High-Speed Machining (HSM) spindles equipped with Active Magnetic Bearings (AMBs) have been envisioned to be
capable of automated self-identification and self-optimization in efforts to accurately calculate parameters for stable
high-speed machining operation. With this in mind, this work presents rotor model development accompanied by
automated model-updating methodology followed by updated model validation. The model updating methodology is
developed to address the dynamic inaccuracies of the nominal open-loop plant model when compared with experimental
open-loop transfer function data obtained by the built in AMB sensors. The nominal open-loop model is altered by
utilizing an unconstrained optimization algorithm to adjust only parameters that are a result of engineering assumptions
and simplifications, in this case Young's modulus of selected finite elements. Minimizing the error of both resonance
and anti-resonance frequencies simultaneously (between model and experimental data) takes into account rotor natural
frequencies and mode shape information. To verify the predictive ability of the updated rotor model, its performance is
assessed at the tool location which is independent of the experimental transfer function data used in model updating
procedures. Verification of the updated model is carried out with complementary temporal and spatial response
comparisons substantiating that the updating methodology is effective for derivation of open-loop models for predictive
The nonlinear model of the cracked Jeffcott rotor is investigated, with the particular focus on study of rotor's vibrational response using tools of nonlinear dynamics. The considered model accounts for nonlinear behavior of the crack and coupling between lateral and torsional modes of vibrations. Load torque is applied to the rotor which is laterally loaded with a constant radial force (gravity force) and unbalance excitation. The co-existence of frequencies of lateral modes in the frequency spectra of torsional mode are characteristics of the coupling response of lateral and torsional vibrations. When only the lateral excitations are applied, vibration amplitude bifurcation plot with the shaft speed as a control parameter, demonstrates some speed ranges for which vibrations of the rotor dramatically increase. Furthermore, the torsional response amplitude at the same speed ranges also increases and chaotic behavior can be observed due to the lateral excitations. These phenomena cannot be observed for pure lateral vibration response with the torsionally rigid rotor assumption.
Critical components of propulsion systems frequently operate at high stress levels for long periods of time. The integrity of these parts must be proven by non-destructive evaluation (NDE) during various manufacturing steps and also during systematic overhaul inspections. Conventional NDE methods, however, have unacceptable limits. Some of these techniques are time-consuming and inconvenient for service aircraft testing. Impedance-based structural-health-monitoring (SHM) uses piezoelectric (PZT) patches that are bonded onto or embedded in a structure; each individual patch both actuates the surrounding structural area and senses the resulting structural response. The size of the excited area varies with the geometry and material composition of the structure. A series of experiments on simple geometry specimens (thin-gage aluminum square plates) was conducted for assessing the potential of E/M impedance method for structural damage detection. Based on the results of this preliminary study, further testing was conducted on a subscale disk specimen. Based on the results it can be concluded that the E/M impedance method has the potential to be used for damage detection of structures. The experimental method, signal processing, and damage detection algorithm should be tuned to the specific method used for structural interrogation.
The transient vibration response of a cracked flexible rotor passing through its critical speed is analyzed for crack detection and monitoring. The effects of different factors such as various crack depths, acceleration, damping, torque, unbalance eccentricity, and rotor weight on the rotor vibrational response are studied. The breathing types of cracks are analyzed using simple hinge model in a case of shallow cracks, and the cosine function is employed in the case of deep cracks. The developed strategy enables the analysis of cracked rotor vibrational response with and without weight dominance, taking into account also the nonsynchronous rotor whirl. In addition, the local cross-flexibility for deep cracks is taken into account. Lastly, the effect of the crack depth on “stalling” of the rotor due to the limited driving torque is investigated.
The dynamic response of a cracked Jeffcott rotor passing through the critical speed with constant acceleration is investigated analytically and numerically. The nonlinear equations of motion are derived and include a simple hinge model for small cracks and Mayes' modified funciton for deep cracks. The equations of motion are integrated in the rotating coordinate system. The angle between the crack centerline and the shaft vibaiton (whirl) vector is used to determine the clsoing and opening of the crack, allowing one to study the dynamic response with and without the rotor weight dominance. Vibration phase response is used as one of possible tools for detection the existence of cracks. The results of parametric studies of the effect of crack depth, unbalance eccentricity orientation with respect to crack, and the rotor acceleration on the rotor's response are presented.
Different approaches are used to sense and to localize a damage of rotating structures. Most of the methods take advantage of the dynamic behavior of the structural model [1-7]. This paper uses the modal and sensor norms, as defined in , to determine damage locations. The proposed approach allows localization of damaged elements within a structure, and provides information concerning the impact of the damage on the structure's natural modes of vibration.