JP2021148673A - Method for estimating apparent viscosity and method for estimating torque of non-newtonian fluid - Google Patents

Abstract

To provide a method for estimating the apparent viscosity of non-Newtonian fluid, enabling the apparent viscosity of non-Newtonian fluid to be accurately estimated even in a high shear rate region, and a method for estimating torque of a non-Newtonian fluid.SOLUTION: A method for estimating the apparent viscosity of non-Newtonian fluid is a method for estimating the apparent viscosity of non-Newtonian fluid existing in a space between two relatively moving members, specifically the apparent viscosity of the non-Newtonian fluid at an optional shear rate is estimated by substituting a yield stress calculated by a relationship between the shear rate and viscosity of the non-Newtonian fluid measured using a rheometer and each constant and by substituting an optional shear rate in the space between the two members into the following formula (1). (η:an apparent viscosity [Pa s], ηoil:the viscosity [Pa s] of a fluid component, τ0:a yield stress [Pa], γ:a shear rate [s-1], n:a constant and m:a constant).SELECTED DRAWING: Figure 3

Description

The present invention relates to a method for estimating the apparent viscosity of a non-Newtonian fluid and a method for estimating the torque when two members are relatively moved in the presence of the non-Newtonian fluid, and in particular, the apparent viscosity of grease sealed in a rolling bearing. The present invention relates to an estimation method and a bearing torque estimation method.

Lubricating grease is sealed inside the rolling bearing for the purpose of reducing rolling friction and sliding friction. Grease-filled bearings filled with grease have a long life, do not require an external lubrication unit, and are inexpensive, so they are often used for general-purpose applications such as automobiles and industrial equipment. Here, the grease sealed in the bearing is subjected to a shearing action to be in a fluid state and contributes to lubrication.

Such bearing lubrication states include a churning period and a channeling period. In the churn period, the grease is largely agitated by the rolling elements and the cage, and the torque in the steady state tends to be high. On the other hand, in the channeling period, the grease adheres to the seal, the cage, and the like, and is in a state where it is hardly agitated, and the torque in the steady state tends to be low. In order to calculate the torque in the churn period, it is necessary to know the viscosity (apparent viscosity) of the grease that undergoes shear between the rolling element and the cage and between the rolling element and the raceway surface.

Here, the grease is a non-Newtonian fluid having thixotropic properties. The relationship between the apparent viscosity of such a Newtonian fluid and the shear rate can be measured using a rheometer. However, the shear rate of grease in each part of the bearing is often in the speed range of 1 to 10 times or more of the shear rate that can be measured by a rheometer, and the apparent viscosity of grease in the bearing cannot always be measured by a rheometer. .. Therefore, for example, in order to estimate the torque in the churn period in a bearing, it is necessary to use the extrapolated value in the calculation model. As a calculation model of the viscosity of a non-Newtonian fluid, a Herchel-Bulkley model (Non-Patent Document 1), a Papanastasiou model (Non-Patent Document 2), and the like are known.

W. H. Herschel, R.M. Bulkley, "Konsistenzmessungen von Gummi-Benzollosungen", Colloid Zeitscrift, 1926, 39, p. 291-300 TC Papanastasiou, "Flows of Materials with Year", Journal of Rheology, 1987, 31, p. 385

In general, the apparent viscosity of non-Newtonian fluids such as grease is estimated to approach the base oil or fluid components such as base oil and thickeners in the high shear rate region. However, in the Herchel-Bulky model, the higher the shear rate, the lower the apparent viscosity of the non-Newtonian fluid. In addition, in the Papanastasiou model, there is a concern about the reproduction of experimental values. Further, in any model, for example, the magnitude of the apparent viscosity in the bearing for each grease does not always match the magnitude of the torque actually measured for each grease. Therefore, it is considered that there is room for improvement as a calculation model for estimating the apparent viscosity of non-Newtonian fluids.

The present invention has been made in view of such circumstances, and an estimation method capable of accurately estimating the apparent viscosity of a non-Newtonian fluid even in a high shear rate region, and a relative motion of two members in the presence of the non-Newtonian fluid. It is an object of the present invention to provide a torque estimation method capable of accurately estimating the torque at the time of shearing.

