# Tooth Root Bending Fatigue Performance of Shot Peening TM210A Steel Spur Gear

Authors: H. J. Xu; Guang-Qiang Yin; X. Y. Tong; S. L. Lv
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

Tooth root bending fatigue performance is the primary consideration in gear design. To investigate the difference between the tooth root fatigue performances of shot peened and base material, TM210A steel gears and double-tooth pulsating bending fatigue experiment with a stress ratio of 0.05 was carried out on the experimental gears by the group method and the staircase method. The fatigue life of experimental gears with different stress levels and the conditional fatigue limit under 1 × 107 cycles were obtained, and the S-N curves were fitted by the double-weighted least squares method. The tooth root residual stress of the shot peened gear was measured by the X-ray diffraction method, the stress field at the tooth root was calculated by the finite element method, and the fatigue failure mechanism of the shot peened gear tooth root was analyzed. The results show that shot peening can significantly enhance the tooth root bending fatigue life and strength of TM210A steel gear, and the tooth root bending fatigue limit of shot peened gear is about 2.18 times that of base material gear. The residual stress generated by shot peening keeps the fatigue source away from the tooth root surface, and the smaller the external load stress, the farther the fatigue source is from the surface, and the smaller the range where the fatigue source can occur.


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## Body

## 1. Introduction

TM210A is a new type of 18Ni-300 ultrahigh strength maraging steel with high strength and toughness, which is widely used in key devices of aircraft high-lift systems [1]. The gear rotary actuator adopts the principle of planetary gear transmission, which is small and light in weight, and can achieve high torque output in a limited space. It has been used increasingly in aircraft high-lift systems and has become the preferred actuator for high-lift actuation systems [2]. During the working process, gears are subjected to alternating loads, resulting in tooth surface contact and tooth root bending fatigue damage, which are common failure modes, among them, tooth root bending fatigue damage is the main failure mode [3]. The bending fatigue strength of the tooth root directly determines the bending fatigue life of the gear, and it is the key basic data for the realization of antifatigue design and reliability design. However, the rotational bending fatigue limit of 18Ni series maraging steel is much lower than half of its tensile strength [4], which means that the bending fatigue strength limit of TM210A steel gear is not particularly high due to its high strength, which cannot meet the design requirements of modern aircraft such as heavy load, long life, and high reliability. For this reason, in practice, it is often necessary to perform a certain surface treatment on the gear to improve its fatigue performance. Shot peening is an important surface strengthening process, which is widely used because of its low cost and obvious strengthening effect [5–8]. A certain shot peening process can form effective compressive residual stress on the surface of the parts and improve its fatigue performance, which is an important means to improve the fatigue performance of gears [9, 10]. The absence of microcracks, a minor increase in surface roughness, nanograined structure, and induced high compressive residual stress in the shot peened layer were responsible for the mechanism of shot peeing increasing the fatigue performance of the component [11]. Therefore, it is necessary to investigate the tooth root bending fatigue performance of TM210A steel gear and the effect of shot peening on its performance.Gorla et al. [12] investigated the bending fatigue properties of austempered ductile iron gears, to determine the reliable values of the limits, which take into account the influence of the production process, to be applied in the design of gearboxes, . In the study by Albertini et al. [13], two gear materials have been investigated to define a baseline from variations, the effects of a thermal spray tungsten carbide coating, and the pitting resistance on the bending fatigue strength. Concli [14] describes the contact and bending fatigue test procedures adopted and the test results, which have been obtained on austempered ductile iron (ADI) for gear specimens using a single tooth fatigue and pitting tests on an FZG type bench respectively. Rosa et al.’s [15] investigation was focused on two main classes of gear steels adopted in the high power density transmissions, that is, case carburizing and nitriding steels, to experimentally characterize the bending fatigue resistance of high strength and high cleanliness gear steels typically used in the main gearbox of helicopter transmissions . Bonaiti et al. [16] investigated the bending fatigue properties of 17-4PH steel applied to gears produced via selective laser melting.The tooth root bending fatigue experiment was carried out by TM210A steel gear with a double-tooth pulsating loading method. The group method and the staircase method were used to determine the group fatigue life of the tooth root bending of the base material and the shot peened TM210A steel gear under different stress levels and the tooth root bending fatigue limit under the specified life of 1 × 107 cycles, respectively. The weighted least squares method was used to fit the experiment data, and the S-N curve of the base material and shot peened TM210A steel gear was obtained, respectively. X-ray diffraction method was used to measure the residual stress of the tooth root of shot peened TM210A steel gear, combined with finite element analysis, and the tooth root bending fatigue failure mechanism of the shot peened TM210A steel gear was investigative to provide the theoretical basis and technical support for its engineering application and reliability design.


