A bearing lubrication condition monitoring method based on impedance signal

Abstract

This invention provides a bearing lubrication condition monitoring method based on impedance signals, relating to the field of rolling bearing technology. This invention uses electrical impedance spectroscopy to determine the film thickness under elastohydrodynamic lubrication conditions and the oil film rupture under mixed lubrication. By constructing a roller-raceway electrical contact model, it achieves quantitative estimation and condition identification of the oil film thickness under actual bearing operating conditions. This method utilizes the electrical impedance signal and equivalent circuit model of the lubrication contact area, does not rely on optical transparency, is applicable to opaque materials and conventional industrial bearings, and enables online monitoring and lubrication control of bearing lubrication conditions.

Description

Technical Field

[0001] This invention relates to the field of rolling bearing technology, and in particular to a method for monitoring bearing lubrication status based on impedance signals. Background Technology

[0002] With increasing global focus on sustainable economic development, energy conservation, emission reduction, and high reliability of machinery and equipment have become core pursuits in the industrial sector. As a key supporting component, rolling bearings play an irreplaceable role in various power transmission systems, and their operating condition directly affects the overall system's energy efficiency and service life. Against this backdrop, reducing internal friction loss and wear in bearings is widely recognized as a crucial means to improve overall machine performance and extend operating cycles. Under ideal operating conditions, bearings should maintain elastohydrodynamic lubrication (EHL), meaning that a thin, high-pressure, stable lubricating oil film establishes a completely isolated contact between the rolling elements and raceways, significantly reducing the contact friction coefficient and effectively suppressing failure modes such as abrasive and adhesive wear. In actual operating conditions, bearings often face complex challenges such as high loads, low speeds, frequent starts, or insufficient lubricating oil viscosity. These factors can easily disrupt EHL conditions, leading to a deterioration of the lubrication state into mixed lubrication or even boundary lubrication. This results in frequent metal-to-metal contact, significantly increased frictional power consumption, and consequently, exacerbated wear and localized fatigue, severely impacting bearing life and system stability.

[0003] Especially under high-speed operation, due to the significantly enhanced entrainment effect of the rolling elements, lubricating oil is prone to local backflow or even cavitation zones at the contact inlet. This recirculation effect induces severe shear deformation, leading to a rapid and aggravated local temperature rise. Increased oil temperature directly causes a decrease in lubricating oil viscosity, further weakening the oil film's load-bearing capacity and thinning the film thickness, significantly increasing the risk of localized mixed lubrication. The change in lubrication state is not determined by a single factor but is governed by the coupled effects of multiple dynamic operating parameters such as rotational speed, load, temperature, and oil viscosity, exhibiting high nonlinearity and time sensitivity. Because the EHL contact area is extremely small (only mm...),... 2 The lubricating film thickness ranges from 50 nm to 1.5 μm, and the roller contact time is only 10 seconds. -5 Up to 10 -3 Accurately measuring the thickness of the lubricating film in the field remains a significant challenge, even down to the second. Obtaining instantaneous oil film thickness is crucial for improving energy efficiency and bearing life.

[0004] To reduce bearing torque, industry and academia have explored various strategies, such as using low-viscosity lubricants, reducing lubricant filler volume, improving sealing structures, and optimizing rolling element geometry. One of the most direct and effective methods is reducing the viscosity of the lubricating oil or the amount of lubricant supplied. However, while this approach can reduce frictional losses, it may accelerate the decomposition of the lubricating film under high-speed, heavy-load, or high-temperature conditions, making it difficult to maintain the EHL state and ultimately leading to direct metal-to-metal contact.

[0005] In actual EHL contact conditions, oil film thickness and its breakup ratio are key parameters for judging lubrication status. An excessively thin oil film leads to insufficient lubrication, increases contact stress, and causes various surface damages such as adhesive wear, pitting, and fatigue spalling between the rolling elements and raceways. Simultaneously, the rolling elements may collide with the cage during movement; this impact load further damages the existing oil film structure, exacerbating the deterioration of lubrication. Therefore, maintaining a "sufficient but not excessive" lubrication film thickness while achieving the bearing's low torque target becomes a critical issue in lubrication design optimization. To accurately grasp the lubrication status of bearings under actual operating conditions, the development of high-resolution, high-sensitivity, and non-invasive film thickness visualization and monitoring technologies has become a research hotspot. Numerous studies have focused on monitoring the lubrication status of EHL contact points, with optical interferometry being the most classic and commonly used method.

[0006] Optical interferometry can accurately determine the oil film thickness at the contact point under laboratory conditions and is widely used in fundamental research such as verifying lubrication theories, studying lubricant formulations, and evaluating the effects of additives. However, its biggest limitation is that it relies on transparent materials (such as quartz or glass) as part of the contact pair to generate interference fringes for film thickness calculation. This makes it unsuitable for direct application to actual metal roller bearing systems, and its deployment is difficult and structurally complex in high-speed rotating, load-changing industrial environments, making online monitoring challenging.

[0007] Numerous studies have explored methods for monitoring the lubrication condition of EHL contact points, with optical interferometry being particularly popular due to its ability to accurately measure oil film thickness at EHL contact points. However, this method requires the use of transparent materials, thus failing to determine the actual lubrication condition of the ball bearing. Existing research has demonstrated that rolling contact pairs exhibit a typical capacitive response under EHL conditions, while a significant resistive component appears under mixed lubrication conditions; therefore, the oil film condition can be inferred through impedance spectroscopy. However, existing methods largely employ empirical regression models, lacking white-box modeling paths based on physical structural parameters, which limits their universality and accuracy. Therefore, there is an urgent need to develop a method for online real-time monitoring of lubrication conditions and identification of oil film thickness changes. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a bearing lubrication condition monitoring method based on impedance signals. By measuring the impedance signal in the lubrication contact area and combining it with an equivalent circuit model, the impedance spectrum response is mapped to the oil film thickness, thereby achieving the assessment of the lubrication condition.

