovsky, A.A. and Astakhov, V.P., Physics of Strength and Fracture
Control: Fundamentals of the Adaptation of Engineering Materials and
Structures to Operating Conditions, CRCPress, 2002.
Astakhov V.P., Metal Cutting Mechanics, CRC Press, 1998/1999.