Method and sensor arrangement for measuring thickness of at least one coating

Abstract

The invention relates to a method and a sensor assembly for non-destructively measuring the thickness of a coating formed on a substrate of a workpiece, in which a first coating made of an electrically conductive and diamagnetic or paramagnetic material is optionally disposed over a second coating made of a ferromagnetic material, the method comprises the steps of: (a) placing an inductive sensor head in proximity to a workpiece; (b) measuring an inductance at a plurality of frequencies within a frequency range to obtain an inductance spectrum, and measuring an inductance at a predetermined frequency at a lower third of the frequency range or below a lower limit of the frequency range; (c) determining a characteristic frequency according to the inductance spectrum, wherein the characteristic frequency is the frequency when the phase angle of the inductor is-90 degrees; (d) calculating the thickness of the first coating according to the characteristic frequency; and (e) calculating the thickness of the second coating according to the inductance at the predetermined frequency and the calculated thickness of the first coating.

Description

Technical Field

[0001] The present invention relates to a method and a sensor assembly for measuring the thickness of at least one coating formed on a substrate of a workpiece, wherein the substrate optionally comprises a first coating made of an electrically conductive and diamagnetic or paramagnetic material disposed above a second coating made of a ferromagnetic, ferrimagnetic or antiferromagnetic material. Background Art

[0002] In order to measure the thickness of a conductive coating on a substrate in a non-destructive manner, an eddy current detector has been developed. For example, patent document US2013 / 0132012-A1 discloses an eddy current detector suitable for measuring the thickness of a coating on a substrate, the eddy current detector being suitable for measuring the impedance of the coated substrate, the impedance including an inductive reactance component and a resistive component. The eddy current detector is configured by using a computer to establish an impedance plane diagram, which indicates the change in the impedance of the coated substrate with the coating thickness and the substrate conductivity, and establishes a calibration curve that is substantially insensitive to the substrate conductivity. Patent document US 2014 / 324384A1 also discloses a method for measuring the thickness of a coating formed on a substrate, the coating and the substrate being composed of a first and a second mutually different conductive material. The method includes positioning an induction device relative to the coating and feeding an alternating current signal to the induction device so as to induce a magnetic field in the workpiece.

[0003] Other known methods for measuring the thickness of a coating utilize Hall sensors, as described, for example, in EP 028487-A1 and US RE 35,703.

[0004] However, these known methods can only determine the thickness of a single coating on a substrate. However, there are important applications in which two coatings are layered on top of each other on a substrate. For example, the anti-wear coating on the copper substrate of the continuous casting mold used in steel foundries typically consists of two layers: an upper layer made of a conductive ceramic or cermet coating, and an interlayer between the upper layer and the copper substrate made of a ferromagnetic nickel-based alloy. The substrate is made of conductive and diamagnetic copper or a copper-based alloy. The upper coating may be thinner than the interlayer, with the total coating thickness varying from approximately 100 μm to several mm. After mold refurbishment, the thickness of each layer may have changed and may not be constant at different locations on the substrate. In particular, during the mold repair process, after applying a new nickel-based coating, the thickness of the nickel-based coating may exceed the recommended thickness. However, this can affect the measurement accuracy of eddy current-based mold level sensors, which are used to control the level of the meniscus of molten steel in the continuous casting mold during casting operations. This can lead to serious instability issues during the casting process. Therefore, it is important to measure the thickness, especially the thickness of nickel-based coatings, before using the crystallizer.

[0005] However, the above-mentioned known solutions based on magnetometers or eddy current sensors can only measure the thickness of a single coating layer (ie the upper coating layer). These solutions cannot be used to measure the thickness of the layers of the conductive coating layer above the ferromagnetic coating layer.

[0006] Patent document CN101532816-A describes an eddy current-based method for measuring the conductivity of two conductive, non-ferromagnetic layers above a substrate, where the conductivity of the two layers can be distinguished from each other. This method relies on eddy current detection equipment based on giant magnetoresistance sensors and an intelligent algorithm containing a neural network. This intelligent algorithm requires training in a time-consuming process that may fail to converge, resulting in limited measurement accuracy. This method is not suitable for measuring the thickness of ferromagnetic coatings.

[0007] Patent document CN103852000-A1 also relates to an eddy current detection device, which consists of a drive coil and a Hall sensor, wherein the drive coil is driven by alternating current (AC) electricity and generates a magnetic field; the Hall sensor probe is positioned between the drive coil and the test object to sense changes in the magnetic field level. The field level changes at two frequencies are related to the thickness of two conductive coatings through a quadratic function, and the quadratic function is solved to determine the thickness of the two coatings. The quadratic function used here is applicable to two conductive (but non-ferromagnetic) coatings with different electrical conductivities. However, for a conductive coating located above a ferromagnetic coating, this prior art is no longer applicable.

[0008] Therefore, there is currently no solution available for non-destructively measuring the thickness of a ferromagnetic layer disposed between a substrate and an upper layer made of a conductive material. Summary of the Invention

[0009] It is therefore an object of the present invention to provide a measurement method and a sensor assembly for measuring the thickness of two or more coatings on a substrate, which measurement method and sensor assembly are simple to implement and perform and provide reliable thickness measurements.

[0010] Another object of the present invention is to provide a method and a sensor assembly for measuring the thickness of a ferromagnetic coating on a metal substrate.

[0011] These objects are met or exceeded by the method for non-destructively measuring the thickness of at least one coating formed on a substrate of a workpiece according to claim 1, and by the sensor assembly according to claim 11. Further advantageous features and embodiments are set forth in the dependent claims.

