Nonlinear Dynamic Analysis of a Polydyne Cam With Translated Roller Follower Mechanism With Clearance

2018 ◽  
Author(s):  
Louay S. Yousuf ◽  
Anis Drira
Keyword(s):  
Fourier Transform ◽  
Lyapunov Exponent ◽  
Power Spectrum ◽  
Phase Plane ◽  
Nonlinear Dynamic Analysis ◽  
Power Spectrum Analysis ◽  
Largest Lyapunov Exponent ◽  
Experimental Setup ◽  
Angular Velocities ◽  
The Impact

In this paper, a polydyne cam with translated roller follower over a range of speeds are analyzed. There is a clearance between the follower and the guide. The dynamic simulation is investigated taking into account the impact and the friction. The simulation has been done by using Solidworks program. The effect of follower guides’ clearances on roller follower non-periodicity is considered based on Lyapunov exponent technique. Rosenstein method is used to calculate largest Lyapunov exponent for different angular velocities of the cam. The experimental setup has been implemented by using OPTOTRAK/3020 through a 3-D infrared markers to track follower motion. The power spectrum analysis of Fast Fourier Transform and phase plane contour are examined roller follower non-periodicity.

Insight Into the Non Periodic Motion of the Knife Follower With a Polydyne Cam Mechanism

2020 ◽  
Author(s):  
Louay S. Yousuf ◽  
Yaakob K. H. Dabool
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Lyapunov Exponent ◽  
Angular Velocity ◽  
Power Spectrum ◽  
Periodic Motion ◽  
Phase Plane ◽  
Power Spectrum Analysis ◽  
Cam Follower ◽  
The Impact

Abstract A polydyne cam and knife follower system are studied. The effect of cam angular velocity and follower guides internal dimensions on Lyapunov parameter is considered. Wolf algorithm is used to quantify largest Lyapunov exponent parameter. The impact between the cam, follower and the two guides is occurred due to the impulse and momentum phenomenon. Positive value of Lyapunov exponent parameter indicates to non-periodic motion and chaos for the follower. Non-periodic motion is examined using power spectrum analysis of Fast Fourier Transform (FFT) and phase plane diagram. The numerical simulation has been done using SolidWorks software. Follower movement is processed experimentally through an infrared 3-D camera device with a high precision optical sensor. A polydyne cam and knife follower system are studied. The effect of cam angular velocity and follower guides internal dimensions on Lyapunov parameter is considered. Wolf algorithm is used to quantify largest Lya-punov exponent parameter. The impact between the cam, follower and the two guides is occurred due to the impulse and momentum phenomenon. Positive value of Lyapunov exponent parameter indicates to non-periodic motion and chaos for the follower. Non-periodic motion is examined using power spectrum analysis of Fast Fourier Transform (FFT) and phase plane diagram. The numerical simulation has been done using Solid-Works software. Follower movement is processed experimentally through an infrared 3-D camera device with a high precision optical sensor. The simulation and experimental results are compared and verified for non-periodic motion of the follower. The follower motion is non-periodic when the orbit of phase-plane diagram diverges with no limit of spiral cycles.

Lyapunov Exponent for a Globoidal Cam With a Roller Follower Mechanism Using Wolf Algorithm

2020 ◽  
Author(s):  
Louay S. Yousuf ◽  
Dan B. Marghitu
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Lyapunov Exponent ◽  
Angular Velocity ◽  
Fast Fourier Transform ◽  
Periodic Motion ◽  
Phase Plane ◽  
Largest Lyapunov Exponent ◽  
Cam Follower ◽  
The Impact

Abstract A globoidal cam and roller follower system is analyzed and discussed for non-periodic motion of the follower. Wolf algorithm is used to calculate the largest Lyapunov exponent. The impact between the cam, follower and the two guides is occurred due to the impulse and momentum phenomenon. The effect of the internal dimension of the follower guide on the non-periodic motion of the follower is considered at distinct angular velocity of the cam. The numerical simulation has been done using SolidWorks software. Follower movement is processed experimentally through an infrared 3-D camera device. Phase plane diagram is used to explain the variation in follower motion. Phase-plane diagram and Fast Fourier Transform (FFT) are used to investigate follower non-periodicity. The follower motion is non-periodic when the orbit of phase-plane diagram diverges with no limit of spiral cycles.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

Non-Linear Dynamic Analysis of a Cam With Flat-Faced Follower Linkage Mechanism

2017 ◽  
Author(s):  
Louay S. Yousuf ◽  
Dan B. Marghitu
Keyword(s):  
Dynamic Analysis ◽  
Linear Analysis ◽  
Largest Lyapunov Exponent ◽  
Linkage Mechanism ◽  
Linear Dynamic ◽  
Non Linear ◽  
Cam Follower ◽  
Angular Velocities ◽  
Set Up ◽  
The Impact

A mechanism with a cam and a flat-faced follower is considered for distinct angular velocities. The dynamic analysis presents follower linkage displacement driven by a cam rotating at a uniform angular velocity. The system has clearances between the flat-faced follower and the guides and the effect of clearance is analyzed. The cam-follower linkage mechanism is simulated using Solidworks program taking into account the impact and the friction between the cam, flat-faced follower, and the guides. The non-linear analysis tools are employed for the movement of the flat-faced follower. An experimental set up is established to capture the motion of the follower. High-resolution optical marker is mounted on the follower stem to capture the follower motion in the y-direction. The simulation and experimental results are compared and verified for largest Lyapunov exponent.

