Analysis of Models for Torsional Vibration of Shaft System With Planetary Gearing

The kinematics of planetary gearing are complex; thus, making it difficult to build an effective dynamic model. In this paper, a single-mass model of a planetary gear and shaft system is developed to study the torsional vibration of the mechanism. Two new models of the system are proposed: (a) a fictitious co-planar model and (b) an equivalent shaft model. The results from the calculations and analyses using these models indicate that: 1) the single-mass model and the general rotary model are both limited, either mathematically or geometrically; 2) the fictitious co-planar model includes all of the geometric and dynamic parameters of the general rotary model, and it can be connected with the shaft system easily; and 3) using a mathematical treatment, the equivalent shaft model is demonstrated to be the most useful and most effective model for the calculation of torsional vibration of a shaft and planetary gear train.

Solving Vibration Control Problems Using Reduced Order Models for Flexible Structures: A Genetic Algorithm Approach

A Genetic Algorithm (GA) based approach for solution of optimal control design of flexible structures is presented in this paper. The method for modeling flexible structures with distributed parameters as reduced-order models with lumped parameters, which has been developed previously, is employed. Due to some restrictions on controller design it is necessary to make a reduced-order model of the structure. Once the model is established the design of flexible structures is considered as a feedback search procedure where a new solution is assigned some fitness value for the GA and the algorithm iterates till some satisfactory design solution is achieved. We propose a pole assignment method to determine the evaluation (fitness) function to be used by the GA to find optimal damping ratios in passive elements. This paper demonstrates the first results of a genetic algorithm approach to solution of the vibration control problem for practical control applications to flexible tower-like structures.

On the Efficacy of Magnetorheological Dampers for Seismic Response Reduction

In this paper, the efficacy of magnetorheological (MR) dampers for seismic protection of structures is investigated through a series of experiments in which an MR damper is used to control a three story test structure subjected to a one-dimensional earthquake motion. Because of the intrinsic nonlinearity of the MR damper, several earthquake amplitudes are considered to investigate the performance, in terms of both peak and rms responses, of this control systems over a range of loading conditions. The results indicate that the MR damper is quite effective for structural response reduction over a wide class of seismic excitations.

Structural Vibration Control for Bridge Towers and its Effect Under Wind Excitation Using a Wind Tunnel

In this paper we present an experimental investigation of active vibration control of a scaled bridge tower model under artificial wind excitation. The control scheme is designed on the basis of a reduced order model of the flexible structures using the LQ control theory, with a collocation of four laser displacement sensors and two hybrid electro-magnetic actuators. The experimental results in the wind tunnel show that both the bending and the twisting vibrations covering the first five modes of the structure are controlled well.

Experimental Investigation of a Piezoelectrically Actuated Rotating Parts Feeder

The parts feeder provides both horizontal and vertical forces to transfer the small parts between stations in automated manufacturing processes. In this paper, the dynamic characteristics of a piezoelectrically actuated rotating parts feeder was evaluated. The model of the piezoelectric bimorph, the key component of the parts feeder, is formulated under DC and AC excitation. Experiments using laser interferometer, impedance analyzer and spectrum analyzer were conducted to measure displacement sensitivity, resonance frequencies and antiresonance frequencies of the electrical/mechanical system. Relations between driving frequencies and vibration amplitudes under various driving voltages were reported. From experimental results, the resonance frequencies of the mechanical system were identified at 176.6 Hz and 535 Hz. The first resonance and anti-resonance frequencies of the electrical system were found at 176.0 Hz and 177.5 Hz. The electromechanical coupling coefficient for piezoelectric actuator using Mason formula is 13%. Operating at the first resonance frequency, the parts feeder feeds at 17.66 mm/sec with a vertical vibration amplitude of 14.2 μ m.

