JP7538671B2 - How to determine the viscosity model, how to estimate the apparent viscosity, and how to estimate the torque - Google Patents

Description

The present invention relates to a method for determining a viscosity model, a method for estimating apparent viscosity, and a method for estimating torque, and in particular to a method for determining a viscosity model for estimating the apparent viscosity of grease sealed in a rolling bearing, a method for estimating the apparent viscosity, and a method for estimating the torque of the rolling bearing.

Grease is sealed inside rolling bearings to reduce rolling and sliding friction. Grease-sealed bearings, which contain grease, are long-lasting, do not require external lubrication units, and are inexpensive, so they are often used for general-purpose applications such as automobiles and industrial equipment. Here, the grease sealed inside the bearings is subjected to a shearing action and becomes fluid, contributing to lubrication.

The lubrication state of such bearings can be classified into churning and channeling periods. In the churning period, the grease is significantly agitated by the rolling elements and cage, and torque in the steady state tends to be high. On the other hand, in the channeling period, the grease adheres to the seals and cage and is hardly agitated, and torque in the steady state tends to be low. To calculate the torque in the churning period, it is necessary to know the viscosity (apparent viscosity) of the grease that is subjected to shear between the rolling elements and cage, and between the rolling elements and raceway surfaces.

Here, grease is a non-Newtonian fluid that has thixotropy. The relationship between the apparent viscosity and shear rate of such a non-Newtonian fluid can be measured using a rheometer, and calculation models such as the Cross Powerlaw model (Non-Patent Document 1) are known as methods for expressing this relationship as a function.

M. M. Cross, “Rheology of non-newtonian fluids: a new flow equation for pseudoplastic systems,” J. Colloid Sci., 1965, 20, p. 417-437

However, the shear rate range (0.001 to 1,000,000 s ^-1 ) that can occur in a bearing is very wide, and it is difficult to measure the apparent viscosity of the grease for each shear rate in a bearing. In general, the measurement of apparent viscosity using a rotational rheometer is limited to only the medium speed range (approximately 10 to 10,000 s ^-1 ) compared to the above shear rate range in a bearing. In the high speed range (for example, 1,000 s ^-1 or higher), the grease will overflow from the experimental equipment due to centrifugal force, making it difficult to measure the apparent viscosity.

On the other hand, in the low shear rate range (for example, 10 s ^-1 or less), the apparent viscosity of the grease is not stable, possibly due to the influence of the orientation of the thickener. Figure 8 shows the relationship between the estimated model and the actual measured value of the rheometer. The plot in Figure 8 shows the apparent viscosity measured by a rotational rheometer, and the solid and dashed lines are estimated models in which the parameters of the calculation model are adjusted to match the results of the rotational rheometer. Both estimated models 1 and 2 are in good agreement with the actual measured value of the rheometer at shear rates of about 10 to 10,000 s ^-1 , but at shear rates of 10 s ^-1 or less, there is a large difference in the apparent viscosity between the two. In this way, it is difficult to obtain an accurate grease model in the low shear rate range by measurement using a rotational rheometer. In addition, there is no knowledge about the low shear rate range. Therefore, for example, in a rolling bearing in which grease is sealed, it is difficult to accurately estimate the bearing torque or simulate the grease behavior in the bearing.

The present invention has been made in consideration of these circumstances, and aims to provide a method for determining a viscosity model for accurately estimating the apparent viscosity of a non-Newtonian fluid in the low shear rate range, a method for estimating the apparent viscosity using the viscosity model, and a method for estimating torque.

The method for determining a viscosity model of the present invention is a method for determining a viscosity model for estimating the apparent viscosity of a non-Newtonian fluid, and is characterized by comprising the steps of: (a) obtaining an estimated model showing a relationship between shear rate and viscosity; (b) measuring the tensile load when the non-Newtonian fluid is deformed in a tensile test in which the non-Newtonian fluid is sandwiched between a fixed plate and a movable plate and the movable plate is moved away from the fixed plate to stretch the non-Newtonian fluid; (c) performing a computational fluid analysis on the estimated model obtained in the step (a) to predict the tensile load when the non-Newtonian fluid is deformed in the tensile test; and (d) comparing the tensile load measured in the step (b) with the tensile load predicted in the step (c), and adjusting the parameters of the estimated model so that these loads match to determine the viscosity model.

