JP5020146B2 - Compressive residual stress evaluation method and gear design method for gears - Google Patents

Description

  The present invention relates to a compression residual stress evaluation method for a gear that evaluates the compression residual stress with respect to the fatigue strength of a shot peened gear after heat treatment, and a gear design method using the compression residual stress evaluation method.

  Conventionally, in order to improve the bending fatigue strength in the tooth root portion of the gear, shot peening is performed and compressive residual stress is applied to the tooth root portion (see, for example, Patent Documents 1 and 2). Patent Document 3 discloses a technique for subjecting a carburized and quenched steel part to shot peening and obtaining an optimum peening strength from an area surrounded by a compressive residual stress distribution curve based on a compressive residual stress in the depth direction of the steel part. Is disclosed.

JP-A-6-145785 JP 2002-166366 A JP 2006-110634 A

  By the way, before the tooth root part of the gear is broken due to fatigue, a first stage in which an initial crack is generated on the outermost surface of the tooth root part, a second stage in which the crack propagates in the depth direction, and a crack is rapid. There is a third stage to progress to. The compressive residual stress has an effect of suppressing the occurrence of the initial crack (acts as a resistance force against the opening) and an effect of preventing the crack propagation after the initial crack is generated. Considering the mechanism of root bending fatigue, the initial crack is first generated on the outermost surface of the tooth root, so the compressive residual stress on the outermost surface of the tooth root is the most important. No progress). In other words, when focusing on the containment of the initial crack, the compressive residual stress near the tooth root surface is dominant to the root bending fatigue strength, and the effect of the compressive residual stress is relatively reduced as it goes inside. It is thought that it will do.

  However, in the technique according to Patent Document 3, the area of the compressive residual stress distribution is simply obtained on the assumption that the effect of the compressive residual stress is equivalent from the surface to the inside, and the obtained area is calculated as the compressive residual stress relative to the fatigue strength. It is an evaluation parameter. Since this evaluation parameter does not accurately reflect the relationship between fatigue strength and compressive residual stress, it is impossible to accurately evaluate how effective the compressive residual stress is with respect to fatigue strength. There is a point. When a gear is designed using the evaluation parameter, there is a problem that a gear having a desired quality cannot be obtained.

  The present invention has been made to solve such problems, and it is possible to accurately evaluate how effective the compressive residual stress is with respect to the fatigue strength of the gear. An object of the present invention is to provide a gear design method capable of obtaining a gear having a desired quality by using the compression residual stress evaluation method.

In order to achieve the above object, a method for evaluating the compressive residual stress of a gear according to the first invention comprises:
In the compression residual stress evaluation method for gears, which evaluates the compression residual stress of gears shot-peened after heat treatment,
Obtaining a compressive residual stress distribution curve based on a measured value of compressive residual stress in the depth direction from the tooth root surface of the gear;
The evaluation target depth is divided into a plurality of closed sections from the root surface to a predetermined depth, and the weight applied to the compressive residual stress in each closed section is a close section close to the root section surface. Determining a weight in each closed section so that the one has a larger value;
A sum of values obtained by multiplying the integral value in each closed section of the compressive residual stress distribution curve by the weight determined for each closed section is a total value in the fully closed section, and the total value is a compression residual stress of the gear. And a step of calculating as an evaluation parameter to be evaluated.

Next, the gear design method according to the second invention is:
A gear design method using the compression residual stress evaluation method for a gear according to the first invention,
The evaluation parameter is calculated for each of a plurality of gears having different combinations of heat treatment conditions and shot peening conditions, and the calculated evaluation parameters are divided by the evaluation target depth to obtain an average value of the compressive residual stress for each gear. The desired process;
Obtaining a root bending fatigue strength for each of the plurality of gears;
A step of calculating an average value of the compressive residual stress corresponding to the requested root bending fatigue strength as an average value of the required compressive residual stress based on the relationship between the average value of the compressive residual stress and the root bending fatigue strength. When,
A gear having an average value of compressive residual stress greater than the average value of the required compressive residual stress is selected from the plurality of gears, and the gear is designed based on a combination of heat treatment conditions and shot peening conditions of the selected gear. And a step of determining a combination of the above heat treatment condition and shot peening condition.