## 2. Experimentation

### 2.1. Materials and Specimens

The chemical composition of the TM210A steel is shown in Table1. After solid solution at 820°C, × 1 h × air cooling (AC) and aging at 510 ± 5°C × 4 h × AC, the mechanical properties at room temperature are shown in Table 2.Table 1
Chemical composition of TM210A steel (wt/%).
CSiMnSPNiCoMoTiAlFe0.00300.090.090.0050.00417.7010.324.300.970.10Bal.Table 2
Mechanical properties of TM210A steel.
Tensile strength (MPa)Yield strength (MPa)Elongation (%)Reduction of area (%)Hardness (HRC)212520659.56055The experimental TM210A steel gear specimen is designed and manufactured by the relevant regulations in GB/T 14230-2021 [17], its basic parameters and schematic illustration of the gear are shown in Table 3 and Figure 1, respectively. The process parameters of shot peening gear specimen are as follows pneumatic shot peening equipment is adopted for shot peening, the shot using cast steel balls is mixed with 50%S070 and 50%S110, and hardness of HRC55～65 under an Almen intensity of 0.2 A∼0.3 A, the shot peening time is 6 sec, the shot peening distance is 180 mm, the shot peening pressure is 0.38～0.45 MPa and the coverage rate is 200%.Table 3
Experimental gear parameters.
ParametersModulusNumber of teethFace widthPressure angleModification coefficientAddendum coefficientClearance coefficientSymbolmZbαxha∗c∗Numerical value1.6 mm6010 mm25°0.30.90.2Table 4
Tooth root bending fatigue experimental data of the base material TM210A steel gear.
Experiment numberMethodsStress level (MPa)Fatigue life (cycles)Comment1Group method800135997Broken2800117882Broken3800185918Broken4700231914Broken5700192639Broken6700298315Broken7600513020Broken8600386087Broken9600494337Broken10600540775Broken1Staircase method5008497357Broken248010000030Run out35005354808Broken448010000034Run out550010000017Run out65203688955Broken750010000021Run out852010000022Run out9540686134Broken1052010000022Run out115403793367Broken1252010000019Run out1354010000022Run out1456010000022Run outFigure 1
Schematic illustration of the gear.