In the present invention, "the loads match" includes not only perfect match but also near match. For example, they can be considered to match when the tensile load predicted in step (c) is included within a predetermined range centered on the tensile load measured in step (b).

ただし、式中の記号は、η：見かけ粘度［Ｐａ・ｓ］、η_ｏｉｌ：流体成分の粘度［Ｐａ・ｓ］、τ_０：降伏応力［Ｐａ］、γ：せん断速度［ｓ^－１］、ｎ：定数、ｍ：定数である。 The estimation model is characterized by being based on the Cross Powerlaw model, the Herchel-Bulkley model, the Papanastasiou model, or a model of the following formula (1).

In the formula, the symbols are: η: apparent viscosity [Pa·s], η _oil : viscosity of fluid component [Pa·s], τ ₀ : yield stress [Pa], γ: shear rate [s ⁻¹ ], n: constant, and m: constant.

The step (a) is characterized in that the viscosity of the non-Newtonian fluid at a predetermined shear rate is measured using a rotational rheometer, and the estimation model is obtained based on the measurement results.

In the step (b), the tensile test is performed under the condition that the non-Newtonian fluid is sandwiched between the fixed plate and the movable plate with an initial thickness of 1 mm and a diameter of 7.4 mm, and the movable plate is then lowered at a speed of 0.005 m/s, and the tensile load is measured when the movable plate travels a distance of 0.01 mm to 1.0 mm.

The step (d) is characterized in that, if the tensile load predicted in the step (c) is included within a predetermined range centered on the tensile load measured in the step (b), the estimation model is determined to be the viscosity model, and, if not, the parameters of the estimation model are adjusted.

The non-Newtonian fluid is characterized as being a grease containing a base oil and a thickener.

The method for estimating an apparent viscosity of the present invention is a method for estimating the apparent viscosity of a non-Newtonian fluid, and is characterized in that the apparent viscosity of the non-Newtonian fluid at an arbitrary shear rate of 10 ^s or less is estimated using a viscosity model determined by the determination method of the present invention.

The torque estimation method of the present invention is a method for estimating torque due to shear of a non-Newtonian fluid generated in a mechanical element, and is characterized in that the torque generated at the arbitrary shear rate is estimated using the apparent viscosity of the non-Newtonian fluid estimated by the apparent viscosity estimation method of the present invention, or the magnitude of the torque generated at the arbitrary shear rate between multiple non-Newtonian fluids.

The mechanical element is a rolling bearing.

The method for determining a viscosity model of the present invention includes the above steps (a) to (d), and the estimated model showing the relationship between shear rate and viscosity is corrected by combining experiments and analysis, resulting in a highly accurate viscosity model. In particular, a tensile test is a test in which a non-Newtonian fluid is pulled at low speed, and the test results are considered to reflect the behavior of the non-Newtonian fluid in the low shear range. Therefore, by adjusting the parameters of the estimated model to match the tensile load when the non-Newtonian fluid is deformed in the tensile test, a viscosity model suitable for estimating the apparent viscosity in the low shear range is obtained. As a result, the apparent viscosity of a non-Newtonian fluid in the low shear range can be accurately estimated, and can be used for torque estimation and grease behavior analysis.

The method for estimating an apparent viscosity of the present invention estimates the apparent viscosity of a non-Newtonian fluid at any shear rate of 10 s ⁻¹ or less using a viscosity model determined by the determination method of the present invention, and therefore can accurately estimate the apparent viscosity in a low shear rate region lower than the range that can be measured by a rheometer.

The torque estimation method of the present invention uses the apparent viscosity of a non-Newtonian fluid estimated by the estimation method of the present invention to estimate the torque of the non-Newtonian fluid at an arbitrary shear rate, or estimates the magnitude of the torque between multiple non-Newtonian fluids at an arbitrary shear rate, so that torque estimation can be performed more accurately.

FIG. 1 is a diagram showing a rolling bearing filled with grease. FIG. 2 is a process diagram showing an outline of a method for determining a viscosity model according to the present invention. FIG. 1 is a schematic diagram illustrating an example of a rheometer. FIG. 1 is a diagram showing an outline of a tensile testing machine. FIG. 1 is a diagram showing the elongation of grease in a tensile test. FIG. 2 is a diagram showing apparent viscosity characteristics of Examples and Comparative Examples. FIG. 1 is a diagram showing the relationship between the moving distance and the tensile load in a tensile test. FIG. 13 is a diagram showing the relationship between an estimated model and actual measured values by a rheometer.

