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

Paper Number: 68778

Start Time: Tuesday, 03:40 PM

68778 - Nonlinear Dynamics Simulation in Contact Force in Cam-Follower System Using Lyapunov Exponent Parameter 

Nonlinear dynamics simulation of contact force is investigated for different cam angular speeds and internal dimensions of the follower guide using Lyapunov exponent parameter. The value of Lyapunov exponent is positive which means that the contact force is close to zero and the detachment between the cam and the follower will be happen, while the value of Lyapunov exponent is negative which inducates that the contact force is in maximum value and the follower with the cam is in permanent contact. Friction is taken also into consideration based on the variable clearance between the follower and its guide. 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. Power spectrum analysis is used to detect the nonlinear periodic motion of the contact force using the amplitude of Fast Fourier Transform (FFT) approach. The amplitude of fundamental frequency and the other frequencies' peaks indicate to periodic motion of the contact force. When the frequencies' peaks have been started disappearing from (FFT) diagram, the orbit of contact force converts from periodic motion to non-periodic motion. SolidWorks is used in the numerical simulation of the contact load. Four different values of internal dimensions of the follower guide such as (16, 17, 18, and 19 mm) are used in the simulation. The contact force is measured by using OPTOTRACK/3020 to track the movement of the follower through an infrared camera device. The macro sensor is a linear variable differential transformer (LVDT) of a model number (DC750- 5001). LVDT converts the analog signal of the follower motion to a digital signal in which it will be readable using an optical sensor. Follower movement is derived twice to determine follower acceleration at the contact point. Newtion’s second law is applied based on the acceleration and the follower mass to calculate the contact force experimentally. The cam is installed on the shaft of the motor which rotates at uniform angular velocity. The value of contact force is checked and verified at different cam angular speeds for the cam.

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

Authors:

Louay S. Yousuf San Diego State University