### 2.2. Experiment Method

The experiment adopts GB/T 14230-2021 [17] for the experiment method B of double-tooth pulsating loading mode. This method has the advantages of high experiment frequency (at about 97 Hz). Since no rolling occurs, consisting of the possibility to perform more than one test with a gear, two teeth can be examined in each test, and there will be no contact or gluing failure. For this, only few experiment specimens and a high utilization rate is required, thereby shortening the experiment time and quickly achieving the experiment purpose. The SINCOTEC MAG 100 kN high-frequency fatigue testing machine and the double-tooth pulsating loading bending fatigue experiment fixture are shown in Figure 2. The experiment environment is the atmospheric room temperature: temperature (25 ± 2°C), humidity (25%∼40%RH), and stress ratio (γ=0.05). The group method is to carry out the fatigue life test in groups under multiple stress levels and obtain life curves under different reliability through statistical processing. During the test, 3∼5stress levels are usually taken, and there should be no less than 3 test points under each stress level. The staircase method is to set multiple stress levels near the estimated fatigue limit stress after a given number of cycles, and calculate the fatigue limit according to the rise and fall distribution of failure or run out at the test point. The group method and the staircase method were used to determine the fatigue life of different stress levels and the fatigue limit under the specified life of 1 × 107 cycles, respectively. The residual stresses distribution along the depth was determined by a model Xstress-3000 X-ray diffraction apparatus combined with the layer-by—by-layer polishing method, the residual stresses along the depth were measured every 50 μm, three points were measured at the depth of each layer, and the mean value was used as the residual stress of the depth of the layer.Figure 2
Experimental setup for tooth root bending fatigue experiments.For the fixture in the form of double-tooth loading, once the parameters of the experimental gear are determined, the number of span teethn of the upper indenter and the position of the force point E pressed on the tooth surface are determined. Its calculation method is as follows:The diameter of the circle where the pointE is(1)dE=dbcosαE.In (1), db is the diameter of the base circle and αE is thepressure angle at point E.The pressure angle at pointE is calculated by (2)tanαE=π2zz−2n−1+2xtanαz+invα.In equation (2), z is the number of teeth, x is the modification coefficient, α is the pressure angle, and n is the number of span teeth.The number of span teethn is calculated by (3)n≈z2ππ−2tanαE−1zπ−4xtanα+2invα.In (3), αa is the pressure angle of the tooth tip.In the actual experiment, the gear is subjected to a pulsating cyclic load from the upper indenter, and the load changes from small to large and then small during the whole process. In order to avoid the vibration, instability, or shock of the experiment system, the minimum value of the load cannot be equal to zero. That is, the stress ratio should beγ=σmin/σmax≠0. In the experiment, the tooth root stress of the experimental gear is calculated by (4) according to the determined position of point E.(4)σF′=Ft⋅YFE⋅YSEb⋅m⋅YST⋅YδrelT⋅YRrelT⋅YXIn equation (4), b is the face width, m is the module, Ft is the nominal tangential force on the indexing circle in the end face (Ft=FE⋅cosαE, FE=F/2), YFE is the tooth profile coefficient when the load acts on the point E, YSE is the stress correction factor when the load acts on the point E, YSE is the stress correction factor of experimental gear, YδrelT is the sensitivity factor of relative tooth root fillet, YRrelT is the relative tooth root surface condition factor, and YX is the dimension factor for bending strength calculation. Among them, YFE and YSE are calculated by the equation given in ISO 6336-1:2019 [18] and ISO 6336-1:2019 [19].Whenγ≠0 in the actual experiment, root stress σF′ should be converted into the pulsating cyclic root stress σF at γ=0, and the conversion equation is(5)σF=1−rσF′1−rσF′/σb+350.In (5), σb is the tensile strength.During the experiment, bending fatigue failure will be judged if any of the following conditions occur: (1) Fatigue cracks visible to the naked eye appear at the tooth root; (2) It is observed through the control interface of the testing machine that the load or frequency decreases by 5% to 10%; and (3) Broken tooth along the tooth root is observed with naked eyes. In addition, it is observed through the control interface of the testing machine that when the number of stress cycles is greater than 1 × 107, it is considered run out.


## 2.1. Materials and Specimens

The chemical composition of the TM210A steel is shown in Table1. After solid solution at 820°C, × 1 h × air cooling (AC) and aging at 510 ± 5°C × 4 h × AC, the mechanical properties at room temperature are shown in Table 2.Table 1
Chemical composition of TM210A steel (wt/%).
CSiMnSPNiCoMoTiAlFe0.00300.090.090.0050.00417.7010.324.300.970.10Bal.Table 2
Mechanical properties of TM210A steel.
Tensile strength (MPa)Yield strength (MPa)Elongation (%)Reduction of area (%)Hardness (HRC)212520659.56055The experimental TM210A steel gear specimen is designed and manufactured by the relevant regulations in GB/T 14230-2021 [17], its basic parameters and schematic illustration of the gear are shown in Table 3 and Figure 1, respectively. The process parameters of shot peening gear specimen are as follows pneumatic shot peening equipment is adopted for shot peening, the shot using cast steel balls is mixed with 50%S070 and 50%S110, and hardness of HRC55～65 under an Almen intensity of 0.2 A∼0.3 A, the shot peening time is 6 sec, the shot peening distance is 180 mm, the shot peening pressure is 0.38～0.45 MPa and the coverage rate is 200%.Table 3
Experimental gear parameters.
ParametersModulusNumber of teethFace widthPressure angleModification coefficientAddendum coefficientClearance coefficientSymbolmZbαxha∗c∗Numerical value1.6 mm6010 mm25°0.30.90.2Table 4
Tooth root bending fatigue experimental data of the base material TM210A steel gear.
Experiment numberMethodsStress level (MPa)Fatigue life (cycles)Comment1Group method800135997Broken2800117882Broken3800185918Broken4700231914Broken5700192639Broken6700298315Broken7600513020Broken8600386087Broken9600494337Broken10600540775Broken1Staircase method5008497357Broken248010000030Run out35005354808Broken448010000034Run out550010000017Run out65203688955Broken750010000021Run out852010000022Run out9540686134Broken1052010000022Run out115403793367Broken1252010000019Run out1354010000022Run out1456010000022Run outFigure 1
Schematic illustration of the gear.


