Bearing steel ball defect detection method and system combining eddy current and ultrasonic testing

Abstract

This invention relates to the field of bearing steel ball defect detection technology, and discloses a method and system for bearing steel ball defect detection combining eddy current and ultrasonic testing. The method includes: first, acquiring the eddy current impedance plane trajectory and ultrasonic A-scan waveform during the continuous rolling process of the bearing steel ball, obtaining preliminary estimates of the eddy current and ultrasonic defect depths respectively, and using these estimates to invert the hardness gradient parameter set of the current bearing steel ball; then, reconstructing the conductivity distribution function and sound velocity distribution function based on the hardness gradient parameter set, performing gradient correction on the preliminary estimates of the eddy current and ultrasonic defect depths to obtain the true defect depth value, and combining this with the designed hardened layer depth to perform a three-level defect classification judgment. This invention can eliminate the dual-modal depth positioning deviation caused by the material radial gradient, achieving high-precision detection and classification judgment of bearing steel ball defect depth.

Description

Technical Field

[0001] This invention relates to the field of bearing steel ball defect detection technology, specifically to a bearing steel ball defect detection method and system that combines eddy current and ultrasonic testing. Background Technology

[0002] With the development of the precision machinery and energy equipment industry, bearing steel balls, as the core basic components of rotating machinery, play a crucial role in ensuring the reliability of equipment operation through surface and near-surface quality inspection. Especially in high-load applications such as large wind turbine bearings, accurate quantitative assessment of defect depth has become an important means of controlling failure rates.

[0003] Among existing nondestructive testing technologies, Chinese patent CN103376290B discloses an eddy current testing method and an eddy current testing device. This technology arranges reference signals at specific locations and adjusts their amplitudes to make the synthesized signal consistent with the actual defect signal, thereby using the amplitude adjustment value to evaluate the defect depth.

[0004] However, for bearing steel balls treated with quenching and low-temperature tempering, a continuous hardness gradient distribution forms inside, from the high-carbon martensite on the surface to the sorbite in the core. Due to the non-uniform evolution of material physical properties with radial depth, this gradient structure produces a nonlinear distortion with opposite properties in the inversion of the detected physical quantities: the increasing conductivity from the surface to the core (martensite has higher resistivity than sorbite) causes the phase angle of the eddy current impedance signal to change more gradually with depth, resulting in a compression of the slope of the phase-depth relationship and a systematic underestimation of the defect depth; while the decreasing sound velocity from the surface to the core (martensite has higher elastic modulus than sorbite) increases the propagation time of the ultrasonic waves, leading to a systematic overestimation of the depth value calculated based on the time of flight. In the transition zone between the hardened layer and the core, the rates of change of conductivity and sound velocity are in extreme ranges, causing significant deviations in the depth determination results of the same defect by the two detection methods. Furthermore, this deviation is affected by fluctuations in the heat treatment process and is difficult to compensate for using static coefficients. This "deep tearing" phenomenon causes the detection system to be unable to make a definitive depth determination in the transition zone where defects are frequent. This not only leads to misjudgment of the workpiece, but also poses a risk of missing high-risk defects due to the selection of incorrect depth values. Summary of the Invention

[0005] To overcome the aforementioned shortcomings of existing technologies, this invention provides a method and system for detecting defects in bearing steel balls that combines eddy current and ultrasonic testing. By simultaneously acquiring the eddy current impedance plane trajectory and ultrasonic A-scan waveform of the bearing steel ball, the individual hardness gradient parameters of the bearing steel ball are inverted using the preliminary depth determination results of the two modes. Furthermore, the radially non-uniform conductivity distribution function and sound velocity distribution function are reconstructed to correct physical field propagation deviations. This invention achieves accurate extraction and three-level classification of the true depth of defects under complex gradient medium constraints, eliminating multi-modal depth positioning conflicts caused by radial non-uniformity of the material. It provides reliable quantitative data support for batch consistency evaluation and feedback optimization of heat treatment processes.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for detecting defects in bearing steel balls combining eddy current and ultrasonic testing includes:

[0008] The eddy current impedance plane trajectory and ultrasonic A-scan waveform of the bearing steel ball during continuous rolling process are obtained in the bearing steel ball rolling test production line. Based on the eddy current impedance plane trajectory, a preliminary estimate of the eddy current defect depth is obtained. Based on the ultrasonic A-scan waveform, a preliminary estimate of the ultrasonic defect depth is obtained. Based on the preliminary estimate of the eddy current defect depth and the preliminary estimate of the ultrasonic defect depth, the hardness gradient parameter set of the current bearing steel ball is inverted.

[0009] The conductivity distribution function and sound velocity distribution function of the current bearing steel ball are reconstructed based on the hardness gradient parameter set. The preliminary estimated values ​​of eddy current defect depth and ultrasonic defect depth are obtained by gradient correction based on the conductivity distribution function and sound velocity distribution function, respectively. The design hardened layer depth of the current batch of bearing steel balls is obtained. The three-level defect classification is performed based on the actual defect depth value and the design hardened layer depth.

[0010] The method for obtaining the eddy current impedance plane trajectory includes:

[0011] A first time reference triggering device is set up at the eddy current flaw detection station of the bearing steel ball rolling inspection production line. When the bearing steel ball passes through the eddy current probe, the first time reference triggering device generates a first trigger signal. The time corresponding to the first trigger signal generated by the first time reference triggering device is recorded as the eddy current detection time reference. Starting from the eddy current detection time reference, the eddy current impedance signal output by the eddy current probe is continuously collected.

[0012] Extract the real and imaginary components of the impedance from the eddy current impedance signal, and construct the eddy current impedance plane trajectory with the real component as the x-axis and the imaginary component as the y-axis.

[0013] The method for calculating the preliminary estimate of the eddy current defect depth includes:

[0014] Identify abnormal offsets from the eddy current impedance plane trajectory, calculate the phase angle of the abnormal offset, record the eddy current anomaly timestamp of each abnormal offset occurrence relative to the eddy current detection time reference, and calculate a preliminary estimate of the eddy current defect depth based on the phase angle of the abnormal offset.

[0015] The method for acquiring the ultrasound A-scan waveform includes:

[0016] An ultrasonic testing station is deployed downstream of the eddy current testing station, equipped with an ultrasonic probe and a second time reference triggering device. When the same bearing steel ball passes the ultrasonic probe, the second time reference triggering device generates a second trigger signal. The time corresponding to the second trigger signal generated by the second time reference triggering device is recorded as the ultrasonic testing time reference, and ultrasonic echo signals are collected from the ultrasonic testing time reference.

[0017] An ultrasound A-scan waveform is constructed based on the ultrasound echo signal, wherein the horizontal axis of the ultrasound A-scan waveform represents the flight time of the ultrasound echo signal, and the vertical axis represents the echo amplitude of the ultrasound echo signal.

[0018] The method for calculating the preliminary estimate of the ultrasonic defect depth includes:

[0019] Abnormal echoes are identified from the ultrasonic A-scan waveform. The ultrasonic abnormality timestamp relative to the ultrasonic detection time reference is recorded. The flight time corresponding to the abnormal echo is read from the horizontal axis of the ultrasonic A-scan waveform. The preliminary estimate of the ultrasonic defect depth is calculated based on the flight time of the abnormal echo according to the time-depth relationship.

[0020] The method for inverting the current hardness gradient parameter set of the bearing steel balls includes:

[0021] Determine whether the abnormal offset and abnormal echo originate from the same defect. If they do, establish a dual-mode paired record that includes the preliminary estimate of the depth of the eddy current defect and the preliminary estimate of the depth of the ultrasonic defect.

[0022] Preliminary estimates of eddy current defect depth and ultrasonic defect depth are extracted from the dual-modal paired records. The preliminary estimate of eddy current defect depth is subtracted from the preliminary estimate of ultrasonic defect depth to obtain the depth deviation value. The hardness gradient parameter set is inverted based on the depth deviation value. The hardness gradient parameter set includes the center depth of the transition zone and the width of the transition zone.

[0023] The method for determining whether abnormal offset and abnormal echo originate from the same defect includes:

[0024] Calculate the ultrasonic anomaly timestamp and spherical angle resolution window after time offset compensation. Compare the eddy current anomaly timestamp with the ultrasonic anomaly timestamp after time offset compensation one by one. When the absolute difference between the two is less than the spherical angle resolution window, it is determined that the corresponding anomaly offset and anomaly echo originate from the same defect.

[0025] The calculation method for the ultrasonic anomaly timestamp and spherical angle resolution window after time offset compensation is as follows:

[0026] The probe spacing between the eddy current probe and the ultrasonic probe along the direction of the bearing steel ball rolling detection production line is obtained. The rolling linear velocity of the bearing steel ball on the bearing steel ball rolling detection production line is measured. The time offset is obtained by dividing the probe spacing by the rolling linear velocity.

[0027] Obtain the diameter of the bearing steel ball, add the time offset to the ultrasonic anomaly timestamp to obtain the time offset compensated ultrasonic anomaly timestamp, and calculate the spherical angular resolution window based on the ball diameter and rolling linear velocity.

[0028] The gradient correction execution method includes:

[0029] Along the radial direction of the bearing steel ball, the depth range from the surface to the preset maximum detection depth is divided into multiple conductivity depth thin layers according to the conductivity distribution function. The phase angle increment of each conductivity depth thin layer is calculated, and the phase angle increment of each conductivity depth thin layer is accumulated to establish a phase angle depth lookup table. The abnormally offset phase angle in the eddy current impedance plane trajectory is found in the phase angle depth lookup table to obtain the eddy current defect depth correction value.

[0030] The method for determining the true depth value of the defect is as follows:

[0031] The absolute difference between the depth correction value of the eddy current defect and the depth correction value of the ultrasonic defect is calculated as the depth correction residual. The relationship between the depth correction residual and the preset convergence threshold and warning threshold is determined to determine the true depth value of the defect.

[0032] The method for determining the three levels of execution defects includes:

[0033] Calculate the safety margin depth based on the design hardened layer depth and the safety margin ratio;

[0034] The actual depth of the defect is compared with the safety margin depth and the designed hardened layer depth to perform a three-level classification judgment, and the result of the three-level classification judgment is qualified, requires re-inspection, or is unqualified.

[0035] A bearing steel ball defect detection system combining eddy current and ultrasonic testing, used to implement the aforementioned bearing steel ball defect detection method combining eddy current and ultrasonic testing, the system comprising:

[0036] The gradient parameter inversion module is used to obtain the eddy current impedance plane trajectory and ultrasonic A-scan waveform of the bearing steel ball during continuous rolling in the bearing steel ball rolling inspection production line. Based on the eddy current impedance plane trajectory, a preliminary estimate of the eddy current defect depth is obtained. Based on the ultrasonic A-scan waveform, a preliminary estimate of the ultrasonic defect depth is obtained. Based on the preliminary estimate of the eddy current defect depth and the preliminary estimate of the ultrasonic defect depth, the hardness gradient parameter group of the current bearing steel ball is inverted.

[0037] The depth correction and classification module reconstructs the conductivity distribution function and sound velocity distribution function of the current bearing steel ball based on the hardness gradient parameter group. Based on the conductivity distribution function and sound velocity distribution function, it performs gradient correction on the preliminary estimated values ​​of eddy current defect depth and ultrasonic defect depth to obtain the true defect depth value. It obtains the design hardened layer depth of the current batch of bearing steel balls and performs a three-level defect classification judgment based on the true defect depth value and the design hardened layer depth.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] This invention obtains preliminary estimates of eddy current impedance plane trajectory and ultrasonic A-scan waveform during the continuous rolling process of a bearing steel ball in a rolling inspection production line. These preliminary estimates yield preliminary values ​​for eddy current defect depth and ultrasonic defect depth, respectively. The hardness gradient parameter set for a single bearing steel ball is then derived from these two preliminary estimates. This allows for non-destructive in-situ characterization of the radial hardness gradient distribution of the bearing steel ball, matching the actual heat treatment gradient state of a single steel ball without relying on batch-fixed correction parameters. Based on the hardness gradient parameter set, the corresponding conductivity distribution function and sound velocity distribution function are reconstructed, further refining the preliminary estimates of eddy current defect depth and ultrasonic defect depth. Gradient correction of the preliminary depth estimate can correct the systematic bias caused by depth inversion based on the assumption of homogeneous materials, so that the depth results obtained by the two detection methods converge to the true depth value of the defect. This solves the problem of inconsistency between the preliminary depth estimates of eddy current defects and ultrasonic defects in the transition zone between the hardened layer and the core. Combined with the design hardened layer depth of the current batch of bearing steel balls, a three-level classification judgment is performed on the defects, providing a reliable depth basis for the assessment of the degree of defect danger. This realizes the standardized classification judgment of defects and provides quantifiable depth data support for the quality control and full life cycle traceability of bearing steel balls. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 A flowchart illustrating a method for detecting defects in bearing steel balls using a combination of eddy current and ultrasonic testing.

[0042] Figure 2 This is a schematic diagram of the radial material gradient distribution of the bearing steel balls provided in an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of the dual-station layout of the bearing steel ball rolling detection production line in this invention;

[0044] Figure 4 This is a schematic diagram illustrating the convergence of eddy current and ultrasonic defect depth correction in this invention;

[0045] Figure 5 This is a flowchart of the three-level hierarchical determination logic in this invention;

[0046] Figure 6 This is a functional module diagram of a bearing steel ball defect detection system that combines eddy current and ultrasonic testing. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] Example 1

[0049] Please see Figure 1 As shown, this embodiment provides a method for detecting defects in bearing steel balls by combining eddy current and ultrasonic testing, including:

[0050] Step S10: Obtain the eddy current impedance plane trajectory and ultrasonic A-scan waveform of the bearing steel ball during continuous rolling process in the bearing steel ball rolling test production line. Based on the eddy current impedance plane trajectory, obtain a preliminary estimate of the eddy current defect depth. Based on the ultrasonic A-scan waveform, obtain a preliminary estimate of the ultrasonic defect depth. Based on the preliminary estimate of the eddy current defect depth and the preliminary estimate of the ultrasonic defect depth, invert the hardness gradient parameter set of the current bearing steel ball.

