A comprehensive analytical subdomain model and its field solutions for surface-mounted permanent magnet machines

This paper presents a comprehensive analytical subdomain model together with its field solutions for predicting the magnetic field distributions in surface-mounted permanent magnet (PM) machines. The tooth tips and slotting effects during open-circuit, armature reaction, and on-load conditions are considered when deriving the model and developing its solutions. The model derivations and field solutions are extended from a previous model, and can be applied to PM machines with any combinations of slot and pole numbers and any magnetization patterns in the magnets. This model is initially formulated according to Laplace's and Poisson's equations in 2-D polar coordinates by the separation of variables technique in four subdomains, such as magnet, airgap, winding slots, and slot-openings. The field solution of each subdomain is obtained applying the appropriate boundary conditions and interface conditions between every two subdomains, respectively, which can precisely account for the mutual influence between slots. Finite element analysis (FEA) is later deployed to validate the analytical results in a surface-mounted PM machine that has nonoverlapping winding arrangement. For validation purposes, PM machines having 3-slot/2-pole with parallel magnetization and 12-slot/10-pole with either parallel or radial magnetizations are used for comparisons. Computation of global quantities for the motor which include the phase back-EMF and cogging torque is also included. The results indicate that the proposed analytical model can accurately predict the magnetic field distributions in each subdomain and the motor's global quantities, which are in good agreement with those obtained from the FEA.

An analytical model for web-warping in variable width flexible roll forming

The development of ultra/advanced high strength steels (U/AHSS) has challenged traditional forming methods due to their higher strength and reduced formability. An alternative method is flexible roll forming, which allows the manufacture of sheet metal of high strength and limited ductility into complex and weight-optimized components. However, one major problem in flexible roll forming is the web-warping defect, which is the deviation in height of the web over the length of the profile. The authors’ previous work developed an analytical model to predict the magnitude of web-warping. That model was purely geometric and neglected the effect of material properties. This work develops an analytical solution for the prediction of web-warping that considers both geometric and material parameters. The model results were validated by comparison with numerical and experimental results. The impact of this new model will be the ability to provide a rapid initial design assessment before an intensive numerical analysis of flexible roll forming is conducted.

Experimental and theoretical investigation of compression of a cylinder using a rotating platen

A rig was constructed to carry out compression of an aluminum cylinder with a monotonically rotating platen. The tests carried out showed that the compression load decreased and the side wall bulge severity reduced when the die was rotated. Not all the work supplied by the rotating dies was transferred to the work-piece; circumferential slippage was frequently observed at the die/material interface. This slippage was quantified by comparing measurements made during interrupted testing with the angular velocity of the die. A compound velocity field based on an exponential cusp description of the barreling was employed in an upper bound analysis. An approximate analytical solution was obtained for the degree of barreling and the compression pressure. The model is able to reproduce the decrease in barreling and compression loads with increasing die rotation.

Deformation behaviour of a cylinder under simultaneous compression and torsion

A number of experiments involving the compression of an Aluminum cylinder with concurrent die rotation were carried out. Two important features were observed: one was that die rotation reduced the degree of bulging and the other was that the compression load decreased. An upper bound analysis with a velocity field consisting of a compound exponential cusp representation was utilized to obtain an approximate analytical solution in a closed form. The theoretical result reproduced the reduction in bulging severity with die rotation as well as the changes in compression pressure.

Analysis of the inverse kinematics problem for 3-DOF axis-symmetric parallel manipulators with parasitic motion

 Determining an analytical solution to the inverse kinematics problem for a parallel manipulator is typically a straightforward problem. However, lower mobility parallel manipulators with 2-5 degrees of freedom (DOFs) often suffer from an unwanted parasitic motion in one or more DOFs. For such manipulators, the inverse kinematics problem can be significantly more difficult. This paper contains an analysis of the inverse kinematics problem for a class of 3-DOF parallel manipulators with axis-symmetric arm systems. All manipulators in the studied class exhibit parasitic motion in one DOF. For manipulators in the studied class, the general solution to the inverse kinematics problem is reduced to solving a univariate equation, while analytical solutions are presented for several important special cases.

