WO1995010783A1

WO1995010783A1 - Detecting and evaluating cracks using microwaves

Info

Publication number: WO1995010783A1
Application number: PCT/US1994/011482
Authority: WO
Inventors: Chin-Yung Yeh; Reza Zoughi
Original assignee: Colorado State University Research Foundation
Priority date: 1993-10-12
Filing date: 1994-10-11
Publication date: 1995-04-20
Also published as: AU7973594A

Abstract

A method and apparatus are disclosed for detecting a surface feature of a metallic object of interest or determining dimensional information regarding an object of interest based on the product of transmitted and reflected signals. In one embodiment, a detector (10) for detecting cracks (18) in a surface (16) is provided. The detector (10) comprises a signal generator (12); a waveguide (14) for receiving a first signal from the generator (12) and a second signal reflected off the surface (16), wherein the first and second signals interact to form a standing wave within the waveguide (14); and a sensor (24) for measuring the standing wave. By monitoring output from the sensor (24) as the waveguide (14) is scanned across the crack (18), the crack (18) can be detected. The detector (10) can also be used for measuring the dimensions of cracks.

Description

DETECTING AND EVALUATING CRACKS USING MICROWAVES

FIELD OF THE INVENTION

The present invention relates generally to devices which employ microwave signals and, in particular, to a novel device which uses the product of transmitted and reflected microwave signals to detect cracks or other surface features of a metallic object of interest. The device can also be used to determine dimensional information regarding an object of interest.

BACKGROUND OF THE INVENTION

In a number of settings, it is desirable to investigate an object which is at least partially comprised of microwave reflective material such as metal to detect certain surface features of the object and/or to determine dimensional information regarding the object. One such detection setting is surface crack detection. Metal fatigue or failure can often be diagnosed through surface crack detection. Such fatigue or failure is of critical importance in many environments, notably including the inspection of aircraft skin and components, nuclear power plant steam generator tubings and steel bridges. Accordingly, many surface crack detection techniques have been investigated or developed, including acoustic emission, dye penetrant, eddy current, ultrasonic, radiography (using x-ray or gamma radiation), magnetic particle, and microwave mode conversion testing. Each of these techniques is subject to one or more of the following limitations: they require complicated instrumentation or numerical analysis which makes the subject equipment expensive and unacceptable for certain applications; surface contact is required which is not practical in all environments; their applicability is temperature dependent; their sensitivity may be unacceptably affected by dirt, paint, rust or the like covering the surface under examination; they introduce a danger of damage, e.g., arc burns, to the surface under examination; they are unacceptably sensitive to material permeability or metal type; they require significant operator expertise; their sensitivity is limited to cracks of a particular size range; they are not readily adapted for use on surfaces of various shapes; and/or they do not allow for testing of large surface areas in a short period of time. There is thus a need for an improved crack detection apparatus.

An example of a setting where dimensional information regarding an object is desired is in measuring the thickness of rubber on a steel-belted tire. As used herein, dimensional information broadly includes information relating to the position, shape, size, orientation and internal structure or spatial relationships of an object. Before a tire can be retread, it is necessary to remove any remaining tread. The conventional approach is to buff or cut the remaining tread rubber from the tire casing by means of rotating knives. Ideally, approximately 2 mm of rubber should be left covering the steel belts within the tire casing.

One common problem associated with this technique is determining when enough rubber has been removed in the buffing operation. If too much rubber is removed and the steel belts are damaged, the tire casing must be discarded. The conventional solution is to periodically halt the buffing process and manually measure the depth of the remaining rubber by inserting a micrometer through the rubber until it contacts the steel belts within the tire. Manual measurement of rubber thickness is typically done only at one randomly selected point along the tire circumference. If the steel belts have a radial bulge in one region of the tire casing, a manual measurement will usually fail to halt the buffing process before the bulge in the steel belts is uncovered and damaged by the knives. In addition, manual measurement adds substantial delay and labor expense to the buffing process. Accordingly, there is also a need for an improved detector for determining the thickness of rubber on a steel-belted tire.

It will be appreciated that many other examples of settings were it is desired to detect surface features of an object or obtain dimensional information regarding an object are possible. Generally, in such settings, there is a need for a reliable and inexpensive detector which is easy to use and is not subject to problems and limitations such as discussed above. SUMMARY OF THE INVENTION

The present invention discloses devices useful for detecting surface features of and/or determining dimensional information regarding objects at least partially comprised of microwave reflective material. The present invention has a number of advantages over conventional devices including ease of use, simplified data processing, rapid information return and a broad range of applicability.