[0051] Specifically, see Figure 2This is a schematic diagram of the radial material gradient distribution of a bearing steel ball. The diagram shows the layered structure of the bearing steel ball from the surface to the center along the radial direction, as well as the corresponding microstructure, electrical conductivity, sound velocity, and hardness characteristics of each region. After heat treatment, the bearing steel ball, such as the yaw bearing steel ball for wind power generation (diameter 45 to 90 mm), exhibits a significant gradient distribution of material structure along the radial direction. From the surface to the center, it is divided into three regions: surface martensite, transition zone, and core sorbite. The surface region forms a high-carbon martensite structure, while the core region retains a sorbite structure. The electrical conductivity and sound velocity of the two structures differ. The martensite structure, due to its high carbon content and high hardness, exhibits low electrical conductivity, high sound velocity, and high hardness, while the sorbite structure exhibits the opposite characteristics of high electrical conductivity, low sound velocity, and low hardness. In the transition zone between the two, the electrical conductivity and sound velocity show a continuous and gradual change along the radial direction. The depth localization mechanisms of eddy current testing and ultrasonic testing rely on the material's electrical conductivity and sound velocity, respectively. When both methods measure the depth of the same defect, the depth readings derived from the assumption of a homogeneous material will exhibit systematic biases due to the radial gradient distribution of material properties. Eddy current depth measurement is underestimated due to the low electrical conductivity of the surface layer, while ultrasonic depth measurement is overestimated due to the high sound velocity at the surface layer. Traditional testing methods treat this difference in dual-modal depth readings as measurement error and attempt to eliminate or average it, effectively abandoning the material gradient information implicit in the difference. Step S10 establishes a time reference synchronization mechanism between the eddy current testing station and the ultrasonic testing station. By combining the kinematic relationship of the revolution and rotation of the bearing steel ball during the rolling process of the bearing steel ball rolling testing production line, the abnormal features in the eddy current impedance signal and the ultrasonic echo signal are accurately paired. This ensures that the preliminary estimated value of the eddy current defect depth and the preliminary estimated value of the ultrasonic defect depth can accurately correspond to the same defect location. Furthermore, the hardness gradient parameter set characterizing the current heat treatment state of the bearing steel ball is derived from the depth deviation value between the two. The depth deviation value, which was originally regarded as an interference factor, is transformed into a quantifiable material information carrier.

[0052] The eddy current impedance plane trajectory refers to the movement trajectory of an impedance point as it changes during the detection process on a two-dimensional plane, with the real component of the eddy current probe's output impedance signal as the abscissa and the imaginary component as the ordinate. When cracks, inclusions, or structural abnormalities exist on or near the surface of the bearing steel ball, the normal distribution of eddy currents is disturbed, and the impedance value of the eddy current probe deviates from the reference impedance point corresponding to a normal bearing steel ball, forming a identifiable abnormal offset. There is a correlation between the phase angle of the abnormal offset on the eddy current impedance plane and the defect depth; the larger the phase angle, the deeper the defect. This relationship stems from the skin effect principle of eddy currents. As the eddy current penetrates from the surface of the bearing steel ball inward, a phase delay accumulates, with deeper defects corresponding to a larger phase accumulation. The ultrasonic A-scan waveform is a one-dimensional waveform diagram with the flight time of the ultrasonic echo as the abscissa and the echo amplitude as the ordinate. The flight time reflects the path integration time of the ultrasonic pulse from the surface of the bearing steel ball to the defect location and back, while the echo amplitude reflects the reflection intensity at the defect interface. When the relationship between flight time and the material's sound velocity is known, the flight time can be converted into defect depth. The hardness gradient parameter set includes two parameters: the center depth of the transition zone and the width of the transition zone. The center depth of the transition zone represents the depth at the intermediate position where the hardness transitions from the surface martensite to the core sorbite, while the width of the transition zone represents the depth range where the hardness change is most drastic. These two parameters together determine the shape of the radial hardness distribution curve of the current bearing steel ball. Step S10 provides a dual-modal paired record and a hardness gradient parameter set for reconstructing the material property distribution for the subsequent gradient correction and defect classification in step S20. The preliminary estimates of the eddy current defect depth and the preliminary estimates of the ultrasonic defect depth contained in the dual-modal paired record serve as the objects to be corrected in the gradient correction in step S20. If the time reference synchronization and spatial position registration operation in step S10 is missing, a certain abnormal offset in the eddy current impedance signal and a certain abnormal echo in the ultrasonic echo signal will not be able to establish a correspondence, and the subsequent calculation of the dual-mode depth deviation value based on the same defect will lose its physical meaning; if the inversion operation of the hardness gradient parameter group is missing, the reconstruction of the conductivity distribution function and the sound velocity distribution function in step S20 will lack input parameters, and the depth correction will not be able to be personalized for the actual heat treatment state of the current bearing steel ball.

[0053] Further, step S10 includes:

[0054] Step S11: Set up a first time reference triggering device at the eddy current flaw detection station of the bearing steel ball rolling inspection production line. When the bearing steel ball passes through the eddy current probe, the first time reference triggering device generates a first trigger signal. Record the time corresponding to the first trigger signal generated by the first time reference triggering device as the eddy current detection time reference. Start from the eddy current detection time reference and continuously collect the eddy current impedance signal output by the eddy current probe.

[0055] See Figure 3, is a schematic diagram of the double-station layout of the bearing steel ball rolling detection production line. The figure shows the eddy current flaw detection station and the ultrasonic flaw detection station arranged in sequence along the rolling direction of the bearing steel ball rolling detection production line, the probe spacing between the two stations, the detection probes and the time reference trigger devices supporting each station, and at the same time marks the rolling direction of the bearing steel ball and the lift-off distance between the probe and the steel ball. The bearing steel ball rolling detection production line refers to an automated detection production line in which the bearing steel balls continuously roll along a preset path in the rolling direction marked in the figure under the action of gravity and track constraints and pass through each detection station in sequence. The movement of the bearing steel balls on the bearing steel ball rolling detection production line includes two components: the revolution movement and the rotation movement. The revolution movement is manifested as the displacement of the bearing steel balls along the direction of the bearing steel ball rolling detection production line, and the rotation movement is manifested as the rotation of the bearing steel balls around their own axes. The coupling of the two movements makes any point on the surface of the bearing steel balls depict a complex spiral trajectory in space. As Figure 3 shown, the eddy current flaw detection station is located at the upstream position of the bearing steel ball rolling detection production line, equipped with an eddy current probe and a first time reference trigger device. The detection surface of the eddy current probe faces the track area where the bearing steel balls roll over and maintains the preset lift-off distance marked in the figure from the surface of the bearing steel balls. The lift-off distance refers to the air gap distance between the detection surface of the eddy current probe and the surface of the detected workpiece. The setting of the lift-off distance needs to balance the detection sensitivity and mechanical avoidance. Too small a lift-off distance will cause mechanical collision between the bearing steel balls and the probe, and too large a lift-off distance will cause a decrease in the excitation intensity of the eddy current, thus reducing the detection sensitivity.

[0056] The first time reference trigger device is implemented by an optoelectronic switch or a proximity switch. The optoelectronic switch consists of a transmitting end and a receiving end. When the bearing steel ball rolls into the detection area between the transmitting end and the receiving end, the light path is blocked, thus generating an electrical signal. The proximity switch generates an electrical signal by detecting the influence of the metal body of the bearing steel ball on the impedance of the probe coil. As Figure 3 shown, the first time reference trigger device is installed at a preset position directly below the eddy current probe. When the geometric center of the bearing steel ball coincides with the detection center axis of the eddy current probe, the first time reference trigger device generates a first trigger signal, and the first trigger signal is recorded by the control unit of the detection system as the eddy current detection time reference. The eddy current detection time reference serves as the reference zero point for the subsequent timing recording of the eddy current impedance signal, making all the eddy current impedance signals collected at the same detection station have a unified time coordinate origin, providing a reference condition for time alignment with the signals of the ultrasonic flaw detection station.

[0057] Starting from the eddy current detection time reference, the detection system continuously acquires the eddy current impedance signal output by the eddy current probe at a preset eddy current sampling frequency. The setting of the eddy current sampling frequency must meet the requirements of the Nyquist sampling theorem, that is, the eddy current sampling frequency is greater than twice the highest frequency component in the eddy current impedance signal to avoid aliasing distortion. The eddy current impedance signal is obtained through an impedance analysis circuit. The eddy current probe acts as the inductive element of the resonant circuit. When the eddy current distribution on the surface of the bearing steel ball changes, the equivalent impedance of the eddy current probe changes accordingly. The impedance analysis circuit converts this change into a digitally acquireable voltage signal. The eddy current probe emits an alternating electromagnetic field onto the surface of the bearing steel ball. The frequency of the alternating electromagnetic field is set by the excitation source. The choice of excitation frequency affects the skin depth of the eddy current. High-frequency excitation corresponds to shallow detection, and low-frequency excitation corresponds to deep detection. Eddy current detection of yaw bearing steel balls in wind power generation typically uses mid-to-low frequency excitation frequencies to cover the depth range of the hardened layer and transition zone. High-frequency excitation refers to the frequency range with an excitation frequency higher than 1MHz. High-frequency excitation produces a smaller skin depth, corresponding to shallow detection, and is suitable for detecting surface defects with a depth of less than 0.5 mm. Low-frequency excitation refers to the frequency range with an excitation frequency lower than 100kHz. Low-frequency excitation produces a larger skin depth, corresponding to deep detection, and is suitable for detecting deep defects with a depth of several millimeters. Mid-low frequency band refers to the frequency range with an excitation frequency between 100kHz and 500kHz. Eddy current detection of yaw bearing steel balls in wind turbine generators usually uses mid-low frequency band excitation frequencies to cover the depth range of the hardened layer and transition zone. The skin depth produced by mid-low frequency band excitation is usually between 1 mm and 5 mm, which can cover the sum of the hardened layer depth and the transition zone depth of the yaw bearing steel balls in wind turbine generators. Alternating electromagnetic fields induce eddy currents on the surface of bearing steel balls. The distribution density of eddy currents is related to the electrical conductivity of the material. Martensite exhibits lower electrical conductivity due to its high carbon content and high hardness, resulting in stronger eddy current retraction within the martensite layer and a correspondingly increased skin depth. Conversely, sorbite exhibits higher electrical conductivity due to its lower carbon content and lower hardness, leading to a correspondingly smaller skin depth for eddy currents within the sorbite layer.

[0058] The technical means of setting up the first time reference triggering device in step S11 enables the timing record of the eddy current impedance signal to have a repeatable absolute time reference, rather than relying solely on the relative timing relationship of the signals. The direct effect of this technique is to establish a time synchronization link between the eddy current testing station and the testing system control unit, allowing the time of each eddy current impedance signal sampling point to be accurately expressed as the time difference relative to the eddy current testing time reference. Based on this, when the same bearing steel ball moves to the downstream ultrasonic flaw detection station, the time reference information left by the same bearing steel ball at the eddy current flaw detection station can be associated with the time reference information of the ultrasonic flaw detection station, thereby achieving cross-station time alignment. This is a prerequisite for the dual-mode signal pairing in the subsequent step S18. Without a first time reference triggering device, the acquisition of eddy current impedance signals will start from any time. The eddy current impedance signals between different bearing steel balls will not be able to establish a unified time coordinate system. The calculation of time offset in step S16 and the comparison of eddy current abnormal timestamp with ultrasonic abnormal timestamp after time offset compensation in step S18 will lose their physical meaning, and accurate pairing of dual-mode signals will not be possible.

[0059] Step S12: Extract the real and imaginary components of the impedance from the eddy current impedance signal, and construct the eddy current impedance plane trajectory with the real component of the impedance as the abscissa and the imaginary component of the impedance as the ordinate.

[0060] Specifically, as an AC signal, a complete description of eddy current impedance signals requires information in both amplitude and phase dimensions, or equivalently, a combination of real and imaginary components. The real impedance component corresponds to the resistive component of the eddy current probe impedance, which is related to the energy loss of the eddy current in the bearing steel ball material. Changes in the conductivity of the bearing steel ball material directly affect the magnitude of the real impedance component. The imaginary impedance component corresponds to the reactive component of the eddy current probe impedance, which is related to the change in the inductance of the eddy current probe. The permeability distribution of the bearing steel ball and the magnetic field reaction of the eddy current affect the magnitude of the imaginary impedance component. The extraction of the real and imaginary impedance components from the eddy current impedance signal is achieved through quadrature demodulation circuits or digital lock-in amplification technology. The quadrature demodulation circuit mixes the eddy current impedance signal with reference signals of the same frequency and phase, and reference signals of the same frequency and quadrature phase, respectively. After low-pass filtering, the DC levels of the real and imaginary impedance components are obtained. Digital lock-in amplification technology performs equivalent operations in the digital domain, offering higher resolution and stronger anti-interference capabilities.

[0061] The eddy current impedance plane is a two-dimensional plane constructed with the real component of impedance as the abscissa and the imaginary component of impedance as the ordinate. Each point on the eddy current impedance plane corresponds to the impedance state of the eddy current probe at a certain detection moment. When a defect-free bearing ball passes through the eddy current probe, the eddy current impedance signal traces a narrow trajectory centered on the reference impedance point on the eddy current impedance plane. The width of the narrow trajectory reflects the noise level of the eddy current impedance signal and slight changes in the surface roughness of the bearing ball. When a defective bearing ball passes through the eddy current probe, the local change in conductivity in the defect area leads to disordered eddy current distribution. The eddy current impedance signal exhibits an abnormal deviation from the reference impedance point on the eddy current impedance plane. The direction and amplitude of this abnormal deviation carry characteristic information about the defect. The reference impedance point is obtained by statistically averaging the eddy current impedance signals of a large number of defect-free standard bearing balls, characterizing the typical impedance state of a normal bearing ball under the current detection parameters.

[0062] The construction of the eddy current impedance plane trajectory transforms the analysis of the eddy current impedance signal from the time domain to the impedance plane domain. While the time-domain signal only reflects the temporal evolution of impedance changes, the impedance plane trajectory can simultaneously present the amplitude and phase information of impedance changes. Visualizing the two-dimensional complex information of the eddy current impedance signal in a geometric form allows for the determination of defect presence and depth estimation to be completed within the same graphical representation. Based on this, the extraction of the abnormal offset phase angle in step S13 can be directly achieved on the eddy current impedance plane through vector angle measurement, without the need for complex phase calculations of the time-domain waveform, simplifying the subsequent calculation process for the preliminary estimate of the eddy current defect depth. The eddy current impedance plane trajectory also has the ability to compensate for changes in lift-off distance. When the lift-off distance fluctuates slightly, the direction of movement of the eddy current impedance trajectory on the eddy current impedance plane differs from the abnormal offset direction caused by the defect. By setting a reasonable discrimination direction threshold, the two influences can be distinguished, improving the stability of defect detection.

[0063] Step S13: Identify abnormal offsets from the eddy current impedance plane trajectory, calculate the phase angle of the abnormal offsets, record the eddy current abnormal timestamp of each abnormal offset occurrence time relative to the eddy current detection time reference, and calculate the preliminary estimate of the eddy current defect depth based on the phase angle of the abnormal offsets.

[0064] Specifically, abnormal offset identification employs a distance threshold method. This method calculates the Euclidean distance between each sampling point on the eddy current impedance plane trajectory and the reference impedance point. When the Euclidean distance exceeds a preset anomaly threshold, the current sampling point is determined to have an abnormal offset. The anomaly threshold is set based on the statistical distribution of the eddy current impedance signal of a defect-free standard bearing steel ball, typically taken as several times the standard deviation of the noise distribution around the reference impedance point. For example, the anomaly threshold can be set to three times the standard deviation, ensuring that the false alarm probability of the defect-free bearing steel ball is controlled below 3‰.