[0009] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0010] A bearing lubrication condition monitoring method based on impedance signal uses electrical impedance spectroscopy to determine the film thickness under elastohydrodynamic lubrication conditions and the oil film rupture during mixed lubrication.

[0011] Specifically, the following steps are included:

[0012] Step 1: Construct a roller-raceway electrical contact model;

[0013] Under radial load, various rolling elements bear different forces and form a load zone; opposite the load zone, there are unloaded rolling elements in the rolling bearing, with clearance under low axial load; in the loaded rolling elements, a Hertzian contact zone with a central lubricating film thickness h0 is formed, while the unloaded rolling elements remain unchanged between the inner and outer rings; in the rolling bearing, when a complete lubricating film is formed in the load zone, the relevant electrical quantity used to describe the electrical behavior is capacitance, the lubricant acts as a dielectric, and the rolling elements and raceways form electrodes;

[0014] Step 2: Measure the bearing impedance using the voltage ratio method;

[0015] By connecting the bearing under test in series with a known reference impedance and then connecting it to an excitation voltage source, the voltage response across the reference impedance is measured using a high-precision voltage acquisition system. By comparing the proportional relationship between the reference voltage and the excitation voltage, the equivalent impedance value of the bearing is indirectly calculated.

[0016] Step 3: Calculate the effective contact area of ​​the contact point;

[0017] Based on Hertzian contact theory, and combined with the load borne by the bearing, the geometric parameters of the rolling elements and the elastic properties of the material, the effective area of ​​the contact elliptical region is calculated. This area reflects the range of actual mechanical and electrical coupling between the rolling elements and the raceway.

[0018] Step 4: Calculate the bearing capacitance, which includes two parts: one is the capacitance formed by the lubricating film in the Hertz contact area, the medium of which is lubricating oil under high pressure, and the film thickness is the average thickness at the contact center; the other is the distributed capacitance formed between the rolling elements and the raceway through the gap in the non-contact area.

[0019] Taking into account the contact angle, raceway curvature, rolling element position and lubricant dielectric properties, a semi-analytical method is used to integrate different regions separately to finally obtain the equivalent capacitance value of the bearing as a whole. This capacitance is a key electrical parameter reflecting the lubrication state, and its value change directly corresponds to the trend of oil film thickness change.

[0020] Step 5: Calculate the oil film thickness;

[0021] After completing the capacitance calculation, the lubrication film thickness under the current working condition is derived by establishing a mapping relationship between capacitance and oil film thickness. Based on the physical characteristics of the lubrication film as a dielectric, the electrical response is converted into a geometric index of the lubrication state by utilizing the sensitivity of capacitance value to film thickness. The obtained oil film thickness is used to determine whether the bearing is currently in metal contact, mixed lubrication, or full lubrication state, and further supports real-time identification and early warning of lubrication state.

[0022] Step 6: Determine the lubrication condition of the bearing based on the physical characteristics of the oil film thickness; lubrication conditions include metal-to-metal contact, mixed lubrication, and complete lubrication;

[0023] In rolling bearings or line contact systems, when the oil film thickness is less than 50 nm, the bearing is in a metal-to-metal contact state; when the oil film thickness is between 50 nm and 300 nm, the bearing is in a mixed lubrication state; when the oil film thickness is greater than 300 nm, it enters the elastohydrodynamic (EHL) lubrication state, and the bearing is in a fully lubricated state, at which point the frictional resistance is minimal and the system operation is most stable.

[0024] Furthermore, the specific method for step 2 is as follows:

[0025] The unknown impedance Z of the bearing under test DUT With a known reference impedance Z ref Connected in series, with excitation voltage v gen ; By measuring the voltage v across the reference impedance with high precision ref The unknown impedance Z of the bearing under test DUT The result is obtained from formula (23):

[0026] (twenty three);

[0027] Among them, the unknown impedance Z of the bearing under test DUT This is the equivalent impedance value of the bearing.

[0028] Furthermore, the specific method of step 3 is as follows:

[0029] Depending on the direction of the applied radial and axial bearing forces, each ball of a ball bearing may bear a different load; when the radial bearing force F r When in operation, the load area is determined by the angle. Description, which leads to distance It depends on the bearing inner diameter. Assuming the bearing has no clearance and only radial force acts on it, only the lower half of the bearing's balls bear the load. For this load distribution with zero bearing clearance, the maximum force Q of each ball at the center of the load area is... max The estimate is:

[0030] (1);

[0031] in, This is the maximum load that the roller can withstand. For radial load, z is the number of rollers. If there is an additional axial force, use the equivalent radial force F. eq Replace F r The effect of the equivalent radial force on the contact is the same as the combination of radial force and axial force, according to formula (1).