Effect of elastic modulus and poisson's ratio on guided wave dispersion using transversely isotropic material modelling

Timber poles are commonly used for telecommunication and power distribution networks, wharves or jetties, piling or as a substructure of short span bridges. Most of the available techniques currently used for non-destructive testing (NDT) of timber structures are based on one-dimensional wave theory. If it is essential to detect small sized damage, it becomes necessary to consider guided wave (GW) propagation as the behaviour of different propagating modes cannot be represented by one-dimensional approximations. However, due to the orthotropic material properties of timber, the modelling of guided waves can be complex. No analytical solution can be found for plotting dispersion curves for orthotropic thick cylindrical waveguides even though very few literatures can be found on the theory of GW for anisotropic cylindrical waveguide. In addition, purely numerical approaches are available for solving these curves. In this paper, dispersion curves for orthotropic cylinders are computed using the scaled boundary finite element method (SBFEM) and compared with an isotropic material model to indicate the importance of considering timber as an anisotropic material. Moreover, some simplification is made on orthotropic behaviour of timber to make it transversely isotropic due to the fact that, analytical approaches for transversely isotropic cylinder are widely available in the literature. Also, the applicability of considering timber as a transversely isotropic material is discussed. As an orthotropic material, most material testing results of timber found in the literature include 9 elastic constants (three elastic moduli and six Poisson's ratios), hence it is essential to select the appropriate material properties for transversely isotropic material which includes only 5 elastic constants. Therefore, comparison between orthotropic and transversely isotropic material model is also presented in this article to reveal the effect of elastic moduli and Poisson's ratios on dispersion curves. Based on this study, some suggestions are proposed on selecting the parameters from an orthotropic model to transversely isotropic condition.

Machining of coarse grained and ultra fine grained titanium

Machining of titanium is quite difficult and expensive. Heat generated in the process of cutting does not dissipate quickly, which affects tool life. In the last decade ultra fine grained (UFG) titanium has emerged as an option for substitution for more expensive titanium alloys. Extreme grain refinement can be readily performed by severe plastic deformation techniques. Grain refinement of a material achieved in this way was shown to change its mechanical and physical properties. In the present study, the microstructure evolution and the shear band formation in chips of coarse grained and UFG titanium machined to three different depths and three different feeding rates was investigated. A change in thermal characteristics of commercial purity Ti with grain refinement was studied by comparing heating/cooling measurements with an analytical solution of the heat transfer boundary problem. It was demonstrated that an improvement in the machinability can be expected for UFG titanium. © 2012 Springer Science+Business Media, LLC.

Determinations of stress wave velocity in a timber pole using wavelet transform

This paper presents an application of Wavelet Transfonn (WT) for determination of stress wave velocity for Non-destructive Testing of timber utility poles in service. For surface Non-destructive Testing (NDT), the hammer impact, which produces generally broadband frequency excitation, is used to generate stress wave. Moreover, due to practicality the impact location for field testing of a utility pole is on the side of the pole and 1.5 m above ground level. And the geometry of utility pole could not guarantee non-dispersive longitudinal wave. All of these issues have resulted in lack of accuracy and reliability of results from surface NDT in field testing. In recognition of such problem, this research explores methods to reliably calculate desired wave velocity by isolating wave mode and studying dispersive nature of utility pole. Fast Fourier Transfonn (FFT) is firstly conducted to determine the suitable frequency from a stress wave data. Then WT is applied on the wave data mentioned to perfonn time-frequency analysis. Velocity can be detennined by time history data of desired frequency from WT results which will be compared with the available analytical solution for longitudinal wave velocity. The results of the investigation showed that wavelet transfonn analysis can be a reliable signal processing tool for non-destructive testing in tenns of velocity detennination, which in tum also helps to detennine the embedded length of the timber pole.

Strain localisation patterns under equal-channel angular pressing

Instabilities of plastic flow in the form of localised shear bands were experimentally observed to result from equal-channel angular pressing (ECAP) of magnesium alloy AZ31. The appearance of shear bands and their spacing were dependent on velocity of the pressing and applied back-pressure. A generic gradient plasticity theory involving second-order strain gradient terms in a constitutive model was applied to the case of AZ31 deformed by ECAP. Linear stability analysis was applied to the set of equations describing the deformation behaviour in the process zone idealised as a planar shear zone. A full analytical solution providing a dispersion relation between the rate of growth of a perturbation and the wave number was obtained. It was shown that the pattern of incipient localised shear bands exhibits a spectrum of characteristic lengths corresponding to admissible wave numbers. The interval of the spectrum of wave numbers of viable, i.e. growing, perturbations predicted by linear stability analysis was shown to be in good agreement with the experimentally observed spectrum. The effect of back-pressure applied during ECAP was also considered. The predicted displacement of the shear band spectrum towards lower wave numbers, shown to be a result of the decreased shear strain rate in the shear zone, was consistent with the experimentally observed increase of the band spacing with increased back-pressure. A good predictive capability of the general modelling frame used in conjunction with linear stability analysis was thus demonstrated in the instance of the particular alloy system and the specific processing conditions considered.

