Method of estimating use condition on rolling bearing

The present invention relates to a method for estimating the usage conditions in which rolling bearings are used, and more specifically, to a method for estimating radial loads, axial loads, rotation speeds, etc., which are the usage conditions in which bearings are used, by X-ray analysis.

It is known that the life of rolling bearings depends on the working load, lubrication conditions, materials and the like. Conventionally, bearing life prediction has been performed using a life calculation formula created in consideration of working load, lubrication conditions, materials, etc. (Non-Patent Document 1). This formula is used to estimate how long a rolling bearing can be used under certain conditions, or under what conditions the rolling bearing should be used so that the bearing will not be damaged during the required usage period. Used to estimate goodness.

Generally, bearings are used under the conditions of use set based on the life calculation formula. Therefore, as long as the bearing is used under normal conditions, the life of the bearing should not be an issue. However, there are often situations where bearing life is a problem in the market. This is partly because the actual bearing operating conditions may differ from the designed conditions.

For bearings that are damaged earlier than the designed life, a survey is conducted to estimate the conditions of use in order to estimate the cause of the damage. The methods for estimating the bearing usage conditions are (1) operating temperature estimation (Non-Patent Document 2), (2) operating surface pressure estimation by X-ray analysis (Non-Patent Document 2), and (3) lubrication condition estimation (Patent Document). 1,2), (4) Load estimation (Patent Documents 3, 4), etc. All of these are used for estimating the cause of bearing damage and estimating the remaining life, but among them, the most basic and most important estimation of usage conditions is load estimation. This is because the most basic factor that determines the life of rolling bearings is a load-related factor called dynamic equivalent load.

Equation (1) shows the formula for calculating the life of rolling bearings.<maths num="1"><img file="JP2011069684A_D0001.tif" /></maths> Dynamic equivalent load for radial bearings: P_r= XF_r+ YF_a (2) Dynamic equivalent load for thrust bearings: P_a= F_a+ 1.2F_r・・・(3)

Here, C is a known value (kgf) for the static rated load, P is a dynamic equivalent load (kgf), p is 3 for a ball bearing, 10/3 for a roller bearing, and X is a known value for the radial load coefficient (non-). Patent Document 3), Y is a known value in axial load coefficient (Non-Patent Document 3), F_rIs a radial load (kgf), F_aIs the axial load (kgf).

The dynamic equivalent load is the radial load F_r(kgf) and axial load F_aObtained from (kgf). However, from the bearing after use, the radial load F_r(kgf) and axial load F_aThere was no rational way to estimate (kgf). On the other hand, although it is not a bearing usage condition, it is also important to know how long the bearing has been used (= bearing rotation speed) in order to estimate the cause of bearing damage. However, there is no method for estimating the number of rotations of a bearing from the bearing after use.

<p><patcit num="1"><text>Japanese Patent Application Laid-Open No. 2005-345132</text></patcit><patcit num="2"><text>Japanese Unexamined Patent Publication No. 2004-20378</text></patcit><patcit num="3"><text>Japanese Patent Application Laid-Open No. 2001-124665</text></patcit><patcit num="4"><text>Japanese Patent Application Laid-Open No. 2002-257797</text></patcit></p>

<p><nplcit num="1"><text>Junzo Okamoto, Dynamic load capacity of rolling bearings and roller bearings-Detailed explanation of Lundberg-Palmgren theory-, Department of Mechanical Engineering, Faculty of Engineering, Chiba University, (1988)</text></nplcit><nplcit num="2"><text>Tsushima Masayuki, Maeda Kikuo, Bearing Engineer, 48 (1984) 1-17.</text></nplcit><nplcit num="3"><text>Published by NTN Corporation, NTN Rolling Bearing General Catalog, CAT. No202- VII / J, (2002).</text></nplcit><nplcit num="4"><text>TA Harris et. Al., Rolling Bearing Analysis 5th ed., CPC Press, (2006), 106p.</text></nplcit><nplcit num="5"><text>KT Johnson (KL Johnson), Contact Mechanics, (1989), 102p.</text></nplcit><nplcit num="6"><text>X-ray stress measurement method standard (2002 edition)-Steel edition, Japan Society of Materials Science, (2002)</text></nplcit></p>

