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Finite element analysis of bending occurring while cutting with high speed steel lathe cutting tools
Abdullah Duran, Muammer Nalbant
(Mechanical Engineering Department, Technical Education Faculty, Gazi University, Ankara, TeknikokuIIar, Turkey)

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ABSTRACT

The bending which occurs on a cutting tool during machining on a lathe affects tool life, surface roughness and dimension correctness. In this research, the bending which has been calculated by Castigliano theorem has been compared with the bending obtained by finite element method. Under the constant cutting conditions, material C1060 has been machined with high speed steel (HSS) lathe cutting tools having 60, 75 and 90 of cutting edge angle. It was determined by using ANSYS finite elements program that the bending of the cutting tool generated by the forces, which varied between 1360 N and 1325 N and occurred during cutting, varied between 0.039958 and 0.04373 mm. According to the results, it has been observed that the bending that was calculated by Castigliano theorem and that varied between 0.03542 and 0.034505 mm was almost the same with the bending determined by finite elements method.

1 INTRODUCTION

Various machine tools and cutting tools are used in metal cutting. Cutting tools for turning can generally be divided into two groups: high speed steels and cemented carbides. High speed steel (HSS) cutting tools can be subdivided into three groups according to their manufacture: single, brazed and index able inserts.
Cutting tool geometry, chip geometry, cutting tool and workpiece material, cutting speed and cutting fluid are the main factors affecting the metal cutting process.
Tool geometry, one of the most important factor affecting metal cutting process, is determined by rake angle, side clearance angle, side cutting edge angle and back rake angle. Tool geometry is an important factor having influence on cutting forces and tool life. For an optimum turning operation, correct selection of cutting parameters as well as the length of tool holder extending from its post are essential. That is because, incorrect selection of cutting parameters leads to rapid tool wear, breakage and plastic deformation. This increases machine tool idle time due to the changing of damaged cutting tools and causes some other problems such as poor surface quality and wrong workpiece dimensions. This, in turn, increases the overall cost.
Determination of cutting parameters through conventional methods is mostly not possible. Approximate solution methods giving very close results to those obtained by the experimental work are appealing as they are easy to use and there is no necessity to carry out costly experimental work. Parallel to the development in the computer technology, finite element analysis (FEM) method, one of the approximate solution methods, has been increasingly used. Finite element method gives very close results to the real values and, therefore, it is now a well accepted numerical method.
In this study, deflection of HSS cutting tool during turning was investigated using ANSYS version 5.4 program based on the tool length extending through the tool post. The deflection of the tool was also calculated using Castigliano theory and the results were compared to those obtained using ANSYS program.

2 BASICS OF THE METAL CUTTING
2.1 Cutting process
Metal cutting is a complex physical phenomenon which involves elastic and plastic deformation, intense friction and heat, chip formation and cutting tool wear. In order to effect cutting action, the cutting tool (as shown in Fig. 1(a)) is forced against the workpiece and is moved relative to the workpiece. As the result, the workpiece is initially deformed elastically (Fig. 1(b)) and when the workpiece_s yield strength is exceeded plastic deformation occurs. Plastic deformation leads to chip formation (Fig. 1(c)). The formed chip leaves the workpiece through the cutting tool rake face. The flow of the chip occurs in various ways depending on the workpiece properties and cutting conditions.
Fig. 1 – Chip formation process.

2.2 Cutting forces
The necessary chip formation force required to overcome the developed stresses during chip formation process can be divided into three components: cutting force (Fs), feed force (Fv) and radial force (Fp). Cutting forces developed during turning are depicted in Fig. 2.
Fig. 2 – Cutting forces acting on the cutting tool during turning.

Cutting force (Fs) acts against the workpiece turning motion and forces the cutting tool downwards perpendicular to the workpiece axis. Feed force (Fv) acts parallel to the workpiece turning axis and is in the reverse direction of the feed. Radial force (Fp) acts perpendicularly to the machined surface and forces the cutting tool backwards.
If a cutting tool fixed on the tool post is considered a cantilever beam as shown in Fig. 3, the deflection of the tool () due to Fs force should be ideally zero during cutting.
Fig. 3 – Representation of the cutting tool as a cantilever beam.

2.3 Castigliano theory
According to Castigliano theory, partial derivation of the total internal stress energy with respect to the one of the applied external forces gives the displacement of the point of applied force in its application direction. The displacement of the equal cross-sectioned beam at point B (Fig. 4(a)) under Fs force can be found using Castigliano theory.
Fig. 4 – Single side cantilever beam

The bending moment at any point of the beam in Fig. 4(b) can be found using the following equation:
If the M moment changes along the beam, internal stress energy developed as the result of basic bending moment in the beam then dx length element strain energy is found using
The total strain energy is calculated in the following way:
The bending in the beam () can be found in the following form:

2.4 Finite elements
In finite elements method, it is assumed that a part is divided into so many small parts. This method is, therefore, called finite element method. The main idea in finite element method is to solve a complex problem by replacing it with a simple problem. By using the existing mathematical methods, in practice real or approximate solutions cannot be found for many problems. However, finite element method can be used to find approximate solutions for these problems. In finite element method, the solution zone is composed of adjacent sub parts which are called finite element. It can be assumed that these sub parts are held together by nuts and screws. It is also assumed that when the bonding is removed, the sub parts are separated…
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