Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.

A Method for Predicting the Influences of Bearing Support Stiffness and Position on the Vibrations of a Flexible Rotor System

The bearing support stiffness and position can greatly affect the vibrations of flexible rotor systems (FRSs). However, most previous works only focused on the effect of the bearing support stiffness on the critical speeds or modal characteristics including the natural frequencies and mode shapes of rigid rotor systems (RRSs). The previous studies missed the combined effects of the bearing support stiffness and position. To overcome this issue, an analytical method of a FRS based on the finite element (FE) method is proposed. Our model considers the bearing support stiffness and rotational inertia of FRS. The frequency equation of FRS is established for solving the critical speeds. The critical speeds and modal deformations of FRS from our model and the numerical model based on a commercial software are compared to verify the effectiveness of the presented method. The effects of the bearing support stiffness and position on the critical speeds of FRS are analyzed. The results show that the critical speeds are positively correlated with the bearing support stiffness. The critical speeds of FRS are also greatly affected by the bearing position. This study can provide some guidance for the optimization design method of bearing support stiffness and position in FRSs.

Rapidly Accelerated Synchronous Generators in CAES Systems for Frequency Support in Power Grids

<p>Modern electrical networks are transformed through the use of intermittent sources of energy, such as small-scale photovoltaic installations and wind turbines. By reducing the carbon footprints associated with centralised power grids, they are made more vulnerable to contingent under-frequency events. The renewable energy sources can't provide the required rotational inertia to make the power grid's frequency stable and to be able to assist in restoring the frequency. In New Zealand, Transpower (system operator) is responsible for normalising the frequency in case of contingent events to avoid blackouts in the networks. In case of contingent events in power grids, additional power must be delivered to the networks with the use of primary frequency support systems. Internationally these systems are represented by under loaded power plants, where power output can be adjusted by controlling the primary governor output. This approach incurs no-load running costs and to avoid these costs generation units should be maintained at rest. The most efficient and technically feasible solution is to use synchronous generators that are already present in the power grids or can be additionally delivered to the grids as stand-alone units. However, with the use of the traditional synchronisation method, the generators cannot be synchronised with power grids in a short timeframe (up to 10 s in some countries). To overcome this disadvantage, a novel synchronisation approach should be designed to synchronise synchronous generators from rest of the electrical networks. This thesis proves that it can be achieved by a ballistic synchronisation approach (and then the improved 2-stage ballistic approach), which computes and follows an acceleration trajectory which simultaneously synchronises both phase and frequency. To achieve this fast acceleration a novel environmentally friendly small-scale compressed air energy storage (ss-CAES) system has been designed. This system utilises a hydraulic drivetrain which transmits very high torque directly to the shaft of a synchronous generator, thus enabling its rapid acceleration. The hydraulic drivetrain is composed of a proportional throttle valve and a variable-displacement hydraulic motor. The central controller from National Instruments outputs a voltage that controls the opening of the proportional valve. It changes the flowrate in the main hydraulic circuit, meaning that it is possible to control the output torque and velocity of the hydraulic motor. Since it is coupled to a synchronous generator, the control system can control the dynamics of the drivetrain by changing its voltage output. Computer simulations indicate that this approach enables very rapid synchronisation of a model system to the grid in < 1.5 s at a 100-kW scale. The modelling of the prototype helped to verify the control parameters of the system before the implementation of the algorithm built into the hardware. It should be noted that this model was simulated with the use of the corresponding manufacturer's data. To increase the accuracy of the mathematical model and verify the control parameters, the system components were experimentally characterised with the use of a ubiquitous high-speed data acquisition system. It resulted in a realistic and accurate mathematical model of the complex electro-hydraulic system, despite the well-known challenges of modelling the hydraulic domain. This model was utilised for the tuning of the control parameters of the system before its experimental testing. Experimental runs confirmed the feasibility of the proposed acceleration and synchronisation approach for synchronisation from the rest of the generator in < 4 s.</p>

Rapidly Accelerated Synchronous Generators in CAES Systems for Frequency Support in Power Grids