<p> Radial load of rolling bearing F_r(kgf), axial load F_a(kgf), Estimating the number of rotations of a bearing is important for estimating the cause of damage, but there was no rational method for estimating it.</p><p> An object of the present invention is to propose a method for estimating the usage conditions of a rolling bearing, which can reasonably estimate the radial load and the axial load, which are the usage conditions of the bearing after use. Another object of the present invention is to propose a method for estimating the operating conditions of a rolling bearing, which can estimate the number of rotations of the bearing, which is the operating condition of the bearing, from the bearing after use.</p>

<p> In the first method for estimating the usage conditions of a rolling bearing in the present invention, X-ray analysis is performed on the rotating wheels and fixed wheels of the rolling bearing after use, and the maximum rolling element load of the rotating wheels is obtained from the result of this X-ray analysis. The process of obtaining an estimated value and the estimated value of the rolling element load at any one or more points of the fixed wheel (S1), The process of estimating the bearing load distribution from the estimated maximum rolling element load of the rotating wheel obtained in this process (S1) and the estimated rolling element load at any one or more points of the fixed wheel (S2). )When, The process (S3) of estimating the radial load and the axial load, which are the conditions of use of the bearing, is included from the estimated load distribution of the bearing and the contact angle between the rolling element and the inner and outer rings of the bearing.</p><p> According to this method, the radial load and axial load of the rolling bearing after use can be reasonably investigated using X-ray analysis. Therefore, it helps to accurately estimate the cause of bearing damage, and the cause of bearing damage can be investigated in more detail. In the above X-ray analysis, the distribution of residual stress and half-value width corresponding to the depth from the surface is measured from the data obtained by X-ray irradiation. From the result of the distribution of the residual stress or the half-value width, the estimated value of the maximum rolling element load of the rotating wheel is obtained. In the X-ray analysis described below, the residual stress and the half-value distribution are measured in the same manner.</p><p> In the present invention, the contact angle between the rolling element and the inner and outer rings of the bearing may be estimated from the rolling surface of the fixed ring of the rolling bearing. The contact angle between the rolling element and the inner and outer rings may be determined from the design value of the rolling bearing.</p><p> The rolling bearing whose usage conditions are estimated by the method of the present invention may be a radial bearing or a thrust bearing.</p><p> In the second method for estimating the usage conditions of a rolling bearing in the present invention, X-ray analysis is performed on the rotating wheels and fixed wheels of the rolling bearing after use, and the maximum rolling element load of the rotating wheels is obtained from the result of this X-ray analysis. The process of obtaining an estimate and the rolling element load at any one or more points of the fixed wheel (S1), The process of estimating the bearing load distribution from the estimated maximum rolling element load of the rotating wheel obtained in this process (S1) and the rolling element load at any one or more points of the fixed wheel (S2). , From the estimated load distribution of the bearing and the result of obtaining the relationship between the number of loads N, the repeated stress S, and the half-value width w (°) obtained by X-ray analysis in advance, the number of rotations used by the bearing is estimated. Includes the process of doing (S4).</p><p> According to this method, the number of rotations of the rolling bearing after use can be reasonably investigated by using X-ray analysis. Therefore, it helps to accurately estimate the cause of bearing damage, and the cause of bearing damage can be investigated in more detail.</p><p> In the second method for estimating the usage conditions of rolling bearings, the relationship between the number of loads N, the repetitive stress S, and the half-value width w (°) obtained by X-ray analysis may be applied to the following equation.<maths num="2"><img file="JP2011069684A_D0002.tif" /></maths> However, w₀Is the half price range without fatigue, σ_YIs the yield stress, and f, g, h, and k are positive constants. In this case, the repeated stress S is the equivalent stress σ._eIt may be.</p><p> In each of the above methods in the method for estimating the usage conditions of the second rolling bearing, the contact angle between the rolling element and the inner and outer rings in the bearing may be estimated from the rolling surface of the fixed ring of the rolling bearing. Further, the contact angle between the rolling element and the inner and outer rings of the bearing may be determined from the design value of the rolling bearing.</p><p> In the second method for estimating the usage conditions of the rolling bearing, the rolling bearing for estimating the number of rotations used may be a radial bearing or a thrust bearing.</p><p> In the third method for estimating the usage conditions of a rolling bearing of the present invention, X-ray analysis is performed on the rotating wheels and fixed wheels of the rolling bearing after use, and the maximum rolling element load of the rotating wheels is obtained from the result of this X-ray analysis. The process of obtaining an estimated value and the estimated value of the rolling element load at any one or more points of the fixed wheel (S1), The process of estimating the bearing load distribution from the estimated maximum rolling element load of the rotating wheel obtained in this process (S1) and the estimated rolling element load at any one or more points of the fixed wheel (S2). )When, From the estimated load distribution of the bearing and the contact angle between the rolling elements and the inner and outer rings of the bearing, the process of estimating the radial load and the axial load, which are the conditions of use of the bearing (S3), From the above-estimated load distribution of the bearing and the result of obtaining the relationship between the number of loads N, the repeated stress S, and the half-value width w (°) obtained by X-ray analysis in advance, the number of rotations of the bearing used ( Including the process of estimating S4).</p><p> According to this method, the radial load, axial load, and rotation speed of the rolling bearing after use can be reasonably investigated using X-ray analysis. Therefore, it helps to accurately estimate the cause of bearing damage, and the cause of bearing damage can be investigated in more detail.</p>