Gyroscopic Effects of a Vibrationally Isolated Rotating Disk and Shaft

An aircraft engine is an example of a rotating machine whose rotating imbalance will be transmitted as vibrational energy into the structure to which it is attached. There is considerable interest in understanding this energy transmission in order to design mounting systems, both passive and active, which can control this transmission the best possible way in order to reduce structurally borne noise in the cabin. It is a well established fact in acoustics[1] that in order to reduce perceived sound at the listener, the noise transmission path must be severed by 1) eliminating the source of the disturbance (usually difficult if not impossible), 2) preventing propagation of energy into the structure and ultimately to structural surfaces, 3) preventing radiation of sound energy from vibrating surfaces, and 4) preventing radiated sound from reaching the listener. In this paper we address only the prevention of energy transmission from the source into the supporting structure through use of some type of mounting system.

Updating Rotor-Bearing Finite Element Models

In this paper, the possibility of updating the finite element model of a rotor-bearing system by estimating the bearing stiffness and damping coefficients from a few measured Frequency Response Functions using a Genetic Algorithm is investigated. The issues of identifiability and parameters estimation errors, computational costs and algorithm tuning are addressed. A simulated example of a flexible rotor supported by orthotropic bearings is used for illustrating the method.

Prevention of Low-Frequency Vibration of High-Capacity Steam Turbine Units

The causes of low-frequency vibration (subsynchronous vibration) of a high pressure turbine were investigated analytically and also via vibration excitation tests on actual machines under operation. From the results, it was concluded that low-frequency vibrations may be caused by either the decrease of the rotor system damping or by external forces, such as flow disturbance in the control stage and the rubbing between the rotor and casing. After identifying the cause of the low-frequency vibration, appropriate countermeasures such as installation of a squeeze-film damper and modification of valve opening sequence were taken. Vibration measurements and vibration excitation tests for the high pressure turbine under actual operating conditions were carried out in order to verify the validity of the countermeasures. These field tests confirmed that the problems of low-frequency vibration can be solved completely by taking the appropriate countermeasure depending on the cause of the vibration. This paper presents some field experiences of low-frequency vibration and the effective solution approach.

Dynamic Vibration Absorber for a Ropeway Carrier

Ropeways such as gondola lifts have attracted increasing interest as a means of transportation in cities. However, swing of ropeway carriers is easily caused by wind, and usually a ropeway cannot operate if the wind velocity exceeds about 15m/s. The study of how to reduce the wind-induced swing of ropeway carriers has attracted many researchers. It had been said that it was impossible to reduce the vibration of pendulum type structures such as ropeway carriers by a dynamic absorber. But in 1993, Matsuhisa showed that the swing of carrier can be reduced by a dynamic absorber if it is located far above or below from the center of oscillation. Based on this finding, a dynamic absorber composed of a moving mass on an arc-shaped track was designed for practical use, and it was installed in chairlift-type carriers and gondola type carriers in snow skiing sites in Japan in 1995 for the first time in the world. It has been shown that a dynamic absorber with the weight of one tenth of the carrier can reduce the swing to half. The liquid dynamic absorber was also investigated. It has the same damping effect as the conventional solid absorber. It is easy to adjust the natural frequency and the damping ratio, and the structure is simple. Therefore, it will be applied for not only ropeway carriers but also ships and rope suspended bridge and others.

Wave Propagation Analysis of an Axially Strained, Rotating Timoshenko Shaft: Part II

In this paper, the wave reflection and transmission characteristics of an axially strained, rotating Timoshenko shaft under general support and boundary conditions, and with geometric discontinuities are examined. As a continuation to Part I of this paper (Kang and Tan, 1997), the wave reflection and transmission at point supports with finite translational and rotational constraints are further discussed. The reflection and transmission matrices for incident waves upon general supports and geometric discontinuities are derived. These matrices are combined, with the aid of the transfer matrix method, to provide a concise and systematic approach for the free vibration analysis of multi-span rotating shafts with general boundary conditions. Results on the wave reflection and transmission coefficients are presented for both the Timoshenko and the Euler-Bernoulli models to investigate the effects of the axial strain, shaft rotation speed, shear and rotary inertia.