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.
New approach to vision-based BGA package inspection
Ball grid array (BGA) techniques have developed very fast due to the advantages of more I/O ports, small size, and so on. In this paper, a vision-based algorithm for BGA package inspection is proposed to accurately estimate center and diameters of solder-balls of BGA packages, so that defects of BGA packages, such as missing or extra balls, oversize or undersize balls, over-height or under-height balls, and pitch can be detected for ensuring the quality of BGA packages.