JP2011064644A - Stress analysis method in rolling fatigue - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a stress analysis method for rolling fatigue which can obtain stress in the rolling fatigue of a metal base by simulating and obtaining the state of the stress and distortion around a nonmetal inclusion present in the metal base of a mechanical structural component without implementing a rolling fatigue test. <P>SOLUTION: A position of a rolling body B pressed to the metal base A is selected from five or more positions within a range forwardly or backwardly separated from a position immediately above the nonmetal inclusion C by the same length dimension d as a depth dimension d on a surface of the nonmetal inclusion C in the rolling direction of the rolling body C among positions at which the rolling body B rolls on a surface of the metal base A. Stress analysis is implemented in two or more cycles as the repetitive rolling times of the rolling body B rolling on the surface of the metal base A. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to rolling fatigue performed to estimate a damage state such as delamination due to the influence of non-metallic inclusions existing in a metal base in a metal mechanical structural part such as a rolling bearing such as a ball bearing or a roller bearing. More specifically, the stress analysis method can be estimated by calculating the stress and strain states of the metal substrate around the non-metallic inclusions by using the finite element method. The present invention relates to a stress analysis method in rolling fatigue.

  The life of metal mechanical structural parts such as rolling bearings originates from non-metallic inclusions such as oxide inclusions, sulfide inclusions, and nitride inclusions in the metal material due to rolling fatigue. Is often determined by the flaking (peeling) that occurs. However, there are many unclear points about the mechanism by which peeling occurs from these nonmetallic inclusions, and there is no clear guideline for improving the service life of bearings and the like. Therefore, in order to elucidate the mechanism by which fatigue cracks occur from non-metallic inclusions and the mechanism by which the cracks propagate, it is important to calculate the damage to the matrix of the metallic substrate surrounding the non-metallic inclusions. . By carrying out the simulation by the calculation, it is assumed that it can be utilized for the development of a long-life bearing and the development of a small and lightweight bearing by accurate life prediction.

  Conventionally, in order to analyze the phenomenon of rolling fatigue, the stress calculation of the matrix of the metallic substrate around the non-metallic inclusion has been carried out using the finite element method (FEM), but the elastic deformation Within the range, the stress calculation when the rolling element is pressed against a certain location on the surface of the metal substrate is performed, or even if the plastic deformation is taken into consideration, the metal substrate containing the non-metallic inclusions Only the stress, elastic strain, and plastic strain generated when the rolling element was moved while being pressed onto the surface were calculated. In these methods, it has not been possible to accurately simulate a phenomenon in which a rolling element repeatedly rolls on the surface of a metal substrate, such as rolling fatigue, and strain (internal damage) accumulates.

  As a method of performing stress calculation of a metal substrate around non-metallic inclusions using a finite element method (FEM), for example, there were actually methods described in Non-Patent Document 1 and Non-Patent Document 2, Non-Patent Document 1 only describes calculating elastic deformation when the rolling element moves only once, and Non-Patent Document 2 takes the yield stress of the material into account. Although it is described that the composition deformation is calculated, neither Non-Patent Document 1 nor Non-Patent Document 2 describes calculating the strain accumulation due to repeated loading, nor does it suggest it. .

Koshiro Yamakawa, 3 others, “Influence of internal defects on the stress field under rolling contact”, Koyo Engineering Journal, 2004, No. 166, p. 24-28 Takefumi Fujimatsu, 3 others, “Stress analysis around non-metallic inclusions under rolling surface”, Sanyo Technical Report, 2006, Vol. 13, no. 1, p. 62-65

  The present invention has been made in view of the above-described conventional situation, and shows the state of stress and strain of the metal base around the non-metallic inclusions inherent in the metal base in a metal mechanical structural part such as a rolling bearing. Therefore, it is possible to provide a stress analysis method in rolling fatigue that can be obtained easily by calculating the stress in the rolling fatigue of a metal base without actually performing the rolling fatigue test by calculating by computer simulation. It is to be an issue.

