Method for estimating dielectric breakdown voltage

Abstract

This method estimates the dielectric breakdown voltage in microscopic liquid environments, such as those found inside bearings. [Solution] Using equation (1), the dielectric breakdown voltage V DC To estimate the following: A, B: Constants dependent on the type of liquid. K, D: Constants dependent on the electrode material and the type of liquid. E, E': Electric field strength (voltage / length). d: Distance between electrodes. p: Surface pressure. S: Contact ellipse area. a: Area effect constant. m, n: Constants. [Math 1] TIFF2026064399000014.tif22147

Description

[Technical Field]

[0001] This invention relates to the estimation of dielectric breakdown voltage in bearings used in automobiles, industrial machinery, wind turbines, and the like. [Background technology]

[0002] Rolling bearings are used in fan motors and servo motors used in industrial machinery, as well as in the drive motors of electric vehicles and hybrid vehicles. These rolling bearings are either sealed with lubricant or have mechanisms in place to allow lubricant to penetrate the contact points in order to provide lubrication.

[0003] In recent years, most motors used in industrial machinery, electric vehicles (EVs), and hybrid vehicles are controlled by inverters to improve efficiency. Inverter control adjusts voltage and frequency according to the set rotational speed, and as the switching frequency of the inverter increases, the frequency of shaft voltage generation increases accordingly. As a result, a potential difference may occur between the raceways in the rolling bearings incorporated into inverter-driven motors. If this potential difference becomes large and exceeds the dielectric breakdown voltage of the oil film formed between the raceways and rolling elements in the bearing, a discharge may occur between the raceways and rolling elements, causing damage called electrolytic corrosion inside the bearing.

[0004] Furthermore, increasing the power supply voltage allows for a smaller current even at the same output, thereby reducing copper losses in cables and inverter elements. However, this also increases the potential difference between the shaft potential and the ground potential, making dielectric breakdown of the oil film and subsequent electrolytic corrosion more likely.

[0005] As bearing damage due to electrolytic corrosion progresses, ridge marks, which are striped irregularities, can form on the rolling surface of the rolling elements, potentially leading to noise and vibration. Therefore, efforts are underway to develop bearings that prevent the formation of ridge marks on the raceway surface.

[0006] As a prerequisite, it is necessary to understand what the dielectric breakdown voltage is that causes electrolytic corrosion. Patent Document 1 discloses a method for detecting dielectric breakdown of an oil film between two objects by applying a voltage.

[0007] On the other hand, it is known that the dielectric breakdown voltage can be estimated using Paschen's law in macroscopic (cm to m units) and gaseous environments (Non-Patent Literature 1). This law states that the voltage at which a spark occurs between parallel electrodes (dielectric breakdown voltage) V is a function of the product of the gas pressure p and the distance between electrodes d (V = f(pd)). [Prior art documents] [Patent Documents]

[0008] [Patent Document 1] Japanese Patent Publication No. 2008-241383 [Non-patent literature]

[0009] [Non-Patent Document 1] F. Paschen, ann. Phys. u. Chem., 37, 69 (1889) [Overview of the project] [Problems that the invention aims to solve]

[0010] However, Paschen's law cannot be applied to liquid environments at the micro to nanoscale, such as inside a bearing, and no laws or formulas were known that could estimate the dielectric breakdown voltage in the environment inside a bearing.

[0011] Furthermore, the detection of dielectric breakdown voltage described in Patent Document 1 involves actually measuring it on an actual material, and it was not possible to measure it without actually causing dielectric breakdown.

[0012] In light of the above background, the problem that this invention aims to solve is to enable estimation of dielectric breakdown voltage in a microscopic liquid environment such as inside a bearing.

Means for Solving the Problem

[0013] To solve the above problems, the present invention employs a first configuration for estimating the breakdown voltage V using the following formula (1) in an environment having a liquid. DC

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[0014] Further, to solve the above problems, the present invention employs a second configuration for estimating the breakdown voltage V using the following formula (2) in an environment having a lubricating oil.

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[0015] ​Furthermore, as an estimation method according to this invention, a third configuration can be adopted in which the dielectric breakdown voltage in a rolling bearing is estimated using formula (1) or formula (2) described in the first or second configuration, and the presence or absence of electrolytic corrosion is estimated by comparing it with the measured voltage applied to the rolling bearing. [Effects of the Invention]

[0016] The estimation method according to this invention makes it possible to estimate the dielectric breakdown voltage in a microscopic environment with an oil film with high accuracy. This makes it possible to estimate whether or not electrolytic corrosion occurs in rolling bearings. [Brief explanation of the drawing]

