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\"Blade Element Rotor Theory presents an extension of the blade element rotor theory to describe the dynamic properties of helicopter rotors. It focuses on the more precise mathematical determination of the forces and moments by which a rotor affects its rotorcraft at specified flight conditions and control positions. The book is intended for graduate students and researchers studying rotor dynamics and helicopter flight dynamics. Analyzing the impact of non-uniform blade parameters, the book covers blade twisting, non-rectangular planform shape of a blade, and inhomogeneous airfoil along a blade\"-- Provided by publisher.

Taking the cantilever rotor of a turbine engine as the research object, a dynamic and finite-element model of the cantilever rotor is established, and the effectiveness of the model is verified by the rotor test platform. The transfer function method is used to balance the rotor system under unbalanced excitation, and the experiments prove that the method adopted in this paper has a good balancing effect and effectively reduces the vibration of the unbalanced rotor. On this basis, the experimental tests and simulation analyses of the rotor vibration response under different unbalanced phases and difference combinations are carried out, and the influence of the unbalanced phase’s difference combinations on unbalance and dynamic balance is analyzed. The results show that the vibration response of the system decreases with the increase in the unbalanced phase difference combinations, and the amplitude of the vibration induced by the unbalance of the reverse combination is smaller than that of the in-phase combination. The work in this paper can provide a theoretical basis for the dynamic balance and vibration control of the flexible rotor of an aero-engine.

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce of bearing is also considered as a point force. The shaft is considered free-ended. A continuous rotor dynamic model is obtained and an analytical solution is proposed to express the unbalance response as function of the position, unbalance, support stiffness and damping. The proposed method is validated by numerical experiments in which unbalance responses obtained by it are compared with that obtained by the two classical methods the finite element method (FEM) and Ricatti method. The results indicate that the proposed method is applicable to calculating unbalance response of multi-disc and multi-span rotor. Moreover, it is closer to FEM than Ricatti and can be applied to actual high speed rotors. Among the three methods, the calculating speed of Ricatti is the fastest, CRDAM is the second fastest and FEM is the slowest. The proposed method, which solves the forward problems of the continuous rotor dynamics for the multi-disc and multi-span rotors, can provide theoretical basis for further studies on inverse problems such as identification of rotor unbalance and bearing stiffness and damping coefficients without test runs and external excitations.

A wide-ranging treatment of fundamental rotordynamics in order to serve engineers with the necessary knowledge to eliminate various vibration problems. New to this edition are three chapters on highly significant topics: Vibration Suppression - The chapter presents various methods and is a helpful guidance for professional engineers. Magnetic Bearings - The chapter provides fundamental knowledge and enables the reader to realize simple magnetic bearings in the laboratory. Some Practical Rotor Systems - The chapter explains various vibration characteristics of steam turbines and wind turbines. The contents of other chapters on Balancing, Vibrations due to Mechanical Elements, and Cracked Rotors are added to and revised extensively. The authors provide a classification of rotating shaft systems and general coverage of key ideas common to all branches of rotordynamics. They offers a unique analysis of dynamical problems, such as nonlinear rotordynamics, self-excited vibration, nonstationary vibration, and flow-induced oscillations. Nonlinear resonances are discussed in detail, as well as methods for shaft stability and various theoretical derivations and computational methods for analyzing rotors to determine and correct vibrations. This edition also includes case studies and problems.

Advanced composite materials provide engineers new possibilities for machine design due to their customization capacity and enhanced physical properties compared to the traditional isotropic materials. Onboard machinery, such as jet engines, transmission shafts, and energy storage flywheels, benefits from the use of composite shafts. Thus, improved mechanical efficiency can be achieved from both the reduced weight and orthotropy properties of composite materials. In this context, the dynamic behavior of a composite rotating machine under base excitation is evaluated. A modified finite element (FE) model based on the simplified homogenized beam theory (SHBT) is used to represent the dynamic behavior of a composite onboard thick-walled shaft. The FE-SHBT model considers transverse stresses, ply orthotropy, directional coupling related to the composite orthotropy, internal damping, and the gyroscopic effect. Experimental validation of the FE-SHBT model was carried out by using a test rig with a twenty-layer thick-walled carbon–epoxy composite hollow shaft, two aluminum discs, and two self-aligning ball bearings. The unknown parameters of the model were tuned to the experimental setup by using an optimization procedure. Various numerical responses concerning the onboard rotor vibration responses are presented to demonstrate the dynamic phenomena associated with the considered composite hollow shaft under base excitation.

Dynamic analysis is a key problem of flywheel energy storage system (FESS). In this paper, a one-dimensional finite element model of anisotropic composite flywheel energy storage rotor is established for the composite FESS, and the dynamic characteristics such as natural frequency and critical speed are calculated. Through the analysis of acceleration transient response, it is found that the flywheel rotor have two critical speeds during acceleration or deceleration process, which are prone to resonance and damage the bearing. Therefore, in order to avoid resonance or reduce resonance peak, the influence of bearing support stiffness, damping and speed-up rate on the critical speed and resonance peak is studied. The calculation results show that the first two order critical speed are affected by the support stiffness. When the stiffness increases, the critical speed of the flywheel rotor increases, but the growth rate decreases. When the damping increases, the critical speed is basically not affected, and the vibration amplitude decreases rapidly. In addition, the resonance peak value of transient response can be effectively reduced by increasing the speed-up rate.

