This article delves into the shot peening technology for spiral bevel gears, a crucial process in enhancing their fatigue life. By establishing a simulation model based on the coupling of discrete element and finite element methods, it accurately predicts the residual stress field on the tooth surface after shot peening. Through experimental verification and parameter analysis, the relationships between shot peening process parameters and residual stress field characteristics are explored, providing a solid foundation for optimizing shot peening processes and improving gear performance.
1. Introduction
Spiral bevel gears are essential components in various mechanical systems, especially in high – speed and heavy – load applications. Their reliable operation directly affects the performance and safety of the entire mechanical equipment. However, under harsh working conditions, spiral bevel gears are prone to fatigue failures, such as tooth breakage and surface pitting. Shot peening has emerged as an effective method to enhance the fatigue life of gears by inducing a residual compressive stress field on the surface.
The principle of shot peening is to use high – velocity projectiles to impact the surface of the workpiece. This causes the surface layer to undergo plastic deformation, resulting in the generation of residual compressive stresses. These stresses can counteract the tensile stresses during the gear’s operation, thereby improving the gear’s fatigue strength, contact fatigue resistance, and anti – scuffing ability.
In the past, the determination of shot peening process parameters mainly relied on trial – and – error methods, which were time – consuming, costly, and lacked accuracy. With the development of computer – aided engineering technology, numerical simulation has become an important means to study shot peening processes. Existing shot peening residual stress prediction models are mainly based on the finite – element method. However, for spiral bevel gears with complex curved surfaces, the collision probability between projectiles is high, and traditional models may not accurately simulate this situation. Therefore, this study aims to establish a more accurate simulation model by coupling the discrete element method and the finite – element method to optimize the shot peening process parameters for spiral bevel gears.
2. Shot Peening Process Experiment
2.1 Experimental Specimens
The shot peening specimens used in this experiment were a certain type of spiral bevel gear made of AISI 9310 high – strength alloy steel. The tooth surface, a key area for shot peening, had a hardness higher than 60HRC within a depth of 0.56 mm after carburizing and quenching treatment. Table 1 summarizes the basic information of the specimens.
| Specimen Information | Details |
|---|---|
| Gear Type | Spiral Bevel Gear |
| Material | AISI 9310 High – Strength Alloy Steel |
| Tooth Surface Hardness (0 – 0.56 mm depth) | >60HRC |
| Heat Treatment | Carburizing and Quenching |
2.2 Experimental Parameters
The experiment was carried out using an MP1000Ti numerical – control shot peening machine. The shot type was ASH110 with a hardness of 55 – 62HRC. The shot peening intensity ranged from 0.178 – 0.228 mmA, the coverage rate was 200%, the nozzle angle was 17°, the air pressure was 0.25 MPa, the moving speed was 70 mm/min, and the shot peening time was 144 s. The nozzle was perpendicular to the target surface and was 150 mm away from it. The gear turntable rotated at a speed of 30 r/min, and the shot flow rate was 5 kg/min. Table 2 details these experimental parameters.
| Experimental Parameter | Value |
|---|---|
| Shot Peening Machine Model | MP1000Ti |
| Shot Type | ASH110 (55 – 62HRC) |
| Shot Peening Intensity | 0.178 – 0.228 mmA |
| Coverage Rate | 200% |
| Nozzle Angle | 17° |
| Air Pressure | 0.25 MPa |
| Moving Speed | 70 mm/min |
| Shot Peening Time | 144 s |
| Nozzle – Target Distance | 150 mm |
| Gear Turntable Rotation Speed | 30 r/min |
| Shot Flow Rate | 5 kg/min |
2.3 Residual Stress Measurement
The residual stress on the tooth surface was measured at specific points. As shown in Figure 1, points a, b, and c were located on the pitch cone line of the tooth surface, which were the quarter – points of the tooth width, with point a close to the large end of the tooth. To obtain the residual stress field in the gear surface layer, the tooth was electrolytically polished along the normal direction of the tooth surface, and the electrolytic polishing depth was measured by a white – light interferometer.
A Canadian Proto company’s X – ray diffractometer was used to measure the residual stress. The measurement conditions included a tube voltage of 25 kV, a tube current of 5 mA, an X – ray tube of \(Cr_K – Alpha\), an aperture diameter of 1 mm, a wavelength of 2.291 Å, an exposure time of 3 s, an exposure number of 7, and a maximum β – angle of 20°. The electrolytic polishing was carried out using an 8818 – V3 electrolytic polishing instrument with a voltage of 40 V, a flow rate of 8, a polishing time of 3 s, and a polishing current of 2.8 – 3 A. Table 3 summarizes the measurement parameters.
