• Journal of the Korean Society for Precision Engineering
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• v.16 no.12
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• pp.99-108
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• 1999

A four-degree-of-freedom non-linear model with time varying mesh stiffness has been developed for the dynamic analysis of spur gear trains. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover. In the model, developed several factors such as time varying mesh stiffness and damping, separation of teeth, teeth collision, various gear errors and profile modifications have been considered. Two computer programs are developed to calculate stiffness of a gear pair and transmission error and the dynamic analysis of modeled system using time integration method. Dynamic tooth and mesh forces, dynamic factors are calculated. Numerical examples have been given, which shows the time varying mesh stiffness ha a significant effect upon the dynamic tooth force and torsional vibrations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.722-728
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• 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 Power System Engineering
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• v.4 no.1
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• pp.60-67
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• 2000

As the speed of rotating machines increases and also their weight decreases, the coupling between lateral and torsional vibrations must be considered. In the past, rotordynamics and geardynamics have tended to treat the lateral and torsional vibrations of the system elements as separate and decoupled mechanisms. In the paper, the coupled lateral-torsional free and forced vibration of rotors trained by gears is analyzed using finite element method. Also the complicated variation of the meshing stiffness as a function of contact point along the line of action is estimated correctly. The gear mesh model is assumed to be linear with constant average mesh stiffness.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.2
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• pp.116-123
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• 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
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• 2000.06a
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• pp.1034-1039
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• 2000

In turbo-machines operated at high speeds through gear speed increasers a precise coupled analysis of lateral and torsional vibrations is required to achieve highly reliable designs with low vibration and low noise levels, where the vibration coupling is due to the gear pair mesh stiffness. In this paper, applying the generalized coupled lateral-torsional finite element model of a gear pair element, has been analyzed a coupled lateral-torsional vibration of the prototype 800 RT turbo-chiller rotor-bearing system with a bull-pinion gear speed increaser. Results have shown that the coupled torsional natural frequencies have decreased due to the coupling effect of lateral vibration and particularly, the 2nd torsional natural frequency and its mode shape have had big changes. However, changes of lateral vibration characteristics have been noticed only at high lateral whirl natural frequencies above 15,000 rpm.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2008.11a
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• pp.31-32
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• 2008

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.6
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• pp.8-14
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• 2001

We develop a method to analyze dynamic behavior off multi-stage gear train system. The example system consists of three shafts supported by ball bearings at the ends of them and two pairs of spur gear set. For exact analysis, the meshing tooth pair of gear set is modeled as spring and damper having time-dependent meshing stiffness and damping. The bearing is modeled as spring. The result of this analysis is compared to that of other model having mean mesh stiffness. The effect of the excitation force by the unbalance off rotor off motor is also analyzed. Finally, the change ova natural frequency of the whole system due to the change of an angle between three shafts is compared in each case, and from this analysis, the avoiding angle for design is advised.

• Tribology and Lubricants
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• v.32 no.4
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• pp.107-112
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• 2016

This paper presents a rotordynamic analysis of the reduction gear system applied to the 250 kW super critical CO₂ cycle. The reduction gear system consists of an input shaft, intermediate shaft, and output shaft. Because of the high rotating speed of the input shaft, we install tilting pad bearings, rolloer bearings support the intermediate and output shafts. To predict the tilting pad bearing performance, we calculate the applied loads to the tilting pad bearings by considering the reaction forces from the gear. In the rotordynamic analysis, gear mesh stiffness results in a coupling effect between the lateral and torsional vibrations. The predicted Campbell diagram shows that there is not a critical speed lower than the rated speed of 30,000 rpm of the input shaft. The predicted modes on the critical speeds are the combined bending modes of the intermediate and output shaft, and the lateral vibrations dominate when compared to the torsional vibrations. The damped natural frequency does not strongly depend on the rotating speeds, owing to the relatively low rotating speed of the intermediate and output shaft and constant stiffness of the roller bearing. In addition, the logarithmic decrements of all the modes are positive; therefore all modes are stable.

• Journal of the Korean Society of Safety
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• v.22 no.1 s.79
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• pp.1-6
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• 2007

In the field of the system dynamics related to the vibration characteristics, there are lots of examples introduced for the translational system, however the analysis of the torsional systems such as driveline in the automobile is rare compared with the translational system. The purpose of this study is to show the simple concepts for the torsional system analysis and explain how to adjust the mathematical methods for the geared motions, which can be applied to the driveline of the automobile. In order to do it, there are several systematical approaches described about how the sub-system motions can be understood with the mathematical descriptions. Based upon this fundamental study, several torsional system modeling methods will be suggested. Therefore, the characteristics of the torsional system and the gear motions will be explained, which can be adjusted in a further study as a next step.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.11 s.176
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• pp.111-117
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• 2005

The vibration problems associated with gear coupled rotors have been the focus of much engineering work. These systems are complex and difficult to analyze in that they have the problems associated with conventional rotors plus those additional problems associated with the gear couplings. This paper examines the problems peculiar to the gear mesh. Because of the meshing action of gears, the elasticity of the gear teeth introduces time-varying stiffness coefficients into the governing equations of motion. This means that system response must be thought of in terms of Mathieu-type equations, where multiple-frequency response occur due to the periodic coefficients. The meshing action of the gears also couples the lateral and torsional gear motions. Gear errors, such as tooth profile and spacing errors, produce forces and torque that excite the system at multiple frequencies, some of which are much higher than shaft rotational speed. To investigate how to the time-varying stiffness in the gear teeth and the gear errors act one the dynamic response of the gear coupled rotors, a three-dimensional dynamic model with lateral-tortional oscillation is developed. The harmonic balance technique is employed to solve this mathieu-type problem.