Multi-axis force sensing with pre-stressed resonant composite plates: An alternative to strain gauge force sensors

Industrial robots embedding multi-axis force sensors at the robot/environment interface presents numerous advantages in terms of safety, dexterity and collaborative perspectives. The key-point of these developments remains the availability of cheap but sufficiently precise multi-axis force sensors. This paper proposes a model-based approach to design a new alternative to commonly used strain gauge sensors. The principle of the device relies on pre-stress resonant composite plates where feedback control and measurement are achieved with piezoelectric transducers. The main originality of this work is that the force to be measured may present multi-axis components. Based on pre-stress and piezoelectric theories, a complete electromechanical model is proposed. This one is used during the design of a resonating composite Mindlin plate, embedding piezoelectric patches. It is shown that the effects of in-plane and out-of-plane external forces can be considered as pre-stress components. These ones, at the root of buckling phenomena, alter the stiffness of the structure and shift the plate resonance frequencies. Then, by solving the eigenvalue problem of the pre-stress vibrating structure, we can find the relationship between the natural frequencies of the structure and the externally applied multi-axis force. The proof of concept of this sensor is achieved on a case study. Finally, numerical results from both, home-made and commercial, finite element software demonstrates the interest of our approach to design integrated and inexpensive multi-axis force sensors solutions.