# Optimization of a Loudspeaker: Minimal Mass

Loudspeakers with MagNet
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 goal of the optimization is to find a loudspeaker designer that has the minimal mass necessary to produce a flux density of 1.8 Tesla in the air gap.

### METHODS and RESULTS

## DESIGN VARIABLES for the LOUDSPEAKERS

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.

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## SPECIFYING the OBJECTIVE & CONSTRAINTS of the OPTIMIZATION

The objective of this optimization is to minimize the mass of the loudspeaker. There are two constraints in this example:

1. The average flux density in the air gap must be 1.8 Tesla

2. While varying geometric parameters, components cannot overlap

Up to 100 constraints can be added with distinct priority weights.

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## GRAPHING the VARIABLES & OPTIMIZATION

As the optimization is progressing, OptiNet displays the changes in the goal, variables, objectives, and constraints. 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 of the OPTIMZATION

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 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. The report also shows the time that it took to arrive at the improved design.

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## PRE-OPTIMIZED MAGNETIC FIELD in the LOUDSPEAKER

The initial design does not satisfy the constraint of 1.8 Tesla in the air gap (highlighted in the white box).

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## FINAL DESIGN FIELD

OptiNet found the minimal mass for which the constraints specified are satisfied. It took OptiNet 10 minutes and 38 seconds to arrive at this design on an Intel Core i7-2600 (8x 3.4GHz processors).

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## WEIGHT of the OPTIMIZED DESIGN

The graph compares the change in weight for each component, as well as the overall weight of the design.

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