Experimental Analysis of Residual Stress and Bending Strength of Gear Tooth Surface after Shot Peening Treatment

The fatigue strength of a gear tooth surface is aﬀected by various factors, which subsequently impacts the transmission performance of gears. Usually, shot peening treatment is carried out during processing to improve the performance of gears. Most current studies focus on theoretical descriptions and simulation analyses of shot peening treatment. However, in this paper, the relationships among shot peening treatment, residual stress, and bending fatigue strength of a gear tooth surface are discussed, through experimental methods. Based on X-ray stress analysis, at select locations on the test samples, the residual stresses on gear tooth surfaces with and without shot peening treatment are determined and contrasted. The results show that shot peening treatment can eﬀectively increase the residual stress on gear tooth surfaces. In addition, an electromagnetic resonance fatigue tester is used to analyze the bending fatigue strength of gear tooth surfaces. The test results indicate that the bending fatigue strength of the gear teeth with shot peening is higher than that of the gear teeth without shot peening. The obtained conclusions lay the foundation for further practical engineering applications of gears.


Introduction
Residual stresses in the parts are caused by various kinds of elastic and plastic deformation in the machining process [1]. e formation of residual stress is related to the material, shape, forming, and processing technology of a part, and residual stresses usually cannot be directly determined through formulas or empirical evidence. Residual stress greatly influences the fatigue strength, stress corrosion, and shape accuracy of the parts. In recent years, many scholars have used different principles and methods to conduct studies pertaining to residual stress, including the measurement and calculation of residual stress, analyses of residual stresses in key parts during service, and analyses of residual stresses in new materials and new technology [2][3][4][5][6][7][8][9][10][11][12].
Gear transmissions are an important part of the modern industry. Related research has gradually focused on producing high-speed, heavy-duty, long-life, and low-cost gear transmissions. Shot peening treatment is usually used in gear processing to provide improved fatigue strength. At present, there are in-depth studies on shot peening strengthening that review the development of traditional shot peening machines and discuss new shot peening methods, such as laser impact technology and ultrasonic impact technology [13][14][15][16][17]. Scholars have found that shot peening treatment can improve material performance because of the residual compressive stress distributed on the part surface. However, the relationship between shot peening and residual stress and the relationship between residual stress and gear performance have gradually become the research focus in recent years.
Due to the limitations in experimental conditions, most studies on the relationship between shot peening and residual stress have been made based on finite element simulation analysis or residual stress measurement with mechanical methods. For studies on gear strength, summarized conclusions have been obtained, but there is little specific experimental data to analyze.
In this paper, gears are subjected to shot peening treatments, wherein the shot peening variables are controlled during processing; other gears from the same batch are not subjected to shot peening and are used as a comparison. Furthermore, experimental studies based on an X-ray stress analyzer and an electromagnetic resonance fatigue tester is proposed. e results from these studies are utilized to determine the relationships among shot peening strengthening, residual stress, and bending strength of gears.

Residual Stress Comparison Test
e gear material used in this experiment was 20CrMnMo, which has good comprehensive mechanical properties. e basic design parameters of the gears are shown in Table 1.
Fifty gears from the same batch were randomly selected and divided into groups A and B. For group A, shot peening treatment was performed on the tooth root after processing, whereas group B was not subjected to a shot peening treatment. Table 2 shows the parameters and the standard used in the shot peening process.
After performing the shot peening procedure, measurements were carried out using a Proto-iXRD type X-ray stress analyzer. ree gears were randomly selected from group A and group B. Locations T 1 , T 2 , and T 3 were also determined along the outer circle of the gear, wherein these locations are separated by 120°. Morever, two test points were selected for each position. e stress analysis site is shown in Figure 1.

Residual Stress Test.
e detected residual stresses on the gear surface for group A and group B are displayed in Table 3. e absolute value of the maximum stress difference between test point 1 and test point 2 was 41 MPa. Obviously, the residual stress was higher on the shot peened gear surface with shot peening treatment than on the gear surface without shot peening treatment. e increases in residual stress varied because of the randomness of the residual stress distribution. To evaluate the overall improvement level, we used the average residual stress as a comparison. e average stresses of group A and group B were −585.833 MPa and −513.278 MPa, respectively. Compared with group B, group A had 14% higher residual strength. us, shot peening treatment can effectively increase the residual stress in gear teeth.

Analysis of the Bending Strength of Shot Peened Gear Teeth
Usually, a gear tooth can be simplified as a cantilever beam under the working condition. Given the normal load on gear teeth, bending stresses will occur on the root of the teeth; as a result, cracks often appear due to the serious stress concentrations. With continuous crack propagation, whole teeth or parts of teeth may fracture [18]. In this section, an analysis of shot peening treatment on the bending strength of gear teeth is discussed by means of experimental comparisons.

