Non-Linear Dynamics of Geared Systems Using the Asymptotic Method, Part 2: Computation of the Phase Angle
The increased interest for improved gear design has led to extensive research into the field of non- linear dynamics of such systems. The paper reveals a complex dynamic model to study the behavior in a gear- pair system taking into consideration backlash and time-dependent mesh stiffness and mesh damping. In many applications including turbo machinery, machine tools and diesel engines non-linearities are present due to tooth stiffness, damping and backlash that induced micro-vibrations of non-linear parametric type. In the mean time the input link of the driver ax and the output link of the driven ax induce non-linearities. The paper presents the use of asymptotic method in order to compute the amplitude of steady state motion. By this way the paper reveals the phenomena's characteristics of multiple jumps specific to the non-linear dynamic behavior of gear-pair due to: non-linearities of the input-output linkages, backlash and self-induced parametric excitations, caused by the tooth stiffness and damping. It was highlighted the interaction between fundamental resonance and the principal parametric resonance.
NON-LINEAR DYNAMICS OF GEAR-PAIR SYSTEMS WITH PERIODIC STIFFNESS AND BACKLASH
The present work investigates dynamics of a gear-pair system involving backlash and time-dependent mesh stiffness. In addition, the system is under the action of external excitation, caused by torsional moments and gear geometry errors. First, the equation of motion is established in a strongly non-linear form. Then, the emphasis is laid on a specific forcing frequency range, corresponding to conditions of simultaneous fundamental parametric resonance and principal external resonance. For these conditions, several types of periodic steady state response are identified and determined by employing suitable methodologies, including techniques applicable to piecewise linear systems and to oscillators with time-periodic coefficients. Moreover, these methodologies are complemented by appropriate procedures revealing the stability properties of the located periodic solutions. In the second part of the work, numerical results are presented. These results verify the validity and effectiveness of the new analytical methodology and provide information on the gear-pair dynamics. First, series of typical response diagrams are obtained, illustrating the effect of the mesh stiffness variation, the damping and the forcing parameters on the gear-pair periodic response. These response diagrams are accompanied by results obtained with direct integration of the equation of motion. In this way, it is demonstrated that for some parameter combinations, the dynamical system examined can exhibit more complicated and irregular response, including crises and intermittent chaos.
An analysis of patients discharged from a hospital‐based glaucoma case‐finding clinic over a 3‐year period
Purpose:  To analyse the false positive referrals by community optometrists to a glaucoma case‐finding clinic over a 3‐year period.