- •16. ADVANCED LADDER LOGIC FUNCTIONS
- •16.1 INTRODUCTION
- •16.2 LIST FUNCTIONS
- •16.2.1 Shift Registers
- •16.2.2 Stacks
- •16.2.3 Sequencers
- •16.3 PROGRAM CONTROL
- •16.3.1 Branching and Looping
- •16.3.2 Fault Detection and Interrupts
- •16.4 INPUT AND OUTPUT FUNCTIONS
- •16.4.1 Immediate I/O Instructions
- •16.4.2 Block Transfer Functions
- •16.5 DESIGN TECHNIQUES
- •16.5.1 State Diagrams
- •16.6 DESIGN CASES
- •16.6.1 If-Then
- •16.6.2 Traffic Light
- •16.7 SUMMARY
- •16.8 PRACTICE PROBLEMS
- •16.9 PRACTICE PROBLEM SOLUTIONS
- •16.10 ASSIGNMENT PROBLEMS
- •17. OPEN CONTROLLERS
- •17.1 INTRODUCTION
- •17.3 OPEN ARCHITECTURE CONTROLLERS
- •17.4 SUMMARY
- •17.5 PRACTICE PROBLEMS
- •17.6 PRACTICE PROBLEM SOLUTIONS
- •17.7 ASSIGNMENT PROBLEMS
- •18. INSTRUCTION LIST PROGRAMMING
- •18.1 INTRODUCTION
- •18.2 THE IEC 61131 VERSION
- •18.3 THE ALLEN-BRADLEY VERSION
- •18.4 SUMMARY
- •18.5 PRACTICE PROBLEMS
- •18.6 PRACTICE PROBLEM SOLUTIONS
- •18.7 ASSIGNMENT PROBLEMS
- •19. STRUCTURED TEXT PROGRAMMING
- •19.1 INTRODUCTION
- •19.2 THE LANGUAGE
- •19.3 SUMMARY
- •19.4 PRACTICE PROBLEMS
- •19.5 PRACTICE PROBLEM SOLUTIONS
- •19.6 ASSIGNMENT PROBLEMS
- •20. SEQUENTIAL FUNCTION CHARTS
- •20.1 INTRODUCTION
- •20.2 A COMPARISON OF METHODS
- •20.3 SUMMARY
- •20.4 PRACTICE PROBLEMS
- •20.5 PRACTICE PROBLEM SOLUTIONS
- •20.6 ASSIGNMENT PROBLEMS
- •21. FUNCTION BLOCK PROGRAMMING
- •21.1 INTRODUCTION
- •21.2 CREATING FUNCTION BLOCKS
- •21.3 DESIGN CASE
- •21.4 SUMMARY
- •21.5 PRACTICE PROBLEMS
- •21.6 PRACTICE PROBLEM SOLUTIONS
- •21.7 ASSIGNMENT PROBLEMS
- •22. ANALOG INPUTS AND OUTPUTS
- •22.1 INTRODUCTION
- •22.2 ANALOG INPUTS
- •22.2.1 Analog Inputs With a PLC
- •22.3 ANALOG OUTPUTS
- •22.3.1 Analog Outputs With A PLC
- •22.3.2 Pulse Width Modulation (PWM) Outputs
- •22.3.3 Shielding
- •22.4 DESIGN CASES
- •22.4.1 Process Monitor
- •22.5 SUMMARY
- •22.6 PRACTICE PROBLEMS
- •22.7 PRACTICE PROBLEM SOLUTIONS
- •22.8 ASSIGNMENT PROBLEMS
- •23. CONTINUOUS SENSORS
- •23.1 INTRODUCTION
- •23.2 INDUSTRIAL SENSORS
- •23.2.1 Angular Displacement
- •23.2.1.1 - Potentiometers
- •23.2.2 Encoders
- •23.2.2.1 - Tachometers
- •23.2.3 Linear Position
- •23.2.3.1 - Potentiometers
- •23.2.3.2 - Linear Variable Differential Transformers (LVDT)
- •23.2.3.3 - Moire Fringes
- •23.2.3.4 - Accelerometers
- •23.2.4 Forces and Moments
- •23.2.4.1 - Strain Gages
- •23.2.4.2 - Piezoelectric
- •23.2.5 Liquids and Gases
- •23.2.5.1 - Pressure
- •23.2.5.2 - Venturi Valves
- •23.2.5.3 - Coriolis Flow Meter
- •23.2.5.4 - Magnetic Flow Meter
- •23.2.5.5 - Ultrasonic Flow Meter
- •23.2.5.6 - Vortex Flow Meter
- •23.2.5.7 - Positive Displacement Meters
- •23.2.5.8 - Pitot Tubes
- •23.2.6 Temperature
- •23.2.6.1 - Resistive Temperature Detectors (RTDs)
- •23.2.6.2 - Thermocouples
- •23.2.6.3 - Thermistors
- •23.2.6.4 - Other Sensors
- •23.2.7 Light
- •23.2.7.1 - Light Dependant Resistors (LDR)
- •23.2.8 Chemical
- •23.2.8.2 - Conductivity
- •23.2.9 Others
- •23.3 INPUT ISSUES
- •23.4 SENSOR GLOSSARY
- •23.5 SUMMARY
- •23.6 REFERENCES
- •23.7 PRACTICE PROBLEMS
- •23.8 PRACTICE PROBLEM SOLUTIONS
- •23.9 ASSIGNMENT PROBLEMS
- •24. CONTINUOUS ACTUATORS
- •24.1 INTRODUCTION
- •24.2 ELECTRIC MOTORS
- •24.2.1 Basic Brushed DC Motors
- •24.2.2 AC Motors
- •24.2.3 Brushless DC Motors
- •24.2.4 Stepper Motors
- •24.2.5 Wound Field Motors
continuous sensors - 23.15
integrated to find velocity and acceleration.