[0065] The phase angle of the abnormal offset is defined as the angle between the vector pointing from the reference impedance point to the abnormal offset point and the positive direction of the horizontal axis of the eddy current impedance plane. The phase angle is calculated using the arctangent function, with the input being the difference between the imaginary and real impedance components between the abnormal offset point and the reference impedance point. The relationship between the phase angle and the defect depth originates from the skin effect of eddy currents. When eddy currents penetrate from the surface of the bearing steel ball into the interior, they experience a continuous phase delay. The amount of delay is related to the conductivity of the bearing steel ball material, the excitation frequency, and the penetration depth. Under the assumption of uniform bearing steel ball material, the phase angle and the penetration depth have an approximately linear relationship. This relationship can be expressed as the phase angle equals the depth multiplied by the phase depth coefficient, and the phase depth coefficient equals the reciprocal of the skin depth. The formula for calculating the skin depth is the reciprocal of the square root of the product of the excitation frequency, the permeability of the bearing steel ball material, and the conductivity of the bearing steel ball material, multiplied by pi. That is, the skin depth equals the square root of the product of 1 divided by pi multiplied by the excitation frequency multiplied by the permeability multiplied by the conductivity, and the phase depth coefficient equals the square root value itself. The preliminary estimate of eddy current defect depth is calculated by substituting the abnormal offset phase angle into the phase-depth relationship to inversely solve for the depth. The phase-depth relationship is a well-known formula derived in the field of eddy current testing based on the skin effect principle. The principle of the phase-depth relationship is as follows: when eddy currents penetrate from the surface of a bearing steel ball inwards, the eddy current density decreases exponentially along the depth direction, accompanied by a continuous phase delay. Under the assumption of homogeneous materials, the phase delay is proportional to the penetration depth, and the proportionality coefficient is the reciprocal of the skin depth. The phase-depth relationship is expressed as: defect depth equals the abnormal offset phase angle multiplied by the skin depth, where the skin depth is equal to the square root of the product of 1 divided by pi, the excitation frequency, the material's magnetic permeability, and the material's electrical conductivity. By substituting the abnormal offset phase angle into the phase-depth relationship and dividing the abnormal offset phase angle by the phase-depth coefficient, the defect depth value can be obtained by inverse solving. The phase-depth coefficient is equal to the reciprocal of the skin depth. Because the phase depth formula is derived based on the assumption of uniform material of the bearing steel ball, while the actual bearing steel ball has a radial conductivity gradient distribution, the preliminary estimate of the eddy current defect depth is a distorted depth value without gradient correction, and is systematically lower than the true depth of the defect. The recording of eddy current anomaly timestamps binds each anomaly offset to the time difference between its occurrence and the eddy current detection time reference. The eddy current anomaly timestamp characterizes the time difference between the moment the defect is detected when it passes through the eddy current probe detection area and the eddy current detection time reference. This time difference is related to the angular position of the defect on the spherical surface and the rolling linear velocity of the bearing steel ball. The accuracy of the eddy current anomaly timestamp depends on the eddy current sampling frequency; the higher the eddy current sampling frequency, the higher the temporal resolution of the eddy current anomaly timestamp. For multiple closely spaced defects on the same bearing steel ball surface, high temporal resolution eddy current anomaly timestamps can achieve independent identification and differentiation of multiple defects.When there are multiple abnormal offsets in the eddy current impedance plane trajectory of the same bearing steel ball, the eddy current abnormal timestamps corresponding to each abnormal offset are arranged in chronological order to form an eddy current abnormal timestamp set. The eddy current abnormal timestamp set records the time location information of all defects detected by the eddy current detection method on the current bearing steel ball.

[0066] In step S13, the simultaneous extraction of the eddy current anomaly timestamp and the preliminary estimate of the eddy current defect depth ensures that each detected anomaly carries features in two dimensions: time location information and depth location information. The time location information is used for pairing and matching with the ultrasonic echo signal in subsequent step S18, and the depth location information is used to calculate the depth deviation value in step S19. Structured defect feature data is extracted from the eddy current impedance plane trajectory, converting the continuous graphic trajectory into a discrete set of feature points, facilitating subsequent data processing and correlation analysis. If the eddy current anomaly timestamp record is missing, the time alignment of the eddy current impedance signal and the ultrasonic echo signal in step S18 will lack a pairing basis; if the preliminary estimate of the eddy current defect depth is missing, the acquisition of the depth deviation value in step S19 cannot be performed, and the inversion of the hardness gradient parameter set will lose input data.

[0067] Step S14: Deploy an ultrasonic testing station downstream of the eddy current testing station, configure an ultrasonic probe and a second time reference triggering device. When the same bearing steel ball passes the ultrasonic probe, the second time reference triggering device generates a second trigger signal. Record the time corresponding to the second trigger signal generated by the second time reference triggering device as the ultrasonic testing time reference, and start collecting ultrasonic echo signals from the ultrasonic testing time reference.

[0068] Specifically, such as Figure 3 As shown, the ultrasonic testing station is located downstream of the eddy current testing station. The probe spacing, as indicated in the diagram, exists between the two stations along the bearing ball rolling inspection production line. The probe spacing must consider both the physical spatial layout of the testing stations and the rotation angle of the bearing ball during its movement from the eddy current testing station to the ultrasonic testing station. Too small a probe spacing can lead to electromagnetic crosstalk or mechanical interference between the signals from the two stations, while too large a spacing increases the bearing ball's rotation angle, thus reducing the spatial registration accuracy of the dual-mode signals. The ultrasonic probe coupling method is selected based on the conditions of the bearing ball rolling inspection production line: contact coupling or immersion coupling. Contact coupling uses a coupling agent between the bearing ball and the ultrasonic probe to achieve sound wave transmission. Immersion coupling involves simultaneously immersing the ultrasonic probe and the bearing ball in a water tank, using water as the coupling medium. Immersion coupling offers more stable coupling efficiency and a lower near-surface detection blind zone, making it suitable for applications requiring accurate detection of surface defects.

[0069] like Figure 3As shown, the second time reference triggering device operates on the same principle as the first time reference triggering device. It is installed at a preset position directly below the ultrasonic probe. When the geometric center of the bearing steel ball coincides with the central axis of the ultrasonic probe's sound beam, the second time reference triggering device generates a second trigger signal. This second trigger signal is recorded by the control unit of the detection system as the ultrasonic detection time reference. The time difference between the eddy current detection time reference and the ultrasonic detection time reference is equal to the time it takes for the bearing steel ball to move from the eddy current flaw detection station to the ultrasonic flaw detection station. This time difference is related to the probe spacing and the rolling linear velocity of the bearing steel ball as indicated in the figure. Since both the first and second time reference triggering devices are managed by the control unit of the detection system, the recording of the two trigger signals uses the same clock source, ensuring the accuracy of the time difference measurement between the eddy current detection time reference and the ultrasonic detection time reference. Starting from the ultrasonic detection time reference, the detection system continuously acquires the ultrasonic echo signal received by the ultrasonic probe at a preset ultrasonic sampling frequency. The ultrasonic sampling frequency setting must meet the requirements for ultrasonic pulse time resolution; a higher ultrasonic sampling frequency results in higher time-of-flight measurement accuracy but a lower corresponding depth resolution. An ultrasonic probe emits ultrasonic pulses into the bearing steel ball. As the ultrasonic pulses propagate through the bearing steel ball material, they encounter discontinuous interfaces that generate reflected echoes. These reflected echoes return along their original path and are received by the ultrasonic probe. Cracks, inclusions, pores, and abnormal tissue areas within the bearing steel ball create interfaces with acoustic impedance differences compared to the matrix material, becoming sources of ultrasonic reflection. The matrix material refers to the normal tissue region within the bearing steel ball, free from defects such as cracks, inclusions, pores, and abnormal tissue. The matrix material possesses continuous and uniform acoustic impedance characteristics; therefore, it does not generate reflected echoes when the ultrasonic pulse propagates through it. Reflected echoes only occur when the ultrasonic pulse propagates to an interface where there is a sudden change in acoustic impedance between the defective area and the matrix material. The ultrasonic echo signal is amplified, filtered, and converted from analog to digital before being stored in the data buffer of the detection system for subsequent step S15 to construct the ultrasonic A-scan waveform.

[0070] By deploying an ultrasonic testing station downstream of the eddy current testing station, the same bearing steel ball undergoes testing using two different physical principles during continuous rolling, achieving time-series acquisition of dual-modal detection signals. Eddy current testing is primarily sensitive to defects on the surface and near-surface of the bearing steel ball, with its detection depth limited by the skin effect. Ultrasonic testing, on the other hand, can detect defects across the entire depth range from the surface to the core of the bearing steel ball. The depth coverage of the two methods overlaps, and this overlap corresponds precisely to the transition zone between the hardened layer and the core, a high-incidence area for quenching cracks and structural abnormalities. The second time reference triggering device provides the ultrasonic echo signal's time-series recording with the same time reference mechanism as the eddy current impedance signal, providing a time reference point for calculating the time offset between the two testing stations in step S16. If the deployment of an ultrasonic flaw detection station is lacking, the detection system will only obtain eddy current single-mode signals and will be unable to calculate the dual-mode depth deviation value, and the inversion of the hardness gradient parameter group will not be possible; if the second time reference triggering device is lacking, the acquisition start point of the ultrasonic echo signal will not be able to establish a time correlation with the acquisition start point of the eddy current impedance signal, and the time pairing operation in step S18 will lose its reference reference.

[0071] Step S15: Construct an ultrasonic A-scan waveform based on the ultrasonic echo signal. The horizontal axis of the ultrasonic A-scan waveform represents the flight time of the ultrasonic echo signal, and the vertical axis represents the echo amplitude. Identify abnormal echoes from the ultrasonic A-scan waveform, record the ultrasonic abnormal timestamp relative to the ultrasonic detection time reference, read the flight time corresponding to the abnormal echo from the horizontal axis of the ultrasonic A-scan waveform, and calculate a preliminary estimate of the ultrasonic defect depth based on the flight time of the abnormal echo according to the time-depth relationship.

[0072] Specifically, the ultrasonic A-scan waveform is the most basic signal representation in ultrasonic flaw detection. It presents the change in ultrasonic echo signal amplitude over time in a two-dimensional graph. The horizontal axis, echo time of flight, is calculated from the moment the ultrasonic pulse is emitted, reflecting the time it takes for the ultrasonic wave to travel back and forth within the bearing steel ball material. The vertical axis, echo amplitude, reflects the degree of acoustic impedance mismatch at the reflecting interface; the greater the acoustic impedance mismatch, the higher the reflected echo amplitude. The ultrasonic A-scan waveform typically first shows the superposition of the residual signal of the emitted pulse and the near-surface interface echo. Subsequently, reflected echoes from different depths within the bearing steel ball appear at different time-of-flight positions, and finally, bottom echo signals from the bottom surface or opposite side surface of the bearing steel ball appear.

[0073] The identification of abnormal echoes employs an amplitude threshold discrimination method. The preset amplitude threshold is set based on the background noise level in the ultrasonic A-scan waveform of a defect-free standard bearing steel ball. When the amplitude of an echo exceeds the preset threshold, it is determined to be an abnormal echo, corresponding to the presence of a defect interface within the bearing steel ball. The flight time of the abnormal echo is directly read from the horizontal axis of the ultrasonic A-scan waveform. The flight time is the round-trip propagation time of the ultrasonic pulse from the surface of the bearing steel ball to the defect location and back to the surface, equal to twice the one-way propagation time. The preliminary estimate of the ultrasonic defect depth is calculated by substituting the flight time of the abnormal echo into the time-depth equation. Under the assumption of homogeneous materials, the time-depth equation is expressed as depth equal to flight time multiplied by the material's sound velocity and then divided by 2. The nominal sound velocity of the bearing steel ball material is selected as the material's sound velocity. Since the time-depth equation is derived based on the assumption of homogeneous materials, and actual bearing steel balls exhibit a radial sound velocity gradient distribution, the preliminary estimate of the ultrasonic defect depth is a distorted depth value without gradient correction. This distorted depth value is systematically higher than the true depth of the defect. The ultrasonic anomaly timestamp records bind each anomalous echo to the time difference between its occurrence and the ultrasonic testing time reference. The ultrasonic anomaly timestamp and the eddy current anomaly timestamp share the same physical meaning, both characterizing the relative moment the defect was detected. The time coordinate systems of the ultrasonic and eddy current anomaly timestamps are respectively based on the ultrasonic testing time reference and the eddy current testing time reference. A fixed time offset exists between the two time coordinate systems, determined by the time it takes for the bearing steel ball to move from the eddy current testing station to the ultrasonic testing station.

[0074] The preliminary estimates of ultrasonic defect depth and eddy current defect depth correspond physically, both being depth readings derived from the assumption of material homogeneity. However, their distortion directions are opposite: the preliminary estimate of eddy current defect depth systematically underestimates the true depth, while the preliminary estimate of ultrasonic defect depth systematically overestimates the true depth. This opposite distortion direction is determined by the physical characteristics of the material gradient distribution after heat treatment of the bearing steel ball. The low conductivity of the surface martensite increases the skin depth of the eddy current while decreasing the phase delay, resulting in a lower eddy current depth. The high sound velocity of the surface martensite shortens the ultrasonic propagation time, leading to an higher ultrasonic depth when converting depth according to the nominal sound velocity. The difference between the two distorted depth values ​​directly encodes the material gradient information at the defect depth, which is the physical source of the material information content in the depth deviation value in step S19.

[0075] Step S16: Obtain the probe spacing between the eddy current probe and the ultrasonic probe along the direction of the bearing steel ball rolling detection production line, measure the rolling linear velocity of the bearing steel ball on the bearing steel ball rolling detection production line, and divide the probe spacing by the rolling linear velocity to obtain the time offset.