[0032] Free contact angle The angle describing the contact point between the ball and raceway and the radial axis is derived under conditions of minimum axial load and no radial load, and it depends on the bearing clearance. , rolling element diameter D RE and raceway consistency ratio f i and f o The calculation method is based on the dimensionless distance between the center points of the raceway radius. Free contact angle The calculation formula is as follows:

[0033] (2);

[0034] For each ball in contact with the wheel, the effective radius is calculated based on Hertz's theory, and then further calculated according to the elastohydrodynamic theory of elliptical contact:

[0035] (3);

[0036] (4);

[0037] in, Define the effective radius in the rolling direction, and It is the effective radius perpendicular to the scrolling direction; subscript parameter This indicates the contact point on the inner ring, while This indicates the contact point on the outer ring; the estimated pitch circle diameter of the bearing is... ;

[0038] Then, calculate the sum of curvature using the two formulas. and curvature difference :

[0039] (5);

[0040] (6);

[0041] Then, for the calculation of the lubricating film thickness, the Young's modulus of the contact object is used. and and Poisson's ratio and To calculate the reduced Young's modulus E of the contact object:

[0042] (7);

[0043] in, The Young's modulus of the rolling element. The Young's modulus of the ring. The Poisson's ratio of the rolling element. The Poisson's ratio for the ring;

[0044] The Hertzian region where the ball contacts the curved raceway is an elliptical region consisting of the major semi-axis a and the minor semi-axis b; the area of ​​this Hertzian region is calculated using formula (8):

[0045] (8);

[0046] in, Let π represent pi, μ and ν be dimensionless Hertzian coefficients, m = 0.3 be Poisson's ratio, and E be the Young's modulus of steel, E = 2.08 × 10⁻⁶. 5 N / mm 2 ∑ρ represents the sum of deflections, and Q represents the maximum load. The contact area is Hertz.

[0047] Furthermore, the specific method of step 4 is as follows:

[0048] The influencing factor of external capacitance is the distance between the spherical surface and the annular raceway; first, define the distance between the center of the toroidal surface and the center of the rolling element. for:

[0049] (9);

[0050] in, The radius of the groove is perpendicular to the rolling direction; It is the radius of the rolling element; It is the gap height without deformation; Free contact angle; It is the raceway radius along the rolling direction; It is expressed as the displacement difference along the x-direction, reflecting the offset of the ball center relative to the raceway center in the rolling direction; It represents the displacement difference along the y-direction, and represents the radial offset between the center of the ball and the center of the raceway. This represents the displacement difference along the z-direction, corresponding to the distance from the sphere to the groove surface in the normal direction;

[0051] Next, in toroidal coordinates In the diagram, t and p are circular coordinates, representing the raceway surface. Described as:

[0052] (10);

[0053] If the origin of the coordinate system is taken at the center of the sphere If the coordinates are in spherical coordinate system, then the sphere... Represented as:

[0054] (11);

[0055] Equal equation (10) to equation (11) and eliminate the difference. ,have to:

[0056] (12);

[0057] in:

[0058] (13);

[0059] The root of equation (13) is 𝑟 groove ( ), representing the distance from the center of the ball to any intersection point on the raceway surface, is solved using numerical methods;

[0060] The distance equation for the edge region is derived similarly, but since the raceway surface is approximately cylindrical, the equation is reduced to a quadratic form, which can be solved analytically as follows:

[0061] (14);

[0062] in, This refers to the clearance between the raceway edge area and the rolling elements;

[0063] Next, for and In respectively , Integrate above; to cover the entire integration region, For fixed integration limits, As a dependent variable; Indicates the radius of the raceway edge;

[0064] Upper limit of integration in the rolling direction Defined as the maximum value in a mathematical sense, to cover the main physical influence area, i.e., the sum of all free electrode surfaces. Determined by the raceway tangent passing through the center of the rolling element, the calculation formula is:

[0065] (15);

[0066] To differentiate between the entrance and exit areas, another integration limit is introduced. The entry area's integration range is... arrive The export zone integral range is from 0 to If the free contact angle Then the left and right sides The values ​​may differ; Θ0 is defined as the contact center at the free contact angle α, excluding the Hertzian region, Θ1 is the groove boundary, and Θ2 is the rim end, as shown in the following three equations:

[0067] (16);

[0068] (17);

[0069] (18);

[0070] Among them, B R B is half the width of the shoulder of the rolling element. L b is the effective length of the bearing, and b is the short half-shaft in the Hertz region;

[0071] If asymmetry exists due to angular contact or combined loads, the integration limits for the left and right sides (r, l) need to be calculated separately; to account for air in the exit area, Θ 0,in Define the upper limit of the inlet integral, where φ is the coordinate of the scrolling direction. When φ < 0, the upper limit of the inlet integral Θ is... 0,in Same as Θ0; when φ≥0, the upper limit of the entrance integral Θ 0,in (φ) along (a / R) RE The direction of φ rises 45° until the end point at the inlet. Where a is the semi-major axis of the Hertzian contact ellipse; the exit region starts from φ=0 and extends to... End. Assuming the mixture consists of part oil and part air, the dielectric constant of the oil film thickness h0 is... The dielectric constant of the air portion is taken as =1; Therefore, the contribution of each part of the capacitance is:

[0072] (19);

[0073] (20);

[0074] (twenty one);

[0075] in, , , These are respectively the inner trench capacitance, outer trench capacitance, and edge capacitance; The variable u represents the vacuum dielectric constant; u1 and u2 represent the lower and upper limits of integration in the rolling direction, corresponding to the integration boundaries of the oil film at the outlet and inlet ends; the variable u represents the integral coordinate in the rolling direction, with the same meaning as φ; Θ1(u) and Θ 0,in (u), Θ 0,out Θ2(u) and Θ2(u) are the groove boundary angle, inlet center angle, outlet center angle and wheel flange end angle, respectively;

[0076] Due to the left-right asymmetry, each item , Both sides need to be calculated separately, so the expression for the total capacitance is:

[0077] (twenty two);

[0078] in, , , and , , These are the inner capacitance, outer capacitance, and edge capacitance of the trenches on both the left and right sides.

