Eddy Current Testing Method and System for Bearing Steel Balls Based on Probe Adjustment

Abstract

This invention relates to the field of eddy current testing technology, and discloses a method and system for eddy current testing of bearing steel balls based on probe adjustment. The method includes: establishing a probe-spherical planar rectangular coordinate system; defining deflection angles and calculating the lift-off value and lift-off acceleration corresponding to each deflection angle of the spherical surface; determining an effective compensation angle range based on the lift-off acceleration; generating a lift-off compensation baseline impedance sequence within the effective compensation angle range; acquiring a measured impedance signal sequence during the rolling process of the bearing steel ball; aligning the sequence with the lift-off compensation baseline impedance sequence at angles; subtracting the residual impedance sequence point by point to extract the residual impedance sequence; and performing crack signal characteristic phase angle range filtering and adaptive amplitude rejection on the residual impedance sequence. This invention achieves high-precision compensation for spherical curvature lift-off interference in eddy current testing of bearing steel balls, improving the accuracy and reliability of crack detection.

Description

Technical Field

[0001] This invention relates to the field of eddy current testing technology, and specifically to a method and system for eddy current testing of bearing steel balls based on probe adjustment. Background Technology

[0002] Bearing steel balls are the core basic components of rolling bearings. The presence of surface defects such as cracks in these balls directly reduces the bearing's operational accuracy, service stability, and lifespan, and can even lead to in-service failure, causing equipment downtime and other safety accidents. Therefore, surface defect detection of bearing steel balls is a critical quality control step in the manufacturing process. Eddy current testing technology, with its non-contact nature, high detection efficiency, and sensitivity to surface and near-surface crack defects in metals, has become the mainstream technology for batch detection of surface defects in bearing steel balls.

[0003] A Chinese patent with authorization announcement number CN118858422B discloses a batch appearance inspection device for bearing steel balls, comprising: adaptively adjusting the position and angle of the coil group by adjusting the motor and adjusting rod to achieve optimal fit between the coil group and the surface of bearing steel balls of different sizes; simultaneously, suspending the bearing steel balls and rotating them around the axis by the magnetic field generated by the coil group, thereby achieving non-contact omnidirectional inspection of the bearing steel balls; integrating multi-frequency eddy current detection and micro-nano probe scanning technology to detect nanoscale defects on the surface of the steel balls; and intelligently analyzing the detection data through a built-in machine learning algorithm to automatically identify the defect type and generate a three-dimensional defect image.

[0004] However, existing eddy current testing technologies for bearing steel balls lack a dedicated geometric quantification and signal compensation mechanism to address the abrupt changes in lift-off acceleration caused by the inherent curvature of the steel ball's surface. The spherical characteristics of the bearing steel ball cause the lift-off distance from each point on the spherical surface to the probe's detection surface to change non-linearly with the deflection angle as the ball rolls along the detection direction. The lift-off acceleration reaches its maximum at the closest point on the spherical surface and decreases sharply with increasing angle. This abrupt change in lift-off acceleration superimposes a transient pulse component onto the impedance signal output by the eddy current probe. The phase angle of this transient pulse component on the impedance plane overlaps with the phase angle of the impedance signal caused by cracks on the steel ball surface. Existing technologies only address this issue by controlling the coil position angle. Defect detection and evaluation methods such as degree adjustment, multi-frequency detection, or reference signal fitting cannot efficiently remove pseudo-crack pulse components from the measured impedance signal. In actual detection, if the amplitude rejection threshold is relaxed to avoid misjudgment caused by pseudo-crack signals, the real small surface crack signals will be masked by noise and cannot be detected. If the original rejection threshold is maintained, the defective bearing steel balls will be rejected due to pseudo-crack signals. In the online flaw detection of large-size bearing steel balls used in wind power generation, the above problems manifest as an abnormally high rejection rate for the entire batch of bearing steel balls, accompanied by the risk of missing real crack defects. It is difficult to balance the accuracy and reliability of the detection results in the batch flaw detection of bearing steel balls. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of existing technologies, this invention provides a method and system for eddy current flaw detection of bearing steel balls based on probe adjustment. By establishing a probe-spherical planar rectangular coordinate system, the spatial geometric relationship between the sphere and the eddy current probe is quantified. The lift-off value and lift-off acceleration corresponding to each deflection angle of the sphere are calculated, the effective compensation angle range is determined, and a lift-off compensation baseline impedance sequence is generated. This achieves high-precision quantification of spherical curvature lift-off interference. Simultaneously, the measured impedance signal sequence of bearing steel ball flaw detection is angularly aligned with the lift-off compensation baseline impedance sequence. After angle alignment, the residual impedance sequence is extracted by point-by-point subtraction. Combined with the characteristic phase angle range screening of crack signals and adaptive amplitude rejection, crack detection is completed, achieving effective separation of pseudo-crack signals from real crack signals. Ultimately, high-precision compensation for spherical curvature lift-off interference in eddy current flaw detection of bearing steel balls is achieved, improving the accuracy and reliability of surface crack detection of bearing steel balls. This method can adapt to the flaw detection needs of bearing steel balls with different nominal diameter specifications.

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

[0007] Eddy current testing method for bearing steel balls based on probe adjustment includes:

[0008] Establish a probe-spherical plane rectangular coordinate system, define the deflection angle in the probe-spherical plane rectangular coordinate system, calculate the lift-off value and lift-off acceleration corresponding to each deflection angle of the spherical surface, determine the effective compensation angle range based on the lift-off acceleration, and generate a lift-off compensation baseline impedance sequence within the effective compensation angle range.

[0009] As the bearing steel ball rolls past the eddy current probe along the rolling direction, a measured impedance signal sequence is acquired and angularly aligned with the lift-off compensation baseline impedance sequence. The measured impedance signal sequence after angular alignment is subtracted point by point from the lift-off compensation baseline impedance sequence to extract the residual impedance sequence. The residual impedance sequence is then subjected to crack signal characteristic phase angle range screening and adaptive amplitude rejection. For bearing steel balls that are rejected and have real surface crack defects, a defect severity classification is performed.

[0010] The probe-spherical rectangular coordinate system has the center of the detection surface of the eddy current probe as the origin, the rolling direction of the bearing steel ball on the detection station as the horizontal axis, and the normal direction of the detection surface of the eddy current probe on the center side of the ball as the vertical axis.

[0011] The deflection angle refers to the angle of deflection along the arc direction on the spherical surface relative to the nearest point on the spherical surface, and the nearest point on the spherical surface refers to the point on the spherical surface that is closest to the detection surface of the eddy current probe.

[0012] The method for calculating the lift-off value and lift-off acceleration corresponding to each deflection angle of the sphere includes:

[0013] Obtain the nominal diameter of the bearing steel balls in the current batch, calculate the ball cross-sectional radius based on the nominal diameter, and obtain the initial lift-off setting value of the eddy current flaw detection equipment at the inspection station;

[0014] The lift-off value analytical function is obtained based on the sphere's cross-sectional radius, initial lift-off setting value, and deflection angle. The lift-off value corresponding to each deflection angle of the sphere is obtained based on the lift-off value analytical function.

[0015] Based on the analytic function of the lift-off value, the second derivative of the lift-off value with respect to the deflection angle is used to obtain the lift-off acceleration.

[0016] The method for determining the effective compensation angle range includes:

[0017] Set an acceleration change judgment threshold, and determine the deflection angle corresponding to the acceleration change judgment threshold when the lift-off acceleration is equal to the curvature gradient zone boundary angle. Calculate the effective detection coverage angle of the eddy current probe, and compare the curvature gradient zone boundary angle with the effective detection coverage angle to determine the effective compensation angle range.

[0018] The method for generating the lift-off compensated baseline impedance sequence includes:

[0019] The effective compensation angle interval is divided into N angle sampling points. The deflection angles of the N angle sampling points are substituted into the lift-off value analytical function to calculate the lift-off value sequence. The lift-off-impedance transfer function of the eddy current probe calibrated with a defect-free standard bearing steel ball is obtained. The lift-off-impedance transfer function is used to map the lift-off value sequence point by point into the lift-off compensation baseline impedance sequence.

[0020] The method for performing angle alignment includes:

[0021] Obtain the angle synchronization reference point. Using the angle synchronization reference point as the time zero point, obtain the rolling linear velocity of the bearing steel ball on the testing station. Based on the angle synchronization reference point, the rolling linear velocity and the ball cross-sectional radius, map the time sampling points in the measured impedance signal sequence to N angle sampling points in the lift-off compensation baseline impedance sequence. Extract the measured impedance signal sequence after aligning the angles corresponding to the N angle sampling points.

[0022] The measured impedance signal sequence contains multiple time sampling points, and records the real part and imaginary part of the measured impedance output by the eddy current probe at each time sampling point.

[0023] The method for obtaining the angle synchronization reference point includes:

[0024] In the measured impedance signal sequence, calculate the absolute value of the imaginary part of the measured impedance at each time sampling point, search for the time sampling point with the smallest absolute value, and define the time sampling point with the smallest absolute value as the angle synchronization reference point.

[0025] The method for filtering the characteristic phase angle range of crack signals in the residual impedance sequence includes:

[0026] For each angle sampling point in the residual impedance sequence, calculate the residual phase angle and residual amplitude to obtain the characteristic phase angle range of the crack signal. Angle sampling points whose residual phase angle falls within the characteristic phase angle range of the crack signal are marked as suspected crack points.

[0027] A probe-adjustable eddy current testing system for bearing steel balls is used to implement the aforementioned probe-adjustable eddy current testing method for bearing steel balls. The system includes:

[0028] The compensation baseline generation module is used to establish a probe-spherical plane rectangular coordinate system, define the deflection angle in the probe-spherical plane rectangular coordinate system, calculate the lift-off value and lift-off acceleration corresponding to each deflection angle of the spherical surface, determine the effective compensation angle range based on the lift-off acceleration, and generate a lift-off compensation baseline impedance sequence within the effective compensation angle range.