<p> In the first method for estimating the usage conditions of the rolling bearing of the present invention, X-ray analysis is performed on the rotating wheel and the fixed wheel of the rolling bearing after use, and the maximum rolling element load of the rotating wheel is obtained from the result of this X-ray analysis. The process of obtaining the estimated value and the estimated value of the rolling element load at any one or more points of the fixed wheel, and the estimated value of the maximum rolling element load of the rotating wheel and the arbitrary of the fixed wheel obtained in this process. From the process of estimating the load distribution of the bearing from the estimated value of the rolling element load at one or more points of the above, and from the estimated load distribution of the bearing and the contact angle between the rolling element and the inner and outer rings in the bearing, the bearing Since it is a method that includes the process of estimating the radial load and axial load, which are the conditions of use of, the radial load and axial load of the rolling bearing after use should be reasonably investigated using X-ray analysis. Can be done. Therefore, it helps to accurately estimate the cause of bearing damage, and the cause of bearing damage can be investigated in more detail.</p><p> In the second method for estimating the usage conditions of a rolling bearing of the present invention, X-ray analysis is performed on the rotating wheels and fixed wheels of the rolling bearing after use, and the maximum rolling element load of the rotating wheels is obtained from the result of this X-ray analysis. The process of obtaining an estimated value and the rolling element load at any one or more positions of the fixed wheel, and the estimated value of the maximum rolling element load of the rotating wheel obtained in this process and any 1 of the fixed wheel. The process of estimating the bearing load distribution from the rolling element load at the position above the point, the estimated bearing load distribution, the number of loads N, the repeated stress S, and the half-value range w (°) obtained by X-ray analysis. Since this method includes the process of estimating the number of times the bearing has been used from the result of obtaining the relationship between the two, the number of times the rolling bearing has been used can be reasonably investigated using X-ray analysis. be able to. Therefore, it helps to accurately estimate the cause of bearing damage, and the cause of bearing damage can be investigated in more detail.</p><p> In the third method for estimating the usage conditions of the rolling bearing of the present invention, X-ray analysis is performed on the rotating wheels and fixed wheels of the rolling bearing after use, and the maximum rolling element load of the rotating wheels is obtained from the result of this X-ray analysis. The process of obtaining the estimated value and the estimated value of the rolling element load at any one or more points of the fixed wheel, and the estimated value of the maximum rolling element load of the rotating wheel and the arbitrary of the fixed wheel obtained in this process. From the process of estimating the load distribution of the bearing from the estimated value of the rolling element load at one or more points of the above, and from the estimated load distribution of the bearing and the contact angle between the rolling element and the inner and outer rings in the bearing, the bearing The process of estimating the radial load and axial load, which are the conditions of use, the load distribution of the bearing estimated above, the number of loads N, the repeated stress S, and the half-value width w (°) obtained by X-ray analysis. Since this method includes the process of estimating the number of times the bearing has been used from the result of obtaining the relationship between the above, the radial load, axial load, and number of times of rotation of the rolling bearing after use are analyzed by X-ray. Can be reasonably investigated using. Therefore, it helps to accurately estimate the cause of bearing damage, and the cause of bearing damage can be investigated in more detail.</p>