Currently accelerometers cost hundreds or thousands per channel. But, advances in micromachining are already beginning to provide integrated circuit accelerometers at a low cost. Their current use is for airbag deployment systems in automobiles.
23.2.4 Forces and Moments
23.2.4.1 - Strain Gages
Strain gages measure strain in materials using the change in resistance of a wire. The wire is glued to the surface of a part, so that it undergoes the same strain as the part (at the mount point). Figure 23.16 shows the basic properties of the undeformed wire. Basically, the resistance of the wire is a function of the resistivity, length, and cross sectional area.
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where, |
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resistance of wire |
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= voltage and current |
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= |
length of wire |
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= width and thickness |
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= |
cross sectional area of conductor |
ρ |
= |
resistivity of material |
Figure 23.16 The Electrical Properties of a Wire
continuous sensors - 23.16
After the wire in Figure 23.16 has been deformed it will take on the new dimensions and resistance shown in Figure 23.17. If a force is applied as shown, the wire will become longer, as predicted by Young’s modulus. But, the cross sectional area will decrease, as predicted by Poison’s ratio. The new length and cross sectional area can then be used to find a new resistance.
w’
t’
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= |
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= Eε |
ε |
= |
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----- |
--------- |
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R' = ρ |
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= ρ w( 1 – νε ) t( 1 – νε ) |
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where, |
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Aside: Gauge factor, as defined below, is a commonly used measure of stain gauge sensitivity.
∆ R
-------
R GF = ------------
ε
Figure 23.17 The Electrical and Mechanical Properties of the Deformed Wire
continuous sensors - 23.17
Aside: Changes in strain gauge resistance are typically small (large values would require strains that would cause the gauges to plastically deform). As a result, Wheatstone bridges are used to amplify the small change. In this circuit the variable resistor R2 would be tuned until Vo = 0V. Then the resistance of the strain gage can be calculated using the given equation.
V+ |
Rstrain |
= |
R2R1 |
when Vo = 0V |
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Rstrain
R5
Figure 23.18 Measuring Strain with a Wheatstone Bridge
A strain gage must be small for accurate readings, so the wire is actually wound in a uniaxial or rosette pattern, as shown in Figure 23.19. When using uniaxial gages the direction is important, it must be placed in the direction of the normal stress. (Note: the gages cannot read shear stress.) Rosette gages are less sensitive to direction, and if a shear force is present the gage will measure the resulting normal force at 45 degrees. These gauges are sold on thin films that are glued to the surface of a part. The process of mounting strain gages involves surface cleaning. application of adhesives, and soldering leads to the strain gages.
continuous sensors - 23.18
stress |
irectiond |
uniaxial |
rosette |
Figure 23.19 Wire Arrangements in Strain Gages
A design techniques using strain gages is to design a part with a narrowed neck to mount the strain gage on, as shown in Figure 23.20. In the narrow neck the strain is proportional to the load on the member, so it may be used to measure force. These parts are often called load cells.
mounted in narrow section to increase strain effect
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Figure 23.20 Using a Narrow to Increase Strain
Strain gauges are inexpensive, and can be used to measure a wide range of stresses with accuracies under 1%. Gages require calibration before each use. This often involves making a reading with no load, or a known load applied. An example application includes using strain gages to measure die forces during stamping to estimate when maintenance is needed.
23.2.4.2 - Piezoelectric
When a crystal undergoes strain it displaces a small amount of charge. In other words, when the distance between atoms in the crystal lattice changes some electrons are forced out or drawn in. This also changes the capacitance of the crystal. This is known as
continuous sensors - 23.19
the Piezoelectric effect. Figure 23.21 shows the relationships for a crystal undergoing a linear deformation. The charge generated is a function of the force applied, the strain in the material, and a constant specific to the material. The change in capacitance is proportional to the change in the thickness.
F
b
+
q
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ε ab |
d |
C = |
-------- |
---- |
c |
i = ε gdtF |
where,
c |
a |
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C = capacitance change
a, b, c = geometry of material
ε = dielectric constant (quartz typ. 4.06*10**-11 F/m)
i = current generated
F = force applied
g = constant for material (quartz typ. 50*10**-3 Vm/N)
E = Youngs modulus (quartz typ. 8.6*10**10 N/m**2)
Figure 23.21 The Piezoelectric Effect
These crystals are used for force sensors, but they are also used for applications such as microphones and pressure sensors. Applying an electrical charge can induce strain, allowing them to be used as actuators, such as audio speakers.
When using piezoelectric sensors charge amplifiers are needed to convert the small amount of charge to a larger voltage. These sensors are best suited to dynamic measurements, when used for static measurements they tend to drift or slowly lose charge, and the signal value will change.