[0012] According to a first aspect, the present invention provides a method for measuring the thickness of at least one coating formed on a substrate of a workpiece, wherein the workpiece optionally comprises a first coating made of an electrically conductive and diamagnetic or paramagnetic material, the first coating being disposed over a second coating made of a ferromagnetic, ferrimagnetic or antiferromagnetic material, wherein the second coating is disposed between the first coating and the substrate, the method comprising the following steps:

[0013] (a) Place the inductive sensor head in close proximity to the workpiece;

[0014] (b) measuring the inductance at a plurality of frequencies within a frequency range to obtain an inductance spectrum, and measuring the inductance at a predetermined frequency located in a lower third of the frequency range or below a lower limit of the frequency range;

[0015] (c) determining a characteristic frequency based on the inductance spectrum, where the characteristic frequency is the zero-crossing frequency of the real part of the inductance, or the frequency when the imaginary part of the inductance is at its minimum, or the frequency when the phase angle of the inductance is -90°;

[0016] (d) calculating the thickness of the first coating layer based on the characteristic frequency, wherein the thickness may also be zero;

[0017] (e) Calculating the thickness of the second coating layer based on the inductance at the predetermined frequency and the calculated thickness of the first coating layer.

[0018] The measurement method of the present invention uses an inductive sensor head (e.g., an inductive coil sensor) to measure the thickness of individual layers of a single or double coating on a substrate, one of which is made of a ferromagnetic material. It has been found that by analyzing the inductance spectrum at multiple frequencies, the thickness of one or more coating layers can be inferred in a simple and accurate manner. The inventive concept can be extended to three or more coating layers.

[0019] The upper coating (also referred to as the first coating) is not ferromagnetic; it may be diamagnetic or paramagnetic. The first coating is at least slightly electrically conductive. For example, at 20° C., the first coating may have a resistivity p of less than 1 Ω·m, preferably less than 1×10 -3 Ω·m, more preferably less than 1μΩ·m. The lower limit of the resistivity may be 1.59x 10 -8Ω·m (resistivity of silver). An example of a material for the first coating is tungsten carbide. The method can also be applied to workpieces without a first coating, or to workpieces where the first coating is present in some locations but not in others (e.g., removed due to wear). In these cases, the thickness of the first coating will be detected as zero. The method is also applicable to workpieces where the first coating is made of an insulator, in which case the thickness will also be detected as zero. The first coating (if present) is disposed above a second coating made of a ferromagnetic, ferrimagnetic, or antiferromagnetic material so that the second coating is disposed between the first coating (if present) and the substrate. This measurement method can be used if the second coating is disposed directly on the substrate, or if there is another coating disposed between the second coating and the substrate. The second coating (also referred to as the lower layer) is preferably ferromagnetic. In the following, the term "ferromagnetic" will be used to include ferrimagnetism and antiferromagnetism. The second coating preferably also has at least a low degree of electrical conductivity. For example, the second coating can have a resistivity ρ of less than 1 Ω·m at 20°C, preferably less than 1x 10 -3 Ω·m, more preferably less than 1μΩ·m. The lower limit of the resistivity may be 1.59x 10 -8 Ω·m (resistivity of silver). The substrate can be made of any material, including conductive and non-conductive materials, i.e., it can be an insulator. In an advantageous application of the measurement method of the present invention, the substrate is made of a conductive material. The substrate is preferably non-ferromagnetic. It can be diamagnetic or paramagnetic. The substrate can be made of a non-ferromagnetic metal or metal alloy.

[0020] The measuring method comprises placing the inductive sensor head in close proximity to the workpiece, preferably to the side or face of the substrate on which the coating is formed. "In close proximity" may mean a distance of less than about 1 mm, preferably less than about 200 μm. Preferably, the inductive sensor head is placed at a predefined distance from the uppermost coating (i.e., the first coating (if present) or otherwise the second coating). The inductive sensor head may be placed directly above the uppermost layer. It may also be kept at a predefined distance from the uppermost coating, for example by a spacer, which may be made of an insulating material such as plastic, ceramic or rubber, wherein the predefined distance may be less than 1 mm, for example, 1 μm to 200 μm. The inductive sensor head may be adapted to measure the thickness of the coating at one location on the workpiece and may be moved over the workpiece to measure the thickness at other locations.

[0021] The workpiece can be any type of tool, industrial equipment, vehicle part, or jewelry. Therefore, the measurement method can be applied to various industries and applications requiring the measurement of coatings on substrates (preferably metal substrates), such as on turbine blades, in nuclear power plants, in the marine industry, in the metal industry, or in the jewelry industry. Preferably, the measurement method is used to measure the thickness of coatings on metal objects, in particular, on copper or copper-based alloys forming a substrate that is part of a mold in a continuous casting machine for continuously casting steel.

[0022] The inductive sensor head can include a drive coil and at least one sensing coil, wherein the drive coil is driven by an AC current, generating a magnetic field that alternates at multiple frequencies (particularly the frequency of the AC current driving the drive coil). The at least one sensing coil senses changes in the magnetic field caused by the presence of a workpiece in the magnetic field. This allows for the generation of an inductive spectrum that is sensitive to the thickness of the coating.

[0023] The inventors have discovered that the characteristic frequency, which can be determined from the inductance spectrum, is sensitive almost exclusively to the thickness of the first (upper) coating. In particular, this characteristic frequency is relatively independent of the thickness of the second ferromagnetic coating. By reducing the size of the sensor coil of the inductive sensor head, the independence of the characteristic frequency from the thickness of the second coating can be further improved, until the dependence is sufficiently low.

[0024] On the other hand, at a single predetermined frequency in the lower third of the frequency range or below the lower limit of the frequency range, the inductance is sensitive to both the first and second coating thicknesses. This predetermined frequency is relatively low, for example, between 10 Hz and 1000 Hz, preferably between 50 Hz and 600 Hz, and more preferably between 100 Hz and 300 Hz. Therefore, the predetermined frequency will be referred to as a "low frequency" hereinafter. A suitable low frequency can be determined based on the electromagnetic properties of the ferromagnetic layer. In particular, the amplitude and real part of the inductance at low frequencies are highly sensitive to the thickness of the second coating, but the effects of the first coating must be corrected.

