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Introduction
The VAS test normally follows the Q and Fs test and generally involves some kind of driver modification. The two most commonly
known tests are the delta mass and delta compliance methods that seek to measure the driver's moving mass and suspension by
modifying the opposite parameter. That is, if a mass is added to the already existing moving mass, it stands to reason that the
resonant frequency will decrease. If the before and after resonances are properly measured, a bit of math will then reveal
the opposing parameter that determines mechanical resonance, which is the spring stiffness.
Spring and Mass Resonances
To begin, it helps to understand the equation for spring and mass resonance. Many people with a technical background may
remember the equations for the resonant frequency of a mass and spring. In this equation, spring stiffness,'K', is
given in Newtons per meter of displacement units and mass, 'M', is in kilograms. The important part is to notice that 'K'
is in the numerator and 'M' is in the denominator. Therefore, if the spring becomes stiffer, so will the resonant frequency.
Similarly, if mass, 'M', becomes heavier, the frequency decreases.
In Thiele-Small modeling, the terminology 'Kms' and 'Cms' are related as the inverse of each other; or Kms = 1/Cms. Cms, or
suspension compliance, is one of the capacitive elements of the equivalent speaker electrical model.
It is the inverse of the
mechanical spring stiffness of the system, Kms.
F = sqrt(K/M)/2*PI Frequency in Hz;
K=spring stiffness in Newtons/meter
M=moving mass in kilograms
W = sqrt(K/M) Frequency in Radians/second
where W=F*2*PI
Fms = sqrt(Kms/Mms) Free air resonance freqeuncy of moving
Mass Mms and suspension stiffness Kms
Spring and Mass Resonances
The delta mass test works on the principle that the resonant frequency of a mass and spring will change if the moving mass is
changed. This is accomplished by adding a known mass to the cone. If we know the drivers free air resonance from the
Q and Fs Test, a solution for Mms and Kms can be found from the new modified mass resonance.
Fms = sqrt(Kms/Mms) Equation for free air resonance
Fmass = sqrt(Kms/(Mms+Madd) Equation for delta mass 'Madd' modified frequency
Mms = Madd * Fmass^2/(Fms^2 - Fmass^2)
Kms = Madd * (Fms^2 * Fmass^2)/(Fms^2 - Fmass^2)
Delta Compliance Test
Math behind the delta compliance test is similar to the delta mass test except that the suspension stiffness is modified and
not mass. This is easily accomplished by mounting the driver into a sealed box with a known volume. The air inside the box then
acts like an air spring, 'Kbox', adding to the suspension spring Kms. If you don't have a test box available, start with the
delta mass test, design and build a box (slightly larger than planned) and then retest the driver with your new box and the
delta compliance test.
Efficiency and Cone Area Test
This test is not intended as a primary method for calculating the remaining Vas parameters. The math is based on reversing the
equation for efficiency by knowing cone area, free air resonance (Fms) and Qes. This in turn can be used to reverse Vas and
BL. Normally, this test is not used to calculated a TS parameter list. Rather, this test is used to create electrically
accurate models that can be used with crossover design packages.
Calculation of Sd, Vas, BL, Rms and Efficiency
Between the Q and Fs and Vas tests, Mms, Kms, Fms, Revc, Qes, and Qms are now known. The remaining TS parameters are then
calculated using the following equations:
Sd = PI*Diam^2/4.0 Cone area in m^2; Diameter measured with a ruler
Vas = C^2*DensityOfAir*Sd^2/Kms; Vas in m^3
BL = sqrt(Revc*Kms/(Qes*Fms*2.0*PI)) Motor force in Newtons/Ampere
Rms = 2.0*PI*Fms*Mms/Qms Mechanical resistance
Eff = 9.64E-10*Fms^3*VasL/Qes Wattage conversion efficiency
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