Design optimization of PM couplings using hybrid Particle Swarm Optimization-Simplex Method (PSO-SM) Algorithm
Introduction
The design of electric machines has long been the field of experience, extrapolation, trial-and-error and a hit of good fortune! Modelling and simulation techniques on the other hand have improved progressively over the last years and have somewhat helped to reduce some of the uncertainty and risk associated with machine design. Formal optimization techniques are readily available and could make a considerable contribution to machine design. The reason why their impact has been relatively minimal lies in the quality of the models that represent the heart of the optimization algorithm. A model of poor quality cannot be expected to give a truly optimal design. The conventional deterministic optimization techniques themselves have problems normally associated with local solutions rather than global solutions and the dependence on their starting point. In this respect, the newer stochastic methods and in particular the PSO algorithm approaches overcome these issues but usually at the cost of relatively increased search times.
The main drawbacks of the conventional deterministic techniques are that their efficiency depends on starting point, the search step length, and the accuracy of the descent direction evaluation. Also, the algorithm generally searches a point of local optimum unless the objective function is uni-modal. These disadvantages are clear in the results of simplex optimization method (SM) in references [1], [2], [3], [4] where convergence of the function to different points indicates the existence of local minima. On the other hand, although the PSO algorithms have been used for many types of applications especially for electric machine control [5], [6], [7], [8], [9], [10], they still have not been tuned to get rid of relatively convergence slowness especially for large search space optimization problems.
This paper aims to give further contribution in the “optimum” design of PM coupling drive using the proposed hybrid PSO-SM Algorithm. The results will be compared with the optimized results obtained by hybrid GA-SM of ref [3], and with that of using the PSO alone in ref [11] for exploring the merits of the proposed hybrid optimization technique.
Section snippets
Optimization Algorithms
In the design optimization of electrical machines, the following issues are worth bearing in mind [12]:
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There are usually many contradictory design objectives, which need to be optimized together and measured in different scales like volume and efficiency.
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Most design methodologies contain relaxable or soft constraints, as well as rigid or hard constraints.
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Sufficient information about the consumer requirements is usually available for the designer to determine his objectives and hence the
PM Coupling Drive
In the last two decades a range of permanent-magnet eddy current couplings was introduced into the industrial market offering the advantages of efficient operation, vibration/electrical isolation and jamming protection. These have found a wide scale application in blowers, compressors, conveyors and pumps [22], [23].
The principle of operation is relatively simple: one shaft is connected to a disc containing a number of embedded alternating polarity magnets. These are magnetized in the axial
Simulation results
A full list of the basic coupling design parameters are summarized in Table 1.The steel relative permeability was fixed at μr = 500 in the optimization because the flux density levels in the original design were low enough to ignore magnetic saturation. The assumed operating temperature was 20 °C which would be unrealistic in practice; however a nominal fixed temperature was used simply to illustrate the success of the optimization in reducing the volume of the standard coupling design and to
Conclusion
A constrained multiobjective optimization of PM drive coupling has been presented using Simplex Method (SM), Particle Swarm Optimization (PSO), and hybrid PSO-SM techniques. The hybrid technique combines the advantages of the PSO algorithm for locating the interval of a global optimal solution in the parameter search space with the faster execution times of classical SM technique in converging to the global solution.
A design optimization of the PM coupling with the objective of minimizing the
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