Fast vision-based catheter 3D reconstruction

Continuum robots offer better maneuverability and inherent compliance and are well-suited for surgical applications as catheters, where gentle interaction with the environment is desired. However, sensing their shape and tip position is a challenge as traditional sensors can not be employed in the way they are in rigid robotic manipulators. In this paper, a high speed vision-based shape sensing algorithm for real-time 3D reconstruction of continuum robots based on the views of two arbitrary positioned cameras is presented. The algorithm is based on the closed-form analytical solution of the reconstruction of quadratic curves in 3D space from two arbitrary perspective projections. High-speed image processing algorithms are developed for the segmentation and feature extraction from the images. The proposed algorithms are experimentally validated for accuracy by measuring the tip position, length and bending and orientation angles for known circular and elliptical catheter shaped tubes. Sensitivity analysis is also carried out to evaluate the robustness of the algorithm. Experimental results demonstrate good accuracy (maximum errors of  ±0.6 mm and  ±0.5 deg), performance (200 Hz), and robustness (maximum absolute error of 1.74 mm, 3.64 deg for the added noises) of the proposed high speed algorithms.

A study of guided wave propagation in timber pole using spectral finite element method

Timber is one of the most widely used structural material all over the world. Round timbers can be seen as a structural component in historical buildings, jetties, short span bridges and also as piles for foundation and poles for electrical and power distribution. To evaluate the current condition of these cylindrical type timber structures, guided wave has a great potential. However, the difficulties associated with the guided wave propagation in timber materials includes orthotropic behaviour of wood, moisture contents, temperature, grain direction, etc. In addition, the effect of fully or partially filled surrounding media, such as soil, water, etc. causes attenuation on the generated stress wave. In order to investigate the effects of these parameters on guided wave propagation, extensive numerical simulation is required to conduct parametric studies. Moreover, due to the presence of multi modes in guided wave propagation, dispersion curves are of great importance. Even though conventional finite element method (FEM) can determine dispersion curves along with wave propagation in time domain, it is highly computationally expensive. Furthermore, incorporating orthotropic behaviour and surrounding media to model a thick cylindrical wave (large diameter cylindrical structures) make conventional FEM inefficient for this purpose. In contrast, spectral finite element method (SFEM) is a semi analytical method to model the guided wave propagation which does not need fine meshes compared to the other methods, such as FEM or finite difference method (FDM). Also, even distribution of mass and stiffness of structures can be obtained with very few elements using SFEM. In this paper, the suitability of SFEM is investigated to model guided wave propagation through an orthotropic cylindrical waveguide with the presence of surrounding soil. Both the frequency domain analysis (dispersion curves) and time domain reconstruction for a multi-mode generated input signal are presented under different loading location. The dispersion curves obtained from SFEM are compared against analytical solution to verify its accuracy. Lastly, different numerical issues to solve for the dispersion curves and time domain results using SFEM are also discussed.

Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile.

We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

Chemistry, spectroscopy and analytical applications of certain chemiluminescent reactions