According to the present invention, surface feature detection or dimensional information acquisition is accomplished by reflecting a microwave signal off of an object of interest, combining the incident and reflected microwave signals to produce a resulting signal (i.e., a standing wave), and analyzing the resulting signal to yield the desired detection or dimensional information. An apparatus constructed in accordance with the present invention thus includes a microwave signal source, a structure for receiving the incident and reflected signals such that the signals interact therein to produce the resulting signal, and an analyzer for analyzing the resulting signal. The structure for receiving the signals preferably comprises a circular or rectangular waveguide. The analyzer can include a sensor disposed within the waveguide for measuring E_x or E_y and associated signal processing components.

In one embodiment, an apparatus for use in detecting and measuring cracks in a metal surface is provided. The apparatus comprises a source for transmitting a first microwave signal, an open ended waveguide and a sensor such as a crystal diode for measuring a local electric field. The open end of the waveguide is positionable adjacent the surface to be tested. The waveguide is operative for receiving a first signal from the signal source and receiving a second signal reflected off of the surface such that interference between the signals results in a standing wave in the waveguide. The sensor can be utilized to sense movement of the standing wave, e.g., due to the presence of a surface crack within the open end of the waveguide as the waveguide is scanned over the surface, thereby providing for crack detection and measurement. Scanning can be performed manually or can be motorized.

The crack detection apparatus of the present invention has a number of advantages. First, the apparatus need not be in contact with the surface under examination, thus providing significant operational flexibility. In addition, the apparatus can be used in high or low temperature environments and is useful even if the crack is filled or covered by dielectric materials such as dirt, paint or rust. Moreover, the apparatus does not require great user expertise and can be arranged in a multiple waveguide array format to allow for scanning of large surface areas in a short time. The apparatus can also be used on curved surfaces such as tubings.

In another embodiment, an apparatus for measuring the thickness of rubber covering the steel belts within a tire is provided. A microwave signal is transmitted through a waveguide towards the outer surface of the tire and the phase difference between the transmitted signal and reflected signal is measured. The transmitted and reflected signals set up a standing wave in the waveguide. A series of detectors are provided in the waveguide to measure the standing wave. Based on the standing wave measurement, the phase of the reflection coefficient and, hence, the thickness of the rubber can be determined. The apparatus can be used in the retreading process to halt buffing when a predetermined minimum rubber thickness has been reached. The apparatus thus allows for continuous, nondestructive measurement of the rubber thickness at all points on the tire circumference. BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a schematic diagram showing the major components of a surface crack detector constructed in accordance with the present invention;

Fig. 2a is a side view showing a portion of the surface crack detector of Fig. 1 positioned on a cracked surface;

Fig 2(b)) is a front view showing a portion of the surface crack detector of Fig. 1 positioned on a cracked surface;

Fig. 3 is a graph comparing the theoretically predicted characteristic curve for a scan over a surface crack and corresponding experimentally determined data; Fig. 4(a) is a graph showing the characteristic curves for scans over cracks of different depths;

Fig. 4(b) is a graph illustrating one method for calibrating crack depth based on sensor output;

Fig. 4(c) is a graph illustrating a mathematically based method for crack sizing;

Fig. 5 is a schematic diagram showing the major components of a surface crack detector constructed in accordance with an alternative embodiment of the present invention;

Fig. 6 shows theoretical curves illustrating the effect of sensor placement on sensor output;

Fig. 7 shows experimentally obtained signals illustrating the higher detection sensitivity achieved by appropriate sensor placement.

Fig. 8 is a schematic block diagram showing the major components of a rubber thickness detector constructed in accordance with the present invention.

Fig. 9 is a simplified diagram showing the manner in which the present invention can be adapted to measure the thickness of the layer of rubber on a rotating tire casing.

Fig. 10 is a graph showing the phase of the reflection coefficient as a function of the rubber thickness (and air gap) at 9.515 GHz (X-band) with an air gap of 0.5 cm and a rubber permittivity of 16.31 - J2.33, based on theoretical calculations.

Fig. 11 is a graph showing the phase of the reflection coefficient as a function of rubber thickness at 4 GHz (C- band) with no air gap and a rubber permittivity of 12 -j2.5, based on theoretical calculations.

Fig. 12 is a graph showing the effect of variations in the air gap (19, 21, and 23 mm) on the phase of the reflection coefficient at 4 GHz (C-band), based on laboratory results.

Fig. 13 is a graph showing the phase of the reflection coefficient as a function of rubber thickness at 4 GHz (C-band) with an air gap of 2.3 cm based on actual test results using a Michelin XZA-1 tire (DOT 347).

Fig. 14 is a graph showing the phase of the reflection coefficient as a function off rubber thickness at 4 GHz (C-band) with an air gap of 2.1 cm based on actual test results using a Michelin 11R22.5XZY tire (DOT 105). DETAILED DESCRIPTION

The detectors of the present invention use the product of a transmitted microwave signal and a reflected microwave signal to detect cracks or other surface features of an object which is at least partially comprised of microwave reflective material. As described below, the detectors can also be used to determine dimensional information regarding such an object. The transmitted and reflected signals interact within an appropriate waveguide to form a resulting signal, e.g., a standing wave. The characteristics of or changes in the resulting signal can then be analyzed in accordance with mathematical models to provide the desired detection or dimensional information. In the following description, the invention will be described in connection with two environments; surface crack detection or sizing and tire tread thickness measurement. However, upon consideration of the present disclosure, it will be appreciated that the subject invention is more generally useful in a broad range of detection applications. The embodiments described below are therefore intended to be exemplary.