<figref num="1">It is a flow chart which shows the use condition estimation method of the rolling bearing which concerns on one Embodiment of this invention.</figref><figref num="2">Radial load F on radial bearing_rIt is a schematic diagram of the load zone when only is acting.</figref><figref num="3">It is explanatory drawing of the situation that the maximum load is acting on a rolling element at time t = 0.</figref><figref num="4">It is explanatory drawing which shows an example of the residual stress distribution map which is the result of X analysis.</figref><figref num="5">It is a graph which shows the relationship between the stress under the surface under the contact surface and the ZΣρ value.</figref><figref num="6">It is explanatory drawing of the measurement principle of X analysis.</figref><figref num="7">It is sectional drawing which shows the example of the various radial bearings which are the estimation target of the use condition estimation method of this embodiment.</figref><figref num="8">It is sectional drawing which shows an example of the thrust bearing which is the estimation target of the use condition estimation method of this embodiment.</figref>

An embodiment of the present invention will be described with reference to the drawings. In the method of estimating the usage conditions of this rolling bearing, X-ray analysis is performed on the rotating wheels and fixed wheels of the rolling bearing after use, and the estimated value of the maximum rolling element load of the rotating wheel is obtained from the result of this X-ray analysis. , The process of obtaining the estimated value of the rolling element load at any one or more points of the fixed wheel (S1), and the estimated value of the maximum rolling element load of the rotating wheel obtained in this process (S1) and the fixed wheel The process of estimating the bearing load distribution from the estimated value of the rolling element load at any one or more points (S2), the estimated bearing load distribution, and the contact angle between the rolling element and the inner and outer rings in the bearing. From the process (S3) of estimating the radial load and axial load, which are the conditions of use of the rolling bearing, the load distribution of the estimated bearing, the number of loads N, the repeated stress S, and X-ray analysis in advance. Includes the process of estimating the number of rotations used of the bearing (S4) from the result of finding the relationship of the half price range w (°) obtained in.

According to this method, the radial load, axial load, and bearing rotation speed can be estimated using X-ray analysis, which helps to accurately estimate the cause of bearing damage and investigate the cause of bearing damage. It will be possible to carry out in more detail.

Below, the radial load F of rolling bearings using X-rays_r (kgf), axial load F_a (kgf), the method of estimating the number of rotations of the bearing will be explained concretely. First of all, radial load F_r (kgf) and axial load F_a The method of obtaining (kgf) will be described. Radial load of rolling bearing F_r (kgf) and F_aThe axial load (kgf) is calculated by the following equations (4) and (5) (Non-Patent Document 1).

<maths num="3"><img file="JP2011069684A_D0003.tif" /></maths> Where J_rIs a constant that is determined by the load factor ε and is a radial integral value, J_aIs a constant determined by the load factor ε and is the axial integral value, Z is the number of rolling elements, Q_maxIs the maximum rolling element load (kgf) and α is the contact angle (rad).

From this, the radial load F_r (kgf) and axial load F_a (kgf) is ε, Q_max It can be estimated if (kgf) and α (rad) are obtained. First, load estimation (Non-Patent Document 2) by conventional X-ray analysis is performed on the rotating wheel of the bearing, and the maximum contact surface pressure of the bearing is Pmax (kgf / mm).²To estimate. After that, the maximum contact surface pressure Pmax (kgf / mm)²) To maximum rolling element load Q_max(kgf) is obtained by a conventional method (Non-Patent Document 4). In addition, α (rad) can be inferred from the trace of the bearing's rolling traces or from the specifications of the bearing design.

