The prediction of vibration in large electric machines

This thesis reports the development of a reliable method for the prediction of response to electromagnetically induced vibration in large electric machines. The machines of primary interest are DC ship-propulsion motors but much of the work reported has broader significance. The investigation has involved work in five principal areas. (1) The development and use of dynamic substructuring methods. (2) The development of special elements to represent individual machine components. (3) Laboratory scale investigations to establish empirical values for properties which affect machine vibration levels. (4) Experiments on machines on the factory test-bed to provide data for correlation with prediction. (5) Reasoning with regard to the effect of various design features. The limiting factor in producing good models for machines in vibration is the time required for an analysis to take place. Dynamic substructuring methods were adopted early in the project to maximise the efficiency of the analysis. A review of existing substructure- representation and composite-structure assembly methods includes comments on which are most suitable for this application. In three appendices to the main volume methods are presented which were developed by the author to accelerate analyses. Despite significant advances in this area, the limiting factor in machine analyses is still time. The representation of individual machine components was addressed as another means by which the time required for an analysis could be reduced. This has resulted in the development of special elements which are more efficient than their finite-element counterparts. The laboratory scale experiments reported were undertaken to establish empirical values for the properties of three distinct features - lamination stacks, bolted-flange joints in rings and cylinders and the shimmed pole-yoke joint. These are central to the preparation of an accurate machine model. The theoretical methods are tested numerically and correlated with tests on two machines (running and static). A system has been devised with which the general electromagnetic forcing may be split into its most fundamental components. This is used to draw some conclusions about the probable effects of various design features

A load-based approach for optimizing a packed-bed thermal store

This paper presents a load-based optimization approach for improving the efficiency of a packed bed. The optimization is based on splitting the work-cycle of the thermal store into two frequency components: low and high. A packed bed is designed for each one of the two profiles. A packed bed can be customised much better for a duty-cycle that contains a narrow range of frequencies.The case study presented considers a 24 h working-cycle (12 h charge / 12 h discharge) with a 10 MW peak power and an exergy storage requirement of 33.3 MW h (76.3 MW h of heat). A packed bed was optimized for this duty-cycle using a one dimensional model that varies the aspect ratio and the rock size. This packed bed is the ‘reference case’ for the study. The aim of the load-based optimization is to create a two-bed system that achieves lower exergy losses than the reference case while keeping the overall storage capacity constant.A sign-preserving filter is used as the signal-splitting tool. Numerous different work-cycle “splits” are explored. Results show that the exergy losses of the packed bed can be considerably reduced. The optimum work-cycle split considers a low-frequency packed bed that supplies 85% of the storage capacity and a high-frequency packed bed that provides the remaining 15%. The combined losses of the two packed beds are 644 kW h, which represents a reduction of 25.5% in comparison to the exergy losses of the reference case. The study demonstrates that the “load-based optimization” allows replacing a packed bed with an equivalent but more efficient two-bed system at almost no additional cost

Deflating quadratic matrix polynomials with structure preserving transformations

AbstractGiven a pair of distinct eigenvalues (λ1,λ2) of an n×n quadratic matrix polynomial Q(λ) with nonsingular leading coefficient and their corresponding eigenvectors, we show how to transform Q(λ) into a quadratic of the form Qd(λ)00q(λ) having the same eigenvalue s as Q(λ), with Qd(λ) an (n-1)×(n-1) quadratic matrix polynomial and q(λ) a scalar quadratic polynomial with roots λ1 and λ2. This block diagonalization cannot be achieved by a similarity transformation applied directly to Q(λ) unless the eigenvectors corresponding to λ1 and λ2 are parallel. We identify conditions under which we can construct a family of 2n×2n elementary similarity transformations that (a) are rank-two modifications of the identity matrix, (b) act on linearizations of Q(λ), (c) preserve the block structure of a large class of block symmetric linearizations of Q(λ), thereby defining new quadratic matrix polynomials Q1(λ) that have the same eigenvalue s as Q(λ), (d) yield quadratics Q1(λ) with the property that their eigenvectors associated with λ1 and λ2 are parallel and hence can subsequently be deflated by a similarity applied directly to Q1(λ). This is the first attempt at building elementary transformations that preserve the block structure of widely used linearizations and which have a specific action