The viscosity model in the present invention is a viscosity model that estimates the apparent viscosity of a non-Newtonian fluid that exists in a gap between two components that are moving relative to one another. Here, a non-Newtonian fluid is a fluid whose viscosity depends on the "shear rate", and the viscosity of a non-Newtonian fluid is generally expressed as an apparent viscosity obtained by dividing the "shear stress" by the "shear rate". In the present invention, pseudoplastic fluids, Bingham fluids, dilatant fluids, etc. are used as non-Newtonian fluids. Among these, pseudoplastic fluids are preferred. Specific examples of pseudoplastic fluids include grease and lubricating oils that are sealed in rolling bearings. The following describes an embodiment in which grease is used as a non-Newtonian fluid.

The grease enclosed in the rolling bearing contains a base oil and a thickener. There are no particular limitations on the base oil, and any common base oil typically used in the field of greases can be used. For example, highly refined oil, mineral oil, ester oil, ether oil, synthetic hydrocarbon oil (PAO oil), silicone oil, fluorine oil, and mixtures of these oils can be used.

The kinematic viscosity of the base oil at 40° C. is not particularly limited, but is preferably 20 mm ² /s to 400 mm ² /s. When a mixed oil is used as the base oil, it is preferable that the mixed oil has a kinematic viscosity within this range.

The thickener is not particularly limited, and any of the general thickeners typically used in the field of greases can be used. For example, soap-based thickeners such as metal soaps and complex metal soaps, and non-soap-based thickeners such as bentone, silica gel, urea compounds, and urea-urethane compounds can be used. Examples of metal soaps include sodium soap, calcium soap, aluminum soap, and lithium soap, while examples of urea compounds and urea-urethane compounds include diurea compounds, triurea compounds, tetraurea compounds, other polyurea compounds, and diurethane compounds.

The grease may also contain other known additives as necessary. Examples of such additives include amine- or phenol-based antioxidants, chlorine-, sulfur-, or phosphorus-based compounds, extreme pressure agents such as organic molybdenum, and rust inhibitors such as petroleum sulfonates, dinonylnaphthalene sulfonates, and sorbitan esters.

An example of a rolling bearing filled with grease will be described with reference to FIG. 1. FIG. 1 is a cross-sectional view of a deep groove ball bearing. In the rolling bearing 1, an inner ring 2 having an inner ring raceway surface 2a on its outer circumferential surface and an outer ring 3 having an outer ring raceway surface 3a on its inner circumferential surface are concentrically arranged, and multiple balls 4 are arranged between the inner ring raceway surface 2a and the outer ring raceway surface 3a. The balls 4 are held by a cage 5. In addition, openings 8a, 8b at both axial ends of the inner and outer rings are sealed by a seal member 6, and grease 7 is filled at least around the balls 4. The inner ring 2, outer ring 3 and balls 4 are made of an iron-based metal material, and grease 7 is interposed between the raceway surface and the balls 4 to lubricate them.

The viscosity model in the present invention is used, for example, to estimate the apparent viscosity of the grease at a predetermined shear rate. The method for determining the viscosity model according to the present invention includes at least four steps (a) to (d) shown in FIG. 2. That is, the method includes (a) an acquisition step for acquiring the estimation model 2, (b) a measurement step for measuring the tensile load 3 when the grease deforms in a tensile test, (c) an analysis step for analyzing the estimation model 2 and predicting the tensile load 4 when the grease deforms in the tensile test, and (d) a determination step for comparing the tensile load 3 with the tensile load 4, and adjusting the parameters of the estimation model 2 so that these loads match to determine the viscosity model 5. Each step is described below.

<Step (a)>
This step is a step of acquiring an estimated model 2 for estimating the apparent viscosity of the grease. In Fig. 2, step (a) includes a primary acquisition step (a1) of acquiring an arbitrary calculation model 1, and a secondary acquisition step of acquiring an estimated model 2 from the calculation model 1 based on the rheology measurement results using a rotational rheometer. Note that step (a) does not necessarily require measurement (actual measurement) using a rotational rheometer. For example, in step (a), an estimated model in which predetermined values are substituted for parameters in advance based on empirical rules or the like may be acquired. Note that the following will describe step (a) in the form shown in Fig. 2.

