JP2020159754A - Pre-load diagnostic method of rolling device - Google Patents

Abstract

To provide a pre-load diagnostic method of a rolling device, which has improved accuracy.SOLUTION: In a pre-load diagnostic method of a rolling device 10 which includes outer members 1, inner members 3, and rolling bodies 5, an AC voltage is applied to an electric circuit which comprises the outer members 1, the rolling bodies 5, and the inner members 3 in a state to rotate the rolling device 10 in a predetermined rotational number region. An impedance and a phase angle of the electric circuit are measured during the application of the AC voltage, so that radius values of Hertzian contact circles of the rolling bodies 5 are calculated on the basis of the measured impedance and phase angle.SELECTED DRAWING: Figure 1

Description

The present invention relates to a method for diagnosing preload of a rolling device.

Rolling devices such as bearings are used in a wide range of industrial fields such as automobiles and various industrial machines.
Here, some rolling devices, such as hub unit bearings, are preloaded on a rolling element. In this preload diagnosis, the actual situation is that only an approximate preload value can be predicted from the bearing torque.

As a bearing diagnostic technique, there is a technique described in Patent Document 1. In Patent Document 1, an AC voltage is applied to the rotating wheel of the rolling element in a non-contact state, and the oil film state of the bearing can be estimated using the measured capacitance. That is, the oil film is regarded as a capacitor, an electrical equivalent circuit is modeled, an AC voltage is applied in a non-contact state to the rotating wheel of the rolling element, and the capacitance of the oil film is measured. Since there is a correlation between the capacitance and the oil film thickness (lubrication film thickness), the state of the oil film is estimated from this correlation.

Japanese Patent No. 4942496

According to the technique disclosed in Patent Document 1, it is possible to measure the oil film thickness. However, with this method, only the oil film thickness can be calculated, and the metal contact ratio and the preload cannot be grasped.

The present invention provides a more accurate preload diagnostic method for rolling devices.

The preload diagnosis method for a rolling device of the present invention is a preload diagnosis method for a rolling device including an outer member, an inner member, and a rolling element, and rotates the rolling device in a predetermined rotation speed region. In this state, an AC voltage is applied to the electric circuit composed of the outer member, the rolling element, and the inner member, and the impedance and phase angle of the electric circuit when the AC voltage is applied are adjusted. The value of the Hertzian contact circle radius of the rolling element is calculated based on the measured impedance and the phase angle.

According to the present invention, it is possible to more accurately diagnose the preload of the rolling device.

FIG. 1 is a graph showing a physical model under mixed lubrication conditions when a ball test piece is pressed against a disc test piece. FIG. 2 shows a diagram of an electric circuit in diagnosing a rolling device, FIG. 2 (a) is a diagram of an electric circuit corresponding to one ball test piece (rolling body) shown in FIG. 1, and FIG. 2 (b). ) Indicates a diagram of the electric circuit of the entire rolling element. FIG. 3 shows a conceptual diagram of the rolling device. FIG. 4 shows a graph of the results of measuring the average oil film thickness and the breaking rate of the oil film while changing the outer ring rotation speed of the rolling element (Example 1). FIG. 5 shows a graph of the results of measuring the average oil film thickness and the breaking rate of the oil film while changing the outer ring rotation speed of the rolling element (Example 2).

Hereinafter, embodiments of a method for diagnosing a rolling device (bearing device) according to the present invention will be described in detail with reference to the drawings.

As an oil film diagnostic technique in a conventional rolling apparatus, there is an inspection apparatus shown in Patent Document 1. The configuration of this inspection device is to model the oil film as a condenser, apply an AC voltage in a non-contact state to the rotating wheels of the rolling device, and measure the capacitance of the oil film. Since there is a predetermined correlation between the capacitance and the oil film thickness, it is possible to estimate the oil film state of the rolling element. However, in the method of Patent Document 1, it is difficult to measure only the oil film thickness and grasp the metal contact ratio. Moreover, since the capacitance outside the Hertz contact area is not taken into consideration, the estimation accuracy of the oil film thickness value itself is not high.

In the present invention, an AC voltage is applied to the EHD (Electro Hydro Dynamics) contact region, and the oil film thickness and the oil film breakage rate in the EHD contact region can be measured from the measured complex impedance Z (impedance method). Was established. By using this method, the oil film thickness can be measured with high accuracy. Here, the process of deriving the oil film thickness and the fracture rate (metal contact ratio) of the oil film based on the impedance method will be described.

