• Tribology and Lubricants
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• 제18권1호
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• pp.24-33
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• 2002

The basic equations are derived for the analysis of a staggered labyrinth gas seal which are generally used in high performance compressors and steam turbines. The Bulk-flow is assumed for a single cavity control volume and the flow is assumed to be completely turbulent in circumferential direction. Moody's wall-friction-factor formula is used for the calculation of wall shear stresses in the single cavity control volume. For the reaction force developed by the seal, linearized zeroth-order and first-order perturbation equations are developed for small motion about a centered position. Integration of the resultant first-order pressure distribution along and around the seal defines the rotordynamic coefficients of the staggered labyrinth gas seal. Theoretical results of leakage and rotordynamic characteristics for the staggered labyrinth gas seal are compared with those of the plain seal and see-through labyrinth seal.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.799-804
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• 2002

In this paper the leakage prediction and rotordynamic analysis of an annular seal with a smooth rotor and spiral-grooved stator are performed. For developing a theoretical model, the three-control-volume analysis of the circumferentially-grooved seal is expanded by considering pressure reduction due to the pumping effect of spiral groove and pressure flow through the spiral groove. Results by the present analysis are compared with available experimental data. For leakage the analysis results generally show a reasonable agreement to the experimental results. For rotordynamic coefficients the analysis results show the same trend as the experimental results for rotor speed with spiral angles, but their magnitudes show somewhat large deviations.

• 소음진동
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• 제9권3호
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• pp.593-599
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• 1999

A rotordynamic analysis is performed with a motor-bull gear rotor system supported on two partial bearings, which is intended to drive a high-speed turbo-chiller compressor impeller shaft through its built-in pinion gear. The motor-bull gear rotor system has a rated speed of 3,600 rpm, and is modeled utilizing the finite element method for analysis. As loadings on the bearings due to the gear action are significant in the system considered, each resultant bearing load is calculated statically by considering the generalized forces of the gear action as well as the rotor itself. The two support partial bearings are designed to take their varying loads along with their varying load angles, and they are also analyzed to give their rotordynamic coefficients. Then, a complex rotordynamic analysis of the motor-bull gear rotor-bearing system is carried out to evaluate its whirl natural frequencies and mode shapes and unbalance responses under various loading conditions. Results show that the bearings and entire rotor system are well designed regradless of operating conditions, i.e., loads and operating speeds.

• Structural Engineering and Mechanics
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• 제50권1호
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• pp.19-36
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• 2014

This paper focuses on a model order reduction (MOR) for large-scale rotordynamic systems by using finite element discretization. Typical rotor-bearing systems consist of a rotor, built-on parts, and a support system. These systems require careful consideration in their dynamic analysis modeling because they include unsymmetrical stiffness, localized nonproportional damping, and frequency-dependent gyroscopic effects. Because of this complex geometry, the finite element model under consideration may have a very large number of degrees of freedom. Thus, the repeated dynamic analyses used to investigate the critical speeds, stability, and unbalanced response are computationally very expensive to complete within a practical design cycle. In this study, we demonstrate that a Krylov subspace-based MOR via moment matching significantly speeds up the rotordynamic analyses needed to check the whirling frequencies and critical speeds of large rotor systems. This approach is very efficient, because it is possible to repeat the dynamic simulation with the help of a reduced system by changing the operating rotational speed, which can be preserved as a parameter in the process of model reduction. Two examples of rotordynamic systems show that the suggested MOR provides a significant reduction in computational cost for a Campbell diagram analysis, while maintaining accuracy comparable to that of the original systems.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 추계학술대회논문집
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• pp.523-530
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• 2006

A rotordynamic analysis was performed with a dry vacuum pump, which is a major equipment in modern semiconductor and LCD manufacturing processes. The system is composed of screw rotors, lobes picking air, helical gears, driving motor, and support rolling element hearings of rotors and motor. The driving motor-screw rotor system has a rated speed of 6,300rpm, and was modeled utilizing a rotordynamic FE method for analysis, which was verified through the results of its 3-D finite element model. As loadings on the bearings due to the gear action were significant in the system considered, each resultant bearing load was calculated determinately and indeterminately by considering the generalized forces of the gear action as veil as the rotor itself. Each resultant hearing loading was used in calculating each stiffness of rolling element bearings. Design goals are to achieve wide separation margins of critical speeds and favorable unbalance responses of the rotor in the operating range. Then, a complex rotordynamic analysis of the system was carried out to evaluate its forward synchronous critical speeds, whirl natural frequencies and mode shapes, and unbalance responses under various unbalance locations. Results show that the entire system is well designed in the operating range. In addition, the procedure of rotordynamic analysis for dry vacuum pump rotor-bearing system was proposed and established.

