Nonlinear stability analysis and numerical continuation of bifurcations of a rotor supported by floating ring bearings

Floating ring bearings have been widely used, over the last decades, in rotors of automotive turbochargers because of their improved damping behavior and their good emergency-operating capabilities. They also offer a cost-effective design and have good assembly properties. Nevertheless, rotors with floating ring bearings show vibration effects of nonlinear nature induced by self-excited oscillations originating from the bearing oil films (oil whirl/whip phenomena) and may exhibit various nonlinear vibration effects which may cause damage to the rotor. In order to investigate these dynamic phenomena, this paper has developed a nonlinear model of a perfectly balanced rigid rotor supported by two identical floating ring bearings with consideration of their vibration behavior mainly governed by fluid dynamics. The dimensionless hydrodynamic forces of floating ring bearings have been derived based on the short bearing theory and the half Sommerfeld solution. Using the numerical continuation approach, different bifurcations are detected when a control parameter, the journal speed, is varied. Depending on the system’s physical parameters, the rotor can show stable or unstable limit cycles which themselves may collapse beyond a certain rotor speed to exhibit a fold bifurcation. Bifurcation analysis is performed to investigate the occurring instabilities and nonlinear phenomena. Such results explain the instabilities characteristics of the floating ring bearing in high-speed applications. It has also been found that the selection of the bearing modulus plays an important role in the characterization of the rotor stability threshold speed and bifurcation sequences. An understanding of the system’s nonlinear behavior serves as the basis for new and rational criteria for the design and the safe operation of rotating machines.

Steady-state and nonlinear stability analysis for the feasibility of different fluids in a supercritical natural circulation loop

A numerical model for a supercritical natural circulation loop is developed to examine the flow instabilities by nonlinear stability analysis. The supercritical natural circulation loop is a loop geometry, which is driven by natural circulation with supercritical fluids as a coolant. A mathematical formulation is developed to study the steady-state and transient solution procedure for supercritical natural circulation loop. This mathematical model is then used to perform various parametric studies with different supercritical fluids (water, [Formula: see text], R134a, ammonia, R22, propane, and isobutane). The behavior of all the fluids is analyzed on identical geometrical and operating conditions. A comprehensive numerical study of the nonlinear stability analysis is presented with particular emphasis on the feasibility of various fluids in a natural circulation loop environment. The 50% increment in loop diameter and height increased the stable operating zones and shifted the marginal stability boundary upward respectively by approximately three times and 25–40% of the previous value. However, further increase in diameter and height reduces the increment of stable operating zones; hence the marginal stability boundary shifts upward marginally than the previous value. Furthermore, the marginal stability boundaries are generated to identify the stable and unstable zones for the available geometrical and operating conditions.

Influence of the Motion of a Spring Pendulum on Energy-Harvesting Devices

Energy harvesting is becoming more and more essential in the mechanical vibration application of many devices. Appropriate devices can convert the vibrations into electrical energy, which can be used as a power supply instead of ordinary ones. This study investigated a dynamical system that correlates with two devices, namely a piezoelectric device and an electromagnetic one, to produce two novel models. These devices are connected to a nonlinear damping spring pendulum with two degrees of freedom. The damping spring pendulum is supported by a point moving in a circular orbit. Lagrange’s equations of the second kind were utilized to obtain the equations of motion. The asymptotic solutions of these equations were acquired up to the third approximation using the approach of multiple scales. The comparison between the approximate and the numerical solutions reveals high consistency between them. The steady-state solutions were investigated, and their stabilities were checked. The influences of excitation amplitudes, damping coefficients, and the different frequencies on energy-harvesting device outputs are examined and discussed. Finally, the nonlinear stability analysis of the modulation equations is discussed through the stability and instability ranges of the frequency response curves. The work is significant due to its real-life applications, such as a power supply of sensors, charging electronic devices, and medical applications.