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MEMS Class 6 Modeling of MEMS Devices Mohammad Kilani

MEMS Class 6 Modeling of MEMS Devices Mohammad Kilani. 20 mm. 10 mm. The Scaling of MEMS Devices. 2 mm. 1 mm. Isometric Scaling. How does electrostatic force change? How does electrostatic force change relative to other forces? How does response time change?. 20 mm. 10 mm.

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MEMS Class 6 Modeling of MEMS Devices Mohammad Kilani

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  1. MEMS Class 6 Modeling of MEMS Devices Mohammad Kilani

  2. 20 mm 10 mm The Scaling of MEMS Devices 2 mm 1 mm Isometric Scaling How does electrostatic force change? How does electrostatic force change relative to other forces? How does response time change?

  3. 20 mm 10 mm The Scaling of MEMS Devices 2 mm 1 mm Isometric Scaling

  4. Water Bug Weight = V S3 Surface Tension = kA S2 Man : 2m Bug: 2 mm S = 1/1000 Surface Tension / Weight S2/S3 = S-1 = 1000 Water bug uses surface tension to walk on water

  5. The Scaling of Forces 20 µm 2000 µm 10 μm Isometric Scaling 1000 μm S = 1/100 Weight = gm = gV S3 Electrostatic Force = kA S2 Electrostatic Force / Weight S2/ S3 = S-1 = 100

  6. The Scaling of Work or Mechanical Energy Gravitational force S3 Wok of gravity S4 If S = 1/100 the gravitational energy required to move an object from the bottom to the top of the machine under consideration decreases by (1/100)4 = 1/100,000,000. Drop an ant from ten times his height, and he walks away. Please do not try this with a horse!

  7. The Scaling of Acceleration A predominance of the forces we use in the microdomain scale as S2. For these forces, the acceleration scales as S−1. If S = 1/100, a increases by a factor of 100. Small systems tend to accelerate very rapidly.

  8. The Scaling of Velocity For the case where the force scales as S2, velocityscales as S-0.5. If S = 1/100, the velocity increases by a factor of 10. Small things tend to be fast.

  9. The Scaling of Response Time The time needed to travel a certain distance, x is given from the relation Assume constant a For the case where the force scales as S2, transit time t scales as S1. If S = 1/100, the transit time decreases by a factor of 100. Small things tend to be fast.

  10. The Scaling of Mechanical Power The time needed to travel a certain distance, x is given from the relation For the case where the force scales as S2, powerscales as S2. If S = 1/100, the power decreases by a factor of 10000. Small things have very small mechanical power.

  11. The Scaling of Magnetic Forces 1. Constant current density Ib Ia L

  12. The Scaling of Magnetic Forces 2. Constant heat flow through the surface of the wire Ib Ia L

  13. The Scaling of Magnetic Forces 3. Constant temperature rise of the wire Ib Ia L

  14. The Scaling of Magnetic Forces 4. Wire and permanent magnet Ia L 1. Constant current density: F S3 2. Constant heat flow: F S2.5 3. Constant temperature rise: F S2

  15. The Scaling of Different Forces

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