Capítulo 4 - MÉTODO
DE INSPEÇÃO POR CORRENTES PARASITAS
traduzido do livro: AIR
FORCE TO 33B-1-1 / ARMY TM 1-1500-335-23 / NAVY (NAVAIR) 01-1A-16-1 -
Manual Técnico - Métodos de Inspeção Não Destrutiva, Teoria Básica
- TABELAS E FÓRMULAS DO ENSAIO DE CORRENTES PARASITAS
- Resistência
- Resistência
- Resistência
- Resistividade
- Condutividade (inverso da resistividade)
- Indutância
- Auto Indutância
- Auto Indutância
- Fill Factor
- Reatância Indutiva e Reatância Capacitiva
- Impedância
- Permeabilidade
- Profundidade de Penetração (δ)
- Frequência Limite
(fg) e Lei da "Similaridade"
- Frequência Característica
- Cobertura da Sonda e Diâmetro Efetivo da
Bobina
- Cálculo da Frequência Própria da
Descontinuidade para Ajuste do Filtro
- Medição da Condutividade
8 EDDY CURRENT EQUATIONS.
Table 8-1. Common Applications of Eddy Current Inspection
Table 8-2. Conductivities of Some Commonly Used Engineering Materials
Table 8-3. Conductivity and Effective Depth of Penetration in Various
Metals
Table 8-4. Conductivity and Effective Depth of Penetration in Nonclad
Aluminum Alloys
Table 4-5. Standard Depths of Penetration for Metal Alloys at Various
Frequencies
Table 8-6. Standard Depths of Penetration for Clad Aluminum Alloys at
Various Frequencies
Table 8-7. Conductivity and Effective Depth of Penetration for Clad
Aluminum Alloys
Table 8-8. Effects of Material and Inspection Variables on the
Sensitivity and Range of Thickness Measurements
NOTE
The following formulas are used by NDI engineers and inspection
developers. Technicians should have a working knowledge of the most
basic electrical component equations as presented in the classroom.
8.1 Resistance. When DC flows through an element of an electric
circuit, or AC flows through a circuit element having negligible
inductance (e.g., a straight section of wire or a carbon resistor), the
impedance is resistance only and is ex
pressed as:
R = E / I
Where:
R = Resistance (ohms)
E = Voltage drop across the resistor (volts)
I = Current flowing through circuit (amperes)
8.1.1 In an AC circuit containing resistance only (i.e., having
negligible inductance), the voltage and the current are in phase. The
term in phase , when used to describe the relationship between the
voltage and current, indicates that changes in current occur at the
same time and in the same manner (direction) as changes in voltage.
Examples of two quantities that are in phase are shown in Figure 4-58.
Figure 8.1. Sinusoidal In-Phase Variation of Alternating Current and
Induced Magnetic Field
8.1.2 Resistance.
Where
l = Length of conductor
ρ= Resistivity
A = Area (cross sectional) of conductor
8.1.3 Resistivity.
8.1.4 Conductivity (inverse of resistivity).
mho / mm ou siemen / mm
1 mho = 1 / ohm
8.2 Inductance. The inductance of an eddy current probe is the result
of magnetic field effects of the alternating electric current in the
probe. Inductance is a measure of the capability of a circuit to induce
current flow in another circuit. It is pro
portional to the ratio of the magnetic flux linking (encircling) a
circuit to the current (I) that produced the flux. When the flux from
one inductor is linked to (passes through) another inductor, the
inductance is called mutual inductance (M). An elec
trical transformer is an example of a device where M is a significant
parameter. For eddy current testing, we consider only the inductance of
a single circuit element, specifically, the coil used to sense changes
in eddy current flows in test speci
mens. This inductance is called self-inductance (L).
Where:
L = in micro-henries
r = mean coil radius
l = coil height
b = coil wrap thickness
N= number of turns
8.2.1 Self Inductance. Self-inductance (L) is expressed in henries. A henry is the inductance by which one volt is
produced across a coil when the inducing current is changed at the rate of one ampere per second. A formula for self- in
ductance expressed in these terms is as follows:
Where:
L = Inductance (henries)
E = Induced Electromotive Force (volts)
I = Change in Current (amperes)
T = Time (seconds)
Because the henry is such a large unit, inductance is more commonly expressed in terms of millihenries (1/1000 henry)
or micro-henries (1/1,000,000 henry). Typical coils used in ET have self-inductances in the range of 10 to several hun
dred micro-henry."