[0017] [Figure 1] (a) Configuration diagram of a verification test apparatus used to verify the dielectric breakdown voltage estimation method according to this invention, (b) Enlarged view of the area near the circumferential surface [Figure 2] An example graph showing the measured voltage and dielectric breakdown voltage when a triangular wave is applied to the device shown in Figure 1. [Figure 3] A graph plotting the dielectric breakdown voltage measured when the oil film thickness was changed by changing the rotation speed. [Figure 4] A graph plotting the dielectric breakdown voltage against oil film thickness, measured using a verification test device. [Figure 5] A graph plotting the dielectric breakdown voltage against the contact elliptical area measured using a verification test device. [Figure 6] A graph plotting the dielectric breakdown voltage against the average surface pressure measured using a verification test device. [Figure 7] A graph comparing the estimated value of dielectric breakdown voltage using Equation 4 with the measured value. [Figure 8] A graph comparing measured and estimated dielectric breakdown voltages in test specimens whose surface roughness has deteriorated due to electrical discharge. [Figure 9] A graph comparing the estimated value calculated using Equation 6, which takes surface roughness into account, with the measured value. [Figure 10] A cross-sectional view showing an example of a rolling bearing to which the dielectric breakdown voltage estimation method according to this invention is applied. [Modes for carrying out the invention]

[0018] This invention provides a method for estimating the dielectric breakdown voltage between electrodes containing a liquid such as lubricating oil, and a method for estimating the presence or absence of electrolytic corrosion in a rolling bearing using this method.

[0019] Paschen's law is well known for determining dielectric breakdown voltage. Prior research by Radmilovic et al. has proposed a modified formula that further extends this law. The paper is titled "An analytical relation describing the dramatic reduction of the breakdown voltage for the microgap devices," authored by Radmilovic-Radjenovic, M. & Radjenovic, B. It is published in Europhysics Letters, Volume 83, Number 2. This paper proposes that the dielectric breakdown voltage can be estimated using a modified Paschen curve formula, as shown in equation (3). However, the environment in which this formula is applied, as verified in this paper, is one where the space between electrodes is gaseous.

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[0020] This invention is based on the estimation formula for dielectric breakdown voltage in a gaseous environment shown in this document, and provides a method for estimating dielectric breakdown voltage in an environment where a liquid such as lubricating oil is present between electrodes. First, abstract factors that affect dielectric breakdown voltage were examined. These abstract factors include the gap distance between electrodes, the pressure on the inter-electrode material, the type of inter-electrode material, the electrode material, and the electrode area. These abstract factors were then concretized in an environment insulated by a liquid such as lubricating oil, as is assumed in bearings such as rolling bearings. The electrodes in a bearing are the raceway rings (inner and outer rings) and rolling elements, and the main specific factors were identified as the distance between electrodes (in bearings, the thickness of the oil film interposed between the raceway rings and rolling elements), surface pressure, viscosity-pressure coefficient, relative permittivity of the liquid (mainly lubricating oil in bearings), electrode (bearing) material, and electrode area (mainly the contact elliptical area in bearings). Of these, oil film thickness is d, and the pressure on the lubricating oil between electrodes is d. While surface pressure is thought to correspond mainly to p, viscosity-pressure coefficient and relative permittivity to A, B, K, and D, and bearing material to K and D, the element relating to electrode area is not reflected in equation (3).

[0021] Dielectric breakdown is thought to occur in a simple proportional manner as the electrode area increases. Therefore, a negative correlation is suggested between dielectric breakdown voltage and electrode area. This effect, which manifests as a negative correlation due to electrode area, is called the area effect.

[0022] Based on equation (3), if we reflect the area effect due to the electrode area S, we get equation (4). Here, a is the area effect constant, and in experimental reports in known literature, a value of around 3 is obtained. We can tentatively set it to 3. Equation (4) allows us to obtain a more accurate dielectric breakdown voltage V that reflects the area effect. DCThis allows for estimation. Furthermore, the element of d is extended to equation (3) as d to the power of n. When n is 1, it approaches the condition of equation (3), but under the conditions inside a bearing that the present invention primarily assumes as an operating environment, n is expected to be around 0.5 to 1.5, and a constant of around n = 1 to 1.25 is preferably applied. In addition, the surface pressure on the lubricating oil between electrodes is also extended to p to the power of m. When m is 1, it approaches the condition of equation (3), but under the scale inside a bearing that the present invention primarily assumes as an operating environment, m is expected to be in the range of 0 to 2.

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[0023] A verification test was conducted to verify the effectiveness of estimating the dielectric breakdown voltage using equation (4). Figure 1 shows a schematic of the verification test apparatus. Driving cylinders 11 and 21 are positioned in the oil bath 10 with their circumferential surfaces 12 and 22 facing each other. The subcurvature of circumferential surface 12 is infinite, i.e., a flat surface, and the subcurvature of circumferential surface 22, which is the test piece, is 60 mm. Each driving cylinder 11 and 21 is rotated by the rotation of motors 13 and 23, which is transmitted via transmission mechanisms 14 and 24. The rotational speed of motors 13 and 23 can be changed arbitrarily.

