A Novel Type of Bi-Gyroscopic System Undergoing Both Rotating and Spinning Motions

In order to explore the influence of combined gyroscopic coupling effect on the gyroscopic system, the dynamics of a beam undergoing both rotating and spinning motions as a bi-gyroscopic system is studied. The natural frequencies, modes, and stability of such a bi-gyroscopic system have been studied by the standard eigenvalue problems. The bifurcation series of frequencies and corresponding modal motions have been presented to show the gyroscopically coupled motions. The complex modes of the proposed bi-gyroscopic systems, such as whirling motions and in-plane reeling motions, have been illustrated.

Dynamic Characteristics of a Rotating Tapered Cantilevered Timoshenko Beam with Preset and Pre-Twist Angles

This paper is concerned with the free vibration of a rotating tapered Timoshenko beam with preset and pre-twist angles. The power series method is used to obtain the frequencies and complex modes of the structure. The rotating velocity related terms are re-classified into three types, namely, static centrifugal terms, dynamic centrifugal terms and the gyroscopic terms. This reclassification provides clearer descriptions of the varying frequencies with respect to the rotating velocity. The gyroscopic coupling among different directions are discussed. The overall contour of the complex modal vibrations is recorded and investigated by time series snapshots of neutral line motions and tip end cross-section motions.

Dynamic response for shock loadings and stress analysis of a trajectory correcting fuse based on fuse–projectile–barrel coupling

This paper creates a fuse–projectile–barrel coupling model and conducts an implicit–explicit sequential finite element dynamic simulation to analyze the response of the components in ammunition to shock loadings during the whole launch process accurately. The engraving process continues at 3.05 ms and leads to the acceleration fluctuation of the fuse bearings. The deflection of the gun barrel due to gravity at 52 degrees quadrant elevation (QE) is acquired. Then the displacement and velocity of the projectile are obtained to verify the gun tube deflection. The bearing axial and radial acceleration in the fuse are depicted. The results indicate that the axial acceleration imposed on the bearings during launch is a major loading, and base pressure and pressure dissipation result in shock loadings on the bearings. The accelerated spin and collision of the projectile with the barrel produce centrifugal inertia force and gyroscopic coupling, which influence the radial acceleration. In addition to this, a calculation method is proposed to work out the maximal contact stress of the bearing’s components. The method is combined with the bearings’ components maximal acceleration from simulation. The results of the research prove that the calculation method is correct and credible. The research conclusions provide some reference for the structural design of a trajectory correcting fuse.

Free Vibration Analysis of Pipes Conveying Fluid Based on Linear and Nonlinear Complex Modes Approach

In this paper, linear and nonlinear complex modes are used to analyze the free vibration of pipes conveying fluid involving the gyroscopic properties of the system. The natural frequencies, complex mode functions and time domain responses of the admissible mode functions based on discretized model are obtained using the invariant manifold method and compared with those of the continuous model. A good agreement has been achieved if the admissible mode functions for the static beams are adopted. The energy contributions of different admissible modes to the modal motions are also studied which explores the gyroscopic coupling variation among the admissible modes for different fluid velocities. Nonlinear complex modes are constructed for the nonlinear case and the morphology of the modal motions is demonstrated for different initial energy to show the contribution of the nonlinear terms. ‘Traveling waves’ are found for the transverse vibrations of the pipes conveying fluid due to the gyroscopic effects, contrary to the “standing waves” found for the pipes without moving fluid.

Development of a meso-scale cycloidal-rotor aircraft for micro air vehicle application

This paper describes the design, controls system development, and hover testing of a 60 -g meso-scale cycloidal-rotor based (cyclocopter) micro air vehicle. The cycloidal rotor (cyclorotor) is a revolutionary vertical take-off and landing concept with a horizontal axis of rotation. The twin-cyclocopter utilizes two optimized cyclorotors and a horizontal tail rotor used to counteract the pitching moment generated by the cyclorotors. An innovative light-weight and high strength-to-weight ratio blade design significantly reduced cyclorotor weight and improved aerodynamic efficiency. In addition, increasing the virtual camber and incidence (by increasing chord-to-radius ratio) and using a symmetric pitching schedule with a maximum ± 45° pitching amplitude also improved rotor efficiency. Due to gyroscopic coupling and inherent instability of the cyclocopter, a closed-loop feedback control system was implemented using a custom autopilot weighing 1.5 g. The 60-g meso-scale twin-cyclocopter successfully demonstrated stable, sustained hover.

