Shaft Inertia Research Articles

An Efficient and Effective WEC Power Take-Off System

A numerical model for a hydraulic wave energy converter power take-off is developed in this study. The system architecture is described and the mathematical model for each component is presented. The accumulators are not used as energy storage devices. Instead, they are used to reduce the stiffness of the system, increase the response time, and improve the controllability. The numerical model was implemented using MATLAB/Simulink. The design variables selected for this study are the maximum displacement in the hydraulic motors, and the shaft inertia. The effect of these design variables on system performance is studied using latin-hypercube sampling to generate the cases to be simulated. The displacement in the hydraulic devices is used as a control input to adjust the pressure in the hydraulic cylinder and then change the force acting on the floating body. The desired force is calculated by a high level controller that estimates the force value to achieve impedance matching in the WEC. The torque in the electric generator is used to control the shaft speed. The system was designed to actively use reactive power flow to maximize the electric power output in the generator. The model developed in this study is a complete wave-to-wire model based on a co-design approach that considers the effect of all the different subsystems on the dynamic behavior of the whole WEC system. Twelve different wave conditions were tested. The most critical metric for this study is the electric power in the generator, which is the objective function of the optimization that was performed for all the wave conditions defined as case study. The wave-to-wire efficiency, which includes the complete wave energy to electrical energy conversion chain, is also calculated in this work.

Modelling and performance analysis of a recuperated gas turbine with low-Btu fuel

• A gas turbine model was estabilished considering recuperator, fuel, and generator. • The recuperator is the dominant component for thermal inertia of smallgas turbine. • 1-D heat soakage model was more proper for radial rotor than 0-D lumped model. • The thermal inertia and volume effect are good for gas turbine with sudden load change. • Overspeed in load shedding and surge in deceleration need to be studied case by case. Low-Btu fuels such as land fill gas and bio-gas are good alternatives to high priced natural gas. Due to the limited production of low-Btu fuel, small gas turbines are widely applied in such applications. For higher power efficiency at full and part load conditions, the small gas turbine is always equipped with a recuperator and a high-speed generator. Due to low shaft inertia, a small gas turbine’s speed response is quick. Therefore, for standard simple cycle gas turbine, control lags from instruments, actuators, thermal inertia, or volume effect may induce control instabilities during transient loading, and resulting in over speed, flow instabilities, and even mechanical failure. However, for recuperated engine burning low BTU fuel, other factors including the large volume of the combustor and recuperator, the thermal inertia of the rotor and recuperator, lags in the fuel valve lags, and efficiency changes caused by rectifiers of the high-speed generators could all induce visible changes and lags in the engine’s transient operations. This paper summarizes the influences of the gas turbine engine itself, the recuperator, and the high-speed generator in one model. It is believed that this is the first time that all these effects and interactions have been analysed together. Heat soakage, volume dynamics, recuperator transient characteristics, and the rectifier model were combined and tuned in detail to understand the separate effects. From the analysis of transient cases such as, load shedding and acceleration, conclusions are drawn made regarding overspeed and recovery time. The recuperator thermal inertia, low-Btu fuel, and combustor and recuperator volume effect interact with each other to produce more than three times larger overspeed or nearly five times more recovery time compared to a natural gas engine with recuperator. The fuel valve with a 0.02 s-time constant was found to be adequate even for the most severe case described in this paper. The recuperated gas turbine did not necessarily lead to lower compressor surge margin and should be investigated on a case-by-case basis. Rectifier system efficiency variation should be taken into account especially for the acceleration process. To convert a natural gas turbine engine into low-Btu gas turbine, the matching point of the gas turbine components needs to be carefully selected for efficiency, surge margin, and transient manoeuvre behaviour.

Time-Scaled Emulation of Electric Power Transfer in the More Electric Engine

One of the main areas of research for the more electric aircraft (MEA) is mounting a generator on the low-pressure (LP) shaft in addition to the starter/generator mounted on the high-pressure (HP) shaft. Given that there are electrical machines on both the LP and HP shafts, there is an “electrical bridge” to establish power exchange between the shafts. Potential improvements in the engine performance in terms of fuel consumption, engine stability, and compatible thrust with flight mission at various flight scenarios under such a transfer have been studied and discussed in the literature. To prove the concept and demonstrate the practicality of power transfer, an engine emulator has been constructed. The emulator will replicate the basic behavior of the engine by using similarity analysis to allow for conducting tests in a scaled environment without the need for an actual physical engine. A unique time-scaling technique is implemented to synchronize the time of the engine model and the test rig for transient studies. This enables scalable flexible engine emulation at different power generation ratings. A new criterion composed of shaft inertia, time, and speed scaling factors is also introduced to assess the validity of shaft inertia emulation. The experimental results are reported to demonstrate and further discuss the feasibility of electric power transfer between the engine shafts.

