Journal of Sound and < ibration (2000) 238(5), 723}756 doi:10.1006/jsvi.1999.3109, available online at http://www.idealibrary.com on EFFECT OF RADIAL INTERNAL CLEARANCE OF A BALL BEARING ON THE DYNAMICS OF A BALANCED HORIZONTAL ROTOR M. TIWARI AND K. GUPTA Mechanical Engineering Department, Indian Institute of ¹ echnology, Delhi, New Delhi 110016, India. E-mail: tiwari.5@osu.edu O. PRAKASH Industrial ¹ribology Machine Dynamics and Maintenance Engineering Center, Indian Institute of ¹ echnology, Delhi, New Delhi 110016, India (Received 30 November 1998, and in ,nal form 30 June 1999) The response of a balanced horizontal rigid motor rotor supported by a deep groove ball bearing is theoretically simulated. The e!ect of radial internal clearance of the ball bearing on the dynamic response of the rotor is studied. The system equations have been numerically integrated, the results of which have been validated with harmonic balance alternating frequency time domain method. Variation of radial internal clearance shifts the peak response as the speed is changed over a range. The results of a parametric study done by taking radial internal clearance have resulted in the observation of a third region of instability which has not been reported in literature. The appearance of regions of periodic, subharmonic and chaotic behavior is seen to be strongly dependent on the radial internal clearance. The system response is analyzed for stability and nature with the help of Floquets method for stability analysis and generation of higher order Poincare maps. The bearing sti!ness is estimated experimentally and the e!ect of variation in radial internal clearance on the bearing sti!ness is studied.  2000 Academic Press 1. INTRODUCTION The study of the dynamic response of a perfectly rigid and balanced, horizontal rotor supported by ball bearings is essentially a study of a non-linear system. The non-linearity is because of the radial internal clearance and the Hertzian contact between the races and the balls; there is also a parametric e!ect because of the varying compliance of the bearing. The varying compliance e!ect was studied theoretically by Perret [1] considering a deep groove ball bearing with the elastic deformation between race and balls modelled by the Hertzian theory and no bending of races. Perret [1] studied the bearing at the instant when the balls are arranged symmetrically around the load line, i.e., with either a ball or a ball gap directly under the load. In the intermediate cage position, however, the balls are non-symmetrically arranged which means that when loaded vertically, the center of the inner ring will undergo a horizontal as well as vertical displacement. Meldau [2] studied theoretically the two-dimensional motion of shaft center. Both Perret [1] and Meldau [2] performed a quasi-static analysis since inertia and damping force were not taken into account. 0022-460X/00/500723#34 $35.00/0  2000 Academic Press