Chemiluminescence, the production of light from a chemical reaction, has found widespread use in analytical chemistry. Both tris (2, 2’-bipyridyl) ruthenium (II) and acidic potassium permanganate are chemiluminescence reagents that have been employed for the determination of a diverse range of analytes. This thesis encompasses some fundamental investigations into the chemistry and spectroscopy of these chemiluminescence reactions as well as extending the scope of their analytical applications. Specifically, a simple and robust capillary electrophoresis chemiluminescence detection system for the determination of codeine, O6-methylcodeine and thebaine is described, based upon the reaction of these analytes with chemically generated tris(2,2'-bipyridyl)ruthenium(III) prepared in sulfuric acid (0.05 M). The reagent solution was contained in a glass detection cell, which also held both the capillary and the cathode. The resultant chemiluminescence was monitored directly using a photomultiplier tube mounted flush against the base of the detection cell. The methodology, which incorporated a field amplification sample introduction procedure, realised detection limits (3a baseline noise) of 5 x 10~8 M for both codeine and O6-methylcodeine and 1 x 10~7 M for thebaine. The relative standard deviations of the migration times and the peak areas for the three analytes ranged from 2.2 % up to 2.5 % and 1.9 % up to 4.6 % respectively. Following minor instrumental modifications, morphine, oripavine and pseudomorphine were determined based upon their reaction with acidic potassium permanganate in the presence of sodium polyphosphate. To ensure no migration of the permanganate anion occurred, the anode was placed at the detector end whilst the electroosmotic flow was reversed by the addition of hexadimethrine bromide (0.001% m/v) to the electrolyte. The three analytes were separated counter to the electroosmotic flow via their interaction with a-cyclodextrin. The methodology realised detection limits (3 x S/N) of 2.5 x 10~7 M for both morphine and oripavine and 5 x 10~7 M for pseudomorphine. The relative standard deviations of the migration times and the peak heights for the three analytes ranged from 0.6 % up to 0.8 % and 1.5% up to 2.1 % respectively. Further improvements were made by incorporating a co-axial sheath flow detection cell. The methodology was validated by comparing the results realised using this technique with those obtained by high performance liquid chromatography (HPLC), for the determination of both morphine and oripavine in seven industrial process liquors. A complimentary capillary electrophoresis procedure with UV-absorption detection was also developed and applied to the determination of morphine, codeine, oripavine and thebaine in nine process liquors. The results were compared with those achieved using a standard HPLC method. Although over eighty papers have appeared in the literature on the analytical applications of acidic potassium permanganate chemiluminescence, little effort has been directed towards identifying the origin of the luminescence. It was found that chemiluminescence was generated during the manganese(III), manganese(IV) and manganese(VII) oxidations of sodium borohydride, sodium dithionite, sodium sulfite and hydrazine sulfate in acidic aqueous solution. From the corrected chemiluminescence spectra, the wavelengths of maximum emission were 689 ± 5 nm and 734 ± 5 nm when the reactions were performed in sodium hexametaphosphate and sodium dihydrogenorthophosphate or orthophosphoric acid environments respectively. The corrected phosphorescence spectrum of manganese(II) sulfate in a solution of sodium hexametaphosphate at 77 K, exhibited two peaks with maxima at 688 nm and 730 nm. The chemical and spectroscopic evidence presented strongly supported the postulation that the emission was an example of solution phase chemically induced phosphorescence of manganese(II). Thereby confirming earlier predictions that the chemiluminescence from acidic potassium permanganate reactions originated from an excited manganese(II) species. Additionally, these findings have had direct analytical application in that manganese(IV) was evaluated as a new reagent for chemiluminescence detection. The oxidations of twenty five organic and inorganic species, with solublised manganese(IV), were found to elicit analytically useful chemiluminescence with detection limits (3 x S/N) for Mn(II), Fe(II), morphine and codeine of 5 x 10-8 M, 2.5 x 10-7 M, 7.5 x 10-8 M and 5 x 10-8M, respectively. The corrected emission spectra from four different analytes gave wavelengths of maximum emission in the range from 733 nm up to 740 nm indicating that these chemiluminescence reactions also shared a common emitting species, excited manganese(II). Whilst several analytical problems were addressed in this thesis and answers to certain questions regarding the fundamentals of acidic potassium permanganate chemiluminescence were proposed, there are several areas that would benefit from further research. These are outlined in the final chapter of this thesis.

Synthesis, characterization and analytical modelling of mechanical behavior of a conducting polymer actuator

Electrochemical synthesis of a tri-layer polypyrrole based actuator optimized for performance was reported. The 0.05 M pyrrole and 0.05 M tetrabutylammonium hexaflurophosphate in propylene carbonate (PC) yielded the optimum performance and stability. The force produced ranged from 0.2 to 0.4mN. Cyclic deflection tests on PC based actuators for 3 hours indicated that the displacement decreased by 60%. PC based actuator had a longer operating time, exceeding 3 hours, compared to acetonitrile based actuators. A triple-layer model of the polymer actuator was developed based on the classic bending beam theory by considering strain electrode material. A tri-layer actuator was fabricated [4, 6], by initially sputter coating a PVDF film with approximately 100nm of gold layer, resulting in a conductive film with a surface resistance of 8-10Ω. The PVDF film was about ~145µm thick had an approximate pore size of 45μm. A solution containing 0.05M distilled pyrrole monomer, 0.05M (TBAPF6) and 1% (w/w) distilled water in PC (propylene carbonate) solution was purged with nitrogen for 15 minutes. The continuity between PPy and PVDF. Results predicted by the model were in good agreement with the experimental data.