[0076] Specifically, probe spacing refers to the horizontal distance along the bearing ball rolling detection production line between the detection center point of the eddy current probe in the eddy current flaw detection station and the detection center point of the ultrasonic probe in the ultrasonic flaw detection station. The probe spacing is determined through precise measurement during the installation and commissioning phase of the detection system and stored as a fixed parameter in the system's configuration file. Probe spacing is measured using a laser rangefinder or precision measuring tape. The measurement accuracy must meet the requirements of subsequent time offset calculations. For example, when the probe spacing is on the order of several hundred millimeters and the rolling linear velocity is on the order of several hundred millimeters per second, the measurement error of the probe spacing should be controlled within the millimeter range to ensure that the calculation error of the time offset is less than the millisecond range. Rolling linear velocity refers to the instantaneous speed at which the bearing ball moves along the bearing ball rolling detection production line. Rolling linear velocity is measured using an encoder or photoelectric gate installed on the bearing ball rolling detection production line. The encoder measurement method couples the encoder's rotating shaft to the drive shaft of the conveyor mechanism in the bearing ball rolling detection production line. The linear velocity of the bearing ball is calculated based on the encoder's pulse count and transmission ratio. The photoelectric gate measurement method places two photoelectric gates at intervals on the bearing ball rolling detection production line. The time difference between the bearing ball triggering the two photoelectric gates is recorded, and the average linear velocity is calculated based on the distance between the two photoelectric gates and the time difference. The rolling linear velocity may change during the detection process due to variations in the load of the bearing ball rolling detection production line or fluctuations in the drive motor speed. The detection system needs to monitor the rolling linear velocity in real time to determine whether it is within the preset stable speed range. If the rolling linear velocity exceeds the stable speed range, the current bearing ball detection data must be marked as an abnormal speed and await manual verification. The method for setting the speed stability range is as follows: Under stable operation of the bearing steel ball rolling inspection production line, the rolling linear velocity of multiple bearing steel balls passing through the inspection station is continuously measured. The mean and standard deviation of the rolling linear velocity are statistically analyzed. The lower limit of the speed stability range is set as the mean rolling linear velocity minus three times the standard deviation, and the upper limit of the speed stability range is set as the mean rolling linear velocity plus three times the standard deviation. For example, when the nominal rolling linear velocity of the bearing steel ball rolling inspection production line is set to 300 mm per second and the measured standard deviation of the rolling linear velocity is 5 mm per second, the speed stability range is set to 285 mm per second to 315 mm per second.

[0077] The time offset is calculated by dividing the probe spacing by the rolling linear velocity. The time offset characterizes the time it takes for the bearing steel ball to move from the eddy current testing station to the ultrasonic testing station; it is the time difference between the eddy current testing time reference and the ultrasonic testing time reference. The time offset establishes a time coordinate transformation relationship between the two testing stations, shifting the time coordinate system of the ultrasonic echo signal to the same time coordinate origin as the eddy current impedance signal, allowing the temporal characteristics of the two signals to be compared on a unified time axis. The calculation of the time offset provides a key parameter for time coordinate transformation in step S18 for the time pairing of the dual-mode signals, eliminating the time coordinate offset caused by the spatial difference between the two testing stations, and enabling the eddy current anomaly timestamp and the ultrasonic anomaly timestamp to be compared under the same time reference system. If the time offset is not calculated, the ultrasonic anomaly timestamp will always lag behind the eddy current anomaly timestamp. Even if two signals originate from the same defect, their timestamp difference will be much larger than the spherical angle resolution window calculated in step S17, resulting in all pairing decisions being negative. The dual-modal pairing record cannot be established, and there will be no data available for the depth deviation value calculation in the subsequent step S19.

[0078] Step S17: Obtain the diameter of the bearing steel ball, add the time offset to the ultrasonic anomaly timestamp to obtain the time offset compensated ultrasonic anomaly timestamp, and calculate the spherical angle resolution window based on the ball diameter and rolling linear velocity.

[0079] Specifically, the sphere diameter is the nominal diameter of the batch of bearing steel balls to be tested. For example, the diameter of the steel balls in a wind turbine yaw bearing is typically in the tens of millimeters range. The sphere diameter is stored as a batch parameter in the configuration file of the testing system, and all bearing steel balls in the same batch are calculated using the same sphere diameter value. The acquisition of the ultrasonic anomaly timestamp after time offset compensation involves adding the time offset calculated in step S16 to each ultrasonic anomaly timestamp recorded in step S15. The compensated timestamp represents the equivalent time in the eddy current time coordinate system when the defect corresponding to the abnormal echo is detected by the ultrasonic probe. After time offset compensation, the eddy current anomaly timestamp and the time-offset compensated ultrasonic anomaly timestamp are in the same time reference system. The difference between the two only reflects the relative time difference of the detection of the same defect at the two testing stations due to the rotation of the bearing steel ball, rather than the spatial position difference between the two testing stations. When multiple abnormal echoes exist in the ultrasonic A-scan waveform of the same bearing steel ball, the time-offset compensated ultrasonic anomaly timestamps corresponding to each abnormal echo are arranged in chronological order to form a set of time-offset compensated ultrasonic anomaly timestamps. The time offset compensation ultrasonic anomaly timestamp set records the time location information of all defects detected by ultrasonic testing methods on the bearing steel ball in a unified time reference system.

[0080] The spherical angle resolution window is calculated based on the influence of the bearing steel ball's rotation on the position of spherical defects. When the bearing steel ball rolls from the eddy current testing station to the ultrasonic testing station, the defect point on the sphere's surface rotates by a certain angle due to the rotation. Only when the spherical testing areas corresponding to the two probes overlap can the two signals originate from the same defect. The spherical angle resolution window characterizes the equivalent uncertainty of the spherical position offset caused by rotation on the time axis. The installation method of the eddy current probe and the ultrasonic probe on the bearing steel ball rolling testing production line ensures that the detection directions of the two probes are consistent, both facing the same side of the bearing steel ball's rolling track. Every time the bearing steel ball completes one full rotation on the bearing steel ball rolling testing production line, every point on the sphere will pass through the probe's detection direction once. Therefore, the detection time offset of the same defect due to rotation will not exceed the revolution time corresponding to one full rotation cycle. When a bearing steel ball rolls purely on a track, its rotational angular velocity equals its rolling linear velocity divided by the ball's radius. The time required for one rotation equals the ball's circumference divided by the rolling linear velocity. The spherical angular resolution window equals the ball's circumference divided by the rolling linear velocity, which is essentially the ball's diameter multiplied by pi and then divided by the rolling linear velocity. Physically, this represents the time interval between revolutions corresponding to one complete rotation of the bearing steel ball. For example, when the ball's diameter is 60 mm and the rolling linear velocity is 300 mm per second, the spherical angular resolution window equals pi multiplied by 60 and then divided by 300, approximately 628 milliseconds. This means that if the difference between the eddy current anomaly timestamp and the ultrasonic anomaly timestamp after time offset compensation is within 628 milliseconds, it can be determined that they originate from the same defect.

[0081] The calculation of the spherical angle resolution window in step S17 considers the influence of the bearing ball's rotation on the spatial registration of dual-modal signals. This is a unique characteristic of bearing ball rolling detection, distinguishing it from static detection or planar workpiece detection. If the influence of rotation is ignored and only time offset compensation is performed, when the same defect is located directly below the sphere in the eddy current testing station but deviates from directly below it in the ultrasonic testing station due to rotation, the two signals, although originating from the same defect, will be detected at different times. This difference will lead to pairing failure. The spherical angle resolution window, as the time tolerance for pairing determination, converts the spherical position offset caused by rotation into an equivalent tolerance range on the time axis, ensuring that the same defect can be correctly paired even when there is a spherical position offset when detected in two testing stations.

[0082] Step S18: Compare the timestamp of the eddy current anomaly with the timestamp of the ultrasonic anomaly after time offset compensation one by one. When the absolute difference between the two is less than the spherical angle resolution window, it is determined that the corresponding abnormal offset and abnormal echo originate from the same defect. Establish a dual-mode pairing record containing the preliminary estimate of the depth of the eddy current defect and the preliminary estimate of the depth of the ultrasonic defect.

[0083] Specifically, the comparison between the eddy current anomaly timestamp and the time-off compensated ultrasonic anomaly timestamp is achieved through a nested traversal. The outer layer traverses each eddy current anomaly timestamp in the set of eddy current anomaly timestamps, while the inner layer traverses each time-off compensated ultrasonic anomaly timestamp in the set of time-off compensated ultrasonic anomaly timestamps. The absolute difference is calculated for each pair of timestamps. When the absolute difference between the eddy current anomaly timestamp and the time-off compensated ultrasonic anomaly timestamp is less than the spherical angle resolution window, it is determined that the corresponding abnormal offset in the eddy current impedance plane trajectory and the corresponding abnormal echo in the ultrasonic A-scan waveform originate from the same defect, and a pairing association is established between them. The establishment of the pairing association creates a one-to-one correspondence between the originally independent eddy current detection results and the ultrasonic detection results. Each established pairing association means that a defect detected simultaneously by both detection methods has been identified. The data structure of the dual-modal pairing record includes the following fields: eddy current anomaly timestamp, ultrasonic anomaly timestamp, preliminary estimate of eddy current defect depth, preliminary estimate of ultrasonic defect depth, and pairing confidence index. The pairing confidence index is derived inversely from the ratio of the absolute difference between the eddy current anomaly timestamp and the time-shifted compensated ultrasonic anomaly timestamp to the spherical angle resolution window. The smaller the absolute difference, the higher the pairing confidence index, indicating a higher degree of reliability in the pairing results. When the absolute difference between the same eddy current anomaly timestamp and multiple time-shifted compensated ultrasonic anomaly timestamps is less than the spherical angle resolution window, the time-shifted compensated ultrasonic anomaly timestamp with the smallest absolute difference is selected to establish a pairing association, and other candidate pairs are marked as pairs to be verified. When a certain eddy current anomaly timestamp cannot find a time-shifted compensated ultrasonic anomaly timestamp with an absolute difference less than the spherical angle resolution window, the eddy current detection defect is determined to be an eddy current single detection defect, which may be located in a very shallow surface area outside the ultrasonic detection depth range or may not generate sufficient ultrasonic echo intensity due to its small size.

[0084] Dual-modal pairing recording integrates eddy current testing and ultrasonic testing from independent methods into a collaborative approach. Traditional dual-modal testing judges the results of the two tests separately and takes the union as the final result, without establishing a pairing relationship for the same defect, and thus cannot utilize the difference information of the depth readings of the same defect by the two methods. Step S18, through time reference synchronization and spatial position registration, accurately maps the signal features from the two testing stations to the same defect entity, enabling the subsequent step S19 to calculate the depth deviation value between the eddy current depth and the ultrasonic depth of the same defect. Without the establishment of dual-modal pairing records, the correspondence between the preliminary estimates of the eddy current defect depth and the preliminary estimates of the ultrasonic defect depth cannot be determined, the calculation of the depth deviation value will be a meaningless combination of arbitrary eddy current depth values ​​and arbitrary ultrasonic depth values, and the inversion of the hardness gradient parameter set will lose its physical basis.

[0085] Step S19: Extract the preliminary estimate of the depth of the eddy current defect and the preliminary estimate of the depth of the ultrasonic defect from the dual-mode paired record. Subtract the preliminary estimate of the depth of the eddy current defect from the preliminary estimate of the depth of the ultrasonic defect to obtain the depth deviation value. Invert the hardness gradient parameter set based on the depth deviation value. The hardness gradient parameter set includes the center depth of the transition zone and the width of the transition zone.

[0086] Specifically, the depth deviation is calculated by subtracting the preliminary estimate of the eddy current defect depth from the preliminary estimate of the ultrasonic defect depth in the dual-modal paired record. The sign and magnitude of the depth deviation carry information about the material gradient state at the depth of the defect. When the depth deviation is positive, it indicates that the ultrasonic depth is greater than the eddy current depth, which is consistent with the theoretical expectation of the gradient medium in the heat treatment of bearing steel balls: the eddy current impedance signal experiences a gradient medium with increasing conductivity as it penetrates from the surface to the interior, and the cumulative rate of phase delay increases with depth, causing the preliminary estimate of the eddy current defect depth to systematically underestimate the actual depth; the ultrasonic echo signal experiences a gradient medium with decreasing sound velocity as it propagates from the surface to the interior, and the cumulative rate of propagation time increases with depth, causing the preliminary estimate of the ultrasonic defect depth converted to nominal sound velocity to systematically overestimate the actual depth. When the depth deviation is zero or close to zero, it indicates that the defect is located in a region with a gentle change in hardness gradient, possibly in a pure surface martensite region or a pure core sorbite region. The material properties in both regions are approximately uniform, and the distortion of the eddy current depth and ultrasonic depth is similar, thus the depth deviation is close to zero. When the depth deviation value is negative, it indicates that the eddy current depth is greater than the ultrasonic depth, which does not meet the theoretical expectation. The dual-modal pairing record needs to be marked as a pairing doubt, and further analysis is needed to determine if there is a pairing error or probe abnormality.

[0087] There is a mapping relationship between depth deviation and hardness gradient steepness. Hardness gradient steepness is defined as the change in hardness per unit depth. The larger the depth deviation, the steeper the hardness gradient at the depth of the defect; the smaller the depth deviation, the gentler the hardness gradient at the depth of the defect. This mapping relationship is established based on standard sample ball test data. The standard sample balls are bearing steel balls from the same batch that have undergone heat treatment and whose true hardness gradient curves have been determined by metallographic sections. Artificial defects with known depths are pre-fabricated on the standard sample balls. Steps S11 to S18 are performed on the standard sample balls to obtain dual-modal pairing records and depth deviation values. Simultaneously, the hardness gradient steepness at the depth of the artificial defect is extracted from the metallographic section data, establishing a conversion function from depth deviation to hardness gradient steepness. The inversion of the hardness gradient parameter set utilizes the S-shaped distribution function characteristic of the hardness gradient curve of the bearing steel ball after heat treatment. The S-shaped distribution function can be fully characterized by two parameters: the center depth of the transition zone and the width of the transition zone. The center depth of the transition zone represents the depth at the intermediate position where the hardness transitions from the surface martensite value to the core sorbite value, and the width of the transition zone represents the depth range where the hardness change is most drastic. When the number of dual-modal paired records of the bearing steel ball to be tested is greater than or equal to 2, there are two or more defect signal pairs at different depth positions. When the number of dual-modal paired records is 2, the first paired record and the second paired record are taken from the dual-modal paired records. The defect corresponding to the first paired record is the first defect, and the defect corresponding to the second paired record is the second defect. The first defect and the second defect are two different defect entities that were simultaneously detected by the eddy current testing method and the ultrasonic testing method, respectively, after being confirmed by the pairing judgment in step S18. The preliminary estimated values ​​for the eddy current defect depth and the ultrasonic defect depth of the first defect are defined as the first eddy current depth and the first ultrasonic depth, respectively. Similarly, the preliminary estimated values ​​for the eddy current defect depth and the ultrasonic defect depth of the second defect are defined as the second eddy current depth and the second ultrasonic depth, respectively. The first depth deviation value is obtained by subtracting the first eddy current depth from the first ultrasonic depth, and the second depth deviation value is obtained by subtracting the second eddy current depth from the second ultrasonic depth. Both the first and second depth deviation values ​​are calculated independently for their respective paired records according to the depth deviation value calculation method described in step S19. Based on the hardness gradient steepness corresponding to the first and second depth deviation values, and the depth position relationship between the first and second defects, the derivative expression of the S-shaped distribution function is substituted to solve for the center depth and width of the transition zone. When the number of dual-mode paired records for the bearing steel ball to be tested is only 1, the transition zone width of the current batch of standard sample balls is used as a substitute value for the transition zone width, and the center depth of the transition zone is inverted only based on a single set of depth deviation values.When the number of dual-mode paired records of the bearing steel ball to be tested is 0, that is, there is no defect that is detected by both testing methods at the same time, it is impossible to invert the hardness gradient parameter group from the test data of the current bearing steel ball. At this time, the center depth and width of the transition zone of the current batch of standard sample balls are used as the substitute values ​​of the hardness gradient parameter group, so that the gradient correction in the subsequent step S20 can still be performed based on the uniform gradient parameters of the batch.

