单质体非线性系统谐波锐共振的谐振同步分析

基于单质体非线性系统的动力学模型,推导出系统在谐波锐共振(主共振频率比z=0.95～1.05)情况下,反向回转的双激振电动机在平衡奇点处的谐振同步条件。并通过数值仿真,研究在不同初始条件下,推导的谐振同步条件的正确性。理论推导过程和仿真试验结果及实际试验数据表明:在系统特性参数保持一定的情况下,单质体非线性系统谐波锐共振的谐振同步现象与系统的谐波锐共振阶次p/q、谐振同步阶次n/m有直接关系,且只有当参与激振的两电动机在符合一定的系统特性条件下的某p/q及n/m比值处,方可出现谐振同步现象,并且主振同步远比谐振同步容易实现。为进一步开发高效的非线性锐共振振动机,提供理论支持和试验依据。

Analysis of Harmonic Oscillation Synchronization for the Single-mass Nonlinear System under Harmonic Wave Sharp Resonance Condition

Based on the dynamic model of single mass nonlinear system, the necessary conditions of harmonic oscillation synchronization motion are deduced, under harmonic wave sharp resonance (main resonant frequency ratio) condition and dual vibration exciters rotating in opposite direction are moving at the balance singular point. Using the numerical simulation, the valid of the harmonic oscillation synchronization conditions are investigated under different initial conditions. The process of theoretical derivation, consequence of simulation tests and actual tests data indicate that if the systemic characteristic parameter remain constant, the vibration synchronization phenomena of single-mass nonlinear system under harmonic wave sharp resonance condition have direct relationship with the harmonic wave sharp resonance order p/q, and harmonic oscillation synchronization order n/m. But the harmonic oscillation synchronization phenomena of the dual vibration exciters only occur at a certain radio of p/q and n/m which conform to the specific mechanical characteristic conditions of nonlinear system. And they also indicate that the realization of system main resonance synchronization is far easier than system harmonic oscillation synchronization. This research provides theoretical support and test basis for further exploitation of efficient and energy-saving nonlinear sharp resonance shaker.