[0029] The flaw detection signal rejection module is used to collect the measured impedance signal sequence and align it with the lift-off compensation baseline impedance sequence as the bearing steel ball rolls over the eddy current probe along the rolling direction. The measured impedance signal sequence after angular alignment is subtracted from the lift-off compensation baseline impedance sequence point by point to extract the residual impedance sequence. The residual impedance sequence is then filtered for crack signal characteristic phase angle range and adaptive amplitude rejection is performed. For bearing steel balls that are rejected and have real surface crack defects, the module performs defect severity classification.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0031] This invention establishes a unified quantitative reference standard for the spatial geometric relationship between the bearing steel ball surface and the eddy current probe detection surface by constructing a probe-spherical Cartesian coordinate system. By defining the deflection angle, the change in lift-off distance during the steel ball's rolling process is transformed into an analytically calculable function. Combined with the calculation of the lift-off value and the acceleration of the lift-off change, the spatial region where abrupt changes in spherical lift-off can be located. The effective compensation angle range determined in this way can match the actual range of lift-off interference. The lift-off compensation baseline impedance sequence generated based on the effective compensation angle range can characterize the probe impedance change law caused by the spherical curvature under defect-free conditions. By aligning the measured impedance signal sequence with the lift-off compensation baseline impedance sequence, It can ensure that the compensation calculation corresponds to the impedance data at the same spatial position on the sphere. By extracting the residual impedance sequence through point-by-point subtraction, the lift-off impedance component caused by the curvature of the sphere can be separated from the measured signal, eliminating the phase angle aliasing between the transient pulse signal induced by the sudden change in lift-off acceleration and the crack signal. By filtering the characteristic phase angle range of the crack signal, the residual data that matches the direction characteristics of the crack signal can be locked. Combined with adaptive amplitude rejection, the crack signal is identified and judged. While avoiding the misjudgment of defect-free bearing steel balls, it can ensure the detection capability of real surface crack defects, so that the detection results of eddy current testing of bearing steel balls have stable accuracy and reliability, and are suitable for bearing steel ball flaw detection scenarios with different nominal diameter specifications. Attached Figure Description

[0032] 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.

[0033] Figure 1 A schematic diagram of a method for eddy current flaw detection of bearing steel balls based on probe adjustment;

[0034] Figure 2 This is a schematic diagram of the probe-spherical plane rectangular coordinate system in this invention;

[0035] Figure 3 This is a schematic diagram illustrating the geometric relationship between the deflection angle and the lift-off value in this invention;

[0036] Figure 4 This is a flowchart illustrating the determination of the effective compensation angle range in this invention;

[0037] Figure 5 This is a flowchart illustrating angle synchronization alignment in this invention;

[0038] Figure 6 This is a schematic diagram of point-by-point subtraction residual extraction in this invention;

[0039] Figure 7 This is a functional block diagram of a bearing steel ball eddy current flaw detection system based on probe adjustment. Detailed Implementation

[0040] 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.

[0041] Example 1

[0042] Please see Figure 1 As shown, this embodiment provides an eddy current flaw detection method for bearing steel balls based on probe adjustment, including:

[0043] Step S10: Establish a probe-spherical plane rectangular coordinate system, define the deflection angle in the probe-spherical plane rectangular coordinate system, calculate the lift-off value and lift-off acceleration corresponding to each deflection angle of the spherical plane, determine the effective compensation angle range based on the lift-off acceleration, and generate a lift-off compensation baseline impedance sequence within the effective compensation angle range.

[0044] Specifically, step S10 addresses the inherent geometric characteristic of the nonlinear change in the distance between the probe and the measured surface (i.e., the lift-off distance) along the rolling direction due to the spherical curvature during eddy current testing of bearing steel balls. This is achieved by establishing a geometric projection relationship between the ball diameter and the probe, transforming the physical property of spherical curvature into a precisely calculable mathematical model. In the field of eddy current testing, the lift-off distance refers to the vertical distance between the detection surface of the eddy current probe and the surface of the conductive material being tested. Changes in this vertical distance directly affect the real and imaginary parts of the output impedance of the eddy current probe, thus forming a signal trajectory on the impedance plane related to the lift-off distance change. When the object being tested is planar, the lift-off distance remains constant during testing, and the impedance signal output by the eddy current probe only reflects changes in the electromagnetic properties of the material itself. When the object being tested is spherical, due to the spherical curvature, even if the center of the sphere remains stationary relative to the probe, the vertical distance from each point on the sphere to the probe's detection surface changes with the angle of that point on the sphere, resulting in a component related to the lift-off distance change being superimposed on the impedance signal output by the eddy current probe. In practical applications of eddy current testing for bearing steel balls, the bearing steel balls roll past the eddy current probe, with each point on the sphere sequentially entering the probe's effective detection area. This causes the lift-off distance to exhibit a nonlinear change pattern that first decreases and then increases over time. This nonlinear change pattern results in a sudden rate change at the point on the sphere closest to the probe. The phase angle of the resulting transient impedance pulse on the impedance plane is close to the phase angle of the actual surface crack signal. This makes it impossible for the eddy current testing equipment to distinguish between the pseudo-crack pulse caused by the spherical curvature and the actual crack signal based solely on the impedance signal. Consequently, defective bearing steel balls are mistakenly identified as defective bearing steel balls and discarded. Step S10 constructs a probe-spherical Cartesian coordinate system and derives an analytical function in this system to show how the lift-off value changes with the deflection angle, making the lift-off distance at each position on the spherical surface a predictable and definite quantity. Further, the second derivative of the analytical function of the lift-off value is obtained to determine the lift-off acceleration, which quantitatively characterizes the rate of change of the lift-off distance itself, thereby accurately locating the spatial region where the lift-off acceleration abruptly occurs—the curvature gradient zone. Within the effective compensation angle range corresponding to the curvature gradient zone, the lift-off value sequence is mapped point-by-point to a lift-off compensation baseline impedance sequence using the lift-off-impedance transfer function obtained during the probe calibration stage. This represents the expected trajectory of the eddy current probe impedance change caused only by the curvature of the spherical surface under the condition that the spherical surface is intact and without defects. This provides a spatial reference system and numerical benchmark for subtracting the expected trajectory from the measured impedance signal sequence in step S20 to extract the residual impedance sequence.

[0045] Further, step S10 includes:

[0046] Step S11: Obtain the nominal diameter of the bearing steel balls in the current batch, calculate the ball cross-sectional radius based on the nominal diameter, obtain the initial lift setting value of the eddy current testing equipment at the testing station, and establish a probe-spherical plane rectangular coordinate system with the center of the eddy current probe's testing surface as the origin and the rolling direction of the bearing steel balls at the testing station as the horizontal axis.

[0047] Specifically, the nominal diameter refers to the numerical value of the diameter of the bearing steel ball, reflecting the geometric dimensional characteristics of the current batch of bearing steel balls. For example, for steel balls used in wind turbine yaw bearings, the nominal diameter typically ranges from 45 mm to 90 mm; for steel balls used in automotive wheel hubs and gearboxes, the nominal diameter typically ranges from less than 45 mm; and for steel balls used in electromechanical applications such as household appliances and elevators, the nominal diameter typically ranges from around 20 mm. The spherical cross-sectional radius R is equal to half the nominal diameter. The spherical cross-sectional radius represents the radius of the circle formed by any cross-section of the bearing steel ball through its center. In subsequent steps, it is used to calculate the distance from various positions on the spherical surface to the probe detection surface and to describe the degree of influence of the spherical curvature on the lift-off distance. The initial lift-off setting h0 refers to the initial distance between the probe detection surface and the nearest point on the bearing steel ball surface, which is preset by the mechanical clamping structure of the eddy current flaw detector at the testing station. The nearest point on the spherical surface is the point on the spherical surface that is closest to the eddy current probe detection surface. The initial distance is determined by the factory calibration parameters of the equipment and is used to ensure that there is both a sufficient safety gap between the probe and the tested spherical surface to avoid mechanical collision, and a sufficiently close distance to ensure the sensitivity of eddy current detection.

[0048] See Figure 2 This is a schematic diagram of the probe-spherical plane rectangular coordinate system. Figure 2This embodiment fully demonstrates the core components of the probe-spherical Cartesian coordinate system constructed in this example, including the horizontal axis, the vertical axis, the eddy current probe, the spherical surface of the bearing steel ball, the center of the ball, the nearest point on the spherical surface, the initial lift-off setting h0, and the radius R of the spherical cross-section, visually presenting the spatial geometric relationships between these components. The method for establishing the probe-spherical Cartesian coordinate system includes: defining the center of the eddy current probe's detection surface as the origin of the coordinate system; defining the normal direction of the eddy current probe's detection surface on the spherical center side as the vertical axis, with the positive direction of the vertical axis pointing towards the center of the bearing steel ball; defining the axial direction of the eddy current probe as the vertical axis, with the direction towards the center of the ball as the positive direction of the vertical axis; and defining the rolling direction of the bearing steel ball on the detection station as the horizontal axis. This forms a probe-spherical Cartesian coordinate system directly related to the probe's detection surface and the rolling direction of the spherical surface. In the probe-spherical plane rectangular coordinate system, the projection of the spherical cross section of the bearing steel ball is an arc with the radius of the spherical cross section as the radius. The center of the arc (i.e. the center of the ball) is located in the positive direction of the vertical coordinate axis. The distance from the center of the arc to the origin of the coordinate system is equal to the sum of the radius of the spherical cross section and the initial lift-off setting value. The intersection of the spherical surface of the bearing steel ball and the vertical coordinate axis is the closest point of the spherical surface. The perpendicular distance from the closest point of the spherical surface to the probe detection surface is the initial lift-off setting value h0.

[0049] Combination Figure 2The spatial geometric relationship is clear. The reason for using the center of the eddy current probe's detection surface as the coordinate origin, rather than the center of the sphere, is that the impedance signal response of the eddy current probe depends on the distance change of the measured surface relative to the probe's detection surface. Using the center of the probe's detection surface as the coordinate origin allows the lift-off values ​​at each location calculated subsequently to directly correspond to the physical input of the probe's impedance response. No additional coordinate translation transformation is needed to substitute the distance parameters in the geometric domain into the impedance response model in the electrical domain. The reason for choosing the rolling direction as the abscissa is that the bearing steel ball rolls past the eddy current probe at the detection station. The sequence of points on the sphere entering the probe's detection area unfolds along the rolling direction. Using the sequence along the rolling direction as the abscissa allows a direct linear correspondence between the angular positions of each point on the sphere and the time series, facilitating the synchronous alignment of the measured impedance signal sequence in the time domain with the lift-off compensation baseline impedance sequence in the angular domain in subsequent step S21. Without the probe-spherical Cartesian coordinate system established in step S11, the subsequent lift-off value calculation in step S12 would lack a unified spatial reference. This would prevent the lift-off values ​​corresponding to bearing steel balls from different batches and with different diameters from being compared and calculated in the same coordinate system. Consequently, the lift-off compensation baseline impedance sequence generated using the lift-impedance transfer function in step S14 would lose its physical basis for subtracting from the measured impedance signal. Step S11 reduces the curvature change problem on the three-dimensional sphere to a circular arc geometry problem on a two-dimensional cross-section, transforming the complex spherical geometric relationship into an analytical form that can be expressed by basic trigonometric functions. This simplifies the calculation process while ensuring the accuracy of the geometric relationship, laying the spatial geometric foundation for deriving the analytical function for the lift-off value in step S12.

[0050] Step S12: Define the angle of deflection along the arc direction relative to the nearest point on the sphere as the deflection angle. Obtain the lift-off value analytical function based on the sphere cross-section radius, the initial lift-off setting value and the deflection angle. Obtain the lift-off value corresponding to each deflection angle on the sphere based on the lift-off value analytical function. Obtain the lift-off rate of change and lift-off acceleration by taking the derivative of the lift-off value analytical function step by step.