• 한국유체기계학회 논문집
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• 제10권3호
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• pp.47-54
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• 2007

A rotordynamic analysis was performed with a dry vacuum pump, which is a major equipment in modem semiconductor and LCD manufacturing processes. The system is composed of screw rotors, lobes picking air, helical gears, driving motor, and support rolling element bearings of rotors and motor. The driving motor-screw rotor system has a rated speed of 6,300rpm, and was modeled utilizing a rotordynamic FE method for analysis, which was verified through the results of its 3-D finite element model. As loadings on the bearings due to the gear action were significant in the system considered, each resultant bearing load was calculated determinately and indeterminately by considering the generalized forces of the gear action as well as the rotor itself. Each resultant bearing loading was used in calculating each stiffness of rolling element bearings. Design goals are to achieve wide separation margins of critical speeds and favorable unbalance responses of the rotor in the operating range. Then, a complex rotordynamic analysis of the system was carried out to evaluate its forward synchronous critical speeds, whirl natural frequencies and mode shapes, and unbalance responses under various unbalance locations. Results show that the entire system is well designed in the operating range. In addition, the procedure of rotordynamic analysis for dry vacuum pump rotor-bearing system was proposed and established.

• 소음진동
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• 제9권5호
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• pp.1042-1049
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• 1999

In the Part I has been reported a rotordynamic analysis of the driving motor-bull gear rotor-bearing system of a turbo-chiller. In this study, Part II, a rotordynamic analysis is performed with the turbo-chiller compressor pinion-impeller rotor system supported on two fluid film bearings. The pinion-impeller rotor system is driven to a rated speed of 14,600 rpm through a speed-increasing pinion-bull gear. It is modeled utilizing the finite element method for analysis. As loadings on the bearings due to the gear action are significant in the system considered, each resultant bearing load is calculated statically by considering the generalized forces of the gear action as well as the rotor itself. The two support bearings, the generalized forces of the gear action as well as the rotor itself. The two support bearings, partial and 3-axial groove bearings, are designed to take their varying loads along with their varying load angles, and they are also analyzed to give their rotordynamic coefficients. Then, a complex rotordynamic analysis of the compressor pinion-impeller rotor-bearing system is carried out to evaluate its stability, whirl natural frequencies and mode shapes, and unbalance responses under various loading conditions. Results show that the bearings and entire rotor system are well designed regardless of operating conditions, i.e., loads and operating speeds.

• Tribology and Lubricants
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• 제32권4호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.528-534
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• 2001

Basic equations and its solution procedure are derived for the analysis of an annular pump seal in which the rotor has a large static displacement from the centered position. The Bulk-flow is assumed for a control volume set in the seal clearance and the flow is assumed to be completely turbulent in axial and circumferential direction. Moody's wall-friction-factor formula is used for the calculation of wall shear stresses in the control volume. For the reaction force developed by the seal, linearized zeroth-order and first-order perturbation equations are developed for small motion about an eccentric position. Flow variables are expanded by using Fourier series for the solution procedure. Integration of the resultant first-order pressure distribution along and around the seal defines the 12 elements of rotordynamic coefficients of the eccentric annular pump seal. The results of leakage and rotordynamic coefficients are presented and compared with the Marquette's experimental results and the San Andres' theoretical analysis.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.1084-1089
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• 2000

The basic equations are derived for the analysis of a stepped labyrinth gas seal which are generally used in high performance compressors, gas turbines, and steam turbines. The Bulk-flow is assumed for a single cavity control volume and the flow is assumed to be completely turbulent in circumferential direction. Moody's wall-friction-factor formula is used for the calculation of wall shear stresses in the single cavity control volume. For the reaction force developed by the seal, linearized zeroth-order and first-order perturbation equations are developed for small motion about a centered position. Integration of the resultant first-order pressure distribution along and around the seal defines the rotordynamic coefficients of the stepped labyrinth gas seal. The leakage and rotordynamic characteristic results of the stepped labyrinth gas seal are presented and compared with Scharrer's theoretical analysis using Blasius' wall-friction-factor formula.