A proposed flicker mitigation scheme of DFIG in weak distribution networks

Wind power is intermittent and fluctuating renewable source that irritates system performance during normal operation. Besides, wind speed changes caused by tower shadow and wind shear effects which known as 3p oscillations increase the level of active power variations and impede wind power expansion. Several power quality concerns such as voltage constancy and flicker emissions manifested owing to lower short circuit ratios and grid impedance angle at the wind turbine point of connection. This article presents a combined active and reactive power mitigation approach for a doubly-fed induction generator DFIG in order to reduce output power pulsations, minimize voltage perturbations so as to alleviate flicker emissions for weak distribution networks. The principal premise of the proposed scheme relies on varying the wind generator speed in order to store the 3p oscillations in the wind turbine WT shaft inertia. Furthermore, an optimal grid impedance angle that cancels voltage fluctuations and hence attains further reduction of flicker is obtained. A detailed system model is built in MATLAB/SIMULINK to explore the system performance for a range of wind speed changes. The obtained results reveal the significance of the proposed methodology to allay flicker emissions of DFIG operated in weak distribution networks and to comply with grid code regulations.

Neuro-Analogical Gate Tuning of Trajectory Data Fusion for a Mecanum-Wheeled Special Needs Chair

Trajectory tracking of mobile wheeled chairs using internal shaft encoder and inertia measurement unit(IMU), exhibits several complications and accumulated errors in the tracking process due to wheel slippage, offset drift and integration approximations. These errors can be realized when comparing localization results from such sensors with a camera tracking system. In long trajectory tracking, such errors can accumulate and result in significant deviations which make data from these sensors unreliable for tracking. Meanwhile the utilization of an external camera tracking system is not always a feasible solution depending on the implementation environment. This paper presents a novel sensor fusion method that combines the measurements of internal sensors to accurately predict the location of the wheeled chair in an environment. The method introduces a new analogical OR gate structured with tuned parameters using multi-layer feedforward neural network denoted as “Neuro-Analogical Gate” (NAG). The resulting system minimize any deviation error caused by the sensors, thus accurately tracking the wheeled chair location without the requirement of an external camera tracking system. The fusion methodology has been tested with a prototype Mecanum wheel-based chair, and significant improvement over tracking response, error and performance has been observed.

Finite Element Multibody Simulation of a Breathing Crack in a Rotor with a Cohesive Zone Model

The breathing mechanism of a transversely cracked shaft and its influence on a rotor system that appears due to shaft weight and inertia forces is studied. The presence of a crack reduces the stiffness of the rotor system and introduces a stiffness variation during the revolution of the shaft. Here, 3D finite element (FE) model and multibody simulation (MBS) are introduced to predict and to analyse the breathing mechanism on a transverse cracked shaft. It is based on a cohesive zone model (CZM) instead of linear-elastic fracture mechanics (LEFM). First, the elastic cracked shaft is modelled by 3D FE. As a second step, the 3D FE model of the shaft is transferred into an MBS model in order to analyze the dynamic loads, due to the crack, and the inertia force acting during rotation at different rotating speeds. Finally, the vibration responses in the centroid of the shaft obtained from MBS have been exported into FE model in order to observe the breathing mechanism. A bilinear crack closure model is proposed. The accuracy of the bilinear crack closure model and the solution techniques have been demonstrated by a comparison with the corresponding results of previous publications.

Influence of Clutch Output Shaft Inertia and Stiffness on the Performance of the Wet Clutch

Being a part of the complex mass, spring, and damper system in a driveline, the choice of design factors such as output shaft stiffness and inertia of a wet clutch system can influence its performance. The effects of these parameters were experimentally evaluated. Widely used commercial paper-based friction plates with standard steel reaction plates were tested with four different stiffness and inertia combinations in a recently developed wet clutch test rig. A low inertia system in general showed a faster degradation and shorter clutch life for high torsional oscillation. In addition, the system became more shudder sensitive for lower natural frequency in the case of a less stiff system. The less stiff output shaft with low inertia showed the highest shudder tendency among the four conditions. The differences in performance for different output shaft conditions were noticeable for numerous clutch engagements or a degraded system. The effect of different shaft design conditions was also illuminated in the topographical analysis of the separators’ surfaces and morphological study of the frictional surfaces. This study revealed the influence of both inertia and stiffness not only on shudder sensitivity of the system but on the clutch frictional performance as well as the overall clutch life.

