Estimation of reaction forces for an elastically-supported rigid body by reconstructed displacements using measurements of accelerometers and potentiometers

Abstract

This paper proposes a scheme for estimating the reaction forces of the rigid body supported by the elastic supports for all frequency bands including both quasi-static and dynamic components. Knowing the elastic supports reaction forces is important for the maintenance of stability, serviceability and durability of the rigid body. However, in order to directly measure the reaction forces of the elastic support, not only the elastic support is damaged but also the maintenance is difficult and the cost is expensive. To solve this problem, there is a previous study in which the acceleration is measured by an accelerometer on the surface of the rigid body, and then the elastic support reaction forces are estimated by using the rigid body kinematics and the displacement reconstruction scheme. However, there is a limitation that only dynamic components can be estimated and quasi-static components cannot be estimated. So, additional potentiometers are used to compensate the quasi-static components that was lacking only by the accelerometers and overcome the limitation, so that the elastic support reaction forces can be estimated for all frequency bands. Applying the global positioning system equation and the rigid body kinematics to the measured values of the potentiometers and applying the rigid body kinematics to the measured values of the accelerometers, the relative displacements and the relative accelerations at the arbitrary point in the rigid body are estimated. The reconstructed displacement at the arbitrary point is restored by the combine displacement reconstruction scheme using not only accelerations but also displacements. If the arbitrary point is set to the elastic supports, the reaction force can be estimated by using the displacement-force relation at the elastic support and if the arbitrary point is set to the center of gravity, the reaction force at the elastic support can be estimated by using displacement-force relation at the center of gravity and the pseudo-inverse. In order to verify the proposed scheme, numerical examples are constructed and applied.

Keywords : potentiometer, global positioning system, rigid body kinematics, displacement reconstruction scheme, elastic support reaction force