Sensors Lecture #5: Position and Displacement using Resistive, Capacitive and Inductive Sensors

Transcription

1 Sensors Lecture #5: Position and Displacement using Resistive, Capacitive and Inductive Sensors Jerome P. Lynch Department of Civil and Environmental Engineering Department of Electrical Engineering and Computer Science University of Michigan CEE370 Sensors, Circuits and Signals University of Michigan 2017

2 Readings: Reading and Objectives Chapter 7 in Fraden Objectives of today s class: Explain the principles of measuring position and displacement Introduce potentiometric, capacitive and inductive readout mechanisms for displacement/position sensing Slide 2

3 Definitions Measure the spatial positioning of physical objects: Position sensors determine body coordinates (x, y, z) in space Displacement sensors measure change in position Proximity sensors are a threshold version of the position sensor Position: x,y,z Body Displacement: Δx, Δy, Δz Body Proximity: yes/no Slide 3

4 Displacement/Proximity Sensors Three primary physical phenomena used: Resistive: ΔR = f(d) Capacitive: ΔC = f(d) Inductive: ΔL = f(d) This class will explore each of these to show illustrations of displacement, position and proximity sensing Slide 4

5 Potentiometric Sensors Displacement easily measured by change in resistance: Linear potentiometer measures linear displacement Rotational potentiometer measures rotational displacement (angle) Utilizes an internal resistor with a brushed connection: Wiper moves along outer surface of the resistor Voltage divider circuit modulates displacement as a voltage V in V out V out = d D range V in Source: Fraden (2010) Slide 5

6 Example of Potentiometers Source: Novotechnik (2014) Source: Celesco (2014) Slide 6

7 Wiper Discretization Wiper contact on internal resistor introduces uncertainty: Wipe may contact one or two wires at a time Result are uneven voltage steps at the sensor output Source: Fraden (2014) Slide 7

8 Thin Film Potentiometer 3/6/17 Jerome P. Lynch, 2017 Slide 8

9 Basics of Capacitors Two metallic bodies with equal amounts of opposite charge: C = q V Parallel plate capacitor with internal dielectric: C = ε o A d Slide 9

10 Cylindrical capacitors: Basics of Capacitors C = 2πε ol ln(b a) Slide 10

11 Capacitance for Displacement Sensing Displacement induces a change in capacitance: Parallel Plate Capacitor Design: Change Area (ΔA) Change plate distance (Δd) Change dielectric (Δε) Cylindrical Capacitor Design: Change length (ΔL) Change dielectric (Δε) Widely used mechanism for sensing displacement in MEMS: MEMS are micro-machined sensors fabricated in silicon Power efficient approach to sensing movement at MEMS-scale Slide 11

12 Change in Area Allow one of the parallel plates to move vertically in plane: Measure change in capacitance (ΔC) Linearly proportional to displacement (δ) δ C = ε oa d = ε o ( L δ )w d = ε olw d ε ow d δ L ΔC = ε o Lw d ε w o d δ ε Lw o d A=(L-δ)w ΔC = ε o w d δ Slide 12

13 Parallel Plate Capacitive Bridge Sensor Two parallel planar electrode sets with separation, d: Stationary electrode set contains four rectangular elements Moving electrode set contains two rectangular elements Stationary set electrodes are cross-connected electrically forming a bridge-type capacitance network Sinusoidal excitation with a differential amplifier outputing voltage Capacitance of two parallel plates is proportional to the area of either plate that directly faces the corresponding area of the other plate Source: Fraden (2014) Slide 13

14 Change in Distance Allow one of the parallel plates to move out of plane: Measure change in capacitance (ΔC) Linearly proportional to displacement (δ) if δ << d d δ C = ε oa d + δ A=Lw L C ε o A d ΔC ε A o d δ 2 1 δ d + δ 2 d! 2 If δ << d Taylor Series Expansion Slide 14

15 Capacitive Displacement Sensor When measuring distance from a metallic target: Probe represents one plate and metallic target the other Dielectric (air) and area remain constant so position alters d Guard around electrode ensures electric field to target is vertical Widely used in manufacturing of conductive materials Sub-micrometer resolution and bandwidths of khz Source: MTI Instruments (2014) Source: MTI Instruments (2014) Slide 15

16 Displacement in MEMS MEMS is for microelectromechanical sensors: Need to measure displacement within a MEMS sensor For example, measure displacement of proof mass in accelerometers Differential capacitance is easier to measure accurately Drive two plates 180 out of phase Middle plate measures potential between the parallel plates As displacement, go from 0V to amplitude proportional to d Source: Fraden (2014) Source Princeton Soboyejo Group (2014) Slide 16

