WO2000022375A1 - Method and device for measuring cross-section of wires - Google Patents

Method and device for measuring cross-section of wires Download PDF

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Publication number
WO2000022375A1
WO2000022375A1 PCT/SE1999/001835 SE9901835W WO0022375A1 WO 2000022375 A1 WO2000022375 A1 WO 2000022375A1 SE 9901835 W SE9901835 W SE 9901835W WO 0022375 A1 WO0022375 A1 WO 0022375A1
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WO
WIPO (PCT)
Prior art keywords
frequency
section
wire
cross
elongated element
Prior art date
Application number
PCT/SE1999/001835
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French (fr)
Inventor
Carl Tyren
Original Assignee
Carl Tyren
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Carl Tyren filed Critical Carl Tyren
Priority to EP99956453A priority Critical patent/EP1151239A1/en
Priority to AU13061/00A priority patent/AU1306100A/en
Publication of WO2000022375A1 publication Critical patent/WO2000022375A1/en

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G01B7/12—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring diameters

Definitions

  • wires e.g. copper wires for electrical windings in e.g. electrical motors or transformers
  • One particular such need is to measure the thickness of insulation coatings applied to the wire during the manufacturing. Control of the insulation thickness and uniformity is a very important quality factor where inconsistencies can cause short circuit failures in electrical machines or devices being manufactured using a faulty copper wire.
  • Prior art wire diameter or strip cross-section dimensions measuring devices such as purely mechanical or laser-based apparatuses, all measure the total outside diameter or dimensions. This is a drawback, because when being produced the wire or strip will have a surface covered by grease, oil or contamination that will pollute a metal cross-section measurement.
  • An object of the invention is to provide a device, which can measure the metal cross-section ignoring the insulation coating. Using then this information in the coating thickness can readily be obtained by simple subtraction calculus.
  • a well-known phenomena in relation to AC electrical signals at high frequencies in electrical conductors is the so-called skin-depth which describes the fact that the high-frequency conduction takes place in a skin layer of the conductor. The penetration depth of the skin is related to the AC signal frequency as well as the electrical resisitivity and magnetic permeability of the conductor itself.
  • ⁇ is the so called skin depth, it corresponds to the thickness from the surface to the center of the wire which the electromagnetic field can penetrate; ⁇ and ⁇ are the magnetic permeability and the electric conductivity of the wire material, respectively; and f is the frequency of the ac electric current. According to this formula, when the frequency increases the skin depth decreases thus reducing the actual cross section of the wire through which the current can flow. This effect produces an increase of the impedance of the wire that can be measured.
  • the effective resistance of the conductor is therefore related to the skin layer cross-section (in product with the resisitivity of the conductor material) which then will vary with the AC signal frequency.
  • a simply measurement of the voltage drop, or resistance at the ac frequency will show a value which is related to the AC frequency.
  • the effective resistance of a conductor is therefore greater than the d.c. or ohmic resistance when carrying alternating current.
  • This relation is basically an inverse square root relation until the frequency when the skin depth reaches and equals the conductor radius (or minimum cross-section dimension for a rectangular conductor). At this point the AC resistance of the conductor will stop to decrease as the AC frequency decreases further. This point is therefore a discontinuity point in the AC resistance to AC frequency relationship.
  • the frequency at which the skin depth equals the radius of the wire will be referred to as the Saturation Frequency (SFr).
  • SFr Saturation Frequency
  • the frequency range close to saturation, where the impedance begins to increase with the frequency, is important for determining the diameter of the wire through the value of its SFr.
  • the Saturation Frequency (SFr) is the lowest frequency of an AC current for which the impedance of the wire behaves linearly (in relation to the frequency).
  • the AC frequency value at the point of the discontinuity will allow the calculation of the conductor diameter according to the skin depth calculation formula.
  • Fig. 1 schematically shows a circular cross section wire conductor with a skin depth part at three different AC frequencies
  • Fig. 2 is a schematic diagram showing a frequency response over a time period from a wire according to Fig. 1
  • Fig. 3 schematically shows two rectangular cross section wire conductors with skin depth parts
  • Fig. 4 is a schematic diagram showing the frequency responses from the wires in Fig. 3,
  • Fig. 5 shows an embodiment of the wire conductor and Fig. 6 is a schematic view of an experimental arrangement.