Surface Crack Detection

In a situation where an electromagnetic wave impinges upon a plane of conductive material, the wave is reflected. Assuming the direction of propagation of the wave is normal to the conductive plane, the plane is unflawed and the plane is a perfect conductor, the wave will be completely reflected normal to the conductive plane. If the transmitted or incident wave and the reflected wave are permitted to interact within a waveguide, interference between the waves traveling in opposite directions results in a standing wave.

. A different situation is presented where the reflecting surface is not flat, i.e., is disturbed by a crack, bulge or other disturbance. In such situations, higher order modes are generated which change the reflection properties of the reflected wave. This, in turn, results in a perturbation in the standing wave which is indicative of the presence and dimensional features of the crack or other disturbance. The standing wave can thus be analyzed to yield crack detection and measurement information.

Referring to Figs. 1 and 2, a surface crack detector constructed in accordance with the present invention is generally identified by the reference number 10. A signal generator 12 produces a microwave signal that is directed by a waveguide 14 towards the surface 16 to be analyzed. One purpose of the illustrated detector 10 is to detect cracks 18 in the surface 16. The detector can also be used to measure cracks 18 as will be described below.

The frequency of the incident microwave signal can be selected based on the desired sensitivity or measure. In particular, cracks 18 which are a fraction of a millimeter thick can be easily detected at frequencies of about 20 GHz or lower. Higher frequencies can be used to detect smaller cracks. The signal generator 12 thus comprises an oscillator capable of providing a microwave signal of the selected frequency. In the illustrated embodiment, the signal generator 12 comprises a conventional oscillator for providing a 24 GHz microwave signal.

In principle, a variety of different types of waveguides including, for example, both circular and rectangular waveguides, can be satisfactorily utilized in detector 10. In this regard, circular waveguides may be preferred for certain applications because crack detection becomes independent of crack orientation. The illustrated waveguide, as shown in Figs. 2a and 2b, is a K-band slotted rectangular waveguide (a=10.67 mm and b=4.32 mm), which operates in its dominate TE₁₀ mode, though other modes may be utilized. Waveguide flange 15 is useful in guiding the waveguide 14 along the surface 16. It will be appreciated that the flange 15 and aperture 20 can be formed to facilitate scanning of curved surfaces such as tubings.

In operation, the aperture 20 of waveguide 14 is manually or mechanically scanned across surface 16 in a direction transverse to crack 18 as generally indicated by arrow 32. When the crack 18 is not within the aperture 20 of waveguide 14, the microwave signal is substantially completely reflected off of surface 16, as noted above, and interference between the incident and reflected signals results in creation of a standing wave in waveguide 14. As the scan continues and crack 18 enters aperture 20 of waveguide 14, higher order modes are induced in the reflected signal as experienced in waveguide 14. As a result, the standing wave in waveguide 14 shifts relative to the flat surface scenario described above. As the crack 18 exits aperture 20 of waveguide 14, the flat surface conditions are restored and the standing wave in waveguide 14 returns to the position described initially.

It is possible to sense this shifting of the standing wave using a single sensor 24 disposed within waveguide 14 for measuring an electromagnetic field in the waveguide 14, through more than one sensor may of course be utilized to accurately monitor standing wave shifts. The illustrated detector 10 employs a single sensor 24 which can comprise a conventional crystal diode for measuring the local electric field, positioned a distance, 1, from aperture 20.

It will be appreciated that the standing wave characteristics generally vary in a sinusoidal manner with respect to detector position relative to aperture 20. As a consequence, the magnitude of the detected change in standing wave characteristics for a given wave shift is dependent on detector location. The distance 1 can thus be selected to enhance detector sensitivity. The illustrated sensor 24, is positioned 9.48 cm from aperture 20. The sensor output is preferably read out via conventional voltmeter 26 and recorder 28 to provide time related information for each surface scan. However, it will be appreciated that mere observation of voltmeter movement is sufficient for crack detection.

Referring to Fig. 3, the crack detection technique as described above can be modeled mathematically. For the purposes of demonstrating the theoretical foundation of the present invention, the theoretically predicted detector output was compared to experimental results for a scan of a crack having a length, L, of 20.1 mm, a width, w, of 0.9 mm, and a depth, D, of 1.45 mm.