## 2.2. Experiment Method

The experiment adopts GB/T 14230-2021 [17] for the experiment method B of double-tooth pulsating loading mode. This method has the advantages of high experiment frequency (at about 97 Hz). Since no rolling occurs, consisting of the possibility to perform more than one test with a gear, two teeth can be examined in each test, and there will be no contact or gluing failure. For this, only few experiment specimens and a high utilization rate is required, thereby shortening the experiment time and quickly achieving the experiment purpose. The SINCOTEC MAG 100 kN high-frequency fatigue testing machine and the double-tooth pulsating loading bending fatigue experiment fixture are shown in Figure 2. The experiment environment is the atmospheric room temperature: temperature (25 ± 2°C), humidity (25%∼40%RH), and stress ratio (γ=0.05). The group method is to carry out the fatigue life test in groups under multiple stress levels and obtain life curves under different reliability through statistical processing. During the test, 3∼5stress levels are usually taken, and there should be no less than 3 test points under each stress level. The staircase method is to set multiple stress levels near the estimated fatigue limit stress after a given number of cycles, and calculate the fatigue limit according to the rise and fall distribution of failure or run out at the test point. The group method and the staircase method were used to determine the fatigue life of different stress levels and the fatigue limit under the specified life of 1 × 107 cycles, respectively. The residual stresses distribution along the depth was determined by a model Xstress-3000 X-ray diffraction apparatus combined with the layer-by—by-layer polishing method, the residual stresses along the depth were measured every 50 μm, three points were measured at the depth of each layer, and the mean value was used as the residual stress of the depth of the layer.Figure 2
Experimental setup for tooth root bending fatigue experiments.For the fixture in the form of double-tooth loading, once the parameters of the experimental gear are determined, the number of span teethn of the upper indenter and the position of the force point E pressed on the tooth surface are determined. Its calculation method is as follows:The diameter of the circle where the pointE is(1)dE=dbcosαE.In (1), db is the diameter of the base circle and αE is thepressure angle at point E.The pressure angle at pointE is calculated by (2)tanαE=π2zz−2n−1+2xtanαz+invα.In equation (2), z is the number of teeth, x is the modification coefficient, α is the pressure angle, and n is the number of span teeth.The number of span teethn is calculated by (3)n≈z2ππ−2tanαE−1zπ−4xtanα+2invα.In (3), αa is the pressure angle of the tooth tip.In the actual experiment, the gear is subjected to a pulsating cyclic load from the upper indenter, and the load changes from small to large and then small during the whole process. In order to avoid the vibration, instability, or shock of the experiment system, the minimum value of the load cannot be equal to zero. That is, the stress ratio should beγ=σmin/σmax≠0. In the experiment, the tooth root stress of the experimental gear is calculated by (4) according to the determined position of point E.(4)σF′=Ft⋅YFE⋅YSEb⋅m⋅YST⋅YδrelT⋅YRrelT⋅YXIn equation (4), b is the face width, m is the module, Ft is the nominal tangential force on the indexing circle in the end face (Ft=FE⋅cosαE, FE=F/2), YFE is the tooth profile coefficient when the load acts on the point E, YSE is the stress correction factor when the load acts on the point E, YSE is the stress correction factor of experimental gear, YδrelT is the sensitivity factor of relative tooth root fillet, YRrelT is the relative tooth root surface condition factor, and YX is the dimension factor for bending strength calculation. Among them, YFE and YSE are calculated by the equation given in ISO 6336-1:2019 [18] and ISO 6336-1:2019 [19].Whenγ≠0 in the actual experiment, root stress σF′ should be converted into the pulsating cyclic root stress σF at γ=0, and the conversion equation is(5)σF=1−rσF′1−rσF′/σb+350.In (5), σb is the tensile strength.During the experiment, bending fatigue failure will be judged if any of the following conditions occur: (1) Fatigue cracks visible to the naked eye appear at the tooth root; (2) It is observed through the control interface of the testing machine that the load or frequency decreases by 5% to 10%; and (3) Broken tooth along the tooth root is observed with naked eyes. In addition, it is observed through the control interface of the testing machine that when the number of stress cycles is greater than 1 × 107, it is considered run out.