[0051] The methods for obtaining the lift-off rate of change and lift-off acceleration by taking the derivative of the lift-off value analytical function step by step include: obtaining the lift-off rate of change by taking the first derivative of the lift-off value with respect to the deflection angle based on the lift-off value analytical function, and obtaining the lift-off acceleration by taking the second derivative of the lift-off value with respect to the deflection angle.

[0052] Specifically, see Figure 3 This is a schematic diagram illustrating the geometric relationship between the deflection angle and the lift-off value. Figure 3This fully demonstrates the eddy current probe, probe detection surface, bearing steel ball surface, ball center, initial lift-off setting h0, deflection angle θ, and the corresponding lift-off value h(θ) at the deflection angle, intuitively presenting the spatial geometric relationship between each core parameter. The nearest point on the sphere refers to the point on the bearing steel ball surface with the smallest vertical distance from the eddy current probe detection surface in the probe-sphere plane rectangular coordinate system established in step S11. The nearest point on the sphere is located on the vertical axis, and its vertical coordinate value is equal to the initial lift-off setting h0 obtained in step S11. When the bearing steel ball rolls on the detection station, the nearest point on the sphere is exactly below the probe, at which point the lift-off distance between the sphere and the probe detection surface reaches its minimum. The deflection angle θ is an angular position parameter measured along the arc direction of the sphere with the nearest point on the sphere as the zero point. Figure 3 As shown, the deflection angle θ is the angle between the line connecting the center of the sphere to the nearest point on the sphere and the line connecting the center of the sphere to any point on the sphere. The deflection angle θ is positive in the rolling direction and negative against the rolling direction, used to describe the spatial position of any point on the sphere relative to the nearest point on the sphere. For any point on the sphere at a deflection angle θ, the x-coordinate of that point in the probe-sphere plane rectangular coordinate system is equal to the product of the sphere's cross-sectional radius R and the sine of the deflection angle θ, i.e. The ordinate y of this point is equal to the sum of the sphere's cross-sectional radius R and the initial lift-off setting h0, minus the product of the sphere's cross-sectional radius and the cosine of the deflection angle θ, i.e. The vertical distance from this point to the detection surface of the eddy current probe is the lift-off value h(θ) corresponding to the deflection angle θ, such as... Figure 3 As shown, the lift-off value h(θ) is the perpendicular distance from the spherical point corresponding to the deflection angle θ to the probe detection surface. Since the probe detection surface is located on a plane with a ordinate of zero, the lift-off value h(θ) is numerically equal to the ordinate of the spherical point corresponding to the deflection angle θ. The specific form of the lift-off value analytic function is that the lift-off value h(θ) equals the radius of the spherical cross-section multiplied by 1 and the deflection angle. The difference in the cosine values, plus the initial lift-off setting, is... .

[0053] The reason why the lift-off value is defined as the perpendicular distance from each point on the sphere to the probe detection surface rather than the distance along other directions is that the alternating magnetic field generated by the eddy current probe decays the fastest in the direction normal to the detection surface, and the probe output impedance is most sensitive to the distance change in the direction normal to the detection surface. In the probe-sphere plane rectangular coordinate system established in step S11, the direction normal to the probe detection surface is exactly the direction of the vertical axis. Therefore, taking the vertical axis value as the lift-off value can accurately reflect the response characteristics of the probe impedance to the distance change in a physical sense. The method of successively differentiating the analytic function of the lift-off value includes: taking the first derivative of the lift-off value with respect to the deflection angle to obtain the lift-off rate of change, which is equal to the product of the radius of the sphere's cross-section and the sine of the deflection angle. Its physical meaning is the ratio of the change in lift-off distance to the change in angle when the contact point on the sphere changes from a certain deflection angle to an adjacent angle due to the rolling of the bearing steel ball; taking the second derivative of the lift-off value with respect to the deflection angle to obtain the lift-off acceleration, which is equal to the product of the radius of the sphere's cross-section and the cosine of the deflection angle. Its physical meaning is the rate at which the lift-off rate of change itself changes with the angle. At zero deflection angle, the lift-off rate of change is zero, indicating that at the closest point on the sphere, the sphere and the probe detection surface are approximately parallel, and the lift-off distance hardly changes with the angle. The lift-off acceleration reaches its maximum value at zero deflection angle, which is equal to the radius of the sphere's cross-section, indicating that the rate of change of the lift-off rate reaches its peak at the closest point on the sphere.

[0054] The reason for calculating the lift-off acceleration rather than just the lift-off value is that the response of the eddy current probe impedance signal to changes in the lift-off distance contains two components: a slowly varying component proportional to the lift-off value itself, and a transient pulse component proportional to the rate of change of the lift-off rate (i.e., the lift-off acceleration). The latter is the source of the spurious crack signal—when the lift-off acceleration drops sharply from its maximum value, the amplitude and phase angle of the transient pulse component fall precisely within the response range of the real crack signal on the impedance plane, causing the two to overlap and become indistinguishable. The characteristic that the lift-off acceleration reaches its maximum value at the point where the deflection angle is zero indicates that the nearest point on the sphere and its surrounding area are the core regions where the lift-off acceleration undergoes abrupt changes, and are also high-incidence areas for spurious crack signals. Step S12 transforms the influence of spherical curvature on probe impedance from an unpredictable interference factor into a precisely calculable quantity by obtaining three analytical functions related to the deflection angle: lift-off value, lift-off rate of change, and lift-off acceleration. This provides a mathematical tool for accurately locating the boundary of the curvature gradient zone in step S13 based on the distribution characteristics of the lift-off acceleration. Without the calculation of the lift-off acceleration in step S12, step S13 would be unable to determine the spatial occurrence region of the pseudo-crack signal, leading to inaccurate coverage of the lift-off compensation baseline impedance sequence generated in step S14. Consequently, the residual extraction in step S20 would be unable to effectively eliminate the pseudo-crack pulse component caused by curvature.

[0055] See Figure 4 Step S13: Set the acceleration change judgment threshold based on the product of the maximum value of the lift-off change acceleration at the deflection angle of zero and the preset acceleration change judgment ratio. Determine the deflection angle corresponding to the lift-off change acceleration equal to the acceleration change judgment threshold as the curvature gradient zone boundary angle. Obtain the coil diameter of the eddy current probe. Calculate the effective detection coverage angle of the eddy current probe based on the coil diameter and the sphere cross-section radius. Compare the curvature gradient zone boundary angle with the effective detection coverage angle to determine the effective compensation angle range and record the coverage mark.

[0056] Specifically, the acceleration mutation judgment ratio is a preset proportional coefficient used to determine at what level the lift-off acceleration decreases to be considered a significant mutation. The preset basis for the acceleration mutation judgment ratio is as follows: within the range of the acceleration mutation judgment ratio, the process of the lift-off acceleration decreasing from its maximum value to the acceleration mutation judgment threshold precisely covers the angle range where the transient pulse component and the real crack signal overlap on the impedance plane. When the acceleration mutation judgment ratio is lower than 0.6, the boundary angle of the curvature gradient zone is too large, including the gently changing region in the compensation range and increasing the amount of invalid calculations; when the acceleration mutation judgment ratio is higher than 0.8, the boundary angle of the curvature gradient zone is too small, missing some areas with high incidence of pseudo-crack signals and reducing the completeness of compensation. The specific value of the acceleration mutation judgment ratio is determined by the eddy current testing equipment during the calibration phase by collecting impedance signals from standard bearing steel balls, selecting a value within the range of 0.6 to 0.8 that minimizes the absolute value of the mean of the residual impedance sequence. The acceleration abrupt change judgment threshold is equal to the product of the maximum value of the lift-off acceleration at the deflection angle of zero obtained in step S12 and the acceleration abrupt change judgment ratio. Since the maximum value is equal to the spherical cross-section radius calculated in step S11, the acceleration abrupt change judgment threshold is equal to the product of the spherical cross-section radius and the acceleration abrupt change judgment ratio. For example, when the acceleration abrupt change judgment ratio is 0.7, the acceleration abrupt change judgment threshold is equal to 0.7 times the spherical cross-section radius. The curvature gradient zone boundary angle refers to the deflection angle corresponding to the lift-off acceleration equal to the acceleration abrupt change judgment threshold. The deflection angle is equal to the inverse cosine value of the acceleration abrupt change judgment ratio. For example, when the acceleration abrupt change judgment ratio is 0.7, the curvature gradient zone boundary angle is approximately 45.6 degrees. The curvature gradient zone refers to the spherical region covered from the negative curvature gradient zone boundary angle to the positive curvature gradient zone boundary angle. The spherical region is the spatial range where the lift-off acceleration drops sharply from its maximum value, and it is also a high-incidence area for pseudo-crack signals.

[0057] The reason the curvature gradient zone boundary angle is defined as the point where the lift-off acceleration decreases to its maximum value, rather than the point where the lift-off value reaches an absolute value, is because the essential cause of the spurious crack signal is the abrupt change in the lift-off acceleration, not the magnitude of the lift-off value itself. Within the range of the deflection angle increasing from zero to the curvature gradient zone boundary angle, the lift-off acceleration drops sharply from its maximum value to the product of that maximum value and the acceleration abrupt change determination ratio. The transient pulse component generated during this sharp decrease has a vector direction on the impedance plane that is close to the vector direction of the real crack signal. Therefore, the spherical region within this curvature gradient zone boundary angle range is the core region that needs compensation. Outside the curvature gradient zone boundary angle, the change in lift-off acceleration tends to be gradual, no longer generating transient pulse components sufficient to confuse with the crack signal. The coil diameter of the eddy current probe refers to the outer diameter of the coil inside the probe that generates the alternating magnetic field. This outer diameter is determined by the physical structure of the probe and determines the spatial range of the probe's effective detection area. The effective detection coverage angle refers to the range of deflection angles corresponding to the spherical area that the eddy current probe can effectively detect. The effective detection coverage angle is equal to the arcsine of the ratio of the coil diameter to twice the radius of the spherical cross-section.