In the above X-ray analysis, the distribution of the residual stress of the main shear stress corresponding to the depth from the surface is measured from the data obtained by the X-ray irradiation. The load estimation by the above-mentioned X-ray analysis is an estimation method for obtaining an estimated value of the maximum rolling element load of the rotating wheel from the measurement result of the residual stress distribution, and is performed as follows. There is a certain relationship between the maximum contact surface pressure Pmax of Hertz acting on the bearing and the contact elliptical minor axis radius of the bearing. The contact ellipse refers to an elliptical contact surface formed around the contact when a load is applied. In addition, there is a certain relationship between the peak position of the main shear stress distribution acting when the bearing is used and the contact elliptical minor axis radius of the bearing. Therefore, if the peak position of the main shear stress distribution generated when the bearing is used can be measured, the maximum contact surface pressure Pmax of Hertz acting on the bearing can be obtained. Estimating the load is an analysis method in which the peak position of the main shear stress distribution acting when the bearing is used is predicted by measuring the residual stress distribution, and the maximum contact surface pressure Pmax of Hertz acting on the bearing is obtained.

A specific method for estimating the load will be described. Depth Z corresponding to the position where maximum shear stress is applied by rolling contact under high contact surface pressure₄₅A residual stress distribution with a compressive stress peak at ° is generated (Fig. 4- (1) Peak example). The contact surface pressure Pmax can be estimated using this peak position. In the bearing used in the actual machine, no peak may be observed in the residual stress distribution due to foreign matter biting or temperature rise (Fig. 1- (2) Example of formation depth). In such a case, the contact surface pressure Pmax is estimated from the residual stress generation depth. In the above X analysis, the residual stress distribution map of FIG. 4 is obtained. [When estimating the load from the peak position of compressive residual stress] The peak position (mm) is applied to the depth Z of the horizontal axis (Σρ × Z) of the shear stress distribution under the contact surface shown in Fig. 5, and the calculated Σρ × Z (Σρ: sum of curvatures between objects in contact) value. Follow (A in Fig. 5) on the dotted line and read the intersection with the straight line P. [When estimating the load from the position of the compression residual stress generation depth] Similarly, apply the generation depth to Z on the horizontal axis of Fig. 5, follow the calculated Σρ × Z value (B in Fig. 5) on the dotted line, and τ._CRead where it intersects the line of = 600 MPa (critical shear stress: the minimum shear stress required to generate residual stress inside the material).

In addition, the above maximum contact surface pressure Pmax (kgf / mm)²) To maximum rolling element load Q_maxIn the method of calculating (kgf), it is calculated as follows. Now, if Pmax is obtained by X-ray analysis, the rolling element load Q, the semi-major axis radius a, and the semi-minor axis radius b of the contact ellipse can be obtained from the following equations, respectively.<maths num="4"><img file="JP2011069684A_D0004.tif" /></maths> Where R_x1, R_x2, R_y1, R_y2Is the radius of curvature of two objects 1 and 2 (not shown) in the x and y directions. Since the maximum contact surface pressure Pmax has already been obtained by X-ray analysis, the rolling element load Q can be obtained as a result.

Next, the procedure for obtaining the load factor ε will be described. Generally, a radial load F on a radial bearing_r(kgf) and axial load F_a When a combined load of (kgf) is applied, the load applied to each rolling element is not uniform. Lundberg and Palmgren (Non-Patent Document 1) examined this problem and found equation (6), which is the relationship between rolling element loads at any angle (rad).

<maths num="5"><img file="JP2011069684A_D0005.tif" /></maths> Where Q_maxIs the maximum rolling element load, α is the contact angle, and t is 1.1 for point contact and 1.5 for line contact according to Hertz's contact theory.

Now, Q from the result of load estimation of the rotating wheel_maxSince (kgf) is known, in order to obtain ε, it is necessary to obtain the rolling element load Q (kgf) acting on a certain angle of the fixed wheel. In general, it is difficult to obtain an accurate load position for a fixed wheel, so load estimation is performed at two points on the fixed wheel . Specifically, any two points ψ in the load range of the fixed wheel₁ (rad), ψ₂= ψ₁The load acting on + φ (rad) can be obtained by load estimation, and ε can be obtained by solving the following simultaneous equations. Where ψ₁ It is necessary to record the angle φ (rad) deviated from (rad).<maths num="6"><img file="JP2011069684A_D0006.tif" /></maths>

This equation is a one-variable nonlinear equation and can be easily solved. If this equation is solved, ψ₁ Since (rad) can be obtained, ε can be obtained by substituting the result into Eq. (7) or Eq. (8). Then, from equations (4) and (5), the radial load F_r (kgf) and thrust load F_a Find (kgf) (if necessary, the dynamic equivalent load (kgf) can also be calculated from equations (2) and (3)).

