• Tribology and Lubricants
• /
• 제10권1호
• /
• pp.62-68
• /
• 1994

The analysis of statically indeterminate bearing-shaft system was investigated. The moment loads and misalignment angles which were induced in the ball bearings were determined, and the influence of span length of this system on the moment loads and fatigue lives was identified. The sliding and spinning speeds between balls and raceways which affected the performance of ball bearing evaluated. The equation to estimate the cage speed of ball bearing under moment loads was proposed. This equation had been verified by the test results of measuring of cage speed, which was useful to the prediction of ball bearing under moment loads.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 2000년도 춘계학술대회 논문집
• /
• pp.663-667
• /
• 2000

The spindle unit is core parts in high precision machine tools. Diverse static and dynamic charateristics of spindle unit are needed for special purpose of machine tools. Specially, high damping ability may be very useful to high precision and high speed spindle unit. But commercial bearing system has very low damping value and high stiffness. In this paper, the combined bearing system with ball-hydrostatic bearing is suggested for high damping spindle unit. The suggested bearing system has 30% damping ability more than general ball bearing's. The average rotational accuracy of spindle with combined bearing in working speed is 24% better than with ball bearing. The unbalance rotating experiment in spindle show that rotating error with combined bearing is only half value of with ball bearing.

• Tribology and Lubricants
• /
• 제16권1호
• /
• pp.39-45
• /
• 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).

• 한국소음진동공학회논문집
• /
• 제14권9호
• /
• pp.792-800
• /
• 2004

This research investigates the non-repeatable runout (NRRO) of a HDD spindle system at elevated temperature by analyzing the characteristics of a ball bearing and the natural vibration characteristics of a HDD spindle system due to the effect of elevated temperature. It shows that the elevated temperature results in the increase of the contact angle and the decrease of the deformation of the ball bearing in a HDD spindle system. The variation of bearing frequencies, which are dependent on the cosine function of contact angle, is almost negligible at elevated temperature. However, the decrease of bearing deformation at elevated temperature reduces the stiffness of the ball bearing and the natural frequencies of a HDD spindle system consequently. The latter has a significant effect on the amplitude and the frequency distribution of NRRO at elevated temperature.

• Tribology and Lubricants
• /
• 제30권1호
• /
• pp.64-70
• /
• 2014

This paper presents a numerical model for investigating the structural dynamics response of a rigid rotor supported on deep-groove ball bearings. The numerical model was used to investigate the influence of race waviness on the dynamic characteristics of a rotor ball bearing system, which is very important from a design viewpoint. The forth-order Runge-Kutta numerical integration technique was applied to determine the time displacement response, Poincare map, and frequency spectra. The analysis demonstrated that the model can be used as a tool for predicting the nonlinear dynamic behavior of a rotor ball bearing system under different operating conditions. The results of this study may help further understanding of the nonlinear dynamics of a rotor bearing system.

• Tribology and Lubricants
• /
• 제29권4호
• /
• pp.248-254
• /
• 2013

This paper presents a numerical model for investigating the structural dynamic response of an unbalanced rotor system supported on deep groove ball bearings. The aim of this work is to develop a numerical model for investigating the effect of the number of balls on the dynamic characteristics of the rotor ball bearing system. The fourth-order Runge-Kutta numerical integration technique has been applied. The results are presented in the form of time displacement responses and frequency spectra. The analysis demonstrates that the model can be used as a tool for predicting the nonlinear dynamic behavior of the rotor ball bearing system under different operating conditions. Moreover, the study may contribute to a further understanding of the nonlinear dynamics of rotor bearing systems.

• 대한기계학회논문집
• /
• 제18권7호
• /
• pp.1654-1663
• /
• 1994

Even if the ball bearing was conservatively designed considering the dynamic capacity and the rating life, sometimes the bearing was early failed on account of the misalignment and the lubricant contaminations etc. Misalignment was generated when bearing-shaft system transmitted large power and when the bearing was inadequately mounted. It was possible to predict the fatigue life of ball bearing under the misalignment considering the motions of ball, cage and raceway, and the factors of the effect on fatigue life. Misalignment affected on ball bearing as radial and moment load and the relationships between misalignment and moment were obtained. In this paper, the analysis of the load distributions between ball and raceway, and the prediction of fatigue life of deep groove ball bearing under radial and moment loads were carried out. And, the new formulation of equivalent dynamic load considering the effects of moment load was proposed.

• 한국신뢰성학회:학술대회논문집
• /
• 한국신뢰성학회 2004년도 정기학술대회
• /
• pp.335-342
• /
• 2004

The failures such as flaking, wear, crack and seizing caused by the high contact pressure accompanied with sliding motion between inner or outer ring and ball are potential failures of ball bearing. In this research, we have qualitatively selected the efficient test items through the analysis of the life and potential failures of ball bearing. The bearing's failures are related closely to the whole system in using the bearing. So, the bearing itself requires an estimation of life in order to opreate the system safely. We have tested ten ball bearings. Our research has applied both radial and axial direction force of maximum torque conditions simultaneously for the accelerated life testing. The result is established by employing the weibull plot and compared the predicted life of ball bearing to the experimental result.

• 대한기계학회논문집A
• /
• 제26권12호
• /
• pp.2636-2646
• /
• 2002

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modeled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian con tact theory is applied to calculate the elastic deflection and nonlinear contact force while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the nonlinear governing equations of the rotor, which are solved by using the Runge-Kutta-Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e. the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing but also between those of two or more ball bearings constrained by the rotor.

• International Journal of Precision Engineering and Manufacturing
• /
• 제3권2호
• /
• pp.61-71
• /
• 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.