Optimization - Minimizing Loudspeaker Mass
This example demonstrates the use of OptiNet with MagNet for the optimization of a loudspeaker design based on its electromagnetic characteristics. MagNet is used to compute the electromagnetic fields, and OptiNet is used to find the optimum design as specified by the user's requirements. The loudspeaker model shown here is made of two iron pieces and a permanent magnet. The permanent magnet drives the flux through the iron and the air gap. The figure below displays the magnetic field in the loudspeaker structure. The goal of the optimization, in this example, is to minimize the mass of the loudspeaker while obtaining a flux density of 1.8 Tesla in the air gap. It should be noted that the initial design specified by the user does not satisfy this constraint.
Results
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The field displayed on the cross-section of the loudspeaker model is the flux obtained from a magnetostatic analysis using the 2-dimensional axisymmetric solver.
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Variables: The geometry of the loudspeaker is defined based on the parameters shown in this figure. Of the 17 parameters shown on the diagram, 14 of them can vary within a range specified by the user -- the remaining parameters do not change. In OptiNet, the user specifies a minimum and a maximum value for those variables that can change, and OptiNet searches within this range to find the optimum design.
Objective function: The mass of the loudspeaker is defined as the objective function and the goal is to minimize this quantity. In OptiNet, basic quantities such as mass are available as pre-defined objectives. The mass is obtained from the volume and mass density of the iron and permanent magnet materials.
Constraints: There are two constraints in this example. The first constraint is that the average flux density in the air gap should be 1.8 Tesla. The second constraint is used to make sure that while OptiNet changes the values of the geometric parameters, no two components end up overlapping.
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Graph of variables: As the optimization is progressing, OptiNet displays the changes in the goal, variables, objectives, and constraints, all in the form of graphs. In this example, each of the fourteen variables' graphs (in groups not exceeding five variables per window) is updated as OptiNet finds a new design. As can be seen, there is a significant change in the value of the variables during the initial steps as OptiNet tries to satisfy the constraint of 1.8 Tesla in the air gap. After this constraint is satisfied, OptiNet tries to find the dimensions that would minimize the mass.
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Results: OptiNet produces a report for each optimization run. In this report, the designs that satisfy the constraints are shown in the order that they are improved. The user can view each design individually. The report also shows the time that it took to arrive at the improved design. The values of all the variables and the optimization function are displayed in this report for every iteration. The values of each parameter can be examined to determine the sensitivity of the design to that particular parameter.
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Initial design: In the initial design that the user supplied to OptiNet, the constraint of 1.8 Tesla was not satisfied. Therefore, OptiNet had to search for designs that would satisfy this constraint.
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Final design: The final design that OptiNet found satisfies the constraints specified by the user and the mass is minimized. It took OptiNet 2149 seconds (about 0.5 hours) on an AMD Athlon XP2800+ (2.08 GHz processor) to arrive at this design.
This example demonstrates the use of OptiNet with MagNet for the optimization of a loudspeaker design based on its electromagnetic characteristics. MagNet is used to compute the electromagnetic fields, and OptiNet is used to find the optimum design as specified by the user's requirements. The loudspeaker model shown here is made of two iron pieces and a permanent magnet. The permanent magnet drives the flux through the iron and the air gap. The figure below displays the magnetic field in the loudspeaker structure. The goal of the optimization, in this example, is to minimize the mass of the loudspeaker while obtaining a flux density of 1.8 Tesla in the air gap. It should be noted that the initial design specified by the user does not satisfy this constraint.
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