  • One practical implement of the method is to apply a frequency modulated (eg sine or triangular modulation) sine wave AC signal along a section of the wire conductor while simultaneously measuring the voltage drop within this section of the conductor. As the AC signal frequency decreases the voltage drop along the conductor will reach a plateau or flat region representing the AC frequency interval during which the skin depth exceeds the conductor radius.
  • a frequency modulated (eg sine or triangular modulation) sine wave AC signal along a section of the wire conductor while simultaneously measuring the voltage drop within this section of the conductor.
  • Fig. 1 a cross section of an electrical conductor 10 is shown at three different frequencies F1 , F2 and F3 of an AC current fed through the conductor.
  • F1 there is a first skin depth d1 that is substantially smaller than the radius R of the conductor.
  • REFF effective conductor resistance
  • the frequency decreases to F2 the corresponding skin depth d2 increases and as a result the effective conductor resistance REFF decreases.
  • the decrease of the effective conductor resistance R E FF is continuous.
  • a decrease of the frequency to F3 will result in a skin depth d3 that is equal to the radius R of the conductor.
  • the effective conductor resistance REFF varies in dependence of the frequency of the applied AC current.
  • the applied AC current signal is frequency modulated.
  • Fmod a sine wave modulation signal
  • the modulation signal is indicated with dashed lines.
  • Different electronic or digital signal processing techniques can be utilised to precisely determine the AC frequency at the amplitude modulation (voltage drop) discontinuity related to the applied frequency modulated AC signal.
  • One such technique is an amplitude demodulation of the AC voltage drop signal followed by subtraction of the FM reference signal and derivations to detect the discontinuity point.
  • the conductor radius detection criteria is a discontinuity in the measuring signal - which easily can be distinguished from continuously varying features in the measuring signal resulting from e.g. frequency related changes in inductance, reflections, capacitive couplings etc.
  • the minimum dimension can be measured by the discontinuity point. Taking the rectangular cross-sections as an example the thickness would be measured through the discontinuity point, remains then however the width.
  • a secondary effect of the skin-depth can be used as shown in Fig. 3 and Fig. 4.
  • ⁇ d which relates to a certain ⁇ f
  • ⁇ REFF the corresponding change in effective resistance
  • Fig. 5 shows one embodiment according to which the wire has been folded.
  • the wire is also wound to reduce effects from inductance.
  • the determination of the SFrs has been carried out by measuring the voltage drop along the Cu wires when they are connected to a constant voltage generator that produces an ac signal with frequencies varying according to a controlled sweep amplitude.
  • FIG. 6 An experimental setup is schematically shown in Fig. 6.
  • a first function generator 13 is used to produce the voltage signal which controls the frequency sweep, and a second function generator 14 is used to feed the wire 10.
  • the available frequency range of both generators is from below 1 Hz up to 13 MHz.
  • the generator that feeds the wire is driven by the signal of the first generator through a VCO connection.
  • An oscilloscope 15 is used to represent the time dependence of the voltage drop across the wire 10 and the voltage signal which controls the frequency sweep.
  • the oscilloscope needs a peak detection function. The possibilities of saving the traces in the internal memory of the oscilloscope have been used although they are not essential for these measurements.
  • the diameters shown in the table were measured using a Digital Micrometer.
  • the coating of the wires was removed chemically before doing the measurements.
  • the dispersion errors arising from 5 measurements in each wire and the systematic error of the Micrometer have been considered.
  • the set of copper wires of different diameters have been measured using the skin-depth effect by the methods described formerly.
  • the SFr of each wire has been measured 10 times using both methods.
  • the following table sums up the values of the SFr and the error bars obtained by taking into account the dispersion of the ten measurements.
  • the diameter values have been obtained from the SFr through the skin depth calculation formula.
  • the absolute and relative errors appended to the diameter values have been calculated from the dispersion errors of the frequencies. As it is seen in the former table, the relative errors in diameters (coming from the errors in frequencies) do not reach the 10 % in any case.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Measurement Of Length, Angles, Or The Like Using Electric Or Magnetic Means (AREA)
  • Investigating Or Analyzing Materials By The Use Of Electric Means (AREA)

Abstract

Method for measurement of the cross-section of an elongated element in wire or strip material production processes. The AC-resistance of the wire is related to the AC-frequency of a signal fed through the wire. The radius is found by relating a discontinuity in the resistance-to-frequency relation as where the skin-depth is equal to the radius.

