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Overview

This overview explores the integration of multiple steps of a single actuator using simple beam theory for a mechanical digital to analog converter. It also discusses the limits of electrostatics, residual stress, and gap closing. Additionally, it covers topics such as comb drive tooth, thermal noise, and force in relation to the actuator. The design of inchworm motors and power dissipation of the actuator springs are also examined.

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Overview

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Presentation Transcript

  1. Overview • Integrating multiple steps of a single actuator • Simple beam theory • Mechanical Digital to Analog Converter

  2. Limits to electrostatics • Residual stress (limits size) • Pull-in • Gap-closing • Comb drive • Tooth (for comb and gap-closing) • Thermal noise

  3. Force/Area L l l W l nl

  4. Energy-Area Ratio L l l W l nl

  5. Va1 Vs1 shoe shoe shuttle F F Va2 Vs2 F F F F shoe shoe Inchworm Motor Design shuttle Add Shoe Actuators

  6. Shoe Actuators Residual Stress Stiction Large Structures Large Force MUMPs Inchworm Motors guides shoes Shuttle Gap Stop

  7. 1mm Silicon Inchworm Motors

  8. Power Dissipation of the Actuator

  9. Springs • Linear beam theory leads to • Ka = Ea3b / (4L3) • Kb = Eab3 / (4L3) b a L Fb Fa

  10. Springs • Linear beam theory leads to • Kqa = Ea3b / (12L) • Kqz = Ea3b / (3(1+2n) L) • Note that Tz results in pure torsion, whereas Ta results in bending as well. Ta Tz

  11. Spring constant worksheet • Assume that you have a silicon beam that is 100 microns long, and 2um wide by 20um tall. Calculate the various spring constants. • Esi ~ 150 GPa; Gsi = Esi / (1+ 2n) = 80 GPa a3b= Ka= Kb= Kqa= Kqz=

  12. Damping • Two kinds of viscous (fluid) damping • Couette: b = m A/g ; m = 1.8x10-5 Ns/m2 • Squeeze-film: b ~ m W3L/g3 • m proportional to pressure • Dynamics: • m a + b v +k x = Fext • If x(t) = xo sin(wt) then • v(t) = w xo cos(wt) • a(t) = - w2xo sin(wt) • -mw2xosin(wt) + bwxocos(wt) +kxosin(wt) = Fext

  13. Dynamic forces, fixed amplitude xo • -mw2xosin(wt) + bwxocos(wt) +kxosin(wt) = Fext Force High damping z~10 Low damping Q~10 wn frequency

  14. increase k wn’ Dynamic forces, fixed amplitude xo • -mw2xosin(wt) + bwxocos(wt) +kxosin(wt) = Fext Force wn frequency Increasing k raises wn but at cost of more force or less deflection

  15. decrease m wn’ Dynamic forces, fixed amplitude xo • -mw2xosin(wt) + bwxocos(wt) +kxosin(wt) = Fext Force wn frequency Decreasing m raises wn at no cost in force or deflection

  16. decrease m wn’ Dynamic forces, fixed amplitude qo • -Jw2qosin(wt) + bwqocos(wt) +kqqosin(wt) = Fext Torque wn frequency Identical result for angular systems with J (angular momentum) instead of m

  17. Mechanical Digital to Analog Converter

  18. Basic Lever Arm Design Output Beam (analog) Folded spring support 6m 6m Stops Input Beam (analog) Input Beam (digital)

  19. 6-bit DAC Implementation (Courtesy of Matthew Last)

  20. Output of a 6-bit DAC 19 cycles

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