  The invention according to claim 1 is a non-mechanical structural part comprising: a metal base having non-metallic inclusions inside; and a rolling element that rolls while being pressed against the surface of the metal base with a constant pressing load. A stress analysis method in rolling fatigue for analyzing stress in rolling fatigue of the metal substrate by calculating stress and strain states of the metal substrate around the metal inclusions, the metal substrate Information on the shape of the rolling element, Young's modulus, and stress-strain characteristics, the shape of the non-metallic inclusion, the Young's modulus, and the depth from the surface of the metallic substrate where the surface of the non-metallic inclusion is located. The first step to be input, the second step to divide the elements based on each information, the pressing position and the pressing load of the rolling element to the metal substrate, the surface of the metal substrate The third step of inputting information related to the number of repeated rolling of the rolling element that rolls back, and the stress and strain of the metal base around the non-metallic inclusions under load are limited for each pressing position by the rolling element. Fourth step of calculating elastoplasticity using the finite element method while calculating elastoplasticity using the element method and stress and strain of the metal substrate around the nonmetallic inclusions when the rolling elements are unloaded. And the above calculation result is output to determine the stress and strain state of the metal base around the non-metallic inclusions, and the pressing position of the rolling element to the metal base is: From the position of the range where the rolling element rolls on the surface of the metal substrate, from the surface of the metal substrate just above the nonmetal inclusion, from the surface of the metal substrate where the surface of the nonmetal inclusion is located Only the same length as the depth The rolling element is set to five or more positions located within a range separated in the front-rear direction of the rolling direction of the rolling element, and the calculation in the fourth step is performed on the rolling element whose rolling element rolls on the surface of the metal base. It is a stress analysis method in rolling fatigue characterized by repeating two or more cycles based on the number of repeated rolling.

  According to the second aspect of the present invention, in the fifth step, the stress and strain states of the metal substrate around the non-metallic inclusions obtained by outputting the calculation result are obtained by changing the shear strain variation range and direction, and / or The stress analysis method in rolling fatigue according to claim 1, which is a fluctuation range and direction of tensile strain.

  According to the third aspect of the present invention, from the fluctuation range and direction of the shear strain around the nonmetallic inclusion obtained in the fifth step and / or the fluctuation range and direction of the tensile strain, The stress analysis method in rolling fatigue according to claim 2, wherein the generation direction is predicted.

  According to the stress analysis method in rolling fatigue according to the present invention, the state of stress and strain of the metal base around the non-metallic inclusions existing in the metal base in the metal mechanical structural part such as a rolling bearing is calculated by the computer. Therefore, the stress in the rolling fatigue of the metal substrate can be easily obtained without actually performing the rolling fatigue test.

It is a flowchart which shows the stress simulation by the stress analysis method in the rolling fatigue which concerns on one Embodiment of this invention. It is a perspective view which shows the outline | summary of metal mechanical structure components. It is the longitudinal cross-sectional view of the metal base | substrate which shows the actual crack generation | occurrence | production state, a lower left is the principal part expanded vertical sectional view of the position of the left side of a nonmetallic inclusion, and the lower right is a principal part of the position of the right side of a nonmetallic inclusion It is an enlarged vertical sectional view. It is a longitudinal cross-sectional view for demonstrating the relationship between the depth position of the nonmetallic inclusion which exists in a metal base | substrate, and the pressing position to the metal base | substrate surface of a rolling element. It is a two-dimensional model figure which shows the stress simulation model used for the stress analysis method in the rolling fatigue which concerns on one Embodiment of this invention. It is a longitudinal cross-sectional view which illustrates the pressing position to the metal base | substrate surface of the rolling element in an Example. It is a graph which shows the calculation result by the analysis of rolling fatigue which made the frequency | count that a rolling element rolls on the surface of a metal base | substrate 3 cycles. It is a longitudinal cross-sectional view of the metal base | substrate which shows the generation | occurrence | production state of the crack calculated | required by the stress simulation which concerns on this invention.

  The present inventors have actually observed the phenomenon that rolling elements repeatedly roll on the surface of a metal substrate, such as rolling fatigue, and strain (internal damage) accumulates near the surface of the metal substrate. In order to find a method that can be accurately simulated by simulation without conducting a test, intensive research was repeated. As a result, the finite element method (FEM) is used to calculate the stress of the matrix of the metallic substrate around the nonmetallic inclusions that cause the accumulation of strain inherent in the vicinity of the surface of the metallic substrate. As a result, the present invention was completed.

