Download MCE380 handout - Cleveland State University

MCE380: Measurements and Instrumentation Lab
Chapter 10: Motion Measurements
Topics:
Position and Velocity Sensing
Holman, Ch. 4: 4.20 thru 4.23; 4.30
Ch.5
Ch.11
Cleveland State University
Mechanical Engineering
Hanz Richter, PhD
MCE380 – p.1/15
Resistance-Based Motion Sensing
We studied the potentiometer as a way to convert displacement to an electrical
signal by means of a variable resistance. (chapter 5 of the handouts).
A potentiometer is often used as an inexpensive way of obtaining a velocity or
position signal. In the picture, a pen plotter uses a potentiometer to generate
a position/velocity signal. This signal is used as feedback for the motor control
MCE380 – p.2/15
Obtaining Position with a Potentiometer
What is the sensitivity of this setup in V/m (position) and V-s/m (velocity)?
+
e
2
High
impedance
reader V
−
a
i
L
2
Va
R
Vb
Vb
x
L
2
−
e
2
Motion
+
−
MCE380 – p.3/15
Problems with Potentiometers
Mechanical problems:
Friction between wiper and resistor (problematic for high-accuracy
systems)
Friction also causes wear.
Contact required between moving object and sensor.
Hysteresis and backlash.
Electrical problem: resistance changes due to heat: inaccuracy.
MCE380 – p.4/15
Capacitive Transducers
We also studied the use of a parallel-plate capacitor to sense distance:
C = 0.225ǫ
A
x
This relates capacitance to position. Special circuitry required to convert to a
measurable electrical signal (current, velocity).
A problem is that output impedance can be really high. Remember that the capacitive
reactance is 1/wC, which can be understood as a frequency-dependent resistance.
This resistance acts as the Thèvenin resistance we studied earlier. The larger this
resistance is, the larger the voltage drop when connecting to a load (in this case the
readout instrument.
If the voltage drops below the noise floor, we can’t make the measurement.
This limits the gap length that can be used. For this reason, “cap gages” are used for
micro- and nano-scale measurements.
More details and experiments in MCE603: Interfacing and Control of Mechatronic Systems.
MCE380 – p.5/15
Tachometers and Strobe Lights
Tachometers are instruments designed to measure speed of rotation.
A tachometer can be entirely mechanical, optical, or electromechanical.
A mechanical tachometer requires shaft contact, a gear reduction and a
counting mechanism.
An optical tachometer operates by simply pointing at the rotating target. A
reflective target must be used as a reference point on the rotating object.
DC generators are often used as tachometers. Generated voltage is
proportional to rotation speed over a wide range. In the lab, the tachometer
attached to the DC motor has a sensitivity of 7V/kRPM.
A strobe light emits pulses at an adjustable frequency. When the shaft appears
stationary, the rotation frequency is a multiple of the frequency of the pulses.
When using the strobe light, we should look for the highest flashing frequency
for which the shaft appears stationary.
MCE380 – p.6/15
Linear Variable Differential Transformer
Principle: Think of the LVDT as a transformer with a moveable core (path for
the coupling magnetic field). The output voltage detects the difference between the voltages induced at the secondaries. When the core is centered,
both voltages are equal: no voltage detected. If the core is displaced to one
side, we increase the magnetic coupling on that side. A net voltage appears. A net voltage of the opposite
sign appears if the core is displaced to
the other side.
MCE380 – p.7/15
LVDT Signal Conditioning
Transformers do not work with DC voltage. A variable voltage (typically AC) is
used.
At a minimum, the signal conditioner must include a peak (envelope) detector
to obtain the amplitude of the output sinewave, which changes with position of
the core.
The output voltage has a sudden sign inversion when passing through the
center position (see Fig. 4.51 in Holman).
Modern LVDTs are available with integral signal conditioning, including fully DC
operation (excitation and output are DC). We have several of this kind in the lab.
