Some characteristic parameters affecting the natural frequency of a rotating shaft supported by defect-free ball bearings

Abstract

It is now well known that the preload and number of rolling elements of an angular contact ball bearing are two important parameters that affect the bearing-induced vibration of a shaft-bearing assembly. Increasing the preload changes the steady state position of the vibration on the non-linear contact-force relation of the bearing, resulting in the shaft mass being supported on stiffer springs. A larger number of rolling elements causes a similar stiffer equivalent spring. The ball set position is another parameter that affects the vibration of the system. These effects have been investigated by different researchers with simulation programs, and their ndings are also supported by the experimental evidence of other researchers. In this paper, therefore, a new analytical investigation into the effects of preload, the number of rolling elements and ball set position is made. Analytical results are found to be in good agreement with simulation results.

Time-Varying Total Stiffness Matrix of a Rigid Machine Spindle-Angular Contact Ball Bearings Assembly: Theory and Analytical/Experimental Verifications

“…The works [1][2][3][4][5][6][7][8][9]15,[17][18][19][21][22][23][24][25][26][27][28][29][30][32][33][34][35][36][38][39][40][41][42][43][44]48,[50][51][52] use summation over the bearing rolling elements in contact to compute bearing total loads. Houpert [10,11] replaced this summation by integration using Sjovall's [12] axial and radial load distribution integrals (J a , J r ).…”

“…Analytical calculation of natural frequencies of a rigid shaft-angular contact ball bearings taking into account the bearing nonlinear stiffness is a complex task and this made different researchers use simple models to estimate frequencies [16][17][18][19][20]. Aini et al [16] experimentally and analytically studied vibrations of a horizontal rigid grinding spindle-angular contact ball bearing system.…”

“…They compared the analytical results with experimental ones. Akturk [17,18] modeled a rigid shaft supported on two angular contact ball bearings using three-DOFs (two lateral, one axial). He linearized stiffness coefficient in the vertical direction around a constant deflection (= axial preload deflection) (no stiffness cross coupling coefficients).…”

In-process modal parameter identification for spindle health monitoring

“…However, dynamics captured on a stationary spindle may not adequately represent the rotating nature of the spindle, since its modal parameters (e.g., natural frequency) may be affected by the actual operating conditions. For example, the natural frequency of a spindle was found to fluctuate with shaft speed and bearing preload [7]. Also, stiffer spring characteristics due to a higher axial bearing preload have been found to result in higher natural frequencies [8].…”

Non-linear vibration signature analysis of a high-speed rotating shaft due to ball size variations and varying number of balls

“…They found that the vibration characteristics of the shaft and its bearings change when the bearings operate in different regions of their non-linear load-deflection characteristics. Aktürk [14] has studied some characteristic parameters affecting the natural frequency of a rotating shaft supported by defect-free ball bearings. The conclusion of this work shows that large values of axial preload cause stiffer spring characteristics and result in higher natural frequency values.…”