Finite element modelling and optimization of solenoid actuators
This thesis is concerned with the application of electromagnetic finite element (FE) analysis, using a general purpose package, OPERA-2d, and optimization techniques to the design of solenoid actuators used in hydraulic control valves. Different methods of force calculations are reviewed, including Maxwell Stress Tensor (MST), multi-solution Virtual Work Principle (VWP), and single-solution based VWP methods. While the MST method enables the calculation of force using a single solution and provides the distribution of force transmitted across various sections of the integration surface enclosing the armature of the actuator, it requires a finer mesh for accurate force calculation compared to VWP. There is no advantage of MST and single-solution VWP methods over multi-solution VWP technique in computing force-displacement characteristics of a d.c. solenoid actuator with constant current source because in all methods a set of FE solutions has to be found anyway at several armature displacements. However, for solenoids where current varies with displacement, e.g. a.c. solenoids, the multi-solution VWP requires a large number of solutions. In this thesis both multi-solution VWP and MST methods are used. Implementation of single-solution methods is not possible using the current version of OPERA-2d. To understand the effect of armature geometry on the shape of the force-displacement characteristic, a parametric study using OPERA-2d has been conducted. A customized design shell environment (CusOP) is developed to aid and simplify the repetitive process of using OPERA-2d. The results of this study were used to design a new proportional solenoid actuator, which was built and tested. It was found that more desirable force displacement characteristics have indeed been achieved. A comprehensive review of available optimization techniques is presented. The most promising of these techniques, including Broyden-Fletcher-Goldfarb-Shanno (BFGS) variable metric procedure, Nelder-Mead simplex method, Gauss-Newton method, Levenberg-Marquardt procedure, Trust region method and Simulated Annealing, have been extensively evaluated by comparing their performance (in terms of number of function evaluations) in the optimization of eighteen general unconstrained problems and eighteen nonlinear least-squares problems. The Levenberg-Marquardt procedure shows clear advantage, displaying consistent performance over the range of problems tested. This method which can only find local optima is preferred to the Simulated Annealing global optimization method, because it does not require too many function calls. Finding local optima is usually sufficient in optimization of solenoid actuators and, therefore, it is chosen for this application. A program called Electromechanical Actuator Modelling and Optimization (EAMON) has been created for the implementation of constrained automated optimization by interfacing the Levenberg-Marquardt technique to OPERA-2d. The program has been used successfully to optimize the design of a proportional solenoid actuator to produce a specified force-displacement characteristic. It has also been used in optimizing an actuator, which was subsequently successfully tested, where the area under the force-displacement characteristic is maximized. The research demonstrates the advantages of using FE modelling and optimization techniques to improve the performance of practical solenoid actuators.