[0088] The sigmoid distribution function is a well-known mathematical model in materials science describing the phase transition characteristics. It is also known as the sigmoid function or logistic function. Its mathematical expression is based on the sigmoid transition characteristic of bearing steel balls where the hardness decreases monotonically along the radial direction. The complete expression is: ,in, This is a function value, specifically the hardness value at depth x. This is the lower limit value, which is the lowest hardness value corresponding to the sorbite structure in the core. This is the upper limit value, which is the highest hardness value corresponding to the surface martensite structure; For shape parameters, Let the depth be the independent variable along the radial direction of the bearing steel ball. The depth of the center of the transition zone, is a natural constant. The physical meaning of this expression is: when x=0, the hardness value approaches the upper limit value U; when x approaches the radius of the steel ball, the hardness value approaches the lower limit value L; when x=x0, the hardness value is (U+L) / 2, which is the arithmetic mean of the surface and core hardness, corresponding to the midpoint of the hardness transition.

[0089] The derivative expression of the sigmoid distribution function is the expression obtained by differentiating the sigmoid distribution function with respect to the independent variable. The specific differentiation process adopts the chain rule of calculus: first, the sigmoid distribution function is transformed into... When differentiating the independent variable x, first differentiate the outer power function of the composite function, then differentiate the inner exponential function, and finally simplify to obtain: , The denominator is the first derivative of the sigmoid distribution function at the independent variable x. As a normalization term, it ensures that the value of the first derivative reaches its maximum value at the center x0 of the transition region and approaches 0 at locations far from the transition region; The term is an exponential function describing the attenuation of hardness as it deviates from the center of the transition zone (x0) by depth: when x = x0, the exponential function term equals 1; as x moves further away from x0, the exponential function term approaches 0. The derivative of the sigmoid distribution function characterizes the rate of change of the function value in the direction of the independent variable, i.e., the kurtosis of the hardness gradient. The mathematical meaning of the derivative expression of the sigmoid distribution function is: the first derivative value reaches an extreme value at the depth position of the center of the transition zone, indicating that the rate of change of hardness is the largest; the derivative value approaches zero at depth positions far from the center of the transition zone, indicating that the change of hardness is gradual. The derivative expression contains two parameters to be determined: the depth of the center of the transition zone and the shape parameter. The shape parameter is inversely proportional to the width of the transition zone. Substituting the hardness gradient kurtosis corresponding to the depth position of the first defect and the first depth deviation value into the derivative expression of the sigmoid distribution function forms the first equation; substituting the hardness gradient kurtosis corresponding to the depth position of the second defect and the second depth deviation value into the derivative expression of the sigmoid distribution function forms the second equation. Solving the first and second equations simultaneously yields the depth of the center of the transition zone and the shape parameter, and then converting the shape parameter into the width of the transition zone. When the number of paired records in the dual-modal model is greater than 2, the least squares method is used to fit the depth deviation values ​​of all paired records to obtain the optimal center depth and width of the transition zone. The specific fitting process is as follows: first, construct the residual sum of squares objective function. ,in This represents the total number of bimodal pairing records. For the first The depth location of the defect. For the first The steepness of the hardness gradient corresponding to each depth deviation value The S-shaped distribution function at depth The derivative value at the point; then the residual squares and the parameters to be determined in the objective function are respectively... and Find the partial derivatives, and set both partial derivatives equal to zero, to obtain the information about... and The system of two nonlinear equations was first solved; then, the Newton-Raphson iterative method, commonly used in engineering, was employed to solve the system of two nonlinear equations, yielding the optimal center depth of the transition zone that minimizes the sum of squared residuals. With optimal shape parameters This leads to the optimal transition region width. .

[0090] The calculation of depth deviation and the inversion of the hardness gradient parameter set transform the difference in bimodal depth readings, which is traditionally considered a measurement error and attempted to be eliminated, into a quantifiable material information carrier. As a direct measure of the difference in response to the same defect between eddy current testing and ultrasonic testing, the depth deviation value has a deterministic physical correlation with the material gradient state at the defect depth. This correlation is rooted in the dependence of the eddy current skin effect on conductivity and the dependence of sound wave propagation velocity on elastic modulus, both of which have empirical relationships with material hardness. The inversion of the hardness gradient parameter set enables the detection system to obtain material state information from the detection signal that is unavailable through traditional methods. It allows for online inference of the heat treatment quality of the bearing steel ball without destructive metallographic sectioning, providing input parameters for gradient correction and process feedback in step S20.

[0091] Step S10 involves deploying eddy current testing and ultrasonic testing stations at different locations on the bearing steel ball rolling inspection production line. A unified time reference system is established using a first and second time reference triggering device. By combining the kinematic relationship between the bearing steel ball's revolution and rotation, the time offset and spherical angle resolution window are calculated. This achieves accurate pairing of abnormal offsets in the eddy current impedance plane trajectory with abnormal echoes in the ultrasonic A-scan waveform, ensuring that the preliminary estimates of eddy current defect depth and ultrasonic defect depth accurately correspond to the same defect entity. This physically integrates the two previously independent testing methods into a collaborative testing system, enabling accurate quantification of the response differences between the two methods to the same defect. Based on this, the calculation of the depth deviation reveals the material gradient information implicit in the response differences between the two testing methods, transforming the signal differences, traditionally considered sources of error in testing methods, into an information carrier for inverting the heat treatment state, thus expanding the dimension of the testing data. The inversion of the hardness gradient parameter set makes each tested bearing steel ball a sampling point for the heat treatment process state. The hardened layer depth and gradient morphology of the bearing steel ball can be inferred online without destructive metallographic sectioning, providing input parameters for personalized depth correction based on the actual material state of the bearing steel ball in subsequent step S20. When the statistical distribution of the hardness gradient parameter set of a batch of bearing steel balls shows anomalies, such as a shift in the batch mean of the transition zone center depth towards a shallower layer or a significant increase in the batch variance of the transition zone width, the drift direction of the heat treatment process parameters can be quickly located. This allows for the inference of whether process parameters such as quenching temperature, quenching time, or cooling rate deviate from the set values, shifting quality control from traditional post-event sampling to real-time process monitoring, thus achieving integrated testing and process monitoring functions. If the dual-mode signal pairing and hardness gradient parameter inversion in step S10 are missing, the gradient correction in step S20 will lack specificity and can only use the batch-uniform average gradient parameter for correction. This will not be able to adapt to the individual differences in heat treatment states between different bearing steel balls within the same batch, and the correction accuracy will decrease significantly. The reliability of defect depth determination and safety margin assessment will not be guaranteed.

[0092] Step S20: Reconstruct the conductivity distribution function and sound velocity distribution function of the current bearing steel ball according to the hardness gradient parameter group. Based on the conductivity distribution function and sound velocity distribution function, perform gradient correction on the preliminary estimated value of eddy current defect depth and the preliminary estimated value of ultrasonic defect depth to obtain the true defect depth value. Obtain the design hardened layer depth of the current batch of bearing steel balls. Perform a three-level defect classification judgment based on the true defect depth value and the design hardened layer depth.

[0093] Specifically, the preliminary estimates of the eddy current defect depth and the preliminary estimates of the ultrasonic defect depth obtained in step S10 are both derived based on the assumption of material homogeneity. The preliminary estimate of the eddy current defect depth is converted using the phase-depth linear relationship under the condition of uniform conductivity, and the preliminary estimate of the ultrasonic defect depth is converted using the flight-time-depth linear relationship under the condition of uniform sound velocity. However, the actual bearing steel ball exhibits a gradient distribution characteristic of increasing conductivity and decreasing sound velocity along the radial direction after heat treatment. Both preliminary depth estimates are distorted values. The preliminary estimate of the eddy current defect depth systematically underestimates the true depth, and the preliminary estimate of the ultrasonic defect depth systematically overestimates the true depth. Step S20 aims to use the hardness gradient parameter set obtained in step S10 to reconstruct the conductivity distribution function and sound velocity distribution function along the radial depth of the bearing steel ball based on the actual material state of the current bearing steel ball. Based on the reconstructed material property distribution function, nonlinear mapping correction is performed on the preliminary estimated value of the eddy current defect depth and the preliminary estimated value of the ultrasonic defect depth, so that the depth readings of the two detection methods for the same defect converge to the same value. The converged depth value is determined as the true depth value of the defect. Based on the comparison between the true depth value of the defect and the designed hardened layer depth, the defect is graded and the current bearing steel ball is graded.

[0094] The electrical conductivity distribution function is a mathematical expression for the change of material conductivity with depth along the radial depth direction of the bearing steel ball. The surface martensitic structure corresponds to a lower conductivity value, the core sorbitic structure corresponds to a higher conductivity value, and the conductivity value in the transition zone lies between the lower conductivity value corresponding to the surface martensitic structure and the higher conductivity value corresponding to the core sorbitic structure, with the rate of change controlled by the width of the transition zone. The sound velocity distribution function is a mathematical expression for the change of ultrasonic wave propagation speed with depth along the radial depth direction of the bearing steel ball. The surface martensitic structure corresponds to a higher sound velocity value due to its higher elastic modulus, while the core sorbitic structure corresponds to a lower sound velocity value due to its lower elastic modulus. Similarly, the sound velocity value in the transition zone lies between the higher sound velocity value corresponding to the surface martensitic structure and the lower sound velocity value corresponding to the core sorbitic structure, with the rate of change controlled by the width of the transition zone. The designed hardened layer depth refers to the effective hardened layer depth expected to be achieved by the heat treatment process specified in the product drawings or customer technical agreements. It characterizes the requirements for the hardened layer thickness of the bearing steel ball during the design stage. The comparison between the actual defect depth and the designed hardened layer depth directly determines the degree of impact of the defect on the bearing's service reliability. The preliminary estimates of eddy current defect depth and ultrasonic defect depth in the dual-modal pairing record output in step S10 serve as the objects to be corrected in the gradient correction in step S20. The two steps together constitute a complete information processing link from the original detection signal to the actual defect depth value and then to the classification result. If the gradient correction operation in step S20 is missing, the preliminary estimates of eddy current defect depth and ultrasonic defect depth will be directly used for classification. Since both are distorted values ​​and the distortion directions are opposite, the classification result will deviate from the true danger level of the defect. Shallow surface defects may be misclassified as deep dangerous defects due to an underestimation of the eddy current depth, and deep dangerous defects may be misclassified as core defects in a deeper location due to an overestimation of the ultrasonic depth. The accuracy of the classification cannot be guaranteed.

[0095] Further, step S20 includes:

[0096] Step S21: Construct a hardness distribution function along the radial depth based on the center depth and width of the transition zone in the hardness gradient parameter set, and convert the hardness distribution function into an electrical conductivity distribution function and a sound velocity distribution function;

[0097] Specifically, the hardness distribution function is constructed based on the physical characteristic that the hardness of bearing steel balls exhibits an S-shaped radial distribution after heat treatment. The S-shaped distribution function is a monotonically decreasing continuous function. The surface martensite hardness value is taken at the surface location with zero depth, the core sorbite hardness value is taken at the core location with depth approaching the ball's center, and the hardness value at the depth equal to the center depth of the transition zone is the arithmetic mean of the surface martensite hardness value and the core sorbite hardness value. The rate of change of hardness value from the surface to the core is controlled by the width of the transition zone; the smaller the transition zone width, the steeper the hardness change, and the larger the transition zone width, the gentler the hardness change. The surface martensite hardness value and the core sorbite hardness value are inherent physical property parameters of the bearing steel material, obtained by hardness measurement after metallographic sectioning of standard sample balls from the same batch. For example, for GCr15 bearing steel, the surface martensite hardness value is typically in the Rockwell hardness range of 60 to 64, and the core sorbite hardness value is typically in the Rockwell hardness range of 35 to 45.

[0098] The mathematical form of the hardness distribution function adopts the standard expression of the sigmoid distribution function. The sigmoid distribution function is a well-known mathematical model in materials science and engineering describing the characteristics of the phase transition region. The function value of the sigmoid distribution function approaches its upper bound as the independent variable approaches negative infinity, approaches its lower bound as the independent variable approaches positive infinity, and takes the midpoint between the upper and lower bounds when the independent variable equals the midpoint of the function. When applying the sigmoid distribution function to construct the hardness distribution function, the independent variable is the depth value, the upper bound is the surface martensite hardness value, and the lower bound is the core sorbite hardness value. The midpoint of the function corresponds to the center depth of the transition region obtained in step S10. The shape parameter controlling the steepness of the transition is inversely proportional to the width of the transition region obtained in step S10. After the hardness distribution function is constructed, the hardness value at any radial depth can be directly calculated by substituting the depth value into the function expression of the hardness distribution function.

[0099] The conductivity distribution function is obtained based on the empirical relationship between hardness and conductivity of bearing steel. This empirical relationship refers to the quantitative correspondence between the hardness value and the conductivity value of a material. For GCr15 bearing steel, the martensitic structure, due to its high carbon content, results in a high degree of lattice distortion and enhanced electron scattering, exhibiting a high resistivity and thus a low conductivity. Conversely, the sorbitic structure, due to the precipitation of carbon atoms forming cementite lamellars and a reduced degree of lattice distortion in the ferrite matrix, exhibits a low resistivity and thus a high conductivity. Higher hardness values ​​correspond to lower conductivity values. The empirical relationship between hardness and conductivity is obtained by fitting hardness and conductivity measurements of GCr15 bearing steel samples under different heat treatment states; this is considered well-known empirical data in the field of materials science. Substituting the hardness distribution function into the empirical formula for hardness conductivity yields the conductivity distribution function, which describes the conductivity variation of the bearing steel ball along the radial depth. The surface conductivity value is taken at the surface position where the depth is zero, and the core conductivity value is taken at the core position where the depth approaches the center of the ball. The surface conductivity value is less than the core conductivity value, and the conductivity increases monotonically along the depth.