Grease is a non-Newtonian fluid and a semi-solid, highly viscous fluid. The viscosity of grease decreases with increasing shear rate. In step (a1), a calculation model 1 expressing this characteristic is obtained, such as the Cross Powerlaw model (formula (2) below), the Herchel-Bulkley model (formula (3) below), or the Papanastasiou model (formula (4) below). Note that η in formulas (2) to (4) below represents the apparent viscosity of the grease.

In the formula, the symbols are: η ₀ : zero shear viscosity (apparent viscosity at shear rate γ=0) [Pa·s], η _oil : base oil viscosity [Pa·s], γ: shear rate [s ⁻¹ ], m: constant, n: constant. In the above formula (2), it is assumed that η approaches η _oil when the shear rate is infinite. n represents the change in apparent viscosity with respect to the change in shear rate, and is determined by the rheology measurement in step (a2).

In the formula, the symbols are τ ₀ : yield stress [Pa], γ: shear rate [s ⁻¹ ], K: constant, and n: constant.

In the formula, the symbols are: η _oil : viscosity of the fluid component [Pa·s], τ ₀ : yield stress [Pa], γ: shear rate [s ⁻¹ ], and m: constant.

The calculation model 1 obtained in step (a1) is not limited to the above-mentioned known calculation model. For example, the model of the following formula (1) can be used as the calculation model 1. The following formula (1) is an improved version of the Papanastasiou model based on experimental data in the high-speed shear region.

In the formula, the symbols are: η _oil : viscosity of the fluid component [Pa·s], τ ₀ : yield stress [Pa], γ: shear rate [s ⁻¹ ], n: constant, and m: constant.

In the case of grease, the viscosity of the fluid component η _oil is calculated by multiplying the dynamic viscosity of the base oil at the actual temperature (for example, the temperature inside the bearing or the temperature of the entire machine) by the density of the base oil. In addition, if the grease contains a viscosity improver, the viscosity of the fluid component η _oil is calculated by the viscosity of the base oil and the viscosity improver.

In the next step (a2), parameters such as the yield stress and each constant in the calculation model 1 are obtained to obtain the estimated model 2. The parameters can be identified based on the evaluation of the rheological properties of the grease using a rotational rheometer. In the evaluation of the rheological properties of the grease, it is preferable to use a rheometer having a cone-plate type cell. An overview of such a rheometer is shown in FIG. 3. As shown in FIG. 3, the rotational rheometer 11 is composed of a cone-plate type cell 12 and a horizontal disk plate 13, and the cell 12 and the plate 13 are arranged so that they are in contact at one point (with a small gap), and the sample grease 14 is placed between them. In this rheometer, the shear rate applied to the grease 14 is the same at any position, regardless of the distance from the center of the cell. Rheology measurement conditions include (1) rotation speed dependence at constant temperature and constant direction rotation, (2) vibration frequency dependence at constant temperature and constant shear strain, and (3) shear stress dependence of dynamic viscoelasticity at constant frequency. In this invention, measurements are mainly performed under condition (1).

Specific rheology measurement conditions are as follows: a rotational rheometer (HAAKE RheoWin MARS1 manufactured by Thermo Fisher Scientific) is used with a cone-plate type cell with a diameter of 20 mm and a tip angle of 178°, and the temperature is 20°C or the like, with constant temperature and constant direction rotation. In this case, the shear rate is increased, and the viscosity is measured when the viscosity reaches a steady state at each shear rate. For example, in the case of the Cross Powerlaw model, η ₀ , m, and n can be obtained from the rheology measurement results. The obtained values are substituted into the above formula (2) to obtain the estimated model 2. At this point, n is determined, and η ₀ and m are identified by carrying out the subsequent steps.

<Step (b)>
This step is a step for measuring the tensile load 3 when the grease is deformed in a tensile test. In the tensile test, the grease is filled between parallel flat plates (two faces) adjusted to a predetermined area and a predetermined distance, and the distance between the flat plates is increased to break the grease.

The tensile test will be described with reference to FIG. 4. FIG. 4 shows a schematic diagram of a tensile tester. The tensile tester 21 includes a cylindrical fixed plate 22 fixed to the top wall, a cylindrical movable plate 23, and a drive unit 24 that moves the movable plate 23 up and down relative to the fixed plate 22. The lower surface of the fixed plate 22 and the upper surface of the movable plate 23 are parallel to each other. The drive unit 24 includes a stage 25 on which the movable plate 23 is placed, a linear guide 26 that regulates the movement of the stage 25, a motor 27, and a ball screw 28 that rotates by the drive of the motor 27. The stage 25 is screwed into the screw groove of the ball screw 28, and moves relatively while sliding on the axis due to the rotation of the ball screw 28. In addition, the fixed plate 22 is provided with a load cell 30 that measures the load applied to the fixed end side when the grease is deformed.