[0025] Therefore, the thicknesses of the two coatings are derived in at least two steps: in a first step (d), the thickness of the first coating is determined based on the characteristic frequencies of the inductance spectrum. This first layer thickness is then used to compensate for the effect of the upper layer on the low-frequency inductance. After this compensation, in a second step (e), the low-frequency inductance (also called the "low-frequency signal") can be used to determine the thickness of the second coating. These two steps involving data analysis can be performed by a data processing unit.

[0026] Therefore, the present invention provides a measurement method that can measure the thickness of two coatings on a substrate (preferably a metal substrate). The thickness of two coatings can be measured simultaneously using the same sensor. The sensor head is easy to construct and can be built for continuous scanning on large coated surfaces. In an embodiment, a measurement model that requires only 4 to 6 parameters (preferably 5 parameters) can be used to infer the thickness of the coating based on the measured inductance value. During the calibration process, multiple reference samples with known coating thicknesses can be used to calibrate the measurement method and sensor assembly before measurement.

[0027] Specifically, the inductive sensor head is used to measure the inductance at multiple frequencies within a frequency range to obtain an inductance spectrum, and to measure the inductance at a predetermined frequency. The inductance can be the mutual inductance of the drive coil and the sensing coil. The inductance is preferably measured as a complex value, that is, with an amplitude and a phase angle, as well as a real part and an imaginary part. The inductance can be measured by measuring impedance. The inductive sensor head can basically work like a metal detector. The drive coil is excited by an alternating current, generating an oscillating magnetic field. When this magnetic field penetrates a workpiece close to the sensor head, it induces eddy currents, thereby generating an opposing magnetic field. This secondary magnetic field generates an induced voltage in the sensing coil, which can be recorded as an induced signal or induction. In a preferred embodiment of the present invention, there can be two sensing coils, and the recorded inductance is the differential inductance of the two sensing coils.

[0028] The inductance spectrum can be measured by measuring the (complex) inductance spectrum L0 at a number of frequencies before starting the actual measurement, preferably in the absence of a workpiece. This step can be performed only once for the sensor head, or once for each series of measurements, with the results stored, for example, in a computer or storage medium connected to a data processing unit that performs the data analysis step.

[0029] After placing the sensor head in close proximity to the workpiece to be measured, the (complex) inductance spectrum L1 can be measured at the same frequency point as L0. The change in the inductance spectrum caused by the workpiece, ΔL, can be calculated as ΔL = L1 - L0. This change in inductance, ΔL, or alternatively, L1, can be used as the (typically complex) inductance spectrum for further processing.

[0030] In the next step (c), the characteristic frequency is derived from the inductance spectrum. The characteristic frequency can be determined as the frequency at which the real part of the inductance crosses zero, that is, the frequency point at which the real inductance is zero, or the frequency at which the imaginary part of the inductance is at a minimum, or the frequency at which the phase angle of the inductance is -90°. In most embodiments, any of these three analysis methods will result in the same frequency, that is, these are alternative methods of determining the characteristic frequency. Since the inductance spectrum can only be measured at a limited number of frequency points, the spectrum can be interpolated to determine the characteristic frequency. For example, the inductance phase spectrum can be interpolated to determine the characteristic frequency point at which the phase angle is -90°. In a similar manner, the real part of the inductance can also be interpolated to find the frequency at which the real part is zero (crosses zero). In an alternative embodiment, a suitable parametric function can be fitted to the inductance spectrum to determine the characteristic frequency point.

[0031] The inventors have found that the characteristic frequency is highly independent of the properties and thickness of the second coating and can be used to determine the thickness of the first coating. This can be accomplished in the next step (d) by performing a simple calculation using a parametric model, the parameters of which may have been determined during a calibration process. The parametric model can be described by a parametric function, in particular a polynomial, exponential, logarithmic, power, root or trigonometric function or a combination thereof. The parametric model preferably can have 1 to 6 parameters, more preferably 2 to 3 parameters. If the first coating does not exist or is made of an insulating material, the thickness of the resulting first coating is zero.

[0032] In the next step (e), the thickness of the second coating is calculated based on the inductance at a predetermined frequency and the calculated thickness of the first coating. This step preferably also uses a parametric model, the parameters of which can be determined during the calibration process. The parametric model can be described by a parametric function, in particular a polynomial, exponential, logarithmic, power, root or trigonometric function or a combination thereof. The parametric model preferably has 1 to 6 parameters, more preferably 2 to 4 parameters. This step (e) can be divided into several sub-steps, in particular two sub-steps. In the first sub-step, the inductance signal at a predetermined low frequency is processed using the previously calculated thickness of the first coating to compensate for the influence of the first coating. In the second sub-step, the thickness of the second coating is determined based on the low-frequency compensated inductance obtained in the previous step.

[0033] Prior to the measurement method, a calibration process may be performed using reference samples to obtain the parameters of the parameter function / model used in the measurement method.

[0034] According to an embodiment, the thickness of the first coating is calculated from the characteristic frequency by means of a first parametric function, the parameters of which have been determined during a calibration process, wherein the first parametric function is in particular

[0035]

[0036] Wherein t1 is the thickness of the first coating layer, p1 and p2 are the parameters of the first parametric function, and f0 is the characteristic frequency.

[0037] A "parametric function" can be any equation that defines a quantity (i.e., coating thickness) as a function of one or several independent variables (called parameters). The parametric function [1] given above has been adapted to numerical simulation data, but it can also be obtained from measured data. The invention is not limited to equation [1], but other functions may be more suitable, for example, for other coating materials.

