Research
Comparison of Nonlinear Dynamic Simulation of Lyapunov Exponent for a Cam and Different Translated Followers with Clearance
In this paper, a cam with translated flat-faced and roller followers are analyzed. There is a clearance between the follower and the guide. The dynamic simulation is investigated taking into account the nonlinear dynamic of Lyapunov exponent parameter. The simulation has been done by using Solidworks program. The effect of follower guides’ clearances on follower non-periodicity is considered based on Lyapunov exponent technique. Nonlinear dynamic package is used to calculate largest Lyapunov exponent for different angular velocities of the cam. The power spectrum analysis of Fast Fourier Transform and phase plane contour are examined forfaced and roller followers non-periodicity. The flat- faced follower with follower guide’s clearance C=2 mm and cam rotational speed N=1200 rpm has more non-periodic motion than roller follower. The values of largest Lyapunov exponent for flat-faced follower are bigger than the values of largest Lyapunov exponent for roller follower at (C = 2 mm and N = 1200 rpm)
Effect of Local Dynamic Stability of a Ploydyne Cam with Translated Follower on Lyapunov Exponent Parameter Over a Range of Speeds
This study quantized the relationship between local dynamic stability and the variation in cam rotational speeds. The dynamic analysis presents follower displacement driven by a cam rotating at a uniform angular velocity. There is a clearance between the follower and the guide. Maximum finitetime Lyapunov exponents were estimated to quantify local dynamic stability. Local stability of a follower attractor in the ydirection was shown to be achieved over multiple cam speeds. The variation in cam rotational speeds was associated with significant changes in Lyapunov exponent values. The numerical part of the dynamic model was investigated using Solid Works simulations. A Solid Works simulation is developed for the planar case using the block commands. Diferent follower guides' clearances have been used in the simulations. An experimental set up is developed to capture the general planar motion of the cam and follower. The measures the follower positions are obtained through high-resolution optical encoders (markers). A good agreement between numerical and experimental parts was obtained.
