Effect of Adding Damping to the Frame Vents

 Driver frame vents open

 Driver frame vents with damping layer

The photos show the same driver, firstly with the damping paper covering the frame holes removed and then with the damping layer intact.  This frame vent damping can be incorporated into our simulations.  In the first instance, I applied damping to the air within the port rather than creating an explicit layer in the CAD.  The reason for this is that the latter would require that the finite element mesh be much more refined, increasing the computational expense of the problem.  This may be reconsidered later.

In the simulation model, volume absorbency is applied to the frame vent holes as a Delany and Bazley model [1], which is relatively easy to apply as the only parameter to be prescribed is the flow resistivity.  This empirical model has a range of validity beyond which extrapolation may produce divergence, however in the interest of making progress in understanding the broad principles of headphone system behaviour, we will proceed with the approach and revisit the absorbency model later.

 

The charts below indicate the difference in SPL between the driver with open frame vent holes and the driver with a damping layer covering the frame vents.  The upper chart is the simulated driver, the lower is the measured driver sample.

The difference due to the damping in the frame vent holes mainly affects frequencies up to the resonance at 3.1kHz (model).  The dip associated with this resonance appears to rise in frequency slightly and reduce in magnitude and is preceded by a small peak that "fills in" the dip of the open case. The acoustics associated with this mid-frequency region is complex and some degeneracy is evident upon inspection of the animated results.  It seems inconvenient that the acoustical system is complicated by narrowband overlapping resonance at a frequency range where the ear is most sensitive.

Below this frequency there is a general drop in output.  From fundamental resonance at ~100Hz, the drop in SPL due to the damping is pretty constant with frequency but then follows a change in gradient towards the 3.1kHz resonance.  This feature is different between the modelled and measured driver, where the change in slope occurs at different frequencies.  The model indicates a constant loss in output from ~45Hz to 100Hz but then slopes positively towards the high frequencies.  In contrast the measured driver seems to have an extended flat loss region from ~100Hz to ~1.4kHz, and then follows a positive slope.  The behaviour seems similar, though encompassing different frequency ranges which may be attributed to the different bass port tunings.  Bearing in mind that the drivers are dissimilar in a number of respects, there may also be an influence of the way the frame vent absorbency was applied to the model and this may be investigated in more detail.

A common characteristic to both model and real driver is the drop in the fundamental driver resonance.  This can be observed clearly in the frequency response of the model, less obvious in the measured (lower chart) case, however the electrical impedance measurements below from the real driver sample present this behaviour more clearly.

 

When frame vent damping is not present, the fundamental resonance frequency is 102Hz, however when the damping layer is applied this drops to 65Hz.  This drop in frequency may be attributed to the presence of the open bass port, the effect of which is heightened as the influence of the frame vents is suppressed.

Another interesting observation from the electrical impedance is that the magnitude of the peak (Zmax) is reduced from ~470 Ohm to 123 Ohm, suggesting that air being forced through the material covering the vents presents a significant viscous effect on the mechanical system.

Below is a photo of the driver being measured using a laser Doppler vibrometer.  This instrument can detect very small vibrations, returning a voltage in proportion to velocity.  Measuring the surface velocity just above the voice coil (you can see the laser spot) informs of the change in dynamic behaviour due to the damping layer, but reduces the potential for detecting mechanical resonances of the diaphragm, which are of less interest to this study.

The chart below shows the magnitude (in dB) and phase of the velocity measured at the top of the voice coil.

These velocity spectra confirm the observations from the electrical impedance measurements.  The maximum values of velocity for open and damped frame vent cases are at different frequencies and lower in magnitude for the damped case.

The variations at ~200Hz are interesting.  This is due to the coil and diaphragm rocking and occurs in both open and damped cases and will be investigated later in more detail.

 

Reference:

[1]  M. E. DELANY and E. N. BAZLEY, "ACOUSTICAL PROPERTIES OF FIBROUS ABSORBENT MATERIALS", National Physical Laboratory, 1969.