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 method for estimating the apparent viscosity of the non-Newtonian fluid of the present invention is a method for estimating the apparent viscosity of the non-Newtonian fluid existing in the gap between two relative moving members, and the non-Newtonian fluid was measured using a leometer. By substituting the yield stress and each constant calculated from the relationship between the shear rate and the viscosity and the arbitrary shear rate in the gap between the two members into the following equation (1), the non-non-newtonian fluid at the arbitrary shear rate is obtained. It is characterized by estimating the apparent viscosity of a Newtonian fluid.

However, the symbols in the formula 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, m: constant.

ただし、式中の記号は、η_ｔ：任意の温度での非ニュートン流体の見かけ粘度［Ｐａ・ｓ］、η_{ｏｉｌ−ｔ}：任意の温度での流体成分の粘度［Ｐａ・ｓ］、Ｃ：定数、Ｄ：定数、ΔＴ：基準温度に対して上昇した温度である。 It is characterized in that the apparent viscosity of the non-Newtonian fluid at an arbitrary temperature is estimated by the following formula (2) in which temperature correction is added to the above formula (1).

However, the symbols in the formula are η _t : apparent viscosity of the non-Newtonian fluid at an arbitrary temperature [Pa · s], η _oil-t : viscosity of the fluid component at an arbitrary temperature [Pa · s], C: Constant, D: constant, ΔT: temperature increased with respect to the reference temperature.

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

The grease is grease sealed in a rolling bearing including an inner ring and an outer ring, a plurality of balls interposed between the inner ring and the outer ring, and a cage having a pocket for holding the balls, and has an arbitrary shear rate. It is characterized in that the shear rate of the pocket gap of the ball with respect to the cage is used.

The method for estimating the torque of the non-Newtonian fluid of the present invention is a method for estimating the torque when the two members move relative to each other, and uses the apparent viscosity of the non-Newtonian fluid estimated by the estimation method of the present invention. , The torque of the non-Newtonian fluid at the arbitrary shear rate is estimated, or the magnitude of the torque between a plurality of non-Newtonian fluids at the arbitrary shear rate is estimated.

The method for estimating the apparent viscosity of the non-Newtonian fluid of the present invention includes the yield stress and each constant calculated from the relationship between the shear rate and the viscosity measured with a leometer for the non-Newtonian fluid, and any arbitrary gap between the two members. This is a method of estimating the apparent viscosity of a non-Newtonian fluid at an arbitrary shear rate by substituting the shear rate into the equation (1). Since this equation (1) is an improved equation of the Papanastasiou model based on experimental data in a high shear rate region, the apparent viscosity of the non-Newtonian fluid can be estimated accurately.

The apparent viscosity of non-Newtonian fluid changes greatly due to changes in atmospheric temperature and heat generation during operation. Based on this, the apparent viscosity of the non-Newtonian fluid at an arbitrary temperature is estimated by the equation (2), which is an equation obtained by adding temperature correction to the equation (1), so that the temperature change of the non-Newtonian fluid can also be taken into consideration. , The apparent viscosity of the non-Newtonian fluid can be estimated more accurately.

The method for estimating the torque of a non-Newtonian fluid of the present invention uses the apparent viscosity of the 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 any arbitrary method. Since the magnitude of the torque between a plurality of non-Newtonian fluids at the shear rate is estimated, the torque can be estimated more accurately.

It is a figure which shows the rolling bearing which filled with grease. It is a schematic diagram which shows an example of a rheometer. It is a figure which shows the relationship between the measured value by a rheometer and the equation (1). It is a figure which shows the relationship between the measured value by the rheometer for each temperature, and the equation (2).

As a result of diligent studies on the apparent viscosity of non-Newtonian fluids, the present inventors used the Papanastasiou model, which is known as a calculation model for non-Newtonian fluids, and even if the experimental coefficients in the equation were adjusted, it was not always an experiment. We found that the values were not reproduced, and obtained equations (1) and (2) as improved models of the Papanastasiou model. Then, it was found that the apparent viscosities estimated by these equations have a better correlation with torque than the apparent viscosities estimated by the Papanastasiou model and the Herchel-Bulkley model. The present invention is based on such findings.

The method for estimating the apparent viscosity of the present invention is a method for estimating the apparent viscosity of a non-Newtonian fluid existing in a gap between two relative moving members. Here, the non-Newtonian fluid is a fluid whose viscosity depends on the "shear rate", and the viscosity of the non-Newtonian fluid is generally expressed by the apparent viscosity obtained by dividing the "shear stress" by the "shear speed". In the present invention, as the non-Newtonian fluid, a pseudoplastic fluid, a Bingham fluid, a dilatant fluid and the like are used. Of these, pseudoplastic fluids are preferred. Specific examples of the pseudoplastic fluid include grease and lubricating oil sealed in rolling bearings. In addition, a form using grease as a non-Newtonian fluid will be described below.