[0058] The purpose of comparing the curvature gradient zone boundary angle with the effective detection coverage angle is to ensure that the coverage range of the compensation baseline neither exceeds the actual detection capability of the probe nor misses areas with a high incidence of pseudo-cracks within the detection range. When the curvature gradient zone boundary angle is less than or equal to the effective detection coverage angle, it indicates that the high incidence area of ​​pseudo-crack signals falls completely within the effective detection range of the eddy current probe. In this case, the effective compensation angle interval is the complete interval from the negative curvature gradient zone boundary angle to the positive curvature gradient zone boundary angle, and the coverage flag is recorded as a complete coverage state. When the curvature gradient zone boundary angle is greater than the effective detection coverage angle, it indicates that the effective detection range of the eddy current probe cannot cover the entire curvature gradient zone. In this case, the effective compensation angle interval is adjusted to the interval from the negative effective detection coverage angle to the positive effective detection coverage angle, and the coverage flag is recorded as a partial coverage state. The coverage flag recorded in step S13 is referenced in step S24 to adjust the safety margin of the ball-by-ball adaptive rejection threshold. For bearing steel balls with a partial coverage flag, a more stringent ball-by-ball adaptive rejection threshold is used to compensate for any uncompensated lift-off components that may remain due to the failure of the effective compensation angle range to cover the complete curvature gradient zone.

[0059] Step S13 precisely locates the spatial region where the spurious crack signal occurs and adaptively adjusts the effective compensation angle range according to different combinations of ball diameters and probe specifications. This ensures that the coverage of the lift-off compensation baseline impedance sequence generated in subsequent step S14 precisely matches the actual area requiring compensation. Without step S13, step S14 cannot determine the distribution range of angle sampling points, potentially leading to invalid compensation for areas outside the detection range (generating compensation values ​​at angle positions that the probe cannot actually detect) or missed compensation for areas within the detection range (missing some angle positions in areas with high spurious crack incidence). Both types of errors will affect the accuracy of residual extraction in step S22, thereby reducing the reliability of the rejection decision in step S24.

[0060] Step S14: Determine the number of angle sampling points N based on the ratio of nominal diameter to coil diameter, divide the effective compensation angle interval into N angle sampling points, substitute the deflection angle of the N angle sampling points into the lift-off value analytical function to calculate the lift-off value sequence, obtain the lift-off-impedance transfer function of the eddy current probe calibrated with a defect-free standard bearing steel ball, and use the lift-off-impedance transfer function to map the lift-off value sequence point by point into the lift-off compensation baseline impedance sequence.

[0061] Specifically, the method for determining the number of angle sampling points N is as follows: Calculate the ratio of the nominal diameter to the coil diameter of the eddy current probe, and set a boundary threshold. This boundary threshold is determined during the calibration stage based on the nonlinear fitting error of the lift-off value of the standard bearing steel ball under different combinations of ball diameter and coil diameter, ensuring that the fitting error is less than a preset upper limit of allowable error. The preset upper limit of allowable error is set based on the detection sensitivity of the eddy current flaw detection equipment for the smallest target surface crack, ensuring that the preset upper limit of allowable error is less than the impedance signal amplitude caused by the smallest target surface crack, so as to ensure that the fitting error caused by angle discretization does not mask the real micro-crack signal. When the ratio is greater than or equal to the boundary threshold, the number of angle sampling points is the integer part of the ratio multiplied by 10 and then added by 1; when the ratio is less than the boundary threshold, the number of angle sampling points is 41. For example, the boundary threshold is 4. The reason for linking the number of angle sampling points to the ratio of the nominal diameter to the coil diameter is that the larger the ball diameter, the higher the nonlinearity of the lift-off value within the curvature gradient zone, requiring denser sampling points to accurately describe the curve shape of the lift-off value changing with the deflection angle; the larger the coil diameter, the lower the spatial resolution of the probe for lift-off changes, allowing for a reduction in sampling points to match the probe's actual detection resolution. The effective compensation angle interval determined in step S13 is divided into N equal angle sampling points, with the angle spacing between adjacent angle sampling points equal to the total angle range of the effective compensation angle interval divided by the number of angle sampling points minus 1. The deflection angle value of each angle sampling point is substituted into the lift-off value analytical function obtained in step S12 to calculate the corresponding lift-off value, thus forming a set of lift-off value sequences arranged in order of angle position. The lift-off value sequence describes the expected lift-off distance at each discrete position on the spherical surface when the bearing steel ball rolls over the eddy current probe.

[0062] The lift-off impedance transfer function refers to the correspondence between changes in lift-off distance and changes in the output impedance of the eddy current probe. The lift-off impedance transfer function contains two output components: the real part of the impedance change corresponding to a given lift-off value and the imaginary part of the impedance change corresponding to a given lift-off value. The lift-off impedance transfer function is obtained during the calibration phase by placing a known defect-free standard bearing ball on the testing station and gradually changing the distance between the standard bearing ball and the eddy current probe's testing surface along the probe's axis. At multiple known lift-off values, the real and imaginary parts of the eddy current probe's impedance are recorded. From this, the mapping relationship between the lift-off value and the change in the real impedance, as well as the mapping relationship between the lift-off value and the change in the imaginary impedance, are fitted. These two mapping relationships together constitute the lift-off impedance transfer function. The reason for using the lift-off impedance transfer function obtained from actual measurements during the calibration phase, rather than the transfer function calculated based on electromagnetic theory, is that the actual impedance response of an eddy current probe is affected by various parameters such as the number of coil turns, wire resistance, core permeability, and detection frequency. These parameters exhibit manufacturing deviations between their actual values ​​in the probe and their theoretical design values. Using measured calibration data eliminates the impact of these manufacturing deviations on the accuracy of the transfer function. Similarly, the reason for using a known, defect-free standard bearing steel ball as the calibration component, rather than a planar standard test block, is that the spherical curvature of the standard bearing steel ball is the same as that of the ball being tested. Using spherical calibration ensures that the lift-off impedance transfer function already includes the influence of spherical curvature on the magnetic field distribution, thus ensuring that the lift-off compensation baseline impedance sequence generated based on the lift-off impedance transfer function remains consistent with the actual spherical detection scenario.

[0063] The method of mapping the lift-off value sequence point by point to a lift-off compensation baseline impedance sequence using the lift-off-impedance transfer function includes: for the lift-off value at each angular sampling point in the lift-off value sequence, calculating the real and imaginary changes in impedance corresponding to the lift-off value using the lift-off-impedance transfer function; and arranging the real and imaginary changes in impedance at each angular sampling point in an orderly manner according to their angular positions to form a lift-off compensation baseline impedance sequence. The lift-off compensation baseline impedance sequence represents the expected trajectory of the eddy current probe impedance change caused only by the change in lift-off distance due to the curvature of the spherical surface, under ideal conditions where the bearing steel ball surface is intact and defect-free. The integrity of the lift-off compensation baseline impedance sequence is verified: it is determined whether the signs of all real part changes in impedance and all imaginary part changes in impedance are consistent. If the signs are consistent, it indicates that the lift-off compensation baseline impedance sequence changes continuously in a single direction on the impedance plane, which conforms to the physical expectation of pure lift-off change and can be used for residual extraction in step S20. If there are inconsistent signs, it indicates that there may be an anomaly in the calibration process of the lift-off impedance transfer function, and it is necessary to re-calibrate using standard bearing steel balls and regenerate the lift-off compensation baseline impedance sequence.

[0064] Step S14 converts the lift-off value from the purely geometric domain in step S12 into a lift-off compensation baseline impedance sequence in the eddy current probe impedance domain. This makes the output of step S10 no longer an abstract distance value but a dimensionless electrical quantity that can be directly arithmetically calculated with the measured impedance signal acquired in step S21. The lift-off compensation baseline impedance sequence is a parameterized curve that automatically adjusts with the ball diameter. For batches of bearing steel balls with different nominal diameters, the ball cross-sectional radius calculated in step S11 is different, the parameters in the lift-off value analytical function obtained in step S12 are different, the effective compensation angle range determined in step S13 is different, and the number of angle sampling points and the lift-off value sequence in step S14 are also different accordingly. The final generated lift-off compensation baseline impedance sequence automatically adapts to the ball diameter specification of the current batch, eliminating the need for operators to manually adjust the compensation parameters for different ball diameters. Without step S14, the lift-off value analytical function obtained in step S12 cannot be converted into a compensation quantity in the impedance domain. This would prevent the lift-off component caused by curvature from being directly subtracted from the measured impedance signal in step S22, thus depriving subsequent residual extraction and rejection decisions of their numerical basis. Step S10 establishes a complete technical chain, starting from the nominal diameter of the bearing steel ball, constructing a probe-spherical plane rectangular coordinate system, deriving the lift-off value analytical function, determining the boundary of the curvature gradient zone, and finally generating the lift-off compensation baseline impedance sequence. This transforms the spherical curvature, the fundamental cause of pseudo-crack signals in eddy current testing, from an uncontrollable interference factor into a precisely predictable quantity, making the expected impedance change at each location on the spherical surface caused only by the spherical curvature a known benchmark. The extraction of the compensation baseline impedance sequence can effectively separate the curvature component and the defect component in the measured impedance signal, enabling the pseudo-crack pulses and real crack signals that were originally indistinguishable on the impedance plane due to phase angle aliasing to obtain a identifiable phase angle separation. The increase in phase angle separation restores the directional discrimination capability of the crack signal characteristic phase angle range screening in step S23, thereby enabling the amplitude rejection decision in step S24 to be based on the dual verification condition. The dual verification condition allows the rejection sensitivity to be improved without increasing the false rejection rate, enabling the detection of tiny crack defects that were originally masked in the pseudo-crack signal, meeting the high reliability requirements of bearing steel ball surface integrity in key application scenarios such as wind power yaw bearings.

[0065] Step S20: As the bearing steel ball rolls past the eddy current probe along the rolling direction, the measured impedance signal sequence is acquired and aligned with the lift-off compensation baseline impedance sequence at an angle. The measured impedance signal sequence after angle alignment is subtracted point by point from the lift-off compensation baseline impedance sequence to extract the residual impedance sequence. The residual impedance sequence is then subjected to crack signal characteristic phase angle range screening and adaptive amplitude rejection. For bearing steel balls that are rejected and have real surface crack defects, the defect severity is graded.