The procedure for tensile testing is described below.

(1) First, a predetermined amount of the grease 29 to be measured is filled onto the upper surface of the movable plate 23. The amount of the grease 29 filled is, for example, 1 cm ³ to 5 cm ³ .

(2) Next, the movable plate 23 is raised to a position where the grease 29 contacts the lower surface of the fixed plate 22. At this time, the position of the movable plate 23 is adjusted so that the grease 29 has a predetermined initial thickness A (see FIG. 5(a)). In the initial state of FIG. 5(a), the distance between the fixed plate 22 and the movable plate 23 becomes the initial thickness A of the grease 29. The initial thickness A is set to, for example, 0.5 mm to 2 mm, specifically 1 mm. The diameter φ of the grease 29 in this initial state is set to, for example, 5 mm to 10 mm, specifically 7.4 mm. As shown in FIG. 5(a), the position of the movable plate 23 may be adjusted so that the grease 29 spreads over the entire fixed plate 22 and the movable plate 23 by using the fixed plate 22 and the movable plate 23 having the same diameter size as the diameter φ of the grease 29. Note that the diameter size and shape of the fixed plate 22 and the movable plate 23 are not limited to those shown in FIG. 5(a). For example, the fixed plate 22 and the movable plate 23 may be shaped other than cylindrical, and a circular grease filling area may be provided on one of the opposing surfaces.

(3) Next, as shown by the black arrow in FIG. 4, the movable plate 23 is lowered at a predetermined speed. The lowering speed of the movable plate 23 is set, for example, to 0.0001 m/s to 0.1 m/s, specifically to 0.005 m/s. As shown in FIG. 4, the grease 29 is deformed by the lowering of the movable plate 23. In step (b), the tensile load when the grease 29 is deformed due to the movement of the movable plate 23 is measured over time, and the tensile load at any moving distance of the movable plate 23 is measured. Note that the tensile load to be compared in the subsequent step (d) is preferably the tensile load at the beginning of the movement of the movable plate 23 (for example, within 1 second). In terms of the moving distance of the movable plate 23, the tensile load is compared at a moving distance within a range of preferably 0.01 mm to 1.0 mm, more preferably 0.01 mm to 0.5 mm, and even more preferably 0.05 mm to 0.3 mm.

The moving distance of the movable plate 23 is calculated by the following formula using the initial thickness A and the distance B between the fixed plate 22 and the movable plate 23 during movement, as shown in FIG.
Movement distance of the movable plate 23=B−A

(4) Returning to FIG. 4, as the movable plate 23 continues to descend, the grease 29 eventually breaks. Whether or not the grease 29 has broken can be confirmed by visual inspection, a high-speed camera, or by measuring the tensile load.

The configuration of the tensile tester shown in FIG. 4 is not limited to this. For example, the movable plate 23 may be formed integrally with the stage 25. Also, instead of pulling the movable plate 23 vertically downward, the movable plate may be pulled up vertically upward.

<Step (c)>
In this step, a computational fluid analysis is performed. For the computational fluid analysis, general-purpose thermal fluid analysis software that performs numerical analysis using the finite volume method is used. In this analysis, the change in tensile load is reproduced when a grease with a given fluid property is applied to the above-mentioned tensile test. The calculation conditions used in the analysis are the test conditions of the tensile test performed in step (b), etc.

In addition, since the number of coefficients can be reduced for the fluid properties of the grease to be applied to the analysis, it is preferable to use an estimated model obtained from the actual measured values of a rotational rheometer. Note that an estimated model obtained based on empirical rules may also be used. As shown in the examples described later, this computational fluid analysis simulates the tensile load 4 when the grease deforms in a tensile test. In this case, the tensile load corresponding to the moving distance of the movable plate obtained in step (b) is simulated.