Load optimization for reducing the cost of an electric vehicle’s battery pack

This paper presents a study on the cost-optimization of the battery pack of a Nissan Leaf. The optimization is based on decomposing the load that the battery pack experiences into two components (low and high frequency), each of which will be handled by an independent battery. The reduction in cost comes from the possibility of manufacturing batteries of different specifications whose cost per unit energy ($/kWh) and per unit power ($/kW) differ considerably from each other. The battery used for the low frequency part of the load will have a low cost per unit energy capacity and a higher cost per unit power whilst the fast-frequency battery is the reverse case.Two case studies have been carried out. The first one uses the load profile seen by the battery pack when the car is subjected to the EPA-LA92 driving cycle. The second case study considers a modified profile with a much higher crest factor. A sign-preserving filter is used in the study to perform the signal splitting. A two-dimensional search space is created with the two control parameters of the filter and numerous different “splits” are explored.Results show than an important reduction in the cost of the battery pack can be achieved. In the optimum configuration found—for the case study carried out with the modified profile—the low-frequency battery supplies 80.14% of the total capacity of the car (24 kWh) and sees a maximum peak power of 37.17 kW; whereas the fast-frequency battery has a smaller capacity of 4.77 kW h but sees a much larger peak power of 88.56 kW. The total cost of this hybrid system is estimated at $5939, which represents a 12.7% reduction in cost with respect to the original battery pack of the vehicle

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving non-classical damping is proposed. An example of modal control successfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components

Gas-to-gas heat exchanger design for high performance thermal energy storage

The mathematical modelling and optimization of a gas-to-gas heat exchanger with a non-constant cross sectional area is presented. The design of the cross sectional area of the heat exchanger analyzed is based on an hexagonal mesh, which would be highly impractical to fabricate in a conventional way but could be built relatively easily through modern manufacturing techniques. The geometric configuration proposed allows attaining a high exergy efficiency and a significant cost reduction, measured in terms of volume per unit of exergy transfer. The relationship that exists between the overall exergy efficiency of the heat exchanger and its cost is thoroughly explained throughout the study. The results obtained from the modelling demonstrate the premise that it is possible to realize designs for heat exchangers that are highly exergy-efficient and very cheap, owing to the small volume of material required, if the constrains imposed by the limitations of traditional manufacturing methods are set aside. Furthermore, the study reveals a very important fact: the volume of material in a heat exchanger increases in quadratic proportion to its characteristic dimension, which implies that scaling up the geometry has a strong impact on its cost-effectiveness

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual o-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving nonclassical damping is proposed. An example of modal control sucessfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components

Superconducting and conventional electromagnetic launch system for civil aircraft assisted take-off

This paper compares three possible linear motor topologies for an electromagnetic launch system to assist civil aircraft take-off. Assisted launch of civil aircraft has the potential of reducing the required runway length, reducing noise and emissions near airports and improving overall aircraft efficiency through reducing engine thrust requirements. A comparison is made of practical designs of a linear induction motor, a linear permanent magnet synchronous motor and a superconducting linear synchronous motor to propel the A320-200 aircraft. The machine design requirements are established considering aerodynamic and engine performance and allow the aircraft to safely complete the take-off procedure. Analytical design of conventional synchronous and asynchronous linear motor will be compared with finite element analysis. A superconducting synchronous motor design is also considered, accounting for full system losses including the cryocooler power requirement and the mechanical & design constraints necessary for the cooler and the superconducting coil

Thermal design of linear induction and synchronous motor for electromagnetic launch of civil aircraft

The engine size of modern passenger transport aircraft is principally determined by take-off conditions, since initial acceleration requires maximum engine power. An elec¬tromagnetic launch (EML) system could provide some or all of the energy required at takeoff so that the aircraft engine power requirement and fuel consumption may be significantly reduced. So far, EML for aircraft has been adopted only for military applications to replace steam catapults on the deck of aircraft carriers. This paper will describe the potential application of EML to propel civil aircraft on the runways of modern air¬ports. A comparison of synchronous and asynchronous electrical motor systems designed to launch an A320-200 sized aircraft is presented. The paper also describes a solution of the transient heat transfer problem applied to the conductive components of EML systems

Optimal internal pressurisation of cylindrical shells for maximising their critical bending load

AbstractThe paper studies the influence of internal pressure on circular thin-walled pipes (D/t>150) subjected to pure bending. Both straight pipes and curved pipes are analysed. Both yield and buckling failures are considered. It is shown that internal pressure decreases the limiting load for yield but increases the limiting load for buckling.The study is mainly FEA-based. A formula to predict critical moment given by linear buckling analysis is proposed. Comments on difference between linear and non-linear analysis results are given. It is shown that a pipe curvature opposite to the bending moment can increase the critical load. It is shown that cylindrical thin-walled shells have an optimal value of internal pressure to which limiting load for yield and critical buckling moment are equal, corresponding to an optimal use of material