  In the gear compressive residual stress evaluation method according to the first aspect of the invention, a compressive residual stress distribution curve is obtained based on the measured value of the compressive residual stress in the depth direction from the tooth root surface of the gear. Further, the evaluation target depth is divided into a plurality of closed sections from the tooth root surface to a predetermined depth as an evaluation target depth, and the weight attached to the compressive residual stress in each closed section is a closed section close to the tooth root surface. The weighting in each closed section is determined so that the value becomes larger. Then, an evaluation parameter for evaluating the compressive residual stress of the gear is obtained by summing a value obtained by multiplying the integral value in each closed section of the compressive residual stress distribution curve by the weight determined for each closed section. The evaluation parameters thus obtained are based on the fact that the compressive residual stress near the root surface is dominant to the root flexural fatigue strength, and that the effect of compressive residual stress decreases relatively as it goes inward. It accurately reflects the relationship between fatigue strength and compressive residual stress effect. Therefore, it is possible to accurately evaluate how effective the compressive residual stress is with respect to the fatigue strength of the gear.

  In the gear design method of the second invention, the heat treatment conditions and the shot peening conditions are calculated based on the evaluation parameters of the first invention that accurately evaluate how effective the compressive residual stress is with respect to the fatigue strength of the gear. An average value of compressive residual stress for each of a plurality of gears with different combinations is obtained, and a root bending fatigue strength is obtained for each of the plurality of gears. Based on the relationship between the average value of compressive residual stress and the root bending fatigue strength, the average value of compressive residual stress corresponding to the requested root bending fatigue strength is calculated as the average value of the required compressive residual stress. . A gear having an average value of compressive residual stress larger than the average value of necessary compressive residual stress is selected from the plurality of gears, and the gear design is based on a combination of the heat treatment condition and shot peening condition of the selected gear. A combination of the above heat treatment conditions and shot peening conditions is determined. Thereby, the gear of desired quality can be obtained.

  Next, specific embodiments of a method for evaluating compressive residual stress and a method for designing a gear according to the present invention will be described with reference to the drawings. In the drawings used for the following description, the residual stress is represented by-(minus) in the compression direction.

  FIG. 1 is a diagram showing an example of a compressive residual stress distribution in the depth direction of a gear shot peened after heat treatment. FIG. 2 is an explanatory diagram of a method for measuring compressive residual stress by X-ray, and FIG. 3 is an explanatory diagram of a mechanism of fatigue crack growth.

  The compressive residual stress distribution curve CL shown in FIG. 1 is shown in FIG. 2 using, for example, an X-ray residual stress measuring device while removing the surface of the tooth root 1a of the gear 1 subjected to shot peening after heat treatment by electropolishing. As described above, X-rays are irradiated from 10 directions at intervals of 10 ° (parallel tilt method), and the process of measuring the compressive residual stress is repeated a plurality of times, and then these measured values are plotted.

  Until the tooth root portion 1a of the gear 1 is broken by the fatigue crack K shown in FIG. 3A, an initial crack K ′ is formed on the outermost surface of the tooth root portion 1a as shown in FIG. A first stage that occurs, a second stage in which the crack propagates in the depth direction as shown in FIG. 3C, and a third stage in which the crack rapidly progresses as shown in FIG. There is. The compressive residual stress has an effect of suppressing the generation of the initial crack K ′ (acts as a resistance force against the opening) and an effect of preventing the crack propagation after the generation of the initial crack K ′. Considering the mechanism of root bending fatigue, the initial crack K ′ is first generated on the outermost surface of the tooth root portion 1a, and therefore, the compressive residual stress on the outermost surface of the tooth root portion 1a is the most important (cracking stress). If there is no occurrence, there will be no crack growth). That is, when focusing on the containment of the initial crack K ′, the compressive residual stress in the vicinity of the surface of the tooth root portion 1a is dominant to the tooth root bending fatigue strength. This effect is expected to decrease.