[0038] In this embodiment, the thickness of the first coating is determined as a function of the characteristic frequency and (in this case) only two parameters p1 and p2 (which can be obtained by a calibration process that will be explained in more detail below). The parametric model can be based on the results of numerical simulations of complex inductance, for example using a first coating of a ceramic or cermet coating (e.g., tungsten carbide) and a second coating of a nickel-based alloy (e.g., NiCo-based alloy). The parametric model proposed herein was obtained by analyzing the simulation results using numerical calculations based on analytical eddy current modeling (Dodd-Deeds model) of a multilayer conductive structure. The simulation resulted in a hyperbolic dependence of the characteristic frequency on the thickness of the first coating, as expressed by the following equation:

[0039]

[0040] According to an embodiment, the thickness of the second coating is calculated from the magnitude or real part of the inductance at a predetermined frequency by means of a second parametric function, the parameters of which have been determined during a calibration process, wherein the second parametric function is in particular:

[0041]

[0042] Where t2 is the thickness of the second coating, p3, p4 and p5 are the parameters of the second parametric function, and L low is the inductance measured at the predetermined frequency.

[0043] Thus, it has been found that the inductance at relatively low frequencies is determined by both the thickness of the first coating and the thickness of the second coating. Knowing the thickness of the first coating, the thickness of the second coating can therefore be determined based on a single parameter function. It has been found that the magnitude or real part of the inductance at a predetermined frequency is primarily indicative of the thickness of the second coating. Therefore, equation [2] given above uses the magnitude of the inductance. An alternative method for determining the thickness of the second coating is to use the real part of the low-frequency inductance, rather than the magnitude of the inductance. Similar models and methods can be applied to measurements.

[0044] According to an embodiment, the thickness t2 of the second coating layer is calculated as follows

[0045] (e1) (first sub-step) uses the thickness of the first coating as an input to the third parameter function to compensate the first coating for the predetermined frequency (f low ) under the influence of inductance, the parameters of the third parameter function have been determined during the calibration process,

[0046] (e2) (second sub-step) determining the thickness of the second coating layer based on the compensated inductance at the predetermined frequency using a fourth parametric function, the parameters of which have been determined during the calibration process.

[0047] In the first sub-step, the effect of the first coating on the inductance can be compensated by inputting t1 into the third parameter equation:

[0048] |L comp (f low )|=F2(t1,L(f low )p3,p4) [3]

[0049] where p3 and p4 are parameters obtained through the calibration process, and L comp is the compensation inductor. In the example, Equation 3 can be:

[0050]

[0051] In a second sub-step, the thickness of the first coating can be determined from the compensated inductance at a predetermined frequency using a fourth function, where p5 is a parameter obtained from the calibration process:

[0052] t2=F2(|L comp (f low )|,p5) [4]

[0053] In an example, Equation 4 may be:

[0054]

[0055] Therefore, the upper coating is sensitive to the predetermined frequency f low The effect of the inductance at a predetermined frequency (which may be, for example, 200 Hz) is compensated using Equation 3. In the next step, the thickness of the second coating layer can be determined based on the compensated inductance at a predetermined frequency using Equation 4. The operations of Equations 3 and 4 can be completed in one step using Equation 2.

[0056] According to an embodiment, the inductance is measured at multiple frequencies within the frequency range, wherein the lower limit of the frequency range is between 10 Hz and 1000 Hz, preferably between 100 Hz and 500 Hz, and the upper limit of the frequency range is between 5 kHz and 800 kHz, preferably between 10 kHz and 400 kHz, and more preferably between 20 kHz and 100 kHz. The upper and lower limits of the frequency range can be adjusted depending on the electromagnetic properties of the coating and the substrate, as well as the desired thicknesses of the first and second coatings. For example, for a first coating made of a cermet coating and having a thickness between about 0.1 mm and 0.6 mm, and a second coating made of a nickel-based alloy and having a thickness in the range of 0.3 mm to 1.3 mm, the frequency range can cover, for example, between about 300 Hz and 20 kHz, since the characteristic frequency can be within this range.

[0057] The predetermined frequency is preferably a low frequency, i.e. it is located in the lower third of the frequency range, or even below the lower limit of the frequency range, preferably in the lower quarter or fifth of the frequency range, or below the lower limit of the frequency range. The predetermined frequency may be one of a plurality of frequencies within the frequency range. Thus, the inductance measurement can be used both to determine the characteristic frequency and to calculate the thickness of the second coating. The predetermined frequency may be between 10 Hz and 1000 Hz, preferably between 50 Hz and 600 Hz, more preferably between 100 Hz and 300 Hz, for example at 200 Hz. The sensor diameter may be adjusted so that the characteristic frequency is only sensitive to the upper layer (i.e. the first coating), while the low-frequency inductance is sensitive to both the first layer and the second layer.

[0058] According to an embodiment, the inductance is measured at 4 to 32 frequencies, preferably 6 to 16 frequencies, for example, at 8 frequency points within the frequency range. Thus, only a limited number of measurement points are required to acquire the inductance spectrum. Alternatively, the inductance can be acquired by sweeping all frequencies within the frequency range. For example, a frequency sweep can cover the frequency range from 1 Hz to 1 MHz in 10 seconds.

[0059] According to an embodiment, the method of the present invention comprises a calibration process comprising the following steps:

[0060] (i) placing the inductive sensor head in close proximity to a plurality of calibration samples having a first coating and a second coating of a plurality of different known thicknesses;

[0061] (ii) for each calibration sample, measuring the inductance at a plurality of frequencies within a frequency range to obtain an inductance spectrum, and measuring the inductance at a predetermined frequency located in a lower third of the frequency range or below a lower limit of the frequency range;

[0062] (iii) determining the characteristic frequency based on the inductance spectrum;

[0063] (iv) determining parameters of a first parametric function based on characteristic frequencies of the plurality of calibration samples using the known thickness of the first coating;

[0064] (v) determining parameters of a second parametric function based on the inductance of the plurality of calibration samples at the predetermined frequency and the known thicknesses of the first coating and the second coating.

