Simulating a Piezoelectric-Haptic MEMS Actuator in Low-Frequency Vibration

When developing a haptic mouse, the authors aimed to exploit a documented phenomenon in which tangential loads to a user’s finger are aliased with positional cues. A flextension-style microelectromechanical system (MEMS) was designed to increase the range of actuation possible with the piezoelectrics preferred by nearly 10. The flextensional system converted the piezoelectric actuator into a two-degree-of-freedom (DOF) system, with the piezoactuator as a cyclic force. The actuator was intended to provide a wide range of feedback, the primary modality being the aliased positional cues with vibration as a secondary feedback mode. A single axis of the complete system was studied and designed for simplicity. Simulations of a piezoelectric actuator vibrating with and without a human finger resting on the actuator were studied. The actuator resembles a two-DOF system without a finger. With a finger, the actuator becomes a three-DOF system. All systems were simulated using MATLAB’s ODE45 solver. The quality of a single-degree-of-freedom reduction depended on whether the user’s finger was considered. Without a finger, no significant deviations in the system’s behavior were found; the equivalent spring, mass, and damper coefficients match those calculated by standard reduction methods without complication. The addition of a finger complicated the simulation. The frequency behavior of the single-degree-of-freedom system dropped an order of magnitude below the frequencies of the multi-degree-of-freedom system. This drop resulted in discrepancies between the simulated behavior of the multi-degree-of-freedom and its single-degree-of-freedom equivalent.