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.
Schwingungs- und Stabilitätsprobleme bei mechanischen Systemen mit harmonischer Erregung†
Die Frage, wie ein mechanisches System resonanzartig auf eine harmonische Erregung antworten kann, ist eine der klassischen Problemstellungen der Schwingungslehre. Zu ihr soll im folgenden ein Beitrag geliefert werden. Er mus sich zwar der Kurze halber in mehrfacher Hinsicht beschranken, namlich bezuglich der behandelten mechanischen Systeme, der verwendeten mathematischen Methode und der abgeleiteten Ergebnisse, soll aber doch von einem neuen Standpunkt aus einen gewissen Uberblick uber die wichtigsten, in der Literatur heute z. T. noch weit verstreuten Tatsachen geben.
A Short-Term and High-Resolution Distribution System Load Forecasting Approach Using Support Vector Regression With Hybrid Parameters Optimization
This paper proposes an approach for distribution system load forecasting, which aims to provide highly accurate short-term load forecasting with high resolution utilizing a support vector regression (SVR) based forecaster and a two-step hybrid parameters optimization method. Specifically, because the load profiles in distribution systems contain abrupt deviations, a data normalization is designed as the pretreatment for the collected historical load data. Then an SVR model is trained by the load data to forecast the future load. For better performance of SVR, a two-step hybrid optimization algorithm is proposed to determine the best parameters. In the first step of the hybrid optimization algorithm, a designed grid traverse algorithm (GTA) is used to narrow the parameters searching area from a global to local space. In the second step, based on the result of the GTA, particle swarm optimization is used to determine the best parameters in the local parameter space. After the best parameters are determined, the SVR model is used to forecast the short-term load deviation in the distribution system. The performance of the proposed approach is compared to some classic methods in later sections of this paper.