[0065] In order to implement the measurement method, a set of calibration samples may be required to calibrate the measurement method, in particular the data analysis steps (d) and (e) and / or the corresponding sensor assembly. The calibration samples, in particular their coating and substrate, preferably have the same electrical conductivity and magnetic permeability as the target workpiece, and the coating is preferably made of the same material. At least 4 calibration samples may be required, of which at least 2 samples have different first coating thicknesses and at least 2 samples have different second coating thicknesses. Based on the characteristic frequencies of the calibration samples, the parameters of the first parameter function can be determined. For example, in Equation 1, p1 and p2 can be determined by simply solving two equations with two unknowns, i.e., equations with different f0 at different thicknesses of the first layer [1]. In an embodiment using 4 calibration samples, the average value f0 of all samples with the same first layer thickness can be used.

[0066] In order to find the parametric model of the second (or third and fourth) parameter function, the normalized inductance magnitude |L at a predetermined frequency at different thicknesses of the first coating layer can be first calculated. comp (f low )|. From this, the parameter required to calculate the thickness of the second coating layer can be determined, namely the parameter p5 in the example equation described herein. In the next step, the inductance amplitude |L(f low )|Converted into compensation inductance amplitude|L comp (f low )|Required parameters p3 and p4. This can be done by fitting the reference equation to the measured data using the known coating thickness.

[0067] The above parameter functions / functions were found using numerical simulations of first and second coatings made of cermet coatings (specifically tungsten carbide) and nickel-based alloys (specifically nickel-cobalt alloys), respectively. Therefore, other parameter functions may be better models for other materials. However, as long as the first coating is non-ferromagnetic and the second coating is ferromagnetic, it is expected that functions 1 through 4 will provide reasonably good models for many different materials.

[0068] The calibration process may further include the step of measuring the inductance at a plurality of frequencies within the frequency range and at a predetermined frequency when the inductive sensor head is not affected by any artifacts.

[0069] The measurement method of the present invention can be advantageously applied to workpieces having a first coating thickness in the range of 0 μm to 3 mm, preferably in the range of 50 μm to 1.5 mm, more preferably in the range of 0.1 mm to 0.6 mm, and a second coating thickness in the range of 50 μm to 3 mm, preferably in the range of 0.1 mm to 1.5 mm, and most preferably in the range of 0.3 mm to 1.3 mm. The measurement method has been found to be particularly sensitive within this thickness range. However, other thickness ranges can also be covered by adjusting the sensor diameter. For example, the sensor diameter can be between 5 mm and 50 mm, more preferably between 10 mm and 30 mm. In the example described herein, the sensor diameter is 18 mm.

[0070] According to an embodiment, the first coating can be made of a ceramic or cermet coating. Cermet is a composite material consisting of ceramic and a metallic material (e.g., tungsten carbide or zirconium carbide). The second coating can be made of a nickel-based alloy (e.g., a nickel-cobalt alloy). However, the first coating can be made of other conductive, diamagnetic materials, and the second coating can also be made of other ferromagnetic materials. The substrate can be made of any material, such as copper, and can have a thickness of, for example, 1 mm to 20 mm, although there is no upper limit to the thickness of the substrate since the measurement method only requires access from one side of the workpiece. However, the method of the present invention is applicable to any material, in particular metal, wherein the first coating is conductive and non-ferromagnetic, and the second coating is ferromagnetic and preferably also conductive.

[0071] According to one embodiment, the method of the present invention can be used to measure the thickness of coatings on a continuous casting mold for steel. In this embodiment, the substrate is typically made of copper or a copper-based alloy, and the thickness of the anti-wear coating made of a cermet coating (e.g., tungsten carbide) and the bonding layer made of a nickel-based alloy need to be determined after mold refurbishment. This is useful because excessively thick nickel-based alloy layers can affect the eddy current sensor used to monitor the meniscus level of the molten steel in the mold during the casting process.

[0072] According to a second aspect, the present invention relates to a sensor assembly for non-destructively measuring the thickness of a coating formed on a substrate of a workpiece, the substrate optionally having a first coating made of an electrically conductive and diamagnetic or paramagnetic material, the first coating being disposed over a second coating made of a ferromagnetic, ferrimagnetic or antiferromagnetic material, such that the second coating is disposed between the first coating and the substrate, the sensor assembly comprising:

[0073] - at least one sensor head comprising at least one coil, wherein the at least one coil is adapted to generate an alternating magnetic field at a plurality of frequencies within a frequency range and to sense changes in the magnetic field due to the presence of a workpiece close to the sensor head;

[0074] an impedance analyzer adapted to determine the inductance at the plurality of frequencies to obtain an inductance spectrum, and adapted to determine the inductance at a predetermined frequency located in the lower third of the frequency range or below a lower limit of the frequency range;

[0075] - a data processing unit, adapted to determine a characteristic frequency based on the inductance spectrum, wherein the characteristic frequency is the zero-crossing frequency of the real part of the inductance, or the frequency when the imaginary part of the inductance is at its minimum, or the frequency when the phase angle of the inductance is -90°; calculate the thickness of the first coating based on the characteristic frequency, wherein the thickness may also be zero; and calculate the thickness of the second coating based on the inductance at the predetermined frequency and the calculated thickness of the first coating.

