Exposición AbetEspol 1Pao2024. Analytical

Presentación Abet

1. Analytical Prediction of Stability Lobes in Milling MECHANIZATION PROCESSES José León Chamba 201910825

2. Important topics 01. Objective 02. Stability Lobe Diagram 03. Chatter 04. Transfer function 05. Force diagram and mathematical model 07. Phase changes, internal and external modulations 06. Mathematical model of the stability lobe diagram 08. Conclusions

3. Objectives The present test aims to demonstrate and detail the method for the analytical prediction of stability lobes in milling. This is based on stability lobes and their mathematical and analytical functions with which these graphs are reached. 27 de agosto de 2023 3

4. Stability lobe diagram The stability lobes are graphs where the speed of rotation or the rotation head is represented in the abscissas and in the ordinate the axial cut depth. This diagram shows us which are the optimal conditions for machining (see Figure 1). This graph has a lobar shape and there are areas where the cut is stable and another where the chatter occurs. This graph has a series of peaks called sweet spot that are the conditions in each area in which productivity is maximum. 27 de agosto de 2023 4

5. Chatter The Chatter can be defined as small or slight vibrations of the cutting tool due to the dynamics of the machining machine. These minimal vibrations generate growth in the cutting thicknesses, which makes the process unstable, which, if there is no good damping, these vibrations are regenerative, which causes a significant increase in vibrations, causing bad surface finishers 27 de agosto de 2023 5

6. Transfer function Starting by representing the analytical system, the transfer function is considered, this function is a linear mathematical function that uses the famous mathematical tool of the Laplace transform and allows to represent the dynamic and stationary behavior of any system. In this context, these are used between the tool and the workpiece, the vibration-free cutting axial depth and the spindle speed are formulated analytically in the transfer functions. 27 de agosto de 2023 6 Example of transfer function for this case.

7. Force Diagram and Mathematical Models To continue with the analysis, we have the diagram, where it details the components of shear force, both tangential and radial. Where both act on the tooth of the bur, which are proportional to the axial depth of cut and the thickness of the chip 27 de agosto de 2023 7

8. Mathematical model of the stability lobe diagram Select a Chatter frequency from the transfer functions around a dominant mode, then solve the following equation with eigenvalues Where: 27 de agosto de 2023 8 And

9. Mathematical model of the stability lobe diagram Calculate critical cutting depth by: Calculate the head velocity from the following equation for each stability lobe k = 0, 1, 2, 3, 4, .... Repeat the procedure by scanning the interference frequencies around all dominant modes of the structure evident in the transfer functions. 27 de agosto de 2023 9

10. Phase changes, internal and external modulations In addition, to list phase change values between the internal and external modulations, one must: Where ψ is in radians, where examples of these modulations could be: For a ψ = 90°, then є = 0 For a ψ = 45°, then є = 0.5 For a ψ = 60°, then є =   27 de agosto de 2023 10

11. Conclusions * The article concludes with the prediction of milling stability limits. These thanks to the formulation of dynamic milling with regeneration in chip thickness, transient variable directional factors and interaction with the structure of the machine tool. * This method was a summary of the more general theory derived for peripheral helical milling of very flexible thin aerospace bands; these have variable structural dynamics also in the direction of the depth of cut. 27 de agosto de 2023 11

12. Thank you 27 de agosto de 2023 12