Vibration Analysis and Identification of Faults in a Spur Geared Rotor System Integrated with Active Magnetic Bearings
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Gearbox is widely used in industrial, transportation and military applications. The gearbox vibrations and noise caused by variation of contact forces often causes failure in the components of gearbox, which are then transmitted to the surrounding structures. The sources of error between the mating gears while in the operation are the gear mesh deformation, transmission error, and runout; resulting in dynamic forces, excessive vibration, and noise. To avoid any undesirable effect on the gear-pair and other supporting structures, it is essential to investigate these forced vibrations in time and frequency domain. The concept of active control of gearbox vibrations with piezoelectric actuators at mounting points of the gearbox is analysed earlier in several studies, then with certain limitations. The aim of this work is to investigate the feasibility of active vibration control with Active Magnetic Bearings (AMBs), being applied for supressing the transverse vibrations in a geared rotor system against transmission error excitations at the gear mesh. The AMBs are capable of suppressing the vibration of the system (transients as well as steady-state) by controlled electromagnetic forces considering the rotor vibrational displacement with a closed loop feedback system. A concept of active vibration control by Active Magnetic Bearings (AMBs) on the shaft of a spur gearbox has been introduced having conventional bearings as well. The AMB suppresses the response of the system by generating controlled electromagnetic forces based on the gear shaft vibration measurement. The AMB force is applied in two mutual perpendicular directions without any physical contact as opposed to mechanical forces in conventional bearings. Hence, an approach to monitor and control the transverse vibration of mating gears is presented with the help of AMBs. To understand the system dynamics and prediction of vibration responses, numerical models have been developed to carry out gear rotordynamic analysis of transverse vibration, transverse vibration with gyroscopic effect and coupled torsional-lateral vibration with geared rotor faults, like the mesh deformation, gear run-out, mass unbalance and asymmetric transmission error. The dynamic transmission error has been modeled as the sum of mean and varying components of error in two orthogonal transverse directions. With a feedback PID controller, the vibration amplitude is observed to get suppressed. The frequency domain analysis is done using a full spectrum, which shows that multiple harmonics of gear mesh frequency is minimized simultaneously. Due to high service load, harsh operating conditions, faults may develop in gears. If the gear faults are not detected early, the health may continue to degrade, causing heavy economic loss or even catastrophe. Early fault detection and diagnosis is much needed for properly scheduled shutdowns to prevent any catastrophic failure and higher cost reduction. While focusing upon the dynamics based gearbox fault modeling, detection and diagnosis, identification algorithm has been developed to estimate the geared rotor fault parameters. Considering full spectrum analysis of the geared rotor system, from rotor vibration and AMB current information, estimation of system parameters, i.e. the equivalent mesh stiffness, mesh damping, gear runouts, the mean and varying transmission error magnitude and phase angles, and the current and displacement constants of AMBs has been performed. Gaussian noise in responses and modeling errors in mathematical models have been added to test the robustness of the proposed algorithm to comply with the experimental settings. Based on the proposed model, an experiment test rig has been set up in the laboratory and the effectiveness of the proposed model is compared with and without the application of AMBs. The approach is based on an active control of the shaft transverse vibration with an electromagnetic actuator. The control forces are applied to the rotor shafts supported on conventional rolling element bearings by an eight-pole radial AMB, as an auxiliary component and a closed-loop linear output feedback control is employed for stable, reliable, and robust operation. A linear PD controller working on differential mode is used to generate the appropriate control signals and the experimental results are presented. Simulation and experimental results showed that there is considerable amount of reduction in the geared rotor vibration levels and correspondingly in overall measured gear noise levels.
Supervisor: Rajiv Tiwari