Dynamic Analysis of Geared Rotors-A Review
Rotor dynamics plays an important role in many engineering fields such as gas turbine, steam turbine, reciprocating and centrifugal compressors, the spindle of machine tools, and so on. Owing to the growing demands for high power, high speed, and light weight of the rotor-bearing system, computations of critical speeds and steady-state response at synchronous and sub critical resonances become essential for system design, identification, diagnosis, and control. The present paper reviews some of the approaches that have been developed to provide a means for understanding and simulations of the characteristics of a geared rotor dynamic system. More emphasis is given on the lateral vibrations of the rotors, effect of coupling of torsional and lateral vibration of rotors especially when the rotors are coupled with gears. Keywords—Critical speed, Geared rotors, Lateral vibrations, Rotor dynamics, Torsional vibrations.
Coupled Torsional-flexural Vibration of a Shaft in a Geared System of Rotors : 1st Report
Coupled torsional-flexural vibration of a shaft in a spur geared system is investigated. Equation of motion which contain the terms of geometrical eccentricity of gears and mass unbalance are introduced. The coupling between torsional and flexural displacements is considered in the equations which assume that surfaces of tooth of meshed gears are always in contact during the rotation. By solving the equation, it is possible to get natural frequencies, mode shapes, and frequency response of the system. It is usual to ignore the effect of the coupling between torsional and flexural vibrations. But comparing the result with them, some new phenomena were revealed. They are: (1) shifts of the critical speeds (2) transformations of the mode shapes (3) a forced vibration which is caused by geometrical eccentricity of a gear.
Changes in Quartz During Heating and the Possible Effects on Si Production
In Si and FeSi production, the main Si source is SiO2, in the form of quartz. Reactions with SiO2 generate SiO gas that further reacts with SiC to Si. During heating, quartz will transform to other SiO2 modifications with cristobalite as the stable high-temperature phase. Transformation to cristobalite is a slow process. Its rate has been investigated for several industrial quartz sources and has been shown to vary considerably among the different quartz types. Other differences in behavior during heating between these quartz sources, such as softening temperature and volume expansion, have also been studied. The quartz-cristobalite ratio will affect the rate of reactions involving SiO2. The industrial consequences and other implications of the observed difference between quartz types are discussed. Initial studies of industrial quartz were published by Ringdalen et al. In the current work, a new experimental method has been developed, and an investigation of several new quartz sources has confirmed the earlier observed large variation between different sources. The repeatability of the data has been studied and the effect of gas atmosphere investigated. The results from the earlier work are included as a basis for the discussion.