[0079] The generator frequency is [frequency], and the carrier frequency is [frequency]. Capacitance C measured by a single contact plate at time M Calculate using the following formula:

[0080] (twenty four);

[0081] in, Let the imaginary part of the measured impedance be... The magnitude of the impedance being measured. For carrier frequency;

[0082] Hertzian region contact capacitance The calculation is as follows:

[0083] (25).

[0084] Furthermore, in step 5, the oil film thickness According to formulas (8) and (25), calculate as follows:

[0085] (26);

[0086] in, It represents the relative permittivity of lubricating oil under pressure and temperature.

[0087] The beneficial effects of adopting the above technical solution are as follows: The bearing lubrication condition monitoring method based on impedance signals provided by this invention is a method for calculating oil film thickness based on electrical impedance to determine the bearing lubrication condition. By constructing a roller-raceway electrical contact model, quantitative estimation and condition identification of the oil film thickness under actual bearing operating conditions are achieved. This method utilizes the electrical impedance signal and equivalent circuit model of the lubrication contact area, does not rely on optical transparency, is applicable to opaque materials and conventional industrial bearings, and can realize online monitoring and lubrication control of bearing lubrication condition. Attached Figure Description

[0088] Figure 1 This is a schematic diagram illustrating the film thickness under elastohydrodynamic lubrication conditions and the oil film rupture during mixed lubrication, as provided in an embodiment of the present invention.

[0089] Figure 2 A schematic diagram of the Hertzian contact area of ​​a single-contact rolling ball bearing under load, provided in an embodiment of the present invention;

[0090] Figure 3 This is an electrical schematic diagram illustrating a single contact between a single ball and a raceway such as an inner or outer ring, provided in an embodiment of the present invention.

[0091] Figure 4 This is a schematic diagram illustrating the contact geometry and key parameter definitions of a rolling ball bearing provided in an embodiment of the present invention.

[0092] Figure 5 This is a schematic diagram of the non-Hertz contact region capacitance integration region division provided in an embodiment of the present invention;

[0093] Figure 6 This is a schematic diagram of the voltage equalization method circuit structure provided in an embodiment of the present invention;

[0094] Figure 7 A flowchart of a bearing lubrication condition monitoring method based on impedance signals provided in an embodiment of the present invention;

[0095] Figure 8 This is a graph showing the change trend of oil film thickness over time during the start-up process of a bearing, provided as an embodiment of the present invention.

[0096] Figure 9 This is a graph showing the change in oil film thickness of a bearing over time after a period of stable operation, provided as an embodiment of the present invention.

[0097] Figure 10The graph shows the trend of oil film thickness over time after bearing damage, as provided in an embodiment of the present invention. Detailed Implementation

[0098] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0099] This embodiment aims to contribute to bearing oil film thickness detection technology by exploring in-situ measurement techniques, particularly electrical impedance spectroscopy, to determine film thickness under elastohydrodynamic lubrication conditions and oil film rupture during mixed lubrication. Figure 1 As shown. The analysis method in this embodiment combines the (theoretical) resistance and capacitance contributions to impedance at all contact points to distinguish between full-film lubrication and mixed lubrication states.

[0100] Under radial loads, the various rolling elements bear different forces, forming a load zone. Opposite the load zone, the rolling bearing has unloaded rolling elements with clearance under low axial loads. Among the loaded rolling elements, such as... Figure 2 As shown, a Hertzian contact region with a central lubricating film thickness h0 is formed, while the unloaded rolling elements remain unchanged between the inner and outer rings. In rolling bearing applications, when a complete lubricating film is formed in the load area, the relevant electrical quantity used to describe the electrical behavior is capacitance, because the metal bodies are separated from each other, and common lubricants exhibit very high resistivity. Therefore, the lubricant acts as a dielectric, and the rolling elements and raceways form electrodes.

[0101] For rolling ball bearings, the analysis method in this embodiment assumes perfect hydrodynamic lubrication, with the balls completely insulated from the raceways by the lubricant; therefore, the lubricant is considered an ideal capacitor. Under these conditions, Figure 3 It shows the electrical representation of a single contact between a single ball and a raceway such as the inner or outer ring.

[0102] Due to the load and the elasticity of the balls, elastic mechanical deformation occurs at the minimum distance from the raceway; this elastic deformation region A Hertz This is called the Hertz region, such as Figure 2 As shown.

[0103] Due to pressure distribution, a central lubricating film thickness h0 will appear between the contacting parts. Depending on the direction of the applied radial and axial bearing forces, each ball of the ball bearing may bear a different load.

[0104] When the radial bearing force F r When in operation, the load area is determined by the angle. Description, which leads to distance It depends on the bearing inner diameter. Assume the bearing has no clearance and only radial force acts on it. In this case, only the balls in the lower half of the bearing bear the load. For this load distribution with zero bearing clearance, the maximum force Q of each ball at the center of the load area is... max The estimate is:

[0105] (1);

[0106] in, This is the maximum load that the roller can withstand. For radial load, z is the number of rollers. If there is an additional axial force, use the equivalent radial force F. eq Replace F r The effect of the equivalent radial force on the contact is the same as the combination of radial force and axial force, according to formula (1).

