Journal of Sound and < ibration (2000) 238(5), 757}779 doi:10.1006/jsvi.1999.3108, available online at http://www.idealibrary.com on DYNAMIC RESPONSE OF AN UNBALANCED ROTOR SUPPORTED ON BALL BEARINGS M. TIWARI AND K. GUPTA Mechanical Engineering Department, Indian Institute of ¹ echnology, Delhi, New Delhi-110016, India AND O. PRAKASH Industrial ¹ribology Machine Dynamics and Maintenance Engineering Center, Indian Institute of ¹ echnology, Delhi, New Delhi-110016, India (Received 10 February 1999, and in ,nal form 6 July 1999) The non-linear dynamic analysis of a horizontal rigid rotor having unbalance and supported on ball bearings has been done. The non-linearity is both due to Hertzian contact and the radial internal clearance. The system is excited by the varying compliance frequency and the rotational frequency. For "nding out the "xed point and stability of the system the concept of higher order Poincare map and interpolation technique has been applied. The results show the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The experimental investigations for a horizontal rotor-bearing system have shown the e!ect of varying compliance and increase in non-linearity due to radial internal clearance of the ball bearing. The orbit plots, cascade plots and frequency plots bring out the e!ect of radial internal clearance on the rotor response.  2000 Academic Press 1. INTRODUCTION Unbalance force in a rotor is an unavoidable e!ect. Howsoever good the balancing may be for a rotor the unbalance force cannot be completely eliminated. For a horizontal Je!cott rotor supported on ball bearings the exciting frequencies are because of the unbalance force and the varying compliance e!ect. The combined e!ect of unbalance and varying compliance has not been considered by Fukata [1], Mevel and Guyader [2] and Sankaravelu [3]; in these works only the varying compliance e!ect is considered. The inclusion of the unbalance force makes the system biperiodically excited. The studies undertaken by Day [4], Kim and Noah [5, 6] have considered the e!ect of unbalance force only, but not varying compliance e!ect. Also, in references [4}6] the bearing is considered to have only clearance non-linearity. In the present analysis, all the three e!ects, i.e., the unbalance, the varying compliance and the clearance are studied in addition to non-linearity due to Hertzian contact. The theoretical results show the appearance of instability and chaos through a route of period doubling and intermittency. The experimental results show the e!ect of radial clearance on the dynamic response of the ball bearing. The non-linearity of the ball-bearing support results in the appearance of subharmonics and sum and di!erence combination of rotational and varying compliance frequencies. 0022-460X/00/500757#23 $35.00/0  2000 Academic Press