[0066] Specifically, step S20 addresses the signal characteristic that the measured impedance signal acquired by the eddy current probe during actual flaw detection is a superposition of lift-off components caused by spherical curvature, defect components caused by actual defects, and random noise components caused by the electromagnetic environment. This is achieved by strictly aligning the measured impedance signal sequence with the lift-off compensation baseline impedance sequence generated in step S10 in terms of spatial angle and performing point-by-point subtraction. This process removes the known lift-off components caused only by spherical curvature from the measured impedance signal sequence, extracting a residual impedance sequence containing only defect components and random noise components. In the field of eddy current flaw detection, the impedance plane is a two-dimensional coordinate plane with the real part of the impedance as the horizontal axis and the imaginary part as the vertical axis. The impedance signal output by the eddy current probe can be represented as a vector on the impedance plane. The amplitude of the vector reflects the signal strength, and the phase angle reflects the directional characteristics of the signal. Signals with different physical causes have different phase angle distribution ranges on the impedance plane, and theoretically, different types of signal sources can be distinguished by phase angle differences. In existing eddy current testing techniques for bearing steel balls, the lift-off acceleration caused by the curvature of the spherical surface undergoes abrupt changes near the nearest point on the spherical surface. The phase angle of the transient pulse component generated by this abrupt change on the impedance plane is close to the phase angle of the actual crack signal, causing them to overlap and become indistinguishable in the phase angle dimension. This renders the phase angle-based crack signal identification method ineffective. Step S20 subtracts the lift-off compensation baseline impedance sequence predicted in step S10 from the measured impedance signal, eliminating the projection of the lift-off component caused by the spherical curvature onto the impedance plane. This ensures that the residual impedance sequence no longer contains pseudo-crack pulse components that overlap with the crack signal phase angle, thereby restoring the phase angle separation between the lift-off direction and the crack direction from an indistinguishable state before compensation to a clearly distinguishable state. Based on this, step S20 calculates the residual phase angle and residual amplitude for each angle sampling point in the residual impedance sequence, uses the characteristic phase angle range of the crack signal to perform directional screening of the residual phase angle to mark suspected crack points, and then establishes a ball-by-ball adaptive rejection threshold based on the statistical characteristics of the residual amplitude to perform amplitude rejection for suspected crack points, so that the rejection decision is based on the dual verification of two independent conditions: the direction of the phase angle entering the crack and the amplitude exceeding the noise level.

[0067] Further, step S20 includes:

[0068] See Figure 5In step S21, as the bearing steel ball rolls past the eddy current probe along the rolling direction, the output impedance of the eddy current probe is continuously acquired to obtain a measured impedance signal sequence. The measured impedance signal sequence contains multiple time sampling points. The real part and imaginary part of the measured impedance output by the eddy current probe at each time sampling point are recorded. The time sampling point with the smallest absolute value of the imaginary part of the measured impedance is searched from the measured impedance signal sequence as the angle synchronization reference point. The angle synchronization reference point is used as the time zero point to obtain the rolling linear velocity of the bearing steel ball on the detection station. According to the angle synchronization reference point, the rolling linear velocity and the ball cross-sectional radius, the time sampling points in the measured impedance signal sequence are mapped to N angle sampling points in the lift-off compensation baseline impedance sequence. The measured impedance signal sequence after angle alignment corresponding to the N angle sampling points is extracted.

[0069] Specifically, when the bearing ball rolls past the eddy current probe along the rolling direction at the testing station of the eddy current testing equipment, the impedance acquisition module of the eddy current testing equipment continuously acquires the output impedance of the eddy current probe. The acquisition frequency is determined by the analog-to-digital converter of the equipment. The acquired measured impedance signal sequence contains multiple time sampling points. Each time sampling point records the real part and the imaginary part of the measured impedance output by the eddy current probe at that moment. The real part of the measured impedance refers to the resistive component of the impedance in the equivalent circuit of the eddy current probe, reflecting the energy loss in the probe coil; the imaginary part of the measured impedance refers to the reactive component of the impedance in the equivalent circuit of the eddy current probe, reflecting the change in the stored energy in the probe coil. The total number of sampling points in the measured impedance signal sequence is determined by the product of the time required for the bearing ball to roll past the probe testing area and the acquisition frequency. The total number of sampling points is greater than the number of angle sampling points determined in step S14 to ensure that the measured data has sufficient time resolution for subsequent angle synchronization alignment.

[0070] The method for determining the angle synchronization reference point includes: calculating the absolute value of the imaginary part of the measured impedance at each time sampling point in the measured impedance signal sequence, searching for the time sampling point with the smallest absolute value, and defining this time sampling point as the angle synchronization reference point. The reason for choosing the moment with the smallest absolute value of the imaginary part of the measured impedance as the angle synchronization reference point is that, as derived in step S12, the lift-off rate of change is equal to the product of the radius of the sphere's cross-section and the sine of the deflection angle. At the point where the deflection angle is zero, the lift-off rate of change is zero. At this time, the closest point on the sphere is exactly below the probe, the lift-off distance does not change with the angle, and the change in the imaginary part of the eddy current probe's impedance approaches zero. The imaginary part of the impedance is sensitive to the rate of change of the lift-off distance. When the lift-off rate of change is zero, the imaginary part of the impedance reaches a steady-state value, and the change in the imaginary part of the impedance relative to this steady-state value is minimal. Therefore, the absolute value of the imaginary part of the measured impedance takes its minimum value at the moment when the closest point on the sphere passes directly below the probe. By searching for the time sampling point corresponding to the minimum value, the moment when the nearest point on the sphere passes through the probe can be accurately located. This moment corresponds to the spatial position where the deflection angle is zero as defined in step S12, thereby establishing a synchronous correspondence between the time domain and the angle domain.

[0071] The validity of the angle synchronization reference point is determined by: obtaining the change in the real part of the impedance corresponding to the point where the deflection angle is zero in the lift-off compensation baseline impedance sequence generated in step S14; setting the upper limit of the effective range as the product of the change in the real part of the impedance and a preset upper limit coefficient; setting the lower limit of the effective range as the product of the change in the real part of the impedance and a preset lower limit coefficient; and determining whether the measured real part of the impedance at the angle synchronization reference point falls within the effective range. The upper and lower bound coefficients are preset based on the following: the change in the real part of the impedance at a deflection angle of zero, taken as the theoretical reference value under normal rolling conditions, is used. A certain range of positive and negative deviations from the theoretical reference value is allowed for the measured real part of the impedance. This range should cover random noise fluctuations in the electromagnetic environment and normal fluctuations caused by system errors in the impedance measurement of the eddy current probe, but should exclude deviations caused by abnormal rolling conditions such as ball bounce or slippage in the bearing. The specific values ​​of the upper and lower bound coefficients are determined by the eddy current testing equipment during the calibration phase, which collects the measured real parts of the impedance from multiple defect-free standard bearing balls, statistically analyzes the deviation distribution of the measured real part of the impedance relative to the theoretical reference value, and takes the coefficients corresponding to the upper and lower envelopes of the deviation distribution as the upper and lower bound coefficients, respectively. For example, the upper bound coefficient is set to 1.2, and the lower bound coefficient is set to 0.8. If the measured impedance at the angle synchronization reference point falls within the valid range, the angle synchronization reference point is confirmed to be correctly positioned, and subsequent steps can continue. If the measured impedance at the angle synchronization reference point exceeds the valid range, it indicates that the bearing ball may have bounced or slipped during rolling, causing the nearest point on the ball surface to not pass directly below the probe. In this case, the bearing ball is marked as a synchronization failure ball and sent to the manual re-inspection channel, and the subsequent automatic rejection steps are not executed. The reason for the validity judgment is that the rolling state of the bearing ball at the inspection station may be affected by surface oil, mechanical vibration, or clamping deviation, resulting in abnormalities. If the subsequent residual extraction and rejection process is still performed on abnormally rolling balls, incorrect rejection results will be produced due to angle synchronization inaccuracy. By excluding abnormally rolling balls from the automatic rejection process through validity judgment, misjudgment caused by synchronization inaccuracy can be avoided, and these balls are sent to the manual re-inspection channel to ensure that no potential defects are missed.

[0072] Using the angle synchronization reference point as the zero point of time, the rolling linear velocity of the bearing steel ball on the inspection station is obtained. The rolling linear velocity is measured by the drive parameters of the conveying mechanism of the eddy current flaw detection equipment or by an external speed sensor. Based on the angle synchronization reference point, the rolling linear velocity, and the ball cross-sectional radius calculated in step S11, a one-to-one correspondence is established between the time sampling points in the measured impedance signal sequence and the angle sampling points in the lift-off compensation baseline impedance sequence. The method for establishing the correspondence includes: for any time sampling point in the measured impedance signal sequence, calculating the time offset between the time sampling point and the angle synchronization reference point; multiplying the time offset by the rolling linear velocity to obtain the arc length displacement; removing the arc length displacement and using the ball cross-sectional radius to obtain the corresponding deflection angle. A linear relationship is established between the arc length and the central angle through the ball cross-sectional radius. This is a basic principle of geometry. By using this basic principle, the sampling points in the time domain are converted into sampling points in the angle domain, so that the time sequence and the spatial angle sequence form a direct correspondence. The measured impedance data points corresponding one-to-one with the angle sampling points of the extracted compensation baseline impedance sequence in step S14 are extracted from the measured impedance signal sequence to form an angle-aligned measured impedance signal sequence. Each angle sampling point in the measured impedance signal sequence records the real and imaginary parts of the measured impedance at the corresponding angle position. Without the angle synchronization alignment in step S21, when subtracting the measured impedance signal sequence from the extracted compensation baseline impedance sequence point by point in step S22, the two sequences will not correspond accurately in spatial position, rendering the subtraction operation physically meaningless—potentially resulting in an error where the measured value at one position on the sphere is subtracted from the expected value at another position. This leaves a large number of spurious components introduced by the alignment deviation in the residual impedance sequence, severely interfering with subsequent crack signal identification. Step S21, by accurately determining the angle synchronization reference point and establishing a time-angle mapping relationship, ensures that the subsequent point-by-point subtraction operation physically corresponds to the measured value minus the expected value at the same spherical position, providing a spatial synchronization basis for the accuracy of residual extraction.

[0073] Step S22: Subtract the lift-off compensation baseline impedance sequence point by point from the measured impedance signal sequence after angle alignment to obtain the residual impedance sequence.

[0074] The method for obtaining the residual impedance sequence includes: subtracting the change in the real part of the impedance at the corresponding angle sampling point in the lift-off compensation baseline impedance sequence from the real part of the measured impedance at each angle sampling point in the angle-aligned measured impedance signal sequence to obtain the real part of the residual impedance; subtracting the change in the imaginary part of the impedance at the corresponding angle sampling point in the lift-off compensation baseline impedance sequence from the imaginary part of the measured impedance at each angle sampling point in the angle-aligned measured impedance signal sequence to obtain the imaginary part of the residual impedance; and forming the residual impedance sequence from the real part and the imaginary part of the residual impedance at each angle sampling point.

