Transduction Based on Changes in the Energy Stored in an Electrical Field

Transcription

1 Lecture 6- Transduction Based on Changes in the Energy Stored in an Electrical Field

2 Actuator Examples Microgrippers Normal force driving In-plane force driving» Comb-drive device F = εav d 1 ε oε F rwv L = d F W = 1 ε oε rlv d

3 Relating Displacement with Voltage Displacement probe by Mechanical Technology Inc. Sensor Examples Arrays of force Sensors (by Neuman and Liu)

4 Sensors and Actuators A miniature hydrophone made using microfabrication techniques The moving electrode is perforated

5 Sensor Example: Micro-accelerometer A typical accelerometer consists of seismic mass supported by a spring and a dashpot. The device is attached to a vibrating machine with amplitude of vibration, x(t) z = y x X, is the maximum amplitude, t is time and ω is the angular frequency

6 Example: Micro-accelerometer If y(t) is the amplitude of vibration of the mass m from its initial equilibrium position, then the relative, or net motion with reference to the base is z(t) Newton s Law of dynamic force equilibrium: Thus m z kz cz my = 0 + cz + kz = mx The transient response is the solution of: + cz + kz o m z = z z z = y x = y x = y x dz dt z = z = d z dt

7 Example: Micro-accelerometer The characteristic equation is ms + cs + k = o s + s + λ ω = n o s = λ ± λ = c m λ ω 1, n Case 1. λ ω > 0 Z n an overdamping situation λt ( ) = t λ ω n t λ ω n t e C e + C e 1

8 Example: Micro-accelerometer Case. λ ω = 0 n Z a critical damping situation t = e λ ( C C t) 1 + Case 3. λ ω < 0 n an underdamping situation Z ( ) ( ) λt t = e C cos λ ω t + C λ ω t 1 n sin n

9 Example: Micro-accelerometer Now consider the steady state response for m z + cz + kz = mx The steady state solution: The maximum amplitude Z and phase of the relative motion of the mass are

10 Example: Micro-accelerometer c c =mω n is the critical damping

11 Example: Micro-accelerometer Consider the machine vibration The acceleration is: If the frequency of the vibration of the machine,ω, is much smaller than the natural frequency of the accelerometer, we will have Z x ( ) t = Xω sin t a ω max n ω Where a max is the maximum acceleration of the vibrating machine on which the accelerometer is attached

12 Example: Micro-accelerometer Consider the dynamic equation again: m z + cz + kz = mx Under constant acceleration conditions, the steady steady displacement Z is directly related to proportional to the input acceleration Z = m k a Steady state condition is reached in a time t>c/m=λ, so light damping and a heavy mass are required. A small spring constant k will ensure a good sensitivity Question: How can we convert the displacement-acceleration relationship to voltage read out?

13 Example: Capacitive Micro-accelerometer Example: Capacitive Micro-accelerometer The displacement of the proof mass can be measured capacitively The series capacitance in the device is Under constant acceleration condition, since the displacement is proportional to the acceleration, the inverse capacitance of each capacitor is then proportional to the acceleration

14 Example: Capacitive Micro-accelerometer Example: Capacitive Micro-accelerometer The performance of a capacitive micro accelerometer using the above arrangement over a range of ±1g with nonlinearity of less than 0.5% For a small displacement x out of a dual element arrangement, the ratio of capacitance is given by Thus measuring the ratio of the capacitances eliminates the temperature dependence of the dielectric constant (and area) Capacitive accelerometers generally have a higher stability, sensitivity, and resolution than piezoresistive ones

15 Micro-accelerometer (a) and (b): Piezoresistive (c): Capacitive (d): strain gauge (e: Force balance (f): Resonant