Description

METHOD AND DEVICE FOR MEASURING CROSS-SECTION OF WIRES
TECHNICAL FIELD
In manufacturing industry for wires, e.g. copper wires for electrical windings in e.g. electrical motors or transformers, there are needs for continuous monitoring of wire dimensions in the production process. One particular such need is to measure the thickness of insulation coatings applied to the wire during the manufacturing. Control of the insulation thickness and uniformity is a very important quality factor where inconsistencies can cause short circuit failures in electrical machines or devices being manufactured using a faulty copper wire.
PRIOR ART
Prior art wire diameter or strip cross-section dimensions measuring devices, such as purely mechanical or laser-based apparatuses, all measure the total outside diameter or dimensions. This is a drawback, because when being produced the wire or strip will have a surface covered by grease, oil or contamination that will pollute a metal cross-section measurement.
SUMMARY OF THE INVENTION
An object of the invention is to provide a device, which can measure the metal cross-section ignoring the insulation coating. Using then this information in the coating thickness can readily be obtained by simple subtraction calculus. A well-known phenomena in relation to AC electrical signals at high frequencies in electrical conductors is the so-called skin-depth which describes the fact that the high-frequency conduction takes place in a skin layer of the conductor. The penetration depth of the skin is related to the AC signal frequency as well as the electrical resisitivity and magnetic permeability of the conductor itself.
Basically, this effect describes the dependence of the wire cross section through which an ac electric current flows on the frequency of the mentioned current. The fundamental equation that arises after a detailed vector analysis of the problem is the following:
δ = 1
V (π f μ σ)
where δ is the so called skin depth, it corresponds to the thickness from the surface to the center of the wire which the electromagnetic field can penetrate; μ and σ are the magnetic permeability and the electric conductivity of the wire material, respectively; and f is the frequency of the ac electric current. According to this formula, when the frequency increases the skin depth decreases thus reducing the actual cross section of the wire through which the current can flow. This effect produces an increase of the impedance of the wire that can be measured.
The effective resistance of the conductor is therefore related to the skin layer cross-section (in product with the resisitivity of the conductor material) which then will vary with the AC signal frequency. As a result a simply measurement of the voltage drop, or resistance at the ac frequency, will show a value which is related to the AC frequency. The effective resistance of a conductor is therefore greater than the d.c. or ohmic resistance when carrying alternating current. This relation is basically an inverse square root relation until the frequency when the skin depth reaches and equals the conductor radius (or minimum cross-section dimension for a rectangular conductor). At this point the AC resistance of the conductor will stop to decrease as the AC frequency decreases further. This point is therefore a discontinuity point in the AC resistance to AC frequency relationship.
The frequency at which the skin depth equals the radius of the wire will be referred to as the Saturation Frequency (SFr). The frequency range close to saturation, where the impedance begins to increase with the frequency, is important for determining the diameter of the wire through the value of its SFr. Hence, it is possible to determine the diameter of any metallic wire with a method that measures accurately its SFr, which relates to the diameter in the following way (skin depth calculation formula):
diameter = 2 1
V(π μ σ) ^SFr)
The Saturation Frequency (SFr) is the lowest frequency of an AC current for which the impedance of the wire behaves linearly (in relation to the frequency).
If the resistivity and permeability of the conductor is known the AC frequency value at the point of the discontinuity will allow the calculation of the conductor diameter according to the skin depth calculation formula.
BRIEF DESCRIPTION OF THE DRAWINGS
A preferred embodiment of the invention will now be described with reference to the accompanying drawings, in which: Fig. 1 schematically shows a circular cross section wire conductor with a skin depth part at three different AC frequencies,
Fig. 2 is a schematic diagram showing a frequency response over a time period from a wire according to Fig. 1 , Fig. 3 schematically shows two rectangular cross section wire conductors with skin depth parts,
Fig. 4 is a schematic diagram showing the frequency responses from the wires in Fig. 3,
Fig. 5 shows an embodiment of the wire conductor and Fig. 6 is a schematic view of an experimental arrangement.
DETAILED DESCRIPTION
One practical implement of the method is to apply a frequency modulated (eg sine or triangular modulation) sine wave AC signal along a section of the wire conductor while simultaneously measuring the voltage drop within this section of the conductor. As the AC signal frequency decreases the voltage drop along the conductor will reach a plateau or flat region representing the AC frequency interval during which the skin depth exceeds the conductor radius.
