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Old Wisdom
When the conventional wisdom is to build a very solid and massive jig, it may seem counterintuitive to go in the opposite direction.
Nevertheless, building a completely resonance free test jig can be rather difficult given that at some point nearly everything
resonates. The solution shown here twists that conventional wisdom by constructing a jig whose resonance is as low as possible.
The solution ended up being a simple bungee cord. The principle is simple: the speaker being tested is a heavy mass suspended
from a soft spring resulting in a resonance that is typically in the 1-2 Hz range. Furthermore, the spring and mass become a
mechanical isolation filter that does not allow vibration to travel up or down through the bungee cord.
Free Air Resonance
The term 'free air resonance' (Fms) in loudspeaker design does not imply a driver floating in free air. Rather, Fms refers to the
characteristic resonance when the cone is not coupled to an enclosed air space in front or behind. This assumes the frame and
magnet are non-moving elements, and this means that to test for Fms, the driver frame is connected to something solid and very
heavy.
On the other hand, the 'bunjiggy' mechanical system is a free floating two mass (Mms and Mdr) system connected by a single
spring (Kms=1/Cms). This affects Fms, as the underlying resonance equation must now either include the driver and jig mass or use
an effective mass and spring stiffness. The equation for a two mass resonant system is given below. The equation indicates that
if the total moving mass (Mjig) is large relative to the cone mass (Mms), the effect on Fms will be small.
Mmsjig = 1/(1/Mms + 1/Mdr) // jig modified effective moving mass
Fmsjig = sqrt(Kms/Mmsjig)/2*PI // jig modified resonance
Fmsjig = sqrt(Kms)*sqrt(1/Mdr+1/Mms)/2*PI
By noting Fms=sqrt(Kms/Mms)/2*PI, useful equations relating Fms and jig resonance Fmsjig can also be written
Fms = Fmsjig*sqrt(Mdr/(Mdr+Mms)) // to get Fms from jig modified resonance
Fmsjig = Fms*sqrt((Mdr+Mms)/Mdr) // to get jig modified resonance from Fms
Fmsjig-Fms = Fms*(sqrt((Mdr+Mms)/Mdr)-1) // Delta of Fmsjig and Fms
A minimum jig+driver mass can also be computed for a given error ratio Err=(Fmsjig-Fms)/Fms, and from that a table relating the
Mdr/Mms ratio.
Err = (Fmsjig-Fms)/Fms = sqrt((Mdr+Mms)/Mdr)-1
Mdr = Mms/((1+Err)^2-1)
Error Mdr/Mms
10% 4.760
1% 49.75 << Typical quality drivers are about here
0.1% 499.75
Simple or Modified Bunjiggy
If an Fms shift is unacceptable, an option would be to place the test driver on a heavy platform hung from the bungee cord.This is
the same concept as used in turntable isolation. The effect in this case is to increase the total driver and jig mass Mdr. A suitable
platform in this case might be a stone or concrete block. Magnetic metals should be avoided as these will interact with the magnet
and therefore affect the driver BL product.
Effects on Other Parameters
In many cases the extremely simplified driver and bungee cord system shown will produce acceptable results. However, if precision
is of utmost concern, keep in mind that the effects of a double moving mass go beyond simply shifting Fms. In particular, the
data shows that Zmax and Qms have shifted significantly. As for Qes, no variation was detected, and since Qes dominates Qts, Qts
did not change much. The good news is that the data taken is clean enough to help formulate a hypothesis.
Test Data
Data was taken using the bungee cord and driver setup as shown, plus additional runs using a heavy subwoofer cabinet as a
platform. Two interleaved tests were run using each method to minimize drift. The average Fms values were found to be
35.362 and 35.0428 Hz resulting in a 0.3192 Hz shift.
Note:
The consistant shift in Zmax and Qms while Qes remained more or less constant. After this, a delta mass Vas test was run to find
the moving mass and other parameters.
Run Setup Revc Fms Qes Qms Qts Zmax
1 Norm 3.4417 35.0615 0.4278 7.1851 0.4038 61.24
2 Bjig 3.4446 35.3620 0.4276 8.2103 0.4064 69.58
3 Norm 3.4452 35.0242 0.4273 7.2643 0.4036 62.01
4 Bjig 3.4488 35.3620 0.4283 8.2053 0.4070 69.52
The Vas test to get the rest of the TS numbers:
Sd = 21408 mm^2
BL = 10.4597 N/A
Cms = 331.2745 um/N
Kms = 3018.6443 N/M
Mms = 61.1474 g
The total driver mass was then measured at ~3.4 kg using a kitchen scale that was maybe 10% acurate. Using the data and
equations above, the calculated jig frequency would be given by knowing Fms=35.362 Hz, Mms=61.1474 g and Mdr=3.4 kg.
Fjig = 35.3620*sqrt(3400/(3400+61.15)) = 35.0490
Results
The error between measured Fjig=35.0428 and predicted Fjig=35.0490 resonances of only 0.006 Hz is a good indication that this
method can lead to quite accurate results. However, though the effect was minor, finding that Qms is affected raises a few
other issues. This effect may be reversable, but this has not yet been proven either in the math or by measurement.
Conclusion
The Bungee Cord and simple hanging driver setup is simple and free of most jig resonances. However, some care should be taken to
consider how this will affect the overall TS model. For example, a small shift in Rms and Qms was observed. It may be possible to
create a mathematical model that backs out these minor effects. The ideal alternative option, besides a conventional setup,
is to hang a heavy mass from the bungee cord and place the test driver on that platform. The advantage will be a test platform
free of external influence.
WT-Pro with Bungee Cord Test Jig
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