M.Sc Thesis

M.Sc StudentRivlin Ben
SubjectMicromechanical Flexures: Non-Linear Springs for Enhancing
the Functionality of Electrostatic Transducers
DepartmentDepartment of Mechanical Engineering
Supervisor PROF. David Elata
Full Thesis textFull thesis text - English Version


Due to unwanted abrasion, sliders and axes are not used in micro-systems. Instead, elastic flexures are used to constrain motion between different elements of the systems. Flexures also serve as elastic springs that balance actuation forces. In most micro-systems the flexures act as linear springs. However, in order to enhance the performance of certain systems, springs with stiffness that varies with their extension are required.

The non-linear response of the parallel-plates electro-mechanical actuator is well known. The actuator consists of a mobile electrode that is suspended on a linear spring above a stationary electrode. The voltage-displacement relation of this system is non-linear due to the electrostatic attraction forces, which are inherently non-linear. In addition, an instability phenomenon called pull-in limits the stable dynamic range of the system. Non-linearity and pull-in are undesired in most applications that require continuous motion along a wide dynamic range. While the double-sided comb-drive actuator solves these two issues, it requires larger area than the parallel-plates actuator, and its fabrication is complicated.

We force the system response to be linear and overcome the instability by using non-linear suspensions with specifically prescribed response. A method for designing non-linear springs with monotonically increasing stiffness is developed. The stiffness of the beams is inversely proportional to the beam lengths cubed. From this we conceived that by continuously shortening the effective length of the beam, its stiffness may be increased. So far, flexures constructed from elastic beams were used as springs, but their stiffness remained constant since the beams length remained constant throughout the deflection process. The method we propose uses rigid cams over which the beams are wrapped or guided.

The shape of the cam determines stiffness or the force-displacement law. Several approaches for designing the cam shape to yield a desired force-displacement law are shown. These approaches include both analytic and numeric methods. They are based predominantly on the Euler-Bernoulli beam theory, and one is also based on the elastica equation.

This work focuses on two non-linear springs to enhance the functionality of the parallel-plates actuator: One causes its response to be linear, while the other causes the system to behave as a mechanical battery that loads and unloads charge at constant voltage.

Two macro-scale experiments were performed in order to measure the force-displacement laws of the two springs. The theoretical predictions agree well with the experimental results.

Micro-scale experiments were designed for future measurements.