[0075] Specifically, see Figure 6 This is a schematic diagram of residual extraction by point-by-point subtraction. Figure 6 This demonstrates the measured impedance signal sequence after angle alignment, the extracted compensated baseline impedance sequence, the operational logic of point-by-point subtraction, and the final output residual impedance sequence. It clearly presents the complete process of stripping the curvature component and extracting the true crack signal from the measured signal containing spherical curvature interference. The execution process of the point-by-point subtraction operation is as follows: [The text then abruptly shifts to a different topic:] ... Figure 6 The measured impedance signal sequence, after angular alignment of the crack signal and curvature component, is superimposed with each angle sampling point from the sequence. Figure 6 In the lift-off compensation baseline impedance sequence containing only curvature components, angle sampling points with the same angular position are found. The real part of the measured impedance is subtracted from the change in the real part of the impedance to obtain the real part of the residual impedance, and the imaginary part of the measured impedance is subtracted from the change in the imaginary part of the impedance to obtain the imaginary part of the residual impedance. The real and imaginary parts of the residual impedance at this angle sampling point are saved as a pair of data in the residual impedance sequence. After performing the above subtraction operation on all angle sampling points one by one, a complete residual impedance sequence is formed. The physical meaning of the residual impedance sequence is as follows: the lift-off compensation baseline impedance sequence represents the expected value of the eddy current probe impedance change caused only by the curvature of the spherical surface under the condition that the bearing steel ball surface is intact and without defects. The angle-aligned measured impedance signal sequence represents the impedance output of the eddy current probe during the actual detection process. The output includes the lift-off component caused by the curvature of the spherical surface, the defect component caused by the spherical defect, and the random noise component caused by the electromagnetic environment. Subtracting the lift-off compensation baseline impedance sequence from the angle-aligned measured impedance signal sequence is mathematically equivalent to removing the known curvature lift-off component from the measured impedance signal, just as... Figure 6 The point-by-point subtraction process reveals that the residual impedance sequence contains only defect components and random noise components. Figure 6 The signal is characterized by curvature components that have been completely eliminated, leaving only the true crack signal and random noise fluctuations.

[0076] The reason for using point-by-point subtraction to eliminate curvature components instead of frequency domain filtering is that the frequency characteristics of the lift-off change caused by spherical curvature overlap with the frequency characteristics of the defect signal in the angular domain. Step S12 has already derived that the lift-off acceleration abruptly changes at the zero deflection angle. The high-frequency components generated by this abrupt change in the frequency domain are difficult to separate from the high-frequency components of the micro-crack signal using a frequency domain filter. If a low-pass filter is used to eliminate the high-frequency components, it will simultaneously filter out the real crack signal; if a high-pass filter is used to retain the high-frequency components, it cannot eliminate the pseudo-crack pulses generated by the abrupt change in lift-off acceleration. Point-by-point subtraction is a deterministic subtraction operation performed directly in the spatial domain, i.e., the angular domain. It does not involve the selection or rejection of frequency components. The elimination of curvature components is deterministic and does not change other components, thus avoiding the accidental deletion of useful signals with frequencies close to the defect signal. On the impedance plane, the lift-off compensation baseline impedance sequence extends along the lift-off direction. After point-by-point subtraction, the components in the lift-off direction in the residual impedance sequence are eliminated, while the crack direction components, which are different from the lift-off direction, are completely preserved. This core effect is achieved in… Figure 6 This is clearly demonstrated in the data: the crack signal, which was originally superimposed on the gradually changing curvature signal and was difficult to distinguish from the curvature interference, becomes a clearly identifiable independent spike signal after point-by-point subtraction, thus restoring the phase angle separation between the two directions from the aliasing state before compensation to a clearly distinguishable state.

[0077] The signal quality assessment of the residual impedance sequence includes: calculating the arithmetic mean of the real part and the arithmetic mean of the imaginary part of the residual impedance at all angle sampling points in the residual impedance sequence; obtaining the maximum value of the change in the real part and the maximum value of the change in the imaginary part of the impedance at all angle sampling points in the lift-off compensation baseline impedance sequence; determining whether the absolute value of the arithmetic mean of the real part of the residual impedance is less than the product of the maximum change in the real part of the impedance and a preset residual mean ratio threshold; and determining whether the absolute value of the arithmetic mean of the imaginary part of the residual impedance is less than the product of the maximum change in the imaginary part of the impedance and a preset residual mean ratio threshold. In other words, the absolute values ​​of the arithmetic mean of the real part of the residual impedance and the absolute values ​​of the arithmetic mean of the imaginary part of the residual impedance share the same residual mean ratio threshold for upper limit comparison. The preset basis for the residual mean ratio threshold is as follows: Under the ideal condition of a defect-free sphere, the arithmetic mean of the residual impedance sequence should be contributed only by random noise components with a mean of zero, and the absolute values ​​of the arithmetic mean of the real part of the residual impedance and the absolute values ​​of the arithmetic mean of the imaginary part of the residual impedance relative to the maximum change in the lift-off compensation baseline impedance sequence should tend to zero. Considering the non-zero fluctuations in the residual mean caused by the electromagnetic noise and quantization error of the eddy current probe, the residual mean ratio threshold is set as the upper limit ratio of the tolerable residual mean to the maximum change. The upper limit ratio is determined by the upper envelope of the ratio of the absolute value of the statistical residual mean to the maximum impedance change of multiple defect-free standard bearing steel balls during the calibration phase of the eddy current flaw detection equipment. For example, the residual mean ratio threshold is set to one-tenth. If both of the above conditions are met, it indicates that the point-by-point subtraction effectively eliminates the systematic impedance shift caused by curvature, and the mean of the residual impedance sequence approaches zero, which meets the physical expectation that the residual tends to zero when there are no defects. Step S23 can then be executed. The reason why the residual mean should approach zero is that, under ideal conditions where the sphere is defect-free, the measured impedance signal should be highly consistent with the lift-off compensation baseline impedance sequence, and the residual after subtracting the two should only contain random noise components with a mean of zero. If the absolute value of the arithmetic mean of the real part of the residual impedance is greater than or equal to the product of the maximum change in the real part of the impedance and the residual mean ratio threshold, or if the absolute value of the arithmetic mean of the imaginary part of the residual impedance is greater than or equal to the product of the maximum change in the imaginary part of the impedance and the residual mean ratio threshold, it is considered that the residual mean deviates from zero. This indicates that the point-by-point subtraction has failed to effectively eliminate the curvature component. Possible reasons include deviations in the positioning of the angle synchronization reference point in step S21, or drift in the calibration of the lift-off impedance transfer function in step S14. If either of the above two conditions is not met, the angle synchronization reference point search in step S21 is re-executed for the bearing steel ball. If the second search still fails, the bearing steel ball is marked as an abnormal compensation ball and sent to the manual re-inspection channel to avoid misjudgment due to insufficient compensation.

[0078] Without the residual extraction in step S22, the crack signal characteristic phase angle range screening in step S23 would be unable to effectively distinguish between pseudo-crack pulses and real crack signals. This is because the phase angle of the pseudo-crack pulses in the measured impedance signal without eliminating curvature components falls exactly within the characteristic phase angle range of the crack signal, causing all angle sampling points to be marked as suspected crack points or all pseudo-crack pulses to be misjudged as real cracks. Step S22 removes the curvature component from the measured impedance signal through a prediction-correction mechanism, fundamentally changing the distribution characteristics of the residual impedance sequence on the impedance plane—the lift-off direction component is suppressed while the crack direction component is retained, creating the signal conditions for restoring the directional discrimination capability in the crack signal characteristic phase angle range screening in step S23.

[0079] Step S23: Calculate the residual phase angle and residual amplitude for each angle sampling point in the residual impedance sequence, obtain the characteristic phase angle range of the crack signal, and mark the angle sampling points whose residual phase angle falls within the characteristic phase angle range of the crack signal as suspected crack points.

[0080] Specifically, the calculation methods for residual phase angle and residual amplitude are based on vector representation on the impedance plane. For each angular sampling point in the residual impedance sequence, the residual phase angle is equal to the arctangent of the ratio of the imaginary part to the real part of the residual impedance. The above calculation uses an arctangent function capable of handling all four quadrants to correctly determine the quadrant in which the phase angle lies. The physical meaning of the residual phase angle is the direction angle of the residual impedance vector relative to the positive direction of the real part on the impedance plane; this direction angle reflects the physical origin characteristics of the residual signal. The residual amplitude is equal to the square root of the sum of the squares of the real and imaginary parts of the residual impedance. The above calculation is based on the Pythagorean theorem to derive the magnitude of the vector on the impedance plane. The physical meaning of the residual amplitude is the magnitude of the residual impedance vector; this magnitude reflects the energy level of the residual signal.

[0081] The method for obtaining the characteristic phase angle range of crack signals includes: During the calibration stage, a standard crack test block with a known artificial crack is used to calibrate the eddy current probe. The standard crack test block is placed below the detection surface of the eddy current probe and adjusted to simulate the lift-off distance during actual detection. The impedance signal when the eddy current probe detects the artificial crack is collected, and the direction angle of the crack signal vector is recorded on the impedance plane. The above calibration process is repeated for multiple artificial cracks of different depths and lengths. The direction angle distribution of all crack signal vectors is statistically analyzed to determine the lower and upper bounds of the characteristic phase angle range of crack signals. The physical meaning of the characteristic phase angle range of crack signals is: when the eddy current probe detects a real surface crack, the crack signal vector generated on the impedance plane by the sudden change in local conductivity caused by the real surface crack falls within the direction angle range. The reason why the crack signal vector has a specific phase angle range is that the surface crack changes the flow path of the eddy current in the measured material, forcing the eddy current to flow around the crack area, resulting in the extension of the eddy current path and the redistribution of the eddy current density. The induced electromotive force change generated in the eddy current probe coil has a definite phase characteristic, which is reflected on the impedance plane as the impedance change within a specific directional angle range.

[0082] The process of screening the characteristic phase angle range of the crack signal includes: for each angle sampling point in the residual impedance sequence, determining whether the residual phase angle of the sampling point falls within the characteristic phase angle range of the crack signal, that is, determining whether the residual phase angle is greater than or equal to the lower bound and less than or equal to the upper bound of the characteristic phase angle range of the crack signal. If the residual phase angle falls within the characteristic phase angle range of the crack signal, the sampling point is marked as a suspected crack point and the residual amplitude of the suspected crack point is retained for amplitude rejection in step S24; if the residual phase angle does not fall within the characteristic phase angle range of the crack signal, the sampling point is marked as a non-crack point, and non-crack points do not participate in the amplitude rejection in step S24. The reason for screening the characteristic phase angle range of the crack signal before performing amplitude rejection is that although the systematic lift-off component caused by the spherical curvature has been eliminated in step S22, a small number of signal components in non-crack directions may still remain in the residual impedance sequence. These signal components may originate from local permeability fluctuations caused by the microscopic inhomogeneity of the bearing steel ball material composition, thermal drift of the probe coil, or transient interference from the electromagnetic environment. The phase angles of these residual components in non-crack directions are different from the characteristic phase angle range of the crack signal on the impedance plane. By first performing directional screening using the characteristic phase angle range of the crack signal, these residual small number of signal components in non-crack directions can be excluded from the rejection candidates, and only residual points with direction angles consistent with the real cracks are retained in the amplitude judgment stage, thereby further reducing the false rejection rate caused by non-crack factors.

