Week 5 - Analog Sensors II Flashcards
Variable-Inductance Transducers
Motion transducers that employ the principle of electromagnetic induction are termed variable-inductance transducers.
When the flux linkage (defined as magnetic flux density x number of turns in conductor) through an electrical conductor changes, a voltage is induced in the conductor.
Three types of variable-inductance transducers
- Self-induction transducers
- Mutual-induction transducers
- Permanent-magnet (PM) transducers
Self-induction transducers
Consists of a magnet core on which a coil is directly wound.
When a plate of iron (also called an armature) or other ferromagnetic material is moved with respect to the magnet, the flux field expands or collapses, and a voltage is induced in the coil.
The self-inductance of a coil is
L = N^2/R
N = number of turns
R = magnetic circuit’s reluctance
The reluctance of the coil is
R = l/mu*A
l = length of the coil
mu = permeability of the coil
A = cross-sectional area of the coil
G (geometric form factor) = A/l
Therefore, L = N^2muG
Mutual Induction Transducer
Consider two coils, having self-inductance L1 and L2.
Mutual inductance of the two coils is given by:
M = Ksqrt(L1L2)
K = coefficient of coupling (depends on distance and orientation of the coils)
Linear Variable Differential Transformer (LVDT)
An LVDT is an electromechanical sensor used to convert mechanical motion or vibrations (rectilinear motion), into a variable electrical current, voltage or electric signals
Advantages of LVDT
Main advantage of LVDT over other types is the high degree of robustness. Because there is no physical contact across the sensing element, there is no wear in the sensing element.
Because the device relies on the coupling of magnetic flux, an LVDT can have infinite resolution.
Therefore, the smallest fraction of movement can be detected by suitable signal conditioning hardware, and the resolution of the transducer is solely determined by the resolution of the data acquisition system.
Signal Conditioning
Signal conditioning associated with differential transformers includes filtering and amplification.
Filtering is needed to improve the signal-to-noise ratio of the output signal.
Amplification is necessary to increase the signal strength for data acquisition and processing.
Signal Conditioning II
Since, the reference frequency, (carrier frequency) is induced into (and embedded in) the output signal, it is also necessary to interpret the output signal properly, especially for transient motions.
The output signal of an LVDT is an amplitude-modulated signal where the signal component at the carrier frequency is modulated by the lower-frequency transient signal as a result of the core motion.
Two methods to interpret the crude output signal from a differential transformer : rectification and demodulation.
Permanent-Magnet Transducers (PM)
A PM transformer has a permanent magnet to generate a uniform and steady state magnetic field.
In a tachometer, the relative motion between the magnetic field and an electrical conductor induces a voltage, which is proportional to the speed at which the conductor crosses the magnetic field (rate of change of flux linkage). This induced voltage is a measure of the speed.
Summary of Inductive Transducers
Advantages
+ Can work in any environmental conditions like humidity and high temperatures
+ High performance in industrial environment
+ High accuracy and stable operating range with a good life span
+ Can be operated at high switching rates
+ Can be operated in a wide range of applications
Disadvantages
- Working and operating range depends on the construction and temperature conditions
- It depends on the magnetic field of the coil
Strain Gauges
Many types of forces and torque sensors are based on strain-gauge measurements.
Although strain gauges measure strain, the measurements can be directly related to stress and force.
What is Strain?
Strain is the amount of deformation of a body due to an applied force. More specifically, strain is defined as the fractional change in length. When a force is applied to a structure, the components of the structure change slightly in their dimensions and are said to be strained.
Strain gauges are devices to measure the small changes in dimensions.
A strain gauge is a type of passive transducer that converts a mechanical displacement into a change in resistance.
It is a thin device that can be attached to a variety of materials.
The ideal sensor for the measurement of strain would
- Have a good spatial resolution (the sensor would measure strain at a point)
- Be unaffected by changes in ambient conditions.
- Have a high-frequency response for dynamic strain measurements.
Resistance Strain Gauge
Most widely used device for measuring strain.
Based on principle that the electrical resistance of a conductor changes when subjected to mechanical deformation.
Generally, an electric conductor is bonded to a specimen, with an insulating cement under no-load conditions.
Load is then applied, deformation results in both specimen and resistance element.
Deformation is determined from a measurement of the change in resistance of the element.
Resistance of the Conductor
R = rho * L/A
rho = Resistivity
L = Length
A = Cross-sectional Area
Gauge factor/Strain factor (F)
F = (1+2mu) + (1/epsilon)(delta R/R)
For most gauges, F is constant over a wide range of strains.
The local strain can be determined by measuring the change in resistance:
strain (epsilon) = (1/F)*(delta R/R)
Poisson’s Ratio
The ratio of the unit strain in the transverse direction to the unit strain in the axial direction
Desired Properties of Strain Gauges
+ Calibration constant should be independent of time, temperature and other environmental factors
+ Measure strains with an accuracy of +- 1 micrometre/m over a very large strain
+ Size of gauge should be small, so strain is measured with a small error
+ Response of gauge can record dynamic strains with high frequency components
+ Permit both in-situ and remote readout
+ Readout should be independent of environmental factors
+ Gauge should be low in cost
+ Easy to install and use
+ Exhibit a linear response to strain over a wide range
+ Suitable for use as a sensing element in other sensors
Wheatstone Bridge
An electrical circuit used to measure an unknown electrical resistance.
Output (delta R/R) of a strain gauge is usually converted to a voltage signal with a Wheatstone bridge
Wheatstone Bridge II
Any of the resistors R1, R2, R3, R4 may be a strain gauge.
DC voltage Vs is applied across the nodes A and C (horizontal), bridge forms a parallel circuit arrangement across these two nodes.
When Vg is zero, there is no voltage drop from B to D, the bridge is in a balanced condition:
R2/R1 = R3/R4
Deflection mode: Replace galvanometer with a voltage measuring device to sense the unbalancing in bridge
One variable arm : Vbd ~ Vs x (delta R / 4R)
Two variable arms : Vbd ~ Vs x (delta R / 2R)
Four variable arms : Vbd = Vs x (delta R / R)
Circuit Sensitivity of a Wheatstone bridge
Sc = delta Vo / (delta R1 / R1) = r/(1+r)^2 x Vs
Sc = r/(1+r) x sqrt(Pg x Rg)
r = R2/R1
Pg = Power dissipated by gauge
Rg = Gauge resistance
