ALGOR SOFTWARE HELPS HARMAN/JBL OPTIMIZE LOUDSPEAKER DESIGN

After analysis, this complex mode shape of a speaker diaphragm shows areas of movement with light dots. The black sections are nodal lines which remain still.

Engineers at Harman/JBL, Northridge, California, are using Algor Finite Element Analysis (FEA) software to model and analyze stereo loudspeaker designs. Analysis results help the firm to see the effects of vibration on speaker parts and enable engineers to modify their designs to optimize speaker life and sound clarity.

David Bie, a loudspeaker development engineer with Harman/JBL, recently used Algor to model and analyze a loudspeaker diaphragm. Bie used modal analysis to find the natural frequencies of the diaphragm, helping him pinpoint unusual surface vibrations.

"The diaphragm vibrates in response to a musical signal delivered from an amplifier," explains Bie. "The surface vibrations of the diaphragm produce sound waves in the air. The human ear is capable of receiving and interpreting signals over a very wide bandwidth - 20 to 20,000 Hertz. For a loudspeaker to sound natural, it must faithfully reproduce signals throughout this entire range."

High frequency speaker diaphragms (tweeters) are usually made of stiff materials such as aluminum, titanium, or beryllium. The diaphragms must be lightweight to respond to the higher frequencies, thus, a typical diaphragm thickness is only .001 inch to .003 inch. This stiff, thin surface is then connected to a stationary frame by some type of flexible surround, allowing the diaphragm to vibrate as a rigid piston. As long as this piston-like motion is maintained, designers can easily predict what sounds the diaphragm will output. At higher frequencies, however, surface waves develop that result in what is commonly referred to as "dome breakup". When this occurs, it becomes virtually impossible for the designer to predict the sound that will be produced by the diaphragm.

Using classical techniques, engineers have a difficult time solving for dome vibrations because of the complex math involved. This makes FEA a very attractive tool. "Analysis results allow me to study the structural integrity of any diaphragm, including those which are difficult or impossible to actually build," Bie states.

Because all modes are symmetrical, Bie models only one-half of the diaphragm, saving time and effort (top). After analysis, SuperView displays a light-shaded view of the model (center) as well as the model's natural frequencies (bottom) - the displacement amplitude and colors are added to make it easier to visualize the mode.

"Loudspeakers come in all sizes and shapes from one-half inch to 24 inches in diameter," continues Bie. "They are built from many materials including paper, plastic, metal, and composites. In all cases, a designer needs to gain an understanding of the vibrations on the surface and correlate these vibrations with the sounds they produce. For many diaphragms, it is not difficult to predict the surface velocity (and the resulting sound pressures) when the diaphragm operates in the first resonance. But at higher frequencies, the surface vibrations are not uniform, making it hard to predict and control the sound produced. In many cases, modal analyses have revealed that once breakup begins, the natural frequencies become very closely spaced. Knowing this, the engineer is able to find the mode frequencies with FEA and predict which frequency range will produce erratic or undesirable results from a given diaphragm."

Bie's typical FEA diaphragm model contains 2000 elements, is analyzed for the first 15 mode frequencies, and takes 12-15 hours to process. "The largest problem we completed had 3500 elements, 35 frequencies, and took about one week to solve," Bie states.

Bie performs his analyses on a 25 MHz 80386 computer with a Weitek coprocessor. His system has 16 MB of RAM, a 330 MB hard disk, and VGA graphics. An uninterruptible power supply (UPS) is also used so that overnight analyses are not disabled by power surges or outages.

David Bie, a development engineer with Harman/JBL, designs stereo loudspeakers with Algor.

"FEA analysis is pointing the direction for better diaphragms," says Bie. "Measurements using a non-contacting displacement sensor allow us to compare the analysis results with real surface vibrations. We also validate analysis results by sprinkling powder on the diaphragm. When the diaphragm vibrates, the powder creates nodal patters as the particles migrate toward areas with the least vibration."

Although Bie has access to a number of higher priced FEA packages, he prefers to use Algor's system. "Algor's best features are the user-friendly pre- and postprocessors, versatile graphics and animation, and the Hyper version's capability to directly utilize a system's extended memory," Bie comments. "I am impressed with how easily I can build and view models, and I've found if I color the model carefully and use slow motion animation I can see diaphragm vibrations which could not otherwise be seen. The Hyper version helps my hardware solve problems with a large number of elements so I can obtain higher frequency modes."

Bie has also used Algor software to perform stress analyses on the suspension system in the speaker. Results help him predict and optimize the life of the speaker, since large vibrations tend to fatigue the flexible surround. Bie has also examined the resonant modes of other associated structures. The walls of the box in which the woofer is mounted, for example, can vibrate and produce undesirable sound. FEA helps Bie develop designs that will minimize this effect.