Modern metal cutting technology is continuously evolving toward high speed, high efficiency, high precision, low cost, resource conservation, and environmental protection. Traditional tool development involves multiple stages such as material research, tool design, manufacturing, cutting tests, feedback adjustments, and final production. This lengthy process struggles to keep up with the rapid demands of modern machining technologies. In recent years, a new approach has emerged—virtual design technology, which integrates multidisciplinary theories like modern mathematics, mechanics, computer science, and advanced algorithms. This technology enables numerical simulations of various engineering problems, significantly accelerating product design and improving accuracy and reliability.
Virtual design technology can also be applied in the development of metal cutting tools. By inputting material properties into a computer, creating finite element models, applying loads, and performing calculations, the entire cutting process can be realistically simulated, allowing for the optimization of tool geometry. This not only shortens the design cycle but also increases the success rate and reliability of the design. At the heart of virtual design lies numerical simulation, with the finite element method (FEM) being the primary analytical technique. As computer technology advances, FEM software like ANSYS has become more powerful, enabling widespread use in virtual design.
In this study, ANSYS was used to simulate stress changes in the tool and the formation of the shear angle during metal cutting. A series of calculations were performed using the tool rake angle as a variable to analyze its relationship with the shear angle. During the cutting process, many factors influence these changes, including tool geometry, cutting parameters, and workpiece material properties. Numerical simulations must account for material nonlinearity, geometric nonlinearity, and state nonlinearity, as well as solver selection and load step control. The nonlinear capabilities of ANSYS make it an ideal choice for such simulations.
**Modeling and Calculation**
Establishing a correct finite element model is essential for accurate numerical simulation. When modeling metal cutting, several key factors must be considered. First, the tool material is typically much harder than the workpiece, so the tool is modeled as an elastic body, while the workpiece is modeled as an elasto-plastic material. Since the material behavior is nonlinear, appropriate yield criteria, flow criteria, and hardening criteria must be selected.
The Von Mises yield criterion is often preferred over Tresca because it accounts for the effect of intermediate principal stresses and provides a smoother yield surface. The flow criterion describes how plastic strain develops under stress, and the multi-linear isotropic hardening (MISO) model is suitable for large strain analysis. Geometric nonlinearity, including large deformation and rotation, must also be considered. Friction between the tool and chip, as well as the tool and workpiece, is modeled using contact algorithms that distinguish between sticking and sliding regions based on shear stress thresholds.
For this study, cemented carbide (WC-TiC-TaC-Co) was used as the tool material, with an elastic modulus of 550 GPa and Poisson’s ratio of 0.3. A3 steel was selected as the workpiece, with an elastic modulus of 210 GPa, Poisson’s ratio of 0.3, yield stress of 320 MPa, ultimate stress of 520 MPa, and ultimate deformation of 20%. A 2D finite element model of right-angle free cutting was created, with the workpiece divided into 1750 elements and the tool into 100 elements.
**Load and Calculation**
A horizontal displacement was applied to the right end of the tool, simulating the cutting motion. The simulation was solved using ANSYS, and results showed the formation of the shear angle (Figure 3) and the distribution of effective stresses on the tool (Figure 4). Using AutoCAD, the shear angle could be measured, and the instantaneous effective stress at any point on the tool could be analyzed. The stress distribution along the tool rake face (Figure 5) confirmed that the highest stress occurs at the tool tip and decreases along the rake.
**Lee & Shaffer Shear Angle Theory**
The Lee & Shaffer theory suggests that when material enters the yield state, plastic zones develop along maximum shear stress directions, forming slip lines. These lines define the shear plane, and the angle between this plane and the tool movement direction is the shear angle. According to the theory, an increase in the tool rake angle leads to a larger shear angle, resulting in thinner chips and less deformation.
To verify this, different tool rake angles (-15° to 15°) were tested, and corresponding shear angles were recorded. The results showed that as the rake angle increased, the shear angle also increased, confirming the theory’s validity.
**Conclusions**
This study successfully simulated the formation of the cutting layer and the stress-strain changes in the shear zone using finite element analysis. The simulation proved that large strain plastic deformation can be effectively modeled. Understanding the tool’s loading conditions is crucial for analyzing its performance. Finite element methods allow transient boundary conditions to be applied, providing detailed stress and strain data throughout the cutting process. This makes numerical simulation a valuable tool for optimizing tool design and performance.
Future work could include studying temperature distribution during cutting and its impact on tool performance, as well as using fracture mechanics to analyze tool wear and damage. Further optimization of tool structure and geometry, as well as the application of 3D finite element models for complex tools, would enhance the accuracy and applicability of the simulation approach.
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