Chaotic Behavior of a Two Mass Bouncing System

1992 ◽  
Author(s):  
Chi-Wook Lee ◽  
Ali Seireg ◽  
Joseph Duffy
Keyword(s):  
Power Spectrum ◽  
Spectrum Analysis ◽  
Phase Plane ◽  
Chaotic Behavior ◽  
Power Spectrum Analysis ◽  
Ground Contact ◽  
Hopping Robots ◽  
Plane Technique ◽  
The Stability ◽  
Spring Constants

Abstract This study investigates the behavior of simple two mass bouncing systems which are released from a certain height. A nonlinearity exists in the discontinuity of the flight and the ground modes, although the behavior of the systems is linear in each mode. Such oscillators provide models for mechanical systems such as legged systems for hopping robots. The phase plane technique and the power spectrum analysis are used to investigate the stability of bouncing systems and the chaos that may occur. The effects of the spring constants and the damping coefficient at the ground contact on the bouncing behavior is also investigated.

Algorithm for sleep scoring in experimental animals based on fast Fourier transform power spectrum analysis of the electroencephalogram

2008 ◽  
Vol 6 (3) ◽  
pp. 163-171 ◽  
Author(s):  
Sayaka KOHTOH ◽  
Yujiro TAGUCHI ◽  
Naomi MATSUMOTO ◽  
Masashi WADA ◽  
Zhi-Li HUANG ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Power Spectrum ◽  
Fast Fourier Transform ◽  
Spectrum Analysis ◽  
Power Spectrum Analysis ◽  
Experimental Animals ◽  
Sleep Scoring

Effect of Eccentricity on the Nonlinear Dynamic Behavior of a Cam and Follower Mechanism With Clearance

2018 ◽  
Author(s):  
Louay S. Yousuf ◽  
Dan B. Marghitu
Keyword(s):  
Fourier Transform ◽  
Lyapunov Exponent ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Phase Plane ◽  
Radial Line ◽  
Simulation Process ◽  
Matlab Program ◽  
Nonlinear Dynamic Behavior ◽  
The Relationship

This study evaluate the relationship between flat-faced follower’s offset and Lyapunov exponent. The nonlinear dynamic behavior has been investigated based Lyapunov exponent value. Two types of follower offset such as (e = 10, and 20 mm) has been examined from each side of the cam radial line. The simulation process has been done by using solidwork program. The power spectrum of Fast Fourier Transform and phase plane have been examined the follower non-periodicity during follower motion. The optimum follower offset that would minimize Lyapunov exponent is determined. The system with follower guide’s clearance C = 2 mm and e = 20 mm has larger Lyapunov exponent than the others at cam rotational speed N = 1200 rpm. The signal of follower motion is processed by using MATLAB program.

scholarly journals EXPERIMENTAL OBSERVATION OF A CHAOS-TO-CHAOS TRANSITION IN LASER DROPLET GENERATION

2011 ◽  
Vol 21 (06) ◽  
pp. 1689-1699 ◽  
Author(s):  
BLAŽ KRESE ◽  
MATJAŽ PERC ◽  
EDVARD GOVEKAR
Keyword(s):  
Lyapunov Exponent ◽  
Accurate Determination ◽  
Period Doubling ◽  
Industrial Applications ◽  
Pulse Power ◽  
Droplet Generation ◽  
Largest Lyapunov Exponent ◽  
Recurrence Plots ◽  
The Impact

We examine the dynamics of laser droplet generation that is dependent on the detachment pulse power. In the absence of the detachment pulse, undulating pendant droplets are formed at the end of a properly fed metal wire due to the impact of the primary laser pulse that induces melting. Eventually, these droplets detach, i.e. overcome the surface tension, because of their increasing mass. We show that this spontaneous dripping is deterministically chaotic by using a positive largest Lyapunov exponent and a negative divergence. In the presence of the detachment pulse, however, the generation of droplets is fastened depending on the pulse power. At high powers, the spontaneity of dripping is completely overshadowed by the impact of the detachment pulse. Still, amplitude chaos can be detected, which similarly as the spontaneous dripping, is characterized by a positive largest Lyapunov exponent and a negative divergence, thus indicating that the observed dynamics is deterministically chaotic with an attractor as solution in the phase space. In the intermediate regime, i.e. for low and medium detachment pulse powers, the two chaotic states compete for supremacy, yielding an intermittent period-doubling to amplitude chaos transition, which we characterize by means of recurrence plots and their properties. Altogether, the transition from spontaneous to triggered laser droplet generation is characterized by a chaos-to-chaos transition with an intermediate dynamically nonstationary phase in-between. Since metal droplets can be used in various industrial applications, we hope that the accurate determination of the dynamical properties underlying their formation will facilitate their use and guide future attempts at mathematical modeling.

scholarly journals Nonlinear dynamics behavior of cam-follower system using concave curvatures profile

2020 ◽  
Vol 12 (9) ◽  
pp. 168781402094592
Author(s):  
Louay S Yousuf ◽  
Dan B Marghitu
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Damping Ratio ◽  
Three Dimensional ◽  
Largest Lyapunov Exponent ◽  
Momentum Theory ◽  
Cam Follower ◽  
Cam Profile ◽  
The Impact ◽  
Contact Parameters

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.

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