Abstract
Nonlinear dynamics behavior of the roller follower is discussed for different follower guides’ internal dimensions and cam angular speeds. A dynamic tool such as Wolf algorithm is used to extract largest Lyapunov exponent parameter. Positive value of Lyapunov exponent parameter indicates non-periodic motion and chaos. The influence of flank curvature of the cam profile on the nonlinear dynamic behavior of the roller follower is investigated. Impulse and momentum theory is used to describe the impact phenomenon based on the contact force between the follower and its guides. Contact parameters such as exponent, sliding contact velocity, contact bodies stiffness, penetration, and damping ratio are used in SolidWorks software to simulate follower movement numerically. Experiment setup has been done by taking into consideration the use of an infrared three-dimensional camera device through a high precision optical sensor. The follower motion is non-periodic when the cross-linking of phase-plane diagram diverges with no limit of spiral cycles.
Highlights
Non-periodic motion could be either quasi-periodic or chaos based on time delay, global embedding dimension, Lyapunov positive, and convergence
The systems with follower guides’ internal dimension (18 and 19 mm) at cam angular speed N = 500 rpm in which it gives the perfect best-fit of linear slope to quantify largest value of largest Lyapunov exponent
The nonlinear curve of average logarithmic divergence when follower guide’s internal dimension (18 and 19 mm) at N = 300 rpm has been fluctuated around the linear slop of curve fitting
Summary
Non-periodic motion could be either quasi-periodic or chaos based on time delay, global embedding dimension, Lyapunov positive, and convergence. The chaos motion of the follower is predicted based on largest positive Lyapunov exponent. Savi used a small perturbation of a scaler time strides in order to stabilize a desirable orbit of a chaotic attractor.[4,5] The abrupt transition from periodic to non-periodic motion is interpreted at high speeds.[6] non-periodic motion of the follower has been taken place due to the oscillation motion in drive speed of the cam.[7] A disc cam with a roller follower mechanism is treated as 1and 2-degree-of-freedom systems to define follower jumping situation at critical angular velocity of the cam.[8] A phase-plane diagram and bifurcation analysis have been used to predict a non-periodic motion and chaos in state space domain.[9] The values of largest
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