• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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• pp.61-71
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• 2002

This paper presents the dynamic analysis of indeterminate rotor systems with angular contact ball bearings subject to axial and radial loads. The reaction forces against applied radial loads significantly influence the dynamic characteristics of angular contact ball bearings. However, the reaction forces are hard to determine in the case of indeterminate rotor-bearing systems. To this end, this paper proposes a finite element model for indeterminate rotor systems with angular contact ball bearings. An improved bearing model is adopted which is originated from the Harris's bearing dynamic model. The bearing model is also extended to include centrifugal forces due to the ball and inner ring. This paper utilizes a new iterative algorithm for general, indeterminate rotor systems with angular contact ball bearings. This examples are provided to illustrate the dynamic characteristics of rotor systems with angular contact ball bearings subject to axial and radial loads. The experimental and numerical results prove that the proposed method is useful for the dynamic analysis of indeterminate rotor systems with angular contact ball bearings.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.389-392
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• 1997

This paper presents the dynamic analysis and experiment for rotor systems supported by angular contact ball bearings subjected to axial displacement preload. A dynamic software, which has been developed by the authors for the analysis of rotor systems supported by angular contact ball bearings, is used to simulate a uniform shaft system supported by two angular contact ball bearings with the axial displacement preload varied. Experiments are also performed to validate the simulation. An experimental system is constructed which consists of a uniform shaft, two bearings and a device for adjusting the axial displacement preload. Through a series of simulation and experiment, the dynamic characteristics of rotor systems with angular contact ball bearings subject to axial displacement preload are investigated.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.4
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• pp.368-373
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• 2014

This paper presents the dynamic modeling and analysis results for a spindle supported by angular contact ball bearings (ACBBs) subjected to angular misalignment. Although ACBBs are widely used in spindle systems, their characteristics in regard to angular misalignment have rarely been investigated. A simulation program was developed to calculate the dynamic characteristics of a simple spindle model that is supported by angular contact ball bearings subjected to angular misalignment. Angular misalignment is shown to introduce anisotropy into the angular contact ball bearings and then split the natural frequencies in spindles. Simulations were also performed to show the possibility of evaluating bearing misalignment using natural frequency measurements.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.247-250
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• 2000

This paper presents the dynamic analysis and experiment for a shaft system supported by angular contact ball bearings. Among others, the dynamic characteristics of bearings are significantly affected by axial preload and radial load applied. This paper rigorously analyzes the dynamic characteristics of a shaft system with angular contact ball bearings subject of axial preload so as to result in eigenvalues as well as bearing stiffness characteristics. Experiments are also performed to identify natural frequencies and stiffness characteristics of bearings implemented. Comparison is made on the theoretical and experimental results.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.5
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• pp.609-615
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• 2010

Angular contact ball bearings in a high speed spindles are under the extreme conditions, such as high temperature, big centrifugal force and thrust cutting forces. So, the assembly contacts between spindle shaft and inner ring bearings, bearing housing and outer ring of bearings are occasionally unstable at high speed revolution. Furthermore, the ball contact angle of a bearing, which influence stiffness and lifetime of bearings, are changed according to loads and rotational speed. To analyze internal forces of a bearing under high speed revolution, the ball contact are calculated using nonlinear equations in consideration of rotational speed, thrust loads and raceway form. Diameter increase of inner and outer ring by influence factors, such as internal forces to inner and outer ring, centrifugal force and temperature of inner and outer rings are calculated to establish stable state in bearing assembly in high speed spindle. Finally, contribution ratio of influence factor to assembly design tolerance of inner and outer rings are shown and the stable assembly design tolerance are proposed.

• KSTLE International Journal
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• v.1 no.1
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• pp.63-68
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• 2000

Angular contact ball bearings are mainly used in the spindle, which requires high speed and stiffness. The heat generation is studied by experiments and simulations using a pair of angular contact ball bearings. The temperature variation of inner and outer races and the temperature increment distribution are measured by using thermocouples for the rotational speed, preload, viscosity of lubricant. The measured values from experiments are used to estimate the heat conduction rate. The method of oil-air lubrication is used for the experiment. The amount of conduction heat transfer to the test spindle and the convection heat transfer coefficients long the spindle are computed by using inverse method with temperature increment distribution. Total heat generation rate is estimated with the heat partition rate which is calculated from temperatures of inner and outer races. In addition, the empirical factor of oil-air lubrication method for Palmgren's heat generation model is suggested. The empirical friction coefficients, which are obtained from the experiments, depend on the preload condition, and can give us more accurate estimation of the heat generation in ball bearings.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2013.05a
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• pp.545-546
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• 2013

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.4
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• pp.740-746
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• 2013

Angular contact ball bearings are often adopted for a high-speed spindle owing to their durability against axial and radial loads. The dynamic characteristics of an angular contact ball bearing, however, are very complicated because they are dependent on the applied loads as well as on the system configuration. This study systematically analyzes the radial-load-dependent characteristics of spindles as well as angular contact ball bearings. Toward this end, a spindle dynamic model along with the bearing dynamics model is established. An iterative solution algorithm is implemented to resolve the statically indeterminate problem associated with spindle-bearing systems subjected to radial load. Two numerical examples are provided to investigate the spindle and bearing characteristics as a function of radial load with regard to the system configuration.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.11a
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• pp.523-524
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• 2010

• Journal of the Korean Society for Precision Engineering
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• v.29 no.6
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• pp.671-679
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• 2012

This paper presents an estimation procedure for axial displacement in spindle equipped with angular contact ball bearings due to rotational speed. High-speed spindle-bearing system experiences axial displacement due to thermal expansion and rotational speed-dependent characteristics of angular contact ball bearings. This paper deals with the axial displacement caused by the rotational speed-dependent effects such as centrifugal force and gyroscopic moments. To this end, a bearing dynamic model is established that includes all the static and dynamic properties of angular contact ball bearing. An analytical formula to calculate the axial displacement based on contact angles between ball and races is derived to discuss the physics regarding the axial displacement in spindle. The proposed dynamic model is compared with a reference and a commercial program. Numerical examples are presented to show the effects of centrifugal force and gyroscopic moment on the axial displacement. The proposed model is also validated with an experimental result.