  Hereinafter, the present invention will be described in more detail based on embodiments shown in the accompanying drawings. FIG. 2 is a diagram illustrating an outline of a metal mechanical structural part such as an actual rolling bearing, wherein A is a metal base constituting the metal mechanical structural part such as a rolling bearing, and B is a metal base A thereof. A rolling element that rolls while being pressed against the surface of the metal with a constant pressing load, C is a non-metallic inclusion such as an oxide inclusion, sulfide inclusion, nitride inclusion, etc., existing in the vicinity of the surface of the metal substrate A It is a thing. As shown in FIG. 3, the crack (crack) 1 that causes flaking (peeling) occurs in the matrix of the metallic substrate A starting from the nonmetallic inclusion C.

  FIG. 1 is a flowchart showing a stress simulation by a stress analysis method in rolling fatigue according to an embodiment of the present invention. The stress simulation will be described below in detail from the first step S1 to the fifth step S5. . The numbers of these steps are shown for convenience, and other steps may be inserted between the first step S1 and the fifth step S5, or before and after that.

  First, in the first step S1, the shape, Young's modulus, and stress-strain characteristics of the metallic substrate A and the rolling element B, the shape and Young's modulus of the nonmetallic inclusion C, and the surface of the nonmetallic inclusion C are positioned. Information relating to the depth d (shown in FIG. 4) from the surface of the metallic substrate A to be input is input to the computer.

  As for the depth d from the surface of the metallic substrate A where the surface of the non-metallic inclusion C is located, basically, an arbitrary depth d may be set and input. A crack 1 is formed starting from a non-metallic inclusion C existing at a depth where the shear stress generated inside the metallic base A is the largest due to the contact between the base A and the rolling element B. As a result, flaking (peeling) occurs. ) Occurs in most cases, and by setting the surface depth d of the nonmetallic inclusion C at the maximum shear stress depth position, the phenomenon that determines the rolling fatigue life can be more reliably simulated. it can.

  When the contact between the metal substrate A and the rolling element B is a simple shape contact, the maximum shear stress position dmax is calculated from the analytical solution to obtain the surface depth d of the nonmetallic inclusion C, or 5, the maximum shear stress position dmax is estimated from the shear stress distribution inside the metal substrate A obtained by the finite element method (FEM), and this maximum shear stress position dmax is determined as a non-metallic inclusion C. The surface depth d may be set. If the surface depth d of the non-metallic inclusion C is set too deep, the stress inside the metallic substrate A generated by the contact with the rolling element B becomes too small to estimate the rolling fatigue life. Is useless. In order to estimate the rolling fatigue life, it is desirable that the surface depth d of the nonmetallic inclusion C is 1.5 times or less the maximum shear stress position dmax. Further, when the surface depth d of the non-metallic inclusion C is set at a position shallower than the maximum shear stress position dmax, it is useful for analyzing the rolling fatigue life. And the surface depth d of the nonmetallic inclusion C may be set between 1.5 times the maximum shear stress position dmax.

  In the second step S2, as shown in FIG. 5, the simulation model is simplified as a two-dimensional model, and in the next third step S3, element division (mesh creation) is performed for elastoplastic calculation using the finite element method (FEM). )I do.

  In element division, the finer the mesh, the better the convergence and the higher the calculation accuracy. However, since the time required for the calculation is enormous, the size of the element division mesh is non-metallic. In the vicinity of the interface between the inclusion C and the matrix of the metallic substrate A, the range may be 0.001 μm to 5 μm. In the present invention, a metal substrate A in which nonmetallic inclusions C of about 10 μm to 100 μm are present is the subject of stress simulation. For example, as shown in FIG. In the vicinity of the matrix interface, the size of the element division mesh may be about 1 μm, and in the position away from the non-metallic inclusion C shown in FIG. It is desirable to respond by changing the size of.

  In the next third step S3, a plurality of pressing positions of the rolling element B to the metal substrate A, a pressing load of the rolling element B to the metal substrate A, and a rolling element B that repeatedly rolls the surface of the metal substrate A. Information on the number of repeated rolling is input to the computer as rolling fatigue conditions.

