# Haptic Soft-Keyboard for Tablet-Sized Touchscreens
## 3 Materials and Methods
### Design of Haptic Actuators for Tablet Touchscreens
#### 3.1.2 Optimal Design of Piezoelectric Benders  
In this study, we focus on maximizing the mechanical displacement \(\delta\) while meeting the size requirements (thickness less than 0.5 mm and width of 8 mm). To maximize the displacement \(\delta\) assuming the material coefficients and the applied voltage to be constant, the layer thickness should be optimized by controlling the number of layers and the layer ratio. Thus, two factors (layers and the ratio of layers) were investigated by simulations, and then the structure of a piezoelectric bender to be mounted underneath the tablet touchscreen was designed and manufactured. There is limited space on the bezel of tablet touchscreens; thus, the width and the thickness of the actuator were fixed to 8 mm and 0.4 mm, respectively, due to the space limit [10 mm width on the bezel and a 0.5 mm gap between the touchscreen and the liquid crystal display (LCD) panel] of commonly used 10.1 inch tablets). A software tool, COMSOL Multiphysics, using a finite element method was used for simulating the bending effects of piezoelectric actuators from a single layer (called unimorph) to three layers. Our intention with the tool is to simulate the behavior of piezo bending in the z axis as a square wave (500 Hz, 20 Vpp) is applied, which will generate a force under the touchscreen that is eventually bent. A rectangle plate [(H) 40 \(\times\) (W) 8 \(\times\) (T) 0.4 mm] was designed and simulated with parameters [pole directions: down (unimorph); up and down (bimorph); up-up-down (three layers), layer thickness: 0.3 mm (unimorph); 0.15 mm each (bimorph); 0.1 mm and 0.14 mm (three layers) for Pe and Pi, respectively]. The pole directions were found by a pilot analysis investigating the bending strength versus pole directions (in series or parallel). The simulation was run on a Windows machine (CPU i5-6500 3.2 Hz, RAM 8 GB, Graphic GTX 1050).  
Figure 1 shows the results of simulating piezoelectric benders driven by a square wave (500 Hz, 20 Vpp). The magnitude of displacement increased as the number of piezo's layers increased. The displacement of the three-layer bender was three times greater than that of the two-layer bender in the series pole direction, which justified the need for three layers. Furthermore, the simulation indicated that the ratio of the three layers could affect the displacement performance. Thus, the other simulation was conducted to figure out the optimum ratio value. For the simulation, three layers were defined as Pe (external layer) and Pi (internal layer), and the ratio was computed by Pi/Pe. The right plot of Figure 1 shows that the max displacement of the bender was obtained at 1.4 (i.e., Pi = 0.14 mm and Pe = 0.1 mm), which demonstrates that the thickness of the internal ceramic layer (Pi) significantly affected the bending performance of the piezo bender. Based on the simulations, a final design of piezoelectric actuators (three layers and 1.4 as its ratio) was determined, as seen in Figure 2. The estimated max displacement was 600 \(\upmu\)m at 100 Vpp.