In the theoretical analysis, the flat plate condition was modeled as a waveguide terminated in a short circuit. The condition where the crack is within the waveguide aperture was modeled as a large waveguide feeding a much smaller short circuited waveguide, where each waveguide had the same broad dimension. By solving known electromagnetic field equations relative to the boundary conditions appropriate for the cases where the crack is outside the waveguide aperture, partially within the aperture, and fully within the aperture, the solid line trace of Fig. 3 was mathematically obtained, where the sensor output voltage is plotted against crack position. Experimentally determined data points are shown as circles in Fig. 3, thus demonstrating good agreement with the theoretical model.

The surface crack detector 10 can be used for crack measurement in addition to crack detection. Referring again to Fig. 3, the crack width is related to features of the illustrated characteristic curve, which includes a pair of dips and peaks corresponding to the crack edges. The crack width can thus be determined by mathematically analyzing the characteristic curves or by calibrating the features of the characteristic curves relative to a library of empirically derived data. In this regard, referring to Fig. 4, it has been observed that for shallow cracks, the crack width is approximately given by the equation:

where p is the distance between the dip minima, p' is the distance between the two turning points (defined as the points of separation between the characteristic curve and lines 30 drawn through the minima tangent to the characteristic curve) and b is the width of the waveguide 14 (as shown in Fig. 2a). Additionally, the crack detector 10 can be used to determine crack depth. Referring to Fig. 4(a), there are shown three characteristic curves corresponding to cracks of three different depths (2mm, 3.4 mm and 3.77 mm). As Fig. 4(b) demonstrates, the shape of the characteristic curves in the region corresponding to presence of a crack within the waveguide aperture 20, is dependent upon crack depth and width. Accordingly, by calibrating the characteristic curves relative to empirically derived data, or by mathematically modeling the characteristic curves as a function of crack depth and width, crack depth information can be provided.

Calibration of the characteristic curves or sensor output to yield crack depth information can be accomplished in a variety of ways. For example, the relationship between the sensor output for a particular scan location and the corresponding crack depth (for cracks of a specified width and length) can be determined empirically. In this regard, the scan location utilized for calibration can be selected to correspond to particular features of the characteristic curves, such as dips or peaks, or the scan location can be an arbitrarily selected location.

One such calibration technique is illustrated in Figs. 4(a) and 4(b). The scan location selected for calibration in this example was δ = 2.5 mm. As shown in Fig. 4(a), three data points representing the sensor output voltage for three different crack depths were obtained, where each of the cracks had an identical width and a length which extended completely across the waveguide aperture 20. In particular, for crack depths of 3.77 mm, 3.4 mm and 2 mm, sensor outputs of approximately 0.03 mV, 0.32 mV and 0.477 mV, respectively, were obtained. These three data points were plotted graphically as shown in Fig. 4(b). A curve was then fitted to the data points for use in estimating unknown crack depths, for cracks of the specified width and length, based on the sensor output at δ = 2.5mm.

It should be appreciated that this simple example is presented for illustration purposes. In practice, it is expected that many such data points would be required for accurate calibration. In addition, other types of data, such as an area defined by a characteristic curve and a reference voltage line, may be used in place of output voltage at a particular scan location. Moreover, the characteristic curve shape is dependent upon crack length and width as well as crack depth. Accordingly, calibration may include consideration of crack width and length in conjunction with crack depth, thereby providing a large library of calibration information.

As previously noted, crack depth can also be determined mathematically. Using an open-ended rectangular waveguide with dimensions a and b to detect a crack with width w and depth d, the reflection coefficient for the dominant mode, TE₁₀, can be expressed as

Then the total E_y-field of the dominant mode is

and the approximate value of |E_y|² can be plotted as a function of w and d for sizing the detected crack, as shown in Fig. 4c. Using the method described above, the width w of the crack can be estimated from the characteristic signal. Knowing the crack width, the crack depth can be determined as a function of |E_y|² by using plotted curves such as shown in Fig. 4c. Conversely, if the crack depth is known, the width can be determined according to the same mathemematical principles.

In the preceding description, the sensor 24 was assumed to project from one of the two major walls of rectangular waveguide 14 so as to measure E_y. It is also possible to detect surface cracks based on measurements of E_x, where E_x is oriented perpendicular to E_y. As previously noted, in the absence of a crack, the incident microwave signal will be substantially completely reflected so that substantially the entire reflected signal back propagates through the waveguide. However, in the presence of a crack, higher order modes as indicated by fluctuations of E are generated. Although these modes attenuate rapidly, they can be detected very near the crack. Because these higher order modes only occur when a crack is present, measurements of E_x can yield positive and highly sensitive crack detection.

A surface crack detector 50 for detecting cracks based on measurements of E_x is shown in Fig. 5. The detector 50 includes a signal generator 52, a waveguide 54, a voltmeter 56 and a recorder 58, which can be identical to the corresponding components described above.