8.3 Fill Factor. Is the ratio of the effective cross-sectional area of the primary internal probe coil to the cross-sectional
area of the tube interior.
Where:
= Fill factor
NAVY (NAVAIR) 01-1A-16-1
= Outside diameter of test part
= Inside diameter of coil
8.3.1 Fill Factor example: if an encircling coil with an internal
diameter of 2.25-inches were used to inspect 2.00-inch di
ameter rod, the fill factor would be:
8.3.2 For internal coils, electromagnetic (inductive) coupling is
determined by the air gap between the external diameter of the coil and
the internal diameter being inspected. Fill-factor is calculated using
the basic formula, but in this case D i is the inside diameter of the
part and D o is the outside diameter of the coil placed in the part.
For example, if a coil with an exter
nal diameter of 1.5-inches is used to inspect tubing with an internal
diameter of 1.6-inches, the fill factor is given by:
8.4 Inductive Reactance and Capacitive Reactance.
Onde:
XL = 2pifL , reatância indutiva em ohms
f = frequência em herts
L = Indutância em henrys
XC = 1 / 2pifC, reatância capacitiva em ohms
C = capacitância em faradas
8.5 Impedance. Impedance is the opposition to current flow and is a two-dimensional parameter consisting of resistance
and reactance. Resistance is the opposition to the flow of both direct and alternating current. Reactance is the opposition to
f
low of alternating current only. Reactance can be either capacitive or inductive. Both resistance and reactance are mea
sured in ohms. Of primary interest in ET are resistance and inductive reactance, the latter due to inductance of a coil. Capaci
tive reactance becomes significant in only a few cases and will be discussed later. The impedance of a test coil is related to
the current flow in and voltage drop across the coil as follows:
Where:
Z = Impedance of coil (ohms)
E = Voltage drop across the coil (volts)
I = Current through coil (amperes)
8.5.1 Impedance formula:
8.6 Permeability.
Where:
µ = permeability
H= magnetizing force oersteds or amp - turns
B = flux density in gauss or tesla (10000 G = 1 T)
8.6.1 Relative Permeability:
Where:
µo of free space = 4 x 10-7
Ferromagnetic µrel >> 1
Paramagnetic µrel 1 Nonferrous
Diamagnetic µrel < 1 Au, I
8.7 Depth of Penetration ( ).
resisitividade em microohms.cm
profundidade de penetração em mm
profundidade de penetração em polegadas
profundidade de penetração em polegadas usando resistividade em microohms.cm
8.7.1 Frequency necessary for one standard depth:
Where:
f = frequency in hertz, Hz
µ = relative permeability
IACS = conductivity as a percentage of the conductivity of copper
= the standard depth of penetration in inches
8.7.2 Phase Lag at one Standard Depth:
Phase lag on impedance diagram is
2 times , signal down and
back at 1 phase lag is 114°
8.8 Limit Frequency, f
g. and the Similarity Law.
= condutividade = m / (ohm.mm2)
Where:
d = diameter of test object in cm
f = frequency I Hz
µrel = .= relative permeability
8.9 Characteristic Frequency. f
g is lowest frequency where eddy currents are induced in a material. Where frequency
and conductivity for one material is known, the frequency for “similar” phase separation can be calculated for another ma
terial of known conductivity.
8.10 Coverage of Coil or Effective Coil Diameter.
Unshielded = coil diameter + 4
Shielded = coil diameter
= Standard depth of penetration
8.11 Calculating Flaw Frequency for Setting Filters. Assume flaw is infinitely narrow compared to coil:
For scanning across a surface, surface speed is how fast the probe is moved across that surface
For a rotating bolt-hole inspection, surface speed depends on the rotational speed of the scanner and the diameter of
the probe. Surface speed may be calculated as follows:
Frequência da Descontinuidade (Hz) = Velocidade de Varredura (mm/s) / Diâmetro Efetivo da Sonda (mm)
8.12 Measurement of Conductivity. Formula: = L/RA = 1/ ; therefore, R = L/A
Where:
= electrical conductivity (mhos/unit-length)
L = length
R = resistance (ohms)
A = cross-sectional area
= resistivity (ohms-unit-length)
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