고속 주축베어링의 볼 접촉각 변동을 고려한 주축 설계공차

이찬홍(Chan Hong Lee) 한국생산제조학회 2010 한국생산제조학회지 Vol.19 No.5

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 of 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 external loads and rotational speed. To analyze internal forces of a bearing under high speed revolution, the ball contact angles 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.

볼 베어링 및 가스 포일 베어링으로 지지되는 소형 고속전동기의 진동 특성

서정화(Jung Hwa Seo),김태호(Tae Ho Kim) 한국트라이볼로지학회 2019 한국트라이볼로지학회지 (Tribol. Lubr.) Vol.35 No.2

High-speed rotating machinery requires low cost and reliable bearing elements with low friction, stable rotordynamic characteristics, and a simple design. This study experimentally evaluates the effects of bearing-support elements on the vibrational characteristics of a small-sized, high-speed permanent magnetic motor. A series of coast down tests from 100 krpm characterize the vibrational behaviors, rotor displacement, and housing acceleration of motors supported by ball bearings, ball bearings with a metal mesh damper, and gas foil bearings, respectively. Two eddy-current sensors installed in the horizontal and vertical directions measure the displacement of the rotor at its front nut, and a 3-axis accelerometer attached to the motor housing measures the housing acceleration. The test results reveal that synchronous (1X) vibration components most significantly affect the rotor displacement and housing acceleration, independent of the bearing-support elements. The motor supported by the deep-groove ball bearings results in the largest rotor vibrations increasing with speed; this is due to the absence of a damping mechanism. Additionally, the metal mesh damper effectively reduces the rotor displacement, housing acceleration, and sound-pressure level in the high-speed region (i.e., above 40 krpm), thus implying its substantial damping performance when installed on the outer race of the ball bearing. Lastly, the gas foil bearing supported motor yields the smallest rotor displacement, housing acceleration, and lowest sound-pressure level because of its hydrodynamic airborne operation, which does not require rolling elements that may cause mechanical friction and vibrations.

베어링 배열방식이 고속 스핀들의 동특성에 미치는 영향

홍성욱(Seong-Wook Hong),최춘석(Chun-Seok Choi),이찬홍(Chan-Hong Lee) Korean Society for Precision Engineering 2013 한국정밀공학회지 Vol.30 No.8

High-speed spindle systems typically employ angular contact ball bearings, which can resist both axial and radial loading, and exhibit high precision and durability. We investigated the effects of the arrangement of the angular contact ball bearings on the dynamics of high-speed spindle systems. The spindle dynamics were studied with a number of spindle-bearing models, and the location of the bearings was varied, along with the rotational speed and the preload. A finite element spindle model and a bearing model were used, and simulated data showed that the bearing arrangement significantly affected the spindle dynamics. Furthermore, the main effects were due to the cross coupling terms between the transverse and rotational motions of the ball bearings. The coupling stiffness terms were found to influence the spindle dynamics, depending on the mode shapes. An extensive discussion is provided on the effects of the bearing arrangement on the dynamics of the spindle.

Simulation of Run-out caused by Imperfection of Ball Bearing for High-speed Spindle Units

Igor Aexeevich Zverev,In-Ung Eun,Won-Jee Chung,Choon-Man Lee 한국정밀공학회 2006 International Journal of Precision Engineering and Vol.7 No.3

For the purpose to improve and to automate designing of high-speed spindle units (SU's), we have developed the mathematical models and software to estimate SU performance characteristics, including the run-out of spindles running on ball bearings. In order to understand better the mechanics of high-speed SUs, the dynamic interaction of ball bearings and SU, and the influence of the bearing imperfections and SU's operational conditions on the run-out, we have carried out computer simulation and experimental studies. Through the study of SU's, we have found out that run-out of SU can vary drastically with variation of rpm. The influences of rotation speed and of accuracy parameters of bearings on the SU accuracy have the greatest importance. The influence of bearing preload has a secondary importance. Comparison of the results of these studies has demonstrated adequacy of the models and software developed to the real SU's.

고속 볼베어링 리테이너 최적화를 위한 원심력 해석

김규복(Kyu Bok Kim),이운주(Woon Ju Lee) 대한기계학회 2017 대한기계학회 춘추학술대회 Vol.2017 No.11

In the case of high-speed ball bearings used for supporting high-speed motors of EV(Electric Vehicle) and HEV(Hybrid Electric Vehicle), high rotational speeds cause large centrifugal forces when the bearings operate. If a large centrifugal force is applied to the retainer, it causes deformation. This causes interference between the retainer and the rolling element, thereby accelerating the heating and wear of the retainer. This is a major cause of reduced fatigue life of high-speed ball bearings. Therefore, in this paper, in order to minimize retainer deformation by centrifugal force, the material and design of the retainer were changed. The deformation by centrifugal force was measured by FEA(Finite Element Analysis) and based on this, we devised optimum design of retainer.

