• Journal of KSNVE
• /
• v.11 no.1
• /
• pp.82-88
• /
• 2001

In a transmission or geared rotor system a coupled phenomenon of lateral and torsional vibrations may occur due to the gear meshing effect. Particularly, in high speed or low vibration and low noise applications of geared rotor systems a coupled rotordynamic analysis is required to precisely predict their dynamic characteristics. In this paper a generalized finite element model of a gear pair element is developed, which actively couples the lateral and torsional vibrations due to the gear meshing effect. In the modeling the generalized forces due to the transmission error. geometrical eccentricities. and unbalances in the gear system are also considered. Then. using the developed gear pair element model a coupled unforced rotordynamic analysis is performed with a prototype 800 RT turbo-chiller rotor-bearing system having a hull-pinion speed increasing gear. Results show that the torsional vibration characteristics experience some changes due to the gear meshing and lateral dynamic coupling effect, but that they have no adverse effect and the lateral ones have no practical changes in an operating speed range.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.13 no.8
• /
• pp.598-604
• /
• 2003

In this paper a general solution method is presented to obtain the unbalance response orbit from the finite element based equations of motion of a gear-coupled two-shaft rotor-bearing system, whose shafts rotate at their different speeds from each other. Particularly, are proposed analytical solutions of the maximum and minimum radii of the orbit. The method has been applied to analyze the unbalance response of a 800 refrigeration-ton turbo-chiller rotor-bearing system having a bull-pinion speed increasing gear. Bumps in the unbalance response of the driven high speed compressor rotor system have been observed at the first torsional natural frequency due to the coupling effect of lateral and torsional dynamics. Further, the proposed analytical solutions have agreed well with those obtained by a full numerical approach. The proposed analytical solutions can be generally applied to obtain the maximum and minimum radii of the unbalance response orbits of dual-shaft rotor-bearing systems coupled by bearings as well.

• Journal of the Korea Society for Simulation
• /
• v.8 no.3
• /
• pp.39-48
• /
• 1999

A finite element model of geared rotor system with flexible bearings were used to simulate the critical speeds and to investigate the effects of bearing coefficients on the dynamic behaviors of the systems. The finite element model includes the effects of tooth mesh stiffness, gyroscopic moment, rotary inertia, shear, and torque of the shaft. The gear mesh was modelled as a pair of rigid disks connected by a spring of time varying stiffness. The time varying mesh stiffness results in the abrupt change of the critical speeds of spur geared systems. As the bearing stiffness increases, critical speeds increase rapidly in case of stiff shafts, compared with flexible shafts.

• 유체기계공업학회:학술대회논문집
• /
• 1998.12a
• /
• pp.159-165
• /
• 1998

Bearing design of turbo type geared centrifugal air compressor for low vibration level has been studied. The Transfer Matrix Method was used in this paper to analyze the air-compressor consisting of impellers, multi-stage geared rotors, and oil-film hearings. We have to consider this air-compressor as multi-geared rotating system, because characteristics of rotor-bearing system are different from conventional characteristics of non-rotating system. From the view point of Rotordynamics, the stiffness and damping coefficient of oil-film bearing in case of compressor system are more sensitive than other design parameters such as shaft length, shaft diameter and the weight of impellers, etc. Therefore, the stiffness and damping coefficients on each bearing were considered as design parameters. As the result of this study, turbo type air compressor with low vibration level can be achieved.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.10a
• /
• pp.50-57
• /
• 1997

A 600HP class high-speed gear driven 3-stage turbo-compressor (IGCC : Integrally Geared Centrifugal Compressor) driven by a 3600 rpm AC induction motor has been designed, of which low speed pinion runs at 35000 rpm and high speed pinion at 50000 rpm nominally. Due to its high speed operation, the system requires very reliable bearing selection and design as well as accurate rotordynamic analysis and prediction of its dynamic behavior to secure the operating reliability. Rotordaynamic analyses of the IGCC rotor-bearing system predicted that the low speed pinion rotor mounted on 5-pad tilting pad bearings has two critical speeds before its design speed and high speed pinion rotor only one critical speed, and estimated critical speeds of both pinion shafts are away from the continuous operating speed enough to satisfy the corresponding API requirement. The forced response analysis with API specified maximum allowable unbalances also showed that unbalance responses are small enough for smooth operation of the system.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.12 no.2
• /
• pp.116-123
• /
• 2002

Applying a general coupled lateral and torsional vibration finite element model of gear pair element, this paper intends to look into in detail the coupled lateral and torsional vibration characteristics of a turbo-chiller rotor bearing system, having a bull-pinion speed increasing gear. Investigations have been carried out systematically by comparing the uncoupled and coupled natural frequencies and their mode shapes upon varying the gear mesh stiffness with considerations on rotating speeds, and also by comparing the strain energies of lateral and torsional vibration modes. Results hale shown that some modes may hale the coupled lateral and torsional mode characteristics as the gear mesh stiffness Increases over a certain value, and moreover that their associated dominant modes may be different from their initial modes, j.e., a certain dominant mode may change from an initial torsional one to a lateral one or from an initial lateral one to a torsional one.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.05a
• /
• pp.220-226
• /
• 2002

A general solution method is presented to obtain the unbalance response orbit from the finite element based equations of motion of a gear-coupled two-shaft rotor-bearing system. Particularly, are proposed the analytical solutions of major and minor axis radii of the orbit. The method has been applied to analyze the unbalance response of a 800 refrigeration-ton turbo-chiller rotor-bearing system, having a bull-pinion speed increasing gear. The bumps of unbalance responses have been observed at the first torsional natural frequency due to the coupling of lateral and torsional dynamics by the gear meshing. Further, the proposed analytical solutions have been validated with results obtained by a full numerical approach.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.05a
• /
• pp.722-728
• /
• 2001

Applying a general coupled lateral and torsional vibration finite element model of gear pair element this paper intends to look into in detail the coupled lateral and torsional vibration characteristics in a turbo-chiller rotor bearing system, having a bull-pinion speed increasing gear. Investigations have been carried out systematically by comparing the uncoupled and coupled analyses natural vibration frequencies and their mode shapes upon varying the gear mesh stiffness, and also by comparing the strain energies of lateral and torsional vibration modes. Results have shown that some modes may have coupled lateral and torsional mode characteristics as the gear mesh stiffness increases over a certain value, and moreover that their associated dominant modes may be different from their initial modes, i.e., the dominant mode changes from an initial torsional one to a lateral one or from an initial lateral one to a torsional one.

• Journal of KSNVE
• /
• v.5 no.2
• /
• pp.183-195
• /
• 1995

The mathematical model of the gear reductioner which consists which consists of the geared rotor-bearing system containing case is developed, assuming as the lumped parameter system. Constraints for vibration suppresion as well as strength of gear teeth, and shaft and kinematic conditions in gear pairs are considered. To find the design parameters satisfing the proposed constraints, a direct search method modified by the technique of Taguchi's experimental scheduling is used. One and two stepped gear reductioners are designed so that the criticl speeds due to the gear transmission error are moved out of the operating speed range.