[0076] All embodiments and advantages described for the measurement method also apply to the sensor assembly, and vice versa. In particular, the sensor head can be as described for the method. The data processing unit can be part of a computer, laptop, cloud computing device, mobile device, or any other processing device. It can be connected to a digital storage device, such as a hard drive, a memory stick, or a cloud database.

[0077] According to an embodiment, a sensor head includes: a drive coil adapted to generate an alternating magnetic field at multiple frequencies within a frequency range; and two sensing coils adapted to sense changes in the magnetic field caused by the presence of a workpiece in proximity to the sensor head; wherein the drive coil is interposed between the two sensing coils, and the magnetic field is measured as the differential output of the two sensing coils. In this embodiment, the drive coil can be arranged between the two sensing coils, wherein all three coils can be arranged parallel to the surface of the coated workpiece. The coils can be cylindrical coils having one or more turns.

[0078] The coils can be connected to an impedance analyzer suitable for measuring impedance. From this the mutual inductance between the coils can be calculated.

[0079] According to an embodiment, the sensor assembly includes a plurality of sensor heads arranged in an array and adapted to simultaneously measure one or more thicknesses of coating(s) at multiple locations on a workpiece. Furthermore, the acquired signals can be processed in parallel by a data processing unit or computer. This allows, for example, rapid inspection of a casting mold at multiple locations.

[0080] The sensor assembly (particularly if it includes multiple sensor heads) can be mounted on an automated robotic scanning system for scanning large surface areas, thereby enabling, for example, efficient inspection of coating thickness on rolled steel products or rolled or extruded aluminum alloy products.

[0081] According to an embodiment, the sensor assembly includes at least one displacement sensor for measuring the surface profile of a workpiece during the process of measuring one or more thicknesses of a coating(s). The displacement sensor may be an optical profilometer sensor. The measurement data may thereby reveal comprehensive data regarding the quality of the workpiece and / or its coatings, in particular information regarding the thickness reduction and structural integrity of the coating(s).

[0082] According to an embodiment, the sensor assembly includes at least one temperature sensor for measuring the temperature of the workpiece, wherein the data processing unit is adapted to compensate for temperature effects on the sensor output. In this embodiment, more calibration samples at different temperatures can be used during the calibration process, and the parametric model is expanded to include temperature effects on material properties, which are reflected in changes in inductance.

[0083] In an embodiment, the measurement data (particularly the measured first coating thickness and the second coating thickness) can be visualized in real time in three dimensions (3D) to quickly assess the coating quality, particularly variations in coating thickness or defects in the coating. These defects may be cracks in the coating or reductions in coating thickness that may occur during use of the workpiece.

[0084] Another aspect of the invention relates to the use of the non-destructive measurement method and sensor assembly according to the invention as described and claimed herein for measuring the thickness of a coating present on a copper or copper-based substrate forming a continuous casting mold for casting steel. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Non-limiting embodiments of the present invention will now be described with reference to the accompanying drawings, in which:

[0086] Figure 1 is a schematic side view of a sensor head according to an embodiment of the present invention;

[0087] Figure 2 is a schematic perspective view of a sensor head according to an embodiment of the present invention;

[0088] Figure 3 Here is an example of 8 inductance values measured at different frequencies expressed in the complex plane;

[0089] Figure 4 is a schematic cross-sectional view of a workpiece that may be studied using the sensor assembly of the present invention;

[0090] Figure 5 is a graph showing the phase angle of the inductance phase spectrum at different thicknesses of the first coating;

[0091] Figure 6 It is a parametric function that describes the relationship between the characteristic frequency and the thickness of the first coating;

[0092] Figure 7 is a graph of the inductance amplitude at 200 Hz for different first coating and second coating thicknesses;

[0093] Figure 8 is a graph showing the relationship between the compensation inductance amplitude and the second coating thickness at 200 Hz.

[0094] Similar elements are denoted by the same reference numerals. DETAILED DESCRIPTION

[0095] Figure 1 The diagram illustrates a sensor head 1 to be used in a method and sensor assembly according to an embodiment of the present invention. The sensor head 1 is positioned adjacent to a workpiece 2 having a coating to be measured. The sensor head 1 is disposed within a housing 10. The sensor head 1 or its housing 10 can be maintained at a small distance 3 from the workpiece 2, for example, by means of spacers (not shown). The sensor head 1 in this embodiment includes three coils 4, 6, and 8 arranged along the axis of a hollow cylinder. Thus, each coil 4, 6, and 8 can have one or several turns and can be elliptical or circular in shape. In this embodiment, each coil 4, 6, and 8 is substantially flat and arranged parallel to the coated surface of the workpiece 2. However, the shape and size of the coils can be adapted to the geometry of the workpiece 2 to be measured and the thickness and material of the coating 16, 18. In this embodiment, the drive coil 4 is disposed so as to be sandwiched between two sensing coils 6, 8. The drive coil 4 can be disposed between the two sensing coils 6, 8, with coil 6 being referred to as the active coil and coil 8 being referred to as the dummy coil. This allows for the measurement of a differential signal between the two sensing coils 6, 8, thereby canceling out any negative environmental effects. The drive coil 4 is excited at multiple frequencies by an alternating current (AC) generator, and the active coil and dummy coils 6 and 8 emit complex inductance signals. The magnetic field generated by the AC current is shown at 12. The drive coil 4 and the sensing coils 6 and 8 are connected to an impedance analyzer 5 for measuring the mutual impedance Z. The mutual inductance L can be determined from the impedance using Z = R + jΩL. The impedance analyzer 5 is also connected to a data processing unit 7 for data storage, processing, and analysis of the acquired signal data.

[0096] Figure 2 Further illustrated is the arrangement of cylindrical or circular coils 6, 4, 8 along the axis of the cylinder filled with air.