The detector 50 further includes a sensor 60 which is adapted for measuring E_x. In this regard, the sensor 60 is disposed in close proximity to the crack and can be placed immediately adjacent aperture 62 of waveguide 54. It may be possible to place the sensor 60 at, or outside of aperture 62. The illustrated sensor 60 is positioned a distance, j, of about 0.2 mm from aperture 62 within waveguide 54. Additionally, the sensor 60 projects from one of the two minor walls of waveguide 54 so as to measure E_x. Crack detection is accomplished as described above by scanning the waveguide aperture 62 across a surface 64 to be tested while monitoring the sensor output. Waveguide flange 67 and the shape of aperture 62 assist in maintaining a perpendicular orientation of the waveguide 54 relative to surface 64 during scanning.

The distance k of separation between the sensor 60 and the wall of waveguide 54 can also be selected to enhance crack detection. This effect is shown by the three theoretically derived characteristic curves illustrated in Fig. 6. The three curves, in which scanning location δ is plotted against E_x ², correspond to sensor positions of k = b/2 (dashed curve), k = b/3 (thick solid line) and k = b/5 (thin solid curve) where b is the minor dimension of rectangular waveguide 54. The curves are based on a signal frequency of 12.4 GHz, a waveguide opening of a = 22.86 mm by b = 10.16 mm, and a crack size of width = 0.14 mm by depth = 1.2 mm.

As shown, when the crack is outside of the waveguide aperture 62 (δ < 0 or δ > 10.16 mm), E_x ² is zero. When the crack is inside of the aperture (0 < δ < 10.16 mm), the maximum value of E_x ² depends upon the position of sensor 60. The positioning of sensor 60 can thus be selected to provide the largest obtainable maximum value of E_x ², thereby enhancing detector signal-to-noise ratio. In this regard, the illustrated sensor 60 is positioned at approximately k = b/6 which provides excellent detection for the specified signal frequency and corresponding waveguide dimensions. Other values of k will be optimal for other signal frequencies.

Fig. 7 illustrates the increase in detection sensitivity which can be achieved by appropriate positioning of the sensor 60. The dashed signal in Fig. 7 was experimentally obtained with the sensor 60 positioned at k = b/6 and the solid signal was obtained with the sensor 60 positioned at k = b/2. The microwave signal (12.4 GHz), waveguide dimensions (22.86 × 10.16 mm) and crack size (0.14 × 1.2 mm) used to obtain the experimental signals of Fig. 7 were identical to the values employed to obtain the theoretical curves of Fig. 6. By comparing the experimental signals of Fig. 7 to the corresponding theoretical curves of Fig. 6, it can be observed that the experimental signal for the sensor position k = b/2 is somewhat obscured by noise and is more difficult to ascertain than for K = b/6. However, the experimental signal for k = b/6 includes a well-defined spike thereby yielding positive crack detection.

Although the crack detectors of the present invention have been described in connection with exemplary embodiments including a single E_y sensor or a single E_x sensor, it will be appreciated that any number of E_x and/or E_y sensors may be employed in a single detector to yield crack information.

Rubber Thickness Measurement

As noted above, electromagnetic waves will completely reflect off of a plane of conductive material, assuming the direction of propagation of the wave is normal to the conductive plane and the plane is a perfect conductor. Also, the reflected wave will have the same amplitude and phase as the incident wave. In such a situation, the magnitude of the reflection coefficient (r = E_r/E_i) is one, and phase of the reflection coefficient is -180°. Expressed as a complex number, r = -1 in this case. The transmission coefficient (T = E_t/E_i) is zero. Interference between the incident wave and reflected wave traveling in opposite directions results in a standing wave in which both the electric and magnetic fields have regularly occurring zeroes (and maxima) at intervals of λ/2.

A more complicated situation arises where a layer of lossy, dielectric material (such as rubber) is placed in front of the conductive plane. In this case, a portion of the incident wave is reflected by the dielectric layer, a portion is transmitted through the dielectric layer to the conductive plane where it is reflected, and a portion is effectively absorbed by the dielectric layer. The net result is that the reflected wave is substantially attenuated in amplitude, and is shifted in phase with respect to the incident beam. In this case, the reflection coefficient is a complex number related to the phase shift introduced by the dielectric layer. Since the reflected signal has a smaller amplitude than the incident signal, interference between the two signals does not produce a standing wave with zeroes, but rather produces a complex wave form having regularly occurring maxima and minima.

Turning to Fig. 8, a block diagram is provided for this embodiment. A signal generator 112 produces a microwave signal that is directed by a waveguide 114 through a small horn antenna in a direction normal to the exterior surface of the tire 120. The tire has a number of layers of rubber 121, 122, and 123 backed by conducting steel belts 124 within the tire casing. These layers of rubber 121, 122, and 123 may or may not be substantially different in compound. The purpose of the system is to measure the total thickness of the rubber layers 121, 122, and 123. Alternatively, this system can be adapted to other applications in which it is necessary to measure the thickness of a layer of dielectric material backed by a layer of conductive material.

