Homework answers / question archive / Problem 2: (40 points) In this problem, you will design a comb drive actuator made of conductive single crystal silicon to meet a set of specifications subject to a set of constraints

Problem 2: (40 points) In this problem, you will design a comb drive actuator made of conductive single crystal silicon to meet a set of specifications subject to a set of constraints

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Problem 2: (40 points) In this problem, you will design a comb drive actuator made of conductive single crystal silicon to meet a set of specifications subject to a set of constraints. Your comb drive actuator will include a set of N moveable comb fingers interleaved with a second set of N+1 fixed comb fingers, so that the fixed fingers surround the moveable fingers completely. The moveable comb fingers are supported on a set of folded flexure springs that allow motion in the lengthwise finger direction with a particular net stiffness k. To make the actuator displace, you apply a voltage between the two sets of fingers to draw them together lengthwise. The device parameters are as follows: . Nr: the number of fingers on the moveable comb. The diagram shows NF-4, but you can change Nf to suit your design. Lf. the length of the fixed fingers and of the moveable fingers . wf: the width of the moveable fingers and of the fixed fingers . t: the thickness (out of the plane) of the moveable fingers and fixed fingers. This is also the out of plane thickness of the folded flexure springs. . go: the initial lengthwise gap between the end of the moveable fingers and the fixed fingers . do: the lateral gap between adjacent moveable fingers and fixed fingers (measured in the same direction as the finger width) V: the voltage that is applied to actuate the comb drive actuator . . . Zmax: the maximum travel of the actuator when the maximum voltage is applied Ws: the width of a single folded flexure spring segment Ls: the length of a single folded flexure spring segment Ns: the number of folded flexure spring segments on each side of the moveable structure. The diagram shows Ns = 4, but you can change Ns to suit your design. The constraints (and a few other useful details) are as follows: . Although single-crystal silicon is anisotropic, for the purposes of this problem, you can assume that it has an approximate, effective Young's modulus of 160 GPa. Maximum lengthwise travel: Zmax = 15 um . Gap at the end of the moveable fingers: When fingers are actuated, the gap at the end of the moveable fingers becomes gmin = go - Zmax. We require gmin 2 4do. Minimum feature width: wf 2 2 um, ws 2 2 um, do 2 2 um. Maximum aspect ratio (ratio of thickness to width): t/wf - 5 and t/Ws S 5 . Maximum length for a single spring segment: Ls < 300 um . Maximum number of folded flexure spring segments on each side of the moveable structure: Ns = 20 Maximum total width of the finger set: (2Nf + 1)(do + wf) < 804 um

Here’s what you need to do: a) Write out all of the equations that will guide your design (both equations that describe the physics and equations that describe the constraints). b) Looking at the equations, design the comb drive actuator so that the maximum travel of the actuator, Zmax, is achieved with the minimum possible applied voltage, me. Find the value of Vmin. c) Optional but recommended (instead of using a calculator) to save time: implement the equations in the software of your choice (excel, matlab, whatever). d) Provide a list of the following parameters and their values (chosen or calculated) for your design: N, LE, wr, t, go, do, ijn, Zmax, W5, Ls, Ns Anchor to substrate Springs that support ?ngers Moveable comb ?ngers Fixed comb ?ngers Anchor to substrate