# Loudspeaker Optimization: Minimal Mass with 1.8 T Flux Density

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.

First, the speaker is optimized to meet the 1.8 T requirement in the air gap. This solution is then re-used as a seed in minimizing the magnet mass, with the air gap field constrained to be 1.8 T.

### 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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## DESIGN VARIABLES in OPTINET

The design variables to be optimized in OptiNet.

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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

The first optimization run was done to meet the air gap flux density requirement of 1.8 T. OptiNet's re-use feature allowed this solution to be used as the initial seed to permit further reduction in the magnet mass, with the air gap field constrained to be 1.8 T. This final solve satisfied the constraints and its field distribution in the air gap is as shown in the figure.

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## MASS of the OPTIMIZED DESIGN

The figure shows the initial and final geometric size of the loudspeaker after optimization. The increase in mass of the loudspeaker was necessary to meet the air gap field requirement of 1.8 T.

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