= Impedance-head mass correction
{title2=$F_{\rm specimen}=F_{\rm gauge}-m_hA$}
An <impedance-head mass correction> removes the inertial <force> required to accelerate material between an <impedance head>'s force-sensing plane and the specimen. The manufacturer's construction places the acceleration sensor above the force gauge and makes the connection to the driving point stiff. Its guidance recommends compensation when the specimen's <mechanical dynamic mass> is comparable to the mass below the gauge.<Impedance Heads: Types 8000 and 8001 by Brüel and Kjær>[Printed pp.1–2, force-gauge placement; p.2, “Measurements on light structures” and Figure2]{ref}
Choose a common positive axis and assume a rigid intervening mass $m_h$ shares specimen acceleration $A$. <Newton's second law> gives
$$
F_g-F_s=m_hA,\qquad F_s=F_g-m_hA.
$$
Here $F_g,F_s,A$ are synchronized <complex amplitudes> at the same <angular frequency>. Hence the corrected <mechanical dynamic mass> is $F_s/A=F_g/A-m_h$, and corrected <mechanical accelerance> is $A/(F_g-m_hA)$. The effective intervening mass must include the applicable mounting hardware; it is not automatically the entire sensor mass.
For an original example, take $m_h=0.020\,\mathrm{kg}$, $A=10\,\mathrm{m/s^2}$ real, and $F_g=(0.60+0.80i)\,\mathrm N$. Then $F_s=(0.40+0.80i)\,\mathrm N$, with magnitude $\sqrt{0.80}\approx0.8944\,\mathrm N$. Subtracting unsigned amplitudes would instead give $1-0.20=0.80\,\mathrm N$ and lose the correct phase. The corrected <mechanical dynamic mass> is $(0.040+0.080i)\,\mathrm{kg}$.
The model requires synchronized channels, appropriate <measurement calibration> and sufficiently rigid motion below the force gauge. If that assembly flexes, its motion cannot be represented by one frequency-independent $m_h$. Subtracting inertia also does not recover the unattached specimen's response: the attached head can still change its <natural frequencies> and mode shapes. A useful apparatus check is a rigid test mass, for which the force/acceleration ratio should agree with the total moving mass in the chosen force plane within the tested range.
Back to article page
