Original Article Stability analysis of a rigid rotor supported by two-lobe hydrodynamic journal bearings operating with a non-Newtonian lubricant Saurabh K Yadav 1 , Arvind K Rajput 2 , Nathi Ram 3 and Satish C Sharma 4 Abstract In the present work, an investigation has been performed on a rigid rotor supported by two-lobe journal bearings operating with a non-Newtonian lubricant. The governing Reynolds equation for pressure field is solved by using non- linear finite element method. Further to study the dynamic stability of the bearing system, governing equation of motion for the rotor position is solved by fourth order Runge–Kutta method. Bifurcation and Poincare ´ maps of two-lobe bearings are presented for different values of the non-Newtonian parameter and bearing ellipticity ratio. The numerical results illustrate that the ellipticity of a bearing with a dilatant lubricant improve the stability of the rotordynamic system. Keywords Rotordynamic stability, bifurcation diagram, vibration, offset ratio, non-Newtonian lubricant Date received: 12 April 2018; accepted: 19 September 2018 Introduction The performance of a rotating machine mainly depends upon the performance of the bearing system. Hydrodynamic journal bearings are widely used in dif- ferent rotatory machineries in industries due to its inherent characteristics to avoid direct metal-to-metal contact and support heavy load in rotating machines with lesser friction. Hydrodynamic journal bearings not only support heavy load but also provide high value of stiffness and damping coefficient to rotor system. Damping and stiffness of these bearings mainly depend on the fluid film profile of the bearing and behavior of the lubricant. Damping and stiffness coefficients of the bearing play a key role in the dynamic response of a rotor. Therefore, it is necessary to investigate the dynamic performance of the bearing and its influence on the behavior of a machine. Generally, rotor bearing systems experience unba- lanced harmonic force due to eccentricity, unbalance mass, misalignment of rotational masses and manu- facturing errors. Such repeating harmonic forces result in chaotic motion of journal and make the machine unsafe and unstable. Hence, it becomes obvi- ous to investigate the dynamic behavior of machine under such conditions. In the past, various studies 1–4 have been conducted to analyze the dynamic response of the bearing. Adileta et al. 1 presented the effect of bearing condi- tions that gives rise to chaotic motion in a bearing. They theoretically analyzed the chaotic motion by using the numerical integration of equation of motion. Bifurcation plot were presented to visually analyze the dynamic behavior of a bearing for the applied condition. 2,3 They performed a number of numerical trials to find the system’s chaotic responses. They also compared the theoretical results with the experimental data. Wang and Chen 4 performed the study on the dynamic analysis of a rotor bearing 1 Department of Mechanical Engineering, Institute of Infrastructure, Technology, Research and Management (IITRAM), Gujarat, India 2 Department of Mechanical Engineering, Shiv Nadar University, Greater Noida, India 3 Department of Mechanical and Automation Engineering, IGDTUW, New Delhi, India 4 Mechanical and Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee, India Corresponding author: Saurabh K Yadav, Department of Mechanical Engineering, Institute of Infrastructure, Technology, Research and Management (IITRAM), Gujarat, India. Email: saurabhme.iitr@gmail.com Proc IMechE Part J: J Engineering Tribology 0(0) 1–15 ! IMechE 2018 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1350650118806377 journals.sagepub.com/home/pij