Session: 07-14-01 Measurement and Analysis Techniques in Nonlinear Dynamic Systems I

Paper Number: 70902

Start Time: Tuesday, 04:20 PM

70902 - Nonlinear Dynamics of a Two-Cam System 

In this paper, a multi body dynamic system is used (two cams, flat-faced follower with joystick stem, and the guide). We consider a two-cam system with input moments functions of the angular velocities. Kane’s method is used to find the nonlinear equations of motion. The equations of motion are solved using numerical methods. SolidWorks is used to simulate the complex system too. The numerical results are compared with the SolidWorks simulation. The system is analyzed with FFT, phase plane, and Poincare diagrams. The cams with different angular velocity are considered. The influence of different angular velocities are taken into consideration. Internal dimensions of the follower guide are used in the simulation. We take into account the friction between the follower stem and the guide.  The clearance between the follower and the guides lead to impacts. The influence of the impact force is analyzed. Phase plane and Poincare maps are developed for different configurations. Wolf algorithm based on MatLab software is used to extract the dominant Lyapunov exponent by monitoring the orbital divergence. A four and ten strides of times of the cam  cycles are selected in which it gives a best fit of linear slopes of average logarithmic divergence.The effect of the clearance and the input angular velocities on the Lyapunov exponents are studied. The follower is moved with three degrees of freedom (up-down, right-left, and rotation about z-axis) by taking into account the gravity in the vertical direction. The algorithm of average mutual information (AMI) and global false nearest neighbors (GFNN) are used to determine the time delay and the embedding dimensions respectively. The first minimum intersection point downward from (AMI) curve represents the time delay. When the global false nearest curve of the neighbors attractor reaches zero along way with the embedding dimensions which gives the value of embedding dimensions. In FFT analysis, the first peak in power spectrum tool refers to fundamental frequency (F).  When the frequencies' peaks have been started disappearing from (FFT) diagram, the motion of the follower converts from periodic motion to non-periodic motion. In phase-plane diagram, when the spiral orbit of the follower movement is one cycle which indicates to periodic motion while when there is no limit to spiral orbit of the follower movement which reflects the non-periodic motion. When a return map of Poincare plot is embedded in a higher dimensional of state space to distinguish non-periodic motion of the follower.

 

Presenting Author: Louay S. Yousuf Al Roomi San Diego State University

Authors:

Louay S. Yousuf Al Roomi San Diego State University
Dan B. Marghitu Auburn University