CAJ | 학술논문

建立考虑非线性轴承力、径向游隙、变柔度等非线性因素和不平衡力的滚动轴承-转子系统动力学方程,并用自适应Runge-Kutta-Felhberg算法对其求解,利用分岔图、Poincaré映射图和频谱图,分析参数、强迫联合激励的滚动轴承-转子系统的响应、分岔和混沌等非线性动力特性.结果表明,滚动轴承-转子系统有多种周期和混沌响应形式,其振动频率不仅有参数振动频率成分和强迫振动频率成分,而且有二者的倍频成分和组合频率成分;随着径向游隙的增大,转子系统的非线性特性增强;不平衡力较小时,系统中参数振动占主导地位,增大不平衡力有利于抑制转子系统的不稳定振动.随不平衡力的增大,强迫振动逐渐增强,大的不平衡力会诱发系统产生混沌振动;转子系统进入混沌的主要途径是倍周期分岔.
건립고필비선성축승력、경향유극、변유도등비선성인소화불평형력적곤동축승-전자계통동역학방정,병용자괄응Runge-Kutta-Felhberg산법대기구해,이용분차도、Poincaré영사도화빈보도,분석삼수、강박연합격려적곤동축승-전자계통적향응、분차화혼돈등비선성동력특성.결과표명,곤동축승-전자계통유다충주기화혼돈향응형식,기진동빈솔불부유삼수진동빈솔성분화강박진동빈솔성분,이차유이자적배빈성분화조합빈솔성분;수착경향유극적증대,전자계통적비선성특성증강;불평형력교소시,계통중삼수진동점주도지위,증대불평형력유리우억제전자계통적불은정진동.수불평형력적증대,강박진동축점증강,대적불평형력회유발계통산생혼돈진동;전자계통진입혼돈적주요도경시배주기분차.
The rolling bearing-rotor system in practice is essentially a nonlinear system under parametrical and external excitations. With unbalance force and the sources of nonlinearity such as Hertzian elastic contact force, internal radial clearance and varying compliance considered, the governing differential equations of motion of a rolling bearing-rotor system are derived first and then solved by Runge-Kutta-Felhberg algorithm. Meanwhile the nonlinear dynamic behaviors maps and frequency spectrum diagrams. Numerical results show that various periodic responses with frequencies of the external forcing one, the parametrical forcing one, or the linear combinations of them, and even chaotic responses may exist. It is also shown that increase of radial internal clearance may enhance nonlinearity of the system. When the unbalance is weak and the parametrical vibration is the dominating one, proper increase of the unbalance force may relieve the risk of parametrical vibration instability. On the other hand, increase of unbalance force makes forced vibration stronger, and an improper increase of unbalance force may induce chaotic response. The main route to chaos for this rotor system is the period doubling bifurcation cascade.