The grease sealed in the rolling bearing contains a base oil and a thickener. The base oil is not particularly limited, and general oils usually used in the field of grease can be used. For example, highly refined oils, mineral oils, ester oils, ether oils, synthetic hydrocarbon oils (PAO oils), silicone oils, fluorine oils, and mixed oils thereof can be used.

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

The thickener is not particularly limited, and general ones usually used in the field of grease can be used. For example, soap-based thickeners such as metal soaps and composite metal soaps, and non-soap-based thickeners such as Benton, silica gel, urea compounds, and urea-urethane compounds can be used. Examples of the metal soap include sodium soap, calcium soap, aluminum soap, lithium soap and the like, and examples of the urea compound and the urea / urethane compound include a diurea compound, a triurea compound, a tetraurea compound, another polyurea compound and a diurethane compound.

In addition, the grease may contain other known additives, if necessary. Examples of this additive include amine-based and phenol-based antioxidants, chlorine-based, sulfur-based, phosphorus-based compounds, extreme pressure agents such as organic molybdenum, petroleum sulfonate, dinonylnaphthalene sulfonate, and rust preventives such as sorbitan ester. Can be mentioned.

An example of a rolling bearing filled with grease will be described with reference to FIG. 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 the outer peripheral surface and an outer ring 3 having an outer ring raceway surface 3a on the inner peripheral surface are concentrically arranged, and a plurality of rolling bearings 1 are arranged between the inner ring raceway surface 2a and the outer ring raceway surface 3a. The balls 4 are arranged. The ball 4 is held by the cage 5. Further, the openings 8a and 8b at both ends in the axial direction of the inner and outer rings are sealed by the sealing member 6, and the grease 7 is sealed at least around the ball 4. The inner ring 2, the outer ring 3, and the ball 4 are made of an iron-based metal material, and grease 7 is lubricated by interposing the grease 7 on the raceway surface with the ball 4.

The estimation method according to the present invention is a method assuming a case where the state of grease in the bearing is in the churn period. In the churning period, the grease itself enters the lubrication target portion and lubrication is performed, and the grease is continuously agitated, so that the torque is affected by the viscous resistance of the grease. In particular, it is considered that the viscous resistance of grease existing in the pocket gap during rotation during the churn period has a great influence on the bearing torque. Since the viscous resistance of grease depends on the shear rate, the tendency of bearing torque can be predicted by estimating the apparent viscosity in consideration of the shear rate received by the grease in the above state.

The present invention is characterized in that the apparent viscosity of a non-Newtonian fluid is estimated using the following formula (1). By using this equation (1), the apparent viscosity η [Pa · s] at an arbitrary shear rate can be calculated (predicted).

However, the symbols in the equation are η _oil : viscosity of the fluid component [Pa · s], τ ₀ : yield stress [Pa], γ: shear rate [s ^-1 ], n: constant, m: constant.

In the case of grease, the viscosity η _oil of the fluid component is the value (viscosity) obtained by multiplying the kinematic viscosity of the base oil at the actual temperature (for example, the temperature inside the bearing or the temperature of the entire mechanical device) by the density of the base oil. .. When the grease contains a viscosity improver, the viscosity of the base oil and the thickener is used as _{the viscosity η oil of the fluid component.}

Further, the yield stress τ ₀ and the constants n and m in the equation (1) can be specified based on the evaluation of the rheological characteristics of the grease using a rheometer. In the evaluation of the rheological characteristics of grease, it is preferable to use a rheometer having a cone plate type cell. An outline of such a rheometer is shown in FIG. As shown in FIG. 2, the 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 as to be in contact with each other at one point (with a slight gap). Then, the grease 14 as a sample is placed between them. In this rheometer, the shear rate applied to the grease 14 is the same at any position, independent of the distance from the cell center. The conditions for rheology measurement are (1) rotation speed dependence at constant temperature / constant direction rotation, (2) vibration frequency dependence at constant temperature / constant shear strain, and (3) dynamic viscoelastic shear at constant frequency. Although there is stress dependence, etc., in the present invention, the measurement is mainly performed under the condition (1).