Dynamics of a Dual-Clutch Gearbox System: Analysis and Experimental Validation

Dynamic simulations and experimental validation tests were performed on a two-stage, two-speed gearbox. The gearbox was driven by two electromagnetic motors and had two electromagnetic, multidisk clutches to control output speed. A dynamic model of the system was created, which included a DC electric motor with proportional–integral–derivative speed control, a two-speed gearbox with dual electromagnetically actuated clutches, and an eddy current dynamometer. A six-degree-of-freedom model of the gearbox accounted for the system torsional dynamics and included gear, clutch, shaft, and load inertias as well as shaft flexibilities and a dry clutch stick-slip friction model. Experimental validation tests were performed on the gearbox in the NASA Glenn gear noise test facility. Gearbox output speed and torque as well as drive motor speed and current were compared to those from the analytical predictions. The experiments correlate very well with the predictions, thus validating the dynamic simulation methodologies.

Dynamic behavior of a coupled elastic shaft–elastic beam system

In this study, a servomotor-driven coupled elastic shaft–elastic beam system is analyzed. The model consists of a servomotor, elastic shaft, disk, and an elastic beam attached to the disk. Equations of motion are derived with respect to the generalized coordinates of the elastic shaft and elastic beam. Nondimensional parametric equations are obtained. Three independent parameters are defined affecting the system. These are the rigidity factor, the ratio of the beam inertia to total inertia, and the ratio of the shaft inertia to total inertia. Simulations demonstrate the important role of these three parameters in the behavior of the system.

Sampling-Induced Resonance in an Encoderless Vector-Controlled Induction Motor Drive

This paper illustrates an effect of sampling in an encoderless vector-controlled induction motor drive with a digital controller. The analysis focuses on the speed observer and the speed control loop which is executed at discrete instants. It is shown that the estimated speed can fluctuate between samples in the speed loop and cause a sustained resonance via feedback. The shaft inertia is not available to smooth the ripple of the estimated speed and the associated resonance could adversely affect the inverter and machine. An analytical model is proposed to evaluate the risk of such a condition in the design and on-site adjustment of control gains. The requirement for a smoothing filter in the speed loop is identified.

Experiments toward MRAC Design with Integral Compensation for Motor Drives

In this paper, a model reference adaptive control (MRAC) with integral compensation for motor drives was proposed. The system's robustness and transient behavior were greatly improved by incorporating a switching controller together with an integral compensation to attenuate the influence due to external disturbance. Modifications were also proposed to alleviate the chattering due to the high-frequency switching activity in control efforts. Furthermore, integrator windup due to integral action under actuator saturation was also considered. Experiments were performed on a single-chip microcomputer to control a DC brushless servo drive with adjustable shaft inertia to demonstrate the effectiveness and applicability of the proposed controller.

A Rayleigh-Type Inclusion of Shaft Inertia in Torsional Vibration Analysis

This paper considers the problem of properly accounting for the shafting inertia in torsional vibration analysis. It begins with a brief review of the two well-established methods: (1) arbitrarily lumping the shaft inertia with that of the disks, and (2) the continuum model, which considers both the flexibility and the inertia as distributed properties. Comments regarding the advantages and disadvantages of each are offered as motivation for the new method to be presented here. The new approach is then developed, using a Rayleigh-type approximation for the displacement between stations, with the full theory underlying it. The results of all three methods are then compared by application to several test cases.

Rotordynamics of a Mechanical Face Seal Riding on a Flexible Shaft

A mechanical face seal is a triboelement intended to minimize leakage between a rotating shaft and a housing, while allowing the shaft to rotate as freely as possible. All dynamic analysis to date have concentrated on the seal itself. In reality, however, especially in high speed turbomachinery, shafts are made flexible and the dynamics of seals must be coupled with the dynamics of shafts. (Perhaps the dynamics of other triboelements, such as gears, bearings, etc., have to be included as well.) In this work the complex extended transfer matrix method is established to solve for the steady state response of a noncontacting flexibly mounted rotor mechanical face seal that rides on a flexible shaft. This method offers a complete dynamic analysis of a seal tribosystem, including effects of shaft inertia and slenderness, fluid film, secondary seal, flexibly mounted rotating element, and axial offset of the rotor center of mass. The results are then compared to those obtained from an analysis that implicitly assumed the shaft rigid. The comparison shows that shaft dynamics can greatly affect the seal performance even at relatively low speeds.

Transient Phenomena in Compressor Stations During Surge

Transient phenomena are generally inherent in the operation of compressor stations: These are either fast or slow transients. A model describing the governing equation for the gas dynamics, control system, compressor and turbine shaft inertias has been developed. The effect of these inertias is manifested by an example of a compressor station operating near the surge control line. Another example deals with a station that has a cooler placed in the recycle path. This alters the rate at which the compressor shaft decelerates upon shutdown and may cause backward spinning depending on the relative magnitude of the shaft inertia with respect to the cooler volume. Backward spinning of compressor shaft has detrimental effects on dry seals and is undesirable. It was found that by keeping the recycle valve closed upon shutdown, the rate of shaft deceleration will be reduced.

