Nonlinear Dynamics of Turning Operation — Lesson 1

This lesson covers the concept of non-linear vibration in manufacturing processes, with a focus on turning operations. It delves into the study of the vibration of the tool and workpiece, deriving the equation of motion and exploring how to solve it. The lesson also revisits previous topics like energy harvesting and vibration absorption, and how they apply in this context. The lesson further discusses the impact of passive and active vibration absorbers on the manufacturing process. It also introduces the concept of delay and internal resonance in the context of turning operations. The lesson concludes with a detailed explanation of how to use the method of multiple scales to solve the governing equation of motion and determine the stability of the system.

Video Highlights

01:39 - Overview of nonlinear dynamics of parametrically excited tool 
03:30 - Equation of motion of tool
28:08 - Perturbation method (MMS)
59:18 - Equation of workpiece and tool

Key Takeaways

- Non-linear vibration plays a crucial role in manufacturing processes, particularly in turning operations.
- The vibration of the tool and workpiece can significantly impact the manufacturing process.
- The equation of motion can be derived and solved to understand the dynamics of the system.
- The method of multiple scales can be used to solve the governing equation of motion and determine the stability of the system.
- Understanding the stability of the system can help in optimizing the manufacturing process and improving the quality of the output.