[0097] By driving the driving coil 4 at different frequencies, the complex inductance L can be measured. Figure 3The complex plane in FIG is shown, where the coordinate axes indicate the real part Re(L) and the imaginary part Im(L) of the complex inductance. Circles 14 illustrate the corresponding complex inductances measured at different frequencies f between 0 and infinity. It can be seen that each inductance 14 has a different magnitude and phase angle.

[0098] Figure 4 The figure shows a workpiece 2 on which a sensor head 1 can be placed for measuring the coating thickness of a first coating 16 and a second coating 18 disposed above a substrate 20. When the workpiece is a continuous casting mold in a steel foundry, the anti-wear coating can include an upper coating or first coating 16 made of a cermet coating, in particular tungsten carbide. The intermediate layer or second coating 18 between the cermet coating and the copper substrate 20 can be made of a ferromagnetic nickel-based alloy, in particular a nickel-cobalt-based alloy.

[0099] Now about Figures 5 to 8 These data were obtained through numerical data analysis but are expected to have good correspondence with actual measurement data.

[0100] In step 1, when no workpiece is present, the complex inductance spectrum L0 is measured at multiple frequencies (eg, at 8 frequencies between 1 kHz and 15 kHz).

[0101] For a series of measurements, step 1 only needs to be performed once and the results stored in the computer.

[0102] In step 2, when sensor head 1 is placed above workpiece 2, the inductance spectrum L is measured at the same frequency point as in step 1. In step 3, the change in inductance spectrum ΔL caused by the workpiece can be calculated as ΔL = L1 - L0. In step 4, the inductance phase spectrum is interpolated to obtain the characteristic frequency point with a phase angle of -90°.

[0103] Figure 5 This step is illustrated in the figure, which shows the 1Hz to 10 6 The inductance phase angle of the frequency spectrum between Hz The inductance spectra are obtained for samples with different first coating thicknesses t1. Figure 5 Several simulation curves 22 are shown for thicknesses between 0.1 μm and 1.0 μm, with the right side of the graph indicating the minimum t1 at 0 and the arrow indicating the direction of increasing t1. Circles 24 indicate the corresponding characteristic frequency of each sample, i.e., the frequency at which the inductance phase angle is -90°. The numerical simulations were performed assuming that the first coating is made of a cermet coating (specifically tungsten carbide) and the second coating is made of a nickel-based alloy (specifically a nickel-cobalt alloy), and that the second coating has a thickness of 0.2 mm and is disposed on a copper substrate with a thickness of 70 mm.

[0104] In step 5, the thickness t1 can be determined by using the corresponding characteristic frequency as input to the first parameter function. Figure 6 , where asterisks indicate numerical data and the straight line in the middle has been fitted using the above formula 1a. It can be seen that the characteristic frequency f0 is a very good indicator of the thickness of the upper layer, at least until the upper layer thickness reaches 1.2 mm.

[0105] In the following step 6, the first coating thickness determined from step 5 is used as an input to another parameter function (eg, equation 3 above) to compensate for the effect of the first layer on the inductance at a predetermined low frequency.

[0106] In step 7, another parameter function (eg, equation 4 above) may be used to determine the thickness of the lower layer based on the compensated inductance at the predetermined low frequency.

[0107] Figure 7 The dependence of the inductance magnitude on the thickness of the first coating layer and the thickness of the second coating layer is shown in FIG. In particular, Figure 7 It is shown that the simulated data indicated by the asterisk can be fitted, for example, to the following formula:

[0108]

[0109] Therefore, it depends on both the first coating thickness and the second coating thickness. The arrow indicates the curve of t1 increase. Once the inductance magnitude |L| compensates for the effect of the first coating, the compensated inductance magnitude |L comp |You can use Figure 8 It can be described by the simple exponential function shown in .

[0110] Steps 4 to 7 are preferably performed sequentially because the first coating thickness can be determined first and used to compensate for its effect on the low-frequency inductance before the second coating thickness is derived. The inductance data measured in steps 1 and 2 can be stored and used to calculate the inductance change caused by the workpiece in step 3.

[0111] The present invention has been fully described herein, and those skilled in the art will recognize that many changes and modifications may be made without departing from the spirit or scope of the present invention as described herein. Any reference signs in the claims should not be construed as limiting the scope of the appended claims.

Claims

1. A method for non-destructively measuring the thickness (t1, t2) of at least one coating layer (16, 18) formed on a substrate (20) of a workpiece (2), wherein the workpiece (2) optionally comprises a first coating layer (16) made of a conductive and diamagnetic or paramagnetic material, and the first coating layer (16) is disposed over a second coating layer (18), the second coating layer (18) being made of a ferromagnetic, ferrimagnetic or antiferromagnetic material, wherein the second coating layer (18) is disposed between the first coating layer (16) and the substrate (20), the method comprising the following steps: (a) placing the inductive sensor head (1) in close proximity to the workpiece (2); (b) measuring the inductance (14) at a plurality of frequencies within a frequency range to obtain an inductance spectrum (22), and measuring the inductance at a predetermined frequency located in the lower third of the frequency range or below a lower limit of the frequency range; (c) determining the characteristic frequency f0(24) based on the inductance spectrum, where the characteristic frequency f0(24) is (ci) the zero-crossing frequency of the real part of the inductance, or (c-ii) the frequency when the imaginary part of the inductance is at its minimum, or (c-iii) the frequency when the phase angle of the inductance is -90°; (d) calculating a thickness t1 of the first coating layer (16) based on the characteristic frequency (24), wherein the thickness may also be zero; (e) calculating the thickness t2 of the second coating layer (18) based on the inductance at the predetermined frequency and the calculated thickness t1 of the first coating layer (16).