FIG. 1 is a graph showing a physical model under mixed lubrication conditions when a ball test piece is pressed against a disc test piece. The disc test piece in this model corresponds to the outer ring or inner ring of the rolling device, and the ball test piece corresponds to the rolling element of the rolling device. The y-axis represents the oil film thickness direction, and the x-axis represents the axis orthogonal to the oil film thickness direction. Further, h ₁ is the oil film thickness at the portion forming the oil film in the EHD contact area, a is the radius of the Hertzian contact circle, r is the radius of the ball test piece, S is the Hertzian contact area, and α is the breaking rate of the oil film. .. Therefore, the area where the oil film is broken in the EHD contact area is represented by αS as shown in FIG. Further, f (x) in FIG. 1 is a function representing the y coordinate of the surface of the ball test piece in a range (a ≦ x ≦ r) other than the EHD contact area, and is represented by the following equation (1).

The actual ball test piece is not strictly a sphere except for the EHD contact area because elastic deformation occurs when a load is applied, but in the present invention, it is assumed that the ball is a sphere even after deformation as shown in the equation (1). ..

Usually, the EHD contact region there is a region with a small oil film called horseshoe, average oil film thickness of the EHD contact region in the present invention (average oil film thickness) was determined h _a. Therefore, if the breakage of the oil film in some EHD contact region is generated by using an average oil film thickness h _a in breakage rate α and the oil film thickness h ₁ of the oil film to obtain, by the following equation (2) expressed.

FIG. 2A shows a diagram of an electric circuit (equivalent electric circuit) E1 obtained by converting the physical model of FIG. 1 into an electrically equivalent electric circuit. However, R ₁ is the resistance in the region where the oil film is broken, C ₁ is the capacitance due to the oil film in the Hertzian contact area, and C ₂ is the distance between the two surfaces of the disc test piece and the ball test piece of x = r in FIG. It is the capacitance generated outside the Hertzian contact area when it is assumed that the position is filled with a lubricant (lubricating oil or grease). That is, in the present invention, the region outside the EHD contact region is also taken into consideration as a capacitor. The oil film in the Hertzian contact area forms a parallel circuit of the capacitor C ₁ (capacitance C ₁ ) and the resistor R ₁ (resistance value R ₁ ), and the parallel circuit and the capacitor C ₂ (capacitance) outside the Hertzian contact area. C ₂₎ are connected in parallel.

FIG. 2B shows an electric circuit E4 when the physical model of FIG. 1 is applied to a rolling device 10 (see FIG. 3) having an outer ring 1 and an inner ring 3. Since each rolling element 5 is in contact with both the outer ring 1 and the inner ring 3, as shown in FIG. 2B, for each rolling element 5, two electric circuits E1 (between the outer ring 1 and the rolling element 5) and An electric circuit E2 in which the inner ring 3 and the rolling elements 5) are connected in series is formed.

Further, when the rolling element 10 is provided with n rolling elements 5, n electric circuits E2 are connected in parallel. Therefore, as shown in FIG. 2B, the rolling device 10 including all n rolling elements 5 forms the electric circuit E3. In diagnosing the rolling device 10 of the present embodiment, an AC voltage is applied from the power source between the outer ring 1 and the inner ring 3 of the rolling device 10, so that the entire electric circuit E4 shown in FIG. 2B is formed. Will be done.

Here, the AC voltage V applied to the electric circuit of FIG. 2A is represented by the following equation (3).

The current I flowing through the entire electric circuit of FIG. 2A is represented by the following equation (4).

Therefore, the overall complex impedance Z of the electric circuit of FIG. 2A is represented by the following equation (5).

Here, j is an imaginary number, t is time, ω is the angular frequency of voltage, and θ is the phase shift between voltage and current, that is, the phase angle. From equation (5), it can be seen that the complex impedance Z is composed of two independent variables, the absolute value | Z | of the complex impedance Z and the phase angle θ. That is, by measuring the complex impedance Z, which means that (in this case the average oil film thickness h _a and breakage rate alpha) 2 two parameters independent of each other can be measured.

Here, the overall complex impedance Z of the electric circuit of FIG. 2A is expressed by the following equation (6).

Further, the following equations (7) and (8) can be derived from the equation (6).

Here, since the resistance R ₁ in the region where the oil film is broken in the formula (7) is inversely proportional to the contact area, it is represented by the following formula (9).

Here, R ₁₀ is a resistance at rest (that is, α = 1). R ₁₀ is represented by the following equation (10) from the equation (6), where the impedance at rest is | Z ₀ | and the phase angle is θ ₀ .

Therefore, the breaking rate α is represented by the following formula (11) from the formulas (7), (9), and (10).