As will be discussed below, the frequency of the microwave signal is one of the factors that can be selected to control the range of rubber layer thicknesses that can be measured without ambiguity. However, experimentation has shown that either the X-band (approximately 8 - 12 Gigahertz) or the C-band (approximately 4 GHz) can be employed for the range of rubber thicknesses commonly encountered in retreading most tires. In the preferred embodiment, the microwave signal generator 112 is a Gunn diode oscillator (e.g. for X-band applications) or a voltage controlled oscillator (e.g. for C-band applications). For operation in the X-band, a rectangular waveguide having cross-sectional dimensions of 2.26 cm by 1.03 cm and a length of approximately 6 inches has been found to operate satisfactorily in its dominant TE₁₀ mode.

The microwave signal propagates along the length of the waveguide 114 and is directed through a small horn antenna at the waveguide port toward the tire 120. The horn antenna is located a predetermined distance from the surface of the tire. Each of the layers of rubber 121, 122, and 123 acts as a lossy, dielectric material that transmits a portion of the microwave signal and reflects a portion of the signal back toward the waveguide 114. The cumulative effect of the rubber layers and steel belts is to produce an attenuated reflected signal which is shifted in phase from the incident signal. A portion of this reflected signal is picked up by the horn antenna and back propagates along the length of the waveguide 114. Interference between the transmitted signal and the reflected signal results in a standing wave pattern within the waveguide 114. Since both the transmitted and reflected signals have the same frequency, the standing wave will have recurring minimums at each half wavelength (i.e. the spacing between adjacent minimums will be λ/2). However, the locations of these minimums along the length of the waveguide will shift as a function of the phase difference between the transmitted and reflected signals.

In the illustrated embodiment, four coaxial probes 116 at predetermined positions along the length of the waveguide 114 permit four crystal detectors 118 to measure the amplitude of the standing wave voltage inside the waveguide 114. The crystal detectors 118 typically operate in their square law regions (i.e., output signal is proportional to the square of the standing wave voltage). Moreover, each of the detectors should be as close to identical in their characteristics as possible. The output signals from the crystal detectors 118 are amplified by an analog amplifier 132 and then digitized by an analog-to-digital convertor 134. The digitized signals can then be processed by a computer processor 136. The analog amplifier 132 and/or computer processor 136 can also be calibrated to compensate for any differences in the characteristics of the crystal detectors 118.

The computer processor 136 calculates the effective phase of the reflection coefficient by the voltages obtained from any three of the crystal detectors. The standing wave voltage at the location of the n^th probe is:

where V is the incident voltage, and Φ_n is the phase shift corresponding to the distance from the n^th probe to the tire and back. p and θ are amplitude and phase parameters respectively of the effective reflection coefficient of the tire. The phase θ of the reflection coefficient is the parameter to be determined by the computer processor 136.

Φ_n is calculated for each of the probes (n = 1, 2, and 3) on a one time basis as a function of the waveguide dimensions and the air gap between the waveguide port and the tire surface, as follows:

where d_n is the distance between the n^th probe and the waveguide port; λ_g is the guide wavelength; d_air is the distance between the waveguide port and the tire (i.e. the air gap); and λ_air is the wavelength in air (free space). Next, equation (4) can be expanded to relate the output of any three of the probes:

If the crystal detectors are operating in their square law regions, then their outputs will be proportional to V_n ². To further simplify the analysis, define S_n as Sin Φ_n and C_n as Cos Φ_n. Thus:

|V_n|² = C_n[2V²pcosθ] + S_n[2V²psinθ] + [V²(1+p²)] (7)

Calling the quantities inside the brackets A, B, and D respectively, and representing the left hand side as P_n (power is proportional to the square of voltage), equation (7) simplifies to: P_n= C_nA + S_nB +D (8)

where:

A = 2 V²pcosθ

B= 2 V²psinθ

(9)

D=V² (1 + p²)

P_n = |V_n|²

For the specific case of a three probe system (i.e. n = 1, 2, 3), this results in three simultaneous equations with three unknowns, namely A, B, and D: D+ C₁A + S₁B - P₁ = 0

D+ C₂A + S₂B- P₂ = 0 (10 )

D+ C₃A + S₃B- P₃ = 0

which can be solved as follows :

It should be noted that the set of equations (10) must be independent. This means that the spacing between each of the probes should not be a multiple of λ/2.

Finally, from equations (9), the phase θ of the reflection coefficient can be determined as a function of A and B, as follows:

The remaining parameters of the standing wave can also be determined as functions of A, B, and D, if desired:

The mathematics of this analysis is derived from the work done by R. Caldecott relating to measurement of reflection coefficients on electrical transmission lines. See,

Caldecott, The Generalized Multiprobe Reflectometer and Its Application to Automated Transmission Line Measurements

(IEEE Transactions on Antennas and Propagation, Vol AP-21,

No. 4, July 1973).