In the following, a method for estimating the number of rotations by X-ray analysis, which can be applied even when the number of rotations of the bearing has not been measured, will be described. This method is a two-step process. First, the maximum rolling element load Q from the result obtained by load estimation_max (kgf) is calculated, and the internal stress acting on the fixed wheel when the rotating wheel rotates is calculated each time the rolling element passes from the value and the specifications of the bearing. Next, the amount of decrease in the half-value width when the internal stress acts is estimated from the relationship between the half-value width, the stress, and the number of loads obtained in the experiment, and is subtracted from the half-value width before receiving the load. This calculation is repeated every time the rolling element passes, and the decrease in the half price range that occurs in the inner and outer rings is simulated. Finally, the number of rotations of the bearing when the decrease in the half price range matches the measured value is obtained.

First, a method of obtaining the internal stress acting on the fixed ring (outer ring) when the rotating wheel (inner ring) rotates each time the rolling element passes through will be described. Figure 2 shows the radial load F on the radial bearing._r Only (kgf) is acting, and the load band when the bearing clearance is 0 (clearance = 0, ε = 0.5) is shown.

At this time, the load distribution Q (kgf) for each angle ψ (rad) in Fig. 2 is expressed by Eq. (6). Load factor ε and maximum rolling element load Q_max (kgf) is already known by analysis. Therefore, since the rolling element load Q (kgf) can be found from Eq. (6), the maximum contact surface pressure Pmax (kgf / mm) at each angle ψ is obtained.²) And the semi-minor axis radius a, b (mm) of the contact ellipse can be estimated by a conventional method (Non-Patent Document 4). That is, the major and minor axis radii a and b of the contact ellipse can be obtained by the above-mentioned equation in paragraph [0034].

On the other hand, the internal stress acting on the inner and outer rings can be assumed to be in a plane strain state, so various stress components σ with respect to the depth z (mm) just below the contact center._x, σ_y, σ_z, τ_xy, τ_yz, τ_zx(kgf / mm²) Can be calculated from the following formula (Non-Patent Document 5).

<maths num="7"><img file="JP2011069684A_D0007.tif" /></maths> Where σ_x, σ_y, σ_z (kgf / mm²) Is the normal stress component, τ_xy, τ_yz, τ_zx (kgf / mm²) Is the shear stress component, and ν is the Poisson's ratio of 0.3.

Therefore, the equivalent stress at the depth z (mm) just below the contact center can be calculated from Eq. (16).<maths num="8"><img file="JP2011069684A_D0008.tif" /></maths>

From the above, the equivalent stress for each depth can be calculated at each position ψ (rad) of the inner and outer rings of the bearing. However, it is unclear under what circumstances this stress is repeated during bearing rotation. Therefore, let us consider under what circumstances the stress acting in the bearing is repeated.

Now the inner ring of the bearing is n_i(min^-1) Suppose it rotates at a speed of). Also, when the time t = 0 (min), the rolling element has the maximum rolling element load Q._max It is assumed that (kgf) is generated. The situation is shown in Fig. 3.

Point A of the inner ring in the figure is Q at time t = 0 (min)._max Under load of (kgf). When the inner ring is rotated from this state, the rotation speed n of the inner ring_i(min^-1) Is the revolution speed n of the rolling elements given by Eq. (17)._eSince it is faster than (min-1), point A of the inner ring catches up with the next rolling element and receives a load. Time t when point A is loaded on the next rolling element₁Since (min) is the point where the rotation position of the inner ring and the revolution position + phase difference of the rolling element match, t₁dmin) can be calculated by Eq. (18).

<maths num="9"><img file="JP2011069684A_D0009.tif" /></maths> Where Z is the number of rolling elements, D_aIs the rolling element diameter (mm), d_pIs the rolling element pitch circle diameter (mm), α is the contact angle (rad), n₀Is the rotation speed of the outer ring (min^-1).