<p>Modern electrical networks are transformed through the use of intermittent sources of energy, such as small-scale photovoltaic installations and wind turbines. By reducing the carbon footprints associated with centralised power grids, they are made more vulnerable to contingent under-frequency events. The renewable energy sources can't provide the required rotational inertia to make the power grid's frequency stable and to be able to assist in restoring the frequency. In New Zealand, Transpower (system operator) is responsible for normalising the frequency in case of contingent events to avoid blackouts in the networks. In case of contingent events in power grids, additional power must be delivered to the networks with the use of primary frequency support systems. Internationally these systems are represented by under loaded power plants, where power output can be adjusted by controlling the primary governor output. This approach incurs no-load running costs and to avoid these costs generation units should be maintained at rest. The most efficient and technically feasible solution is to use synchronous generators that are already present in the power grids or can be additionally delivered to the grids as stand-alone units. However, with the use of the traditional synchronisation method, the generators cannot be synchronised with power grids in a short timeframe (up to 10 s in some countries). To overcome this disadvantage, a novel synchronisation approach should be designed to synchronise synchronous generators from rest of the electrical networks. This thesis proves that it can be achieved by a ballistic synchronisation approach (and then the improved 2-stage ballistic approach), which computes and follows an acceleration trajectory which simultaneously synchronises both phase and frequency. To achieve this fast acceleration a novel environmentally friendly small-scale compressed air energy storage (ss-CAES) system has been designed. This system utilises a hydraulic drivetrain which transmits very high torque directly to the shaft of a synchronous generator, thus enabling its rapid acceleration. The hydraulic drivetrain is composed of a proportional throttle valve and a variable-displacement hydraulic motor. The central controller from National Instruments outputs a voltage that controls the opening of the proportional valve. It changes the flowrate in the main hydraulic circuit, meaning that it is possible to control the output torque and velocity of the hydraulic motor. Since it is coupled to a synchronous generator, the control system can control the dynamics of the drivetrain by changing its voltage output. Computer simulations indicate that this approach enables very rapid synchronisation of a model system to the grid in < 1.5 s at a 100-kW scale. The modelling of the prototype helped to verify the control parameters of the system before the implementation of the algorithm built into the hardware. It should be noted that this model was simulated with the use of the corresponding manufacturer's data. To increase the accuracy of the mathematical model and verify the control parameters, the system components were experimentally characterised with the use of a ubiquitous high-speed data acquisition system. It resulted in a realistic and accurate mathematical model of the complex electro-hydraulic system, despite the well-known challenges of modelling the hydraulic domain. This model was utilised for the tuning of the control parameters of the system before its experimental testing. Experimental runs confirmed the feasibility of the proposed acceleration and synchronisation approach for synchronisation from the rest of the generator in < 4 s.</p>

Attitude stability control of micro-nano satellite orbit maneuver based on bias momentum

In this paper, an attitude stability control strategy based on cold air micro propulsion microsatellite orbital maneuver is designed. Firstly, the influence of environmental disturbance moment, uncertainty of rotational moment of inertia and thrust eccentricity moment on the attitude stability of the micro-nano-satellite is considered, and the attitude dynamics model of the micro-nano-satellite based on biased momentum wheel and magnetic moment device is established. Then, the disturbance moments such as environmental disturbance moments, rotational inertia uncertainty and thrust eccentricity moments are analyzed. In order to suppress the influence of various internal and external disturbance factors on the stability of the micro-nano-satellite during the deorbiting process, a robust adaptive sliding mode variable structure controller is designed. The designed robust adaptive sliding mode controller is able to compensate for various disturbances adaptively. The robust adaptive sliding-mode variable structure controller is designed with a reasonable distribution of torque considering the characteristics of bias momentum wheel control and magnetic control. Finally, numerical simulations are performed, and the simulation results show that the system has good robustness.