Therefore, based on the mechanism of fatigue crack growth shown in FIGS. 3B to 3D, the evaluation object is defined as the evaluation object depth D from the surface of the tooth root part 1a to the predetermined depth as shown in FIG. The depth D is divided into three closed sections, a first closed section D ₁ , a second closed section D _2, and a third closed section D ₃ . Furthermore, the maximum weight W ₁ is assigned to the compressive residual stress in the first closed section D ₁ that has the greatest influence on the root bending fatigue strength, and the influence on the root bending fatigue strength is the first closed section D _1. given the small weight W ₂ than the weight W ₁ of the first closed interval D ₁ for the lower second closed interval D ₂ of the compressive residual stress than the compressive residual stress, influence of the dedendum bending fatigue strength By applying a weight W ₃ smaller than the weight W _{2 in} the second closed section D _{2 to} the compressive residual stress in the third closed section D ₃ , which is lower than the compressive residual stress in the second closed section D ₂ , Appropriate weighting can be performed from the viewpoint of the effect of compressive residual stress on the root bending fatigue strength.

In the compressive residual stress distribution curve CL shown in FIG. 1, the integrated value in the first closed section D ₁ is S ₁ , the integrated value in the second closed section D ₂ is S ₂ , and the integrated value in the third closed section D ₃ is S. _If it is ₃ , the evaluation parameter Pa for evaluating the compressive residual stress of the gear 1 is obtained from the following equation (1).

Pa = S ₁ × W ₁ + S ₂ × W ₂ + S ₃ × W ₃ (1)

That is, the weight W determined for each closed section D ₁ , D ₂ , D ₃ in the integral values S ₁ , S ₂ , S ₃ in each closed section D ₁ , D ₂ , D _{3 of} the compressive residual stress distribution curve CL. _The values obtained by multiplying ₁ , W ₂ , and W ₃ are summed to obtain the sum value of the fully closed sections D _{1 to} D ₃ , and the sum value is calculated as the evaluation parameter Pa.
Note that the integral values S _{1 to} S ₃ may be obtained by calculating the area of each closed section in the figure, or by dividing each closed section into a plurality of sections and performing division quadrature.
The evaluation parameter Pa thus determined is that the compressive residual stress in the vicinity of the surface of the tooth root portion 1a is dominant with respect to the tooth root bending fatigue strength, and the effect of the compressive residual stress is relatively reduced as it goes inward. It accurately reflects the relationship between root bending fatigue strength and compressive residual stress.
Therefore, it is possible to accurately evaluate how effective the compressive residual stress is with respect to the fatigue strength of the gear 1 based on the evaluation parameter Pa.

  Next, a gear design method using the evaluation parameter Pa will be described below. FIG. 4 is a diagram showing an example of the relationship between the average value of compressive residual stress and the root bending fatigue strength.

In the gear design method using the evaluation parameter Pa, the evaluation parameter Pa is calculated by the above-described method for each of a plurality of gears having different combinations of heat treatment conditions and shot peening conditions, and each calculated evaluation parameter Pa is evaluated. By dividing by the depth D (see FIG. 1), an average value σ _ave of compressive residual stress for each gear is obtained. Further, for example, a tooth root bending fatigue test is performed on each of the plurality of gears to determine a tooth root bending fatigue strength σ _str of each gear. When the average value σ _ave of the compressive residual stress and the root bending fatigue strength σ _str thus obtained can be approximated by a straight line indicated by a symbol SL in FIG. 4, the required tooth is obtained based on the straight line SL. Original bending fatigue strength σ _str : Average compressive residual stress value σ _ave : -a corresponding to A is calculated as an average value of necessary compressive residual stress. Then, a gear having an average value σ _ave of the required compressive residual stress σ _ave : -a greater than the average value σ _ave of the compressive residual stress is selected from the plurality of gears by comparing the absolute values, and the selected one or more gears The combination of the heat treatment condition and the shot peening condition in the gear design is determined based on the combination of the heat treatment condition and shot peening condition of the gear. According to this gear design method, a desired quality gear having a desired strength can be obtained.