[0083] Step S23 works in conjunction with step S22. The curvature compensation in step S22 makes the crack signal characteristic phase angle range screening in step S23 feasible and effective. Before step S22 is executed, the phase angle of the lift-off acceleration abrupt pulse caused by the spherical curvature falls exactly within the crack signal characteristic phase angle range on the impedance plane. This is the phase angle aliasing problem described in step S10, which makes it impossible to distinguish between pseudo-cracks and real cracks when screening the crack signal characteristic phase angle range. No matter how the boundary of the crack signal characteristic phase angle range is set, either pseudo-cracks are included in the suspected crack points, or real cracks are excluded from the suspected crack points. After eliminating the curvature component by point-by-point subtraction in step S22, the lift-off direction component on the impedance plane is suppressed. There are no longer pseudo-crack pulses with phase angles aliased with crack signals in the residual impedance sequence. The crack signal characteristic phase angle range screening restores its due directional discrimination capability and can accurately screen out residual points with phase angles entering the crack direction as suspected crack points. If the phase angle screening in step S23 is missing, step S24 will perform amplitude rejection on all angle sampling points in the residual impedance sequence. If the amplitude of a small number of signal components in non-crack directions accidentally exceeds the ball-by-ball adaptive rejection threshold, they will be misjudged as cracks, increasing the false rejection rate. At the same time, since the ball-by-ball adaptive rejection threshold needs to be set to a high value to avoid misjudgments caused by non-crack components, real micro-crack signals may be missed because their amplitude is smaller than the ball-by-ball adaptive rejection threshold, reducing the detection rate. Step S23 limits the rejection candidates to the residual points whose phase angle characteristics are consistent with the real cracks through phase angle screening, so that the amplitude rejection in step S24 focuses on the locations where cracks may actually exist, which reduces the false rejection rate and creates conditions for improving detection sensitivity.

[0084] Step S24: Calculate the statistical mean and statistical standard deviation based on the residual amplitude of all angle sampling points in the residual impedance sequence. Determine the ball-by-ball adaptive rejection threshold based on the statistical mean and statistical standard deviation. Perform adaptive amplitude rejection based on the residual amplitude of suspected crack points and the ball-by-ball adaptive rejection threshold. Perform defect severity classification on bearing steel balls whose rejection result is that there are real surface crack defects.

[0085] Specifically, the statistical mean and statistical standard deviation are calculated as follows: The statistical mean is obtained by summing the residual amplitudes at all angular sampling points in the residual impedance sequence and dividing by the total number of angular sampling points. The statistical standard deviation is obtained by squared differences between all residual amplitudes and the statistical mean, summed, divided by the total number of angular sampling points, and then taking the square root. The statistical mean reflects the overall level of the residual amplitudes; under ideal conditions of a defect-free sphere, this overall level should be determined by the background level of random noise. The statistical standard deviation reflects the dispersion of the residual amplitudes relative to the statistical mean; under ideal conditions of a defect-free sphere, this dispersion should be determined by the fluctuation range of random noise.

[0086] The method for determining the ball-by-ball adaptive rejection threshold includes: setting a safety factor, where the ball-by-ball adaptive rejection threshold equals the statistical mean plus the safety factor multiplied by the statistical standard deviation. The value of the safety factor is determined based on the application scenario of the current batch of bearing steel balls: for application scenarios with a high risk of in-service fracture, a larger safety factor is used to ensure sensitivity in detecting microcracks; for application scenarios with a low risk of in-service fracture, a smaller safety factor is used to balance the detection rate and the false rejection rate. For example, for steel balls used in wind turbine yaw bearings, because in-service fracture of these steel balls could lead to serious consequences such as wind turbine collapse, a safety factor of 5 is used; for steel balls used in automotive wheel hubs and gearboxes, a safety factor of 4 is used; and for steel balls used in electromechanical applications such as household appliances and elevators, a safety factor of 3 is used. The reason for basing the ball-by-ball adaptive rejection threshold on the statistical characteristics of the residual amplitude of each bearing ball, rather than using a fixed absolute threshold, is that there are slight differences in the material homogeneity among different bearing balls, and the electromagnetic noise levels at different detection times are not entirely the same. These factors lead to inter-ball differences in the residual noise floor level of different balls. If a fixed absolute threshold is used, when the noise floor of a bearing ball is too high, the fixed threshold has insufficient noise margin relative to the bearing ball, and the noise peak may be misjudged as a crack signal, leading to false rejection. When the noise floor of a bearing ball is too low, the fixed threshold has too large a noise margin relative to the bearing ball, and the real micro-crack signal may be masked below the overly lenient threshold and missed. The ball-by-ball adaptive rejection threshold, by linking the threshold to the noise level of each bearing ball, ensures that the rejection sensitivity maintains a consistent statistical significance level across all individual bearing balls, preventing false rejection due to high noise of a particular bearing ball and avoiding missed detection due to low noise of a particular bearing ball.

[0087] The coverage flag recorded in step S13 is conditionally judged: if the coverage flag is in a partial coverage state, that is, the curvature gradient band boundary angle determined in step S13 is greater than the effective detection coverage angle, the safety multiple is reduced by the preset adjustment amount and the ball-by-ball adaptive rejection threshold is recalculated to compensate for the impact of the uncompensated lift-off component that may remain on the quality of the residual impedance sequence signal because the effective compensation angle interval fails to cover the complete curvature gradient band. The preset basis for the adjustment amount is as follows: the adjustment amount should cause the adaptive rejection threshold for each ball in the partial coverage state to decrease relative to the full coverage state; the decreased adaptive rejection threshold for each ball should be sufficient to detect minute crack signals, which refer to true surface crack signals masked by residual uncompensated lift-off components; at the same time, it should avoid the misjudgment of random noise peaks as cracks due to excessive reduction in the safety factor; the specific value of the adjustment amount is determined by the eddy current flaw detection equipment during the calibration phase by collecting residual impedance sequences of standard bearing steel balls with a curvature gradient zone boundary angle greater than the effective detection coverage angle, on the premise that the statistical significance level of random noise peaks in the residual impedance sequence is consistent with that in the full coverage state. The adjustment amount is usually taken as a positive integer. For example, the adjustment amount is 1, that is, the safety factor minus 1. The reason for tightening the ball-by-ball adaptive rejection threshold in the partial coverage state is that when the effective compensation angle range is smaller than the curvature gradient zone, the lift-off component in the edge region of the curvature gradient zone cannot be completely eliminated by the point-by-point subtraction in step S22. The remaining uncompensated lift-off component increases the background level and fluctuation range of the residual impedance sequence. If the same safety factor as in the full coverage state is still used, the ball-by-ball adaptive rejection threshold will be relatively high, which may miss small cracks. By reducing the safety factor to tighten the ball-by-ball adaptive rejection threshold, the detection sensitivity of cracks can be maintained even when the quality of the residual signal decreases.

[0088] The adaptive amplitude rejection process includes: for each angle sampling point marked as a suspected crack point in step S23, comparing the residual amplitude with the ball-by-ball adaptive rejection threshold. If the residual amplitude of the suspected crack point is greater than or equal to the ball-by-ball adaptive rejection threshold, it is determined that there is a real surface crack defect at the angle position corresponding to the sampling point; if the residual amplitude of all suspected crack points is less than the ball-by-ball adaptive rejection threshold, it is determined that there is no crack defect on the surface of the bearing steel ball, and the bearing steel ball is sent into the qualified product channel. The reason why the rejection decision needs to simultaneously meet two conditions, namely the phase angle pointing into the crack direction and the amplitude exceeding the noise level, is that a single condition criterion has inherent defects: judging solely based on the phase angle may misjudge extremely small noise fluctuations as cracks, and judging solely based on the amplitude may misjudge amplitude interference in non-crack directions as cracks. The dual-condition rejection requires that the residual signal both points in the characteristic phase angle range of the crack signal in direction and exceeds the reasonable fluctuation range of the noise statistical distribution in intensity. The simultaneous satisfaction of the two independent conditions greatly reduces the probability of misjudgment, making the rejection decision more reliable.

[0089] The defect severity grading process includes: for bearing steel balls determined to have actual surface cracks, calculating the difference between the residual amplitude of the suspected crack point and the ball-by-ball adaptive rejection threshold, and comparing the difference with the statistical standard deviation. If the difference between the residual amplitude and the ball-by-ball adaptive rejection threshold is less than the product of the statistical standard deviation and the preset severity threshold multiple, the defect is graded as a minor defect, and the bearing steel ball is sent to the ultrasonic testing re-inspection channel for secondary confirmation based on the ultrasonic testing results; if the difference between the residual amplitude and the ball-by-ball adaptive rejection threshold is greater than or equal to the product of the statistical standard deviation and the preset severity threshold multiple, the defect is graded as a severe defect, and the bearing steel ball is directly discarded. The severity cutoff multiple is preset based on the following: Under ideal conditions where the sphere is defect-free, the residual amplitude approximately follows a random distribution centered on the statistical mean and fluctuating on the statistical standard deviation. The difference between the residual amplitude and the sphere-by-sphere adaptive rejection threshold reflects the degree to which the residual signal exceeds the range of noise statistical fluctuations. When the difference is less than the product of the statistical standard deviation and the severity cutoff multiple, the residual signal just exceeds the statistical significance level corresponding to the sphere-by-sphere adaptive rejection threshold, and there is a possibility that it is caused by accidental strong noise fluctuations, requiring secondary confirmation through ultrasonic flaw detection. When the difference is greater than or equal to the product of the statistical standard deviation and the severity cutoff multiple, the residual signal has exceeded the reasonable fluctuation range of the noise statistical distribution, and the corresponding defect has a high confidence level. The specific value of the severity cutoff multiple is selected according to the confidence level of the standard normal distribution. For example, the severity cutoff multiple is 2, corresponding to a 95% confidence level. The reason for adding an ultrasonic testing re-inspection step for balls with minor defects is that eddy current testing and ultrasonic testing have complementary sensitivities to defect types: eddy current testing is sensitive to surface and near-surface cracks but not to volumetric internal defects, while ultrasonic testing is sensitive to internal defects and deeper cracks but not to very shallow surface cracks. For balls with minor defects where the difference between the residual amplitude and the ball-by-ball adaptive rejection threshold is less than the product of the statistical standard deviation and the severity threshold multiple, there are two possibilities: either a tiny surface crack does exist, or there is significant noise fluctuation but no actual crack. Re-inspection using ultrasonic testing: if ultrasonic testing also detects the defect, the ball is confirmed for rejection; if ultrasonic testing does not detect the defect, re-inspection or release can be considered. Combining both methods improves the overall reliability of the detection. Without the ball-by-ball adaptive rejection threshold mechanism in step S24, rejection would rely on a fixed threshold. When there are significant differences in noise floor between balls, the fixed threshold cannot adapt to individual differences, leading to a higher false rejection rate for some bearing balls and a higher false negative rate for others, resulting in inconsistent detection quality across different individual bearing balls. Step S24 links the ball-by-ball adaptive rejection threshold to the noise statistical characteristics of each bearing ball, ensuring that the rejection decision for all individual bearing balls is based on the same statistical significance level, thus achieving consistency in detection quality across individuals.