An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients

In this work, a novel methodology for the identification of stiffness and damping rotordynamic coefficients in a rotor-bearing system is proposed. The mathematical model for the identification process is based on the algebraic identification technique applied to a finite element (FE) model of a rotor-bearing system with multiple degree-of-freedom (DOF). This model considers the effects of rotational inertia, gyroscopic moments, shear deformations, external damping and linear forces attributable to stiffness and damping parameters of the supports. The proposed identifier only requires the system’s vibration response as input data. The performance of the proposed identifier is evaluated and analyzed for both schemes, constant and variable rotational speed of the rotor-bearing system, and numerical results are obtained. In the presented results, it can be observed that the proposed identifier accurately determines the stiffness and damping parameters of the bearings in less than 0.06 s. Moreover, the identification procedure rapidly converges to the estimated values in both tested conditions, constant and variable rotational speed.

A study on body sway of car-trailer combinations considering dry friction in steering subsystem

Considering the stability of vehicle system, static instability and dynamic instability are two different instability problems. Because of the dynamic coupling between car and trailer, the problem of dynamic stability of car-trailer combination (CTC) is more obvious. This instability is called body sway or flutter in engineering, its boundary is often described by dynamic critical speed ( vcrit). It has been proved by experiments that the steering system characteristics have an important impact on the dynamic stability of CTC, but the specific mechanism is not clear. In this paper, the characteristic and influence of steering subsystem are studied for the first time. Firstly, a 6-DOF nonlinear dynamic model of CTC is established by Lagrange equation. The steering subsystem characteristics, incl. stiffness, damping, rotational inertia, and dry friction, are considered in theoretical modeling. On this basis, the influences of steering characteristics, especially the dry friction, on vcrit and axle cornering stiffness of CTC are analyzed. Simulation results show that the vcrit can increase by 16% and 23.2% respectively via adjusting the steering stiffness and the sliding friction factor. Therefore, a fine selection of steering subsystem characteristics can effectively improve the dynamic stability and safety of CTC. The research results of this paper can provide reference for the design of steering system considering dynamic stability.

Investigation of Inertia Response and Rate of Change of Frequency in Low Rotational Inertial Scenario of Synchronous Dominated System

The shift to a sustainable energy future is becoming more reliant on large-scale deployment of renewable and distributed energy resources raising concerns about frequency stability. Rate of Change of Frequency (RoCoF) is necessary as a system inertia metric in order for network operators to perform control steps to preserve system operation. This paper presents in a straightforward and illustrative way several relevant aspects of the inertia response and RoCoF calculation that could help to understand and explain the implementation and results of inertial response controllers on power converter-based technologies. Qualitative explanations based on illustrative numerical experiments are used to cover the effects on the system frequency response of reduced rotational inertia in synchronous dominated power systems. One main contribution of this paper is making evident the importance of the governor action to avoid the synchronous machine taking active power from the system during the recovering period of kinetic energy in an under frequency event.

Parabolic velocity profile causes shape-selective drift of inertial ellipsoids

Understanding particle drift in suspension flows is of the highest importance in numerous engineering applications where particles need to be separated and filtered out from the suspending fluid. Commonly known drift mechanisms such as the Magnus force, Saffman force and Segré–Silberberg effect all arise only due to inertia of the fluid, with similar effects on all non-spherical particle shapes. In this work, we present a new shape-selective lateral drift mechanism, arising from particle inertia rather than fluid inertia, for ellipsoidal particles in a parabolic velocity profile. We show that the new drift is caused by an intermittent tumbling rotational motion in the local shear flow together with translational inertia of the particle, while rotational inertia is negligible. We find that the drift is maximal when particle inertial forces are of approximately the same order of magnitude as viscous forces, and that both extremely light and extremely heavy particles have negligible drift. Furthermore, since tumbling motion is not a stable rotational state for inertial oblate spheroids (nor for spheres), this new drift only applies to prolate spheroids or tri-axial ellipsoids. Finally, the drift is compared with the effect of gravity acting in the directions parallel and normal to the flow. The new drift mechanism is stronger than gravitational effects as long as gravity is less than a critical value. The critical gravity is highest (i.e. the new drift mechanism dominates over gravitationally induced drift mechanisms) when gravity acts parallel to the flow and the particles are small.