Electromagnetic testing asnt level iii study guide et by charlie Chong

Electromagnetic Testing

Study Guide Electromagnetic Testing My ASNT Level III Pre-Exam Preparatory Self Study Notes 17th April 2015

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E&P Applications

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E&P Applications

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http://independent.academia.edu/CharlieChong1 http://www.yumpu.com/zh/browse/user/charliechong http://issuu.com/charlieccchong

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Fion Zhang at Shanghai 17th April 2015

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乱七八糟 – 随看随记

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乱七八糟 – 随看随记

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IVONA TTS Capable.

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Chapter 1 Principles of Eddy Current Testing

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EDDY CURRENT an Overview Description of Eddy Current Detectors Coil configurations Appropriate coil selection is the most important part of solving an eddy current application, no instrument can achieve much if it doesn’t get the right signals from the probe. Coil designs can be split into three main groups: 1. 2. 3.

Surface probes used mostly with the probe axis normal to the surface, in addition to the basic ‘pancake’ coil this includes pencil probes and special-purpose surface probes such as those used inside a fastener hole. Encircling coils are normally used for in-line inspection of round products, The product to be tested is inserted though a circular coil. ID probes are normally used for in-service inspection of heat exchangers. The probe is inserted into the tube. Normally ID probes are wound with the coil axis along the centre of the tube.

Absolute probes These categories are not exhaustive and there are obviously overlaps, for example between non-circumferential wound ID probes and internal surface probes. To this point we have only discussed eddy current probes consisting of a single coil. These are commonly used in many applications and are commonly known as absolute probes because they give an ‘absolute’ value of the condition at the test point. Absolute probes are very good for metal sorting and detection of cracks in many situations, however they are sensitive also to material variations, temperature changes etc.

Differential’ probe Another commonly used probe type is the ‘differential’ probe this has two sensing elements looking at different areas of the material being tested. The instrument responds to the difference between the eddy current conditions at the two points. Differential probes are particularly good for detection of small defects, and are relatively unaffected by lift-off (although the sensitivity is reduced in just the same way), temperature changes and external interference. (assuming the instrument circuitry operates in a "balanced“ configuration)

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http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

Note the characteristic "figure of eight for differential probe" response as first one probe element, then the other, move over the defect. In general the closer the element spacing the wider the "loop" in the signal. Lift-off should be cancelled out assuming that the probe is perfectly balanced, but there will still be a "wobble" response as the probe is moved and tilted slightly.

Reflection or driver pick-up probes have a primary winding driven from the oscillator and one or more sensor windings connected to the measurement circuit. Depending on the configuration of the sensor windings reflection probes may give response equivalent to either an absolute or differential probe. The two coils (differential or absolute plus balancing coil) form the â&#x20AC;&#x2DC;legsâ&#x20AC;&#x2122; of a bridge. When the bridge is balanced the measured voltage will be zero. Any change in the condition of either coil will result in an unbalanced bridge, the degree of imbalance corresponds to the change in coil impedance.

The diagram shows a typical response from a differential probe.

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Driver pick-up: As can be seen the essential elements are the same for a driver pick-up configuration as for a bridge, the necessary changes can be achieved by simple switching or probe connection changes

http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

Tangential Probe

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http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

Orthogonal Probe

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http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

Electromagnetic Testing Advantages The following characteristics of the method can be used to advantage :  it can be used without making physical contact with the product ;  it does not need a coupling medium such as water ;  it is capable of being used at high throughput speeds.

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EN 12084 : 2001

Factors Affecting Eddy Current Responses The basic parameters which influence the measured quantity are all of the following properties of the product to be tested, alone or in combination :    

the conductivity of the material ; the magnetic permeability of the material ; (magnetic factor) the size and geometry of the product to be tested ; (magnetic factor) the geometry between the eddy current probe and the product to be tested. (magnetic factor)

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EN 12084 : 2001

Factors Affecting Eddy Current Response Material conductivity The conductivity of a material has a very direct effect on the eddy current flow: the greater the conductivity of a material the greater the flow of eddy currents on the surface. Conductivity is often measured by an eddy current technique, and inferences can then be drawn about the different factors affecting conductivity, such as material composition, heat treatment, work hardening etc.

Permeability This may be described as the ease with which a material can be magnetised. For non-ferrous metals such as copper, brass, aluminum etc., and for austenitic stainless steels the permeability is the same as that of ‘free space’, i.e. the relative permeability (μr) is one. For ferrous metals however the value of μr may be several hundred, and this has a very significant influence on the eddy current response, in addition it is not uncommon for the permeability to vary greatly within a metal part due to localised stresses, heating effects etc.

Frequency As we will discuss, eddy current response is greatly affected by the test frequency chosen, fortunately this is one property we can control.

Geometry In a real part, for example one which is not flat or of infinite size, geometrical features such as curvature, edges, grooves etc. will exist and will effect the eddy current response. Test techniques must recognise this, for example in testing an edge for cracks the probe will normally be moved along parallel to the edge so that small changes may be easily seen. Where the material thickness is less than the effective depth of penetration (see below) this will also effect the eddy current response

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http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

Proximity / Lift-off The closer a probe coil is to the surface the greater will be the effect on that coil. This has two main effects: The "lift-off" signal as the probe is moved on and off the surface. A reduction in sensitivity as the coil to product spacing increases.

Depth of penetration The eddy current density, and thus the strength of the response from a flaw, is greatest on the surface of the metal being tested and declines with depth. It is mathematically convenient to define the "standard depth of penetration" where the eddy current is 1/e (37%) of its surface value. The standard depth of penetration in mm is given by the formula:

Where: δ is standard depth in mm ρ is resistivity in μΩ.cm f is frequency in Hz μr is relative permeability

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http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

from this it can be seen that depth of penetration: 1. Decreases with an increase in frequency 2. Decreases with an increase in conductivity 3. Decreases with an increase in permeability: this can be very significant penetration into ferrous materials at practical frequencies is very small.

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The graph above shows the effect of frequency on standard depth of penetration. It is also common to talk about the "effective depth of penetration" usually defined as three times the standard depth, where eddy current density has fallen to around 3% (5%?) of its surface value. This is the depth at which there is considered to be no influence on the eddy current field.

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http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

The Impedance Plane Eddy current responses of a single coil may be conveniently described by reference to the "impedance plane". This is a graphical representation of the complex probe impedance where the abscissa (X value) represents the resistance and the ordinate (Y value) represents the inductive reactance.

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http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

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The Impedance Plane

http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

Note that, while the general form of the impedance plane remains the same, the details are unique for a particular probe and frequency. The display of a typical CRT eddy current instrument represents a â&#x20AC;&#x2DC;windowâ&#x20AC;&#x2122; into the impedance plane, which can be rotated and "zoomed" to suit the needs of the application. For example in the above impedance plane diagram a rotated detail of the "probe on aluminum" area would appear as below:

This shows the display when moving over a series of simulated cracks of varying depths. Note that in the example shown both the amplitude and the phase of response from the different sized cracks varies.

Reliability Eddy currents are often generated in transformers and lead to power losses. To combat this, thin, laminated strips of metal are used in the construction of power transformers, rather than making the transformer out of one solid piece of metal. Insulating glue, which confines the eddy currents to the strips, separates the thin strips. This reduces the eddy currents, thus reducing the power loss. Beside that, Eddy-Current Detectors are very reliable as far as their industrial usage. They are so reliable that nuclear plants are using robots to the tests, instead of risking real human beings.

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http://www.eng.morgan.edu/~hubert/IEGR470/eddycurrent.html

Robotic

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Robotic

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Measurement Techniques (EN!) a) Absolute measurement. The measurement of the deviation from a fixed reference point. The reference point is defined by a calibration procedure and can be generated by a reference voltage or coi l. This technique can be used for sorting the product into classes based on physical properties such as hardness, dimensions or chemical composition. It can also be used for the identification of continuous or gradually changing discontinuities.

b) Comparative measurement. The subtraction of two measurements, one of which is taken as a reference. This technique is normally used to sort the product into classes.

c) Differential measurement. The subtraction of two measurements made at a constant distance between the measurement locations and on the same scanning path. This measurement technique reduces the background noise due to slow variations in the product to be tested. (?)

d) Double differential measurement. The subtraction of two differential measurements. This measurement technique provides high-pass filtering of a differential measurement independent of the relative speed between the probe and the product to be tested.

e) Pseudo differential measurements The subtraction of two measurements made at a constant distance between the measurement locations.

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EN 12084 : 2001

Historical Background Before discussing the principles of eddy current testing, it seems appropriate to briefly discuss the concept of magnetism and electromagnetism that serve as the foundation for this study. In the period from 1775 to 1900, scientific experimenters Andre Marie Ampere, Franรงios Arago, Charles Augustin coulomb, Michael Faraday, Lord William Thomson Kelvin, James Clerk Maxwell and Hans Christian Oersted had investigated and cataloged most of what is known about magnetism and electromagnetism. Arago discovered that the oscillation of a magnet was rapidly damped when a nonmagnetic conductor disk was placed near the magnet. He also observed that by rotating the disk, the magnet was attracted to the disk. In effect, Arago had introduced a varying magnetic field into the metallic disk causing eddy currents to flow in the disk. This produced a secondary magnetic field in the disk that affected the magnet. Arago's simple model is a basis for many automobile speedometers used today. This experiment can be modeled as shown in Figure 1.1.

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http://pegna.vialattea.net/2Arago_Disk.htm

Figure 1.1 Aragoâ&#x20AC;&#x2122;s Experiment

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Aragoâ&#x20AC;&#x2122;s Disk Experiment Arago discovered that the oscillation of a magnet was rapidly damped when a nonmagnetic conducting disk was placed near the magnet. He also observed that by rotating the disk, the magnet was attracted to the disk. In effect, Arago had introduced a varying magnetic field into the metallic disk causing eddy currents to flow in the disk. This produced a secondary magnetic field in the disk that affected the magnet. Arago's simple model is a basis for many automobile speedometers used today.

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https://www.youtube.com/embed/sChcqdkcLGE

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Oersted discovered the presence of a magnetic field around a current carrying conductor and observed magnetic field developed in a perpendicular plane to the direction of current flow in a wire. Ampere observed that equal and opposite currents flowing in adjacent conductors cancelled this magnetic effect. Ampere's observation is used in differential coil applications and to manufacture non inductive precision resistor. Faraday's first experiments investigated induced currents by the relative motion of magnet and a coil (Figure 1.2). Faraday's major contribution was the discovery of electromagnetic induction. His work can be summarized by the example shown in Figure 1.3. A coil "A" is connected to a battery through a switch, "S", A second coil, B, connected to a voltmeter is near by. When switch S is closed it produces a current in coil A in the direction shown (a). A momentary current is also induced in coil in direction (b) opposite to the current flow in coil A. If S is now opened, a momentary current will appear in coil B having the direction of (c). In each case current flows in coil B only while the current in coil A is changing.

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Figure 1.2: Induced current with coil and magnet

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Figure 1.3: Induced current electromagnetic technique A coil "A" is connected to a battery through a switch, "S", A second coil, B, connected to a voltmeter is near by. When switch S is closed it produces a current in coil A in the direction shown (a). A momentary current is also induced in coil in direction (b) opposite to the current flow in coil A. If S is now opened, a momentary current will appear in coil B having the direction of (c). In each case current flows in coil B only while the current in coil A is changing.

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Electromagnetic induction is the production of an electromotive force across a conductor when it is exposed to a varying magnetic field. It is described mathematically by Faraday's law of induction, named after Michael Faraday who is generally credited with the discovery of induction in 1831. Electromagnetic induction was first discovered by Michael Faraday, who made his discovery public in 1831. It was discovered independently by Joseph Henry in 1832. In Faraday's first experimental demonstration (August 29, 1831), he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar to a modern toroidal transformer). Based on his assessment of recently discovered properties of electromagnets, he expected that when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. He plugged one wire into a galvanometer, and watched it as he connected the other wire to a battery. Indeed, he saw a transient current (which he called a "wave of electricity") when he connected the wire to the battery, and another when he disconnected it. This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected. Within two months, Faraday found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near the bar magnet with a sliding electrical lead ("Faraday's disk"). Faraday explained electromagnetic induction using a concept he called lines of force. However, scientists at the time widely rejected his theoretical ideas, mainly because they were not formulated mathematically. An exception was Maxwell, who used Faraday's ideas as the basis of his quantitative electromagnetic theory. In Maxwell's model, the time varying aspect of electromagnetic induction is expressed as a differential equation which Oliver Heaviside referred to as Faraday's law even though it is slightly different from Faraday's original formulation and does not describe motional EMF. Heaviside's version (see Maxwellâ&#x20AC;&#x201C; Faraday equation below) is the form recognized today in the group of equations known as Maxwell's equations. Heinrich Lenz formulated the law named after him in 1834, to describe the "flux through the circuit". Lenz's law gives the direction of the induced EMF and current resulting from electromagnetic induction (elaborated upon in the examples below). Following the understanding brought by these laws, many kinds of device employing magnetic induction have been invented.