By substituting the viscosity η _{oil of the fluid component, the yield stress τ 0} obtained by the rheology measurement using a rheometer, and the constants n and m into the above equation (1), the appearance of the non-Newtonian fluid at an arbitrary shear rate is obtained. The viscosity can be estimated.

The shear rate is the shear rate applied to the grease existing in the pocket gap during the rotation in the churn period, and can be calculated from the set bearing rotation speed or the like. For example, assuming that the ball is positioned in the pocket center of the cage, when the inner ring rotation speed ¹⁰ 4 ^{min -1} at 6204 bearing, shear rate of the grease pocket portion corresponds to ¹⁰ 5 ^{s -1} orders. By substituting an arbitrary shear rate into the above equation (1), the apparent viscosity of the grease existing in the pocket gap during the rotation in the churn period at the shear rate can be obtained as a predicted value.

Here, the apparent viscosity of the grease in the bearing changes significantly due to a change in the atmospheric temperature or heat generation of the bearing due to operation. Therefore, in order to estimate the bearing torque more accurately, it is preferable to consider the temperature change. Based on this, in another embodiment of the present invention, the apparent viscosity of the non-Newtonian fluid is estimated using the following formula (2). The following equation (2) is an equation obtained by adding temperature correction to the above equation (1).

However, the symbols in the formula are η _t : apparent viscosity of the non-Newtonian fluid at an arbitrary temperature [Pa · s], η _oil-t : viscosity of the fluid component at an arbitrary temperature [Pa · s], C: Constant, D: constant, ΔT: temperature increased with respect to the reference temperature.

In the case of grease, the value (viscosity) obtained by multiplying the kinematic viscosity of the base oil at an arbitrary temperature by the density of the base oil is used for _{the viscosity η oil-t of the fluid component.} When the grease contains a viscosity improver, the viscosity of the base oil and the thickener at an arbitrary temperature is used as _{the viscosity η oil of the fluid component.}

Further, the yield stress τ ₀ and the constants n and m in the equation (2) can be specified based on the evaluation of the rheological characteristics of the grease using a rheometer as described above. Further, the constants C and D can be obtained by fitting with the measured value from the rheological characteristic results of a plurality of temperature differences of the same grease.

By substituting each value obtained by actual measurement or the like into the above equation (2), the apparent viscosity of the non-Newtonian fluid at an arbitrary temperature can be estimated. As a result, the temperature change of the non-Newtonian fluid can be taken into consideration, and the apparent viscosity of the non-Newtonian fluid can be estimated more accurately.

Here, in general, the larger the apparent viscosity of grease, the larger the bearing torque. Therefore, by using the apparent viscosity estimated by the above method, the bearing torque can be estimated, or the magnitude of the bearing torque can be estimated among a plurality of greases. The bearing torque can be estimated, for example, by calculating the apparent viscosity of grease assuming that the temperature of the entire mechanical device including the bearing is the temperature inside the bearing. This makes it possible to select grease (evaluate with a rheometer) based on the required bearing torque. Further, the magnitude of the bearing torque between the plurality of greases can be estimated by comparing the magnitude of the apparent viscosity of each grease. For example, the grease having the lowest apparent viscosity from a plurality of greases can be selected as the grease having the lowest bearing torque.

In FIG. 1, ball bearings are illustrated as rolling bearings in which grease is sealed. In addition to ball bearings, cylindrical roller bearings, tapered roller bearings, self-aligning roller bearings, needle roller bearings, thrust cylindrical roller bearings, and thrust It can also be applied to tapered roller bearings, thrust needle roller bearings, thrust self-aligning roller bearings, and the like.

In the above, the grease and the rolling bearing filled with the grease have been described, but the non-Newtonian fluid which is the target of the estimation method of the present invention is not limited to the grease, but a gel, a sol, or other fluid having thixotropy or a semi-thixotropic property. It may be solid. Further, the two relative moving members in which the non-Newtonian fluid undergoes shearing are not limited to the bearing members of the rolling bearing, and may be applied to other mechanical elements. Other mechanical elements include, for example, linear guides, clutches, cams, joints, chains, gears, plain bearings and the like.

Estimation method of the present invention, because it can also accurately estimate an apparent viscosity at a high shear rate region, 10000s ^-1 or more shear rate region, more preferably estimation of non-Newtonian fluids used in 20000S ^-1 or more shear rate region Suitable for.