[0107] To calculate the basic geometric parameters, the free contact angle needs to be calculated. This parameter describes the angle between the ball-raceway contact point and the radial axis, and is derived under conditions of minimum axial load and no radial load. It depends on the bearing clearance. The diameter D of the rolling element RE and raceway consistency ratio f i and f o The calculation method is based on the dimensionless distance between the center points of the raceway radius. Free contact angle The calculation formula is as follows:

[0108] (2);

[0109] For each ball in contact with the wheel, the effective radius is calculated based on Hertz's theory, and then further calculated according to the elastohydrodynamic theory of elliptical contact:

[0110] (3);

[0111] (4);

[0112] Where, d m That is the pitch circle diameter. Therefore, The effective radius in the rolling direction is defined, and This is the effective radius perpendicular to the rolling direction. Parameter The contact points on the inner ring are described, while This describes the contact points on the outer ring. The pitch circle diameter of the bearing can be estimated as... Then, the sum of curvature can be calculated. and curvature difference .

[0113] (5);

[0114] (6);

[0115] Then, the thickness of the lubricating film can be calculated using the Young's modulus of the contact objects. and and Poisson's ratio and To calculate the reduction in Young's modulus E of the contact object.

[0116] (7);

[0117] in, The Young's modulus of the rolling element. The Young's modulus of the ring. The Poisson's ratio of the rolling element. Let be the Poisson's ratio of the raceway. The Hertzian region where the ball contacts the curved raceway is an elliptical region formed by the major semi-axis a and the minor semi-axis b. This Hertzian region is calculated using formula (8):

[0118] (8);

[0119] in, Let π represent pi, μ and ν be dimensionless Hertzian coefficients, m = 0.3 be Poisson's ratio, and E be the Young's modulus of steel, E = 2.08 × 10⁻⁶. 5 N / mm 2 ∑ρ represents the sum of deflections, and Q represents the maximum load. The contact area is Hertz.

[0120] Then, a semi-analytical method is used to approximate the capacitance contribution of the region without elastic deformation (i.e., the external region) relatively effectively. Improvements were made to make it applicable to rolling ball bearings. The main influencing factor of external capacitance is the distance between the spherical surface and the annular raceway (toroidal surface). First, the distance between the center of the toroidal surface and the center of the rolling element is defined. (like Figure 4 As shown below:

[0121] (9);

[0122] in, The radius of the groove is perpendicular to the rolling direction; It is the radius of the rolling element; It is the gap height without deformation; Free contact angle; It is the raceway radius along the rolling direction. It is expressed as the displacement difference along the x-direction, reflecting the offset of the ball center relative to the raceway center in the rolling direction; It represents the displacement difference along the y-direction, and represents the radial offset between the center of the ball and the center of the raceway. This represents the displacement difference along the z-direction, corresponding to the distance from the sphere to the groove surface in the normal direction.

[0123] Next, in toroidal coordinates In the diagram, t and p are circular coordinates, representing the raceway surface. Described as:

[0124] (10);

[0125] If the origin of the coordinate system is taken at the center of the sphere If the coordinates are in spherical coordinate system, then the sphere... Represented as:

[0126] (11);

[0127] Equal equation (10) to equation (11) and eliminate the difference. ,have to:

[0128] (12);

[0129] in:

[0130] (13);

[0131] The root of equation (13) is 𝑟 groove (Θ, φ) describes the distance (in spherical coordinates) from the center of the sphere to any intersection point on the raceway surface. This is a quartic equation, which usually requires numerical methods to solve. The distance equation for the edge region is derived similarly, but since the raceway surface can be approximated as a cylinder, the equation is reduced to a quadratic form and can be solved analytically.

[0132] (14);

[0133] in, This refers to the clearance between the raceway edge area and the rolling element. This indicates the radius of the raceway edge.

[0134] Next, for and In respectively , Integrate. To cover the entire integration region, For fixed integration limits, For dependent variables, such as Figure 5 As shown.

[0135] Upper limit of integration in the rolling direction Defined as the maximum value in a mathematical sense, covering the main physical influence area (i.e., the sum of all free electrode surfaces), it is determined by the raceway tangent passing through the center of the rolling element, and is calculated using the following formula:

[0136] (15).

[0137] To differentiate between the entrance and exit areas, another integration limit is introduced. The entry area's integration range is... arrive The export zone integral range is from 0 to If the free contact angle Then the left and right sides The values ​​may differ. Integral limits in the rolling direction. like Figure 4 and Figure 5 As shown. Θ0 is defined as the contact center at the free contact angle α (excluding the Hertzian region), Θ1 is the groove boundary, and Θ2 is the rim end:

[0138] (16);

[0139] (17);

[0140] (18);

[0141] Among them, B R B is half the width of the shoulder of the rolling element. L denoted as , where b is the effective length of the bearing, and b is the short half-shaft in the Hertz region.