Experimental Scheme.
is experiment adopted a highfrequency pulsation gear test, wherein the tested gear is always in a state of rest within the testing apparatus. Moreover, the pressure head applied a pulsating cyclic load on the tested gear teeth to allow the gear teeth to break off. e test equipment used for this test was a Zwick/Amsler 250 HFP 5100 electromagnetic resonance fatigue testing machine (Germany), as shown in Figure 2. e testing machine possessed a high loading precision: the static-dynamic loading was ±0.5%, the static loading range was ±150 kN, and the dynamic unidirectional pulsation was ±125 kN. e loading frequency range was 35-300 Hz.
According to GB/T 14230-1993 [19], the following can be determined through calculations and simulations with the tested gear parameters while the gear was clamped. e test was performed on five teeth of the tested gears. e distance between the high point of action and the low point of action was 68.523788 mm, which was the same as the length of the common normal line spanning 5 teeth. e dimensional error during installation was controlled within ±0.1 mm.   is test adopted group and staircase methods. e test load can also be divided into four load levels. e group method was used to determine the diagonal part of the P-S-N curve, and the staircase method was used to determine the straight line in the curve. e test load was set in accordance with GB/T14230-1993. e number of bending stress cycles of each test point at the highest stress level was ≥0.5 × 10 5 . Random sampling in all products can reflect the general features. e test aimed to fully utilize each gear tooth and minimize the mutual effect of loading gear teeth. Two gear teeth separated every two tested gear teeth, and each loaded gear tooth was numbered accordingly. e tested gears can be divided into two categories under three kinds of numbering, which adhered to the following principles: (1) In this test, a gear with shot peening treatment was an A series and a gear without shot peening treatment was defined as a B series. (2) According to the test order of the same gear series, the tested gear teeth were numbered as 1, 2, 3, etc. (3) e test load level was labeled.
Shock and Vibration 3 For example, B1-1-78 kN means testing the first tooth of the No. 1 gear without shot peening treatment with a load of 78 kN. e tested gear teeth were in a certain order of test. e high working teeth were numbered 1, 2, 3, and 4, whereas the corresponding low working teeth were numbered 1′, 2′, 3′, and 4′.      Figure 3. e criteria for stopping the bending fatigue test are as follows.
During the test, if one of the following conditions occurs, then the bending is terminated: (1) Fatigue cracks observed in the tooth root.
(3) e tooth broke along the root. If the gear does not fail within the 3 × 10 6 stress cycle, then the test will also be stopped.

Tooth Root Stress Calculation.
According to the load capacity calculation method for an involute cylindrical gear [20], the equation for tooth root stress calculation is shown as follows: where F t is the nominal tangential force of the pitch circle in the end face (N), b is the tooth width, m is the tooth modulus, Y FA is the tooth profile coefficient of the action point of the gear teeth under load, Y SA is the stress correction coefficient of the action point of the gear teeth under load, Y ST is the stress correction coefficient of the tested gear, Y δrelT is the relative sensitivity coefficient of the root fillet, Y RrelT is the relative condition coefficient of the root surface, and Y x is the bending strength calculation dimension coefficient. Table 4 shows the parameters settings for the calculation of the root stress in this test.
Substituting the parameter values into the equation above indicated that the relationship of root stress and load is as follows: Due to the limitations in the test equipment, the loading pressure head created instability in the clamp and the test piece.
erefore, to avoid this instability effect, a certain minimum load, which is the cyclic performance coefficient R � F min /F max , is maintained in the test. e actual root stress should be converted to the pulsating cycle root stress σ F when R � 0. e conversion equation is as follows: where σ b is the tensile strength (N/mm 2 ).

Test with Group Method and Data Processing.
rough the gear root stress calculations and the preliminary experiments, the experimental load with the group method was determined, as shown in Table 5.
e results of the test with the group method are shown in Table 6.
Lognormal distribution and three-parameter Weibull distribution tests were performed on the fatigue life at the load levels above.

Shock and Vibration
Weibull distribution is derived from the weakest link model. It can be simply described that a chain is formed by many chain links in series. When both ends are under tension, any one of the links breaks and the chain fails. Obviously, the chain fracture occurs in the weakest link. e life of components, parts, devices, and equipment stopping whole running due to a certain local failure can be regarded as following the Weibull distribution, while the fatigue strength, fatigue life, and wear life in machinery mostly follow the Weibull distribution. e probability density function and distribution function of three-parameter Weibull distribution are defined as    where β, c, and η are three parameters for describing Weibull distribution, β is a shape parameter, which determines the shape of the distribution curve, c is a position parameter and it determines the starting position of the distribution curve, and η is a scale parameter, which reflects the dispersion of the life data. e correlation coefficients (R) were calculated, and the results are shown in Table 7.
e three-parameter Weibull distribution exhibited the best fitting effect on the bending fatigue life of the gear. us, the three-parameter Weibull distribution calculation in each stress level is shown in Table 8. e position parameter r showed that the lifetime of the gear without shot peening treatment followed the three-parameter Weibull distribution at stress levels I, II, and IV.
is gear also followed the two-parameter Weibull distribution at stress level III.