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http://en.wikipedia.org/wiki/Electromagnetic_induction

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http://en.wikipedia.org/wiki/Electromagnetic_induction

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http://en.wikipedia.org/wiki/Homopolar_generator

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http://en.wikipedia.org/wiki/Homopolar_generator

Faraday's Law - Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc. Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

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http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

The law of physics describing the process of electromagnetic induction is known as Faraday's law of induction and the most widespread version of this law states that the induced electromotive force in any closed circuit is equal to the rate of change of the magnetic flux enclosed by the circuit. Or mathematically,

ε = dфB/ dt where ε (epsilon) is the electromotive force (EMF) and ΦB (Φ= BA) is the magnetic flux. The direction of the electromotive force is given by Lenz's law. This version of Faraday's law strictly holds only when the closed circuit is a loop of infinitely thin wire, and is invalid in some other circumstances. A different version, the Maxwell–Faraday equation (discussed below), is valid in all circumstances. For a tightly wound coil of wire, composed of N identical turns, each with the same magnetic flux going through them, the resulting EMF is given by

ε = -N dфB/ dt Faraday's law of induction makes use of the magnetic flux ΦB through a hypothetical surface Σ whose boundary is a wire loop. Since the wire loop may be moving, we write Σ(t) for the surface. The magnetic flux is defined by a surface integral:

фB = ∫Σ(t) B(r,t)∙dA where dA is an element of surface area of the moving surface Σ(t), B is the magnetic field, and B·dA is a vector dot product (the infinitesimal amount of magnetic flux). In more visual terms, the magnetic flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop.

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http://en.wikipedia.org/wiki/Electromagnetic_induction

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http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

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http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

Lenz's Law When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. In the examples below, if the B field is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to try to keep it constant.

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http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

Magnetic Force The magnetic field B is defined from the Lorentz Force Law, and specifically from the magnetic force on a moving charge:

The implications of this expression include: 1. The force is perpendicular to both the velocity v of the charge q and the magnetic field B. 2. The magnitude of the force is F = q∙v∙B sin θ where θ is the angle < 180 degrees between the velocity and the magnetic field. This implies that the magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero. 3. The direction of the force is given by the right hand rule. The force relationship above is in the form of a vector product.

When the magnetic force relationship is applied to a current-carrying wire, the right-hand rule may be used to determine the direction of force on the wire. From the force relationship above it can be deduced that the units of magnetic field are Newton seconds /(Coulomb meter) or Newtons per Ampere meter. This unit is named the Tesla. It is a large unit, and the smaller unit Gauss is used for small fields like the Earth's magnetic field. A Tesla is 10,000 Gauss. The Earth's magnetic field at the surface is on the order of half a Gauss Charlie Chong/ Fion Zhang

Lorentz force In physics, particularly electromagnetism, the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

F = - qâ&#x2C6;&#x2122; [ E + (v x B) ] (in SI units). Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a charged particle which might be traveling near the speed of light (relativistic form of the Lorentz force). The first derivation of the Lorentz force is commonly attributed to Oliver Heaviside in 1889, although other historians suggest an earlier origin in an 1865 paper by James Clerk Maxwell. Hendrik Lorentz derived it a few years after Heaviside.

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http://en.wikipedia.org/wiki/Lorentz_force

Generation of Eddy Currents When a conductor is place in the area influence by the primary field, eddy current is induced in the conductor, see Fig. 1.4. Following Lenz’s law, the induced eddy current IE will produce a secondary field фE that oppose the фP. The magnitude of фE is proportional to IE. The test objet, conductor B’s characteristic like, material conductivity, permeability and geometry will affect the IE, this in turn cause variation in фE. The variation in фE is reflected in conductor CA by фE influences on фp. The variations are recorded in media like meter, CRT, digital read out or chart. The

Ip = Primary Current Фp =Primary magnetic flux ФE = Secondary Eddy current magnetic flux IE = Secondary Eddy current Figure 1.4: Induced current relationships

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Generation of Eddy Currents

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http://www.suragus.com/en/company/eddy-current-testing-technology

Factors Affecting Inductance There are four basic factors of inductor construction determining the amount of inductance created. These factors all dictate inductance by affecting how much magnetic field flux will develop for a given amount of magnetic field force (current through the inductor's wire coil): NUMBER OF WIRE WRAPS, OR "TURNS" IN THE COIL: All other factors being equal, a greater number of turns of wire in the coil results in greater inductance; fewer turns of wire in the coil results in less inductance. Explanation: More turns of wire means that the coil will generate a greater amount of magnetic field force (measured in amp-turns!), for a given amount of coil current. L â&#x2C6;? N2

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http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

COIL AREA: All other factors being equal, greater coil area (as measured looking lengthwise through the coil, at the cross-section of the core) results in greater inductance; less coil area results in less inductance. Explanation: Greater coil area presents less opposition to the formation of magnetic field flux, for a given amount of field force (amp-turns). L â&#x2C6;? A

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http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

COIL LENGTH: All other factors being equal, the longer the coil's length, the less inductance; the shorter the coil's length, the greater the inductance. Explanation: A longer path for the magnetic field flux to take results in more opposition to the formation of that flux for any given amount of field force (amp-turns). L ∝ (l)-1

COIL LENGTH

L ∝ (l)-1

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COIL LENGTH

L ∝ (l)-1

http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

CORE MATERIAL: All other factors being equal, the greater the magnetic permeability of the core which the coil is wrapped around, the greater the inductance; the less the permeability of the core, the less the inductance. Explanation: A core material with greater magnetic permeability results in greater magnetic field flux for any given amount of field force (amp-turns). L∝μ

μ0 = 4π x 10-7 H.m-1

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μr = 600, μiron = 600 x μ0 μ0 = 4π x 10-7 H.m-1

http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

Coil Inductance L An approximation of inductance L, for any coil of wire can be found with this formula: The electromagnetic field produced about an unloaded test coil can be described as decreasing in intensity with distance from the coil and also varying across the coil's cross section. The field is most intense near the coil's surface. The field produced about this coil is directly proportiona1 to the magnitude of applied current, rate of change of current or frequency and the coil parameters. Coil parameters inc1ude inductance, diameter, length， thickness, number of turns of wire and core material.

L = μr• (N2 x A /l) • 1.26 x 10-6 Henry μ0 = 4π x 10-7 H.m-1 or 1.26 x 10-6 H.m-1 EMF = L di/dt Volt Where: L= inductance in Henry H N = Numbers of turn in coil wire (straight wire N=1) μr = relative permeability l = average length of coil in m A = area of coil (not wire area?) in m2 μo = relative permeability in air 4π x 10-7 H.m-1 or 1.26 x 10-6 H.m-1

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http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

Coil Inductance L

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Note the direction of the primary current (Ip) and the resultant eddy current (IE). IE extends some distance into the test object. Another important observation is that IE is generated in the same plane in which the coil is wound. Figure 1.6 emphasizes this point with a loop coil surrounding a cylindrical test object (4).

Important observation is that IE is generated in the same plane in which the coil is wound.

Figure 1.6 Induction current flow in a cylindrical part. Charlie Chong/ Fion Zhang

Important observation is that IE is generated in the same plane in which the coil is wound & in opposite direction of Ip

Figure 1.6 Induction current flow in a cylindrical part. Charlie Chong/ Fion Zhang

Generation of Eddy Current With a primary current 1p flowing through the coil, a primarr electromagnetic field Ń&#x201E;p is produced about the coil. When this excited test coil is placed on an electrically conductive test object, eddy currents IE will be generated in that test object Figure 1.5 illustrates this concept.

Figure 1.5 Generation of eddy current IE in a test object

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It must be understood that this formula yields approximate figures only. One reason for this is the fact that permeability changes as the field intensity varies (remember the nonlinear "B/H" curves for different materials). Obviously, if permeability (Âľ) in the equation is unstable, then the inductance (L) will also be unstable to some degree as the current through the coil changes in magnitude. If the hysteresis of the core material is significant, this will also have strange effects on the inductance of the coil. Inductor designers try to minimize these effects by designing the core in such a way that its flux density never approaches saturation levels, and so the inductor operates in a more linear portion of the B/H curve. If an inductor is designed so that any one of these factors may be varied at will, its inductance will correspondingly vary. Variable inductors are usually made by providing a way to vary the number of wire turns in use at any given time, or by varying the core material (a sliding core that can be moved in and out of the coil). An example of the former design is shown in this photograph:

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http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

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Permeability changes as the field intensity varies (remember the nonlinear "B/H" curves for different materials).

Figure 1: This unit uses sliding copper contacts to tap into the coil at different points along its length. The unit shown happens to be an air-core inductor used in early radio work. Figure 2: A fixed-value inductor is shown in the next photograph, another antique air-core unit built for radios. The connection terminals can be seen at the bottom, as well as the few turns of relatively thick wire: Figure 3: Here is another inductor (of greater inductance value), also intended for radio applications. Its wire coil is wound around a white ceramic tube for greater rigidity: Figure 4: The two inductors on this circuit board are labeled L1 and L2, and they are located to the right-center of the board. Two nearby components are R3 (a resistor) and C16 (a capacitor). These inductors are called "toroidal" because their wire coils are wound around donut-shaped ("torus") cores. Figure 5: Like resistors and capacitors, inductors can be packaged as "surface mount devices" as well. The following photograph shows just how small an inductor can be when packaged as such: A pair of inductors can be seen on this circuit board, to the right and center, appearing as small black chips with the number "100" printed on both. The upper inductor's label can be seen printed on the green circuit board as L5. Of course these inductors are very small in inductance value, but it demonstrates just how tiny they can be manufactured to meet certain circuit design needs.

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http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

A Dual1: Variable inductors Figure This unit uses sliding copper contacts to tap into the coil at different points along its length. The unit shown happens to be an air-core inductor used in early radio work.

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Figure 2: A fixed-value inductor is shown in the next photograph, another antique air-core unit built for radios. The connection terminals can be seen at the bottom, as well as the few turns of relatively thick wire:

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Figure 3: Here is another inductor (of greater inductance value), also intended for radio applications. Its wire coil is wound around a white ceramic tube for greater rigidity:

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Figure 4: The two inductors on this circuit board are labeled L1 and L2, and they are located to the right-center of the board. Two nearby components are R3 (a resistor) and C16 (a capacitor). These inductors are called "toroidal" because their wire coils are wound around donut-shaped ("torus") cores.

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http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

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Figure 5: Like resistors and capacitors, inductors can be packaged as "surface mount devices" as well. The following photograph shows just how small an inductor can be when packaged as such: A pair of inductors can be seen on this circuit board, to the right and center, appearing as small black chips with the number "100" printed on both. The upper inductor's label can be seen printed on the green circuit board as L5. Of course these inductors are very small in inductance value, but it demonstrates just how tiny they can be manufactured to meet certain circuit design needs.

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http://www.allaboutcircuits.com/vol_1/chpt_15/3.html

Grundig radio satellit 750

â&#x2013; https://www.youtube.com/embed/yD7WAcSwz8o

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http://www.universal-radio.com/catalog/portable/0750.html

Phasor Vector Diagram of Coil Voltage A more precise method of describing the relationships of magnetic flux, voltage and current is the phase vector diagram or phasor diagrams (4). Figure 1.7 compares the electromagnetic events associated with an unloaded test coil and what happens when that same coil is placed on a nonferromagnetic test object. The components of phasor diagrams are as follows:

Fig.17(b) Ep = Primary coil voltage I = Exciting current (Primary coil current) Фp = Primary flux Фs = Secondary flux

Fig.17(b) Ep = Primary coil voltage I = Exciting current (Primary coil current) Фp = Primary flux Фs = Secondary flux Es = Secondary voltage ET= Total voltage ФT = Total flux

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Figure 1.7: Phasor Diagram of Coil Voltage (?)