Fig. 9 shows a typical application of this sensor system to continually measure the thickness of the rubber layers on a rotating tire 160. Two spacing arms 150 cause the port of the waveguide 114 to ride at a substantially constant distance above the tire surface. The sensor assembly is mounted on and supported by a telescoping arm 140 which permits radial movement of the waveguide port in response to any variation in the tire radius. The arrangement shown in Fig. 9 can be used to provide continuous monitoring of the thickness of the rubber layers throughout the buffing process.

Fig. 10 is a graph showing theoretical calculation of the phase θ of the reflection coefficient as a function of rubber thickness (plus the air gap) at 9.515 GHz (X-band) with an air gap of 0.5 cm and a rubber permittivity of ∈_r = 16.31 - j2.33. Experimental results have been shown to closely follow these theoretical calculations. Fig. 10 shows that as the rubber thickness decreases the phase θ remains positive until the rubber thickness reaches approximately 2.1 mm (5 mm air gap + 2.1 mm rubber thickness = 7.1 mm), at which point the phase undergoes an abrupt change into negative values. This corresponds to the point at which the arctangent function in equation (9) undergoes phase reversal from 180 degrees to -180 degrees. The other relative minima shown to the right in Fig. 10 correspond to other phase reversals in the arctangent function which occur at regular spacing intervals of λ/2. Moving to the right in Fig. 10, each subsequent relative minima is progressively less severe, and only the initial minima at 7.1 mm actually results in a negative phase. Fig. 10 suggests that this phase reversal can be used to stop the buffing process, particularly when this phase reversal is made to occur at a rubber thickness prescribed by the operator (i.e. 0.100 inches) by adjusting the air gap between the waveguide port and the tire surface.

An additional improvement can be attained by selecting the wavelength of the microwave signal such that only one phase reversal occurs throughout the range of rubber thicknesses to be measured. For example, Fig. 11 provides a graph based on theoretical calculations of the phase θ of the reflection coefficient as a function of the rubber thickness at 4 GHz (C-band) with no air gap and a rubber permittivity of e = 12.5 - j2.5. Again, these theoretical calculations have been closely confirmed by experimental results. The longer wavelength at 4 GHz permits unambiguous measurement of the rubber thickness at all times during the buffing process by effectively eliminating the recurring minima found in Fig. 11 for the relevant range of rubber thicknesses.

Figs. 12 - 14 demonstrate how these two features can be combined both to provide a means for unambiguous measurement of the rubber thickness during the buffing process, and to provide a rapid phase reversal at a predetermined rubber thickness to trigger a halt to the buffing process. Fig. 12 shows the effect of variations in the air gap (19, 21, and 23 mm) on the phase of the reflection coefficient at 4 GHz (C-band), based on laboratory results. Fig. 13 is a graph showing actual measurements of the phase of the reflection coefficient as a function of rubber thickness at 4 GHz (C-band) with an air gap of 2.3 cm using a Michelin XZA-1 tire (DOT 347). Fig. 14 is a graph showing the phase of the reflection coefficient as a function of rubber thickness at 4 GHz (C-band) with an air gap of 2.1 cm for a Michelin 11R22.5XZY tire (DOT 105). In each of these examples, the air gap between the waveguide port and the tire surface is adjusted to cause a sharp phase reversal to occur at a predetermined rubber thickness, as depicted at the left side of Figs. 12 - 14. This air gap can either be determined by empirical testing or theoretical calculations using equations (11) and (10). To avoid the problems associated with recurring local minima as shown in Fig. 11, the wavelength should be long enough to have only one minima within the range of rubber thicknesses to be measured. As demonstrated in Figs. 12 - 14, the C-band (approximately 4 GHz) has been found to be satisfactory for many types of tires. The buffing process typically begins toward the right side of the curve (see Figs. 13 - 14u) and progresses along the curve toward the left as the thickness of the rubber layer is reduced by buffing. The curve provides an unambiguous measurement of the rubber layer thickness at each point, thereby enabling the operator to judge how rapidly to proceed with the buffing operation. At the point where the phase shifts to negative values, the desired rubber thickness has been reached and the buffing process is terminated. This rapid phase reversal can be used to generate a signal for the operator or can be sensed by a control system to automatically end the buffing process.

The above disclosure sets forth a number of embodiments of the present invention. Other arrangements or embodiments, not precisely set forth, could be practiced under the teachings of the present invention and as set forth in the following claims.

Claims

What is claimed is:

1. A microwave apparatus for one of detecting surface features of and determining dimensional information regarding an object including microwave reflective material, said apparatus comprising:

microwave source means for generating a first microwave signal;

microwave interaction means for receiving said first signal from said microwave source and receiving a second signal reflected by said object, wherein said first signal and said second signal interact within said interaction means to produce a standing wave; and

means for analyzing said standing wave for one of detecting surface features of and determining dimensional information regarding the object.