<Step (d)>
In this step, first, the tensile load 3 at a predetermined moving distance of the movable plate measured in step (b) is compared with the tensile load 4 at the same moving distance of the movable plate simulated in step (c) to determine whether these loads match. Specifically, it is determined whether each tensile load is within a predetermined range (e.g., ±10%). Then, it is determined that the loads match when each tensile load is within the predetermined range, and it is determined that the loads do not match when each tensile load is not within the predetermined range. For example, it is determined that the loads match when the tensile load 4 is included within a predetermined range (e.g., ±10%) centered on the tensile load 3, and it is determined that the loads do not match when the tensile load is not included. Note that the tensile loads to be compared are not limited to the moving distance of one point of the movable plate, and it may be compared using tensile loads at moving distances of multiple points. When using tensile loads at multiple moving distances, it is determined that the tensile loads 3 and 4 match when the tensile loads at each moving distance of both are all within the predetermined range.

If it is determined that the two loads match, the estimation model 2 acquired in step (a) is deemed to be accurate, and the estimation model 2 is determined to be the viscosity model 5. On the other hand, if it is determined that the two loads do not match, the parameters of the estimation model 2 are adjusted. For example, in the case of the Cross Powerlaw model, the coefficients η ₀ and m are changed as parameters. Note that in the case of the Herchel-Bulkley model, τ ₀ and K are changed, in the case of the Papanastasiou model, τ ₀ and m are changed, and in the case of the model of the above formula (1), τ ₀ and m are changed.

After that, the computational fluid analysis (step (c)) is performed again, and the tensile load 4 and tensile load 3 obtained in that analysis are compared to determine again whether these loads match. Then, the parameters of the estimation model 2 are repeatedly changed until the two tensile loads match. If the two tensile loads match, it can be said that the viscosity characteristics estimated by the estimation model 2 represent the actual viscosity of the grease.

In this way, by comparing the grease tensile load obtained from the tensile test analysis and the experiment, the validity of the estimation model can be verified. Furthermore, by matching the tensile load during the tensile test between the experiment and the analysis, a highly accurate viscosity model that more accurately reflects the actual viscosity of the grease can be obtained.

The method for estimating apparent viscosity according to the present invention is a method for estimating apparent viscosity at any shear rate using a viscosity model determined by the above-mentioned determination method. The shear rate is the shear rate acting on the grease present in the pocket gap during rotation in the churning phase, and can be calculated from the set bearing rotation speed, etc. For example, assuming that the ball is located at the center of the pocket of the cage, in the case of a 6204 bearing with an inner ring rotation speed of 10 ⁴ min ^-1 , the shear rate of the grease in the pocket corresponds to an order of 10 ⁵ s ^-1 . By substituting any shear rate into the obtained viscosity model, the apparent viscosity of the grease present in the pocket gap during rotation in the churning phase at that shear rate can be obtained as a predicted value.

Here, generally, the greater the apparent viscosity of the grease, the greater the bearing torque. Therefore, by using the apparent viscosity estimated by the above-mentioned method, it is possible to estimate the bearing torque or to estimate the magnitude of the bearing torque between multiple greases. The bearing torque can be estimated, for example, by assuming that the temperature of the entire machine including the bearing is the temperature inside the bearing and calculating the apparent viscosity of the grease. This makes it possible to select a grease (evaluated with a rheometer) based on the required bearing torque. In addition, the magnitude of the bearing torque between multiple greases can be estimated by comparing the apparent viscosity of each grease. For example, the grease with the lowest apparent viscosity among multiple greases can be selected as the grease with the lowest bearing torque.

In Figure 1, a ball bearing is shown as an example of a rolling bearing in which grease is sealed, but the invention can also be applied to cylindrical roller bearings, tapered roller bearings, spherical roller bearings, needle roller bearings, thrust cylindrical roller bearings, thrust tapered roller bearings, thrust needle roller bearings, and thrust spherical roller bearings.

Although the above describes grease and rolling bearings filled with the grease, the non-Newtonian fluid that is the subject of the estimation method of the present invention is not limited to grease, but may also be a gel, a sol, or other thixotropic fluid or semi-solid. Furthermore, the two members in relative motion that subject the non-Newtonian fluid to shear are not limited to the bearing members of rolling bearings, and may be applied to other machine elements. Examples of other machine elements include linear guides, clutches, cams, joints, chains, gears, and sliding bearings.

The estimation method of the present invention can accurately estimate the apparent viscosity even in a low shear region, and is therefore suitable for estimating non-Newtonian fluids used in a shear rate region of 10 s ^-1 or less, more preferably in a shear rate region of 1 s ^-1 or less. Specifically, it is suitable for estimating the apparent viscosity of grease sealed in a rolling bearing for low-speed rotation. The viscosity model of the present invention can also adequately estimate the apparent viscosity in a high-speed shear region.