Veering and Strong Coupling Effects in Structural Dynamics

Mode veering is the phenomenon associated with the eigenvalue loci for a system with a variable parameter: two branches approach each other and then rapidly veer away and diverge instead of crossing. The veering is accompanied by rapid variations in the eigenvectors. In this paper, veering in structural dynamics is analyzed in general terms. First, a discrete conservative model with stiffness, mass, and/or gyroscopic coupling is considered. Rapid veering requires weak coupling: if there is instead strong coupling then there is a slow evolution of the eigenvalue loci rather than rapid veering. The uncoupled-blocked system is defined to be that where all degrees-of-freedom (DOFs) but one are blocked. The skeleton of the system is the loci of the eigenvalues of the uncoupled-blocked system as the variable parameter changes. These loci intersect at certain critical points in the parameter space. Following a perturbation analysis, veering is seen to comprise rapid changes of the eigenvalues in small regions of the parameter space around the critical points: for coupling terms of order ε veering occurs in a region of order ε around the critical points, with the rate of change of eigenvalues being of order ε−1. This is accompanied by rapid rotations in the eigenvectors. The choice of coordinates in the model and application to continuous systems is discussed. For nonconservative systems, it is seen that veering also occurs under certain circumstances. Examples of 2DOFs, multi-DOFs (MDOFs), and continuous systems are presented to illustrate the results.

A Dimensionless Quotient for Determining Coupling Strength in Modal Energy Analysis

Modal energy analysis (MODENA) is an energy-based method recently proposed to estimate the dynamic response of a coupled structure/acoustic cavity system. The accuracy of MODENA is affected by the coupling strength between structural and acoustic modes. A dimensionless coupling quotient which is equal to the ratio of the gyroscopic coupling coefficient and the critical coefficient at modal frequencies is defined to determine the coupling strength in MODENA. The coupling strength of the system is classified as weak, moderate, or strong, according to the coupling quotient with a proposed criterion. When computing the modal input power in MODENA, the mobility of the uncoupled mode can be used if the modes are weakly coupled, but the mobility of the coupled mode should be adopted to obtain accurate results if many modes are moderately coupled. The effectiveness of the proposed criterion is validated via a numerical example where a plate is coupled with an acoustic cavity. Results show that many low-order structural and acoustic modes are moderately coupled while almost all high-order modes are weakly coupled. Errors of the energy responses appear in a low-frequency band, but accurate results are acquired in a mid- to high-frequency band when the mobility of uncoupled mode is used.

Experimental and Analytical Study of Coriolis Effects in Bladed Disk

Modern aero-engines have reached a high level of sophistication and only significant changes will lead to the improvements necessary to achieve the economic and environmental targets of the future. Open rotors constitute a major leap in this direction, both in terms of efficiency and of technological innovation. This calls for a revision of the accepted design practices, and a new focus on phenomena that have been little investigated in the past, such as the Coriolis effect, or the gyroscopic coupling of the blades with the shaft. Experimental results from modern fans, with large blades and strong stagger angles, are showing dependence on Coriolis gyroscopic effects already, an effect that is expected to be strongly enhanced with the proposed open rotor designs. For an accurate prediction of the Coriolis and gyroscopic effects in rotating assemblies a fully experimentally validated approach is needed. Today’s FE models can capture the basic physical phenomena, but experimental confirmation is still needed for the evolution of the mode shapes with angular speed, and the influence of damping and geometric nonlinearities when gyroscopic coupling is considered. To support this validation effort a new rotating test rig will be introduced, initial measurement data will be discussed, and a comparison with a finite element analysis presented. Different forcing patterns, including forward and backward travelling-wave engine order excitation could be experimentally excited in the new rig, Coriolis-induced frequency splits were found in the dynamic response, showing a significant change in the dynamic behaviour of the investigated dummy disk, and only a minor impact of the mistuning was observed on the frequency splits due to Coriolis effects. The experimental results have been compared to a finite element analysis, and after some updating a good agreement between the predicted and measured Campbell diagrams could be obtained, demonstrating the reliability of the modelling approach.

Switching Action in Rotor-AMB Systems for Smooth Vibration Control

Rotating machines may, for reasons of gyroscopic coupling and aerodynamic influences, exhibit speed dependent characteristics. For systems that incorporate active magnetic bearings (AMBs) for rotor levitation, a range of control strategies are available for implementation to achieve desired closed loop dynamic characteristics. Over a large operating speed range, it may not be possible stabilize a rotor by using only one linear time-invariant (LTI) H∞ controller that has speed independent characteristics. This paper addresses that problem by introducing a switching controller system. The system contains a number of (LTI) H∞ controllers, designed to cover particular speed ranges, together with an external signal to drive the switching action. When speed dependent unbalance forcing acts, each of the controllers is able to attenuate vibration of the rotor over the specific speed ranges. The controller switching points are selected according to a metric that takes account of measured rotor lateral vibration. However, a sudden switching action may induce significant transient disturbance and give rise to rotor vibration overshoot, possibly to the extent of causing rotor-stator contact. To alleviate this problem, a ramp switching signal may be introduced such that two controllers may be switched smoothly over a given time period. Further smoothing modifications are possible to avoid ‘over-control’ and obtain a better transient performance. The unstable points of each H∞ controller are also discussed with respect to upper threshold speeds, above which controller switching is not allowable.