## 3. Results and Discussion

### 3.1. Experimental Results

The tooth root bending fatigue experiment stress of the base material (800 MPa, 700 MPa, and 600 MPa) and the shot peened (1460 MPa, 1270 MPa, and 1200 MPa) TM210A steel gears are carried out step by step from high to low, respectively. When the gear teeth have a failure or the number of cycles reaches the cycling base of 1 × 107 cycles, the experiment is terminated, and the number of cycles, abnormal phenomena, and specimen damage are recorded. The tooth root bending fatigue experiment results of the base material and shot peened TM210A steel gears are shown in Tables 4 and 5, respectively.Table 5
Tooth root bending fatigue experimental data of the shot peened TM210A steel gear.
Experiment numberMethodsStress level (MPa)Fatigue life (cycles)Comment1Group method1460122789Broken21460140293Broken31460195551Broken41270811123Broken51270387269Broken61270335954Broken712001229039Broken812001079320Broken91200827213Broken101200314657Broken1Staircase method110010000018Run out21120996017Broken3110010000035Run out411202455601Broken5110010000023Run out6112010000036Run out71140991191Broken811204304444Broken9110010000032Run out10112010000020Run out11114010000020Run out1211601860227Broken13114010000018Run out1411601859416BrokenTable 6
Tooth root bending fatigue life of the base material TM210A steel gear with 50% survival rate.
Smax (MPa)800700600516N50 (cycles)143913237083479733107


## 3.1. Experimental Results

The tooth root bending fatigue experiment stress of the base material (800 MPa, 700 MPa, and 600 MPa) and the shot peened (1460 MPa, 1270 MPa, and 1200 MPa) TM210A steel gears are carried out step by step from high to low, respectively. When the gear teeth have a failure or the number of cycles reaches the cycling base of 1 × 107 cycles, the experiment is terminated, and the number of cycles, abnormal phenomena, and specimen damage are recorded. The tooth root bending fatigue experiment results of the base material and shot peened TM210A steel gears are shown in Tables 4 and 5, respectively.Table 5
Tooth root bending fatigue experimental data of the shot peened TM210A steel gear.
Experiment numberMethodsStress level (MPa)Fatigue life (cycles)Comment1Group method1460122789Broken21460140293Broken31460195551Broken41270811123Broken51270387269Broken61270335954Broken712001229039Broken812001079320Broken91200827213Broken101200314657Broken1Staircase method110010000018Run out21120996017Broken3110010000035Run out411202455601Broken5110010000023Run out6112010000036Run out71140991191Broken811204304444Broken9110010000032Run out10112010000020Run out11114010000020Run out1211601860227Broken13114010000018Run out1411601859416BrokenTable 6
Tooth root bending fatigue life of the base material TM210A steel gear with 50% survival rate.
Smax (MPa)800700600516N50 (cycles)143913237083479733107