2. The apparatus of Claim 1, wherein said microwave interaction means comprises a waveguide.

3. The apparatus of Claim 1, wherein said microwave interaction means comprises a rectangular waveguide having an open end which is exposed to the object so as to receive said second signal reflected by the object.

4. The apparatus of Claim 1, wherein said means for analyzing comprises a sensor for sensing an electromagnetic property of said standing wave.

5. The apparatus of Claim 1, wherein said microwave interaction means comprises a waveguide having an open end and said means for analyzing comprises a sensor disposed a predetermined distance from said open end.

6. The apparatus of Claim 1, wherein said means for analyzing is operative for one of detecting and measuring a crack in a surface of the object.

7. The apparatus of Claim 1, wherein said microwave interaction means comprises a rectangular waveguide having a major wall of width a and a minor wall of height b, where a is greater than b, and said means for analyzing comprises a sensor extending from one of said major and minor walls.

8. The apparatus of Claim 1, wherein said means for analyzing comprises means for measuring a component of an electromagnetic field in said microwave interaction means, said component being aligned with one of two mutually orthogonal axes, each of said axes being transverse to a direction of propagation of said first signal through said microwave interaction means.

9. The apparatus of Claim 1, wherein said means for analyzing comprises:

means for sensing said standing wave and producing an output indicative of said standing wave;

means for monitoring said output over a time period corresponding to movement of said microwave interaction means relative to the object; and

means for using said monitored output for one of detecting surface features of and determining dimensional information regarding the object.

10. The apparatus of Claim 1, wherein said means for analyzing comprises:

means for monitoring changes in said standing wave relative to movement of said microwave interaction means; means for identifying a position of said microwave interaction means associated with an extremum value of said measured standing wave; and

means for using said identified position to determine dimensional information regarding the object.

11. The apparatus of Claim 1, wherein said means for analyzing is operative for determining a width of a surface crack in the object and comprises means for measuring a magnitude of said standing wave during a time period corresponding to movement of said microwave interaction means across said surface crack, identifying positions associated with two extrema of said magnitude measured during said time period, determining a distance between said identified positions, and using at least said determined distance and a dimension of said microwave interaction means to determine said width of said surface crack.

12. The apparatus of Claim 1, wherein said means for analyzing is operative for determining a depth of a surface crack in the object and comprises means for measuring said standing wave at at least one time during a time period corresponding to movement of said microwave interaction means across said surface crack and using said measurement obtained at said at least one time to determine said depth of said surface crack.

13. The apparatus of Claim 1, wherein said means for analyzing is operative for determining a reflection coefficient phase of said second signal.

14. An apparatus for use in detecting a surface crack in a surface, comprising:

a microwave source for transmitting a first microwave signal;

a waveguide having an open end positionable adjacent said surface, said waveguide being operative for receiving said first microwave signal therein and allowing said first microwave signal to propagate through said waveguide in a first direction towards said open end wherein said first signal is directed via said waveguide at said surface so as to impinge on said surface and reflect therefrom; and

a sensor for sensing an electromagnetic field component adjacent said open end of said waveguide, said component being transverse to said first direction.

15. The apparatus of Claim 14, further comprising means for orienting said waveguide relative to said surface such that said first direction is substantially normal to said surface.

16. The apparatus of Claim 14, wherein said sensor is disposed within said waveguide.

17. The apparatus of Claim 14, wherein said waveguide has a rectangular cross section defined by a major wall of width a and a minor wall of height b, where a is greater than b, and said sensor extends from said minor wall.

18. The apparatus of Claim 14, wherein said waveguide has a rectangular cross-section defined by a pair of opposing major walls of width a and a pair of opposing minor walls of height b, where a is greater than b, and said sensor is disposed a distance b/6 from one of said major walls.

19. A method for use in one of detecting and measuring a crack in a metallic surface, comprising the steps of:

generating a first microwave signal;

reflecting said first signal off of said metallic surface, thereby producing a second signal;

receiving said first signal and said second signal within a waveguide, wherein said first signal and said second signal interact within said waveguide to produce a third signal;

scanning said waveguide across said crack; and monitoring said third signal during said step of scanning.

20. The method of Claim 19, wherein said step of monitoring comprises providing a sensor within said waveguide and recording an output of said sensor during said step of scanning.

21. The method of Claim 19, wherein said step of monitoring includes:

storing received information regarding said third signal; and

analyzing said stored information to determine a size of said crack.

22. The method of Claim 19, wherein said step of monitoring includes determining a width of the crack by measuring a magnitude of said third signal during said step of scanning, identifying positions associated with two extrema of said magnitude measured during said step of scanning, determining a distance between said identified positions, and using at least said determined distance and a dimension of said waveguide to determine the width of the crack.

23. The method of Claim 19, wherein said step of monitoring includes determining a depth of the crack by measuring the third signal at at least one time during said step of scanning and using said measurement obtained at said at least one time to determine the depth of the crack.