[0024] The driving cylinder 11 is fixed. On the other hand, the driving cylinder 21 can adjust the load applied between the circumferential surfaces 12 and 22 by applying a load to the support portion 25 of the transmission mechanism 24.

[0025] This verification test apparatus is connected by a circuit 31 so that an arbitrary voltage can be applied between the driving cylinders 11 and 21. A function generator 32 is connected to the circuit 31. The function generator 32 is a device that can generate a voltage of any waveform. The voltage of any waveform generated by this function generator 32 is applied to the liquid (lubricating oil) at a controlled gap d between the circumferential surfaces 12 and 22.

[0026] This function generator 32 provides a triangular wave with a modified peak voltage. Dielectric breakdown does not occur as long as the flowing current follows the triangular wave, and when the flowing current stops following the triangular wave, it can be considered that the oil film has broken down.

[0027] A constant load is applied between the circumferential surfaces 12 and 22 by the support part 25. That is, the circumferential surfaces 12 and 22 are in contact (d=0) when the motors 13 and 23 are not rotating. When the motors 13 and 23 rotate, liquid (lubricating oil) is drawn into the space between the circumferential surfaces 12 and 22. As the rotational speed of the driving cylinders 11 and 21 increases, the amount of liquid drawn into the space between the circumferential surfaces 12 and 22 increases, the pressure rises, and the gap (oil film thickness d) gradually expands. Therefore, the thickness of the oil film between the circumferential surfaces 12 and 22 can be increased by increasing the rotational speed.

[0028] In the verification test using the verification test apparatus shown in Figure 1, polyalphaolefin 6 (PAO6) was used in the oil bath, and the load from the support part 25 was fixed at 20 kgf. The radius of the major axis of the contact ellipse on the elliptical circumferential surface 22 was 686 μm, the radius of the minor axis of the contact ellipse was 212 μm, and the contact ellipse area (corresponding to the electrode area) was 0.457 mm². 2 That is the case.

[0029] The rotation speed of motors 13 and 23 was set to 300 rpm. A triangular wave voltage with a period of 10 seconds and a peak voltage of 1 V was applied between the surfaces 12 and 22 using the function generator 32. Figure 2 shows a graph plotting the measured voltage against the applied voltage. The measured voltage plateaus at approximately 0.3 V, and it is presumed that dielectric breakdown occurs at this point. At this time (300 rpm), the gap (oil film thickness d) was 177 nm.

[0030] When motors 13 and 23 were set to a rotational speed of 500 rpm, the gap (oil film thickness d) was 251 nm, and the dielectric breakdown voltage estimated from the measured voltage was 0.46 V. When motors 13 and 23 were set to a rotational speed of 800 rpm, the gap (oil film thickness d) was 346 nm, and the dielectric breakdown voltage estimated from the measured voltage was 0.57 V.

[0031] Figure 3 shows a graph plotting the measurement results at 300 rpm, 500 rpm, and 800 rpm, with the oil film thickness (spacing d: nm) on the horizontal axis and the breakdown voltage (V) on the vertical axis. From this data, the approximate formula was obtained as y = 0.0017×x, and it was confirmed that the breakdown voltage can be approximated to be proportional to the oil film thickness.

[0032] A verification test using this formula (4) for specific measurements was conducted. In the apparatus with the structure shown in Figure 1, the surface pressure (p) applied to the peripheral surface 12 of the driving cylinder 11 and the contact elliptical area (S) were changed by the load applied to the support portion 25, and an attempt was made to verify by changing the oil film thickness (d) by changing the rotational speed. The triangular wave generated by the function generator 32 had a peak voltage of 2 V and a period of 80 s. The lubricating oil was PAO6. The results are shown in Table 1.

[0033]

Table 1

[0034] Figure 4 shows a graph plotting the breakdown voltage against the oil film thickness (d) (Examination Examples 1 to 3). It was confirmed that there is a positive correlation between the breakdown voltage (V DC ) and the oil film thickness (d). This is considered to correspond to the formula (4) in which d is linearly in the numerator and logarithmically in the denominator. Also, Figure 5 shows a graph plotting the breakdown voltage (V DC ) against the contact elliptical area (S) (Examination Examples 4 and 5). It was suggested that there is a negative correlation between the breakdown voltage (V DC ) and the contact elliptical area (S). This is considered to correspond to the formula (4) in which S is in the denominator. Furthermore, Figure 6 shows a graph plotting the breakdown voltage against the average surface pressure (p) (Examination Examples 5 and 6). No correlation was observed between the breakdown voltage (V DC ) and the average surface pressure (p). This is considered to correspond to the formula (4) in which p is part of the term in the numerator and logarithmically in the denominator. The average surface pressure is the average value of the values calculated from the load, test piece shape, and test piece material.

