Dynamic analysis of a geared rotor system considering a slant crack on the shaft

The vibration problems associated with geared systems have been the focus of research in recent years. As the torque is mainly transmitted by the geared system, a slant crack is more likely to appear on the gear shaft. Due to the slant crack and its breathing mechanism, the dynamic behavior of cracked geared system would differ distinctly with that of uncracked system. Relatively less work is reported on slant crack in the geared rotor system during the past research. Thus, the dynamic analysis of a geared rotor-bearing system with a breathing slant crack is performed in the paper. The finite element model of a geared rotor with slant crack is presented. Based on fracture mechanics, the flexibility matrix for the slant crack is derived that accounts for the additional stress intensity factors. Three methods for whirling analysis, parametric instability analysis and steady-state response analysis are introduced. Then, by taking a widely used one-stage geared rotor-bearing system as an example, the whirling frequencies of the equivalent time-invariant system, two types of instability regions and steady-state response under the excitations of unbalance forces and tooth transmission errors, are computed numerically. The effects of crack depth, position and type (transverse or slant) on the system dynamic behaviors are considered in the discussion. The comparative study with slant cracked geared rotor is carried out to explore distinctive features in their modal, parametric instability and frequency response behaviors.     

Dynamic behavior analysis of cracked rotor

In the present study, the additional slope is used to consider the crack breathing, and is expressed explicitly in the equation of motion as one of the inputs to produce the bending moment at the crack position. Inversely, the additional slope is calculated by integrating on the crack region based on a fracture mechanics concept. The response of a cracked rotor is formulated based on the transfer matrix method. The transient behavior due to the crack breathing is considered by introducing a ‘moving’ Fourier-series expansion concept to the additional slope. The time-varying harmonic components of the additional slope are used to calculate the harmonic responses. The application considered is a general rotor model composed of multiple shafts, disks and cracks, and resilient bearings at both ends. Verification analysis is carried out for a simple rotor model similar to those found in the literature. Using the additional slope, the cracked rotor behavior is explained by the crack depth and rotation speed increase. It is shown that region on the crack front line having the dominant stress intensity factor value moves from the central area to both ends, as the crack depth increases. The result matches well with the crack propagation pattern shown in a bench mark test in the literature. Whirl orbits near the critical and sub-critical speed ranges of the rotor are discussed. It is shown that there exists some speed range near the critical speed, where the temporary whirl direction reversal and phase shift exist. When an unbalance is applied, the peculiar features, such as the whirl direction reversal and phase shift, disappear.     

The existence of periodic motions in rub-impact rotor systems

The existence of rub-impact periodic motions in an eccentric rotor system is considered. A criterion for the periodicity condition of n-periodic impacts is derived and other conditions for real rub-impacts are also discussed. A method consisting of analytical and numerical techniques is presented to solve the existence problem of rub-impact periodic motions. Some special results are obtained by theoretical analyses for rub-impact rotor systems, including the existence of grazing circle motions and that of single-impact periodic motions.     

A tapered beam finite element for rotor dynamics analysis

The stiffness, mass and gyroscopic matrices of a rotating beam element are developed, a cubic function being used for the transverse displacement. Shear deflection is included by use of end nodal variables of shear strain, along with transverse displacement and cross-section rotation; rotatory inertia effects are included in the energy functional to provide a Timoshenko beam formulation. The gyroscopic effects for small perturbations are linearized as a skew symmetric damping matrix. The formulation is implemented by numerical integration for a linearly tapered circular beam. A technique of reduction of the shear nodal variable prior to global assembly is shown to provide little loss in accuracy with reduced system bandwidth. Numerical comparisons for three previously published beam models are included, with results presented for the case of forward and reverse precession to verify the gyroscopic effects. The utility of the element in a general program for rotor dynamics analysis is identified.     

Stability analysis of the rotor of ultrasonic motor driving fluid directly

The stability of the rotor of ultrasonic motor driving fluid directly is a key to its applications and control. This paper introduced the acoustic streaming and acoustic viscous stress near the boundary layer. Following this, the effect of acoustic viscous force on the stability of the rotor of ultrasonic motor driving fluid directly was presented in detail. The result showed that this system can be equivalent to a mass-spring and the spring constant can be used to weigh the stability of the rotor. By this model and relevant experiments, factors that affect the stability of the rotor such as the driving frequency, the rotor's weight and radius, the saturated acoustic streaming velocity, the mode number of stator vibration, the fluid's height and type are investigated and useful guidelines for design and application are obtained.     