2. The method according to claim 1, wherein the thickness t1 of the first coating (16) is calculated from the characteristic frequency (24) by means of a first parameter function, the parameters of which have been determined during a calibration process, wherein the first parameter function is in particular Where t1 is the thickness of the first coating (16), p1 and p2 are parameters of the first parametric function, and f0 is the characteristic frequency (24).

3. The method according to claim 1 or 2, wherein the thickness t2 of the second coating (18) is calculated from the magnitude or the real part of the inductance (L) at the predetermined frequency by means of a second parametric function, the parameters of which have been determined during a calibration process, wherein the second parametric function is in particular Where t2 is the thickness of the second coating (18), p3, p4 and p5 are the parameters of the second parametric function, and L low is the inductance measured at the predetermined frequency.

4. The method according to claim 1 , wherein the thickness t2 of the second coating layer ( 18 ) is calculated as follows: (e1) using the thickness t1 of the first coating layer (16) as an input of the third parameter function to compensate the first coating layer (16) for the predetermined frequency (f low ), the parameters of the third parameter function have been determined during the calibration process; and (e2) determining the thickness t2 of the second coating layer (18) based on the compensated inductance at the predetermined frequency using a fourth parametric function, the parameters of which have been determined during the calibration process.

5. The method according to claim 1 , wherein the lower limit of the frequency range is between 10 Hz and 1000 Hz, preferably between 100 Hz and 500 Hz, and the upper limit of the frequency range is between 5 kHz and 800 kHz, preferably between 10 kHz and 400 kHz, more preferably between 20 kHz and 100 kHz.

6. Method according to one of the preceding claims, wherein the predetermined frequency is between 10 Hz and 1000 Hz, preferably between 50 Hz and 600 Hz, more preferably between 100 Hz and 300 Hz.

7. The method according to claim 1 , comprising a calibration process comprising the following steps: (i) placing an inductive sensor head (1) in close proximity to a plurality of calibration samples having first and second coatings (16, 18) of a plurality of different known thicknesses; (ii) for each calibration sample, measuring inductance at a plurality of frequencies within a frequency range to obtain an inductance spectrum, and measuring inductance at a predetermined frequency located in a lower third of the frequency range or below a lower limit of the frequency range; (iii) determining the characteristic frequency based on the inductance spectrum; (iv) determining parameters of a first parametric function based on characteristic frequencies of the plurality of calibration samples using the known thickness of the first coating (16); (v) determining parameters of a second parametric function based on the inductance of the plurality of calibration samples at the predetermined frequency and the known thicknesses of the first and second coatings (16, 18).

8. The method according to claim 1 , wherein the first coating layer ( 16 ) has a thickness in the range of 0 μm to 3 mm, preferably 50 μm to 1.5 mm, more preferably 0.1 mm to 0.6 mm, and the second coating layer ( 18 ) has a thickness in the range of 50 μm to 3 mm, preferably 0.1 mm to 1.5 mm, most preferably 0.3 mm to 1.3 mm.

9. The method as claimed in one of the preceding claims, wherein the first coating (16) is made of a ceramic or cermet coating and / or the second coating (18) is made of a nickel-based alloy.

10. Method according to one of the preceding claims, for measuring the thickness of a coating (16, 18) on a continuous casting mold for steel (2), preferably formed by a base plate (20) made of copper or a copper-based alloy.

11. A sensor assembly for non-destructively measuring the thickness of a coating (16, 18) formed on a substrate (20) of a workpiece (2), the substrate optionally having a first coating (16) made of an electrically conductive and diamagnetic or paramagnetic material, the first coating (16) being disposed over a second coating (18) made of a ferromagnetic, ferrimagnetic or antiferromagnetic material, wherein the second coating (18) is disposed between the first coating (16) and the substrate, the sensor assembly comprising: - at least one sensor head (1) comprising at least one coil (4, 6, 8), wherein the at least one coil is adapted to generate an alternating magnetic field (12) at a plurality of frequencies within a frequency range and to sense changes in the magnetic field due to the presence of a workpiece (2) close to the sensor head; - an impedance analyzer (5) adapted to determine the inductance at the plurality of frequencies to obtain an inductance spectrum, and adapted to determine the inductance at a predetermined frequency located in the lower third of the frequency range or below the lower limit of the frequency range; - a data processing unit (7) adapted to determine a characteristic frequency (24) based on the inductance spectrum, wherein the characteristic frequency (24) is the zero-crossing frequency of the real part of the inductance, or the frequency at which the imaginary part of the inductance is at its minimum, or the frequency at which the phase angle of the inductance is -90°; The thickness of the first coating (16) is calculated according to the characteristic frequency (24), wherein the thickness may also be zero; and the thickness of the second coating (18) is calculated according to the inductance at the predetermined frequency and the calculated thickness of the first coating (16).

12. The sensor assembly of claim 11, wherein the sensor head (1) comprises: a drive coil (4) adapted to generate an alternating magnetic field at a plurality of frequencies within a frequency range; and two sensing coils (6, 8) adapted to sense changes in the magnetic field caused by the presence of a workpiece (2) close to the sensor head; wherein the drive coil (4) is interposed between the two sensing coils (6, 8), and the magnetic field changes are measured as differential outputs of the two sensing coils.

13. A sensor assembly according to claim 11 or 12, comprising a plurality of sensor heads (1) arranged in an array and adapted to simultaneously measure one or more thicknesses of a coating (16, 18) at a plurality of locations on a workpiece (2).

14. The sensor assembly of one of claims 11 to 13, comprising at least one displacement sensor for measuring the surface profile of the workpiece (2) during a process of measuring one or more thicknesses of a coating (16, 18) formed on a substrate (20) of the workpiece (2).

15. Sensor assembly according to one of claims 11 to 14, comprising at least one temperature sensor for measuring the temperature of the workpiece (2), wherein the data processing unit is adapted to compensate for temperature effects on the sensor output.

Images