两机反向旋转的振动同步系统在远共振和亚共振状态下的运动选择特性

Motion selection characteristics of a vibrating synchronization system driven by two exciters rotating in opposite directions under sub-resonance and super-resonance states

针对目前振动同步系统在远共振和近共振情况下稳态运动特性尚不够明确的问题,建立了一类平面两机反向旋转的振动同步系统模型来致力于研究其在亚共振和远共振情况下的稳态运动规律。采用拉格朗日方法建立双机反向旋转的振动同频系统的运动方程并利用小参数法求出其稳态解,利用Hamilton原理推导出系统的同步运转的频率俘获条件、稳定性判据及其运动规律;通过实验研究验证了理论的正确性。研究表明:在远共振工况下,当l_0<l_ψ时,两激振器的相位差稳定在0°附近;当l_0~2μ_i>l_ψ~2时,相位差稳定在180°附近;在亚共振工况下,结论正好与之相反。该研究为工程中双机反向旋转同步机械的设计提供了理论依据和实验参照。

Arming at the problem that the steady motion features of a vibrating synchronization system under superresonance states and sub-resonance states are not clear enough,the model of a vibrating synchronization system driven by two exciters rotating in opposite directions was established to investigate its steady state motion laws under sub-resonance and super-resonance states. Using Lagrange equations,the dynamic equations of the vibrating system were obtained. Then,their steady state solution was obtained with the small parameters method. Adopting Hamilton's principle,the frequency capture condition,the stability criterion and the motion laws for the system synchronization operation were derived. Finally,the correctness of the theory mentioned above was verified with experiments. The study showed that under super-resonance states,when l_0< l_ψ,the two exciters' phase difference is close to 0° stably,when l_0~2μ_i>l_ψ~2,it is close to 180° stably; under sub-resonance states,the results are opposite. The study results provided a theoretical basis and an experimental reference for design of vibrating synchronization machines driven by two exciters rotating in opposite directions.