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This paper studies the effects of shaft rub on a rotating system's vibration response with emphasis on heat generation at the contact point. A 3D heat transfer code, coupled to a 3D vibration code, was developed to predict the dynamic response of a rotor in the time domain. The shaft bow is represented by an equivalent bending moment and the contact forces by rotating external forces. The seal ring is modeled as a linear spring, which exerts a normal force to the rotor. The tangential force is then calculated as the product of the normal force with the friction coefficient. Stable or unstable spiraling and oscillating modes were seen to occur in well defined shaft speed zones. In the main, for the configurations studied, the shaft vibration was found to be unstable for speeds below the first critical speed and stable for speeds above the first critical speed. Limit cycle behavior was observed when the phase angle between the unbalance force and the response was around 90 deg. The vibration behavior with rub during startup and shutdown was studied by considering the effects of acceleration/deceleration rate, friction coefficient, and mass unbalance. It was found that friction coefficient and increasing mass unbalance amplified the rub effects while acceleration/deceleration rate reduced it. [DOI: 10.1115/1.4000904] Keywords: Shaft/seal rub, coupled analysis for heat transfer and vibration, thermal bending moment, rub at startup and shutdown

A simplified analytical approach for modeling the synchronous instability phenomenon known as the Morton effect is presented. The analysis is straightforward and easily applied to any rotor supported on fluid film bearings. The analysis clarifies the interaction of three distinct machine characteristics, which combine to create a case of the Morton effect. Some example calculations are shown illustrating the possible types of spiral vibration. In addition, an analytical approach is described for estimating the magnitude of the shaft temperature difference in a journal bearing as a direct function of the shaft orbit. It is significant that this method can readily be applied to any type of journal bearing, from plain sleeve bearings to tilting pad bearings. Example calculations using the method are shown. [DOI: 10.1115/1.4001512]

When both ends of an elastic continuous rotor are supported simply by double-row self-aligning ball bearings, the geometrical nonlinearity appears due to the stiffening effect in the elongation of the rotor if the movement of the bearings in the longitudinal direction is restricted. As the rotor becomes more slender, the geometrical nonlinearity becomes stronger. In this paper, we study on unique nonlinear phenomena caused by both of the nonlinear spring characteristics and an initial axial force in the vicinity of the major critical speed [[omega].sub.c] and twice [[omega].sub.c] in a very slender continuous rotor. When the rotor is supported horizontally, the difference in support stiffness and the asymmetrical nonlinearity appear as a result of shifting from the equilibrium position. By the influences of the internal resonance and the initial axial force, the nonlinear resonance phenomena become very complicated. For example, the peak resonance splits into two peaks, and these two peaks leave each other and then one becomes a hard spring type while the other becomes a soft spring type, respectively. Moreover, almost periodic motions and chaotic vibrations appear. In this paper, we prove the above phenomena theoretically and experimentally. [DOI: 10.1115/1.4000841]

Autobalancers for rotor/bearing systems are passive devices consisting of eccentrically mounted balance masses that freely revolve around the rotor's axis of rotation. At certain supercritical speeds, the balancer mass positions naturally adjust to cancel the rotor imbalance. This automatic-balancing phenomena occurs as a result of nonlinear dynamic interaction between the balancer masses and the rotor's lateral vibration. Previous studies have found that autobalancers can effectively compensate for mass imbalance in planar rigid rotors such as hard-disk drives and flywheels, however, their use in bladed-disk and turbomachinery applications has not been previously considered. This study explores the dynamics and stability of a flexible bladed-disk/rotor-bearing system equipped with a dual-ball automatic-balancing device. It is found that the autobalancer effectively compensates for both mass and aerodynamic imbalances produced by a bladed-loss condition over a wide revolutions/minute range at speeds above the first lateral natural frequency. It is also shown that for stable automatic balancing to occur, the ratio of automatic balancer damping to the blade aerodynamic drag coefficient must be above some critical value. The analysis demonstrates that the automatic balancer is able to simultaneously reduce both bearing loads and blade deflections for a simulated blade-loss event. DOI: 10.2514/1.43832

This paper presents a simulation to actively control transverse vibration of a flexible rotor shaft system mounted on a moving vehicle (e.g., a ship or an aircraft). Discretizing the rotor continuum with beam finite elements, equations of motion are written with respect to a noninertial frame attached to the frame of the moving vehicle. Such equations are linear but contain time-varying parametric terms due to the motion of the carrier vehicle. Through numerical simulation, it is shown that the transverse response in the bending vibration of the rotor shaft relative to the supporting structure is significantly influenced by the inertia force, as well as the parametric excitations due to vehicle motion. A control strategy is proposed using an electromagnetic actuator placed at a suitable location along the span of the rotor, and it is found extremely useful in reducing the vibration of the rotor and improving its stability. Examples are given in support by studying both the uncontrolled and the controlled motion of a rotor shaft system carried by an aircraft undergoing two different kinds of maneuvers. DOI: 10.2514/1.43378