Rheology measurements were performed on grease (base oil: ester oil (dynamic viscosity at 40 ° C.: 26 mm ² / s, thickener: lithium soap). The measurement was performed using a cone plate type cell with a tip angle of 178 °. The rheology measurement conditions are constant temperature and rotation in a certain direction, and the temperature is 20 ° C. The shear rate is 100 to 5000 (unit: 1 / s). The speed was increased to, and the apparent viscosity at each shear rate when the steady state was reached was measured. FIG. 3 plots the measured values.

Further, from these actually measured values, the yield stress τ ₀ and the constants n and m in the above equation (1) were obtained. As a result, the yield stress τ ₀ = 750 Pa, the constant n = 0.838, and the constant m = 10. In FIG. 3, the approximate expression obtained by substituting each value into the equation (1) is shown by a solid line. As shown in FIG. 3, the approximate expression fits the measured value very well, and it can be seen that the apparent viscosity (measured value) on the rheometer is accurately reproduced. In addition, this approximate expression is asymptotic to _{the viscosity η oil} of the base oil, which is a fluid component, in the high shear rate region.

Subsequently, using 10 types of greases (greases A to J) having different types of base oil, kinematic viscosity of base oil, and types of thickener, the correlation between the estimated value of apparent viscosity and the bearing torque (measured value). Was evaluated. As the estimated value of the apparent viscosity, an estimated value based on the formula (1) (Example 1), an estimated value based on the Herschel-Bulkley model (Comparative Example 1), and an estimated value based on the Papanastasiou model (Comparative Example 2) were used. .. Table 1 shows the apparent viscosities of the greases estimated by the approximate formulas for each grease. The shear rate was set to ^{20000s -1} as the shear rate between the cage pockets.

Example 1
The apparent viscosity of each grease at a shear rate of 20000s- ¹ was estimated by each approximate equation (based on equation (1)) derived by the rheology measurement using the rheometer described above.

Comparative Example 1
The apparent viscosity of each grease at a shear rate of 20000s- ¹ was estimated using the following equation (3), which is a Herchel-Bulky model. Yield stress and each constant were obtained by rheological measurement using the rheometer described above.

However, the symbols in the equation are τ ₀ : yield stress [Pa], γ: shear rate [s ^-1 ], K: constant, n: constant.

Comparative Example 2
The apparent viscosity of each grease at a shear rate of 20000s- ¹ was estimated using the following equation (4), which is a Papanastasiou model. Yield stress and constants were obtained by rheological measurements using the rheometer described above.

However, the symbols in the equation are η _oil : viscosity of the fluid component [Pa · s], τ ₀ : yield stress [Pa], γ: shear rate [s ^-1 ], m: constant.

<Bearing torque test>
A test bearing was obtained by encapsulating each grease in a deep groove ball bearing 6204 (bearing size: inner diameter 20 mm, outer diameter 47 mm) so that the encapsulation amount was 100% of the rest space ratio. The test bearing was rotated under the conditions of a load of 20 N, a rotation speed of 1800 min ^-1 , and a room temperature of 25 ° C., and the bearing torque after 10 minutes of operation was measured. Note that 1800 min ^{-1 is about 20000 s -1} in terms of the shear rate between the cage pockets. This "shear velocity between the cage pockets" is a value obtained by (rotation speed of the ball / distance between the ball and the cage pocket) assuming that the ball is located at the center of the pocket portion of the cage. Table 1 shows the bearing torque when each grease is used.

As shown in Table 1, it can be seen that in Example 1, the magnitude relationship between the apparent viscosity and the bearing torque is very well matched. On the other hand, in Comparative Example 1 and Comparative Example 2, the magnitude relationship between the apparent viscosity and the bearing torque may not match. For example, in Comparative Example 1, the magnitude of the apparent viscosity and the magnitude of the bearing torque are reversed between the greases AB, EF, EH, GH, GJ, and IJ. Further, in Comparative Example 2, the magnitude of the apparent viscosity and the magnitude of the bearing torque are reversed between the greases EF, EG, and HI.

From this result, it can be seen that the magnitude of the bearing torque can be estimated accurately by using the apparent viscosity (estimated value) based on the equation (1). Further, it can be seen that the apparent viscosities of Example 1 are not limited to their magnitude relations, but the degree of difference between them also reflects the difference between bearing torques. Considering that the bearing torque increases as the viscosity of the grease increases, it is considered that the estimated value based on the equation (1) accurately reproduces the apparent viscosity of the grease.