Rheological measurements were performed on the grease. Measurements were performed using a cone-plate type cell with a diameter of 20 mm and a tip angle of 178° in a rheometer (HAAKE RheoWin MARS1 manufactured by Thermo Fisher Scientific). The shear rate was increased from 10 to 5000 (unit: 1/s), and the apparent viscosity was measured when the viscosity reached a steady state at each shear rate. The measured values are plotted in Figure 6.

The Cross Powerlaw model shown in the above formula (2) was used as the calculation model. From the above rheology measurement results, the coefficients (η ₀ , m, n) in the above formula (2) were calculated to obtain an estimation model. The viscosity η _oil of the base oil was calculated by Walther's formula.

The obtained coefficients are shown in Table 1. Table 1 shows the coefficient values of the two estimation models of the Example and Comparative Example. Note that the viscosity η _oil of the base oil and n are the same values in the Example and Comparative Example, and these values are determined at this point.

In Fig. 6, the approximation formula obtained by substituting the values in Table 1 into the above formula (2) is shown by a solid line (Example) and a dashed line (Comparative Example). As shown in Fig. 6, at shear rates of about 10 to 10,000 s ^-1 , both the Example and the Comparative Example match the results measured by the rotational rheometer. On the other hand, at shear rates of 10 s ^-1 or less, differences are seen between the two, and it is difficult to determine which viscosity characteristic is more accurate based on the rheology measurement results alone.

Next, the tensile test shown in Figures 4 and 5 was performed to measure the tensile load when the grease was deformed. The thickness of the grease before the test (initial thickness A) was 1 mm, and the diameter φ was 7.4 mm. Cylindrical flat plates with a diameter of 7.4 mm were used for the fixed plate and the movable plate. The movable plate was lowered at a speed of 0.005 m/s, and the tensile load was measured when the movable plate moved 0.05 mm, 0.25 mm, and 0.5 mm (see Figure 7).

In addition, a computational fluid analysis was performed using thermal fluid analysis software to simulate the tensile load when the moving distance of the movable plate in the tensile test was 0.05 mm, 0.25 mm, and 0.5 mm. The calculation conditions for the analysis were the test conditions of the actual tensile test, and the fluid properties based on the estimated model of the example and the estimated model of the comparative example. The tensile load obtained by this analysis is shown in Figure 7.

As shown in FIG. 7, the tensile load simulated from the estimation model of the embodiment closely matched the tensile load obtained in the experiment. Specifically, the error from the experimental value of the tensile load when the moving distance of the movable plate was 0.05 mm, 0.25 mm, and 0.5 mm was within ±10%. On the other hand, the tensile load simulated from the estimation model of the comparative example did not match the tensile load obtained in the experiment. Specifically, the error from the experimental value of the tensile load when the moving distance of the movable plate was 0.05 mm, 0.25 mm, and 0.5 mm was 20% or more. If the actual viscosity of the grease differs from the apparent viscosity of the estimation model, the stress acting in the grease also differs. In this case, it can be said that the apparent viscosity characteristic of the comparative example cannot express the actual grease viscosity, and the apparent viscosity characteristic of the embodiment can express the actual grease viscosity.

As shown in Figure 7, the tensile load decreases as the moving distance of the movable plate increases. This is thought to be because a larger stress acts on the grease at the beginning of deformation. The degree of deviation between the comparative example and the experimental data also decreases as the moving distance of the movable plate increases. In other words, the moving distance may affect the judgment results when comparing with the experimental data. Therefore, in order to more accurately judge whether the tensile loads match or not, it is thought to be preferable to make the judgment using the tensile load in an area with a short moving distance.

The viscosity model is determined by the above-mentioned determination of the coincidence of the tensile loads. For example, in the case of the estimation model of the embodiment, the estimation model is determined to be the viscosity model. On the other hand, in the case of the estimation model of the comparative example, the parameters of the estimation model are adjusted. Specifically, the values of η ₀ and m are changed by increasing or decreasing them. Then, using the changed estimation model, the tensile load during deformation of the grease is simulated again by computational fluid analysis, and the parameters are adjusted until it coincides with the tensile load of the tensile test, and finally the viscosity model is determined. In this way, the apparent viscosity of the grease may not coincide with the actual viscosity characteristics when identified only by the rotational rheometer, but it can be made to coincide by combining it with the results of the tensile test.