## 4. Discussions

According to the statistical theory, the experiment results in Tables4 and 5 are processed to obtain the median tooth root bending fatigue life of the base material and shot peened TM210A steel gears with a 50% survival rate under different stress levels, and the median tooth root bending fatigue limit when the number of cycles is 1 × 107, as shown in Tables 6 and 7, respectively.Table 7
Tooth root bending fatigue life of the shot peened TM210A steel gear with 50% survival rate.
Smax (MPa)1460127011201124N50 (cycles)149899472607862558107As given in Table6 and 7, when the cycle base is 1 × 107 cycles, the median tooth root bending fatigue limits of the base material and the shot peened TM210A steel gear are 516 MPa and 1124 MPa, respectively, and the tooth root bending fatigue limit of the shot peened TM210A steel gear is about 2.18 times that of the base material TM210A steel gear.To describe the tooth root bending fatigue performance of the base material and shot peening TM210A steel gear more intuitively, the three-parameter power functionS-N curve model is used to characterize the stress-life relationship, and the model equation as(6)NSmax−S0H=C.In (6), Smax is the maximum stress; N is the fatigue life; S0 is the theoretical fatigue limit; and H and C are the undetermined constants. The curve equation was fitted by the double-weighted least squares method [20], and the parameters H and C of the equation were calculated by MATLAB.From Tables4 and 6, the parameters of the three-parameter power function equation of the tooth root bending fatigue of the base material TM210A steel gear are obtained by fitting S0 = 485.8519 MPa, H = 1.2925, C = 2.1101 × 108. Therefore, the tooth root bending fatigue S-N curve equation with the 50% survival rate of the base material TM210A steel gear is given as(7)NSmax−485.85191.2925=2.1101×108.From Tables5 and 7, the three-parameter power function equation parameters of the tooth root bending fatigue of the shot peened TM210A steel gear are obtained by fitting S0 = 1111.3000 MPa, H = 1.2068, and C = 1.8014 × 108. Therefore, the tooth root bending fatigue S-N curve equation with the 50% survival rate of the shot peened TM210A steel gear is given as(8)NSmax−1111.30001.2068=1.8014×108.According to (7) and (8), the tooth root bending fatigue S-N curves with a 50% survival rate in the base material and shot peened TM210A steel gear can be obtained, as shown in Figure 3. It can be seen that the tooth root bending, fatigue life, and strength of the TM210A gears treated by shot peening are significantly improved, and the lower the fatigue stress, the more obvious the effect of improving the fatigue life.Figure 3
Tooth root bending fatigueS-N curves of base material and shot peened TM210A steel gears with 50% survival rate.Regarding the bending fatigue failure at the tooth root fillet, it can be considered as a short cantilever beam with a load applied to one side of the beam. The maximum tensile stress is on the tooth root surface of the loaded tooth, the maximum compressive stress is at the tooth root surface on the other side of the tooth, and the zero stress point is near the intersection of the tooth center line and the tooth root circle. Once a crack is initiated, it will propagate toward the zero stress point, eventually leading to the crack path as shown in Figure4. Figure 4(a) shows the bending failure model of the tooth root fillet, and Figure 4(b) shows the contour map of the equivalent (von-Mises) stress.Figure 4
Bending fatigue failure mechanism of the tooth root fillet. (a) Bending failure model of the tooth root fillet and (b) contour map of the equivalent (von Mises) stress.
(a)(b)To further analyze the effect of shot peening bending, fatigue performance at the tooth root fillet of the TM210A steel gear and fatigue fracture at the tooth root fillet was observed under a Quanta400 environmental scanning electron microscope appearance. Figures5(a) and 5(b) show the fatigue source positions at the tooth root fillet of the shot peened and base material TM210A steel gears, respectively. The distance between A and the tooth root fillet surface is h = 0.14 mm, and B is at the tooth root fillet surface. It can be seen that the shot peening pushes the TM210A steel gear bending fatigue source at the tooth root fillet from the tooth root fillet surface from the inside.Figure 5
Microscopic morphology of the crack source. (a) Shot peened TM210A gear and (b) base material TM210A gear.
(a)(b)For the analysis of the gear experimental results, it is assumed that the internal fatigue limit of the surface treatment is the same as the stress fatigue limit of the core base material. Assuming that the stiffness of the mechanical pulsator structure is much higher than the gear stiffness, only the gear specimen and the loading anvils are included in the analyses. Furthermore, since the gear anvils subsystem is symmetric concerning two orthogonal planes, only a quarter of this subsystem is considered, while the effects of the other portions are reproduced by applying adequate boundary conditions. The gear model is further simplified by assuming that the teeth far from the loaded tooth do not influence the root fillet stress distribution and the contact between the gear flank and the contact surface of the anvil is frictionless. The finite element analyses are performed to establish a precise correlation between the applied loaded teeth and the corresponding maximum bending stress at the tooth root fillet. The finite element model is established by ANSYS 17.2, it is meshed using tetrahedral elements with second-order shape functions, and about 380 thousand elements are generated, as shown in Figure6(a). Loading is performed at the position shown in Figure 6(a), and the contour map of the maximum principal stress at the tooth root fillet of the loaded tooth is shown in Figure 6(b).Figure 6
Finite element model of the loaded tooth. (a) Finite element mesh and (b) contour map of the maximum principal stress.
