# Relative Motion in Accelerometer Calibration

## Sensor Mounting Considerations

In the back to back calibration method, the known sensitivity of the reference accelerometer combined with its measured output is used to determine the acceleration level of the shaker. This information combined with the measured output of the Sensor Under Test (SUT) is used to determine the SUT sensitivity thus completing the calibration. The obvious, yet sometimes overlooked, assumption in this method is that both sensors are subjected to the same acceleration input, bringing up the topic of this article.

Relative motion, as the name suggests, occurs when two arbitrary points have any displacement between them or when one moves “relative” to the other. In vibration calibration, the arbitrary points that we are interested in are the sensing element faces of the reference sensor and SUT. If we were to envision our SUT being mounted to our reference sensor through a soft spring, it would be obvious that we would be adding another degree-of-freedom to the measurement. As a result, we would not get accurate calibration results since there is no longer an identical motion relationship between the two vibration sensors. The most common causes of relative motion between the sensors is: 1. inadequate stiffness of the SUT mounting means, or 2. deflection of the mounting platform/surface.

To tackle the mounting consideration, first consider that sensors have mass and as a result also exhibit inertia. When the sensor is excited, the inertia of the sensor naturally resists this motion. This inertial force, which actually compresses/extends the crystal sensing element to create the measuring transaction, can also compress and extend the mounting means with which the sensor is attached. Deflection of the mounting means causes deviation from the sensors ideal flat response. In both test and calibration we attempt to ensure that the sensor is firmly mounted to the reference or test article to provide a flat frequency response.  Other techniques to ensure intimate contact of the sensor/structure interface (and avoiding relative motion) include removing any nicks or burs from the bottom of the sensor or mounting plate, using grease as a coupling agent between the surfaces to fill any irregularities in the lapping and using a mounting stud with proper torque. In calibration, the goal is to measure and characterize the ideal response of the accelerometer. In practical installation, the sensor's mount may be made by various adhesive means which will effectively limit the sensor's frequency response.

Addressing potential deflection of the mounting surface in calibration requires an understanding of structural dynamics. Most modern calibration exciters utilize an imbedded reference below a mounting platform. The natural frequencies and modes of the mounting platform will contribute to relative motion between the SUT and reference if the natural frequency is in, or near, the frequency range of calibration. To avoid this effect, avoid steel or aluminum mounting platforms in favor of a very stiff and lightweight material such as Beryllium which is the ideal material for this purpose and is found on most high performance calibration shakers.