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Figure 1.7(b) represents the action of placing the coil on a nonferromagnetic test object Observing the figure, one can see by vectorial addition of Ep and Es that a new coil voltage (ET) is arrived at for the loaded condition. The primary magnetic flux фp and secondary magnetic flux фs are also combined by vectorial addition to arrive at a new magnetic flux (фT) for the loaded coil.

In Figure 1.7(a) the current (I) and primary magnetic flux (фp) are plotted in phase. The primary voltage (Ep) is shown separated by 90 electrical degrees. The secondary magnetic flux (фs) is plotted at zero because without a test object no secondary flux exists. Figure 1.7(b) represents the action of placing the coil on a nonferromagnetic test object Observing the figure, one can see by vectorial addition of Ep and Es that a new coil voltage (ET) is arrived at for the loaded condition. The primary magnetic flux фp and secondary magnetic flux фs are also combined by vectorial addition to arrive at a new magnetic flux (фT) for the loaded coil. Notice that for the condition of the test object in the test coil, фT is no longer in phase with the excitation current I. Also observe that the included angle between the excitation current and the new coil voltage ET is no longer at 90 electrical degrees. These interactions will be discussed in detaillater in this study guide.

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Current Density The distribution of eddy currents in a test object varies exponentially. The current density in the test object is most dense near the test coil. This exponential current density follows the mathematical rules for a natural exponential decay curve (1/ e) where Îľ (epsilon) is 2.718. Usually a natural exponential curve is illustrated by a graph with the ordinate (Y axis) representing magnitude and the abscissa (X axis) representing time or distance. A common point described on such a graph is the knee of the curve. The knee occurs at the 37% value on the ordinate axis. This 37% point is chosen because changes in X axis values produce significant changes in Yaxis values from 100% to 37% and below 37% changes in X axis values Ăžroduce less signlficant changes in Y axis values (?).

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Applying this logic to eddy current testing, a term is developed to describe the relationship of current distribution in the test object. The eddy current generated at the surface of the test object nearest the test coil is 100%. The point in the test object thickness where this current is diminished to 37% of its previous strength is known as the standard depth of penetration. The term Î´ (delta) is used to represent this point in the material. Figure 1.8 is a relative eddy current density curve for a plane wave of infinite extent with magnetic field parallel to the conducting test object surface.

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Figure 1.8: Relative eddy current density

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The current density at any depth can be calculated as:

Jx =J0 e - x√(πfμσ) Where: Jx = Electrical density at depth x in A∙m-2 J0 = Electrical density at the surface x=0 x = distance fro surface in meter m f = Frequency of the AC primary current Hz μ = Permeability of the test object in H∙m-1 σ = Conductivity of the test object in Siemen∙m-1 e = Natural logarithm

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Relative Magnetic Permeability

Permeability of free space μ0 = 4π x 10-7 HM-1 Permeability of material can be expressed as relative to μ0 μmaterial = μr∙μ0

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The Standard Depth of Penetration δ The Standard Depth of Penetration can be expressed as:

δ = (πfμσ) -½ Where:

δ = One standard depth of penetration; 1/e of the surface current density (37%) in meter, m f = Frequency of the AC primary current in Hz μ = Permeability of the test object in Henry per meter, H∙m-1 σ = Conductivity of the test object in Siemens per meter, S∙m-1

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It should be observed at this point that as frequency, conductivity or permeability is increased, the penetration of current into the test object will be decreased. The graph in Figure 1.8 is used to demonstrate many eddy current characteristics. Using an example of a very thick block of stainless steel being interrogated with a surface or probe coil operating at a test frequency of 100 kHz, the standard depth of penetration can be determined and current densities observed at other depths. Stainless steel (300 Series) is nonferromagnetic. Magnetic permeability (μ) is 4πX 10-7 H∙m-1, the conductivity σ is 0.14 X 107 siemens (mhos) per meter for 300 Series stainless steel. δ = (πfμσ) -½ δ = (π x 100 x 103 x 4 x π x 0.14) -½ δ = 0.00135m or 1.35mm#

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δ = (π x 100 x 103 x 4 x π x 0.14) -½ as 1000*(pi*x*4*pi*0.14*10^3)^(-.5)

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http://graph-plotter.cours-de-math.eu/

δ = (π x 100 x 103 x 4 x π x 0.14) -½ as 1000*(pi*x*4*pi*0.14*10^3)^(-.5)

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http://fooplot.com/

δ = (π x 100 x 103 x 4 x π x 0.14) -½ as 1000*(pi*x*4*pi*0.14*10^3)^(-.5)

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http://rechneronline.de/function-graphs/

Using 1.35 mm as depth x from surface, a ratio of depth/depth of penetration would be 1 Referring to Figure 1.8, a depth/ depth of penetration of 1 indicates a relative eddy current density of 0.37 or 37%. What is the relative eddy current density at 3 mm? The relative standard depth Drelative of x = 3mm is: Drelative = 3/Î´ = 3/1.53 mm = 2.22Î´ This ratio indicates a relative eddy current densityof about 0.1 or 10% [ (1/e)2.22 = 10.9% ]. With only 10% of the available current flowing at a depth of 3 mm, detectability of variables such as conductivity, permeability and discontinuities would be very difficult to detect. The obvious solution for greater delectability at a depth of 3 mm depth is to lower the test frequency. Frequency selection will be covered in detaillater in this text.

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Relative current density

f(x) = (1/e)x where x = depth/Î´

Relative Standard depth x = depth/Î´

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http://rechneronline.de/function-graphs/

Standard Depth for Different Conductive Materials

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https://www.nde-ed.org/EducationResources/CommunityCollege/EddyCurrents/Physics/PopUps/applet7/applet7.htm

Phase/Amplitude and Current Time Relationships Figure 1.9 reveals another facet of eddy current. Eddy currents are not generated at the same instant in time throughout the part. Eddy currents require time to penetrate the test part. Phase and time are analogous meaning - phase is an electrical term used to describe timing relationships of electrical waveforms. Phase Lag = x/Î´ radian Where: x =depth below surface Î´ = Standard depth

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Current (?) Lagging Voltage lagging or current lagging?

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Current (?) Lagging Voltage lagging or current lagging?

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σº∙πμ■δ∝∞ωΩθ√ρβααδπ

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Phase is u,sually expressed in either degrees or radians. There'are 2πradians per 360 degrees. Each radian therefore is about 57 degrees (360/2π). Using the surface eddy current near the test coil as a reference, the deeper the eddy current the greater the phase lag. The amount of phase lag is determined by:

β = x/δ = x∙√(πfμσ) β or Φ = Phase lag angle in radian. Others as defined earlier

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Figure 1.9 should be used as a relative indicator of phase lag. The exact phase relationship for a particular system may be different due to other variables, such as coil parameters and excitation methods. The amount of phase lag for a given part thickness is an important factor when considering resolution. Resolution is the ability to separate variables occurring in the test object; for example, distinguishing two discontinuities occurring at different depths in the same test object. As an example, using a standard depth of penetration at 1 mm in a 5 mm thick test object. Refer to Figure 1.9 and observe the phase lag of the current at one standard depth of penetration. Where depth of interest (x) is 1 mm and depth of penetration (Î´) is 1 mm, the x/ Î´ ratio is 1 and the current at depth x lags the surface current by 1 radian or 57 degrees.

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Projecting this examination, observe the phase lag for the entire part thickness. The standard depth of penetration is 1 mm, the part thickness is 5 mm; therefore, the ratio x/Î´ equals to 5. This produces phase lag of 5 radians or about 287 degrees for the part thickness. Having a measurement capability of 1 degree increments, the part thickness could be divided into 287 parts each part representing 0.017mm. That would be considered excellent resolution. There is an obvious Iimitation. Refer to Figure 1.8 and observe the resultant relative current density with an x/Î´ ratio of 5. The relative current density is near 0. It should become apparent that the frequency can be adjusted to achieve optimum results for a particular variable. These and other variables will be discussed in Chapter 5 of this Study Guide.

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Figure 1.8: Relative eddy current density

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Chapter 1 Review Questions

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Q.1.1 Generation of eddy currents depends on the principle of: A. wave guide theory. B. electromagnetic induction. C. Magnetostriction force D. All of the above Q.1.2 A secondary field is generated by the test object and is; A. Equal and opposite to the primary field B. Opposite to the primary field but much smaller C. In the same plane as the coil is wound. D. In phase with the primary field. Q.1.3 When a non ferromagnetic part is placed in the test coil, The coil' s voltage: A. increases B. remains constant because this is essential. C. decreases. D. shifts 90 degrees in phase.

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Q.1.4 Refer to Figure 1.7(b). If ET was produced by the test object being stainless steel, what would the effect be if the test object were copper? A. ET would decrease and be at a different angle. B. ET would increase and be at a different angle. C. Because both materials are non-ferromagnetic, no change occurs D. None of the above.

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Q.1.5 Eddy current generated a test object flow; A. in the same plane as magnetic flux B. in the same plane as the coil is wound C. 90 degrees to the coil winding plane. D. eddy currents have no predictable direction. Q.1.6 The discovery of electromagnetic induction is credited to A. Arago B. Oersted. C. Maxwell. D. Faraday. Q.1.7 A standard depth of penetration is defined as the point in a test object where the relative current density is reduced to: A. 25%. B. 37% C. 50%. D. 100%

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Q.1.8 Refer to Figure 1.8. If one standard depth of penetration was established at 1 mm in an object 3 mm thick, what is the relative current density on the far surface? A. 3 B. <0.1 C. 1/3 D. indeterminate

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Q.1.9 Refer to Figure1.9 using example in question 1.8, what is the phase difference between the near and far surfaces? A. the far surface current leads the near surface current by 57 degrees. B. the far surface current leads the near surface current by 171 degrees. C. the far surface current lags the near surface current by 171 degrees. D. the far surface current lags the near surface current by 570 degrees. Q.1.10 Calculate the standard depth of penetration at 10KHz in Copper with σ = 5.7 x 107 Siemens per meter. A. 0.1 mm (3.9 x10-3 in.) B. 0.02 mm (7.9 x10-4 in.) C. 0.66 mm (0.026 in.) D. 66 mm (2.6 in.) β = x/ δ x 57.3º δ = (πfμσ) -½ = √(10 x 103 x π x 4 π x 10-7 x 5.7 x 107) x 1000 mm

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The Answers

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Chapter 2 The Coil Arrangements

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Test Coil Arrangement Test coils can be categorized into three main mechanical groups: probe coils, bobbin coils and encircling coils. (Surface coil, internal bobbing coil, encircling coil)

Probe Coils Surface coil, probe coil, flat coil or pancake coil are all common terms used to describe the same test coil type. Probe coils provide a convenient method of examining the surface of a test object. Figure 2.1 below illustrates a typical set of probe coils used for several surface scanning applications.

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Probe coils and probe coil forms can be shaped to fit particular geometries to solve complex inspection problems. As an example, probe coils fabricated in a pencil shape (pencil probe) are used to inspect threaded areas of mounting studs and nuts or serrated areas of turbine wheels and turbine blade assemblies. Probe coils may be used where high resolution is required by adding coil shielding (2). When using a high resolution probe coil, the test object surface must be carefully scanned to ensure complete inspection coverage. This careful scanning is very time consuming. For this reason, probe coil inspections of large test objects are usually limited to critical areas. Probe coils are used extensively in aircraft inspection for crack detection near fasteners and fastener holes. In the case of fastener holes (bolt holes, rivet holes), the probe coil may be rotated either manually or mechanically to provide a helical scan of the hole using a spinning probe technique (Figure 2.2).

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Figure 2.2: Bolt hole inspection probes

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Encircling Coils Encircling coil, outside diameter coil and feed through coil are terms commonly used to describe a coil that surrounds the test object. Figure 2.3 illustrates a typical encircling coil. Encircling coils are primarily used to inspect tubular and bar-shaped products. The tube or bar is fed through the coil (feed through) at relatively high speed. The cross section of the test object within the test coil is simultaneously interrogated. For this reason, the circumferential location of discontinuities cannot be determined with an encircling coil. The volume of material examined at one time is greater using an encircling coil than a probe coil; therefore, the relative sensitivity is lower for an encircling coil. The additional advantage that a probe coil would have over the encircling coil is that the probe coil could define where within the circumferential plane the discontinuity exists. The encircling coil cannot make that distinction. If there are multiple signal sources within the coil's field of view the encircling coil response will indicate the average of all of those events.