  It is not possible to accurately simulate actual rolling fatigue simply by calculating the surface position of the metallic substrate A directly above the non-metallic inclusion C as the pressing position of the rolling element B against the metallic substrate A. However, when the rolling element B is rolled while being pressed against the surface of the metal base A with a constant pressing load, the rolling element B is in a position where the rolling element B is rolling away from the non-metallic inclusion C by a certain dimension or more. The stress generated when B and the metallic substrate A contact each other does not reach the nonmetallic inclusion C. Accordingly, among the positions in the range where the rolling element B rolls on the surface of the metal base A, the rolling element B has a plurality of positions within the range where the stress generated when the rolling element B and the metal base A are in contact with each other. The pressing position on the metal substrate A is set.

  Specifically, as shown in FIG. 4, the depth from the surface of the metallic substrate A where the surface of the nonmetallic inclusion C is located from the surface position of the metallic substrate A which is directly above the nonmetallic inclusion C. A plurality of pressing positions of the rolling element B against the metal base A may be set within a range separated by the same length d as the dimension d in the front and rear directions in the rolling direction of the rolling element B. The reason is that, as shown in the right enlarged view of FIG. 5, the shear stress generated in the metal base A is increased at a position approximately 45 ° from the pressing position of the rolling element B.

  Further, the pressing position by the rolling element B is 5 or more in the sense that the actual rolling fatigue can be accurately simulated, but the surface position of the metallic substrate A directly above the nonmetallic inclusion C is From the position, the front and rear two points separated by the same length dimension d as the depth dimension d from the surface of the metallic substrate A where the surface of the non-metallic inclusion C is located are separated from each other in the rolling direction of the rolling element B. The position and the intermediate position are desirable in the sense that it is possible to more accurately simulate actual rolling fatigue. The intermediate position may be at least one or more positions that are separated from each other in the rolling direction of the rolling element B, and the pressing position by the rolling element B is about 5 to 25 if the time required for calculation is taken into consideration. It is desirable to do. In FIG. 6, the example which made 9 pressing positions by the rolling element B is shown.

  In the next fourth step S4, first, the stress and strain of the metal base A matrix around the non-metallic inclusion C at the time of load application (pressing load) at the first pressing position by the rolling element B are determined as finite elements. Elasto-plastic calculation using the method. Subsequently, the stress and strain of the matrix of the metallic substrate A around the non-metallic inclusion C when the rolling element B at the initial pressing position by the rolling element B is unloaded are similarly calculated using the finite element method. Elasto-plastic calculation. After completing the calculation at the time of loading and unloading of the first pressing position by the rolling element B, the process proceeds to the next pressing position set in the third step S3, and the load at the next pressing position is reached. Evaluate elastoplasticity during loading and elastoplasticity during unloading. Further, the process proceeds to the next pressing position, and the elasto-plastic calculation at the time of load application and the elasto-plastic calculation at the time of unloading are performed, and these calculations are sequentially performed up to the final pressing position. Note that the constitutive equations used for the elastoplastic calculation are not particularly limited. For example, the constitutive equation of Brandle-Reuss can be used for the elastoplastic calculation.

  In the above elastoplastic calculation, the amount of deformation of the matrix of the metallic substrate A around the nonmetallic inclusion C when the rolling element B passes the surface of the metallic substrate A for the first time is particularly large, and the second or more times. Therefore, the amount of deformation is stabilized (illustrated in FIG. 7). Therefore, the elastoplastic calculation in the fourth step S4 is performed on the rolling element B that repeatedly rolls while being pressed against the surface of the metal base A with a constant pressing load. It is necessary to perform two or more cycles according to the number of repeated rolling.

  Finally, as the calculation result in the fifth step S5, necessary information about the stress and strain state of the matrix of the metallic substrate A around the nonmetallic inclusion C is output. In analyzing rolling fatigue, strain information by elasto-plastic calculation is useful. For example, the variation range and direction of shear strain, the variation range and direction of tensile strain are output, and the crack 1 that maximizes the variation is output. It can be used as an index for predicting the occurrence position and the crack generation direction.

  Further, the flaking (peeling) generated from the nonmetallic inclusion C as a starting point depends on whether the nonmetallic inclusion C and the matrix of the surrounding metallic substrate A are bonded or separated (stress). Distribution) changes greatly. Therefore, in order to accurately simulate the actual rolling fatigue phenomenon by simulation, it is effective to incorporate the adhesion state at the interface between the matrix of the nonmetallic inclusion C and the surrounding metallic substrate A in the calculation. For example, the simulation can be performed in a state closer to the actual state by calculating not only a state where the interface is completely adhered but also a state where a part or all of the interface is peeled off.