  Next, specific examples of the method for evaluating the compressive residual stress of a gear and the method for designing a gear according to the present invention will be described with reference to the drawings. In addition, this invention is not limited to the Example described below. In the drawings used for the following description, the residual stress is represented by-(minus) in the compression direction.

Example 1
As shown in Table 1, the heat treatment conditions, shot peening conditions, gear modules and the like are different. 1-No. Twelve test gears were prepared.

After repeating the process of measuring the compressive residual stress by the parallel tilt method as shown in FIG. 2 using an X-ray residual stress measuring device for various test gears, plot these measured values. A residual stress distribution curve CL as shown in FIG. 6A was obtained for each of the various test gears. When the crack grows to approximately 60 μm or more, it reaches the final fracture all at once. Therefore, in Example 1, the evaluation target depth D was set to 60 μm from the outermost surface. Further, based on the mechanism of fatigue crack growth shown in FIGS. 3B to 3D, as shown in FIG. 6A, from the tooth surface outermost surface 0 μm to the depth 60 μm, the first closed The section was divided into three closed sections: 0 to 10 μm, second closed section: 10 to 30 μm, and third closed section: 30 to 60 μm. Further, the first closed section: a weight of 0.7 is applied to the compressive residual stress of 0 to 10 μm, the second closed section: a weight of 0.2 is applied to the compressive residual stress of 10 to 30 μm, Third closed section: A weight of 0.1 was applied to the compressive residual stress of 30 to 60 μm. Then, the evaluation parameter Pa is obtained from the above equation (1), and the obtained evaluation parameter Pa is divided by the evaluation target depth D (= 60 μm) as shown in the following equation (2) to obtain the average value σ of the compressive residual stress. _{The ave} was calculated.

σ _ave = Pa / D (2)

The tooth root bending fatigue test shown in FIG. 5 was performed on the various test gears, and the tooth root bending fatigue strength σ _str was determined for each of the various test gears.
The test method of the root bending fatigue test is shown below.
〔Test method〕
(1) As shown in FIG. 5, using a general-purpose servo pulser, the two teeth of the test gear are sandwiched between two upper and lower jigs, and a load is applied repeatedly to break a tooth on one side.
(2) Test load: A strain gauge is attached to the tooth base of the test gear and a load that generates a desired stress is applied.
Here, the root bending fatigue strength σ _str is, for example, 4 × 10 ^6, which is a load that generates a stress in the root portion when the root bending fatigue test shown in FIG. 5 is performed on the test gear. It is defined as the stress value when the tooth does not break even when it is repeatedly applied.

The average value σ _ave of compressive residual stress based on the evaluation parameter Pa is taken on the horizontal axis, and the root bending fatigue strength σ _str is taken on the vertical axis. 1-No. When plotting each of the 12 various test gears, a relationship diagram as shown in FIG. 6B was obtained. As shown in FIG. 6B, the relationship between the root bending fatigue strength σ _str and the average value σ _ave of the compressive residual stress based on the evaluation parameter Pa is as shown by the straight line SL _{1 in} the figure. Can be approximated by a straight line, and both have a strong correlation. Based on the straight line SL ₁ shown in this FIG. 6 (b), the requested dedendum bending fatigue strength sigma _str against compressive residual stress needed to satisfy the dedendum bending fatigue strength ( "necessary compressive residual The average value σ _ave of “stress”) can be easily obtained. A test gear having an average value σ _ave (comparative absolute value) of compressive residual stresses larger than the average value of necessary compressive residual stresses thus determined is selected from various test gears, and the heat treatment conditions for the selected test gears Further, heat treatment conditions and shot peening conditions for obtaining a gear having a desired quality in terms of gear design can be determined from the shot peening conditions.