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Figure 2.3: Encircling coil

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Discussion Subject; Encircling Coil If there are multiple signal sources within the coil's field of view the encircling coil response will indicate the average of all of those events. Question: Why average? why not sum of all signals?

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When using an encircling coil, it is important to keep the test object centered in the coil. If the test object is not centered, a uniform discontinuity response is difficult to obtain. To ensure proper centering it is corrunon practice to run the calibration standard several times, each time indexing the artificial discontinuities to a new circumferential location in the coil. As in all discontinuity detection schemes, it is essential to select a reasonable operating frequency, properly adjust the system display parameters and ensure that the tube is centered in the coil at all times to achieve optimum test sensitivity.

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Bobbin Coils Bobbin coil, inside diameter coil and inside probe are terms that describe coils used to inspect from the inside diameter or bore of a tubular test object. Bobbin coils are inserted and withdrawn from the tube inside diameter by long, semi flexible shafts or simply blown in with air and retrieved with an attached pull cable. These mechanisms will be described later in the text. Bobbin coil information follows the same basic rules stated for encircling coils. Figure 2.4 illustrates a typical bobbin coil.

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Coil Arrangements Probe coils, encircling coils and bobbin coils can be additionally classified. These additional classifications are determined by how the coils are electrically connected. The three coil categories are absolute, differential and hybrid. Figure 2.5 shows various types of absolute and differential coil arrangements.

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Figure 2.5: Test coil configurations for eddy current testing of small-diameter tubing

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

Absolute



Differential- Self comparisons, external reference



Thru transmission



Reflection (Double) Sending & Receiving

Absolute Coils An absolute coil makes its measurement without direct reference or comparison to a standard as the measurement is being made (6). Some applications for absolute coil systems would be measurements of conductivity, permeability, dimensions and hardness.

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Differential coils Differential coils consist of two or more coils electrically connected to oppose each other. Differential coils can be categorized into two types: (1) self comparison differential and (2) external reference differential. a) The self-comparison differential coil compares one area of a test object to another area on the same test object. A common use is two coils, connected opposing, so that if both coils are affected by identical test object conditions, the net output is 0 volts or no signal change. The self-comparison arrangement is insensitive to test object variables that occur gradually. Variables such as slowly changing wall thickness, diameter or conductivity are effectively discriminated against with the selfcomparison differential coil. Only when a different condition affects one or the other test coils will an output signal be generated. The coils usually being mechanically and electrically similar allows the arrangement to be very stable during temperature changes. Short discontinuities such as cracks, pits or other localized discontinuities with abrupt boundaries can be readily detected using the self-comparison differential coli.

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b) The external reference differential coil, uses an external reference to affect one coil while the other coil is affected by the test object. Figure 2.6 illustrates this concept. This system is used to detect differences between a standard object and test objects. It is particularly useful for comparative conductivity, permeability and dimensional measurements. Obviously in Figure 2.6 it is imperative to normalize (or balance) the system with one coil affected by the standard object and the other coil affected by an acceptable test object. The external reference differential coil system is sensitive to all measurable differences between the standard object and test object. For this reason it is often necessary to provide additional discrimination to separate and define variables present in the test object.

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Figure 2.6: External reference differential system

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Hybrid Coils Hybrid coils may be defined as driver/pickup, through transmission, reflection or primary/secdndary coil assemblies. Hybrid coils may or may not be the same size and are not necessarily adjacent to each other. Figure 2.7 shows one possible hybrid coil arrangement. In the through transmission coil, the excitation coil is on one side of the test object and the sensing coil is on the other. The driver coil induces eddy currents and a secondary magnetic field in the test specimen. Any variation of these secondary events should be detected by the smaller probe coil on the opposite side of the thin plate.

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Figure 2.7: Hybrid coil (through transmission)

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A hybrid coil arrangement consists of an excitation coil and a sensing coil (reflection coils). In most cases a single probe housing assembly contains both the driver and the pickup coil(s). The primary magnetic flux interacts with both coils. The voltage developed in the sensing coil is a function of the current magnitude and frequency applied to the excitation coil, coil parameters of the exciting and sensing coils and the test object characteristics. Most hybrid coils are designed to improve test sensitivity for a specific application. One example of this is for better detection of subsurface discontinuities in multilayer structures. The concept of using a smaller pickup coil enhances the ability to detect lower level impedance variations from small volume discontinuities deeper in the test sample. It should be pointed out that if larger volume discontinuities are encountered that a measurable impedance change might be generated by both the exciter and the pick up coil(s).

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Additional Coil Characteristics Coil configuration is but one of many factors to consider when setting up test conditions. Other coil characteristics of importance are mechanical, thermal and electrical stability; sensitivity, resolution and dimensions. The geometry of the coil is usually dictated by the geometty of the test object. Selection of smaller probe sizes may affect test sensitivity and/or resolution. The relative importance of the coil characteristics depends on the nature of the test. A blend of theory and experience usually succeeds in selection of proper coil parameters. Coil design and interactions with test objects will be discussed later in this Study Guide.

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Chapter 2 Review Questions

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Q.2.1 Differential coils are usually used in: A. bobbin coils. B. probe coils. C. outside diameter coils. D. any of the above. Q.2.2 When using a probe coil to scan a test object: A. the object must be dry and polished. B. the object must be scanned carefully to ensure inspection coverage. C. the object must be scanned in circular motions at constant speeds. D. the probe must be moving at all times to get a reading. Q.2.3 A spinning probe would most likely be: A. a bobbin coil B. an inside diameter coil. C. an outside diameter coil. D. a probe coil.

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Q.2.4 A feed through coil is: A. a coil with primary/ secondary windings connected so that the signal is fed through the primaq to the secondary. B. an encircling coil. C. an outside diameter coil. D. both Band C. Q.2.5 When inspecting a tubular product with an encircling coil, which statement is not true? A. Outside diameter discontinuities can be found. B. Axial discontinuity locations can be noted. C. Circumferential discontinuity locations can be noted. D. Inside diameter discontinuities can be found.

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Q.2.6 An absolute coil measurement is made: A. by comparing one spot on the test object to another. B. without reference to or direct comparison with a standard. C. only with probe coils. D. by comparative measurement to a known standard. Q.2.7 When coils in a self-comparison differential arrangement are affected simultaneously with the same test object variables, the output signal: A is directly proportional to the number of variables. B. is 0 or near 0. C. is indirectly proportional to the number of variables. D. is primarily a function of the exciting current.

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Q.2.8 Which coil type inherently has better thermal stability? A bobbin B. absolute C. outside diameter D. self-comparison differential Q.2.9 A hybrid coil is composed of two or more coils. The coils: A. must be aligned coplanar to the driver axis. B. may be of widely different dimensions. C. must be impedance matched as closely as possible. D. are very temperature sensitive. Q.2.10 Proper selection of test coil arrangement is determined by: A. shape of test object. B. redolution required. C. sensitivity required. D. stability. E. all of the above.

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The Answers

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Chapter 3 Test Coil Design

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As discussed earlier test coil design and selection is a blend of theory and experience. Many factors must be considered. These important factors are determined by the inspection requirement for resolution, sensitivity, impedance, size, stability and environmental considerations. To better understand coil properties and electrical relationships, a short refresher in alternating current theory is necessary. First, the electrical units must be examined. For example, current and its representative symbol I. Current not only suggests electron flow but also the amount. The amount of electrons flowing past a point in a circuit in 1 second is expressed in amperes: 2Ď&#x20AC; x 1018 electrons passing a point in 1 second is called 1 ampere.

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Ampere The ampere (SI unit symbol: A), often shortened to "amp", is the SI unit of electric current (dimension symbol: I) and is one of the seven SI base units. It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics. The ampere is equivalent to one coulomb (roughly 6.241×1018 times the elementary charge) per second. Amperes are used to express flow rate of electric charge. For any point experiencing a current, if the number of charged particles passing or the charge on the particles is increased, the amperes of current at that point will proportionately increase. The ampere should not be confused with the coulomb (also called "ampere-second") or the ampere-hour (A·h). The ampere is a unit of current, the amount of charge transiting per unit time, and the coulomb is a unit of charge. When SI units are used, constant, instantaneous and average current are expressed in amperes (as in "the charging current is 1.2 A") and the charge accumulated, or passed through a circuit over a period of time is expressed in coulombs (as in "the battery charge is 30000 C"). The relation of the ampere to the coulomb is the same as that of the watt to the joule, and that of metre per second to metre.

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http://en.wikipedia.org/wiki/Amperec

Demonstration model of a moving iron ammeter. As the current through the coil increases, the plunger is drawn further into the coil and the pointer deflects to the right.

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http://en.wikipedia.org/wiki/Amperec

Resistance Resistance is an opposition to the flow of electrons and is measured in ohms. Ohm's Law is stated by the equation: E = IR Where: I = Current in Ampere A R = Resistance in Ohm â&#x201E;Ś E = Electrical potential difference in volt V

The resistance of a coil is determined primarily by the length of wire used to wind the coil; its specific resistance is determined by the type of wire (e.g., copper, silver) and the cross-sectional area of the wire. Resistance = (Specific resistance X Length) / Area Resistance =

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Thus, the resistance of a 10 ft length of 40 gage copper wire with a specific resistance of 10.4 circular-mil-foot at 20ยบC would be found as follows: R = (10.4 X 10) / 9.888 = 10.518 ohm. In an alternating current circuit containing only resistance, the current and voltage are in phase. In phase means the current and voltage reach their minimum and maximum values, respectively, at the same time. The power dissipated in a resistive circuit appears :in the form of heat. For example, electric toasters are equipped with resistance wires that become hot when current flows through them, providing a heat source for toasting bread.

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Circular-Mill-Foot A circular-mil-foot (figure 1-3) is a unit of volume. It is a unit conductor 1 foot in length and has a cross-sectional area of 1 circular mil. Because it is a unit conductor, the circular-mil-foot is useful in making comparisons between wires consisting of different metals. For example, a basis of comparison of the RESISTIVITY (to be discussed shortly) of various substances may be made by determining the resistance of a circular-mil-foot of each of the substances. In working with square or rectangular conductors, such as ammeter shunts and bus bars, you may sometimes find it more convenient to use a different unit volume. A bus bar is a heavy copper strap or bar used to connect several circuits together. Bus bars are used when a large current capacity is required. Unit volume may be measured as the centimeter cube. Specific resistance, therefore, becomes the resistance offered by a cube-shaped conductor 1 centimeter in length and 1 square centimeter in cross-sectional area. The unit of volume to be used is given in tables of specific resistances.

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http://www.tpub.com/neets/book4/11b.htm

SPECIFIC RESISTANCE OR RESISTIVITY Specific resistance, or resistivity, is the resistance in ohms offered by a unit volume (the circular-mil-foot or the centimeter cube) of a substance to the flow of electric current. Resistivity is the reciprocal of conductivity. A substance that has a high resistivity will have a low conductivity, and vice versa. Thus, the specific resistance of a substance is the resistance of a unit volume of that substance. Many tables of specific resistance are based on the resistance in ohms of a volume of a substance 1 foot in length and 1 circular mil in cross-sectional area. The temperature at which the resistance measurement is made is also specified. If you know the kind of metal a conductor is made of, you can obtain the specific resistance of the metal from a table. The specific resistances of some common substances are given in table 1-1.

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http://www.tpub.com/neets/book4/11b.htm

The resistance of a conductor of a uniform cross section varies directly as the product of the length and the specific resistance of the conductor, and inversely as the cross-sectional area of the conductor. Therefore, you can calculate the resistance of a conductor if you know the length, cross-sectional area, and specific resistance of the substance. Expressed as an equation, the "R" (resistance in ohms) of a conductor is

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http://www.tpub.com/neets/book4/11b.htm

Problem: What is the resistance of 1,000 feet of copper wire having a cross-sectional area of 10,400 circular mils (No. 10 wire) at a temperature of 20°C? Solution: The specific resistance of copper (table 1-1) is 10.37 ohms. Substituting the known values in the preceding equation, the resistance, R, is determined as R = ρ∙ l / A = 10.37 x 1000 / 10400 = 1Ω approximately This equipment operates on the principle that the resistance of a line varies directly with its length. Thus, the distance between the test point and a fault can be computed accurately.