某型内转子光电雷达稳定平台的模态分析与优化

为了更好地设计某型内转子光电雷达稳定平台,运用Pro-E软件对其进行了三维实体建模,合理简化后,进入Ansys软件建立有限元模型.应用有限元理论和Ansys软件对该平台进行了模态分析,得到稳定平台前八阶模态的固有频率和振型.其中对比了不同网格、不同材料产生的不同模态,对同类分析提供了参考,也为此稳定平台的设计优化提供了...     

直升机旋翼三维动态变形测量与可视化分析

针对直升机旋翼动载荷飞行试验测试需求,提出一种直升机旋翼三维动态变形测量与可视化分析方法。首先,根据直升机旋翼的结构特点和高速旋转特性,设计了以一组双目高清摄像头为核心的旋翼动态变形影像测量与监控及分析系统;其次,基于双目立体视觉测量理论,论述了测量系统标定、实时单点变形测量、散斑影像匹配、旋翼表面三维重建与三维动态变形可视化分析原理/方法;最后,在地面进行了模拟实测环境的仿真试验,实现了试验系统搭建、试验数据采集、处理与分析。试验结果证明,该方法可获得最大误差优于4 mm的定位测量精度,能很好地实现直升机旋翼三维动态变形测量,为飞行试验旋翼载荷测试数据分析等提供直观、可靠的数据与技术支撑。     

冷氦气闭式循环冷却的高温超导电机转子降温分析

高温超导电机转子一种常见的冷却方式为G-M制冷机提供冷量,氦气为冷媒,氦气泵提供循环动力,其转子降温过程是一个多参数耦合的复杂过程,针对该种冷却方式,阐述了一种基于集总参数法的转子降温分析简易方法,进行了降温计算,并与试验值进行了比较,分析了降温过程中转子与冷头的温度变化特点。     

制冷系统中双转子压缩机建模与性能分析

双转子压缩机主要用于热泵制冷系统中,该系统以CO2作为制冷剂,具有无毒、不易燃等特点,但是CO2体系制冷效能较低.为了提高制冷效能,有必要对双转子压缩机进行建模和分析.主要对CO2压缩机的工作过程进行了建模和分析,并编制仿真分析程序,对双转子压缩机模型第一、二级内部压力进行了连续测量,给出了详细的性能分析结果,给出了双...     

Sensitivity analysis of vibrating systems

In this paper a method for the analysis of the sensitivity dynamical characteristics of mechanical linear systems to variations in the parameters is presented. The method presented has a general character and applies to conservative as well as non-conservative systems. In the method use is made of the Taylor formula for a matrix function of many variables, proved in reference [1]. Use of the result enables the sensitivity analysis to be carried out with parallel changes in all the parameters (M, C and K).The method is illustrated by a numerical example of a seven-degree-of-freedom system.     

Vibro-acoustic analysis of complex systems

A general method is presented for predicting the ensemble average steady-state response of complex vibro-acoustic systems that contain subsystems with uncertain, or random, properties. The method combines deterministic and statistical techniques to produce a non-iterative hybrid method that incorporates equations of dynamic equilibrium and power balance. The method is derived explicitly without reference to statistical energy analysis (SEA); however, it is seen that the wave approach to SEA can be viewed as a special case of the proposed method. The proposed method provides a flexible way to account for necessary deterministic details in a vibro-acoustic analysis without requiring that an entire system be modeled deterministically. The method therefore provides a potential solution to the mid-frequency problem (in which a system is neither entirely deterministic nor entirely statistical). The application of the method is illustrated with a numerical validation example.     

Coupled lateral and torsional vibration characteristics of a speed increasing geared rotor-bearing system

The goal of this study was to examine the coupled vibration characteristics of a turbo-chiller rotor-bearing system having a bull-pinion speed increasing gear, using a coupled lateral and torsional vibration finite element model of a gear pair, and to provide the mechanism of the characteristic changes. The investigations were systematically carried out by comparing the uncoupled and coupled natural frequencies and their mode shapes with varying gear mesh stiffness, taking into account rotating speeds, and by comparing the strain energies of the lateral and torsional vibration modes. The results show that some modes may yield coupled lateral and torsional mode characteristics when the gear mesh stiffness increases over a certain value and, in addition, that their associated dominant modes may be different from their initial modes, i.e., a given dominant mode may change from an initial torsional one to a lateral one or vice versa.