On the Critical Speeds of a Continuous Rotor

Abstract

An analytical investigation was made on the effect of axial torque on the critical speeds of a continuous rotor whose motion was described by a set of partial differential equations including the effects of transverse shear, rotatory inertia, and gyroscopic moments. The equations of motion and associated boundary conditions for long and short bearings were cast in nondimensional form to facilitate the study of the influence of the aforementioned effects on a torque-transmitting rotor’s critical speeds. The results of this study were compared to classical results of Bernoulli-Enter and Timoshenko to determine the relative importance of the rotor’s “secondary phenomena” in a critical speed calculation.

Vibrational Analysis in Condition Monitoring and faults Diagnosis of Rotating Shaft - Over View

“…The vibration Produced due to unbalance may damage critical parts of the machine, such as bearings, seals, gears and couplings etc. In actual practice, rotors can never be perfectly balanced because of manufacturing errors like non-uniform density of material, tolerances in manufacturing, loss of material during operation, porous casting [13]. Mechanical malfunctions such as, rotor unbalance and shaft misalignment are the most common causes of vibration in rotating machineries.…”

Vibration Analysis of Locomotive Rotor System

“…撑下系统振动响应。欧卫林 [7] 针对存在非平行轴的 多分支齿轮耦合复杂转子系统，求解复杂条件下系 统振动。DEBABRATA [8] 等分析带有裂纹的功能转 子轴承系统，利用有限元法研究其临界转速变化， 转子幅频响应变化。ESHLEMAN [9] 研究了带有弹性 轴承支撑下， 转子的临界转速解及系统的动态响应。 唐 [10] 等建立了齿面间隙和径向间隙的动力学模型， 着重分析研究了齿轮系统的混沌和分岔现象。高洪 波等 [11] 综合考虑了动态侧隙、偏心及摩擦等因素， 研究了齿轮全齿磨损和偏心磨损下系统的振动特 性。LUCZKO 等 [12] ，建立铁木辛柯单元梁模型，分 析了转子动力学响应。SHIAU [13] 求解了简支撑下旋 转多轴的临界转速。PALAZZOL 和 GUNTER [14] 给 出了确定多质量柔性转子系统不平衡分布的响应及 计算模态方法。 通过前面的文献研究可以看出，现有转子传动 系统动力学模型大多数只考虑齿轮-轴承质量的影 响，忽略了边界支撑、转轴质量及外部激励等因素 的影响，且很少有考虑带转轴-齿轮-轴承-轮对机车 传动系统的振动模型。本文在前人基础上，综合考 虑轴承支撑、轮轨接触、齿轮啮合刚度的影响，建 立了机车传动系统的多轴有限元动力学模型，求解 了其临界转速及其振型响应，讨论了轴承支撑、轮 轨激励及齿轮刚度等参量变化对传动系统动力学特 性的影响。 1 动力学模型 考虑轮对轴承、齿轮啮合刚度、随机轮轨激励、 轮对刚性支撑、复杂条件下的机车传动系统动力学 模型，如图 1 所示。 …”

Modal projections for synchronous rotor whirl

“…Many subsequent papers used more sophisticated theories and considered greater loading complexities but still modelled the rotor using beam or shaft elements. Eshleman & Eubanks (1969) included the effects of transverse shear, rotary inertia and gyroscopic moments and investigated the effects of an externally applied axial torque on the critical speeds. Similar considerations were made by Joshi & Dange (1976).…”