 Impedance-head mass correction

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.^[ref]

Choose a common positive axis and assume a rigid intervening mass $m_h$ shares specimen acceleration $A$. Newton's second law givesHere $F_g,F_s,A$ 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 $A/(F_g-m_{h}A)$. The effective intervening mass must include the applicable mounting hardware; it is not automatically the entire sensor mass.

For an original example, take $m_h=0.020\mathrm{kg}$, $A=10m/{\mathrm{s}}^2$ real, and $F_g=(0.60+0.80i)\mathrm{N}$. Then $F_s=(0.40+0.80i)\mathrm{N}$, with magnitude $\sqrt{0.80}\approx 0.8944\mathrm{N}$. 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.