From this, the time t at which point A of the inner ring receives the load from the first rolling element.₁ (min) becomes equation (20).<maths num="10"><img file="JP2011069684A_D0010.tif" /></maths>

Similarly, point A of the inner ring receives a load from the ath rolling element t_aTime (min^-1) And the angle of point A at that time ψ_a (rad) can be calculated from equations (21) and (22).<maths num="11"><img file="JP2011069684A_D0011.tif" /></maths>

In addition, the load Q (ψ) at which point A of the inner ring receives the load from the first rolling element._a) (Kgf) becomes equation (23).<maths num="12"><img file="JP2011069684A_D0012.tif" /></maths>

From the above, the angle ψ at which the inner ring A point receives the load from the ath rolling element._a (rad) can be calculated, and the rolling element load Q (ψ] at that time_a) (Kgf) can be calculated, so finally the angle (ψ)_a) The internal stress at (rad) can be calculated. Here, the above calculation focuses on only one point of the inner ring, but if the number of rotations of the bearing increases, the load becomes random, and it can be considered that the same load is received at any position. Therefore, it is not necessary to separately consider the load situation for other regions having different phases (Non-Patent Document 1). Further, although this calculation is based on the rotation of the inner ring, the same calculation can be performed on the rotation of the outer ring.

Next, the procedure for calculating how the change of the half-value width w (°) occurs from the internal stress will be described. The degree of steel fatigue is the repetitive stress σ_e (kgf / mm²) And the number of loads N. The change in half-price range w (°) indicates the degree of steel fatigue. Therefore, half-value width w (°), repetitive stress σ_e (kgf / mm²), If the relationship between the number of loads N is known, the number of loads N can be estimated from the repeated stress and the half-value width w (°). Now, half-value width w (°), repetitive stress σ_e (kgf / mm²), It is assumed that the relationship of the number of loads N can be expressed by Eq. (24).

<maths num="13"><img file="JP2011069684A_D0013.tif" /></maths> Where w₀Is the value of the half-value range w (°) without fatigue, f, g, h, k are positive constants, σ_eIs the repetitive stress and the value of the equivalent stress (kgf / mm)²), Σ_YYield stress 106kgf / mm²Is.

This equation has no physical meaning, but the half-value range w (°) is the number of loads N and the repetitive stress σ._e (kgf / mm²) Increases and simply decreases, the number of loads N and the repeated stress σ_e (kgf / mm²The experimental results can be adapted to the increase in) regardless of whether the change is linear or non-linear. Also, the repetitive stress σ_e (kgf / mm²) Indicates the equivalent stress σ indicating the degree of plastic deformation_e (kgf / mm²) Is applied, and the yield stress σ_Y (kgf / mm²) Below, the half-price range w (°) does not decrease, so the form of the equation takes this into consideration. Here, the yield stress σ_Y(kgf / mm²), 600 × 3 106kgf / mm²It was adopted. The constants of f, g, h, k are the experimental results (half-value width w (°) obtained in the experiment, repeated stress σ)._e (kgf / mm²), The relationship of the number of loads N) is determined by nonlinear multiple regression analysis with Eq. (24). From this, the number of loads N is an arbitrary repeating stress σ_e (kgf / mm²) And the half price range w (°).

Next, the procedure for calculating the decrease in the half price range w (°) will be described with a concrete example. Now, a radial load of 700 kgf is acting on the 6206 ball bearing, and at time t = 0min, the inner ring is 1 min from the state shown in Fig. 2.^-1Suppose that it starts to rotate. First, the maximum rolling element load Q just below the inner ring A point at t = 0 min_maxCalculate (kgf). Now time t = 0min, load; F_r= 700kgf, number of rolling elements Z = 9, contact angle α = 0 (rad), rolling element pitch diameter d_P= 45.5mm, rolling element diameter D_P= 9.525mm, radial integral value of ball bearing J_r= 0.2288 (ε = 0.5), inner ring speed n_i(min^-1), Therefore, the rolling element load at point A can be obtained as follows.

