Modeling and Analysis of Multiple Electrostatic Actuators on the Response of Vibrotactile Haptic Device

Abstract

In this research, modeling, and analysis of a beam-type touch screen interface with multiple actuators is considered. A mechanical model of a touch screen system, as thin beams, is developed with embedded electrostatic actuators at different spatial locations. This discrete finite element-based model is developed to compute the analytical and numerical vibrotactile response due to multiple actuators excited with varying frequency and amplitude. The model is tested with spring-damper boundary conditions incorporating sinusoidal excitations in the human haptic range. An analytical solution is proposed to obtain the vibrotactile response of the touch surface for different frequencies of excitations, number of actuators, actuator stiffness, and actuator positions. The effect of the mechanical properties of the touch surface on vibrotactile feedback provided to the user feedback is explored. Investigation of optimal location and number of actuators for a desired localized response, such as the magnitude of acceleration and variation in acceleration response for a desired zone on the interface, is carried out. It has been shown that a wide variety of localizable vibrotactile feedback can be generated on the touch surface using different frequencies of excitations, different actuator stiffness, number of actuators, and actuator positions. Having a mechanical model will facilitate simulation studies capable of incorporating more testing scenarios that may not be feasible to physically test.

Modeling and Experimental Evaluation of Haptic Localization Using Electrostatic Vibration Actuators

“…Here, the matrix C e contains only the damping due to the ERAs at the boundaries. Assembling the elemental mass, stiffness, damping, and external forces matrices, we obtain their global versions as M, K, C A , and f. The details on the derivation can be found in [27]. It is important to note that the matrix C A contains the damping information at the boundaries due to the actuators only.…”

“…We use an efficient analytical solution method for that purpose which gives the displacements and slopes across different degrees of freedom of the FE model for zero initial conditions, as shown in equation (6). Details on the derivation of the analytical solution method can be found in [27].…”

“…Here, P i , Q i are constant vectors defining harmonic motion with the same frequency ω i having different amplitudes at different degrees of freedom. The steady-state accelerations at different global nodes of the touch bar are given as [27],…”

“…Localized vibrotactile haptic stimulation on large TSDs with a limited number of actuators depends on factors like the type of actuators used, the type of excitations, and the placement of the actuators [27]. Physically constructing different large TSD systems with different configurations of these factors is not practical.…”

“…In this study, a finite element model of the large touch bar or beam-type display with two ERAs is proposed. The finite element model is based on our previous study [27] with augmentation of material damping and estimated actuator parameters to make it more realistic. The proposed finite element model supports multi-frequency excitations and can be conveniently extended to actuators or touch surfaces of different types.…”