MCE380 – p.8/15
Piezoelectric Sensing
Piezoelectricity refers to the property of certain crystals to produce force
and displacement in response to an applied electrical input (voltage,
charge or electric field).
The opposite effect also exists: an applied force or strain will result in the
generation of electric charge.
The enormous advantage of piezoelectric devices lies in the absence of
internally moving mechanical parts in the construction of the transducer
itself: no friction, no backlash.
In addition, piezoelectric actuators and sensors are capable of
sub-nanometer accuracy and precision.
As a drawback, piezoelectric ceramic sensors are fragile and require specialized signal conditioning. Also, the sensing range is very limited.
MCE380 – p.9/15
Basic 1-D Piezoelectric Equation
The general equations of piezoelectricity are somewhat involved. We study
them in detail and conduct experiments in MCE603.
The voltage generated when a pressure p is applied to a uniform piezoelectric
slab of thickness t is
dtp
E=
ǫ
where d is a piezoelectric constant of the material that applies to this loading
case and ǫ is the dielectric constant of the piezoelectric material. The “voltage
sensitivity” g = d/ǫ for several materials is listed in Table 4.4.
As you can see in Example 4.13, the open-circuit voltage generated by a
piezoelectric actuator is quite high.
A commonly-used piezoelectric material is Lead Zirconate-Titanate, or PZT.
People usually refer to any piezoelectric element as “the PZT”, but this is wrong.
PZT is just one kind of piezoelectric material and there are several PZTs: PZT-5,
PZT-3, etc.
MCE380 – p.10/15
Reflective Optical Sensors
An reflective-optical sensor is made of a
light emitter and and a light receiver sideby-side. The light returning from the surface changes the current flowing through
the phototransistor according to distance.
The current can then be used to obtain
information about the distance to the surface. Infrared light is used to minimize interference from visible light. An advantage is the non-contact feature. A disadvantage is the limited range. A typical
distance-current curve will have a peak
(optimal distance), similar to the one seen
for the Fotonic sensor at the beginning of
the semester.
MCE380 – p.11/15
Doppler Effect and Interference
The Doppler effect involves the apparent compression or stretching of
waves emanating from a moving object.
When an ambulance passes, we hear a distinct change in pitch due to
the Doppler effect. The effect also applies to light waves. Stars which
move away faster appear to emit red light.
Interference between waves of different wavelengths creates a fringe
pattern. Try the following Matlab code:
» x=[0:0.001:100];
» y1=sin(10*x);y2=sin(10.1*x);y3=sin(10.2*x);
»
subplot(2,1,1);plot(x,y1+y2);subplot(2,1,2);plot(x,y1+y3)
As you can see, the peaks of the superimposed waves form a regular
fringe pattern. The spacing between fringes depends on the difference
between frequencies.
MCE380 – p.12/15
Principle of Laser Doppler Velocimetry
A monochromatic (single-frequency wave) laser light is shined at the
moving target. The reflected light will have a different frequency,
according to:
fv
f′ = f ±
c
where f is the outgoing frequency in Hz, v is the relative velocity (use +
when objects move towards each other, - for the opposite case) in m/s
and c = 3 × 108 m/s is the speed of light. When frequencies f ′ and f are
superimposed, the fringes appear at a frequency f − f ′ .
Electronic circuitry is used to obtain f − f ′ . Since f is known, the
velocity can be calculated.
Main advantage: High accuracy, with the laser head far away from the
target.
Main disadvantage: Extremely expensive ($100k).
MCE380 – p.13/15
Linear and Rotary Digital Encoders
An encoder is a device that relies on pulse-counting to calculate the
position or velocity of an object. The rotary version is shown.
MCE380 – p.14/15
Incremental Encoders
The light detectors will generate trains of pulses corresponding to each code
track. A quadrature encoder generates two trains of pulses with ±90◦ phase
shift. Counting pulses in either track gives the displacement. The direction of
rotation is obtained by determining the sign of the phase shift.
A third track is sometimes used with only one pulse per revolution. This is used
to provide a zero point.
MCE380 – p.15/15