Modeling and Analysis of Nonlinear Chaotic Mechanical Dynamics in Laser Scanning Systems

Abstract

This paper presents a novel approach to modeling and analyzing chaotic mechanical vibrations in laser scanning systems. The model explicitly incorporates nonlinear friction using the LuGre friction model. Experimental validation demonstrates chaotic behavior manifested in irregular velocity fluctuations. Dominant frequencies and maximum vibration amplitudes were identified under various operational conditions. A maximum disturbance amplitude of $ 1.65\,\mathrm{rad/s^2}$ was observed under the most demanding conditions (25~RPS, $\pm$15° inclination). The proposed model was validated experimentally, providing insights into the interplay of chaotic vibrations and nonlinear friction. A robust control strategy was introduced to mitigate these effects. This strategy is supported by Lyapunov stability analysis and computational implementation. The results demonstrate the effectiveness of the control strategy in reducing the negative effects of friction and chaotic vibrations. The findings could benefit precision engineering, nonlinear dynamics research, and machine vision.

Keywords

• Chaos theory
• Nonlinear dynamics
• Friction
• Vibrations
• Laser scanning

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