<Evaluation by temperature>
Rheology measurements were performed on grease (base oil: ester oil (dynamic viscosity at 40 ° C.: 26 mm ² / s, thickener: lithium soap). The measurement was performed using a cone plate type cell with a tip angle of 178 °. The rheology measurement conditions were constant temperature and rotation in a constant direction, the temperatures were 20 ° C, 40 ° C, 60 ° C, and 80 ° C. The shear rate was 100. The speed was increased from 1 to 5000 (unit: 1 / s), and the apparent viscosity at each shear rate when the steady state was reached was measured. FIG. 4 plots the measured values for each temperature.

From these actually measured values, the constants C and D in the above equation (2) were obtained. The constant C = 1.002 and the constant D = 1.002. The above-mentioned numerical values were used for the yield stress τ ₀ , the constant n, and the constant m. The reference temperature was 20 ° C. In FIG. 4, each approximate expression obtained by substituting each value into the equation (2) is shown by a solid line. From the top in FIG. 4, the approximate expression at 20 ° C., the approximate expression at 40 ° C., the approximate expression at 60 ° C., and the approximate expression at 80 ° C.

As shown in FIG. 4, the approximate expression for each temperature fits very well to the measured values of each temperature, and it can be seen that the apparent viscosity (measured value) on the rheometer is accurately reproduced. According to this equation (2), the apparent viscosity of grease can be accurately estimated even in an environment where the temperature of grease changes due to a change in atmospheric temperature or heat generation of bearings. Further, by using the apparent viscosity (estimated value) based on the equation (2), it is possible to predict the bearing torque in consideration of the temperature change.

The method for estimating the apparent viscosity of a non-Newtonian fluid of the present invention can accurately estimate the apparent viscosity of a non-Newtonian fluid even in a high shear rate region, and by extension, the torque when two members are relatively moved in the presence of the non-Newtonian fluid. Can be suitably used for confirming the validity of experimentally measured values of bearing torque and selecting grease for low torque bearings, for example, in the development process and manufacturing process of grease-filled bearings.

1 Rolling bearing 2 Inner ring 3 Outer ring 4 Ball 5 Cage 6 Sealing member 7 Grease 8 Opening 11 Rheometer 12 Cone plate type cell 13 Horizontal disk plate 14 Grease

Claims (5)

It is a method of estimating the apparent viscosity of a non-Newtonian fluid existing in the gap between two members that move relative to each other.
Substitute the yield stress and each constant calculated from the relationship between the shear rate and the viscosity measured for the non-Newtonian fluid using a leometer, and an arbitrary shear rate in the gap between the two members into the following equation (1). A method for estimating the apparent viscosity of a non-Newtonian fluid, which comprises estimating the apparent viscosity of the non-Newtonian fluid at an arbitrary shear rate.

However, the symbols in the formula 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, m: constant. The method for estimating the apparent viscosity of a non-Newtonian fluid according to claim 1, wherein the apparent viscosity of the non-Newtonian fluid at an arbitrary temperature is estimated by the following formula (2) in which temperature correction is added to the above formula (1). ..

However, the symbols in the formula are η _t : apparent viscosity of the non-Newtonian fluid at an arbitrary temperature [Pa · s], η _oil-t : viscosity of the fluid component at an arbitrary temperature [Pa · s], C: Constant, D: constant, ΔT: temperature increased with respect to the reference temperature. The method for estimating the apparent viscosity of a non-Newtonian fluid according to claim 1 or 2, wherein the non-Newtonian fluid is a grease containing a base oil and a thickener. The grease is grease sealed in a rolling bearing including an inner ring and an outer ring, a plurality of balls interposed between the inner ring and the outer ring, and a cage having a pocket for holding the balls.
The method for estimating the apparent viscosity of a non-Newtonian fluid according to any one of claims 1 to 3, wherein the shear rate of the gap between the ball pockets with respect to the cage is used as the arbitrary shear rate. .. This is a method of estimating the torque when the two members move relative to each other.
Using the apparent viscosity of the non-Newtonian fluid estimated by the estimation method according to any one of claims 1 to 4, the torque of the non-Newtonian fluid at the arbitrary shear rate is estimated, or the torque of the non-Newtonian fluid is estimated. A method for estimating torque, which comprises estimating the magnitude of torque between a plurality of non-Newtonian fluids at an arbitrary shear rate.

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