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http://www.tpub.com/neets/book4/11b.htm

Inductance Heat generation is an undesirable trait for an eddy current coil. If the 10 ft length of wire used in the previous example was wound into the shape of a coil, it would exhibit characteristics of alternating current other than resistance. By forming the wire into the shape of a coil, the coil also would have the property of inductance. The role of inductance is analogous to inertia in mechanics, because inertia is the property of matter that causes a body to oppose any change in its velocity. The unit of inductance is the Henry (H). A coil is said to have the property of inductance when a change in current through the coil produces a voltage in the coil. More precisely, a circuit in which an electromotive force of 1 V is induced when the current is changing at a rate of 1 Ampere per second will have an inductance of 1 H.

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The inductance of a multilayer air core coil can be expressed by its physical properties or coil parameters. Coil parameters such as length, diameter, thickness and number of turns of wire affect the coil's inductance. Figure 3.1 illustrates typical coil dimensions required to calculate coil :inductance. An approximation of small, multilayer, air core coil inductapce is as follows: L = 0.8(rN)2 ∙ (6∙r+9∙l+10∙b) -1 μHenry L = self inductance in μH N = number of turns r = mean radius in inches l = length of coil in inches b = coil depth

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Multi Layer Induction Coil

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http://info.ee.surrey.ac.uk/Workshop/advice/coils/air/area.xhtml

Example: A coil whose dimensions are as follows: r = 0.1 in I = 0.1 in b = 0.1 in N = 100 turns

for L = 0.8(rN)2 ∙ (6∙r+9∙l+10∙b)-1 μH L = 0.8(0.1x100)2 (6x0.1+9x0.1+10.0.1)-1 L = 32 μH As stated earlier, this inductance is analogous to inertia in mechanical systems in that inductance opposes a change in current as inertia opposes a change in velocity of a body. In alternating current circuits the current is always changing; therefore inductance is always opposing this change. As the current tries to change, the inductance reacts to oppose that change. This reaction is called innductive reactance.

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Inductive Reactance The unit of inductive reactance (XL) is in ohms. For a given coil the inductive reactance is a function of the rate of change of current or frequency. A formula relating frequency, inductance and inductive reactance is: XL = ωL = 2πf L Where: XL = Inductive reactance Ohm f = Frequency Hz L = Inductance Henry

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Example: Using the 32 μH coil calculated earlier operating at 100 KHz, its inductive reactance would be found as follows:

L = 32 μH or 0.000032 H f = 100 KHz or 100000 Hz

XL = ωL = 2πfL = 2π x 100 x 103 x 32 x 10-6 = 20.106Ω Therefore, this coil would present an opposition of 20.096 ohms to currents with a rate of change of 100 kHz due to its reactive component. Unlike a resistive circuit, the current and voltage of an inductive circuit do not reach their minimum and maximum values at the same time. In a pure inductive circuit the voltage leads the current by 90 electrical degrees. This means that when the voltage reaches a maximum value, the current is at 0.

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Power is related to current and voltage as follows: Power P = E x I P = Power E = Potential volt I = Current in Ampere

Notice that in a pure inductive circuit, when the voltage is maximum, the current is 0. Therefore, the product P = E x I = 0, Inductive reactances consume no alternating power where resistive elements consume power and dissipate power in the form of heat. The opposition to current flow because of the resistive element of the coil and the reactive element of the coil do not occur at the same time; therefore, they cannot be added as scalar quantities. . A scalar quantity is one having only magmtude, that is a quantity fully described by a number, but which does not involve any concept of direction. Gallons in a tank, temperature in a room, miles per hour, for example, are all scalars.

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Impedance To explain the addition of reactance and resistance witha minimum of mathematical calculations, it is ·possible to use vector or phasor diagrams. A vector diagram constructed with imaginary units on the ordinate or Y axis and real units on the abscissa or X axis is shown in Figure 3.2. Z=√(XL2+R2) Observation of Figure 3.2 reveals XL, R and Z appear to form the sides of a right triangle. The mathematical solution of right triangles states the square of the hypotenuse is equal to the sum of the squares of the other two sides, or c2 = a2 + b2

Figure 3.2 Vector Diagram

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Substituting Z, XL and R, the statement becomes: Z2 = XL2 + R2, further simplified Z = √(XL2+R2)

Example: Example: What is the impedance of a coil having an inductance. of 100μH and a resistance of 5 ohms and being operated at 200 kHz? XL = 2π x 200 x 103 x 100 x 10-6 = 125.7Ω Z =√(XL2 + R2) = (125.72 + 52) .5 = 125.8 Ω First, convert inductance to inductive reactance and then, by vector addition, combine inductive reactance and resistance to obtain the impedance.

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Maximum transfer of power is accomplished when the driving impedance and load impedance are matched. If, for instance, an eddy current instrument had a driving impedance of 50 ohms, the most efficient test coils would also have impedances of 50 ohms. Other, more common examples of impedance matching are home stereo systems rated at 100 W per channel into 8 ohms. Impedance can be discussed in a more detailed manner by mathematically noting variables using imaginary numbers). The square root of a negative number is known as an imaginary number (√-1). The imaginary number √(-16) could be written as √(-1x16) or √-1∙ √(16) or √(-1)∙4. The notation √(-1) is used extensively and is mathematically noted by a lower case letter "i". Because i is also used in electrical terms for current, the i notation for electrical calculations is changed to the letter "j". The term j, often called operator j, is equal to the √(-I). Instead of noting √(-16) as √(-1)∙4. note it as j4. Because reactance is known as an imaginary component, then impedance In Cartesian form:

Z = R + jXm where the real part of impedance is the resistance R and the imaginary part is the reactance X.

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http://en.wikipedia.org/wiki/Electrical_impedance

Rectangular Notation Because reactance is known as an imaginary component, then impedance In Cartesian form: Z = R + jX = |Z|∠ θ = The term R + jX is known as a rectangular notation. As an example, a resistance of 4 ohms in series with an inductive reactance of 3 ohms could be noted as Z = 4 + j3 ohms. The impedance

j3 ohms

|∠ 5 | =

. Ω º 8.59

Z = 4 + j3 ohms.

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Rectangular Notation j3 ohms

. Polar Notation Ω º 9 5 . 8 4 ∠ | 5 =|

Z = 4 + j3 ohms.

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Polar and Rectangular Notation In order to work with these complex numbers without drawing vectors, we first need some kind of standard mathematical notation. There are two basic forms of complex number notation: polar and rectangular. Polar form is where a complex number is denoted by the length (otherwise known as the magnitude, absolute value, or modulus) and the angle of its vector (usually denoted by an angle symbol that looks like this: ∠). To use the map analogy, polar notation for the vector from New York City to San Diego would be something like “2400 miles, southwest.” Here are two examples of vectors and their polar notations: (Figure below)

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Vectors With Polar Notations. Standard orientation for vector angles in AC circuit calculations defines 0º as being to the right (horizontal), making 90º straight up, 180º to the left, and 270º straight down. Please note that vectors angled “down” can have angles represented in polar form as positive numbers in excess of 180º, or negative numbers less than 180. For example, a vector angled ∠ 270º (straight down) can also be said to have an angle of -90º. (Figure below) The above vector on the right (7.81 ∠ 230.19º) can also be denoted as 7.81 ∠ -129.81º.

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The Vector Compass Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides. Rather than describing a vector's length and direction by denoting magnitude and angle, it is described in terms of “how far left/right” and “how far up/down.” These two dimensional figures (horizontal and vertical) are symbolized by two numerical figures. In order to distinguish the horizontal and vertical dimensions from each other, the vertical is prefixed with a lower-case “i” (in pure mathematics) or “j” (in electronics). These lower-case letters do not represent a physical variable (such as instantaneous current, also symbolized by a lower-case letter “i”), but rather are mathematical operators used to distinguish the vector's vertical component from its horizontal component. As a complete complex number, the horizontal and vertical quantities are written as a sum: (Figure below)

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Rectangular Notation – Prefix “j” These two dimensional figures (horizontal and vertical) are symbolized by two numerical figures. In order to distinguish the horizontal and vertical dimensions from each other, the vertical is prefixed with a lower-case “i” (in pure mathematics) or “j” (in electronics). These lower-case letters do not represent a physical variable (such as instantaneous current, also symbolized by a lower-case letter “i”), but rather are mathematical operators used to distinguish the vector's vertical component from its horizontal component. As a complete complex number, the horizontal and vertical quantities are written as a sum: (Figure below)

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Rectangle & Polar Notation  In rectangular notation, the vertical and horizontal components’ ordinate and abscissa are shown. Z = R + jX, where j denoting vertical component.  In polar notation, vector length hypotenuse and angle are shown |Z|∠ θ, where |Z| denoting vector length and ∠ θ denoting the angle. Z = R + jXm = |Z|∠ θ =

j3 ohms

|∠ 5 | =

. Ω º 8.59

Z = 4 + j3 ohms.

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Imaginary Component In “rectangular” form the vector's length and direction are denoted in terms of its horizontal and vertical span, the first number representing the horizontal (“real”) and the second number (with the “j” prefix) representing the vertical (“imaginary”) dimensions. The horizontal component is referred to as the real component, since that dimension is compatible with normal, scalar (“real”) numbers. The vertical component is referred to as the imaginary component, since that dimension lies in a different direction, totally alien to the scale of the real numbers. (Figure below)

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Vector compass showing real and imaginary axes. The “real” axis of the graph corresponds to the familiar number line we saw earlier: the one with both positive and negative values on it. The “imaginary” axis of the graph corresponds to another number line situated at 90º to the “real” one. Vectors being twodimensional things, we must have a two-dimensional “map” upon which to express them, thus the two number lines perpendicular to each other: (Figure below)

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Imaginary

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Vector compass with real and imaginary “j” number lines. Either method of notation is valid for complex numbers. The primary reason for having two methods of notation is for ease of longhand calculation, rectangular form lending itself to addition and subtraction, and polar form lending itself to multiplication and division. Conversion between the two notational forms involves simple trigonometry. To convert from polar to rectangular, find the real component by multiplying the polar magnitude by the cosine of the angle, and the imaginary component by multiplying the polar magnitude by the sine of the angle. This may be understood more readily by drawing the quantities as sides of a right triangle, the hypotenuse of the triangle representing the vector itself (its length and angle with respect to the horizontal constituting the polar form), the horizontal and vertical sides representing the “real” and “imaginary” rectangular components, respectively: (Figure below)

To convert from polar to rectangular notation

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To convert from rectangular to polar notation, find the polar magnitude through the use of the Pythagorean Theorem (the polar magnitude is the hypotenuse of a right triangle, and the real and imaginary components are the adjacent and opposite sides, respectively), and the angle by taking the arctangent of the imaginary component divided by the real component: Z = 4+j3 Magnitude vector in terms of real (4) and imaginary (j3) components.

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REVIEW on Rectangular & Polar Notations  Polar notation denotes a complex number in terms of its vector's length and angular direction from the starting point. Example: fly 45 miles ∠ 203º (West by Southwest).  Rectangular notation denotes a complex number in terms of its horizontal and vertical dimensions. Example: drive 41 miles West, then turn and drive 18 miles South.  In rectangular notation, the first quantity is the “real” component (horizontal dimension of vector) and the second quantity is the “imaginary” component (vertical dimension of vector). The imaginary component is preceded by a lowercase “j,” sometimes called the j operator.  Both polar and rectangular forms of notation for a complex number can be related graphically in the form of a right triangle, with the hypotenuse representing the vector itself (polar form: hypotenuse length = magnitude; angle with respect to horizontal side = angle), the horizontal side representing the rectangular “real” component, and the vertical side representing the rectangular “imaginary” component.

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More Reading on Polar & Rectangular Vector Notations http://en.m.wikipedia.org/wiki/Vector_notation http://www.daycounter.com/Calculators/Polar-To-RectangularCalculator.phtml https://filebox.ece.vt.edu/~LiaB/Lectures/Ch_9/Slides/Mathematics.pdf http://www.allaboutcircuits.com/vol_2/chpt_2/5.html

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The term Z = R + jX is known as a rectangular notation. As an example, a resistance of R= 4 ohms in series with an inductive reactance of jX = 3 ohms could be noted as Z = 4 + j3 ohms. The impedance calculation is then : Z = √(42 + 32) = √(25) = 5Ω In coil design it is often helpful to know also the included angle between the resistive component and impedance. A convenient method of notation is the polar form where tan θ =XL+ R and θ is the included angle between resistance and impedance. In the previous example the impedance magnitude is 5 ohms, but at what angle? A proper form of notation is Z∠θ where Z is impedance and ∠θ is the included angle. Therefore, the complete notation for R=3, XL=4 is: Z = √(42 + 32) = √(25) = 5Ω tan θ = ¾ = 0.750 = 36.9º Z = |5|∠ 36.9º or Z = 3+j4

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Eddy current coils with included impedance angles of 60 degrees to 90 degrees usually make efficient test coils. As the angle between resistance and impedance approaches 0 degrees, the test coil becomes very inefficient with most of its energy being dissipated as heat.

