Surface energy-driven adhesion of two opposing microcantilevers

Summary This paper studies surface energy-driven adhesion of two parallel microcantilevers oriented in opposite directions. Adhesion becomes possible when an attached state of the two opposing cantilevers becomes an equilibrium state at which the release rate of the strain energy with respect to the attached length is equal to the surface energy per unit length. The analytical model developed here predicts that the critical values of surface energy for initial adhesion and full adhesion of two opposing cantilevers increase monotonically with increasing overlap length. This is attributed to the fact that increasing overlap length leads to a decrease in the unattached suspended length of the cantilevers and then an increase in the release rate of the strain energy, which requests a higher surface energy for adhesion of the two cantilevers. Therefore, the strength of two opposing cantilevers against adhesion can be enhanced by increasing the overlap length. When adhesion occurs, because of lower surface energy and shorter attached length, the attached state of two beams of small or moderate overlap length always has a higher total energy than the unattached straight beams before the full adhesion is reached. On the other hand, because of higher surface energy and longer attached length, the total energy of the attached state of two beams of large overlap length can be lower than the total energy of the unattached straight beams even before the full adhesion is reached. In particular, for the first time to our knowledge, the present results show quantitatively how much the critical values of surface energy density for adhesion of two opposing cantilevers are lower than the critical values of surface energy density for adhesion of a single cantilever attracted by a rigid substrate or other similar problems studied in the literature. These results could have significant consequences to MEMS design especially for combdrive technology.     

Evaluation of superposition technique for calculating cogging torque in permanent-magnet brushless machines

We evaluate the superposition method for calculating the cogging torque in permanent-magnet brushless machines, the resultant torque being synthesized from cogging torque components associated with a pair of magnets. Although finite-element analyses and measurements show that the resultant cogging torque cannot be synthesized directly from the torque components due to a single magnet, we use the concept of a fictitious single magnet to analytically establish the relationship between the cogging torque and key design parameters. The method is particularly useful in assessing the influence of the slot number and pole number combination.