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.

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.

Non-periodic motion reduction in globoidal cam with roller follower mechanism

2021 ◽  
pp. 095440622110336
Author(s):  
Louay S Yousuf
Keyword(s):  
Numerical Simulation ◽  
Periodic Motion ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Nonlinear Response ◽  
Phase Plane ◽  
Infrared Camera ◽  
Power Spectrum Analysis ◽  
Dynamic Movement ◽  
Acquisition Technique

Non periodic motion has been investigated using power spectrum analysis of Fast Fourier Transform (FFT), Lyapunov exponent parameter using Wolf algorithm, and Phase-plane mapping. A multi degrees of freedom (spring-damper system) are added at the end of the follower stem to reduce the nonlinear dynamic behavior of the follower. In the experiment setup, data acquisition technique with signal processing approach is used through an infrared camera device to capture the nonlinear dynamic movement of the follower. A numerical simulation is done using SolidWorks software. An OPTOTRAK/3020 with an infrared camera device is used to track the follower position experimentally. The peak of nonlinear response of the roller follower is reduced by (20.89%, 47.76%, 58.2%, and 67.16%) after using multi degrees of freedom systems.

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 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.

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.

scholarly journals Cosmological model parameter dependence of the matter power spectrum covariance from the DEUS-PUR Cosmo simulations

2020 ◽  
Vol 500 (2) ◽  
pp. 2532-2542
Author(s):  
Linda Blot ◽  
Pier-Stefano Corasaniti ◽  
Yann Rasera ◽  
Shankar Agarwal
Keyword(s):  
Dark Energy ◽  
Power Spectrum ◽  
Cold Dark Matter ◽  
Matter Density ◽  
Density Fluctuations ◽  
Matrix Analysis ◽  
Model Parameter ◽  
Matter Power Spectrum ◽  
Non Gaussian ◽  
The Impact

ABSTRACT Future galaxy surveys will provide accurate measurements of the matter power spectrum across an unprecedented range of scales and redshifts. The analysis of these data will require one to accurately model the imprint of non-linearities of the matter density field. In particular, these induce a non-Gaussian contribution to the data covariance that needs to be properly taken into account to realize unbiased cosmological parameter inference analyses. Here, we study the cosmological dependence of the matter power spectrum covariance using a dedicated suite of N-body simulations, the Dark Energy Universe Simulation–Parallel Universe Runs (DEUS-PUR) Cosmo. These consist of 512 realizations for 10 different cosmologies where we vary the matter density Ωm, the amplitude of density fluctuations σ8, the reduced Hubble parameter h, and a constant dark energy equation of state w by approximately $10{{\ \rm per\ cent}}$. We use these data to evaluate the first and second derivatives of the power spectrum covariance with respect to a fiducial Λ-cold dark matter cosmology. We find that the variations can be as large as $150{{\ \rm per\ cent}}$ depending on the scale, redshift, and model parameter considered. By performing a Fisher matrix analysis we explore the impact of different choices in modelling the cosmological dependence of the covariance. Our results suggest that fixing the covariance to a fiducial cosmology can significantly affect the recovered parameter errors and that modelling the cosmological dependence of the variance while keeping the correlation coefficient fixed can alleviate the impact of this effect.

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