17 Change in Dielectric Allow the internal dielectric in cylindrical cap to move: Measure change in capacitance (ΔC) As dielectric displaces, Dielectric L δ C = 2πεL ln b a ( ) ε 1 = f (δ ) ε 1 δ L C = 2π L ln b a + ε o ( ) ε + δ ( L ε ε o ) ( ) ( ) ΔC = 2π ε ε o δ ln b a δ L Slide 17

18 Level Sensor Measure level of fluid/granular materials using capacitance: No moving parts and consists of a static probe and metallic container Fluid and granular material is the dielectric that moves 2 nd reference electrode Conductive tank Fluid/granular material can be conductive Teflon covered primary electrode (no shorting) Source: Omega (2014) Slide 18

19 Induction 1831 Michael Faraday (England) & Joseph Henry (US): Variation in a magnetic field induces an electromotive force (e.m.f.): e = dφ B dt [Wb/s = V] If magnetic field is applied to a solenoid of constant area with N turns: V = N dφ B dt Source: Wikipedia (2014) Slide 19

20 Current in a solenoid coil: Induction Produces a magnetic field, B Magnetic field also produces back e.m.f. in coil (Faraday s Law) N is number of turns and n is number of turns per unit length If no magnetic material in vicinity: V = d ( NΦ B ) dt = d( Li) dt = L di dt Source: Fraden (1996) Slide 20

21 Coupled Coils Let us now consider two coils sharing same longitudinal axis: Second coil experiences e.m.f. from current in first coil Coefficient of mutual induction, M 21 V 2 = M 21 di 1 dt Coefficient of mutual induction can be found for simple geometries: M 21 = µ o π R 2 nn Source: Fraden (1996) Slide 21

22 Induction for Displacement Sensing Illustration of using induction to measure displacement: Magnetic field, B Magnetic Flux enclosed by loop, Φ=Blx V = N dφ B dt = N d dt ( Blx) = NBl dx dt V = NBl!x Source: Fraden (1996) Slide 22

23 Induction for Displacement Sensing Displacement can be used to alter the field between coils: Coupled coils termed primary and secondary coils: Primary coil carries AC voltage (V ref ) Secondary coil develops steady AC voltage (V out ) based on Faraday s Law Nonmagnetized ferromagnetic medium between coils: Movement of medium alters reluctance (and hence mutual inductance) Source: Fraden (2010) Slide 23

24 LVDT Linear variable differential transformer (LVDT): Primary coil driven with regulated AC voltage signal (V in ) AC signal developed in 2 secondary coils connected in opposite phase Ferromagnetic chute (core) is centered between 2 secondary coils As chute moves, the balance between the secondary coils is disrupted As chute moves, output voltage linearly proportional to displacement High frequency AC source to minimize transformer harmonics AC output proportional to chute displacement Square wave signal showing amplitude timing on primary coil Two secondary coils in opposite polarity (phase) Source: Fraden (2010) Slide 24

25 LVDT Source: Macro Sensors (2014) Slide 25

26 LVDT Accurate displacement sensor: High bandwidth (if driving AC signal is 10x higher) Miniscule friction of chute meaning relatively non-contact approach No hysteresis in the sensor Low output impedance makes interface to DAQ straightforward Incredible resolution (< 1 mm) Source: Macro Sensors (2014) Slide 26

27 Magnetostrictive Displacement Sensor Magnetostriction: Materials that expand or contract when placed in magnetic field Ferromagnetic materials include iron, nickel, cobalt and their alloys Magnetostrictive position sensors: Similar to an LVDT in design based on magetostriction principles Uses a magnetic chute that moves along a linear waveguide Source: Fraden (2010) Slide 27

28 Magnetostrictive Displacement Sensor Magnetostrictive position sensors: Conductive waveguide is electrically pulsed - creates a magnetic field Superposition of waveguide field and magnetic field induces a torque at the point of the magnet (i.e., Wiedemann effect) Torque pulse travels along waveguide at speed of sound Interrogation circuit times pulse and reception of torque pulse to position the magnetic chute Source: Fraden (2010) Slide 28

29 Magnetostrictive Displacement Sensor Advantages of magnetostructive displacement sensor: Outstanding linearity (0.05% FS) Excellent resolution and repeatability (<10 um) Non-contact Extremely low sensitivity to thermal variations (<5 ppm/c ) Source: Megatron Elektronik AG (2014) Slide 29

30 Ultrasonic sensor: Ultrasonic Sensors Radiates an ultrasonic (>20 khz) pulse Operates under same principles of positioning used by bats Energy radiates diffusively (180 ) Position is based on time of light (based on the speed of sound): Easier that microwave positioning which operates at speed of light Velocity is based on returned pulse frequency (based on Doppler) L = vt cosθ 2 Source: Fraden (2010) Slide 30

31 Other Positioning Sensors Eddy current sensors Hall effect displacement and rotation sensors Micropower radar sensors Light emitting diode position sensors Transverse inductive sensors. And many more Slide 31