A stochastic hub-height wind speed estimation algorithm for wind turbines, which requires only the rotor angular velocity measurement in the presence of observation noise is proposed. It is assumed that the power curve and the total inertia of the rotor are known a priori. We use the maximum likelihood estimator to identify the hub-height wind speed, which is formulated as one of the state variables in the nonlinear model. The theory and algorithm are verified by both simulated and experimental data in the presence of measurement noise. The effects of the initial guess, the noise variance, and the time history are discussed. [DOI: 10.1115/1.4000604]

Unstable vibration occurs in the vicinities of the major critical speeds of asymmetrical shaft and rotor systems. It occurs also in a wide rotational speed range higher than the major critical speed of a shaft with a hollow disk partially filled with liquid. The occurrence of the unstable vibrations is a serious problem because the amplitude increases exponentially, and finally, the system is destroyed. The active vibration control can suppress unstable vibrations but the method is generally complicated and costly. No simple effective method to suppress unstable vibrations has been developed yet. In the previous paper, the authors proposed a simple method by utilizing discontinuous spring characteristics, which can suppress steady-state resonances. This paper shows that this method is also effective to suppress unstable vibrations. By using this method, the unstable vibrations can be changed into almost periodic motions, and the amplitudes are suppressed to the desired small level even in an unstable range. The validity of the proposed method is also verified by experiments. [DOI: 10.1115/1.4000842]

An unbalanced rotor dynamic model supported on ball bearings is established. In the model, three nonlinear factors of ball bearing are considered, namely, the clearance of bearing, nonlinear Hertzian contact force between balls and races, and the varying compliance vibrations because of periodical change in contact position between balls and races. The numerical integration method is used to obtain the nonlinear dynamic responses; the effects of the rotating speed and the bearing clearance on dynamic responses are analyzed; and the bifurcation plots, the phase plane plots, the frequency spectra, and the Poincare maps are used to carry out the analyses of bifurcation and chaotic motion. Period doubling, quasiperiod loop breaking, and mechanism of intermittency are observed as the routes to chaos. [DOI: 10.1115/1.3142883]

This paper is to study ground-based vibration response of a spinning, cyclic, symmetric rotor through a theoretical analysis and an experimental study. The theoretical analysis consists of three steps. The first step is to analyze the vibration characteristics of a stationary, cyclic, symmetric rotor with N identical substructures. For each vibration mode, we identify a phase index n and derive a Fourier expansion of the mode shape in terms of the phase index n. The second step is to predict the rotor-based vibration response of the spinning, cyclic, symmetric rotor based on the Fourier expansion of the mode shapes and the phase indices. The rotor-based formulation includes gyroscopic and centrifugal softening terms. Moreover, rotor-based response of repeated modes and distinct modes is obtained analytically. The third step is to transform the rotor-based response to ground-based response using the Fourier expansion of the stationary mode shapes. The theoretical analysis leads to the following conclusions. First, gyroscopic effects have no significant effects on distinct modes. Second, the presence of gyroscopic and centrifugal softening effects causes the repeated modes to split into two modes with distinct frequencies [[omega].sub.1] and [[omega].sub.2] in the rotor-based coordinates. Third, the transformation to ground-based observers leads to primary and secondary frequency components. In general, the ground-based response presents frequency branches in the Campbell diagram at [[omega].sub.1] [+ or -] k[[omega].sub.3] and [[omega].sub.2] [+ or -] k[[omega].sub.3], where k is phase index n plus an integer multiple of cyclic symmetry N. When the gyroscopic effect is significantly greater than the centrifugal softening effect, two of the four frequency branches vanish. The remaining frequency branches take the form of either [[omega].sub.1] + k [[omega].sub.3] and [[omega].sub.2] - k[[omega].sub.3] or [[omega].sub.1] - k[[omega].sub.3] and [[omega].sub.2] + k[[omega].sub.1]. To verify these predictions, we also conduct a modal testing on a spinning disk carrying four pairs of brackets evenly spaced in the circumferential direction with ground-based excitations and responses. The disk-bracket system is mounted on a high-speed, air-bearing spindle. An automatic hammer excites the spinning disk-bracket system and a laser Doppler vibrometer measures its vibration response. A spectrum analyzer processes the hammer excitation force and the vibrometer measurements to obtain waterfall plots at various spin speeds. The measured primary and secondary frequency branches from the waterfall plots agree well with those predicted analytically. [DOI: 10.1115/1.3025847]

Aerodynamic and acoustic experiments were carried out to investigate the induced inflow distribution and noise characteristics of a scissors rotor in hover. The aerodynamic experiment was conducted on a model rotor rig and the induced inflows for two different scissors rotor configurations (the L configuration and U configuration) were measured. The experimental results indicate that the induced velocity near the lower blades is consistently larger than that near the upper blades. A free-wake analysis was used to predict the aerodynamic characteristics. The variation of the induced velocity with different scissors angles was simulated analytically and the results were compared with test data. The acoustic experiment was conducted in an anechoic aeroacoustic laboratory and the noise levels for both the scissors rotor configuration and a conventional configuration were measured. The effects of different scissors angles on rotor noise were investigated. It was shown that the noise level of a scissors rotor depends on both the azimuthal and vertical spacing and is not necessarily less than that of a conventional configuration.