The viscosity characteristics obtained in this way can be used to accurately estimate the actual bearing torque and grease behavior. For example, when a bearing rotates at low speed, the apparent viscosity of the grease during low-speed shear is the main factor in torque, so if the apparent viscosity cannot be accurately estimated, the estimated torque will deviate from the actual torque. Furthermore, the behavior of the grease inside the bearing will vary greatly if the viscosity is different. For these reasons, it is desirable to use the viscosity model determined by the determination method of the present invention for torque estimation, grease behavior analysis, etc.

The viscosity model determined by the determination method of the present invention allows for accurate estimation of the apparent viscosity of a non-Newtonian fluid in the low shear rate range, and therefore allows for accurate estimation of the torque required to move two components relative to each other in the presence of a non-Newtonian fluid. This makes it suitable for use in, for example, selecting grease for rolling bearings used at low rotation speeds.

REFERENCE SIGNS LIST 1 rolling bearing 2 inner ring 3 outer ring 4 balls 5 cage 6 seal member 7 grease 8 opening 11 rheometer 12 cone-plate type cell 13 horizontal disc plate 14 grease 21 tensile tester 22 fixed plate 23 movable plate 24 drive unit 25 stage 26 linear guide 27 motor 28 ball screw 29 grease 30 load cell

Claims (6)

A method for determining a viscosity model for estimating the apparent viscosity of a grease containing a base oil and a thickener as a non-Newtonian fluid, comprising the steps of:
(a) obtaining an estimated model showing a relationship between shear rate and viscosity;
a step (b) of measuring a tensile load when the non-Newtonian fluid is deformed in a tensile test in which the non-Newtonian fluid is sandwiched between a fixed plate and a movable plate, and the movable plate is moved away from the fixed plate to stretch the non-Newtonian fluid;
A step (c) of performing a computational fluid analysis on the estimated model obtained in the step (a) to predict a tensile load during deformation of the non-Newtonian fluid in the tensile test;
and (d) a step of comparing the tensile load measured in the step (b) with the tensile load predicted in the step (c) and adjusting parameters of the estimation model so that these loads match, thereby determining a viscosity model ;
The estimation model is based on a Cross Powerlaw model, a Herchel-Bulkley model, a Papanastasiou model, or a model of the following formula (1):
The method for determining a viscosity model , wherein the step (a) comprises measuring the viscosity of the non-Newtonian fluid at a predetermined shear rate using a rotational rheometer, and obtaining the estimated model based on the measurement results .

In the formula, the symbols are: η: apparent viscosity [Pa·s], η _oil : viscosity of fluid component [Pa·s], τ ₀ : yield stress [Pa], γ: shear rate [s ⁻¹ ], n: constant, and m: constant. The method for determining a viscosity model according to claim 1, characterized in that in step (b), the tensile test is performed under the condition that the non-Newtonian fluid is sandwiched between the fixed plate and the movable plate with an initial thickness of 1 mm and a diameter of 7.4 mm, and the movable plate is lowered from that state at a speed of 0.005 m/s, and the tensile load is measured when the movable plate moves a distance of 0.01 mm to 1.0 mm. 3. The method for determining a viscosity model according to claim 1 or 2, characterized in that the step (d) determines the estimation model to be the viscosity model when the tensile load predicted in the step (c) is included within a predetermined range centered on the tensile load measured in the step (b), and adjusts the parameters of the estimation model when the tensile load predicted in the step ( c) is not included within the predetermined range. 1. A method for estimating the apparent viscosity of a non-Newtonian fluid, comprising:
A method for estimating an apparent viscosity of the non-Newtonian fluid at an arbitrary shear rate of 10 s ^-1 or less, using a viscosity model determined by the method for determining a viscosity model according to any one of claims 1 to 3 . A method for estimating torque due to shear of a non-Newtonian fluid generated in a machine element, comprising the steps of:
5. A torque estimation method, comprising: estimating a torque generated at the arbitrary shear rate, or estimating a magnitude of a torque generated at the arbitrary shear rate between a plurality of non-Newtonian fluids, using the apparent viscosity of the non-Newtonian fluid estimated by the estimation method according to claim 4. 6. The method for estimating torque according to claim 5 , wherein the mechanical element is a rolling bearing.

Images