Tilt errors of translational accelerometers attached to dynamic systems with tilt motion caused by the system response

Translational inertia sensors - like the accelerometer - can measure the translational acceleration but they are incapable of distinguishing between translational and tilt motions. As an accelerometer tilts, it will measure a component of the gravitational acceleration along with the translational acceleration of the sensors. This results in a tilt error on the measured acceleration that masks the actual translational acceleration. In this paper, tilt error is studied for accelerometers attached to linear, stationary, and dynamic systems where the tilt motion origins from the system response. Mathematical formulations of the tilt errors are introduced where an impulse and frequency response function matrix for the measured acceleration from accelerometers is derived. It is proven that the tilt error is pollution by the rotational displacement on the translational acceleration of the accelerometers. Thus, the displacement of a dynamic system merges with its acceleration in the presence of tilt errors and the level of tilt error depends on the system and the excitation. In this paper, a method is introduced to reduce the tilt error. Both theory and tilt reduction are verified on a test-specimen in the laboratory.