For example, when the requested root bending fatigue strength is “A”, the average value of the compressive residual stress corresponding to the required root bending fatigue strength: A is “−a” based on the straight line SL _1. This is an average value of the necessary compressive residual stress. The average value of the necessary compressive residual stress: The test gear having an average value (absolute value comparison) of compressive residual stress greater than -a is No. 1 to No. 6 test gears. These No. 1 to No. Among the test gears of No. 6, No. 6 having the smallest absolute value of the average value σ _ave of the compressive residual stress, for example. By determining the heat treatment conditions and shot peening conditions in the gear design based on the heat treatment conditions and shot peening conditions of the test gear of No. 6, a gear having a desired quality can be obtained.

(Example 2)
In Example 2, as shown in FIG. 7A, the evaluation target depth D is set to 70 μm from the outermost surface, and the first closed section: 0 to 20 μm from the uppermost surface of the tooth base part to 70 μm in depth. The second closed section was divided into three closed sections of 20 to 40 μm and the third closed section: 40 to 70 μm. Hereinafter, in the same manner as in Example 1, a relationship diagram between the average value σ _ave of compressive residual stress and the root bending fatigue strength σ _str as shown in FIG. 7B was obtained. As shown in FIG. 7B, the relationship between the root bending fatigue strength σ _str and the average value σ _ave of the compressive residual stress based on the evaluation parameter Pa is as indicated by the straight line SL _{2 in} the figure. Can be approximated by a straight line, and both have a strong correlation. According to the second embodiment, basically the same effect as that of the first embodiment can be obtained.

(Example 3)
In Example 3, as shown in FIG. 8 (a), the evaluation target depth D is 70 μm from the outermost surface, and the first closed section: 0 to 40 μm from the uppermost surface of the tooth root portion to 70 μm in depth. The second closed section: 40 to 60 μm and the third closed section: 60 to 70 μm were divided into three closed sections. Hereinafter, in the same manner as in Example 1, a relationship diagram between the average value σ _ave of compressive residual stress and the root bending fatigue strength σ _str as shown in FIG. 8B was obtained. As shown in FIG. 8B, the relationship between the root bending fatigue strength σ _str and the average value σ _ave of the compressive residual stress based on the evaluation parameter Pa is as shown by the straight line SL _{3 in} the figure. Can be approximated by a straight line, and both have a strong correlation. According to the third embodiment, basically the same effect as that of the first embodiment can be obtained.

(Comparative Example 1)
In Comparative Example 1, as shown in FIG. 9A, the first closed section: 0 to 10 μm, the second closed section from 0 μm to 60 μm in depth, similar to the first embodiment, as in Example 1. Divided into three closed sections of 10 to 30 μm and third closed section: 30 to 60 μm. A weight of 0.33 was uniformly applied to the compressive residual stress in each closed section. Hereinafter, in the same manner as in Example 1, a relationship diagram between the average value σ _ave of compressive residual stress and the root bending fatigue strength σ _str as shown in FIG. 9B was obtained. As shown in FIG. 9B, the relationship between the root bending fatigue strength σ _str and the average value σ _ave of the compressive residual stress based on the evaluation parameter Pa is not a linear relationship, but a correlation is seen. Absent. Therefore, the average value σ _ave of the compressive residual stress necessary for the required root bending fatigue strength σ _str cannot be obtained, and heat treatment conditions and shot peening conditions for obtaining gears of desired quality are determined. I can't.

(Comparative Example 2)
In Comparative Example 2, as shown in FIG. 10 (a), the same as in Example 1, from the top surface of the tooth root part to 0 μm to the depth of 60 μm, the first closed section: 0 to 10 μm, the second closed section: Divided into three closed sections of 10 to 30 μm and third closed section: 30 to 60 μm. The first closed section: a weight of 0.1 is applied to a compressive residual stress of 0 to 10 μm, the second closed section: a weight of 0.2 is applied to a compressive residual stress of 10 to 30 μm, Third closed section: A weight of 0.7 was applied to the compressive residual stress of 30 to 60 μm, and a weight opposite to that in Example 1 was applied. Hereinafter, in the same manner as in Example 1, a relationship diagram between the average value σ _ave of compressive residual stress and the root bending fatigue strength σ _str as shown in FIG. 10B was obtained. As shown in FIG. 10B, the relationship between the root bending fatigue strength σ _str and the average value σ _ave of the compressive residual stress based on the evaluation parameter Pa is not a linear relationship, but a correlation is observed. Absent. Therefore, the average value σ _ave of the compressive residual stress necessary for the required root bending fatigue strength σ _str cannot be obtained, and heat treatment conditions and shot peening conditions for obtaining gears of desired quality are determined. I can't.