Test with Staircase Method and Data Processing.
e test loads with the staircase method are shown in Table 9.
e test data with the staircase method are shown in Table 10. Table 10 shows that the test from the 6th testing point through the 18th testing point satisfies the following stability error condition:    e up-and-down test results obtained with the staircase method are shown in Figure 4. e total number of samples was 18, of which 9 broke. e median load of this gear can be obtained as F � 70.5 kN through calculation with the staircase method. e median fatigue strength of the gear is shown as follows: e P-S-N curve of the bending fatigue strength of the gear without shot peening treatment is displayed in Figure 5.
According to the results in the figure above, the ultimate bending strength of the gear without shot peening treatment under different degrees of reliability is shown in Table 11.

Test with Group Method and Data Processing.
e test loads were determined, as shown in Table 12. e results of the test with group method are displayed in Table 13.
Lognormal distribution and three-parameter Weibull distribution tests were also performed on the fatigue life at the load levels above. e R values are shown in Table 14.
e three-parameter Weibull distribution exhibited the best fitting effect on the bending fatigue life of the gear. us, the three-parameter Weibull distribution calculation at each stress level is depicted in Table 15.
e location parameter showed that the bending fatigue life of the shot peened gear followed the two-parameter Weibull distribution at stress levels I, II, and IV and followed the three-parameter Weibull distribution at stress level III.

Test with Staircase Method and Data Processing.
rough preliminary tests with the test data collected from the group method, the test loads with the staircase method were obtained, as shown in Table 16. e results of the test with the staircase method are also shown in Table 17. Table 17 shows that the staircase test from the 3rd testing point through the 16 th testing point satisfies the stability error σ n ≤ 0.5%. e up-and-down test results with the staircase method are shown in Figure 6. e total number of samples was 16, of which 8 broke.
e median load of this type of gear can be obtained as F � 73.875 kN through calculation with the staircase method. e median fatigue strength of the gear is shown as follows: e P-S-N curve of the gear with shot peening treatment is displayed in Figure 7. Table 18 shows the ultimate bending strength of the gear with shot peening treatment under different degrees of reliability, according to Figure 7.

Results and Discussion.
In accordance with reliability theory, the P-S-N curves of the gears with and without shot peening treatment and the bending fatigue strength of these gears under different reliability degrees can be obtained. e results are summarized in Table 19.
e shot peening treatment increased the bending fatigue strength by 14.35% at a reliability degree of 99%. e residual stress test indicated that the residual compressive stress in the shot peened gear roots (group A) was 14% higher than that of gear roots without shot peening (group B). e mean values of the gear residual compressive stress with and without shot peening were −585.5 MPa and   −513.3 MPa, respectively. e data showed that the residual compressive stress layer distributed at the root of the gear teeth after shot peening treatment can effectively increase the gear tooth bending fatigue strength.
Further study on analysis of the microstructure and surface roughness of gear tooth surface after shot peening treatment will be carried out. And, the influences of different shot peening conditions on microstructure and surface roughness will also be analyzed.

Conclusions
e relationships among shot peening treatment, residual stress, and bending fatigue strength of the gear tooth surface were discussed based on the experimental study in this paper. Based on X-ray stress analysis, the residual stresses on gear tooth surfaces with and without shot peening treatment were determined and contrasted. e average residual stress in group A (shot peening treatment) and group B (without shot peening treatment) were −585.833 MPa and −513.278 MPa, respectively, illustrating that shot peening produced a 14% increase in residual stress.
us, shot peening treatment can effectively improve the residual stress of gear teeth. e bending fatigue strength of the gear tooth surfaces was also analyzed with an electromagnetic resonance fatigue tester. e test results indicated that the bending fatigue strength of the gear teeth with shot peening was higher than that of gear teeth without shot peening; the shot peening treatment increased the bending fatigue strength of the gears by 14.35% at a reliability degree of 99%. erefore, the data showed that the residual compressive stress layer distributed at the root of the gear teeth after shot     peening treatment can effectively increase the gear tooth bending fatigue strength.

Data Availability
All data generated or analyzed during this study are included within this article.

Conflicts of Interest
e authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.