[0100] The sound velocity distribution function is obtained based on the empirical relationship between hardness and sound velocity in bearing steel. This relationship refers to the quantitative correspondence between the material's hardness value and the ultrasonic wave propagation speed. For GCr15 bearing steel, the martensitic structure exhibits a higher sound velocity due to lattice distortion and increased elastic modulus caused by carbon atoms dissolving in the iron matrix. Conversely, the sorbitic structure exhibits a lower sound velocity due to decreased matrix elastic modulus caused by carbon atoms precipitating as cementite. Higher hardness values ​​correlate with higher sound velocity values. The empirical relationship between hardness and sound velocity is obtained by fitting hardness and sound velocity measurements of GCr15 bearing steel samples under different heat treatment states. Substituting the hardness distribution function into the empirical relationship yields the sound velocity distribution function, which describes the change in sound velocity along the radial depth of the bearing steel ball. The surface sound velocity value is taken at a depth of zero, while the core sound velocity value is taken at a depth approaching the center of the ball. The surface sound velocity value is greater than the core sound velocity value, and the sound velocity decreases monotonically with depth.

[0101] The reconstructed conductivity and sound velocity distribution functions must meet the verification of physical rationality constraints. These constraints include a monotonically increasing conductivity distribution function along depth, a monotonically decreasing sound velocity distribution function along depth, and both conductivity and sound velocity values ​​falling within the reasonable range of material properties. If the conductivity or sound velocity distribution function exhibits non-monotonic changes or extreme value anomalies, it indicates a deviation in the inversion results of the hardness gradient parameter group in step S10. Possible causes include mismatched dual-mode pairing records, local material states at the depth of the defect deviating from the global S-shaped model assumption, and insufficient accuracy in the mapping relationship of the standard sample ball detection data. Bearing steel balls that violate physical rationality constraints are marked as gradient reconstruction anomalies, and subsequent gradient correction operations are temporarily suspended, with the process proceeding to manual review.

[0102] The conductivity distribution function and sound velocity distribution function are reconstructed based on the hardness gradient parameter set, transforming the two gradient parameters obtained in step S10 into spatial distribution information of material properties that can be used for depth correction calculation. Traditional detection methods use fixed average conductivity and average sound velocity values ​​for depth conversion, ignoring the radial gradient changes of material properties, leading to a systematic deviation between the depth conversion result and the true depth. Step S21 reconstructs the property distribution function based on the actual hardness gradient parameter set of the current bearing steel ball, enabling the depth correction in subsequent steps S22 and S23 to be performed on the actual material state of the current bearing steel ball, rather than using batch-uniform average parameters, thus improving the correction accuracy. The reconstruction of the conductivity and sound velocity distribution functions also provides conditions for verifying physical rationality constraints. When the reconstruction result violates the monotonicity constraint, anomalies in the hardness gradient parameter set inversion can be detected in time, preventing incorrect gradient parameters from being used in subsequent corrections and causing distortion of the correction results. If the material property distribution function reconstruction in step S21 is missing, the depth correction in steps S22 and S23 will lack the spatial distribution information of material properties and can only use linear correction based on the assumption of uniform materials. It cannot eliminate the nonlinear depth distortion caused by the material gradient. The corrected eddy current defect depth correction value and the ultrasonic defect depth correction value will still have differences, and the convergence verification in step S24 will fail.

[0103] Step S22: Along the radial direction of the bearing steel ball, the depth range from the surface to the preset maximum detection depth is divided into multiple conductivity depth thin layers according to the conductivity distribution function. The phase angle increment of each conductivity depth thin layer is calculated. The phase angle increment of each conductivity depth thin layer is accumulated to establish a phase angle depth lookup table. The abnormally offset phase angle in the eddy current impedance plane trajectory is searched in the phase angle depth lookup table to obtain the eddy current defect depth correction value.

[0104] Specifically, the preset maximum detection depth refers to the upper limit of the depth that the eddy current testing method can effectively detect under the current excitation frequency. The setting of the preset maximum detection depth needs to comprehensively consider the eddy current excitation frequency, the conductivity range of the bearing steel ball material, and the physical laws of the skin effect. Since eddy current testing mainly targets defects in the surface and near-surface areas of the bearing steel ball, an effective detection depth covering the hardened layer and transition zone is sufficient to meet the testing requirements. For example, for eddy current testing of yaw bearing steel balls in wind turbines, the preset maximum detection depth is typically set to 1.5 to 2 times the design depth of the hardened layer to ensure that defects in both the hardened layer and the transition zone are within the effective detection range. The selection of the excitation frequency must ensure that the skin depth of the eddy current testing is greater than 3 to 5 times the preset maximum detection depth, so that the phase resolution in the depth direction meets the testing requirements. The depth range is divided into multiple discrete conductivity depth thin layers from the surface depth of zero to the preset maximum detection depth. Each conductivity depth thin layer has the same thickness. The setting of the thin layer thickness needs to strike a balance between calculation accuracy and calculation efficiency. The smaller the thin layer thickness, the higher the depth resolution but the greater the calculation load. For example, the thin layer thickness can be set to 1‰ to 1% of the preset maximum detection depth.

[0105] The conductivity value of each conductivity depth thin layer is taken as the conductivity value at the center depth of the thin layer. The center depth of the thin layer is equal to the arithmetic mean of the upper boundary depth and the lower boundary depth of the thin layer. Substituting the center depth of the thin layer into the conductivity distribution function reconstructed in step S21 yields the conductivity value of the thin layer. Since the conductivity increases monotonically along the radial depth direction of the bearing steel ball, the conductivity depth thin layers located on the surface have lower conductivity values, while those located in deeper layers have higher conductivity values. The calculation of the phase angle increment of each conductivity depth thin layer is based on the physical law of the eddy current skin effect. The skin effect refers to the phenomenon that when an alternating electromagnetic field penetrates a conductive material, the current density decreases exponentially with depth. The skin depth is the depth corresponding to when the current density decreases to about one-third of the surface value. The skin depth is inversely proportional to the square root of the material conductivity and inversely proportional to the square root of the excitation frequency. The phase angle increment characterizes the accumulated phase delay when eddy current penetrates a single conductivity-depth thin layer. The phase angle increment is proportional to the thickness of the thin layer, the square root of the conductivity value of the thin layer, the square root of the excitation frequency, and the square root of the material's magnetic permeability. The calculation of the phase angle increment follows the well-known phase delay calculation formula in the field of eddy current detection, that is, the phase angle increment is equal to the thickness of the thin layer divided by the skin depth corresponding to the thin layer. The skin depth corresponding to the thin layer is calculated using the skin depth formula described in step S13 with the conductivity value of the thin layer as the conductivity input.

[0106] The phase angle depth lookup table is established using a layer-by-layer accumulation method. Starting from the surface, the phase angle increment of the first conductivity depth thin layer is taken as the cumulative phase angle when the depth equals the lower boundary depth of the first thin layer. The sum of the phase angle increments of the first and second conductivity depth thin layers is taken as the cumulative phase angle when the depth equals the lower boundary depth of the second thin layer, and so on. The sum of all phase angle increments from the first to the Nth conductivity depth thin layer is taken as the cumulative phase angle when the depth equals the lower boundary depth of the Nth thin layer. The phase angle depth lookup table uses the cumulative phase angle as the index and the corresponding depth value as the lookup result, establishing a nonlinear correspondence between the phase angle and the true depth in the gradient medium. Since conductivity increases with depth, the phase angle increment of the deeper conductivity depth thin layer is greater than that of the shallower conductivity depth thin layer. The relationship between the cumulative phase angle and depth in the phase angle depth lookup table exhibits an upward convex nonlinear characteristic; the same phase angle increment corresponds to a smaller depth increment in the deeper layer than in the shallower layer.

[0107] The eddy current defect depth correction value is obtained by using the phase angle of the abnormal offset of the eddy current impedance plane trajectory calculated in step S13 as the lookup input. The cumulative phase angle entry that matches or is closest to the input phase angle value is searched in the phase angle depth lookup table, and the corresponding depth value is read as the eddy current defect depth correction value. When the input phase angle is located between two adjacent cumulative phase angle entries in the phase angle depth lookup table, the corresponding depth value is calculated using linear interpolation, a well-known numerical method in engineering calculations. The eddy current defect depth correction value reflects the true depth location of the defect corresponding to the eddy current impedance signal phase angle, considering the radial gradient distribution of conductivity. Since the slope of the phase angle-depth relationship decreases at depth in a gradient medium, the true depth corresponding to the same phase angle in a gradient medium is greater than the assumed depth in a homogeneous medium. Therefore, the eddy current defect depth correction value is greater than the preliminary estimate of the eddy current defect depth calculated in step S13, and the correction direction is towards deeper layers.

[0108] Step S22 employs deep thin-layer segmentation and phase angle increment accumulation to discretize the continuously varying conductivity gradient medium, enabling the nonlinear relationship between phase depth and depth in the gradient medium to be calculated using a layer-by-layer accumulation numerical method. Traditional eddy current depth estimation uses a linear phase depth formula based on the conductivity of uniform materials, which cannot adapt to the radially increasing gradient characteristics of conductivity in bearing steel balls after heat treatment. This leads to a systematic underestimation of the true depth in the initial estimate of eddy current defect depth, with the degree of underestimation increasing with the defect depth. Step S22 establishes a phase angle depth lookup table to achieve a nonlinear mapping from phase angle to true depth in the gradient medium, eliminating depth distortion caused by the uniform material assumption. This improves the depth positioning accuracy of the eddy current detection method from a rough estimate dependent on batch average conductivity to an accurate correction adapted to the individual material gradient state. Once established, the phase angle depth lookup table can be reused. When correcting the depth of multiple defects on the same bearing steel ball, there is no need to repeatedly calculate the phase angle increment accumulation, improving the correction efficiency for multi-defect bearing steel balls. If the eddy current depth gradient correction in step S22 is missing, the preliminary estimate of the eddy current defect depth will directly proceed to the convergence verification in step S24. Since the preliminary estimate of the eddy current defect depth is systematically low while the preliminary estimate of the ultrasonic defect depth is systematically high, the difference between the two will be much greater than the convergence threshold, causing the convergence verification to fail and the true defect depth value to remain undetermined. The basis and method for setting the convergence threshold are explained in detail in step S24. The convergence threshold is determined based on the statistical distribution of the depth correction residuals of the standard sample sphere. For example, when the quantile corresponding to the 95% confidence level of the depth correction residual distribution of the standard sample sphere is 0.08 mm, the convergence threshold is set to 0.08 mm. That is, convergence is determined when the absolute difference between the eddy current defect depth correction value and the ultrasonic defect depth correction value is less than or equal to 0.08 mm.

[0109] Step S23: Along the radial direction of the bearing steel ball, the depth range from the surface to the preset maximum detection depth is divided into multiple sound velocity depth thin layers according to the sound velocity distribution function. The propagation time of each sound velocity depth thin layer is calculated, and the propagation time of each sound velocity depth thin layer is accumulated to establish a time-of-flight depth lookup table. The time of flight of the abnormal echo in the ultrasonic A-scan waveform is searched in the time-of-flight depth lookup table to obtain the ultrasonic defect depth correction value.

[0110] Specifically, the preset maximum detection depth in step S23 is the same as the preset maximum detection depth used in step S22, ensuring consistent depth range coverage between eddy current depth correction and ultrasonic depth correction. The effective detection depth of ultrasonic testing is much greater than that of eddy current testing, covering the entire depth range from the surface of the bearing steel ball to its core. However, for depth correction of dual-mode paired defects, the overlapping area of ​​depth coverage between eddy current and ultrasonic testing methods is the hardened layer and the transition zone. Therefore, using the same preset maximum detection depth as eddy current depth correction for ultrasonic depth correction is sufficient. The depth range is divided in the same way as in step S22, dividing the continuous depth interval from zero surface depth to the preset maximum detection depth into multiple discrete sound velocity depth layers. Each sound velocity depth layer has the same thickness, set to the same thickness as the conductivity depth layer in step S22, ensuring consistent depth resolution between eddy current depth correction and ultrasonic depth correction. The sound velocity value for each sound velocity depth thin layer is taken as the sound velocity value at the center depth of the thin layer. Substituting the center depth of the thin layer into the reconstructed sound velocity distribution function in step S21 yields the thin layer sound velocity value. Since the sound velocity monotonically decreases with depth, the sound velocity depth thin layers located on the surface have higher thin layer sound velocity values, while those located in deeper layers have lower values. The propagation time of each sound velocity depth thin layer is calculated based on the time path relationship of ultrasonic wave propagation in the medium. The propagation time equals the propagation path length divided by the propagation speed. For a single sound velocity depth thin layer, the propagation time of the ultrasonic pulse penetrating the thin layer equals the thin layer thickness divided by the thin layer sound velocity value. Since the ultrasonic echo is the signal of the ultrasonic pulse propagating from the surface to the defect location and then reflecting back to the surface, the flight time of the echo is equal to twice the one-way propagation time. Therefore, when establishing the time-of-flight depth lookup table, the cumulative one-way propagation time needs to be multiplied by 2.

[0111] The time-of-flight depth lookup table is also built using a layer-by-layer accumulation method. Starting from the surface, the propagation time of the first sound velocity depth layer is multiplied by 2 to obtain the cumulative flight time when the depth equals the lower boundary depth of the first layer. The sum of the propagation times of the first and second sound velocity depth layers is multiplied by 2 to obtain the cumulative flight time when the depth equals the lower boundary depth of the second layer, and so on. The time-of-flight depth lookup table uses the cumulative flight time as the index and the corresponding depth value as the lookup result, establishing a nonlinear correspondence between flight time and true depth in the gradient medium. Since the speed of sound decreases with depth, the propagation time of the deeper sound velocity depth layers is greater than that of the shallower ones. The relationship between cumulative flight time and depth in the time-of-flight depth lookup table exhibits a concave nonlinear characteristic; the same increase in flight time corresponds to a smaller increase in depth at a deeper level than at a shallower level.

[0112] The ultrasonic defect depth correction value is obtained by using the abnormal echo time of flight read from the horizontal axis of the ultrasonic A-scan waveform in step S15 as the lookup input. The cumulative time of flight entry matching or being closest to the input time of flight value is searched in the time-of-flight depth lookup table, and the corresponding depth value is read as the ultrasonic defect depth correction value. When the input time of flight is between two adjacent cumulative time of flight entries in the time-of-flight depth lookup table, the corresponding depth value is calculated using linear interpolation. The ultrasonic defect depth correction value reflects the true depth location of the defect corresponding to the ultrasonic echo time of flight, considering the radial gradient distribution of sound velocity. Since the slope of the time-of-flight depth relationship increases at depth in a gradient medium, the true depth corresponding to the same time of flight in a gradient medium is less than the assumed depth in a homogeneous medium. Therefore, the ultrasonic defect depth correction value is less than the preliminary estimate of the ultrasonic defect depth calculated in step S15, and the correction direction is towards the shallower layers.