  The gear residual compression stress evaluation method and gear design method according to the present invention have been described based on one embodiment and a plurality of examples. However, the present invention is not limited to the configurations described in the above examples. However, the configuration can be changed as appropriate without departing from the spirit of the invention.

Diagram showing an example of compressive residual stress distribution in the depth direction of gears shot-peened after heat treatment Illustration of X-ray compression residual stress measurement method Illustration of fatigue crack growth mechanism Diagram showing an example of the relationship between the average value of compressive residual stress and the root bending fatigue strength Schematic illustration of gear tooth root bending fatigue test Explanatory drawing (a) of the weighting in each closed section in Example 1, and the figure showing the relationship between the average value of compressive residual stress, and tooth root bending fatigue strength (b) Explanatory drawing (a) of the weighting in each closed section in Example 2, and the figure showing the relationship between the average value of compressive residual stress, and tooth root bending fatigue strength (b) Explanatory drawing (a) of weighting in each closed section in Example 3, and the figure showing the relationship between the average value of compressive residual stress, and tooth root bending fatigue strength (b) Explanatory drawing of weighting in each closed section in Comparative Example 1 (a) and a diagram showing the relationship between the average value of compressive residual stress and root bending fatigue strength (b) Explanatory drawing (a) of the weighting in each closed section in the comparative example 2, and the figure showing the relationship between the average value of compressive residual stress, and tooth root bending fatigue strength (b)

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Gear 1a Root part CL Compression residual stress distribution curve D Evaluation object depth D ₁ 1st closed area D ₂ 2nd closed area D ₃ 3rd closed area W ₁ weight (1st closed area)
W ₂ weight (second closed section)
W ₃ weight (third closed section)
S ₁ integral value (first closed section)
S ₂ integral value (between second closed interval)
S ₃ integral value (third closed section)
σ _ave average compressive residual stress σ _str root bending fatigue strength

Claims (2)

In the compression residual stress evaluation method for gears, which evaluates the compression residual stress of gears shot-peened after heat treatment,
Obtaining a compressive residual stress distribution curve based on a measured value of compressive residual stress in the depth direction from the tooth root surface of the gear;
The evaluation target depth is divided into a plurality of closed sections from the root surface to a predetermined depth, and the weight applied to the compressive residual stress in each closed section is a close section close to the root section surface. Determining a weight in each closed section so that the one has a larger value;
A sum of values obtained by multiplying the integral value in each closed section of the compressive residual stress distribution curve by the weight determined for each closed section is a total value in the fully closed section, and the total value is a compression residual stress of the gear. And a step of calculating as an evaluation parameter to be evaluated. A gear design method using the compression residual stress evaluation method for a gear according to claim 1,
The evaluation parameter is calculated for each of a plurality of gears having different combinations of heat treatment conditions and shot peening conditions, and the calculated evaluation parameters are divided by the evaluation target depth to obtain an average value of the compressive residual stress for each gear. The desired process;
Obtaining a root bending fatigue strength for each of the plurality of gears;
A step of calculating an average value of the compressive residual stress corresponding to the requested root bending fatigue strength as an average value of the required compressive residual stress based on the relationship between the average value of the compressive residual stress and the root bending fatigue strength. When,
A gear having an average value of compressive residual stress greater than the average value of the required compressive residual stress is selected from the plurality of gears, and the gear is designed based on a combination of heat treatment conditions and shot peening conditions of the selected gear. And a step of determining a combination of the above heat treatment condition and shot peening condition.

Images