[0142] If asymmetry exists due to angular contact or combined loads, the integration limits for the left and right sides (r, l) must be calculated separately. To account for air in the exit area, such as... Figure 5 As shown, Θ 0,in Define the upper limit of the inlet integral, where φ is the coordinate of the scrolling direction. When φ < 0, the upper limit of the inlet integral Θ is... 0,in Same as Θ0; when φ≥0, the upper limit of the entrance integral Θ 0,in (φ) along (a / R) RE The direction of φ rises 45° until the end point at the inlet. Where a is the semi-major axis of the Hertzian contact ellipse. The exit region starts from φ=0 and extends to... End. Assuming the mixture consists of part oil and part air, the dielectric constant of the oil film thickness h0 is... The dielectric constant of the air portion is taken as =1. Therefore, the contribution of each part of the capacitance is:

[0143] (19);

[0144] (20);

[0145] (twenty one);

[0146] in, , These are respectively the inner trench capacitance, outer trench capacitance, and edge capacitance. Represented as the vacuum dielectric constant, u1 and u2 represent the lower and upper limits of integration in the rolling direction (i.e., the integration direction), corresponding to the integration boundaries of the oil film at the outlet and inlet ends. The variable u represents the integral coordinate in the rolling direction, with the same meaning as φ; Θ1(u) and Θ 0,in (u), Θ 0,out Θ2(u) and Θ2(u) are the groove boundary angle, inlet center angle, outlet center angle, and wheel rim end angle, respectively.

[0147] Due to the left-right asymmetry, each item , Both sides need to be calculated separately, so the expression for the total capacitance is:

[0148] (twenty two);

[0149] in, , , and , , These are the inner capacitance of the trenches on the left and right sides, the outer capacitance of the trenches, and the edge capacitance.

[0150] The voltage ratio method is used to measure the bearing impedance; the unknown impedance Z of the bearing to be measured is... DUT With a known reference impedance Z ref Connected in series, with excitation voltage v gen The voltage v across the reference impedance is measured with high precision. ref Its circuit diagram structure is as follows: Figure 6 As shown.

[0151] Unknown impedance Z of the bearing under test DUT It can be calculated using formula (23):

[0152] (twenty three);

[0153] The generator frequency is [frequency], and the carrier frequency is [frequency]. Capacitance C measured by a single contact plate at time M Calculate using the following formula:

[0154] (twenty four);

[0155] in, Let the imaginary part of the measured impedance be... The magnitude of the impedance being measured. Given the carrier frequency. Calculate the contact capacitance in the Hertz region. for:

[0156] (25).

[0157] The oil film thickness can then be calculated using formulas (8) and (25). :

[0158] (26);

[0159] in, EHL is the relative permittivity of the lubricating oil under pressure and temperature. Once the parameters mentioned above are determined, the oil film thickness under mixed lubrication and metal-to-metal contact conditions can be directly estimated by monitoring the impedance during operation.

[0160] The classification of lubrication states can be clearly defined based on the physical properties of oil film thickness. In rolling bearings or line contact systems, when the oil film thickness is less than approximately 50 nm, the lubricating medium is insufficient to isolate microscopic surface peaks, and direct metal-to-metal contact occurs at the contact interface. At this point, the risks of wear, friction, and localized heat generation significantly increase, classifying it as a metal-to-metal contact state. When the oil film thickness is between 50 nm and 300 nm, although a certain oil film exists, its thickness is insufficient to completely cover microscopic irregularities, providing only limited fluid isolation. This is a typical mixed lubrication state or thin lubrication film, where the friction state is influenced by both lubricant properties and surface roughness. When the oil film thickness is greater than 300 nm, the lubricating film has essentially formed a continuous coverage, completely separating the two contact surfaces and preventing any direct contact, entering the elastohydrodynamic (EHL) lubrication state. At this point, frictional resistance is minimal, and the system operates most stably. These thresholds reflect the transition process of the lubrication system from failure to stability and are important criteria for assessing bearing operating conditions and electrical contact risks.

[0161] The process of measuring oil film thickness using a non-contact measurement method based on electrical impedance is as follows: Figure 7 As shown.

[0162] To further verify the applicability of the method in this embodiment, a set of typical operating condition tests were conducted, using SKF 6007 bearings, with a radial force of 3000 N, a rotational speed of 3000 rpm, and an ambient temperature of 60°C. The sampling frequency was 20 kHz. The results are shown below.

[0163] Figure 8This study demonstrates the change in oil film thickness over time during bearing startup. It can be seen that the oil film thickness is close to zero in the initial stage. This is because, in the early stages of bearing startup, due to the extremely low rotational speed, the relative sliding between the shaft and bearing is insufficient to establish effective hydrodynamic lubrication. The lubricating oil cannot form a stable flow pressure between the shafts, resulting in the oil film not yet forming or being extremely thin, thus remaining in a boundary lubrication state. At this time, microscopic contact may exist on the metal surfaces, hence the measured oil film thickness is close to zero. Subsequently, the oil film forms, causing its thickness to increase rapidly, and then stabilizes after approximately 0.1 seconds, indicating a transition from thin-film lubrication to elastohydrodynamic lubrication.

[0164] Figure 9 This paper demonstrates the change in oil film thickness over time after the bearing has been running stably for a period of time. It can be seen that the oil film thickness generally remains between 320 and 360 nm, exhibiting slight high-frequency fluctuations, indicating that the system is in a relatively stable fluid lubrication state. These fluctuations are mainly due to micro-vibrations of the shaft, minor changes in load, and viscosity fluctuations caused by lubricating oil temperature, and may also be affected by noise from the measuring equipment. Overall, the oil film thickness fluctuates within a reasonable range, reflecting smooth bearing operation and good lubrication.