[0113] See Figure 4 This is a schematic diagram illustrating the convergence of eddy current and ultrasonic defect depth correction. The diagram shows the depth coordinate axis extending radially inward from the bearing steel ball surface, the reference position of the true defect depth, and also marks the initial positions of the preliminary estimates of the eddy current defect depth (with systematic shallowness) and the preliminary estimates of the ultrasonic defect depth (with systematic deepness), as well as the correction directions and final convergence process for both depth values. The correction direction for the eddy current defect depth correction value in step S22 is... Figure 4 The correction direction for the depth correction and the ultrasonic defect depth correction value in step S23, as indicated in the annotation, is as follows: Figure 4The shallow-layer correction, indicated by the annotation, involves two correction directions moving in opposite directions. This corrects the distortion caused by the initial underestimation of eddy current defect depth and the initial overestimation of ultrasonic defect depth. The corrected eddy current and ultrasonic values ​​converge towards the true depth of the same defect. The method of depth thin-layer segmentation and propagation time accumulation is consistent with the phase angle increment accumulation method in step S22 in terms of numerical processing framework, ensuring the symmetry and comparability of the calculation methods for eddy current depth correction and ultrasonic depth correction, facilitating the convergence verification of the two corrected depth values ​​in step S24. Traditional ultrasonic depth estimation uses a linear time-of-flight depth formula based on the sound velocity of uniform materials, which cannot adapt to the gradient characteristics of the radially decreasing sound velocity after heat treatment of bearing steel balls. This leads to a systematic overestimation of the true depth in the initial ultrasonic defect depth estimate, with the overestimation increasing with the defect depth. By establishing a time-of-flight depth lookup table, a nonlinear mapping from time of flight to true depth in gradient media is achieved, eliminating the depth distortion caused by the homogeneous material assumption. Without the ultrasonic depth gradient correction in step S23, the preliminary estimate of the ultrasonic defect depth will directly proceed to the convergence verification in step S24. The difference between this estimate and the preliminary estimate of the eddy current defect depth will still be too large, and the convergence verification will fail. Steps S22 and S23 form a symmetrical gradient correction pair, respectively correcting the depth positioning mechanisms based on the different physical principles of eddy current detection and ultrasonic detection. This corrects the depth reading deviations of both detection methods in gradient media. Eddy current detection depth positioning relies on the phase delay caused by the eddy current skin effect, while ultrasonic detection depth positioning relies on the relationship between sound wave propagation time and path length. The two mechanisms respond to material gradients in opposite directions, and the gradient correction directions are also opposite. The process of the depth readings of the two detection methods converging towards the true depth after correction demonstrates the complementarity and consistency verification function of the dual-modal detection method in gradient media.

[0114] Step S24: Calculate the absolute difference between the eddy current defect depth correction value and the ultrasonic defect depth correction value as the depth correction residual, determine the relationship between the depth correction residual and the preset convergence threshold and warning threshold, and determine the true depth value of the defect.

[0115] When the depth correction residual is less than or equal to the preset convergence threshold, the average of the eddy current defect depth correction value and the ultrasonic defect depth correction value is determined as the true depth value of the defect, and the depth correction residual is recorded and saved as a local non-uniformity index of the defect. When the depth correction residual is greater than the convergence threshold but less than the preset warning threshold, the average of the eddy current defect depth correction value and the ultrasonic defect depth correction value is determined as the true depth value of the defect, and the depth correction residual is recorded and saved as a local non-uniformity index of the defect. When the depth correction residual is greater than or equal to the warning threshold, the defect is marked as a depth uncertainty marker pending manual verification.

[0116] Specifically, the depth correction residual is calculated by subtracting the eddy current defect depth correction value obtained in step S22 from the ultrasonic defect depth correction value obtained in step S23 and taking the absolute value. The depth correction residual characterizes the degree of difference in the depth positioning of the same defect by the two detection methods after gradient correction. If the gradient correction process completely eliminates the depth distortion caused by the material gradient, the eddy current defect depth correction value and the ultrasonic defect depth correction value should be exactly equal, and the depth correction residual should be zero. In actual detection, due to the influence of factors such as measurement noise, hardness gradient parameter set inversion error, and local material inhomogeneity, the depth correction residual is usually a small non-zero amount.

[0117] The convergence threshold is a limit value for determining whether the depth correction values ​​of eddy current defects and ultrasonic defects have converged to the same level. The convergence threshold is set based on the depth positioning accuracy requirements of the detection system and the accuracy level of the material gradient model. The method for determining the convergence threshold is as follows: For multiple standard sample spheres with artificial defects at known depths, steps S11 to S23 are sequentially performed for dual-modal detection and gradient correction. The absolute difference between the depth correction values ​​of the eddy current defects and ultrasonic defects on each standard sample sphere is calculated as the depth correction residual for that artificial defect. The depth correction residuals of all artificial defects on all standard sample spheres are summarized and arranged according to their numerical values ​​to form a depth correction residual distribution. The distribution characteristics of the depth correction residuals are statistically analyzed, and the upper quartile or the quantile corresponding to a specified confidence level is used as the convergence threshold. The warning threshold is a limit value for determining whether the depth correction residual is too large to make the correction result unreliable. The warning threshold is greater than the convergence threshold, and its setting is based on the degree of influence of local material inhomogeneity on depth correction. The warning threshold is determined as follows: The convergence threshold determined in the preceding steps is obtained, and the warning threshold is calculated by combining it with a preset multiplier factor. Since local structural anomalies in the bearing steel balls can cause nonlinear distortion of the physical propagation path of the detection signal, thus amplifying the depth correction residual of the dual-mode depth fixation, the preset multiplier factor is set to 2 to 3. By directly setting the warning threshold to 2 to 3 times the convergence threshold, the normal algorithm correction error and the depth steady-state deviation caused by internal structural anomalies in the material can be effectively distinguished.

[0118] The determination of the true depth value of the defect is based on the comparison results of the depth correction residual with the convergence threshold and the warning threshold, and is handled in three cases. When the depth correction residual is less than or equal to the convergence threshold, it is determined that the depth correction value of the eddy current defect and the depth correction value of the ultrasonic defect have converged to the same value, and the depth positioning results of the two detection methods for the same defect have good consistency. The arithmetic mean of the depth correction values ​​of the eddy current defect and the ultrasonic defect is determined as the true depth value of the defect. The arithmetic mean can integrate the depth correction results of the two detection methods. When there is a small difference between the two, the median value is taken as the estimation result. At the same time, the depth correction residual is recorded and saved as a local non-uniformity index of the defect. At this time, the value of the local non-uniformity index is small, indicating that the material state at the depth location of the defect is in good agreement with the global S-shaped hardness gradient model. The global S-shaped hardness gradient model refers to the overall hardness distribution law of the bearing steel ball along the radial depth direction described by the hardness distribution function constructed based on the hardness gradient parameter group in step S21. The global S-shaped hardness gradient model uses an S-shaped distribution function as its mathematical expression. The S-shaped distribution function is the Sigmoid function described in step S19. The parameters of the global S-shaped hardness gradient model include the surface martensite hardness value, the core sorbite hardness value, the center depth of the transition zone, and the width of the transition zone. When the depth correction residual is greater than the convergence threshold but less than the warning threshold, it is determined that the eddy current defect depth correction value and the ultrasonic defect depth correction value have not fully converged, but the difference is within an acceptable range. The arithmetic mean of the eddy current defect depth correction value and the ultrasonic defect depth correction value is still determined as the true depth value of the defect. At the same time, the depth correction residual is recorded and saved as a local non-uniformity index. The local non-uniformity index reflects the degree to which the material state at the depth of the defect deviates from the global S-shaped hardness gradient model. Possible reasons include the presence of microstructural anomalies such as secondary quenching zones, bainite islands, and retained austenite enrichment zones. When the depth correction residual is greater than or equal to the warning threshold, it is determined that the difference between the depth correction value of the eddy current defect and the depth correction value of the ultrasonic defect is too large, and the depth correction result is unreliable. The defect is marked as a depth uncertainty marker, and the true depth value of the defect is temporarily uncertain. The bearing steel ball is then transferred to the manual review process or verified by destructive metallographic sectioning.

[0119] The depth correction residual calculation and convergence verification mechanism in step S24 cross-validates the depth correction results of the two detection methods, utilizing the redundant information from dual-modal detection to determine the reliability of the correction results. Traditional single-modal detection methods lack independent verification of depth positioning results, and depth positioning errors cannot be detected when the material state deviates from the assumed model. Step S24 compares the correction depths of the same defect by two detection methods based on different physical principles. When the two converge, the reliability of the depth positioning results is enhanced; when the difference is too large, potential correction anomalies or material anomalies can be identified, preventing erroneous depth positioning results from being used in subsequent grading and leading to misjudgment. The recording of local non-uniformity indices provides auxiliary criteria for the grading determination in the subsequent step S25, enabling the grading process to comprehensively consider both the defect depth location and the material state of the defect area, thus improving the accuracy of the grading results in predicting the bearing's service reliability. If the convergence verification in step S24 is missing, the eddy current defect depth correction value and the ultrasonic defect depth correction value will be used for grading without difference. When there is a large difference between the two for various reasons, the grading criteria will be contradictory, and the reliability of the grading result cannot be guaranteed.

[0120] Step S25: Obtain the design hardened layer depth of the current batch of bearing steel balls, calculate the safety margin depth based on the design hardened layer depth and the safety margin ratio, compare the actual defect depth value with the safety margin depth and the design hardened layer depth to perform a three-level classification judgment, and output the defect classification result of the current bearing steel ball.

[0121] See Figure 5 The three-level classification method is as follows: when the actual depth of the defect is less than the safety margin depth, it is judged as qualified; when the actual depth of the defect is greater than or equal to the safety margin depth and less than or equal to the designed hardened layer depth, if the local non-uniformity index is lower than the tissue abnormality threshold, it is judged as qualified; if the local non-uniformity index is higher than or equal to the tissue abnormality threshold, it is judged as needing re-inspection; when the actual depth of the defect is greater than the designed hardened layer depth, it is judged as unqualified.

[0122] Specifically, the three-level grading judgment in step S25 only applies to defects whose true depth value has been determined in step S24. For defects marked as having uncertain depth in step S24, they do not enter the automatic grading judgment process; instead, the grading result is directly marked as requiring re-inspection and transferred to the manual review process. The designed hardened layer depth is specified by the product drawings or customer technical agreements, representing the effective hardened layer depth expected to be achieved by the heat treatment process. The setting of the designed hardened layer depth is based on the calculation of contact stress distribution and fatigue life requirements during bearing service, ensuring that the hardened layer can withstand rolling contact fatigue loads without surface spalling. The safety margin ratio refers to the ratio of the safety margin depth to the designed hardened layer depth. The setting of the safety margin ratio is based on the service reliability requirements of the bearing steel balls and the safety factor design principle. The value of the safety margin ratio must be greater than 0 and less than 1. For example, the safety margin ratio can be set in the range of 0.6 to 0.8, so that the safety margin depth covers the main surface part of the designed hardened layer depth. The safety margin depth equals the designed hardened layer depth multiplied by the safety margin ratio. The safety margin depth delineates the boundary between the safe surface area and the transition zone edge area within the hardened layer. The designed hardened layer depth is determined by the effective hardened layer depth specified in the product drawings or customer technical agreements for the current batch of bearing steel balls. The determination of the designed hardened layer depth is based on the calculated Hertzian contact stress distribution experienced by the bearing during service and the set fatigue life requirements. The designed hardened layer depth must ensure that the hardened layer thickness is greater than the depth corresponding to the location of the maximum shear stress in the Hertzian contact stress field, so that the bearing steel ball does not experience subsurface crack initiation and surface spalling due to rolling contact fatigue within the set fatigue life cycle. The designed hardened layer depth is stored as a batch parameter in the configuration file of the testing system, and all bearing steel balls in the same batch use the same designed hardened layer depth value. For example, for wind turbine yaw bearing steel balls, the designed hardened layer depth is typically in the range of 3 mm to 6 mm. The safety margin depth is equal to the design hardened layer depth multiplied by the safety margin ratio. The safety margin depth defines the boundary between the safe surface area and the edge area of ​​the transition zone within the hardened layer.

[0123] The three-level grading system classifies defects into three categories based on their actual depth location, thus assessing the severity of the defect. Category 1 corresponds to defects with an actual depth less than the safety margin depth. The defect is located in the safe surface region within the hardened layer. This region has high material hardness and wear resistance, and the surface defect is more likely to be worn down by rolling contact during bearing service rather than developing into fatigue cracks. The risk of the surface defect developing into a spalling pit due to contact fatigue is low. Therefore, the defect is classified as an acceptable surface defect, and the grading result is marked as acceptable. Category 2 corresponds to defects with an actual depth greater than or equal to the safety margin depth but less than or equal to the designed hardened layer depth. The defect is located in the transition zone between the hardened layer and the core. This transition zone is where the hardness gradient changes most drastically and is a high-risk area for quenching cracks and structural abnormalities. Defects in the transition zone experience complex stress states during bearing service and require further evaluation in conjunction with local non-uniformity indicators. If the local non-uniformity index recorded in step S24 is lower than the tissue abnormality threshold, the defect is judged as a general defect in the transition zone, and the classification result is marked as qualified; if the local non-uniformity index is higher than or equal to the tissue abnormality threshold, the defect is judged to be accompanied by tissue abnormality, and the classification result is marked as requiring re-inspection. The setting of the tissue abnormality threshold is based on materials science knowledge and testing experience, and is determined by analyzing the statistical distribution of local non-uniformity indices of bearing steel ball samples known to have tissue abnormalities. The method for determining the tissue abnormality threshold is as follows: Steps S11 to S24 are performed on a group of bearing steel ball samples known to have local tissue abnormalities and a group of bearing steel ball samples known to have normal material conditions, respectively. The distribution of local non-uniformity indices of the two groups of samples is statistically analyzed, and the midpoint between the upper boundary value of the local non-uniformity index distribution of the normal sample group and the lower boundary value of the local non-uniformity index distribution of the abnormal sample group is set as the tissue abnormality threshold. For example, when the upper boundary value of the local non-uniformity index distribution in the normal sample group is 0.15 mm and the lower boundary value of the local non-uniformity index distribution in the abnormal sample group is 0.25 mm, the tissue abnormality threshold is set to 0.20 mm. Category three corresponds to a defect with a true depth greater than the designed hardened layer depth. The defect has invaded the core safety margin area, the core material has low hardness and high toughness, and the core defect may become the starting point for fatigue crack propagation during bearing service. Therefore, the defect is classified as a dangerous core defect, and the classification result is marked as unqualified.

[0124] Bearing steel balls that fail the initial assessment are rejected and removed from the rolling inspection line, with defect information recorded for quality traceability. Bearing steel balls requiring re-inspection are transferred to a manual re-inspection station for further confirmation using auxiliary testing methods. Bearing steel balls that pass the initial assessment are released for subsequent processing or assembly. Upon release, the pass mark and local non-uniformity index values ​​are recorded, serving as a reference for bearing selection and quality grading in subsequent assembly processes. The assessment results are also uploaded to the MES system for recording and storage, forming part of the bearing steel ball quality archive and supporting quality traceability and statistical analysis throughout the product lifecycle.

