摘要
针对两端刚性支承的Jeffcott转子,导出了固定坐标系中裂纹轴的刚度矩阵,建立了裂纹转子的弯扭耦合振动非线性微分方程。通过数值仿真手段,着重分析了转子升速过程中弯振和扭振的瀑布图、Bode图以及加速度的影响。研究表明,升速过程中,弯振和扭振都出现了1/2阶和1/3阶亚谐共振现象,它们的1X,2X和3X分量共振峰对应转速下的相位角有180°的突变,且在除各分量峰值转速外的其他转速处(如ω0,1/2ω0和1/3ω0)相位角也有一定的波动。弯振响应分别在1/3ω0,1/2ω0,ω0,3/2ω0,2ω0和左右弯扭耦合区处出现共振峰值,而扭振响应则在tω0和左右弯扭耦合区处出现峰值。有无裂纹情况下的弯振和扭振受加速度的影响大致相同,但在相同加速度下,裂纹转子较无裂纹转子的临界峰值更大,对应的临界转速则更小。
A rigid supported,rotating,jeffcott rotor system with a transverse crack is considered.The flexural stiffness matrix of the cracked shaft is derived.And the nonlinear differential equations of coupled flexural and torsional vibrations are established.Through numerical simulation,the waterfall plot,bode plot and the influence of acceleration on flexural and torsional vibrations are analyzed.The results show that 1/3X and 1/2X sub-syntonic resonances of flexural vibration and torsional vibration occur with the shaft accelerated.The phases of vibrations resonance peak of 1X,2X and 3X components change 180 degree.And the phases corresponding to 1/3ω_0,1/2ω_0 and ω_0 fluctuate too.The resonance peaks of flexural vibration response are present at 1/3ω_0,1/2ω_0,ω_0,3/2ω_0,2ω_0and left and right coupling regions of flexural-torsional vibrations,and that of torsional response are present at ω_t0and left and right coupling regions.The influence of acceleration on flexural vibration is similar with torsional vibration with or without cracks.Under the condition of a same acceleration,the critical peak of the shaft with cracks is more bigger than that of the shaft without cracks,and the critical speed is more smaller.
出处
《振动．测试与诊断》
EI
CSCD
2006年第3期226-230,共5页
Journal of Vibration,Measurement & Diagnosis
关键词
裂纹
转子
弯扭耦合振动
瞬态振动
cracks rotors coupled flexural and torsional vibrations transient vibration