Problem Nonlinear vibrations in helicopter systems present considerable challenges to performance and stability. Control Scheme This paper presents a novel control framework tailored for a fuzzy-proportional-integral-derivative (FPID) controller, specifically focusing on nonlinear vibration management and helicopter rotor dynamics control. The constraints of controller are optimized using a hybrid Giza Pyramid Construction Teaching Learning Based Optimization algorithm. We utilize a nonlinear helicopter hardware model as a benchmark, subjecting it to external disturbances created by high-speed fans to replicate real-world scenarios. Computation By employing the MATLAB/Simulink platform, our computational technique effectively mitigates disturbances while minimizing critical fitness functions: Integral-Time-Square-Error (ITSE), Integral-Square-Error (ISE), and Integral-Absolute-Error (IAE). Conclusion The results demonstrate that our hybridized algorithm outperforms existing optimization techniques, showcasing improved stability and reliability in both simulations and real-time applications. This research significantly advances helicopter control methodologies and enhances the overall performance of helicopter systems under challenging conditions.

As the efficiency of advanced aero engines improves, the operational speed of their rotors increases. This heightened operational speed makes the rotor dynamics highly sensitive to changes in the rotor’s mass asymmetry state, or unbalance state. During the use of a dual-spool turbofan engine, when its supercritical high-pressure rotor (HPR) exceeds a certain operational speed, the rotor’s vibration spikes and continues to increase with the operational speed until it drops sharply near the maximum operational speed. Analysis of the bolt joints in the faulty rotor reveals various phenomena such as joint interface damage, changes in bolt loosening torque distribution, and alterations in rotor initial unbalance. This paper proposes that at high operational speeds, the bolt joint of the HPR undergoes sudden angular deformation, resulting in the slanting of the principal axis of inertia of the turbine disk. This slant leads to changes in the unbalanced state of the HPR. The additional unbalance causes a sudden rotational inertia load excitation, triggering the rotor vibration failure. Subsequently, a rotor dynamic model that incorporates the angular deformation of the joints is established to simulate how this joint deformation influences the dynamic response of the rotor. The simulation results align well with the observed failure phenomenon and validate the proposed failure mechanism. Finally, troubleshooting measures are proposed and implemented in the faulty engine, effectively mitigating the vibration fault.

In this paper a comparative study of five different stability computational methods based on the Floquet theory is presented. These methods are compared in terms of accuracy and CPU performance. Tests are performed on a set of nonlinear problems relevant to rotating machinery with rotor-to-stator contact and a variable number of degrees of freedom, whose periodic solutions are computed with the Harmonic Balance Method (HBM).

Uncertainties in rotating machines are unavoidable, which affect their parameters and dynamic response. So, instead of employing deterministic models, data-driven meta-modeling techniques which incorporate unpredictability and randomness are necessary for the response variation analysis of rotating systems. The performance of the meta-model relies heavily on the quality and amount of the training dataset. In reality, however, only a tiny amount of high-fidelity data is obtainable from high-dimensional finite element simulation or experimental investigation, although low-cost low-fidelity data may be numerous. The objective of this paper is to develop a novel neural network model for multi-level response prediction by obtaining a high number of low-fidelity data quickly through model order reduction and a limited amount of high-fidelity data correctly from a full-order model. The accuracy of the meta-model is demonstrated by comparing against a classical deep neural network. Two different types of meta-model are established by using two model reduction techniques: Guyan reduction and modified system equivalent reduction expansion process. The performance of the model is demonstrated by employing frequency response variation characterization of a complex rotor as a case example. The results reveal that the multi-fidelity neural network performs better than the low-fidelity frequency response curves alone, which is observed to have a lot of inaccuracies. The deep neural network, on the other hand, is unable to reflect on the dynamic response of the full model. A regression of more than 90% shows that the meta-model has high effectiveness in properly predicting the frequency responses. The mean squared error values for the meta-model are found to be less than 0.1, which is typically regarded as acceptable. Frequency response curves of four test samples are selected at random for comparison. It is observed that the meta-model frequency response moves much closer to the full model than compared to that of the low-fidelity model reduction. The performance resilience of the model is tested by using five different training runs with random data splits. Minor changes in the values of logarithm mean absolute error and logarithm root mean squared error under different training runs show appropriate curve fitting and signify superior accuracy. It is concluded that the multi-fidelity neural network can reach a higher level of accuracy with a limited amount of high-fidelity data. The model effectively identifies both the linear and complex nonlinear correlation between the high-and low-fidelity data, resulting in enhanced efficacy in contrast to state-of-the-art methods.