Dynamic Analysis of Geared Shaft Systems By Using a Continuous System Model

In this study dynamic mesh forces and dynamic factors in a geared shaft system are studied by using a continuous system model. The system consists of a gear pair, two shafts carrying gears, and two inertias representing drive and load in the system. A continuous system model is used to include the shaft inertias, which are usually disregarded even in most of the sophisticated models. The primary aim of this work is to provide a tool for studying the effect of shaft inertia in gear dynamics, and to present some case studies. The results of the continuous system model are compared with those of a discrete system model in which the shaft inertias are neglected, and with the results of previous studies. Typically, the dynamic factors obtained by using the discrete system model are found to be greater than those obtained from the continuous system model, especially when shaft masses are large. It is concluded that the computation of dynamic factors by using the continuous system model suggested in this study in order to include the effects of shaft masses is a very good alternative to finite element models which are much more expensive to use.

A Control System for a High-Quality Generating Set Equipped With a Two-Shaft Gas Turbine

A control system has been developed for a high-quality generating set (150-kW) equipped with a two-shaft gas turbine featuring a variable power turbine nozzle. Because this generating set satisfies stringent frequency stability requirements, it can be employed as the direct electric power source for computer centers without using constant-voltage, constant-frequency power supply systems. Conventional generating sets of this kind have normally been powered by single-shaft gas turbines, which have a larger output shaft inertia than the two-shaft version. Good frequency characteristics have also been realized with the two-shaft gas turbine, which provides superior quick start ability and lower fuel consumption under partial loads.

Considerations for low-inertia AC drives in machine tool axis servo applications

The important differences encountered in applying AC permanent magnet servomotors that might have one-tenth of the shaft inertias of their torque-equivalent predecessors to machine tool axis servo applications are examined. Experimental results demonstrating these differences and corroborating the conclusions drawn are provided. Experimental testing was accomplished on a motor test stand and in a machine tool axis servo application. The test stand had two AC servomotors coupled in a motor/dynamometer configuration. Analytical and experimental results demonstrate that in addition to affecting the acceleration or command-following capabilities of the servomotor, reduction of shaft inertia affects the controller tuning robustness, bandwidths, and dynamic stiffness characteristics and also has implications for the drive/controller sampling rate. The process of selecting an appropriate servomotor for such axis servo applications is reviewed, and the factors that are affected by motor/magnet technology are summarized.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On Dynamic Loads in Parallel Shaft Transmissions: Part II—Parameter Study

Solutions to the governing equations of a spur gear transmission model, developed in Part I, are presented. Factors affecting the dynamic load are identified. It is found that the dynamic load increases with operating speed up to a system natural frequency. At operating speeds beyond the natural frequency the dynamic load decreases dramatically. Also, it is found that the applied load and shaft inertia have little effect upon the dynamic load. Damping and friction decrease the dynamic load. Finally, tooth stiffness has a significant effect upon dynamic loading: the higher the stiffness, the lower the dynamic loading. Also, the higher the stiffness the higher the rotating speed required for peak dynamic response.

Flexural motion of a radially rotating beam attached to a rigid body

Flexural motion of a radially rotating beam attached to a rigid body is investigated. Fully coupled non-linear equations of motion are derived by using the extended Hamilton's Principle. Spatial dependence is suppressed by using the extended Galerkin method. A torque profile is used to drive the rotating body so that the rigid body motion is not known a priori. The effect of the coupling terms upon the vibration waveforms are investigated by using both a linearized analysis and numerical solution of the differential equations. It is found that for small values of the ratio of the flexible beam and rigid shaft inertia uncoupled equations can lead to substantially incorrect results, particularly with regard to frequencies.

A Fully Coupled Variable Properties Thermohydraulic Model for a Cryogenic Hydrostatic Journal Bearing

The goal set forth here is to continue the work started by Braun et al. [11] and present an integrated analysis of the behavior of the two row, 20 staggered pockets, hydrostatic cryogenic bearing used by the turbopumps of the space shuttle main engine (SSME). The variable properties Reynolds equation is fully coupled with the 2-D fluid film energy equation [η = η(P, T)]. The 3-D equations of the shaft and bushing model the boundary conditions of the fluid film energy equation. The effects of shaft eccentricity, angular velocity and inertia pressure drops at pocket edge are incorporated in the model. Their effects on the bearing fluid properties, load carrying capacity, mass flow, pressure, velocity and temperature form the ultimate object of this paper.