In Fig. 1 a cross section of an electrical conductor 10 is shown at three different frequencies F1 , F2 and F3 of an AC current fed through the conductor. At the first frequency F1 there is a first skin depth d1 that is substantially smaller than the radius R of the conductor. At this frequency the effective conductor resistance REFF is high. When the frequency decreases to F2 the corresponding skin depth d2 increases and as a result the effective conductor resistance REFF decreases. The decrease of the effective conductor resistance REFF is continuous. A decrease of the frequency to F3 will result in a skin depth d3 that is equal to the radius R of the conductor. A further decrease of the frequency from F3 will not result in a further decrease of the effective conductor resistance REFF- At DC and at low frequencies the whole cross section of the conductor is used. At higher frequencies the central part 11 of the conductor becomes in-active and current flows in an annular part 12.
As shown in Fig. 2 the effective conductor resistance REFF varies in dependence of the frequency of the applied AC current. In Fig. 1 and Fig. 2 F1 > F2 > F3. By measuring the frequency response it is possible to detect the discontinuity point where d = R. The applied AC current signal is frequency modulated. In Fig. 2 a sine wave modulation signal Fmod is used, but also other signals can be used. The modulation signal is indicated with dashed lines.
Different electronic or digital signal processing techniques can be utilised to precisely determine the AC frequency at the amplitude modulation (voltage drop) discontinuity related to the applied frequency modulated AC signal. One such technique is an amplitude demodulation of the AC voltage drop signal followed by subtraction of the FM reference signal and derivations to detect the discontinuity point.
One particular advantage of the invention is that the conductor radius detection criteria is a discontinuity in the measuring signal - which easily can be distinguished from continuously varying features in the measuring signal resulting from e.g. frequency related changes in inductance, reflections, capacitive couplings etc.
Therefore this method could also well be implemented on-line in wire production machines using capacitive, instead of galvanic, coupling to even an insulated wire moving past at high speed. For very small wire diameters where the AC frequency range to be used will be very high a radio coupling to the wire can also be applied in which case the antenna impedance of the wire will show the discontinuity.
Considering now non-circular cross-sections, e.g. rectangular, the minimum dimension can be measured by the discontinuity point. Taking the rectangular cross-sections as an example the thickness would be measured through the discontinuity point, remains then however the width. To measure that a secondary effect of the skin-depth can be used as shown in Fig. 3 and Fig. 4. For a certain change in skin-depth, Δd, which relates to a certain Δf, the corresponding change in effective resistance, ΔREFF will depend on the width w1 and w2, respectively. More generally it will depend on the cross- sections profile. From Fig. 4 and from what is stated above it can be concluded that
ΔREFFI / Δf ~ w1 p and ΔREFF2 / Δf ~ w2ρ.
It is important that other factors than the internal impedance of the wire at a specific frequency are avoided. Therefore, it is appropriate to reduce inductive and capacitive effects of the wire. Fig. 5 shows one embodiment according to which the wire has been folded. Preferably the wire is also wound to reduce effects from inductance.
The determination of the SFrs has been carried out by measuring the voltage drop along the Cu wires when they are connected to a constant voltage generator that produces an ac signal with frequencies varying according to a controlled sweep amplitude.
An experimental setup is schematically shown in Fig. 6. A first function generator 13 is used to produce the voltage signal which controls the frequency sweep, and a second function generator 14 is used to feed the wire 10. The available frequency range of both generators is from below 1 Hz up to 13 MHz. The generator that feeds the wire is driven by the signal of the first generator through a VCO connection.
An oscilloscope 15 is used to represent the time dependence of the voltage drop across the wire 10 and the voltage signal which controls the frequency sweep. The oscilloscope needs a peak detection function. The possibilities of saving the traces in the internal memory of the oscilloscope have been used although they are not essential for these measurements.
In one experiment nine Cu wires of different diameters were prepared and measured using the skin-depth technique. The different wires and the experimental results are listed in the table below.
Figure imgf000009_0001
The diameters shown in the table were measured using a Digital Micrometer. The coating of the wires was removed chemically before doing the measurements. The dispersion errors arising from 5 measurements in each wire and the systematic error of the Micrometer have been considered.
The set of copper wires of different diameters have been measured using the skin-depth effect by the methods described formerly. The SFr of each wire has been measured 10 times using both methods. The following table sums up the values of the SFr and the error bars obtained by taking into account the dispersion of the ten measurements.
The diameter values have been obtained from the SFr through the skin depth calculation formula. The absolute and relative errors appended to the diameter values have been calculated from the dispersion errors of the frequencies. As it is seen in the former table, the relative errors in diameters (coming from the errors in frequencies) do not reach the 10 % in any case.
For materials where the permeability and/or the resisitivity can be controlled by internal influence special procedures need to be applied to know the values of these parameters during the process of skin-depth geometry measurements.