Simulation of Run-out caused by Imperfection of Ball Bearing for High-speed Spindle Units

Zverev Igor Aexeevich,Eun In-Ung,Chung Won-Jee,Lee Choon-Man Korean Society for Precision Engineering 2006 International Journal of Precision Engineering and Vol.7 No.3

For the purpose to improve and to automate designing of high-speed spindle units (SU's), we have developed the mathematical models and software to estimate SU performance characteristics, including the run-out of spindles running on ball bearings. In order to understand better the mechanics of high-speed SUs, the dynamic interaction of ball bearings and SU, and the influence of the bearing imperfections and SU's operational conditions on the run-out, we have carried out computer simulation and experimental studies. Through the study of SU's, we have found out that run-out of SU can vary drastically with variation of rpm. The influences of rotation speed and of accuracy parameters of bearings on the SU accuracy have the greatest importance. The influence of bearing preload has a secondary importance. Comparison of the results of these studies has demonstrated adequacy of the models and software developed to the real SU's.

회전속도에 따른 고속 스핀들의 돌출량 예측에 관한 연구

배규현(Gyu-Hyun Bae),이찬홍(Chan-Hong Lee),황주호(Jooho Hwang),홍성욱(Seong-Wook Hong) Korean Society for Precision Engineering 2012 한국정밀공학회지 Vol.29 No.6

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.

볼 베어링 및 가스 포일 베어링으로 지지되는 고속 전동기의 회전체 관성정지 및 가속 성능 연구

문형욱(HyeongWook Mun),서정화(JungHwa Seo),김태호(TaeHo Kim) 한국트라이볼로지학회 2019 한국윤활학회지(윤활학회지) Vol.35 No.2

This study characterizes the coastdown performances of two small electric motors supported on high-speed ball bearings (BBs) and gas foil bearings (GFBs), and it predicts their acceleration performances. The two motors have identical permanent magnetic rotors and mating stators. However, the shaft of the GFBs has a larger mass and polar/transverse moments of inertia than that of the BBs. Motor coastdown tests demonstrate that the rotor speed decreases linearly with the BBs and nonlinearly with the GFBs. A simple model for the BBs predicts a constant drag torque and linear decay of speed with time. The test data validate the model predictions. For the GFBs, the hydrodynamic lubrication model predictions reveal that the drag torque increases linearly with speed, and the speed decreases exponentially with time. The predictions agree very well with the test data in the speed range of 100–30 krpm. The boundary lubrication model predicts a constant drag torque and linear decay of speed with time. The predictions agree well with the test data below 15 krpm. Mixed lubrication occurs in the speed range of 30–15 krpm. Rotor acceleration performances are predicted based on the characteristics of deceleration performances. The GFBs require more time to reach 100,000 krpm than the BBs because of their larger shaft polar moment of inertia. However, predictions for the assumed identical polar moment of inertia reveal that the GFBs have a nearly identical acceleration performance to that of the BBs with a motor torque greater than 0.03 N·m.

Influence of Structural Parameters and Tolerance on Stiffness of High-Speed Ball Bearings

Zhaohui Yang,Baotong Li,Tianxiang Yu 한국정밀공학회 2016 International Journal of Precision Engineering and Vol.17 No.11

High-speed ball bearings are widely used in aerospace, high-speed machining tool and other complex mechanical systems. And the stiffness is one of most critical parameter of bearings to decide the machine performance. This paper attempts to construct a 5-DOF stiffness matrix based on quasi-dynamic model of high-speed ball bearings to analyze the variation of stiffness with different work condition precisely, and the variation of stiffness with structural parameter and manufacturing errors are calculated for the optimization of tolerance. In this method, the effect of combined loads and lubrication effect are considered, which can achieve high precision analysis of the relationship between contact load and displacement. And then a 5-DOF stiffness matrix can be calculated precisely. The results can be used to optimize the design bearing for improving stiffness.

Analysis of high speed bearing based on virtual rods model

Guang Zeng,Chunjiang Zhao,Xiaokai Yu,Yufeng Yin,Zhigang Xiao,Yijie Feng 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.5

The traditional high-speed ball bearing analysis is based on the quasi-static model proposed by Jones-Harris (J-H). This study gives another bearing analysis model based on the relative position of the ball center and the centers of curvature of the raceway grooves, described by the virtual rods. Specifically, the load and deformation of the virtual rods are determined according to the principle of force transmissibility, the translation theorem of a force, and elastic-contact deformation between steel ball bearings and raceway grooves. And the iterative variables such as the axial, radial and angular deformations are gradually introduced into the calculation model to solve the force and kinematic parameters under pure axial load, bidirectional and tri-directional combined loads. The correctness of the virtual rods model is verified by the contact angle for axial and bidirectional load. The influence of gyroscopic moment and raceway grooves control parameter on the actual contact angle under tridirectional loading conditions are calculated and analyzed respectively. The proposed model uses fewer equations and lower-dimension parameters than those used by the traditional highspeed ball bearing analysis method, improves the solution rate of the equations.