Growing The Loudspeaker Ecosystem:
Pistonic Motion and The Speed of Sound
Understanding how beryllium’s unique qualities translate into better HF performance begins by looking closely at what’s happening inside a transducer during operation.
A transducer is an extremely complex electromechanical ecosystem where the entire assembly is required to move very quickly, and in perfect synchronicity. Any deviation from the desired motion, or deformation due to stress can cause unwanted resonances or “breakups” that we hear as distortion.
To better understand how breakup occurs, it’s helpful to examine it at the component level. A diaphragm, for example, should move in a perfect pistonic motion (like a piston), with all points moving in uniform and only in the desired direction. Breakup occurs when the forces acting upon the diaphragm overpower its structural integrity and different points on the surface begin moving in different times relative to one another. Because beryllium is extremely light and stiff, it does a better job of maintaining its structural integrity under load and avoiding these breakups.
Even more critical, however, is the efficiency at which sound travels through beryllium. This is important because the frequency at which the first breakup occurs in any metal, is analogous to the speed of sound through that metal. The speed of sound through beryllium is nearly 2.5 times faster than that of aluminum or titanium. This means the first breakup will occur at a much higher frequency–well outside the audible range in most cases. What’s more, when breakup does occur, beryllium’s greater stiffness ultimately reduces the amount (amplitude) of those breakups.
The remainder of this article will explore these exact qualities in greater detail. Evaluations will be conducted in three phases, comparing aluminum, beryllium and titanium in each phase. The first phase will use mathematical modeling to evaluate theoretical benefits of all three as a diaphragm material. The second will measure physical performance of individual domes through vibration testing, and the final phase involves actual acoustic analyses of a fully- assembled compression driver.
Modeling the difference
It’s relatively easy using mathematical (Finite Element Analysis – FEA) modeling to evaluate a theoretical diaphragm’s motion.
A finite element model was constructed using an identical, 100mm diaphragm geometry with the only variable being the material. This analysis intentionally ignores outside influences such as acoustical load, phase plug and horn geometry, in order to focus exclusively on the unique fidelity of each metal.
In turn, the unique properties of aluminum, titanium and beryllium were fed into the model while the actual geometry of the theoretical diaphragm was unaltered. The first six bending (breakup) modes are shown in figure 1 and charted in figure 2.
All the results clearly show that while the breakup modes for each metal are somewhat similar, the beryllium diaphragm’s breakup occurs at a much higher frequency than the other two (approximately 2.5 times higher), thereby shifting resonant frequencies outside the audible range.
Measuring the Vibrations
The vibrations of aluminum, titanium and beryllium compression driver domes were measured using a Klippel SCN laser scanner. These geometric and vibration scans make it easier to see how the predicted results match the measured results in the next section.
For simplicity, 2D (cross-section) measurements of each dome’s total vibration at four frequencies are presented. Beginning at 5kHz, relatively minor bending (breakup) occurs on all the domes. As the frequency goes up, bending waves become more visible.
In looking at the cross sections (figure 3) it’s clear that the beryllium dome remains significantly more settled at high frequencies than the other two.
As suggested by our theoretical analysis, its’ easy to see (figure 4) that the speed of sound of beryllium is roughly 2.5 times that of aluminum or titanium. These
measurements confirm this to be true and demonstrate beryllium’s inherent effectiveness at pushing breakup largely outside the audible range.
|Frequency||Number of bending waves (/radius)|
Figure 4: This chart presents similar data by simply counting the number of wavelengths up one side of each dome.
About the Vibration Testing Procedure
These test are performed using actual diaphragm domes with best possible profile and thickness consistency between them (it’s impossible to achieve the same degree of consistency between physical components as with mathematically modeled components).
The domes were mounted to the same compression driver motor assembly using a custom fixture that ensures repeatable position. To minimize the effects of different suspension methods, these scans were limited to a 51mm radius, 1mm outside the nominal voice coil radius. This restricts the measurements to only the metallic part of each dome.
Looking at Acoustic Performance
Frequency Response and Harmonic Distortion
These measurements confirm the benefits of beryllium’s better pistonic behavior, high frequency response linearity, and distortion. The data shows the actual frequency response and harmonic distortion performance of four different diaphragms on the same motor assembly using a plane wave tube, which was selected to eliminate the effects that a specific horn would introduce.