Nonlinear dynamics phenomenon detection in a polydyne cam with an offset flat-faced follower mechanism using multi shocks absorbers systems

Abstract

The influences of the internal distance of the guide from inside (I.D.), the constant speeds of the cam (N), and the followers' offsets (O) on the chaotic phenomena are studied in this research. The chaotic phenomena is investigated using Phase-plane portrait with Poincare’ Maps, Power Density Function of Fast Fourier Transform (FFT), and Largest Lyapunov Exponent. The chaos analysis of the offset flat-faced follower due to the contact with the polydyne cam profile is controlled using multi linear and nonlinear shocks absorbers systems. The suspensions of the shocks absorbers are described using (spring-damper-mass) systems. The nonlinear response of the flat-faced follower due to the offset shift is calculated at different internal distance of the follower guide (I.D), different speeds of the cam (N), and different followers’ offsets (O). The analytic solution of the nonlinear follower motion is done using the second-order ordinary differential equation. The numerical results of the nonlinear response of the follower is determined using SolidWorks program, while OPTOTRAK 30/20 equipment with high speed camera is used in the experiment inspection. Largest Lyapunov exponent has a maximum values when the follower offsets to the right, while the largest Lyapunov exponent has a minimum values when the follower offsets to the left. The transition to chaos when the follower offsets to the left is faster than when the follower offsets to the right at (O = 50 mm). The chaos phenomenon in cam follower system in the presence of follower offset is increased with the increasing of (I.D.), (N), and (O).