Estimation of the Dynamic Parameters of the Bearings in a Flexible Rotor System Utilizing Electromagnetic Excitation by a Built-In Motor

Estimation of the dynamic parameters of bearings is essential in order to be able to interpret the performance of rotating machinery. In this paper, we propose a method to estimate the dynamic parameters of the bearings in a flexible rotor system. By utilizing the electromagnetic excitation generated by a built-in PM motor and finite element (FE) modeling of the rotor, safe, low-cost, and real-time monitoring of the bearing dynamics can be achieved. The radial excitation force is generated by injecting an alternating d-axis current into the motor windings. The FE model of the rotor and the measured frequency responses at the motor and bearing locations are used to estimate the dynamic parameters of the bearings. To evaluate the feasibility of the proposed method, numerical simulation and experiments were carried out on a flexible rotor system combined with a bearingless motor (BELM) having both motor windings and suspension windings. The numerical simulation results show that the proposed algorithm can accurately estimate the dynamic parameters of the bearings. In the experiment, the estimates made when utilizing the excitation force generated by the motor windings are compared with the estimates made when utilizing the excitation force generated by the suspension windings. The results show that most of the stiffness and damping coefficients for the two experiments are in good agreement, within a maximum error of 8.92%. The errors for some coefficients are large because the base values of these coefficients are small in our test rig, so these coefficients are sensitive to deviations. The natural frequencies calculated from the dynamic parameters estimated from the two experiments are also in good agreement, within a maximum relative error of 3.04%. The proposed method is effective and feasible for turbomachines directly connected to motors, which is highly significant for field tests.

Spectral subtraction-based filter for experimental modal analysis under harmonics excitation force

In modal analysis, measurement of input force and vibration response are crucial to accurately measure the transfer function of the structure. However, under operating condition, the force induced by operating machinery is impossible to be measured due to the sensor placement issue. In this case, the ambient response induced by the operating force should be suppressed to minimize the error in the Frequency Response Function (FRF) calculation. This paper presents the utilization of a modified spectral subtraction filter for ambient suppression. The introduction of effective ambient magnitude in gain function calculation has increased the efficiency of spectral subtraction filter. This parameter is calculated based on the phase information of the reconstructed artificial ambient response. The measurement using EMA was carried out on a motor-driven structure to verify the proposed technique. Two sets of data under shutdown and running condition were recorded to observe the effect of ambient operating force. Under the operating condition, the measured FRF show the non-identical features at operating frequencies as compared to the baseline data. The utilization of filtering process shows the ambient features contained in the transfer function was effectively suppressed. The output of filtering algorithm could provide an alternative option to perform EMA procedure under running condition.

Development and Parametric Analysis of Vibration System Controlled by Hydraulic Shock Rotary Vibrator

The improvement of the energy utilization rate of a hydraulic vibration-excitation system is critical to the research and development of hydraulic vibration equipment. In this paper, a hydraulic vibration-excitation system controlled by a new type of shock rotary vibrator is proposed. A system model considering the pipeline effect was established for the hydraulic shock phenomenon. In addition, the model was compared with the one that does not consider the pipeline effect. The effectiveness of the proposed model was verified experimentally. Finally, the shock phenomenon during the process of switching the working state of the vibrator and the influence of certain important parameters of the system on the vibration output were investigated based on the proposed model. The results showed that (1) the hydraulic shock phenomenon occurred when the working state of the hydraulic vibrator was switched and (2) the hydraulic shock wave could effectively improve the excitation force of the system. The excitation force increased with an increase in the oil supply pressure, spindle speed, and load. However, it was negatively correlated with the spring stiffness. The amplitude of the vibration waveform output was positively correlated with the oil supply pressure and negatively correlated with the spindle speed and load. The amplitude first increased and then decreased as the stiffness of the vibration spring increased. The only influence of the precompressed length of the spring on the system output was its alteration of the vibration center of the system output vibration.

A novel strategy for force identification of nonlinear structures

Dynamic force is the key indicator for monitoring the condition of a mechanical product. These mechanical structures always encompass some nonlinear factors. Most previous studies focused on obtaining the dynamic force of linear structures. Consequently, this study focuses on the nonlinear mechanical structure, and a novel identification strategy is proposed to indirectly identify the excitation force. For the identification strategy, based on a nonlinear state-space model, a force identification equation for the nonlinear structure is built, wherein the transfer matrix consists of coefficient matrices of the nonlinear state-space model, and these coefficient matrices are calculated by a nonlinear subspace identification algorithm. Then, under the generalized cross-validation criterion, the truncated total least squares method is introduced to solve the ill-posed equation to eventually obtain the excitation force of the nonlinear structure. The identification results from two numerical simulation cases and one experimental case illustrate that the proposed identification strategy can stably and accurately identify the excitation force of nonlinear structures.