Wednesday, July 27, 2011

Resonance frequency calculations

The bottom layer (the passive one) has lower CTE, whereas the top layer (the active one) has higher CTE. In our project, the bottom layer has properties of an electric heater resistor connected with an electric supply. Due to mismatch between the CTE of the materials the bimorphs after the forming process curl out-of-plane and make the whole device a 3D structure. When electric current is passed through the heater resistor, the temperature 2D raster image on a screen. The raster scanning system creates a light beam that produces a single bright pixel. The last one is scanned in two dimensions to create an image. The light beam moves with a high speed along a horizontal line, and next, with a lover speed, come back to the beginning the second line situated below the first line. The movement of the light beam along the horizontal line (with a high speed) is called the raster scanning, whereas the movement of the light beam in vertical direction. In the proposed design the high precision of scanning action is achieved due to a special position of the mirror centre with respect to its rotation axes. Namely, the mirror centre lies on the line going through the centres of two attached cantilevers, Figure 1b. The above position assures, that the distance of the mirror from the light source is the same during the whole scanning process. Additional advantage is the fact that the inertial moments resonant frequency for the raster scanning. Higher frequencies result more accurate projecting image because of greater image refreshing.
On the other hand, more precise motion of the mirror causes less image distortion. The kinematical behaviour of the scanner was presented in [2] in details. It was proved that for the angles of mirror rotations from the  , the distance of the mirror centre from the light source may be taken as equal to L/2 with sufficient accuracy. The initial flexure of actuators appears during the forming process. When flat bimorph beams are cooled from the temperature 300. To find the fundamental resonance frequency analytically, we consider model of the system shorter actuators + micromirror shown at Fig.3. When the mirror oscillates with rotating motion around its centre C 0, the force F and the moment M act at the end of the cantilever. Because The point C 0 is practically motionless [2], one can assume that the force F.

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