Nonintrusive Measurement of Contact Forces During Vibration Dominated Impacts

Impact force estimation is done indirectly through, e.g., strain measurements away from the contact point, because inserting a force transducer between the contacting objects changes the force. Most prior contact force measurements involved a single contact interval. Here we study transverse impacts of a slender beam and a clamped-free plate; contact occurs more than once within one impact. Strain gauge data, electrical contact detection, and a dynamic model of the beam are used to estimate the contact force. The problem of force estimation from strain gauge data is ill-posed, and Tikhonov regularization fails initially. A reduced-order model is then developed using symmetry, and better initial conditions are estimated using a Kalman filter. Subsequently, Tikhonov regularization gives excellent force estimates, empirically supported by the contact duration measurements. Two other methods that explicitly use the contact duration measurements are also given. The first uses Tikhonov regularization within each contact interval, followed by Kalman filtering during noncontact to get initial conditions for the next contact. The second uses truncated Fourier sine series in each contact interval and is, computationally, the simplest. All three methods provide consistent force estimates. Our work complements recent work by Inoue and coworkers where the impulse response of the colliding object was measured separately using a Hopkinson bar, and electrical contact was not monitored.