The influence of kinematic parameters of motion on the vibration and strength of flexible elements of drive systems

摘要

Отримано співвідношення, які описують основні параметри резонансних коливань. На їх основі проаналізовано вплив швидкості поздовжнього руху на напруження у двовимірних гнучких елементах систем приводу. Analytical investigation of dynamic processes in flexible elements of powertrain systems is associated with significant difficulties. There is a nonlinearity of the mathematical models that describe the process and the presence of mixed derivative on linear and temporal variables. The last takes into account the speed of longitudinal movement. Even its fixed component does not allow the analysis of the simplified (linear) process model to apply classical methods of partial differential equations. Despite the mentioned fact, the work, based on the wave concept, describes the motion of a linear model. Using the last and distribution of the basic idea of the method of Van der Pol on new classes of problems, an equation it is obtained in a standard form, determining the influence of various natural factors on the basic parameters of the waves. It is shown that for large values of longitudinal movement the frequency of natural oscillations is smaller. The method can be used for solving specific problems. A resonant case is the most interesting and difficult at the same time. For this case the received appreciation for lengthening flexible element and it is made a comparativeanalysis of the maximum stretching effort from static case (the system with fixed ends). It is shown that the flexible element with a resonance threshold value speed oflongitudinal movement in which stress may even exceed a few times of tension when resonance vibrations in the case of flexible element with fixed ends. The technique can be used for the research of other classes of systems, mathematical models of which are differentially equations considered in the work, including granular media.