[0090] Step S20 establishes a complete signal processing chain from measured impedance signal acquisition, angle synchronization alignment, residual extraction, phase angle screening to adaptive amplitude rejection. This signal processing chain precisely removes the lift-off component caused by the predicted spherical curvature in step S10 from the measured impedance signal, ensuring that the residual impedance sequence no longer contains pseudo-crack pulse components that overlap with the real crack signal phase angle. This restores the identifiable phase angle separation between the pseudo-crack pulses and the real crack signal, which were previously indistinguishable due to phase angle overlap on the impedance plane. The restoration of phase angle separation enables the screening of the crack signal's characteristic phase angle range to regain directional discrimination capability, accurately identifying residual points whose phase angles enter the crack direction while excluding residual components in non-crack directions. Based on this, the ball-by-ball adaptive rejection threshold is dynamically adjusted according to the noise statistical characteristics of each bearing ball, ensuring that the rejection sensitivity maintains a consistent statistical significance level across all individual bearing balls. The dual-condition rejection mechanism requires the residual signal to simultaneously meet two independent conditions: the direction of the crack entering at the phase angle and the amplitude exceeding the reasonable fluctuation range of the noise statistical distribution. This provides dual assurance for the reliability of the rejection decision. The defect severity grading mechanism classifies defects according to the degree to which the residual amplitude exceeds the ball-by-ball adaptive rejection threshold. For balls with minor defects, ultrasonic testing is added for re-inspection to improve the overall detection reliability. Balls with severe defects are directly rejected to ensure the surface integrity of the finished products. The above-mentioned technical link in step S20 reduces the false rejection rate caused by spherical curvature without sacrificing the actual crack detection rate. At the same time, it tightens the ball-by-ball adaptive rejection threshold compared to the fixed threshold when curvature compensation is not performed, improving the detection sensitivity to detect tiny crack defects that were originally hidden in the false crack signal. This meets the high reliability requirements for the surface integrity of bearing steel balls in key application scenarios such as wind power yaw bearings.

[0091] Example 2

[0092] This embodiment, based on Embodiment 1, provides a bearing steel ball eddy current flaw detection system based on probe adjustment, such as... Figure 7 As shown, it includes:

[0093] The compensation baseline generation module is used to establish a probe-spherical plane rectangular coordinate system, define the deflection angle in the probe-spherical plane rectangular coordinate system, calculate the lift-off value and lift-off acceleration corresponding to each deflection angle of the spherical surface, determine the effective compensation angle range based on the lift-off acceleration, and generate a lift-off compensation baseline impedance sequence within the effective compensation angle range.

[0094] The flaw detection signal rejection module is used to collect the measured impedance signal sequence and align it with the lift-off compensation baseline impedance sequence as the bearing steel ball rolls over the eddy current probe along the rolling direction. The measured impedance signal sequence after angular alignment is subtracted from the lift-off compensation baseline impedance sequence point by point to extract the residual impedance sequence. The residual impedance sequence is then filtered for crack signal characteristic phase angle range and adaptive amplitude rejection is performed. For bearing steel balls that are rejected and have real surface crack defects, the module performs defect severity classification.

[0095] Furthermore, in the compensation baseline generation module, the probe-spherical plane rectangular coordinate system takes the center of the detection surface of the eddy current probe as the origin, the rolling direction of the bearing steel ball on the detection station as the horizontal axis, and the normal direction of the detection surface of the eddy current probe on the center side of the ball as the vertical axis.

[0096] The deflection angle refers to the angle of deflection along the arc direction on the spherical surface relative to the nearest point on the spherical surface, and the nearest point on the spherical surface refers to the point on the spherical surface that is closest to the detection surface of the eddy current probe.

[0097] The calculation methods for the lift-off value and the lift-off acceleration include:

[0098] Obtain the nominal diameter of the bearing steel balls in the current batch, calculate the ball cross-sectional radius based on the nominal diameter, and obtain the initial lift-off setting value of the eddy current flaw detection equipment at the inspection station;

[0099] The lift-off value analytical function is obtained based on the sphere's cross-sectional radius, initial lift-off setting value, and deflection angle. The lift-off value corresponding to each deflection angle of the sphere is obtained based on the lift-off value analytical function.

[0100] Based on the analytic function of the lift-off value, the second derivative of the lift-off value with respect to the deflection angle is used to obtain the lift-off acceleration.

[0101] The method for determining the effective compensation angle range includes:

[0102] Set an acceleration change judgment threshold, and determine the deflection angle corresponding to the acceleration change judgment threshold when the lift-off acceleration is equal to the curvature gradient zone boundary angle. Calculate the effective detection coverage angle of the eddy current probe, and compare the curvature gradient zone boundary angle with the effective detection coverage angle to determine the effective compensation angle range.

[0103] 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.

[0104] 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.

[0105] 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 eddy current testing of bearing steel balls based on probe adjustment, characterized in that, The method includes: Establish a probe-spherical plane rectangular coordinate system, define the deflection angle in the probe-spherical plane rectangular coordinate system, calculate the lift-off value and lift-off acceleration corresponding to each deflection angle of the spherical surface, determine the effective compensation angle range based on the lift-off acceleration, and generate a lift-off compensation baseline impedance sequence within the effective compensation angle range. As the bearing steel ball rolls past the eddy current probe along the rolling direction, a measured impedance signal sequence is acquired and angularly aligned with the lift-off compensation baseline impedance sequence. The measured impedance signal sequence after angular alignment is subtracted point by point from the lift-off compensation baseline impedance sequence to extract the residual impedance sequence. The residual impedance sequence is then subjected to crack signal characteristic phase angle range screening and adaptive amplitude rejection. For bearing steel balls that are rejected and have real surface crack defects, a defect severity classification is performed.

2. The eddy current flaw detection method for bearing steel balls based on probe adjustment according to claim 1, characterized in that, The probe-spherical rectangular coordinate system has the center of the detection surface of the eddy current probe as the origin, the rolling direction of the bearing steel ball on the detection station as the horizontal axis, and the normal direction of the detection surface of the eddy current probe on the center side of the ball as the vertical axis.

3. The eddy current flaw detection method for bearing steel balls based on probe adjustment according to claim 2, characterized in that, The deflection angle refers to the angle of deflection along the arc direction on the spherical surface relative to the nearest point on the spherical surface, and the nearest point on the spherical surface refers to the point on the spherical surface that is closest to the detection surface of the eddy current probe.

4. The eddy current flaw detection method for bearing steel balls based on probe adjustment according to claim 3, characterized in that, The method for calculating the lift-off value and lift-off acceleration corresponding to each deflection angle of the sphere includes: Obtain the nominal diameter of the bearing steel balls in the current batch, calculate the ball cross-sectional radius based on the nominal diameter, and obtain the initial lift-off setting value of the eddy current flaw detection equipment at the inspection station; The lift-off value analytical function is obtained based on the sphere's cross-sectional radius, initial lift-off setting value, and deflection angle. The lift-off value corresponding to each deflection angle of the sphere is obtained based on the lift-off value analytical function. Based on the analytic function of the lift-off value, the second derivative of the lift-off value with respect to the deflection angle is used to obtain the lift-off acceleration.

5. The eddy current flaw detection method for bearing steel balls based on probe adjustment according to claim 4, characterized in that, The method for determining the effective compensation angle range includes: Set an acceleration change judgment threshold, and determine the deflection angle corresponding to the acceleration change judgment threshold when the lift-off acceleration is equal to the curvature gradient zone boundary angle. Calculate the effective detection coverage angle of the eddy current probe, and compare the curvature gradient zone boundary angle with the effective detection coverage angle to determine the effective compensation angle range.

6. The eddy current flaw detection method for bearing steel balls based on probe adjustment according to claim 5, characterized in that, The method for generating the lift-off compensated baseline impedance sequence includes: The effective compensation angle interval is divided into N angle sampling points. The deflection angles of the N angle sampling points are substituted into the lift-off value analytical function to calculate the lift-off value sequence. The lift-off-impedance transfer function of the eddy current probe calibrated with a defect-free standard bearing steel ball is obtained. The lift-off-impedance transfer function is used to map the lift-off value sequence point by point into the lift-off compensation baseline impedance sequence.

7. The eddy current flaw detection method for bearing steel balls based on probe adjustment according to claim 6, characterized in that, The method for performing angle alignment includes: Obtain the angle synchronization reference point. Using the angle synchronization reference point as the time zero point, obtain the rolling linear velocity of the bearing steel ball on the testing station. Based on the angle synchronization reference point, the rolling linear velocity and the ball cross-sectional radius, map the time sampling points in the measured impedance signal sequence to N angle sampling points in the lift-off compensation baseline impedance sequence. Extract the measured impedance signal sequence after aligning the angles corresponding to the N angle sampling points.

8. The eddy current flaw detection method for bearing steel balls based on probe adjustment according to claim 7, characterized in that, The measured impedance signal sequence contains multiple time sampling points, and records the real part and imaginary part of the measured impedance output by the eddy current probe at each time sampling point. The method for obtaining the angle synchronization reference point includes: In the measured impedance signal sequence, calculate the absolute value of the imaginary part of the measured impedance at each time sampling point, search for the time sampling point with the smallest absolute value, and define the time sampling point with the smallest absolute value as the angle synchronization reference point.

9. The eddy current flaw detection method for bearing steel balls based on probe adjustment according to claim 8, characterized in that, The method for filtering the characteristic phase angle range of crack signals in the residual impedance sequence includes: For each angle sampling point in the residual impedance sequence, calculate the residual phase angle and residual amplitude to obtain the characteristic phase angle range of the crack signal. Angle sampling points whose residual phase angle falls within the characteristic phase angle range of the crack signal are marked as suspected crack points.

10. A bearing steel ball eddy current testing system based on probe adjustment, used to implement the bearing steel ball eddy current testing method based on probe adjustment as described in any one of claims 1-9, characterized in that, The system includes: The compensation baseline generation module is used to establish a probe-spherical plane rectangular coordinate system, define the deflection angle in the probe-spherical plane rectangular coordinate system, calculate the lift-off value and lift-off acceleration corresponding to each deflection angle of the spherical surface, determine the effective compensation angle range based on the lift-off acceleration, and generate a lift-off compensation baseline impedance sequence within the effective compensation angle range. The flaw detection signal rejection module is used to collect the measured impedance signal sequence and align it with the lift-off compensation baseline impedance sequence as the bearing steel ball rolls over the eddy current probe along the rolling direction. The measured impedance signal sequence after angular alignment is subtracted from the lift-off compensation baseline impedance sequence point by point to extract the residual impedance sequence. The residual impedance sequence is then filtered for crack signal characteristic phase angle range and adaptive amplitude rejection is performed. For bearing steel balls that are rejected and have real surface crack defects, the module performs defect severity classification.

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