# Modeling and Design Enhancement of Electothermal Actuators for Microgripping Applications
## 3 Results
The initial gap for the microgripper is set at 10 \(\upmu\)m (the voltage actuation is switched off). A nonlinear increasing trend in the gap opening is obtained when increasing the applied voltage. The case of the double row of square perforations shows a superior performance. The highest gap opening of 21.240 \(\upmu\)m is obtained for the case of the double-row square-perforated microgripper when applying a voltage of 8 V. The simulation results reveal the importance of the shape and distribution of the perforations as design aspects for the performance and operational reliability of microgrippers. For the tip temperature analysis, only the upper tip of the gripping arm is reported since the values for upper and lower tip temperatures are found close to each other. Figure 17 shows the variations in the tip temperatures with the applied voltage obtained for the different microgrippers under study. The incorporation of perforations on the surface of the hot arm results in lower tip temperatures, which constitutes an important aspect for microgripping applications in which operating at high temperatures may cause complications to the surrounding electronics and to the gripped object. Moreover, the simulation results reveal that more perforations result in more reduction in the tip temperature. Low voltage actuation leads to relatively low tip displacement and temperature which makes the effect of the perforation minimal. On the other hand, this effect is more pronounced at higher voltages given the significant increase in the tip temperature and displacement that can be achieved thanks to the Joule effect. For example, when applying a voltage of 2 V, switching from no perforations to a double row of square perforations results in an 8.51% decrease in the tip temperature, whereas the temperature decrease reaches 25.24% when adding perforations and operating at a voltage of 8 V.  
Figure 16: Variations in the total gap opening of microgrippers with the applied voltage for different numbers and types of perforations. Figure 15: Upper and lower tip displacements of the microgrippers with different number and types of perforations. The displacement contour plots for the case of the non-perforated microgripper and the double-row square-perforated microgripper are shown at 8 V.  
To gain more insight into the temperature distribution over the entire group of microgrippers during operation, the temperature contour plots for different microgrippers are displayed in Figure 18. The simulation results are shown for different applied voltages, ranging from 2 V to 8 V. As expected, in all cases, the hot arm of the microgripper is subjected to higher temperatures than the other parts of the microgripper. Moreover, the overall structure of the microgrippers with double rows of square and circular perforations reach lower temperatures than the other cases as indicated by the brighter colors in Figure 18.  
One essential design consideration is to inspect any potential mechanical failures that may result from the electrothermal actuation. As such, a stress analysis is performed,  
Figure 17: Variations of the upper tip temperature of microgrippers with the applied voltage for different numbers and types of perforations. Figure 18: Temperature distributions obtained for different microgrippers at different applied voltages. and the obtained results are presented as contour plots of von-Mises stresses for the different microgrippers under investigation (see Figure 19). The highest von-Mises stresses in all cases take place at the hinges connecting the hot/cold arm to the anchors. This observation is consistent with the results reported in the literature which revealed the same location of the stress concentration [17,18]. The simulation results obtained for all microgrippers at 8 V are summarized in Figure 14:0 The maximum von-Mises stress of the microgrippers under investigation is found between 1.89 GPa and 2.26 GPa, all below the yield strength of polysilicon [48].