<maths num="14"><img file="JP2011069684A_D0014.tif" /></maths>

Next, from the obtained rolling element load, the semi-major axis radius a (mm) and semi-minor axis radius b (mm) of the contact ellipse and the maximum contact surface pressure P_max (kgf / mm²) Is calculated. Now, each radius of curvature is R from the specifications of 6206 ball bearings._x1mm, R_x2 mm, R_y1 mm, R_y2 Since it is mm, a (mm), b (mm), P_max(kgf / mm²) Is as follows. a = 2.705352mm b = 0.193283mm P_max= 304.048kgf / mm²

Next, the obtained a (mm), b (mm), P_max (kgf / mm²), Calculate the internal stress. Now, as an example, calculate the internal stress at a depth of z = 0.2mm.

<maths num="15"><img file="JP2011069684A_D0015.tif" /></maths>

Next, the repetitive stress σ obtained by the above calculation_e (kgf / mm²) Is added once, and the half price range w (°) is calculated. Temporarily, from the experiment, half-value width w (°), repetitive stress σ_e (kgf / mm²), It is assumed that Eq. (26) is obtained as the relation of the number of loads N.<maths num="16"><img file="JP2011069684A_D0016.tif" /></maths>

Assuming that the unfatigue half-value width w0 (°) is 7 ° (actually obtained by experiment), the repetitive stress σ obtained in the above calculation_eThe half price range w (°) after adding once can be calculated as follows.<maths num="17"><img file="JP2011069684A_D0017.tif" /></maths>

This is because the half-value width w (°) at a depth of z = 0.2 mm is 1.44E-07 (°) when the point A of the inner ring loaded at 700 kgf is loaded once at time t = 0min. ) Indicates a decrease. As can be seen from the form of Eq. (26), the change in the half-value width w (°) becomes non-linear with respect to the load after the second time, so the half-value width w ( The formula for estimating the amount of decrease in °) is formula (27), which is a partial derivative of this formula with respect to the number of loads N.

<maths num="18"><img file="JP2011069684A_D0018.tif" /></maths>

As described above, the behavior of the decrease in the half price width w (°) can be obtained by calculating the change when the bearing rotates for each load. When this calculation is repeated, the half-value width w (°) gradually decreases, and finally, when it matches the half-value width obtained in the experiment (in this example, the value measured at the depth position z = 0.2 mm). Is coming. At this time, the rotation angle of the bearing ψ_aIs calculated at the same time, so the number of rotations of the bearing can be calculated by dividing this angle by 2π. As described above, the number of rotations of the bearing can be obtained by X-ray analysis.

Next, the measurement principle of the X-ray analysis performed in the above-mentioned X-ray analysis process S1a will be described with reference to FIG. 6 (see Non-Patent Document 6). When an X-ray having a certain wavelength is incident on a substance at a certain angle, the incident X-ray is diffracted at a specific angle depending on the substance, as shown in FIG. 6 (A). The angle and intensity of this diffracted X-ray depends on the type of atom in the substance and its composition. Therefore, the state (phase) of a substance can be identified by injecting X-rays into the substance and measuring the angle and intensity of the reflected X-rays. The X-ray analysis in this embodiment utilizes this X-ray diffraction, and is originally an analysis for identifying the state (phase) of the crystal. The interaction between the diffraction angle and the substance is expressed by Bragg's equation (λ is the wavelength of the incident X-ray and n is an integer). Bragg reflection conditional expression: 2d · sin θ = nλ The spacing d of the lattice planes is included in this equation. If compressive or tensile stress is applied, the interplanar spacing in the material will change slightly. The measurement of this change in surface spacing is the measurement of residual stress by X-ray analysis. On the other hand, the half price range indicates the variation in the surface spacing. The hardened material is rapidly transformed and the lattice planes are not aligned. Therefore, the variation in the surface spacing is large. When fatigue such as rolling is received, the lattice is shaken, so that the original surface spacing of iron before quenching is relaxed, and as a result, the half-value range of the X-ray analysis value becomes smaller.

Note that FIG. 7 shows an example of various radial bearings to be estimated by the usage condition estimation method of this embodiment, and FIG. 8 shows an example of a thrust bearing to be estimated by the usage condition estimation method of the embodiment.

S1: X-ray analysis / rolling element load estimation process S2: Load distribution estimation process S3: Radial load. Axial load estimation process S4: Rotation speed estimation process