By the way, the capacitance C ₁ due to the oil film in the Hertzian contact region is represented by the following equation (12) using the dielectric constant ε of the lubricant used in the test.

On the other hand, the capacitance C ₂ generated outside the Hertzian contact area is such that an annular capacitor having a minute width dx, a length 2πx, and a height f (x) as shown in the shaded area in FIG. 1 has a ≦ x ≦ r. It can be considered that they are connected in parallel within the range of. Therefore, the capacitance C ₂ is represented by the following equation (13).

Here, since r »a and r» h ₁ are generally used, the capacitance C ₂ can be approximated by the following equation (14) based on the equation (13).

From the above equations (8), (12), and (14), the following equation (15) can be obtained.

Here, in order to obtain h ₁ in the equation (15), the Lambert W function (Lambert W function) is used. For any complex number z, Lambert W function W (z) is defined by the following equation (16).

Therefore, equation (2), (15), represented by more, the average oil film thickness _{h a} of obtaining the following equation (17) (16).

In other words, equation (11) and (17), by measuring the impedance and phase at the time of resting and oil film formation, it is possible to calculate the breakage rate of the average oil film thickness h _a, and the oil film alpha.

Here, if the oil film thickness is known, the value of the known oil film thickness, by entering the left side (h _a) of the above formula (17), can be calculated back Hertzian contact circle radius a It will be possible. Then, if the preload is large, the ball test piece (see FIG. 1) is pressed more strongly against the disc test piece, and the value of the Hertzian contact circle radius a becomes large. That is, since there is a positive correlation between the size of the Hertzian contact circle radius a and the preload, it is possible to more accurately diagnose the preload of the rolling element based on the back-calculated value of the Hertzian contact circle radius a. It becomes.

The above description is exclusively for the basic electric circuit E1 of FIG. 2A, but by considering the number of rolling elements 5 of the rolling device 10 and the like, the electric circuit of FIG. 2B is taken into consideration. It can also be applied to E4. In the electric circuit E4, the two contact points where the rolling element 5 contacts the outer ring 1 and the inner ring 3 correspond to the electric circuit E2 formed by connecting the two electric circuits E1 in series. The total number (n) of the rolling elements 5 in the rolling device 10 corresponds to the number of electric circuits E2 in which two electric circuits E1 are connected in series. Further, when a plurality of rolling elements 10 themselves are present, the electric circuit E3 of FIG. 2B is connected in parallel with respect to the AC voltage.

Hereinafter, examples of the present invention will be described.

FIG. 3 shows a conceptual diagram of the rolling device (bearing device) 10. The rolling device 10 includes an outer ring (outer member) 1, an inner ring (inner member) 3, a raceway surface formed on the inner peripheral surface of the outer ring 1, and a raceway surface formed on the outer peripheral surface of the inner ring 3. A plurality of rolling elements 5 intervening are provided. Further, an oil film (lubricating film) made of a lubricant such as oil or grease supplied for lubrication exists between the outer ring 1 and the rolling element 5 and between the inner ring 3 and the rolling element 5. The rolling device 10 is applied to a moving body such as an automobile, a motorcycle, a railroad vehicle, an industrial machine, a machine tool, and the like, but the applicable device is not particularly limited.

As the rolling device 10, the inner diameter was filled with grease hub unit bearings 32 mm, an outer diameter Fai148mm, using a hub unit bearings of height 79.5 mm (double row ball bearing), the average oil film thickness _{h a} and the oil film The breaking rate (metal contact ratio) α was measured. More specifically, the outer ring (outer member) 1 of the rolling device 10 shown in FIG. 3 is made rotatable, and a general LCR meter (also serving as an AC voltage) is connected to the rolling device 10. did. Then, the frequency ω of the AC voltage and the voltage V of the AC voltage were input to the LCR meter, and the impedance (absolute value) | Z | and the phase angle θ of the rolling element 10 were measured by the LCR meter. The measurement conditions at this time are a preload of 500 N, an outer ring rotation speed of 30 to 1000 rpm, a temperature of indoor room temperature (25 ° C.), and a grease filling amount of 10.8 g.

Next, using equation (11) and (17) were measured α breakage rate of the average oil film thickness h _a, and the oil film while changing the wheel rotating speed N. FIG. 4 is a graph showing the measurement result. The dashed line in the graph is the theoretical oil film thickness h _c (Hamrock BJ and Dowson D. Isothermal elastohydrodynamic lubrication of point contacts: part III-fully flooded results. ASME Trans J Lubricat Technol 1977; 99) in which the experiment was conducted. : 264-275.) Is shown. The same applies to the broken line shown in FIG. 5 described later.