[0035] Based on these test data, the predetermined values ​​were substituted into equation (4) to approximate each constant, and equation (5) was obtained. m=0, n=1.25, A×K=5×10 -4 , D+B is -5×10 -2 , a is set to 10 / 3.

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[0036] [Table 2]

[0037] Further verification involved measuring the dielectric breakdown voltage of the driving cylinder of the verification test apparatus shown in Figure 1, using a test piece that had already undergone dielectric breakdown. In this case, it was observed that the measured value deviated significantly from the estimated dielectric breakdown voltage using equation (4). The verification results are shown in Table 3 and Figure 8. The surface pressure and contact ellipse area were fixed, and the estimated and measured values ​​were compared when the oil film thickness was changed by adjusting the rotation speed. In particular, it was observed that the deviation between the estimated and measured values ​​tended to become more pronounced as the oil film thickness increased.

[0038] [Table 3]

[0039] From these results, it was inferred that the surface roughness of the electrodes, which changes due to discharge, is a factor that affects the dielectric breakdown voltage. Therefore, based on equation (4), parameter fitting was performed using the data in Table 2, and for new test specimens, equation (6) was established to estimate the dielectric breakdown voltage based on the combined mean square roughness Rq between the two surfaces, using the surface roughness specified at the time of test specimen manufacturing.

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[0040] By parameter fitting using the above test data, the parameters that can be estimated for the structure in Figure 1 were calculated, and equation (6) was obtained as equation (7) below. Using this equation (7), the estimated values ​​obtained under the same conditions as above using the measuring device shown in Figure 1 were compared with the values ​​actually measured in tests No. 13 to 16. The results are shown in Table 4 and Figure 9.

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[0041] [Table 4]

[0042] One environment in which dielectric breakdown voltage can be estimated using these formulas is the inside of a rolling bearing. Figure 10 shows a cross-sectional view of a rolling bearing 40 in which lubricating oil 45 is sealed around the rolling elements 43 as an example. The rolling elements 43 absorb the lubricating oil 45 and maintain an insulating state between the inner ring 41 and the outer ring 42. The dielectric breakdown voltage estimation method according to this invention makes it possible to estimate the dielectric breakdown voltage when dielectric breakdown occurs between the raceway surface 41a of the inner ring 41 and the rolling elements 43 inside the bearing 40, and between the raceway surface 42a of the outer ring 42 and the rolling elements 43.

[0043] By using these formulas to estimate the dielectric breakdown voltage and comparing it to the actual voltage applied to the rolling bearing, it is possible to estimate whether or not electrolytic corrosion is occurring. If the voltage does not reach the estimated dielectric breakdown voltage, it can be estimated that electrolytic corrosion is unlikely to occur. If cases are found where the voltage exceeds the estimated voltage, it can be estimated that there is a high probability that electrolytic corrosion is occurring. [Explanation of Symbols]

[0044] 10 Oil Bath 11, 21 Driving Cylinders 12, 22 circumferential surface 13, 23 motors 14, 24 Transmission Mechanism 25 Support part 31 lines 32 Function Generators 40 Rolling bearings 41 Inner circle 41a Inner ring raceway surface 42 Outer ring 42a Outer ring raceway 43 Rolling element 44 Cage 45 Lubricating oil d Oil film thickness

Claims

1. A method for estimating the dielectric breakdown voltage in an environment where there is liquid between electrodes, using the following formula (1). [Math 1] A, B: Constants that depend on the type of liquid. K, D: Constants that depend on the electrode material and the type of liquid. E, E': Electric field strength (voltage / length) d: Distance between electrodes (oil film thickness) p: Surface pressure (force / length) ２ ) S: Area of ​​the ellipse in contact (length) ２ ) a: Area effect constant n: constant (0.5 to 1.5) m: constant (0 to 2)

2. A method for estimating the dielectric breakdown voltage in an environment where there is liquid between electrodes, using the following formula (2). [Math 2] A, B: Constants that depend on the type of liquid. K, D: Constants that depend on the electrode material and the type of liquid. x: constant (0 to 2) y: constant (0.5 to 1.5) S: Area of ​​the ellipse at contact. Λ: Oil film parameter (d / Rq). d: Distance between electrodes (oil film thickness). Rq: Mean square roughness of the combined two surfaces.

3. An estimation method for estimating the dielectric breakdown voltage in a rolling bearing using the estimation method described in claim 1 or 2, and for estimating whether or not electrolytic corrosion has occurred by comparing it with a measured value of the voltage applied to the rolling bearing.

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