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# Modal hammer calibration

### Question

I would like to check the sensitivity of the modal hammer with the so called "relative method", with the use of an accelerometer. Could you please let me know how to do this?

To calibrate a modal hammer, with the relative method, you will need

• Known mass suspended so it can swing freely

• Calibrated accelerometer of know mass and sensitivity

• Modal hammer

• Oscilloscope / data acquisition system

Accelerometer selected has to be mounted to the mass as show in the picture below. Mounting of the accelerometer should be with a mounting stud/screw or attached with double sided adhesive tape, as those two methods ensure the flattest broad band amplitude vs. frequency response.

The known mass has to be a rigid body with a resonant frequency much higher than the highest frequencies that could be excited during the impact test. According to Newton's second law, F=m*a, the acceleration caused by the modal hammer hit shall be proportional to the force and counter-proportional to the mass of a suspended "known mass" and accelerometer attached to it (a=F/m). Once the accelerometer and modal hammer are connected to the vibration analyzer or compatible oscilloscope, their voltage (IEPE) outputs can be measured, allowing the sensitivity (mV/lb-f [mV/N]) of the modal hammer to be calculated from the following formula. SF - Force sensor sensitivity [mV/N] Sacc - Accelerometer sensitivity [mV/ (m/s^2)] m - Mass of suspended mass and accelerometer [kg] VF - Voltage output of force sensor - peak value [mV] Vacc - Voltage output of accelerometer - peak value [mV]

Conclusion

Therefore we can assume a flat transfer function of the suspended mass and the movement of the suspended mass, with the accelerometer attached to it. With a constant mass there is a direct proportion between acceleration and the applied force from the modal hammer during impact.

Due to the particular modal hammer impacts possibly differing between each other (force, angle of impact, etc.) the final sensitivity shall be averaged between 10 impact tests.

Pertinent equations

a = F/m
m = F/a
F = ma
N = (kg)(m/s2)

*To convert Newtons to lb-f, multiply Newtons by 0.2248