Dynamic Stability Analysis of the Toothed Belt Transmission system

• Main Authors: Tzeng, Gwo Liang, 曾國良
• Other Authors: Huang, Jeng Sheng
• Format: Others
• Language: zh-TW
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/59615826988120551302

碩士 === 中原大學 === 機械工程研究所 === 82 === The thesis studies the vibration of the toothed belt/wheels system. By using Hamilton's principle, we can derive non-linear partial differential equations of motion of the system. We obtain solution of the equilibrium configuration by equating the time derivative be zeros. To study the characteristic under equilibrium configuration. We consider small motions around the equilibrium configuration, then the non-linear partial differential equations can be simplify as linear partial differential equations. Moreover, the Galerkin's method is employed to transfer the equations of motion into the ordinary differential equation. To study dynamic response, by using numerical methods and transfermation of variable. Then the homogenous part of the equation is considered for stability analysis, apply Bolotins method and transformed into Hill's type of equation , and get the stable and unstable regions. The purpose of this thesis, is to discussed that characteristic under equilibrium configuration, small motions around the equilibrium configuration and homogenous part of the equation is considered for stability analysis with belt tension and contact tooth. Due to the equation of motion and bounday condition in the system, we get the couple nonhomegeneous boundary condition in the condition that the pricipal span is not equal to the secondary span. The nonhomegeneous boundary condition will effect the behavies of the systems and the character of the system. Due to discuss the characteristic of the equilibrium configuration, the critical speed is increasing as the tension of the span, but the equilibrium configuration displacement of nontrivial solution increase, when the speed of traslation exceed the critical speed, Similary we get the some result when the numbers of the contact toothed change. In the analysis of stability, we know that the increase in the tension of the span and the numbers of contact toothed will make the region of unstable shift out.