[0165] Figure 10 The study shows the trend of oil film thickness over time after bearing damage. It can be observed that the oil film thickness generally increases gradually, with significant fluctuations. This phenomenon reflects a change in the lubrication state of the bearing after damage; the oil film thickness is no longer stable and gradually thickens. This may be due to decreased lubrication performance caused by factors such as lubricant contamination, increased temperature, and increased wear particles.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A method for monitoring bearing lubrication status based on impedance signals, characterized in that: The method uses electrical impedance spectroscopy to determine the film thickness under elastohydrodynamic lubrication conditions and the rupture of the oil film during mixed lubrication. Specifically, the following steps are included: Step 1: Construct a roller-raceway electrical contact model; Under radial load, various rolling elements bear different forces and form a load zone; opposite the load zone, there are unloaded rolling elements in the rolling bearing, with clearance under low axial load; in the loaded rolling elements, a Hertzian contact zone with a central lubricating film thickness h0 is formed, while the unloaded rolling elements remain unchanged between the inner and outer rings; in the rolling bearing, when a complete lubricating film is formed in the load zone, the relevant electrical quantity used to describe the electrical behavior is capacitance, the lubricant acts as a dielectric, and the rolling elements and raceways form electrodes; Step 2: Measure the bearing impedance using the voltage ratio method; By connecting the bearing under test in series with a known reference impedance and then connecting it to an excitation voltage source, the voltage response across the reference impedance is measured using a high-precision voltage acquisition system. By comparing the proportional relationship between the reference voltage and the excitation voltage, the equivalent impedance value of the bearing is indirectly calculated. Step 3: Calculate the effective contact area of ​​the contact point; Based on Hertzian contact theory, and combined with the load borne by the bearing, the geometric parameters of the rolling elements and the elastic properties of the material, the effective area of ​​the contact elliptical region is calculated. This area reflects the range of actual mechanical and electrical coupling between the rolling elements and the raceway. Step 4: Calculate the bearing capacitance, which includes two parts: one is the capacitance formed by the lubricating film in the Hertz contact area, the medium of which is lubricating oil under high pressure, and the film thickness is the average thickness at the contact center; the other is the distributed capacitance formed between the rolling elements and the raceway through the gap in the non-contact area. Taking into account the contact angle, raceway curvature, rolling element position and lubricant dielectric properties, a semi-analytical method is used to integrate different regions separately to finally obtain the equivalent capacitance value of the bearing as a whole. This capacitance is a key electrical parameter reflecting the lubrication state, and its value change directly corresponds to the trend of oil film thickness change. Step 5: Calculate the oil film thickness; After completing the capacitance calculation, the lubrication film thickness under the current working condition is derived by establishing a mapping relationship between capacitance and oil film thickness. Based on the physical characteristics of the lubrication film as a dielectric, the electrical response is converted into a geometric index of the lubrication state by utilizing the sensitivity of capacitance value to film thickness. The obtained oil film thickness is used to determine whether the bearing is currently in metal contact, mixed lubrication, or full lubrication state, and further supports real-time identification and early warning of lubrication state. Step 6: Determine the lubrication condition of the bearing based on the physical characteristics of the oil film thickness; lubrication conditions include metal-to-metal contact, mixed lubrication, and complete lubrication; In rolling bearings or line contact systems, when the oil film thickness is less than 50 nm, the bearing is in a metal-to-metal contact state; when the oil film thickness is between 50 nm and 300 nm, the bearing is in a mixed lubrication state; when the oil film thickness is greater than 300 nm, it enters an elastohydrodynamic lubrication state, and the bearing is in a fully lubricated state, at which point the frictional resistance is minimal and the system operation is most stable.

2. The bearing lubrication condition monitoring method based on impedance signal according to claim 1, characterized in that: The specific method for step 2 is as follows: The unknown impedance Z of the bearing under test DUT With a known reference impedance Z ref Connected in series, with excitation voltage v gen ; By measuring the voltage v across the reference impedance with high precision ref The unknown impedance Z of the bearing under test DUT The result is obtained from formula (23): （23）； Among them, the unknown impedance Z of the bearing under test DUT This is the equivalent impedance value of the bearing.

3. The bearing lubrication condition monitoring method based on impedance signal according to claim 2, characterized in that: The specific method for step 3 is as follows: Depending on the direction of the applied radial and axial bearing forces, each ball of a ball bearing may bear a different load; when the radial bearing force F r When in operation, the load area is determined by the angle. Description, which leads to distance It depends on the bearing inner diameter. Assuming the bearing has no clearance and only radial force acts on it, only the lower half of the bearing's balls bear the load. For this load distribution with zero bearing clearance, the maximum force Q of each ball at the center of the load area is... max The estimate is: （1）； in, This is the maximum load that the roller can withstand. For radial load, z is the number of rollers. If there is an additional axial force, use the equivalent radial force F. eq Replace F r The effect of the equivalent radial force on the contact is the same as the combination of radial force and axial force, according to formula (1). Free contact angle The angle describing the contact point between the ball and raceway and the radial axis is derived under conditions of minimum axial load and no radial load, and it depends on the bearing clearance. , rolling element diameter D RE and raceway consistency ratio f i and f o The calculation method is based on the dimensionless distance between the center points of the raceway radius. Free contact angle The calculation formula is as follows: （2）； For each ball in contact with the wheel, the effective radius is calculated based on Hertz's theory, and then further calculated according to the elastohydrodynamic theory of elliptical contact: （3）； （4）； in, Define the effective radius in the rolling direction, and It is the effective radius perpendicular to the scrolling direction; subscript parameter This indicates the contact point on the inner ring, while This indicates the contact point on the outer ring; the estimated pitch circle diameter of the bearing is... ; Then, calculate the sum of curvature using the two formulas. and curvature difference : （5）； （6）； Then, for the calculation of the lubricating film thickness, the Young's modulus of the contact object is used. and and Poisson's ratio and To calculate the reduced Young's modulus E of the contact object: （7）； in, The Young's modulus of the rolling element. The Young's modulus of the ring. The Poisson's ratio of the rolling element. The Poisson's ratio for the ring; The Hertzian region where the ball contacts the curved raceway is an elliptical region consisting of the major semi-axis a and the minor semi-axis b; the area of ​​this Hertzian region is calculated using formula (8): （8）； in, Let π represent pi, μ and ν be dimensionless Hertzian coefficients, m = 0.3 be Poisson's ratio, and E be the Young's modulus of steel, E = 2.08 × 10⁻⁶. 5 N / mm², ∑ρ is the sum of deflections, and Q is the maximum load. The contact area is Hertz.

