Simulation Parameters

Simulation Parameters and Output Responses
For each simulation, two key response variables were recorded:

· Equivalent stress (MPa)

· Vibration response (frequency response)
The complete set of experimental runs and simulation outputs is listed in Table 4.

 Effect of Process Parameters on Vibration rESPONSE

The simulation results provide clear insight into the effect of machining parameters—cutting speed, tool tip radius, and depth of cut—on the vibration response, equivalent stress, and deformation of the cutting tool. The vibration frequency exhibited noticeable variation with changes in process parameters. An increase in cutting speed generally led to a rise in the vibration frequency. This can be attributed to the enhanced dynamic interaction between the tool and workpiece at higher speeds, which stimulates higher-order vibration modes. For example, when the tool radius and depth of cut were held constant, increasing the cutting speed from 100 mm/s to 140 mm/s resulted in a gradual increase in vibration frequency. Similarly, an increase in tool tip radius resulted in higher vibration frequencies in several cases. This behavior can be explained by the increase in stiffness due to a broader contact surface, though the relationship is not entirely linear due to the complex nature of the cutting process. Depth of cut also had a significant impact. At greater depths, more material engages with the tool, leading to increased cutting forces and higher vibration levels.

4.4 Effect on Equivalent Stress and Deformation

In addition to vibration response, the simulation revealed how process parameters influenced the equivalent von Mises stress and total deformation in the cutting tool. Equivalent stress increased slightly with cutting speed due to greater mechanical loads on the tool. Tool tip radius had a mixed influence; while larger radii helped distribute forces over a wider area, thereby reducing stress concentrations, they also led to increased stiffness that in some cases elevated stress values depending on depth of cut. The most substantial effect was observed with changes in depth of cut. A deeper cut significantly increased both stress and deformation. For instance, increasing the depth of cut from 0.5 mm to 1.5 mm, while keeping other parameters constant, led to a substantial rise in equivalent stress and deformation. The maximum deformation occurred under high-speed, high-depth cutting conditions, indicating a potential risk of tool instability or failure under aggressive machining setups.

These findings underline the importance of careful selection of cutting parameters. Excessive vibration and deformation can lead to premature tool wear, poor surface finish, and reduced machining accuracy. Therefore, understanding the parametric influence on tool dynamics is critical for predictive wear modeling and optimal tool design.

4.5  Mathematical Validation of FEA Stress Results

To validate the finite element analysis (FEA) results, a theoretical stress calculation was performed for one of the simulated cases (Experiment No. 1) using the classical formula for normal stress:

Where F is the applied force and A is the contact area at the tool tip. For this case, the reaction force from the simulation was approximately 128.28 N.

The contact area was calculated based on the rectangular region of contact at the tool tip. For this case, where both horizontal and vertical depths of cut are 0.5 mm, we considered a square contact patch approximated as:

A= bh= 0.5 mm0.5 mm= 0.25 mm2

Here,

· b=0.5mm represents the width of the contact area across the tool tip.

· h=0.5mm is the effective depth of contact into the workpiece.

· Both dimensions were extracted from the CAD model based on the tool geometry at this cutting condition.

Substituting into the stress equation:

This result was then compared to the FEA-computed equivalent stress for the same condition, which was 424.05 MPa. The deviation between the theoretical and simulated stress values was calculated as:

While this deviation appears significant, it is important to note that the theoretical calculation assumes a simplified and constant contact area, whereas the FEA accounts for complex stress distributions, tool-workpiece interactions, and material behaviour. Therefore, the comparison still supports the qualitative trend and helps establish the validity of the simulation setup.