  The result of this stress simulation can be utilized for the analysis of the generation position and direction of the crack 1 and the analysis of the life until the crack 1 occurs. As a stress parameter at that time, equivalent stress, shear stress (mode II), tensile stress (mode I), or the like can be selected.

  EXAMPLES Hereinafter, the present invention will be described more specifically with reference to examples. However, the present invention is not limited by the following examples, and the present invention is implemented with appropriate modifications within a range that can meet the gist of the present invention. These are all included in the technical scope of the present invention.

  In order to examine the validity of the present invention, stress analysis in rolling fatigue was performed by elastoplastic finite element analysis (solver is ABAQUS 6.5). An outline of the stress simulation model used for this analysis is shown in FIG. This stress simulation model is simplified as a two-dimensional model so that the influence of various inclusion forms can be analyzed, a circular model (φ9.6 mm) simulating the rolling element B, and a metal substrate (bearing steel) A is simulated. The strain when pressed against the plate model by displacement control was confirmed by analysis. In addition, the size of the element division mesh of the matrix of the nonmetallic inclusion C existing in the metallic substrate A and the surrounding metallic substrate A is 1 μm, which is farthest from the nonmetallic inclusion C shown in FIG. In consideration of the speed of calculation, the mesh size is set to 1 mm at the position, and the mesh size is sequentially changed between them.

Further, the material of the plate model simulating the metal base A was an elastic perfect plastic body having a yield stress of 1960 MPa. In this plate model, an elastic body model simulating the nonmetallic inclusion C made of Al ₂ O _{3 is included} , and the surface of the elastic body model of the nonmetallic inclusion C is made a circular model simulating the rolling element B. The maximum shear stress position dmax when pressed was set. The elastic modulus of the elastic body model simulating this non-metallic inclusion C was 400 GPa.

  In the present embodiment, the analysis was performed by simulating the rolling behavior of the rolling element B while being pressed against the surface of the metal base A with a constant pressing load. However, considering the convergence of the analysis and the calculation time, As shown in FIG. 6, the pressing position of the rolling element B is limited to nine locations. (1) Load load → Unload → Move → (2) Load load →... (9) Load load → Unload (in FIG. ○ The analysis was repeated in the order of: The results obtained by setting the number of times the rolling element B rolls on the surface of the metal substrate A as 3 cycles are summarized in the graph of FIG.

  In this analysis, the shape of the elastic body model of the non-metallic inclusion C is a square, and the calculation results of the strain at the positions corresponding to the top and bottom vertices (element a and element b shown in FIG. 7) are summarized in a graph. From this graph, the strain in the first cycle is larger than the strain in the second cycle and thereafter in both the elements a and b, and in order to simulate the fatigue phenomenon due to repeated loading, the strain after the second cycle where the strain is stabilized is evaluated. It turns out that is reasonable.

  Further, in order to consider the occurrence of crack 1 in rolling fatigue, the shape of the elastic body model of the nonmetallic inclusion C is a square (15 × 15 μm, longitudinal elastic modulus: 400 GPa) with the apexes positioned vertically and horizontally. FIG. 8 shows the analysis result when the maximum surface pressure is −4500 MPa. Assuming that crack 1 occurs due to mode I deformation due to tensile stress, the change in tensile component strain (Δε) of an arbitrary vector was obtained from the analysis result. FIG. 8 shows the vector direction in which Δε is maximized (double-directional arrow) and the value of Δε (Δεmax). Further, in FIG. 8, the direction of the crack 1 estimated based on this assumption is indicated by a dotted line. From FIG. 8, it is estimated that the direction of the crack 1 progresses in an obliquely upper right direction or an obliquely lower left direction from any part.

On the other hand, in order to prove that this stress simulation result is correct, a rolling fatigue test was actually performed. FIG. 3 shows the result of observing the crack 1 by cutting the metal substrate (bearing steel) A during the test. According to FIG. 3 which is a diagram of an actual cross-sectional photograph, the crack 1 has progressed from the non-metallic inclusion (Al ₂ O ₃ ) C in the matrix of the metallic substrate A in the upper right direction or the lower left direction. This result agrees with the analysis result by the stress simulation of the present invention shown in FIG.