[0125] The three-level grading system transforms continuously changing defect depth values ​​into discrete grading categories, enabling grading results to directly correspond to subsequent handling decisions. Traditional defect detection only determines the existence of a defect or provides a depth reading without gradient correction. Inspectors must subjectively interpret the results based on experience before making grading decisions, resulting in inconsistent grading standards. Step S25 establishes objective grading criteria based on a quantitative comparison between the actual defect depth and the designed hardened layer depth, standardizing the grading process and eliminating the subjectivity and inconsistency of manual grading. The dual threshold setting of safety margin depth and designed hardened layer depth divides the hardened layer depth range into three functional zones: a safe surface area, a transition area, and a core area. Differentiated grading criteria are set for the hazardous characteristics of defects at different depths, reducing over-rejection of minor surface defects while ensuring product reliability and improving product pass rates. The application of the local non-uniformity index in grading category two enables the grading process to identify defects in the transition zone accompanied by tissue abnormalities. For such defects, a more cautious re-inspection grading is required, avoiding the risk of missed detection due to ignoring tissue abnormalities.

[0126] The depth correction values ​​for eddy current defects and ultrasonic defects converge towards the true depth, utilizing the physical characteristic that the two detection methods exhibit opposite distortion directions in gradient media. This allows the depth readings from both methods to mutually verify and constrain each other after gradient correction, resulting in a more reliable true depth value compared to a single detection method. The depth correction residual, acting as a local inhomogeneity index, transforms material anomaly information that might otherwise lead to correction failure into an auxiliary input for the grading process. This enables the detection system to not only obtain the depth and location information of the defect but also perceive the material state information of the defect area. The three-level grading judgment is based on a quantitative comparison between the true defect depth value and the designed hardened layer depth, transforming subjective grading relying on human experience into grading based on objective data, making the grading results traceable and interpretable.

[0127] Example 2

[0128] This embodiment, based on Embodiment 1, provides a bearing steel ball defect detection system combining eddy current and ultrasonic testing, such as... Figure 6 As shown, it includes:

[0129] The gradient parameter inversion module is used to obtain the eddy current impedance plane trajectory and ultrasonic A-scan waveform of the bearing steel ball during continuous rolling in the bearing steel ball rolling inspection production line. Based on the eddy current impedance plane trajectory, a preliminary estimate of the eddy current defect depth is obtained. Based on the ultrasonic A-scan waveform, a preliminary estimate of the ultrasonic defect depth is obtained. Based on the preliminary estimate of the eddy current defect depth and the preliminary estimate of the ultrasonic defect depth, the hardness gradient parameter group of the current bearing steel ball is inverted.

[0130] The depth correction and grading module reconstructs the conductivity distribution function and sound velocity distribution function of the current bearing steel ball based on the hardness gradient parameter group. Based on the conductivity distribution function and sound velocity distribution function, it performs gradient correction on the preliminary estimated values ​​of eddy current defect depth and ultrasonic defect depth to obtain the true defect depth value. It obtains the design hardened layer depth of the current batch of bearing steel balls and performs a three-level defect grading judgment based on the true defect depth value and the design hardened layer depth. The three-level grading judgment result is qualified, requires re-inspection, or unqualified.

[0131] Furthermore, in the gradient parameter inversion module, the method for obtaining the eddy current impedance plane trajectory includes:

[0132] A first time reference triggering device is set up at the eddy current flaw detection station of the bearing steel ball rolling inspection production line. When the bearing steel ball passes through the eddy current probe, the first time reference triggering device generates a first trigger signal. The time corresponding to the first trigger signal generated by the first time reference triggering device is recorded as the eddy current detection time reference. Starting from the eddy current detection time reference, the eddy current impedance signal output by the eddy current probe is continuously collected.

[0133] Extract the real and imaginary components of the impedance from the eddy current impedance signal, and construct the eddy current impedance plane trajectory with the real component as the x-axis and the imaginary component as the y-axis.

[0134] The method for calculating the preliminary estimate of the eddy current defect depth includes:

[0135] Identify abnormal offsets from the eddy current impedance plane trajectory, calculate the phase angle of the abnormal offset, record the eddy current anomaly timestamp of each abnormal offset occurrence relative to the eddy current detection time reference, and calculate a preliminary estimate of the eddy current defect depth based on the phase angle of the abnormal offset.

[0136] The method for acquiring the ultrasound A-scan waveform includes:

[0137] An ultrasonic testing station is deployed downstream of the eddy current testing station, equipped with an ultrasonic probe and a second time reference triggering device. When the same bearing steel ball passes the ultrasonic probe, the second time reference triggering device generates a second trigger signal. The time corresponding to the second trigger signal generated by the second time reference triggering device is recorded as the ultrasonic testing time reference, and ultrasonic echo signals are collected from the ultrasonic testing time reference.

[0138] An ultrasound A-scan waveform is constructed based on the ultrasound echo signal, wherein the horizontal axis of the ultrasound A-scan waveform represents the flight time of the ultrasound echo signal, and the vertical axis represents the echo amplitude.

[0139] The method for calculating the preliminary estimate of the ultrasonic defect depth includes:

[0140] Abnormal echoes are identified from the ultrasonic A-scan waveform. The ultrasonic abnormality timestamp relative to the ultrasonic detection time reference is recorded. The flight time corresponding to the abnormal echo is read from the horizontal axis of the ultrasonic A-scan waveform. The preliminary estimate of the ultrasonic defect depth is calculated based on the flight time of the abnormal echo according to the time-depth relationship.

[0141] The inversion method for the hardness gradient parameter set includes:

[0142] Determine whether the abnormal offset and abnormal echo originate from the same defect. If they do, establish a dual-mode paired record that includes the preliminary estimate of the depth of the eddy current defect and the preliminary estimate of the depth of the ultrasonic defect.

[0143] Preliminary estimates of eddy current defect depth and ultrasonic defect depth are extracted from the dual-modal paired records. The preliminary estimate of eddy current defect depth is subtracted from the preliminary estimate of ultrasonic defect depth to obtain the depth deviation value. The hardness gradient parameter set is inverted based on the depth deviation value. The hardness gradient parameter set includes the center depth of the transition zone and the width of the transition zone.

[0144] The method for determining whether abnormal offset and abnormal echo originate from the same defect includes:

[0145] Calculate the ultrasonic anomaly timestamp and spherical angle resolution window after time offset compensation. Compare the eddy current anomaly timestamp with the ultrasonic anomaly timestamp after time offset compensation one by one. When the absolute difference between the two is less than the spherical angle resolution window, it is determined that the corresponding anomaly offset and anomaly echo originate from the same defect.

[0146] The methods and systems of this application may be implemented in many ways. For example, they may be implemented by software, hardware, firmware, or any combination of software, hardware, and firmware. The above-described order of steps for the method is for illustrative purposes only, and the steps of the method of this application are not limited to the order specifically described above, unless otherwise specifically stated.

[0147] In addition, the parts of the technical solutions provided in the embodiments of this application that are consistent with the implementation principles of the corresponding technical solutions in the prior art have not been described in detail, so as to avoid excessive elaboration.

[0148] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for detecting defects in bearing steel balls by combining eddy current and ultrasonic testing, characterized in that, The method includes: The eddy current impedance plane trajectory and ultrasonic A-scan waveform of the bearing steel ball during continuous rolling process are obtained in the bearing steel ball rolling test production line. Based on the eddy current impedance plane trajectory, a preliminary estimate of the eddy current defect depth is obtained. Based on the ultrasonic A-scan waveform, a preliminary estimate of the ultrasonic defect depth is obtained. Based on the preliminary estimate of the eddy current defect depth and the preliminary estimate of the ultrasonic defect depth, the hardness gradient parameter set of the current bearing steel ball is inverted. The conductivity distribution function and sound velocity distribution function of the current bearing steel ball are reconstructed based on the hardness gradient parameter set. The preliminary estimated values ​​of eddy current defect depth and ultrasonic defect depth are obtained by gradient correction based on the conductivity distribution function and sound velocity distribution function, respectively. The design hardened layer depth of the current batch of bearing steel balls is obtained. The three-level defect classification is performed based on the actual defect depth value and the design hardened layer depth.

2. The method for detecting defects of a bearing steel ball by combining eddy current and ultrasonic waves according to claim 1, characterized in that, The method for obtaining the eddy current impedance plane trajectory includes: A first time reference triggering device is set up at the eddy current flaw detection station of the bearing steel ball rolling inspection production line. When the bearing steel ball passes through the eddy current probe, the first time reference triggering device generates a first trigger signal. The time corresponding to the first trigger signal generated by the first time reference triggering device is recorded as the eddy current detection time reference. Starting from the eddy current detection time reference, the eddy current impedance signal output by the eddy current probe is continuously collected. Extract the real and imaginary components of the impedance from the eddy current impedance signal, and construct the eddy current impedance plane trajectory with the real component as the x-axis and the imaginary component as the y-axis.

3. The method according to claim 2, wherein The method for calculating the preliminary estimate of the eddy current defect depth includes: Identify abnormal offsets from the eddy current impedance plane trajectory, calculate the phase angle of the abnormal offset, record the eddy current anomaly timestamp of each abnormal offset occurrence relative to the eddy current detection time reference, and calculate a preliminary estimate of the eddy current defect depth based on the phase angle of the abnormal offset.

4. The method according to claim 3, wherein The method for acquiring the ultrasound A-scan waveform includes: An ultrasonic testing station is deployed downstream of the eddy current testing station, equipped with an ultrasonic probe and a second time reference triggering device. When the same bearing steel ball passes the ultrasonic probe, the second time reference triggering device generates a second trigger signal. The time corresponding to the second trigger signal generated by the second time reference triggering device is recorded as the ultrasonic testing time reference, and ultrasonic echo signals are collected from the ultrasonic testing time reference. An ultrasound A-scan waveform is constructed based on the ultrasound echo signal, wherein the horizontal axis of the ultrasound A-scan waveform represents the flight time of the ultrasound echo signal, and the vertical axis represents the echo amplitude of the ultrasound echo signal.

5. The method according to claim 4, wherein The method for calculating the preliminary estimate of the ultrasonic defect depth includes: Abnormal echoes are identified from the ultrasonic A-scan waveform. The ultrasonic abnormality timestamp relative to the ultrasonic detection time reference is recorded. The flight time corresponding to the abnormal echo is read from the horizontal axis of the ultrasonic A-scan waveform. The preliminary estimate of the ultrasonic defect depth is calculated based on the flight time of the abnormal echo according to the time-depth relationship.

6. The method according to claim 5, wherein The method for inverting the current hardness gradient parameter set of the bearing steel balls includes: Determine whether the abnormal offset and abnormal echo originate from the same defect. If they do, establish a dual-mode paired record that includes the preliminary estimate of the depth of the eddy current defect and the preliminary estimate of the depth of the ultrasonic defect. Preliminary estimates of eddy current defect depth and ultrasonic defect depth are extracted from the dual-modal paired records. The preliminary estimate of eddy current defect depth is subtracted from the preliminary estimate of ultrasonic defect depth to obtain the depth deviation value. The hardness gradient parameter set is inverted based on the depth deviation value. The hardness gradient parameter set includes the center depth of the transition zone and the width of the transition zone.

7. The method according to claim 6, wherein The method for determining whether abnormal offset and abnormal echo originate from the same defect includes: Calculate the ultrasonic anomaly timestamp and spherical angle resolution window after time offset compensation. Compare the eddy current anomaly timestamp with the ultrasonic anomaly timestamp after time offset compensation one by one. When the absolute difference between the two is less than the spherical angle resolution window, it is determined that the corresponding anomaly offset and anomaly echo originate from the same defect.

8. The method according to claim 7, wherein the method is characterized by, The calculation method for the ultrasonic anomaly timestamp and spherical angle resolution window after time offset compensation is as follows: The probe spacing between the eddy current probe and the ultrasonic probe along the direction of the bearing steel ball rolling detection production line is obtained. The rolling linear velocity of the bearing steel ball on the bearing steel ball rolling detection production line is measured. The time offset is obtained by dividing the probe spacing by the rolling linear velocity. Obtain the diameter of the bearing steel ball, add the time offset to the ultrasonic anomaly timestamp to obtain the time offset compensated ultrasonic anomaly timestamp, and calculate the spherical angular resolution window based on the ball diameter and rolling linear velocity.

9. The bearing steel ball defect detection method combining eddy current and ultrasonic testing according to claim 8, characterized in that, The gradient correction execution method includes: Along the radial direction of the bearing steel ball, the depth range from the surface to the preset maximum detection depth is divided into multiple conductivity depth thin layers according to the conductivity distribution function. The phase angle increment of each conductivity depth thin layer is calculated, and the phase angle increment of each conductivity depth thin layer is accumulated to establish a phase angle depth lookup table. The abnormally offset phase angle in the eddy current impedance plane trajectory is found in the phase angle depth lookup table to obtain the eddy current defect depth correction value.

10. The bearing steel ball defect detection method combining eddy current and ultrasonic testing according to claim 9, characterized in that, The method for determining the true depth value of the defect is as follows: The absolute difference between the depth correction value of the eddy current defect and the depth correction value of the ultrasonic defect is calculated as the depth correction residual. The relationship between the depth correction residual and the preset convergence threshold and warning threshold is determined to determine the true depth value of the defect.

11. The method for detecting defects in bearing steel balls by combining eddy current and ultrasonic testing according to claim 10, characterized in that, The method for determining the three levels of execution defects includes: Calculate the safety margin depth based on the design hardened layer depth and the safety margin ratio; The actual depth of the defect is compared with the safety margin depth and the designed hardened layer depth to perform a three-level classification judgment, and the result of the three-level classification judgment is qualified, requires re-inspection, or is unqualified.

12. A bearing steel ball defect detection system combining eddy current and ultrasonic testing, used to implement the bearing steel ball defect detection method combining eddy current and ultrasonic testing as described in any one of claims 1-11, characterized in that, The system includes: The gradient parameter inversion module is used to obtain the eddy current impedance plane trajectory and ultrasonic A-scan waveform of the bearing steel ball during continuous rolling in the bearing steel ball rolling inspection production line. Based on the eddy current impedance plane trajectory, a preliminary estimate of the eddy current defect depth is obtained. Based on the ultrasonic A-scan waveform, a preliminary estimate of the ultrasonic defect depth is obtained. Based on the preliminary estimate of the eddy current defect depth and the preliminary estimate of the ultrasonic defect depth, the hardness gradient parameter group of the current bearing steel ball is inverted. The depth correction and classification module reconstructs the conductivity distribution function and sound velocity distribution function of the current bearing steel ball based on the hardness gradient parameter group. Based on the conductivity distribution function and sound velocity distribution function, it performs gradient correction on the preliminary estimated values ​​of eddy current defect depth and ultrasonic defect depth to obtain the true defect depth value. It obtains the design hardened layer depth of the current batch of bearing steel balls and performs a three-level defect classification judgment based on the true defect depth value and the design hardened layer depth.

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