4. The bearing lubrication condition monitoring method based on impedance signal according to claim 3, characterized in that: The specific method for step 4 is as follows: The influencing factor of external capacitance is the distance between the spherical surface and the annular raceway; first, define the distance between the center of the toroidal surface and the center of the rolling element. for: （9）； in, The radius of the groove is perpendicular to the rolling direction; It is the radius of the rolling element; It is the gap height without deformation; Free contact angle; It is the raceway radius along the rolling direction; It is expressed as the displacement difference along the x-direction, reflecting the offset of the ball center relative to the raceway center in the rolling direction; It represents the displacement difference along the y-direction, and represents the radial offset between the center of the ball and the center of the raceway. This represents the displacement difference along the z-direction, corresponding to the distance from the sphere to the groove surface in the normal direction; Next, in toroidal coordinates In the diagram, t and p are circular coordinates, representing the raceway surface. Described as: （10）； If the origin of the coordinate system is taken at the center of the sphere If the coordinates are in spherical coordinate system, then the sphere... Represented as: （11）； Equal equation (10) to equation (11) and eliminate the difference. ,have to: （12）； in: （13）； The root of equation (13) is 𝑟 groove ( ), representing the distance from the center of the ball to any intersection point on the raceway surface, is solved using numerical methods; The distance equation for the edge region is derived similarly, but since the raceway surface is approximately cylindrical, the equation is reduced to a quadratic form, which can be solved analytically as follows: （14）； in, This refers to the clearance between the raceway edge area and the rolling elements; Next, for and In respectively , Integrate above; to cover the entire integration region, For fixed integration limits, As a dependent variable; Indicates the radius of the raceway edge; Upper limit of integration in the rolling direction Defined as the maximum value in a mathematical sense, to cover the main physical influence area, i.e., the sum of all free electrode surfaces. Determined by the raceway tangent passing through the center of the rolling element, the calculation formula is: （15）； To differentiate between the entrance and exit areas, another integration limit is introduced. The entry area's integration range is... arrive The export zone integral range is from 0 to If the free contact angle Then the left and right sides The values ​​may differ; Θ0 is defined as the contact center at the free contact angle α, excluding the Hertzian region, Θ1 is the groove boundary, and Θ2 is the rim end, as shown in the following three equations: （16）； （17）； （18）； Among them, B R B is half the width of the shoulder of the rolling element. L b is the effective length of the bearing, and b is the short half-shaft in the Hertz region; If asymmetry exists due to angular contact or combined loads, the integration limits for the left and right sides (r, l) must be calculated separately; to account for air in the exit area, Θ0, in Define the upper limit of the inlet integral, where φ is the coordinate of the scrolling direction. When φ < 0, the upper limit of the inlet integral is Θ0. in Same as Θ0; when φ≥0, the upper limit of the entrance integral Θ0, in (φ) along (a / R) RE The direction of φ rises 45° until the end point φ2 at the inlet, where a is the semi-major axis of the Hertz contact ellipse; the outlet region starts from φ=0 and extends to... End. Assuming the mixture consists of part oil and part air, the dielectric constant of the oil film thickness h0 is... The dielectric constant of the air portion is taken as =1; Therefore, the contribution of each part of the capacitance is: （19）； （20）； （21）； in, , , These are respectively the inner trench capacitance, outer trench capacitance, and edge capacitance; The variable u represents the vacuum dielectric constant; u1 and u2 represent the lower and upper limits of integration in the rolling direction, corresponding to the integration boundaries of the oil film at the outlet and inlet ends; the variable u represents the integral coordinate in the rolling direction, with the same meaning as φ; Θ1(u), Θ0, ᵢ n (u), Θ0, o ᵤ t Θ2(u) and Θ2(u) are the groove boundary angle, inlet center angle, outlet center angle and wheel flange end angle, respectively; Due to the left-right asymmetry, each item , Both sides need to be calculated separately, so the expression for the total capacitance is: （22）； in, , , and , , These are the inner capacitance, outer capacitance, and edge capacitance of the trenches on both the left and right sides. The generator frequency is [frequency], and the carrier frequency is [frequency]. Capacitance C measured by a single contact plate at time M Calculate using the following formula: （24）； in, Let the imaginary part of the measured impedance be... The magnitude of the impedance being measured. For carrier frequency; Hertzian region contact capacitance The calculation is as follows: （25）。 5. The bearing lubrication condition monitoring method based on impedance signal according to claim 4, characterized in that: In step 5, the oil film thickness According to formulas (8) and (25), calculate as follows: （26）； in, It represents the relative permittivity of lubricating oil under pressure and temperature.

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