From FIG. 4, in the high speed region where the outside wheel rotating speed N exceeds 100 rpm, it can be seen that the average oil film thickness h _a is smaller than the theoretical oil film thickness h _c. From this result, it was suggested that depleted lubrication (a state in which the lubricant is removed from the transfer surface of the rolling element and the outer ring or the inner ring and sufficient lubrication is not achieved) occurs in the high speed range where the rotation speed is high.

On the other hand, the outside wheel rotating speed N is in a low speed region of less than 50 rpm, because the apparent viscosity of the grease increases, the average oil film thickness h _a is larger than the theoretical oil film thickness h _c.

Thus, 100 rpm region from the outside wheel rotating speed N 50 have been found to oil film thickness _{h a} substantially coincides with the theoretical oil film thickness _{h c.} Therefore, this region is interpreted as a predetermined rotation speed region. In the present application, "almost the same" means that the absolute value of the difference between the average oil film thickness h _a and the theoretical oil film film h _c is less than a predetermined value d = 0.1.

From the above, it can be seen that the preload diagnosis of the rolling element can be performed based on the devised impedance method. That is, the impedance of the rolling element is measured in the predetermined rotation speed region where the average oil film thickness h _a and the theoretical oil film film h _c substantially coincide with each other. Then, the Hertzian osculating circle radius a is back-calculated using the equation (17). This inverse operation is possible by inputting the theoretical oil film thickness h _c on the left side h _a of formula (17). Then, there is a positive correlation between the value of the back-calculated Hertzian contact circle radius a and the preload. Therefore, it is possible to diagnose the preload of the rolling element based on the value of the Hertzian contact circle radius a calculated back.

FIG. 5 shows a measurement result when the conditions are partially changed from the above-mentioned Example 1. In Example 2, 0.2 g of the base oil of the grease is sealed in place of the grease used in Example 1. Other conditions are the same as in Example 1.

Similar to FIG. 4, also in FIG. 5, in the high rotation region where the outside wheel rotating speed N exceeds 100rpm has occurred depletion lubrication, that the average oil film thickness h _a is smaller than the theoretical oil film thickness h _c Recognize.

On the other hand, in the low rotation region of FIG. 5, unlike FIG average oil film thickness h _a is not is larger than the theoretical oil film thickness h _c. This is considered to be because the base oil does not contain a thickener, so the measurement result is in agreement with the theoretical oil film thickness h _c .

Therefore, in the example of FIG. 5, the predetermined rotation speed region in which the average oil film thickness h _a substantially coincides with the theoretical oil film thickness h _c is set to exceed 30 rpm and less than 100 rpm. By measuring the impedance of the rolling element in this predetermined rotation speed region, it is possible to back-calculate the value of the back-calculated Hertzian contact circle radius a as in the first embodiment. Therefore, it is possible to diagnose the preload of the rolling element based on the value of the Hertzian contact circle radius a calculated back.

From the viewpoint of bearing preload diagnosis, it was found that lubrication with oil (Example 2), which can have a wider predetermined rotation speed region, is more preferable.

The present invention is a technique applicable to bearings in general (balls, rollers, cones, self-alignment, needles, double rows) regardless of oil lubrication or grease lubrication, and is a linear motion product (linear guide, ball screw). The preload diagnosis can be performed in the same manner.

The present invention is not limited to the above-described embodiment, and can be appropriately modified, improved, and the like. In addition, the material, shape, size, numerical value, form, number, arrangement location, etc. of each component in the above-described embodiment are arbitrary and are not limited as long as the present invention can be achieved.

1 Outer ring (outer member)
3 Inner ring (inner member)
5 Rolling body 10 Rolling device (bearing device)

Claims (3)

A preload diagnostic method for a rolling device including an outer member, an inner member, and a rolling element.
With the rolling device rotated in a predetermined rotation speed region, an AC voltage is applied to an electric circuit composed of the outer member, the rolling element, and the inner member.
The impedance and phase angle of the electric circuit when the AC voltage is applied are measured.
Based on the measured impedance and the phase angle, the value of the Hertzian osculating circle radius of the rolling element is calculated.
Preload diagnostic method for rolling equipment. The preload diagnostic method according to claim 1.
The predetermined rotation speed region is a rotation speed region in which the absolute value of the difference between the average oil film thickness and the theoretical oil film thickness calculated based on the impedance and the phase angle is less than a predetermined value.
Preload diagnostic method for rolling equipment. The preload diagnostic method according to claim 1 or 2.

By inputting the theoretical oil film thickness on the left side of, the value of the Hertzian osculating circle radius of the rolling element is calculated.
Preload diagnostic method for rolling equipment.

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