Claims

1. Method for measurement of the cross-section of an elongated element in wire or strip material production processes, the elongated element having an AC-resistance that is related to an
AC-frequency of a signal fed through the elongated element, c h a r a c t e r i s e d by relating a discontinuity in the AC- resistance-to-AC-frequency relation where the skin-depth is equal to the wire radius or the strip minimum cross-section dimension.
2. Method as claimed in claim 1 , c h a r a c t e r i s e d by relating the cross-section geometry to the rate of change of effective AC resistance with the rate of change of AC frequency.
3. Method as claimed in claim 1 , further including the steps of applying a frequency modulated AC-current signal to a circular section elongated element, varying the frequency of the applied AC-current signal between a first frequency F1 at which an effective resistance of the elongated element is higher than an ohmic resistance and below a second frequency F3 at which the effective resistance of the elongated element is equal to the ohmic resistance, determining the saturation frequency (SFr) where the skin depth equals the wire radius or the strip minimum cross-section dimension, and calculating the diameter d of the elongated element on the basis of the formula:
d = 2 1 (π μ σ) ^{SFή , where μ is the magnetic permeability and σ is and the electric conductivity of the wire material.
4. Method as claimed in claim 1 and 2 for measuring the cross- section of an elongated element having a core and an electrically insulating coating, further including the use of a second cross- section measuring device to measure the total cross-section of the wire and by calculating the thickness of the electrically insulating coating or coatings applied onto the core as the difference between the total cross-section and core cross- section.
5. Method for measurement of the cross-section of an elongated element in wire or strip material production processes as in claim 1 and 2 c h a r a c t e r i z e d b y non-galvanic coupling of an
AC measuring signal to the measurement object.
PCT/SE1999/001835 1998-10-11 1999-10-11 Method and device for measuring cross-section of wires WO2000022375A1 (en)

Priority Applications (2)

Application Number Priority Date Filing Date Title
EP99956453A EP1151239A1 (en) 1998-10-11 1999-10-11 Method and device for measuring cross-section of wires
AU13061/00A AU1306100A (en) 1998-10-11 1999-10-11 Method and device for measuring cross-section of wires

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
SE9803506A SE9803506D0 (en) 1998-10-11 1998-10-11 Method for measuring cross-section geometry based on AC signal skin-depth penetration
SE9803506-6 1998-10-11

Publications (1)

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WO2000022375A1 true WO2000022375A1 (en) 2000-04-20

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AU (1) AU1306100A (en)
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4593244A (en) * 1982-08-06 1986-06-03 Australian Wire Industries Pty. Ltd. Determination of the thickness of a coating on a highly elongated article
US4947132A (en) * 1986-11-25 1990-08-07 Battelle Memorial Institute Method for detecting thickness variations in the wall of a tubular body which conducts electricity
WO1990015965A1 (en) * 1989-06-22 1990-12-27 Benoit De Halleux Process and device for measuring the cross-section or the diameter of long cylindrical products made of conductive material
EP0629837A1 (en) * 1993-06-15 1994-12-21 Tokyo Gas Co., Ltd. Method of measuring inner diameter of pipe
CA2232348A1 (en) * 1997-03-24 1998-09-24 Centro Automation Spa Method to measure the variations in section of a rolled bar

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4593244A (en) * 1982-08-06 1986-06-03 Australian Wire Industries Pty. Ltd. Determination of the thickness of a coating on a highly elongated article
US4947132A (en) * 1986-11-25 1990-08-07 Battelle Memorial Institute Method for detecting thickness variations in the wall of a tubular body which conducts electricity
WO1990015965A1 (en) * 1989-06-22 1990-12-27 Benoit De Halleux Process and device for measuring the cross-section or the diameter of long cylindrical products made of conductive material
EP0629837A1 (en) * 1993-06-15 1994-12-21 Tokyo Gas Co., Ltd. Method of measuring inner diameter of pipe
CA2232348A1 (en) * 1997-03-24 1998-09-24 Centro Automation Spa Method to measure the variations in section of a rolled bar

Also Published As

Publication number Publication date
EP1151239A1 (en) 2001-11-07
AU1306100A (en) 2000-05-01
SE9803506D0 (en) 1998-10-11

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