Nonlinear Dynamics Investigation of Contact Force in Ploydyne Cam and Flat-Faced Follower System (Published)
Nonlinear dynamics behavior of contact force is investigated for different cam angular speeds (N) and different internal dimensions of the follower guide (F.G.I.D.). Largest Lyapunov exponent parameter conception is used to detect either the follower will detach from the cam or stays in permanent contact. Power spectrum analysis and Poincare’ maps with phase-plane diagram are added to detect the non-periodic motion of the contact force. The follower is moved with three degrees of freedom. Multi degrees of freedom (spring-damper-mass) systems are added at the end of the follower stem to suppress the nonlinear dynamics behavior of the contact force of the follower. SolidWorks software is used in the numerical simulation of the contact force. Contact force and follower displacement are determined at different coefficient of restitution values. The friction and impact are considered between the cam and the follower and between the follower and its guide. The contact force is measured experimentally using OPTOTRACK/3020 by tracking the position of the follower through an infrared camera device. The value of contact force has declined with the increasing of cam angular speeds (N) and internal dimension of the follower guide (F.G.I.D.). The peak of nonlinear response of the follower displacement is reduced to (15 %, 32 %, 45 %, and 62 %) after using multi degrees of freedom system.
- A multi degrees of freedom (spring-damper-mass) systems at the end of the follower stem are used to suppress the nonlinear dynamics phenomena of the contact force of the follower.
- The power density function with dominant frequency is calculated numerically for contact force and follower displacement using SolidWorks software.
- An OPTOTRAK / 3020 with an infrared camera device is used to track the follower position and measure the contact force experimentally.
- A phase-plane diagram with Poincare maps, Fast Fourier Transform (FFT), Lyapunov exponent conception are used to detect the non-periodic motion of the offset follower movement.
Nonlinear dynamic response of the follower movement is investigated at different follower guides’ internal dimensions (F.G.I.D.), cam angular velocities (N), and coefficient of
Equilibrium Effect Modelling Of Contact and Seepage Forces on the Failure of Water Borehole (Published)
Continuum and discontinuum problems were considered in the solid-liquid medium under study. The necessitated the use of combined finite-discrete element method to generate model expressions from contact force and seepage force considered to be the major forces contributing to the flow of fluid through soil mass and boiling or quicksand effect when seepage force becomes more in effect under critical hydraulic gradient and / or critical hydraulic head. The equilibrium model has deduced an expression for the safe hydraulic head during well pumping as = and this has been verified using a laboratory check; prototype well failure test. It has been established that there is strong agreement between model result and the laboratory check at 1.8m flow distance and the correlation analysis carried out has also shown a perfect correlation of 0.989879999701. Note, a perfect correlation lies between -1 (perfect negative) and 1 (perfect positive) (Agunwamba, 2007; Inyama and Iheagwam, 1995).For safe pumping and corresponding yield in the borehole system, inter-granular force between granular particles should equal the seepage force and this is achieved by ensuring that the deduced model expression is used to determine the safe hydraulic head. For the system under study, the safe hydraulic head must be maintained. Finally, as long as the model hydraulic head expression deduced is used under the above conditions, safe pumping can be achieved at any voltage between 150volts and 240volts.