  In addition, stress simulation is performed by sequentially changing the number of positions of the pressing load by the rolling element B (the number of pressing positions) and the number of times the rolling element B rolls the surface of the metal substrate A (number of cycles). Table 1 shows the correspondence between the calculation time required for the above and the observation result of actual crack 1 generation.

  The calculation time was shown as ◎ when it was less than 8 hours, ◯ when it was between 8 hours and less than 24 hours, and × when it took more than 24 hours. Correspondence with the observation result of the actually generated crack 1 (coincidence with the observation result) indicates that the position where the calculated strain change (Δε) is high and the observation result of the actual crack 1 match, If they do not match, they are indicated as x.

  The number of positions of pressing load by the rolling elements B (the number of pressing positions) and the number of times the rolling elements B roll on the surface of the metal substrate A (number of cycles) satisfy the requirements of the present invention. 1 and No. The result of 2 was that the calculation time required for the stress simulation and the corresponding situation with the observation result of actual crack 1 generation were both o or better and passed. In particular, the number of times (the number of cycles) the rolling element B rolls on the surface of the metal substrate A is 5 cycles. In 2, the time required for calculation was particularly short and excellent.

  On the other hand, the number of times (number of cycles) the rolling element B rolls on the surface of the metal base A was only 1 cycle. 3 and no. For No. 4, the stress simulation did not correspond to the actual observation result. This is presumably because, when the rolling element B rolls the surface of the metal substrate A (the number of cycles) is only one cycle, the strain is not stable to simulate the fatigue phenomenon.

  In addition, when the rolling element B rolls the surface of the metal base A (number of cycles), No. No. 5 required 24 hours (one day) or more for calculation, and was not suitable for performing a stress simulation.

A ... Metal substrate B ... Rolling element C ... Non-metallic inclusion 1 ... Crack S1 ... First step S2 ... Second step S3 ... Third step S4 ... Fourth step S5 ... Fifth step

Claims (3)

A metal base around the non-metallic inclusions in a mechanical structural part comprising a metallic base with non-metallic inclusions inside and a rolling element that rolls while being pressed against the surface of the metallic base with a constant pressing load. A stress analysis method in rolling fatigue for analyzing stress in rolling fatigue of the metal substrate by calculating the stress and strain state of the substrate,
The shape, Young's modulus, and stress-strain characteristics of the metallic substrate and rolling element, the shape and Young's modulus of the nonmetallic inclusion, and the depth from the surface of the metallic substrate where the surface of the nonmetallic inclusion is located. A first step of entering information about the length;
A second step of performing element division based on each piece of information;
A third step of inputting information relating to a position and a pressing load of the rolling element to the metal base, and the number of repeated rolling of the rolling element that repeatedly rolls on the surface of the metal base;
For each pressing position by the rolling element, the stress and strain of the metal base around the non-metallic inclusion at the time of loading are calculated elasto-plastically using a finite element method, and the rolling element is unloaded. A fourth step of elastoplastic calculation of the stress and strain of the metallic substrate surrounding the non-metallic inclusions using a finite element method;
The fifth step is to output the above calculation result and obtain the stress and strain state of the metal base around the non-metallic inclusion,
The pressing position of the rolling element to the metal substrate is determined from the position of the metal substrate surface immediately above the non-metallic inclusions in the range where the rolling element rolls on the surface of the metal substrate. And at least five positions located within a range separated by the same length as the depth from the surface of the metallic substrate on which the surface of the non-metallic inclusion is located ,
The stress analysis method in rolling fatigue characterized in that the calculation in the fourth step is repeated two or more cycles based on the number of repeated rolling of the rolling element on which the rolling element rolls on the surface of the metal substrate.   In the fifth step, the state of stress and strain of the metallic substrate around the non-metallic inclusions obtained by outputting the calculation result is the variation range and direction of the shear strain and / or the variation range and direction of the tensile strain. The stress analysis method in rolling fatigue according to claim 1.   The crack generation position and crack generation direction are predicted from the fluctuation range and direction of the shear strain around the nonmetallic inclusion determined in the fifth step and / or the fluctuation range and direction of the tensile strain. The stress analysis method in rolling fatigue as described.

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