In this work, we study the implementation of magnetorheological fluid (MRF) to the semi‐active suspension. Owing to the nonlinear hysteretic phenomenon, the analysis and synthesis of a controller are not trivial. The kinematic energy and spring potential function of the suspension system plus an integral term of the hysteretic component of an MR damper is chosen as the Lyaupnov function to verify the stability and dissipativity of the system. Then, a multi‐level controller, which is constructed in virtue of stability analysis, turns out to be effective in vibration suppression. Through numerical examples, the controller is shown to be robust. In addition, the controller algorithm is simple and easy to implement, requiring only the measurements of relative displacement and velocity between sprung and unsprung masses, along with the damping force of the MR damper.
It is very common for aircraft engines to have dual rotor or even triple rotor designs. Due to the complexity of having multiple rotor design, the transfer matrix methods have used in the past to deal with multiple rotor-bearing systems. However, due to transfer matrix method’s assumptions, sometimes resulted in numerical stability problems or root-missing problems. The purpose of this paper is to develop a systematic theoretical analysis of the dynamic characteristics of turbomachinery dual rotor-bearing systems. This dual rotor-bearing system analysis will start with a finite element (FEM) rotor-bearing system dynamic model, then using different methods to verify the analysis results including critical speed map and bearing stiffness. In an inertia coordinate system, a general model of continuous dual rotor-bearing systems is established based on a lagrangian formulation. Gyroscopic moment, rotary inertia, bending and shear deformations have been included in the model. From a point of view of the systematic approach, a solution of the finite element method is used to calculate the critical speeds by several different methods, which in turn can help to verify this dual rotor-bearing system approach. The effects of the speed ratio of dual rotors on the critical speed will be studied, which in turn can be used as one of the dual rotor design parameters. Also, both critical speeds are in effect functions of dual rotor speeds. Finally, the bearing stiffness between high speed and low speed shafts not only affect the critical speeds of the dual rotor system, but also affect the mode shapes of the system. Therefore, the bearing stiffness in between is of even greater importance in turbomachinery dual rotor or multiple rotor design.
A microturbine of 12-pound thrust was developed for the Unmanned Aerial Vehicle (UAV) applications. Recent tests of the microturbines reveal problems associated with rear ball bearing integrity after extended run times. The microturbine rotor design originally calls for a critical speed margin of at least 15∼20% to prevent excessive vibrations. However, the microturbine was using an existing turbocharger rotor component with unknown margins. Therefore, the purpose of this paper is to perform both theoretical and experimental analyses of the dynamic characteristics of the 12-pound thrust microturbine rotor-bearing system. This rotor-bearing system analyses will start with a finite element (FEM) rotor-bearing system dynamic model, then using modal testing and dynamic engine test to verify the analysis results including critical speed map and bearing stiffness. In this paper, the rotor-bearing system dynamic model will be established under an inertia coordinate system. Through finite element method, this model can be used to predict natural frequencies, critical speed map, and bearing stiffness. Also, under free-free condition, a modal testing will be performed, and its results are used to compare with the FEM model. Then the gyroscopic moment effects are included in the FEM model to calculate the critical speed map. Finally the critical speed map is used to compare with the results of the dynamic experiments of the 12-pound thrust microturbine engine and the bearing stiffness is estimated through an optimization approach. Examination of the microturbine engine and recent product developments indicate that thrust performance and engine life goals can be improved to upgrade the present design. With the rotor-bearing system analysis, the goal of increasing the current engine life and improved performance is sought as a practical goal for the microturbine design.
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