• Tribology and Lubricants
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• 제16권1호
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• pp.39-45
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• 2000

In this paper, the effects of shaft and bearing flexibilities are investigated for the accurate modeling of a shaft-bearing system supported by ball bearings. Generally, rolling bearings are modeled by simple rigid pin-joint in the mechanical design. However, they can no longer be modeled by ideal boundary conditions in the advanced applications because the rigid pin-joint model cannot satisfy the current trends of mechanical design decreasing mass and reducing volume. Consequently the flexible support model of ball bearing is investigated using the static analysis module developed by A .B. Jones and T. A. Harris. A simple two-bearing system, supported by two deep groove ball bearings and radially loaded on the shaft midway between the bearings, is utilized to validate the coupled model of shaft-bearing system. Numerical computations using the model indicate that the shaft span length, locating/floating bearing arrangements and applied bearing size are significant factors in determining the mechanical behaviors. The flexible support model of ball bearing can be escaped to over-estimate in the bearing fatigue life. The proposed simple design formulation obtained by numerical simulations can approximately predict a rate of bearing life reduction as a function of shaft span length/shaft diameter (L/d).

• Journal of Mechanical Science and Technology
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• 제15권2호
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• pp.152-159
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• 2001

In this paper it is intended to set-up a sound model of the 60,000rpm 100kW prototype APU gas turbine rotor-bearing system, and particularly to investigate the influences of the tie shaft on the rotordynamic characteristics of the entire APU gas turbine rotor-bearing system, employing the dual shaft model. Firstly, a mock-up APU rotor has been constructed to test and verify the model. Analytical natural frequency results have agreed with the corresponding modal test ones to within 5% difference. Then, the rotordynamic characteristics of the prototype APU rotorbearing system have been investigated. Natural vibration and unbalance response analyses results have shown that the inner tie shaft resonance can cause high enough vibration of the outer main rotor shaft. This could be a concern as the rotor journals operate on very thin air film at high speed. It is concluded as a conservative design practice that the inner tie shaft should be explicitly modeled in the rotordynamic analysis of the APU rotor-bearing system.

• Design & Manufacturing
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• 제6권1호
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• pp.45-51
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• 2012

The main goal of this paper is to establish an interference tolerance for determining optimal amount of clearance in the shaft-bearing system supported by radial ball bearings. The 2-D frictional contact model was employed for the FE analysis between the shaft and the inner raceway. Several examples were simulated using different material properties for the solid shaft. Efforts were focused on the deformation applied in the radial direction to select suitable bearings. The analysis results showed that the initial axial preload applied on the bearings plays a significant role to reduce bearing fatigue life. The proposed design parameters obtained by numerical simulations can approximately predict a rate of bearing life reduction as a function of shaft diameter ratio. This analysis can also be used to calculate the optimal initial radial clearance in order to obtain a shaft-bearing system design for high accuracy and long life.

• 한국기계가공학회지
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• 제18권6호
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• pp.19-25
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• 2019

We have developed a tool that uses finite element analysis (FEA) to rapidly evaluate a shaft-bearing system of machine tools. We extracted commercial data on suitable clamping units and defined the inner profile of the shaft to avoid needing direct user input to define the profile. We use a splitting algorithm to convert the shaft into beam elements with two diameters and length. To validate the tool, we used it to design and evaluate a shaft-bearing system and found that our tool automated the construction of an FE system model in a commercial FEA package as well as the static stiffness evaluation; both tasks were completed in seconds, demonstrating a significant reduction from the minutes normally required to complete these tasks manually.

• Tribology and Lubricants
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• 제11권5호
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• pp.162-171
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• 1995