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Q or Figure of Merit The term used to describe coil efficiency is Q or merit of the coil. The higher the Q or merit of a coil, the more efficiently the coil performs as an inductor. The merit of a coil is mathematically stated as: Q = XL / R For example, a coil having an inductive reactance of 100 ohms and a resistance of 5 ohms would have a Q of 20.

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Permeability and Shielding Effects The addition of permeable core in certain designs dramatically improves â&#x20AC;&#x153;Qâ&#x20AC;? factor. For example, are wound on a form that allow the powdered iron rod or slug to be placed in the center of coil. It is common to increase the coil impedance by a factor of 10 by the addition of coil materials. This increase in impedance without addition winding greatly enhances the Q of the coil. Some core materials are cylindrical or cup shaped. A common term is cup core (Fig3.3). the coil is first wound and then placed inn the cup core. In the case of a probe coil in the cup core,not only is the impedance increased, but the benefit of shielding is also gained. Shielding with a cup core, prevent the electromagnetic field from spreading at the sides of the coil. This greatly reduces signal produced by edge effect of adjacent member of the test area, such as fasteners on air wings. Shielding, while improving resolution, usually sacrifices some amount of penetration into fue part.

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Figure 3.3: Effects of cup cores

(a) Unshielded coil -field spread might be up to twice the coil diameter. (b) Shielded coil - magnetic field extension restricted to the core geometry.

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Another technique of shielding uses high conductivity material, such, as copper or aluminum, to suppress high frequency interference from other sources and also to shape the electromagnetic field of the test coil. A copper cup would restrict the electromagnetic field in much the same manner as the powdered iron cup core. A disadvantage of high conductivity, low or no permeability shielding is that the coil's impedance is reduced when the shielding material is placed around the test coil. The net effect is that the coil's â&#x20AC;&#x153;Qâ&#x20AC;? factor is less than it was when the coil was surrounded by air.

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Discussion Subject 1: Shielding, while improving resolution, usually sacrifices some amount of penetration into fue part. Subject 2: A disadvantage of high conductivity, low or no permeability shielding is that the coil's impedance is reduced when the shielding material is placed around the test coil. The net effect is that the coil's â&#x20AC;&#x153;Qâ&#x20AC;? factor is less than it was when the coil was surrounded by air.

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Saturation Approach Another coil design used for inspection of ferromagnetic materials is the saturation approach. A predominant variable that prevents eddy current penetrating in ferromagnetic material is called permeability. Permeability effects exhibited by the test object can be reduced by means of magnetic saturation(Figure 3.4). Saturation coils for steels are usually very large and surround the test object and test coil. A steady state (DC) current is applied to the saturation coil. When the steel test object is magnetically saturated it may be inspected in the same manner as a nonferromagnetic material. In the case of mild steel many thousands of tesla are required to produce saturation. In some inherently nonferromagnetic tubing materials like high temperature nickel chromium alloy there may be low level permeability variations because of manufacturing discontinuities. In this case the use of small permanent magnets adjacent to the bobbin probe coils may improve the inspection quality by reducing the permeability effects. Figure 3.5 shows the use of disk type magnets placed close to the coil. It is also possible to use an array of bar magnets arranged around the probe housing if higher magnetic potential is required to offset the material permeability characteristics.

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Figure 3.4: Magnetic saturation inspection process

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Figure 3.5: Magnetic bias probe

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Coil Fixtures Coil fixtures or holders may be as varied as the imagination of the designers and users. After the size, shape and style have been decided on, the next consideration should be the test environment. Characteristics of wear, temperature, atmosphere, mechanical stress and stability must be considered (4). Normally wear can be reduced by selection of wear resistant compounds to protect the coil windings. If severe wear is expected, artificial or genuine jewels may be used. Less expensive and very effective wear materials, such as aluminum oxide or ceramics, are more commonly used. Temperature stability may be accomplished by using coil holder material with poor heat transfer characteristics. Metals have high heat transfer characteristics and often coils made with metal holders are sensitive to temperature variations caused by human touch. For high temperature applications, materials must be chosen carefully. Most common commercial copper coil wire may be used up to 150째C to 200째C. For temperatures above 200 ac, silver or aluminum wire with ceramic or high temperature silicone insulation must be used.

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Materials must be chemically compatible with the test object. As extreme examples, a polystyrene coil form would not be used to inspect an acetone cooler or a lead or graphite housing allowed to come in contact with a high temperature nickel chromium alloy jet engine tail cone. The chemical interactions between these material combinations could cause cracking and lead to component failure. Mechanical and electrical stability of the test coil can be enhanced by an application of epoxy resin between each layer of coil winding. This accomplishes many objectives: 1) it seals the coil to exclude moisture; 2) it provides additional electrical insulation; and 3) it provides mechanical stability. Characteristics listed are not in order of importance. The importance of each characteristic is determined by specific test requirements.

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Chapter 3 Review Questions

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Q.3.1 A coil's resistance is determined by: A. wire material. B. wire length. C. wire cross-sectional area. D. all of the above. Q.3.2 Inductance might be referred to as being analogous to: A. force. B. volume. C. inertia. D. velocity. Q.3.3 The unit of inductance is the: A. henry. B. maxwell. C. ohm. D. farad.

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Q.3.4 The inductance of a multilayer air core coil with the dimensions I = 0.2, r = 0.5, b = 0.1 and N = 20, is: L = 0.8(rN)2 ∙ (6∙r+9∙l+10∙b) -1 μHenry A. 1.38 H. L = self inductance in μH B. 13.8 μH. N = number of turns r = mean radius in inches C. 13.8 ohms. l = length of coil in inches D. 1.38 ohms. b = coil depth

Q.3.5 The inductive reactance of the coil in Q.3.4, operating at 400 kHz, would be: A. 1380 ohms. XL= 2πfL = (2π∙400∙103∙13.8∙10-6) B. 5520 ohms. C. 34.66 ohms. D. 3466 oluns. Q.3.6 The impedance of a 100μH coil with a resistance of 20 ohms operating at 100kHz would be: A. 62.8 ohms. XL = 2πfL, Z =√(XL2 + R2) B. 4343.8 ohms. C. 628 ohms. D. 65.9 ohms. Charlie Chong/ Fion Zhang

Q.3.7 The Q or merit of a coil is denoted by the ratio: A. Z/XL B. XL/Z c. XL/R D. R/XL Q.3.8 The incorporation of ferromagnetic shielding materials around a coil: A. improves resolution. B. decreases field extension. C. increases impedance. D. Does all of the above. Q.3.9 The purpose of a steady state winding w near a test coil is to: (? â&#x20AC;&#x201C; scanned copy missing wording) A. reduce material permeability effects. B. produce possible magnetic saturation in the test material. C. provide a balance source for the sensitive coil. D. both A and B.

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Q.3.10 The most important consideration when selecting a test coil is: A. sensitivity. B. resolution. C. stability. D. meeting established inspection criteria

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The Answers

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Chapter 4 Effects of Test Object on Test Coil

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Jackfruit Tree

Operating or Test Variables As previously seen, the eddy current technique depends on the generation of induced currents within the test object. Disturbances in these small induced currents affect the test coil. The result is a variation of the test coil impedance due to test object variables. These variances are called operating or test variables. The range of test variables encountered might include electrical conductivity, magnetic permeability, skin effect, lift off, fill factor; end effect, edge effect and signal-to-noise ratio. Coil impedance was discussed at length in Chapter.3. In this chapter coil impedance changes will pe represented graphically to more effectively explain the interaction of the operating variables.

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Electrical Conductivity Ď&#x192; In electron theory the atom consists of a positive nucleus surrounded by orbiting negative electrons. Materials that allow these electrons to be easily moved out of orbit around the nucleus are classified as conductors. In conductors electrons are moved by applying an outside electrical force. The ease with which the electrons are made to move through the conductor is called conductance. A unit of conductance is the siemens (mho). The siemens is the reciprocal of the ohm or conductance G = l / R where G is conductance in siemens and R is resistance in ohms. In eddy current testing, instead of describing conductance in absolute terms, an arbitrary unit has been assigned. Since the relative conductivity of metals and alloys varies over a wide range, the need for a conductivity bench-mark is of prime importance.

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The International Electrochemical Commission established in 1913 a convenient technique of comparing one material to another. The commission established that a specific grade of high purity copper, 1 m in length, with a uniform cross section of 1 mm2, measuring 0.017241 ohms at 20Â°C would be arbitrarily considered to be 100% 'conductive. The symbol for conductivity is Ď&#x192; (sigma) and the unit is percent IACS or percent of the International Annealed Copper Standard. Table 4.1 lists materials by their electrical properties: conductivity and resistivity. A statement can be made about a conductor in terms of conductance or resistance. Note that a good conductor is a poor resistor. Conductance and resistance are direct reciprocals as stated earlier. Conductivity and resistivity, however, have different origins and units; therefore, the conversion is not so direct.

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As previously discussed, conductivity is expressed on an arbitrary scale in percent IACS. Resistivity is expressed in absolute terms of micro-ohmcentimeters. To convert values on one scale to the other system of units a conversion factor of 172.41 is required. Once you know either the conductivity or the resistivity value for a material the other electrical property can be calculated.

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172.41 Charlie Chong/ Fion Zhang

%IACS & Resistivity ρ (rho) in micro-ohm-centimeter ■

%IACS = 172.41 / ρ micro-ohm-centimeter (μΩ∙cm)

■

ρ micro-ohm-centimeter = 172.41 / %IACS

These numerical values will be necessary when additional calculations are needed to determine issues of frequency choice, depth of penetration and I or phase spread to meet specific inspection criteria. As the test coil is influenced by different conductivities, its impedance varies inversely to conductivity. A higher conductivity causes the test coil to have a lower impedance value. Figure 4.1 illustrates this concept.

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Figure 4.1; Conductivity curve

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Discussion Subject: A higher conductivity causes the test coil to have a lower impedance value. Figure 4.1 illustrates this concept.- Reason out the statement.

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The coil's inductive reactance is represented by theY axis and coil resistance appears on the X axis. The 0% conductivity point, or air point, is when the coil's empty reactance (XL) is maximum. Figure 4.1 represents a measured conductivity locus . Conductivity is influenced by many factors. Table 4.1 is a comparative listing of materials with various chemical compositions. There are various manufacturing or in situ factors that must be considered when hying to measure the conductivity of various alloys. In metals, .as. the temperature is increased, the conductivity wlll decrease. This is a major factor to consider when accurate measurement of conductivities is required.

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Figure 4.1; Conductivity curve Key Word: The 0% conductivity point Air point

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Effects of Heat Treatment on Conductivity Heat treatment affects electrical conductivity by redistributing elements in the material. Dependent on materials and degree of heat treatment, conductivity can either increase or decrease as a result of heat treatment. Stresses in a material due to cold working produces lattice distortion or dislocation. This mechanical process changes the grain structure and harness of the material, changing its electrical conductivity. Hardness in age hardened aluminum alloy changes the electrical conductivity of the alloy. The electrical conductivity decreas as hardness increase. As an example Brinell hardness 60 is represented by conductivity 23 while Brinell hardness 100 of the same alloy would have a conductivity of 19.

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Table 4.1: Electrical resistivity and conductivity of several metals and alloys

Ď = 172.41 / %IACS

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Permeability Permeability of any material is a measure of the ease with which its magnetic domains can be aligned or the ease with which it can be establish lines of force. Materials are rated on a comparative basis. Air is assigned a permeability of 1. Ferromagnetic metals and alloys including nickel, iron and cobalt tend to concentrate magnetic flux lines. As discussed in Chapter 3, some ferromagnetic materials or sintered ionic compounds are also useful in concentrating magnetic flux. Magnetic permeability is not constant for a given material. The permeability in a test sample depends on the magnetic field acting on it. As an example, consider a magnetic steel bar placed in an encircling coil. As the coil current is increase, the magnetic field of the coil will increase. The magnetic flux within the steel will increase rapidly at first and then will tend to level off as the steel approaches magnetic saturation. This phenomenon is called the saturation effect.