(a)(b)As shown in Figure5, the weak link of the tooth root bending fatigue of shot peened TM210A steel gear is 0.14 mm away from the surface. To explain the reason for the formation of the fatigue source, the critical conditions for the formation of the fatigue source near the tooth root are analyzed, as shown in Figure 7. The strengthening effect of shot peening on the tooth root bending fatigue performance is due to the compressive residual stress on the tooth root surface. Due to the existence of residual stress, the critical load stress required to form an internal fatigue source is the superposition of the internal fatigue limit and residual stress [21]. When the external load stress of an internal point under the action of fatigue load is greater than the critical stress for forming a fatigue source, the point is a weak link, which provides mechanical and probabilistic conditions for the formation of a fatigue source.Figure 7
The critical condition analysis diagram of tooth root fatigue source of shot peened TM210A steel gear.The tooth root stress curve along the depth direction under the action of fatigue limit load is calculated by the finite element, as shown in curve 1 in Figure7. Using an X-ray residual stress tester and electrolytic polishing method, the tooth roots of the shot peened TM210A steel gear specimens were peeled off layer by layer, and the residual stress distribution along the depth of the shot peened TM210A steel gear tooth roots was measured, as shown in curve 2 in Figure 7. It can be seen that the surface of the shot peened TM210A steel gear tooth root has a small compressive residual stress. With the increase of the depth, it reaches a peak at about 0.06 mm from the surface and then gradually decreases, and the total depth of the residual stress field is about 0.2 mm. Due to the existence of compressive residual stress in the surface layer, the critical load stress that forms the internal fatigue source is obtained by superimposing the internal fatigue limit and compressive residual stress (curve 2), as shown in curve 3 in Figure 7. The stress distribution under external load is calculated by the finite element. Taking the external load stress of 1460 MPa as an example, calculate the maximum principal stress distribution at the root fillet along the depth direction under this stress level, as shown in curve 4 in Figure 7.The abscissa of the intersection of curves 3 and 4 in Figure7 is the critical position for forming the fatigue source. It can be seen that curves 3 and 4 intersect at 0.13 mm and 0.73 mm from the surface. Within 0.13 mm from the surface, curve 4 is lower than curve 3, that is, the external load stress is less than the critical stress for forming the fatigue source; within 0.13 mm∼0.73 mm from the surface, curve 4 is higher than curve 3, and the external load stress begins to greater than the critical stress for forming the fatigue source; curve 4 is again lower than curve 3 after 0.73 mm from the surface. Under the external load stress of 1460 MPa for shot peened TM210A steel gear, the possible position of the fatigue source is within the range of 0.13∼0.73 mm from the surface, and beyond this range, there is no condition to form the fatigue source. Compared with the position of the fatigue source obtained by the test in Figure 5(a), it can be seen that the position of the experiment fatigue source is within the analysis range. Similarly, under the external load stress of 1270 MPa and 1200 MPa for shot peened TM210A steel gears, the fatigue source positions were formed in the range of 0.17∼0.67 mm and 0.18∼0.63 mm from the surface, respectively. It can be seen that due to the existence of the residual stress at the tooth root of the shot peened TM210A steel gear, the fatigue source is pushed into the interior from the surface of the tooth root, and the external load stress is smaller, the deeper the critical position of the fatigue source is from the surface, and the possible range of the fatigue source is smaller. Based on the finite element analysis, the possible initiation position of the fatigue source is obtained. From the distance and range of the possible initiation position of the fatigue source and the surface, the bending fatigue life and fatigue limit of the gear tooth root can be preliminarily estimated. The finite element analysis is used to obtain the position of the possible fatigue source. From the distance and range of the possible fatigue source and surface, the tooth root bending, fatigue life, and fatigue limit of the gear can be preliminarily estimated.


## 5. Conclusions

The proposed method was checked against the experimental results of TM210A steel gear. The major conclusions are as follows:(1)
Through the double-tooth pulsating loading experiment, the tooth root fatigue life data of the base material and shot peened TM210A steel gear under different stress levels were obtained, and the tooth root fatigue limits of the base material and shot peened TM210A steel gear were obtained as 516 MPa and 1124 MPa, respectively. It can be seen that proper shot peening treatment can significantly improve the tooth root bending, fatigue life, and fatigue limit of TM210A steel gear.(2)
Scanning electron microscope was used to observe the microstructure of the tooth root fracture of the base material and the shot peened TM210A steel gear, and the tooth root bending fatigue failure mechanism of the base material and the shot peened TM210A steel gear was obtained. It can be seen that the tooth root bending fatigue source of the shot peened TM210A steel gear is pushed into the interior from the surface.(3)
The residual stress along the depth direction of the shot peened TM210A steel gear tooth root was measured, combined with the finite element analysis, the critical condition for forming the tooth root bending fatigue source of the shot peened TM210A steel gear was obtained. It can be seen that the smaller the external load stress, the deeper the distance between the critical position of the fatigue source and the surface, and the smaller the possible generation range.



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*Source: 5701083-2022-09-08.xml*