International Journal of Non-Linear Mechanics 41 (2006) 949 – 957 www.elsevier.com/locate/nlm Improvement of rotor performance under rubbing conditions through active auxiliary bearings Jun Jiang a , ∗ , Heinz Ulbrich b , Alvaro Chavez b a MOE Key Laboratory of Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, China b Institute of Applied Mechanics, Technical University of Munich, 85748 Garching, Germany Received 21 April 2005; received in revised form 4 June 2006; accepted 28 August 2006 Abstract This paper develops a new concept to enhance the adaptive capability of rotating machinery to the rubbing conditions through active auxiliary bearings. To demonstrate the feasibility of this idea, a model with a Jeffcott rotor and an active auxiliary bearing, which accounts for both the dynamics of the auxiliary bearing and the deformation on the contact surface, is investigated. The dynamics and the stability of the non- linear piecewise-smooth passive rotor/stator (auxiliary bearing) system are first studied. Then, two control approaches are proposed with the aim to reduce the rubbing severity during the rotor/stator rubbing. It is shown that by using an optimal controller, the harmful heavy rubbing between the rotor and the stator can be well stabilized to the mild light rub through the active auxiliary bearing, and the already established rotor-to-stator rubbing can even be released by using PD-controllers.  2006 Elsevier Ltd. All rights reserved. Keywords: Rotor/stator rubbing; Stability analysis; Active control; Active auxiliary bearings 1. Introduction Rotor-to-stator rub is a serious malfunction in the operation of a rotating machine, which can seriously degrade the machine performance and can even lead to a complete failure of the machine. Rotor-to-stator rubs may occur under the changing operation environments, i.e., the loss of blade or subjected to an extreme outside excitation etc. In order to make a deep insight into the dynamical behavior of the rotor-to-stator rubbing and to find the relationship between different rubbing responses and the system parameters, a large number of researchers devoted to the investigation of rub-related dynamical phenomena of the rotor/stator systems, partly as summarized in [1]. Through the studies various rubbing responses of rotor/stator systems are revealed, i.e., synchronous full annular rubs [2–4], sub- and super-harmonic motions [5,6], quasi-periodic partial rubs [7,8], chaotic responses [9,10] and destructive dry friction backward whirl [2,11,12]. In the literature two rotor/stator models are ∗ Corresponding author. Tel.: +86 29 82669089; fax: +86 29 82669093. E-mail address: jun.jiang@mail.xjtu.edu.cn (J. Jiang). 0020-7462/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijnonlinmec.2006.08.004 most often used in the study of the rub-related phenomena. The first model is the rotor/stator system with the stator being mod- eled as an added stiffness. This model physically describes the rotor in contact with a non-rotating susceptible circumferential stator or a mechanical seal. The second rotor/stator model takes into account the dynamics of the stator and depicts the stator as an elastically supported ring with some mass. This model is also widely used in modeling retainer bearings. When the sta- tor (ring) is considered to be rigid, some analytical results on the synchronous full annular rubs and dry friction backward whirl are available [2,11]. When the stator is taken as an elastic ring, that is, there would be some penetration between the rotor and the stator during they fall into contact, theoretical analy- sis was thought to be impossible and numerical methods were usually employed to exploit the rubbing responses [13–15]. In this paper the stability analysis of the synchronous full annular rub solution of this model will be carried out after successfully deriving the explicit form of the solution. The procedure and the results of the stability analysis on the synchronous full an- nular rubs will serve as a basis for the design of controllers to suppress the rubbing severity in the rotor/stator system with piecewise-smooth non-linearity.