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BH Curve

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When increases in the magnetizing force produce littile or no change on the flux within the steel bar, the bar is magnetically saturated. When ferromagnetic materials are saturated, permeability becomes constant. With magnetic permeability constant, ferromagnetic materials may be inspected using tpe eddy current method. Without magnetic saturation ferromagnetic materials exhibit such a wide range of permeability variation that signals produce by discontinuities or conductivity variations are masked by the permeability signal.

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Skin Effect Electromagnetic tests in many applications are most sensitive to test object variables nearest the test coil because of skin effect. Skin effect is a result of mutual interaction of eddy currents, operating frequency, test object conductivity and permeability. The skin effect, the concentration of eddy currents in the test object nearest the test coil, becomes more evident as test frequency, test object conductivity and permeability are increased. For current density or eddy current distribution in the test object, refer to Figure 1.8 in Chapter 1. δ = (πfμσ) -½

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Skin Effect

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Edge Effect The electromagnetic field produced by an excited test coil extends in all directions from the coil. The coil's field precedes the coil by some distance determined by coil parameters, operating frequency and test object characteristics. As the coil approaches the edge of a test object, eddy current flow in the test sample becomes distorted by the edge. This is known as edge effect. Edge effect can create a change in the coil's impedance that is similar to a discontinuity (Figure4.2). The response would move back along the conductivity curve toward the air point. The coil is responding to a slightly less conductive situation (air) at the leading edge of the coil's field of view. It is therefore essential that edge effect be eliminated as a variable during a surface scanning test. Response to the edges of test objects can be reduced by: incorporating magnetic shields around the test coil, increasing the test frequency, reducing the test coil diameter or by changing the scanning pattern used. Edge effect is a term most applicable to the inspection of sheets or plates with a probe coil.

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Discussion Subject: Response to the edges of test objects can be reduced by: incorporating magnetic shields around the test coil, increasing the test frequency, reducing the test coil diameter or by changing the scanning pattern used.

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Figure 4.2: Edge effect

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Lift Off Electromagnetic coupling between test coil and test object is of prime importance when conducting an eddy current examination. The coupling between test coil and test object varies with spacing between the test coil and test object. This spacing is called lift off (4). The effect on the coil impedance is called lift off effect. Figure 4.3 shows the relationship between air, conductive materials and lift off. The electromagnetic field, as previously discussed, is strongest near the coil and dissipates with distance from the coil. This fact causes a pronounced lift off effect for small variations in coil to object spacing. As an example, a spacing change from contact to 0.0254 mm (0.001 in.) will produce a lift off effect many times greater than a spacing change of 0.254mm (0.010 in.) to 0.2794 mm (0.011 in.) (15), Lift off effect is generally an undesired effect causing incre,ased noise and reduced coupling resulting in po6r measming ability (12). In some instances, equipment having phase discrimination capability can readily separate lift off from conductivity or other variables. Lift off can be used to advantage when measuring nonconductive coatings on conductive bases. A nonconductive coating such as paint or plastic causes a space between the coil and conducting base, allowing lift off to represent the coating thickness. Lift off is also useful in profilometry and proximity applications. Lift off is a term most applicable to testing objects with a surface or probe coil.

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Fill Factor Fill factor is a term used to describe how well a test object will be ectromagnetically coupled to a test coil that surrounds or is inserted into the test object. Fill factor then pertains to inspections using bobbin or encircling coils. Like lift off, electromagnetic coupling between test coil and test object is most efficient when the coil is nearest the surface of the part. The area of a circle (A) is determined using the equation: A Area = πd2/4 Fill factor can be described as the ratio of test object diameter to coil diameter squared (Figure 4.4). The diameters squared is a simplified equation resulting in the.division of effective coil and part areas. Because the term π /4 both the numerator and the denominator of this fractional equation the term π/4 cancelled out, leaving the ratio of the diameters squared; η (eta) = d2/D2 , fill factor

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Fill factor will always be a number less than 1 and efficient fill factors approaching 1, fill factor of 0.99 is more desirable than a fill factorof 0.75. The effect of fill factor on the test system is that poor fill factors do not allow the coil to be sufficiently coupled to the test object. This is analogous to the effect of drawing a bow only slightly and releasing an arrow. The result is, with the bow slightly drawn and released, little effect is produced to propel the arrow. In electrical terms it is said that the coil is loaded by the test object. How much the coil is loaded by the test object due to fill factor can be calculated in relative terms. A test system with constant current capabilities being affected by a conductive nonmagnetic bar placed into an encircling coil can be used to demonstrate this effect.

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For this example, the system parameters are as follows: (a) Unloaded coil voltage equals 10 V. (b) Test object effective permeability equals 0.3 (c) Test coil inside diameter equals 25.4 mm (1 in.) (d) Test object outside diameter equals 22.9 mm (0.9 in.) η (eta) = d2/D2 , fill factor = (0.9/1)2 = 0.81 An equation demonstrating coil loading is given by: E = Eo (1- η + η∙μeff ) Where: Eo = Coil voltage with coil affected by air E = Coil voltage with coil affected by the test material η = Fill factor μeff = Effective Permeability

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Figure 4.4: Fill factor ratios

Whena nonfermmagnetic test object is inserted into the test coil, the coil's voltage will decrease. E = Eo (1- η + η∙μeff ) E = 10 (1-0.81 + 0.81 x 0.3) E = 4.33 Volts This allows 10- 4.3 or 5.7 V available to respond to test object changes caused by discontinuities or decreases in effective conductivity of the test object. It is suggested that the reader calculate the resultant loaded voltage developed by a 12.7 mm (0.5 in.) bar of the same material and observe the relative sensitivity difference. Charlie Chong/ Fion Zhang

Figure 4.4: Fill factor ratios

Whena nonfermmagnetic test object is inserted into the test coil, the coil's voltage will decrease. ∆E = Eo (1- η + η∙μeff ) ∆E = 10 (1-0.81 + 0.81 x 0.3) ∆E = 4.33 Volts This allows 10- 4.3 or 5.7 V available to respond to test object changes caused by discontinuities or decreases in effective conductivity of the test object. It is suggested that the reader calculate the resultant loaded voltage developed by a 12.7 mm (0.5 in.) bar of the same material and observe the relative sensitivity difference. Charlie Chong/ Fion Zhang

Example: Calculate the resultant loaded voltage developed by a 12.7 mm (0.5 in.) bar of the same material and observe the relative sensitivity difference. η (eta) = d2/D2 , fill factor = (0.5/1)2 = 0.25 An equation demonstrating coil loading is given by: ∆E = Eo (1- η + η∙μeff) ∆E = 10 (1-0.251 + 0.25 x 0.3) ∆E = 8.25 Volts This allows 10- 8.25 or 1.75 V available to respond to test object changes caused by discontinuities or decreases in effective conductivity of the test object.

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Discontinuities Any discontinuity that appreciably changes the normal eddy current flow can be detected. Discontinuities, such as cracks, pits, gouges, vibrational damage and corrosion, generally cause the effective conductivity of the test object to be reduced. Discontinuities open to the surface are more easily detected than subsurface discontinuities. Discontinuities open to the surface can be detected with a wide range of frequenciesi subsurface investigations require a more careful frequency selection. Discontinuity detection at depths greater than 12.7 mm (0.5 in.) in stainless steel is very difficult. This is in part due to the sparse distribution of magnetic flux lines at the low frequency required for such deep penetrations.

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Figure 1.8 is again useful to illustrate discontinuity response because of current distribution. As an example, consider testing a nonferromagnetic tube at a frequency that establishes a standard depth of penetration at the midpoint of the tube wall. This condition would allow a relative current density of about 20% on the far surface of the tube. With this condition, identical near and far surface discontinuities would have greatly different responses. Due to current magnitude alone, the near surface discontinuity response would be nearly five times that of the far surface discontinuity. Discontinuity orientation has a dramatic effect on response. As seen earlier, discontinuity response is maximum when eddy currents and discontinuities are at 90 degrees or perpendicular. Discontinuities parallel to the eddy current flow produce little or no response. The easiest technique to ensure detectability of discontinuities is to use a reference standard or model that provides a consistent means of adjusting instrumentation.

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Figure 1.8: Relative eddy current density

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Signal-to-Noise Ratio Signal-to-noise ratio is the ratio of signals of interest to unwanted signals. Common noise sources are test object variations of surface roughness, geometry and homogeneity. Other electrical noises can be due to such external sources as welding machines, electric motors and generators. Mechanical vibrations can increase test system noise by physical movement of test coil or test object. In other words, anything that interferes with a test system's ability to define a measurement is considered noise. Signal-to-noise ratios can be improved by several techniques. If a part is dirty or scaly, signalto-noise ratio can be improved by cleaning the part. Electrical interference can be shielded or isolated. Phase discrimination and filtering can improve signal- to-noise ratio. It is common practice in non destructive testing to require a minimum signal-to-noise ratio of 3 to 1. This means a signal of interest must have a response at least three times that of the noise at that point.

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Chapter 4 Review Questions

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The Answers

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Q.4.1 Materials that hold their electrons loosely are classified as: A. resistors. B. conductors. C. semiconductors. D. insulators. Q.4.2 100% IACS is based on a specified copper bar having a resistance of: A. 0.01 ohms. B. 100 ohms. C. 0.017241 ohms. D. 172.41 ohms. Q.4.3 A resistivity of 13 Îźohm cm is equivalent to a conductivity in percent IACS of: A. 11.032. B. 0.0625. c. 1652. D. 13.26.

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Q.4.4 A (?) prime factor affecting conductivity is: A. temperature. B. hardness, C. heat treatment. D. all of the above. Q.4.5 Materials that tend to concentrate magnetic flux lines are: A. conductive. B. permeable. c. resistive. D. inductive. Q.4.6 Diamagnetic materials have: A. a permeability greater than air. B. a permeability less than air. C. a permeability greater than ferromagnetic materials. D. no permeability.

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Q.4.7 Edge effect can be reduced by: A. shielding. B. selecting a lower frequency. C. using a smaller coil. D. both A and C. Q.4.8 Calculate the effect of fill factor when a conducting bar 12.7 mm (0.5 in.) in diameter with an effective permeability of 0.4 is placed into a 25.4 mm (1 in.) diameter coil with an unloaded voltage of 10V. The loaded voltage is: A. 2V. η = (0.5)2 = 0.25 B. 4.6V: ∆E = Eo ( 1-η+ ηxμeff) C. 8.5V: ∆E = Eo ( 1-0.25 + .25x.4) = 8.5 Volts D. 3.2V. Q.4.9 Laminations are easily detected with the eddy current method. A. True B. False

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Q.4.10 Temperature changes, vibration and environmental effects are test coil inputs that generate: A. unwanted signals. B. magnetic fields. c. eddy currents. D. drift.

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Chapter 5 Selection of Test Frequency

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Test Frequencies It is the responsibility of nondestructive testing engineersand technicians to provide and perform non destructive testing that in some way ensures the quality, usefulness of industly products. To apply a nondestructive test, it is essential that the parameters affecting the test be understood. Usually industry establishes a product or component and then seeks a method to inspect it. This practice establishes test object geometry, conductivity and permeability before the application of the eddy current examination. Instrument, test coil and test frequency selection become the tools used to solve the problem of inspection. Test coils were discussed previously and instrumentation will be discussed later in this text. Test frequencies and their selection will be examined in detail in this Chapter.

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Frequency Selection In Chapter 1, it was observed that eddy currents are exponentially reduced as they penetrate the test object. In addition, a time or phase difference in these currents was observed (current lagging with penetration w.r.t surface current). The currents near the test coil happen first or lead the current that is deeper in the object. A high current density allows good detectability and a wide phase difference between near and far surfaces allows good resolution. Keypoint: Current deeper into the test object lag the surface current by Î˛ = x/Î´ radian.