The application of reciprocating engine crankshaft bearings is of particular importance and interest among the plain bearing, not only because the sheer volume of intemal combustion engines now produced, but because the severe operating conditions they are subjected to. Demands for better performances of crankshaft bearings have provide an important impetus in the development of bearings and bearing materials. As engine design progresses toward higher outpt and higher efficiency, crankshaft bearings must perform under more seveve operating conditions. Higher load, temperature, and speed as well as lower viscosity oil are applied to the bearing sysem, resulting in a smaller minimum oil film thickness. This means more solid-solid contact between the shaft and bearing, and the bearing is exposed to more danger of seizure. Some engines may experience bearing seizure problems. However, understanding about the seizure behavior and mechanism is far from being enough. Seizure resistance of a bearing-shaft system will be affected by the properties of the shaft and bearing, especially their materials and surface texture. Commonly used engine bearing materials include Al-Pb-Si, Al-Sn-Si, Al-Sn, and Cu-Pb with Pb-Sn-Cu overlay. These materials have very different properties. They showed different behaviors dering seizure tests and seizure may occur with different mechanism for different bearing material. Shaft materials also affect the seizure resistance of the system. Surface texture of the bearing and shaft have apparent effects on the lubrication and solid-solid contact pattern, and therefore will affect the seizure behavior of the system. Bearings and shafts which are made of different materials and have different surface textures have been tested and analyzed. Their effects on seizure resistance are discussed and possible seizure mechanisms for different beatings are presented in this paper.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.1051-1057
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• 2000

A projected 100 kW APU gas turbine rotor-bearing system has a main outer shaft, which is composed of some numbers of segmented sections for manufacturing and assembly conveniences. For a secure assembly of the segmented sections a tie shaft or inner shaft is installed inside of the outer shaft and a tensional axial preload of 50,000 N is provided to it. In this paper it is intended to set-up a sound modeling method of the APU rotor system, and particularly, the influences of the tie shaft on the rotordynamic characteristics of the entire APU gas turbine rotor-bearing system are investigated. Analysis results show that as a conservative design practice the inner tie shaft should be actively modeled in the rotordynamic analysis of the APU rotor-bearing system, and its effects on the dynamic behaviors of the outer shaft should be thoroughly design-reviewed.

• Journal of Mechanical Science and Technology
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• 제20권12호
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• pp.2105-2114
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• 2006

In this paper, a simplified model is studied to predict analytically the vibration from the helical gear system due to an axial excitation of helical gears. The simplified model describes gear, shaft, bearing, and housing. In order to obtain the axial force of helical gears, the mesh stiffness is calculated in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer matrices for the rod and bearing are used, using a spectral method with four pole parameters. The model is validated by finite element analysis. Using the model, parameter studies are carried out. As a result, the linearized dynamic shaft force due to the gear excitation in the frequency domain was proposed. Out-of-plan displacement from the forced vibrating circular plate and the renewed mode normalization constant of the circular plate were also proposed. In order to control the axial vibration of the helical gear system, the plate was more important than the shaft and the bearing. Finally, the effect of the dominant design parameters for the gear system can be investigated by this model.

• 한국소음진동공학회논문집
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• 제13권8호
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• pp.598-604
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• 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 Advanced Marine Engineering and Technology
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• 제33권1호
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• pp.28-36
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• 2009

In this paper, based on the measured data of hull deflection, an approximated hull deflection curve is drawn using reverse analyzed hull deflection data and the estimation method for flexibility analysis of shaft alignment is proposed by use of the approximate hull deflection curve. Generally an offset value of after stern tube bearing is a datum point with an fore stern tube bearing however the shaft alignment has a tendency which is able to get higher flexibility if the shafting system has the deflection value from after stern tube bearing as reference to bottom direction according to results of on this study. By applying this result of study, the shaft alignment for next similar ships will be able to estimate how to follow the hull deflection and how to be influenced by hull deflection at shaft alignment analysis state using the approximated hull deflection curve.

• 소음진동
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• 제8권3호
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• pp.450-456
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• 1998

A rotordynamic analysis is performed with a centrifuge rotor-bearing system for the raing speed of 100,000 rpm. The system is composed of a centrifuge rotor(or simply the rotor), flexible shaft, motor rotor and shaft, and two support rolling element bearings of the motor shaft. Design goals are to achieve wide separation margins of critical speeds and favorable unbalance responses of the rotor at the associated critical speeds. The latter requirements are especially important as the system crosses multiple numbers of critical speeds and as the system may not have enough separaton margins around the rating speed. As the system adopts an extra-flexible shaft, it is shown that the rotor has satisfactory small unbalance responses over higher criticals while having an unsatisfactory large one at the first critical. To supress this a bumper ring or guide bearing needs to be installed at a suitable location of the flexible shaft. It is also shown that even with the flexible shaft the dynamics of the motor must be incoporated into the full system model to accurately identify the fourth critical speed, which is close to the rating speed, and higher ones. The analysis is based on the finite element method.