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Single Frequency Systems Unfortunately, if a low frequency is selected to provide good penetration and detectability, the phase difference between near and far surface is reduced. Selection of frequency often becomes a compromise. It is common practice in inservice inspection of thin-wall, nonferromagnetic tubing to establish a standard depth of penetration just past the midpoint of the tube wall. This permits about 25% of the available eddy current to flow at the outside surface of the htbe wall. In addition, this establishes a phase difference of about 150 degrees to 170 degrees between the inside and outside surface of the tube wall. The combination of 25% outside, or surface current and 170 degrees included phase angle provides good detectability and resolution for thin-wall tube inspection. (This is accomplished by properly selecting the driving frequency of the coil to limit the penetration)

Calculation: δ = (πfσμ) -½ β = x/ δ radian = x / δ∙ 57.3º Where: x = depth below surface

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Standard penetration depth δ The depth that eddy currents penetrate into a material is affected by the frequency of the alternating current, the electrical conductivity and magnetic permeability of the sample. The depth of penetration decreases with increasing frequency and increasing conductivity and magnetic permeability. The depth at which eddy current density has decreased to 1/e, or about 37% of the surface density, is called the standard depth of penetration (δ or 1 δ) and used as criteria of ideal measurement. At three standard depth of penetration (3δ), the Eddy Current density is down to only 5% of the surface density. So, defects or variation deeper than the three standard depth of penetration cannot be recognized because the EC density in this depth is too low to detect. Thus, achieving the standard penetration depth is the most important factor at Eddy Current testing and this is realized by selecting appropriate frequency suitable for a material property.

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Eddy Current Density Since the sensitivity of Eddy Current inspection depends on the Eddy Current density at the defect location, it is important to know the strength of the Eddy Currents at this location. When detect flaws, a frequency is often selected which places the expected flaw depth within one standard depth of penetration. This assures that the strength of the Eddy Currents would be sufficient to produce a flaw indication.

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Eddy Current Density of a Solid bar D=2δ

D=2δ

δ 1/e = 37% of surface current density 2δ (1/e)2 = 13.5% of surface current density

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Applicable Scenario Eddy Current Density of a Solid bar Dâ&#x2030;¤2c

The field in air on the far surface ?

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Eddy Current Density of a Solid bar D>3δ 100% surface current density δ

D>3δ 2δ

32δ

1/e = 37% of surface current density (1/e)2 = 13.5% of surface current density (1/e)3 = 5% of surface current density at 3δ

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Standard Depth δ Formula The depth of penetration formula discussed in Chapter 1, although correct, has rather cumbersome units. Conductivity is usually expressed in percent of the International Annealed Copper Standard (% IACS). Resistivity is usually expressed in terms of micro-ohm-centimeter (μΩcm) (16). Depths of penetration are normally much less than 12.7 mm (0.5 in.). A formula using these units may be more appropriate and easier to use. In Chapter 1 a formula for calculating depth of penetration in the metric units was presented. Another derivative of this formula using resistivity, frequency and permeability with δ expressed in mm or inches can be expressed as follows: (standards form δ = (πf∙σμrμo)-½ , σ = 1/ρ)

δ = K√ [ρ/(fμr)] ， δ = K [ρ/(fμr)] ½ Where: δ = Standard penetration in mm or inches K = 50 for δ in mm and 1.98 for δ in inches ρ = Resistivity in micro-ohm-centimeter (μΩcm) f = Frequency μr = Relative permeability (for non-magnetic conductor μr=1)

δ = K√ [ρ/(f)] for non-magnetic conductor where μr=1

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Frequency Selection – Non Ferromagnetic Conductor The prime variable is frequency. By adjusting frequency technicians can be selectively responsive to test object variables. Solving the nonferromagnetic depth of penetration formula for frequency requires a simple algebraic manipulation as follows: δ = K√ [ρ / (f)] for non-magnetic conductor where μr=1 ρ /f = (δ/K)2, f = ρ∙(K/δ)2

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Example 1: As an example of how this may be used, consider inspecting a 7.6 mm (0.3 in.) thick aluminum plate, fastened to a steel plate at the far surface. Effects of the steel part are undesirable and require discrimination or elimination. The aluminum plate has a resistivity of 5 μΩ∙cm. By establishing a depth of penetration at 2.54 mm (0.1 in., the far surface current will be less than 10% (5%) of the available current, thus reducing response to the steel part. The frequency required for this can be calculated by applying: δ = 0.1” f = ρ∙(K/ δ)2 , f = 5(1.98/0.1)2 = 1960Hz (use inches)

0.3 in. Thick Al.

Steel plate

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Example 2: If detection of the presence of the steel part was required, the depth of penetration could be reestablished at 7.6 mm (0.3 in.) in the aluminum plate and a new frequency could be calculated. δ = 0.3 in. f = ρ∙(K/ δ)2 , f = 5(1.98/0.3)2 = 218Hz (use inches)

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Frequency Selection – Ferromagnetic Conductor

For ferromagnetic conductor δ = K√ [ρ/(fμr)], the parameter μr ≠ 1, need to be addressed in the above example:

f = ρ /μr ∙(K/ δ)2 instead of f = ρ ∙ (K/ δ)2

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Bessel function for fg (?)

Another approach to frequency selection uses argument A of the Bessel function where argument A is equal to unity or 1.

A = f μrσd2 / 5066 Where: f = frequency Hz μr = Relative permeability σ = Conductivity in meter / Ω.mm2 d = Diameter of the coil in cm

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A frequency can always selected to established factor A = 1, the frequency is known as limiting frequency and is denoted by fg. By substituting 1 for A and fg for f, the equation becomes;

1 = fg∙ μr∙ σ∙ d2 / 5066 fg = 5066/ (μr∙ σ∙ d2) Limiting frequency fg is then established in term of conductivity, permeability, some dimensional properties and a constant 5066. Because limiting frequency fg is based on these parameters, a techniques of frequency determination using a test frequency to limit frequency ration f/fg can be accomplished. High f/fg ratios are used for near surface tests and lower f/fg ration is used for subsurface tests.

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Often results of such tests are represented graphically by diagrams,These diagrams are called impedance diagrams. Impedance illustrated by vector diagrams in Chapter 3 shows inductive reactance represented onthe Y axis, ordinate and resistance on the X axis, abscissa. The vector sum of the reactive and resistive components is impedance. This impedance is a quantity with magnitude and direction that is directly proportional to frequency. To construct a universal impedance diagram valid for all frequencies, the impedance must be normalized (4). Figure 5.1 illustrated a normalization process.

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Figure 5.1(a) shows the effect on primary impedance Zp with changes in frequency (ω= 2πf). Figure 5.1(a) represents primary impedance without a secondary circuit or test object. Figure 5.1(b) illustrates the effect of frequency on primary impedance with a secondary circuit or test object present. The primary resistance R, in Figure5.1(a) has been subtracted in Figure 5.1(b) because resistance is not affected by frequency. The term ωLsG in Figure 5.1(b) represents a reference quantity for the secondary impedance. The units are secondary conductance (G) and ωLs (secondary reactance).

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Figure 5.1: Effects of frequency change (a) Primary impedance without secondary circuit (b) Primary impedance with secondary circuit. XL =ωL = 2πf∙L

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Figure 5.1: Effects of frequency change (a) Primary impedance without secondary circuit (b) Primary impedance with secondary circuit.

B, C, D, E, F, loci for selected values of Zp G = secondary conductance Zp =primary impedance ω = angular frequency = 2πf ωLs = secondary reactance

G The primary resistance R, in Figure5.1(a) has been subtracted in Figure 5.1(b) because resistance is not affected by frequency.

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Further normalization is accomplished by dividing the reactive and resistive components by the term ωLo or the primary inductive reactance without a secondary circuit present. Figure 5.2 shows a typical normalized impedance diagram. The terms ωL/ωL0 and R/ωL0 represent the relative impedance of the test coil as affected by the test object. Signals generated by changes in ωL or R caused by test object conditions such as surface and subsurface discontinuities may be noted by ∆ωL or ∆R. The ∆ωL and ∆R notation indicates a change in the impedance.

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Figure 5.2: Normalized impedance diagram for long coil encircling solid cylindrical nonferromagnetic bar and for thin-wall tube. Coil fill factor = 1.0 k = √(ωμσ) = Electromagnetic wave propagation constant for conducting material r = radius of the conductor in m μ = magnetic permeability of bar = 4π∙10-7 H.m-1 if bar is non-magnetic (μ = μo) ω = angular velocity = 2πf √(ωLoG) = equivalent of √(ωμσ) for simplified electrical circuit, where G=conductance (Siemens) and Lo = inductance in air (Henry)

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Figure 5.3 shows the impedance variation in a nonferromagnetic cylinder caused by surface and subsurface discontinuities. Figure 5.3 also illustrates a sensitivity ratio for surface and subsurface discontinuities. Notice with an flfg ratio of 50, a relatively high frequency, the respouse to subsurface discontinuities is not very prononounced. Figure 5.4 shows responses to the same discontinuities with an f/fg ratio of 15. This lower frequency allows better detection of subsurface discontinuities as shown in Figure 5.4.

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Figure 5.3: Impedance variations caused by surface and subsurface cracks Impedance variations caused by surface and subsurface cracks in nonferromagnetic cylinders, at a frequency ratio f/fg = 50.

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Figure 5.3: Impedance variations caused by surface and subsurface cracks

Figure 5.4: Impedance variations caused by surface and subsurface cracks

Impedance variations caused by surface and subsurface cracks in nonferromagnetic cylinders, at a frequency ratio f/fg = 15.

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Figure 5.4: Impedance variations caused by surface and subsurface cracks

Multiparameter Techniques It becomes obvious that the technician must have a good working knowledge of current density and phase relationships to make intelligent frequency choices. The frequency choice discussed to date deals with coil systems driven by only one frequency. Test systems driven by more than one frequency are called multifrequency or multi parameters systems. It is common for a test coil to be driven with three or more frequencies. Although several frequencies may be applied simultaneously or sequentially to a test coil, each of the individual frequency techniques follows rule established by a single frequency techniques. Signals generated at the various frequencies are often combined or mixed in electronic circuits that algebraically add or subtract signals to obtain the desired result.

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Multiparameter Techniques â&#x20AC;&#x201C; Broadband Signals One multifrequency approach is to apply a broadband signal, with many frequency components to the test coil. The information transmitted by the signal is proportional to its bandwidth and the logarithm of 1 plus the signalto-noise power ration. The relation is stated by the equation: C = Bâ&#x2C6;&#x2122;Log2(1+ S/N) C = rate of information transmitted in bits per second B = bandwidth of the signal S/N = signal-to-noise ratio This is known as the Shannon-Hartley theorem.

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Multiparameter Techniques - Multiplexing Another approach to multiparameter techniques is to use multiplexing process. The multiplexing process places one frequency at a time on the test coil. This results in zero crosstalk between each frequency and eliminates the need for channel specific band pass filters. The major advantages of a multiplex system, in addition to the crosstalk reduction issues, are lower cost and greater flexibility in frequency selection. If the multiplexing switch rate is sufficiently high, both broadband and multiplex systems have essentially the same results. The characterization of eddy current signals by their phase angle and amplitude is a common practice and provides a basis for signal mixing to suppress unwanted signals from test data. Two frequencies are required to remove each unwanted variable.

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Example â&#x20AC;&#x201C; Multiparameter Technique Practical multi parameter frequency selection can be demonstrated by the following example: Problem: Eddy current inspection of installed thin wall nonferromagnetic heat exchanger tubing. Tubing is structurally supported by ferromagnetic tube supports at several locations. It is desired to remove the tube support response signal from tube wall data. Solution: Apply a multiparameter technique to suppress the tube support signal response.

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First, a frequency is selected to give optimum phase and amplitude information about the tube wall. This is called the prime frequency. At the prime frequency, the response to the tube support and to a calibration through wall hole are about equal in amplitude. They may also have about the same phase angle. A second frequency called the subtractor frequency is selected on the basis of the phase angle of the tube support response. Because the tube support surrounds the outside diameter of the tube, a lower frequency is selected. At the subtractor frequency the tube support signal response is about 10 times greater than the calibration through wall hole. The phase difference between the support signal and the through wall hole in this lower frequency will be about 90 degrees. Parameter separation limitations are greatest for those parameters producing nearly similar signals, such as dents .

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If the prime and subtractor channels have been selected properly then signal subtraction algorithms should be able to suppress the tube support signal leaving only slightly attenuated prime data (discontinuity) information. For suppression of inside or near surface signals, a higher subtractor frequency would be chosen. A combination of prime, low and high subtractor frequencies is often used to suppress both near and far surface signals, leaving only data pertaining to the part thickness and its condition. Bandwidth of the coil is of prime importance when operation over a wide frequency range is required in multifrequency/multi parameter testing. Optimization of a test frequency (or frequencies) will therefore depend on the desired measurement or parameter(s) of interest.

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More Reading on Characteristic Parameter Pc / Frequency fg

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