| Measurement Instrument | Parameter | Value |
|---|---|---|
| X – ray Diffractometer | Tube Voltage | 25 kV |
| Tube Current | 5 mA | |
| X – ray Tube | \(Cr_K – Alpha\) | |
| Aperture Diameter | 1 mm | |
| Wavelength | 2.291 Å | |
| Exposure Time | 3 s | |
| Exposure Number | 7 | |
| Maximum β – angle | 20° | |
| Electrolytic Polishing Instrument | Voltage | 40 V |
| Flow Rate | 8 | |
| Polishing Time | 3 s | |
| Polishing Current | 2.8 – 3 A |
3. Simulation Model Establishment
3.1 Discrete Element Model
3.1.1 Model Establishment
The discrete element model was set up using EDEM simulation software to simulate the process of projectiles from the nozzle to the tooth surface. The model parameters were set according to the experimental parameters in Section 2.2. The geometric model is shown in Figure 2. The tooth surface was meshed using Hypermesh software to extract the impact information at the target position on the tooth surface. In the model, the nozzle was set perpendicular to the tooth root, convex surface, and concave surface of the gear, and was 150 mm away from the target surface, moving along the tooth width direction. The initial velocity of the projectiles was determined by the empirical formula \(v=\frac{163.5P}{1.53q_{m}+10P}+\frac{295P}{0.598d+P}+48.3P\), where \(d\) is the projectile diameter (mm), \(q_{m}\) is the shot flow rate (kg/min), and \(P\) is the nozzle air pressure (MPa).
3.1.2 Data Extraction and Processing
The calculation results were exported from EDEM software, and the impact point position was determined by the element number. The impacts at the four – equal – division points on the pitch cone line of the tooth surface were selected for data processing.
- Impact Velocity Vector: Since the gear has a curved surface and the angles between different positions and the projectile beam are different, and the target plate in the finite – element model is a local area on the tooth surface, it is necessary to convert the absolute velocity of the projectile into the relative velocity between the tooth surface element and the projectile. As shown in Figure 3, for a certain area \(OABC\) on the tooth surface, after meshing, it is simplified to a quadrilateral \(OABC\). A Cartesian coordinate system is established with \(O\) as the origin, \(OA\) as the \(x’\) – axis, \(OC\) as the \(y’\) – axis, and the \(z^{r}\) – axis determined by the right – hand rule of the space coordinate system. The velocity vector of projectile \(i\) in the global coordinate system is \(v_{i}(x_{i},y_{i},z_{i},0)\), and in the new coordinate system is \(v_{i}'(x_{i}’,y_{i}’,z_{i}’,0)\). According to the axis – transformation principle, \(v_{i}’=v_{i}\cdot\left[\begin{array}{cccc}x_{1}&x_{2}&x_{3}&0\\y_{1}&y_{2}&y_{3}&0\\z_{1}&z_{2}&z_{3}&0\\0&0&0&1\end{array}\right]\).
- Impact Number: When the actual shot peening time is \(t_{1}\), the unit – area impact number \(n_{0}\) at the target position is calculated by the formula \(n=\frac{n_{1}}{S_{1}}\times\frac{t_{1}}{t_{desm}}\), where \(n_{1}\) is the number of impacts between the element and the projectile, \(S_{1}\) is the area of the element, and \(t_{desm}\) is the calculation time of the EDEM model.
3.2 Finite Element Model
3.2.1 Mesh Generation and Boundary Conditions
The finite – element model was established based on the ABAQUS/CAE commercial finite – element software to calculate the residual stress field on the tooth surface of the gear after shot peening. The projectile diameter was 0.3 mm, and the element type was C3D8R. The target plate size is shown in Figure 4. Except for the infinite – element body mesh, the target plate size was 1 mm×1 mm×0.5 mm, and the element type was also C3D8R. A predefined field was set in this area, and the measured residual stress value of the tooth surface before shot peening was used as the initial residual stress of the model. Area I was used to limit the impact center position of the projectiles and extract the residual stress calculation results. Areas I and II were the mesh – refined parts with an element size of 10 μm×10 μm×10 μm. Area III was the transition area from fine to coarse finite – element meshes. The mesh type of Area IV was the infinite – element body CIN3D8, which was used to eliminate the reflection of stress waves at the boundary of the target plate.
The bottom surface of the target plate was completely fixed in the model. The contact relationship between the projectile and the target plate was defined as Surface to Surface. The normal behavior was defined as “hard” contact, and the tangential behavior was defined as penalty friction with a friction coefficient of 0.2.
3.2.2 Material Model
The projectile was set as an elastoplastic body using an isotropic constitutive model. The projectile parameters were set as follows: Young’s modulus \(E = 210\) GPa, Poisson’s ratio \(\mu=0.3\), density \(\rho = 7800\) kg/m³, and yield strength \(\sigma_{s}=1400\) MPa. The target material was 9310 carburized and quenched steel. Its material parameters were set as Young’s modulus \(E = 210\) GPa, Poisson’s ratio \(\mu = 0.3\), density \(\rho = 7800\) kg/m³. The plastic stress – strain curve adopted the Johnson – Cook model, which is expressed by the formulas \(\sigma=(A + B\varepsilon^{n})(1 + C\ln\frac{\dot{\varepsilon}}{\dot{\varepsilon}_{0}})(1-(T^{+})^{n})\) and \(T^{*}=\frac{T – T_{ren}}{T_{melt}-T_{rosat}}\). The parameters \(A = 1234.38\), \(B = 881\), \(C = 0.018\), \(n = 0.238\), \(m = 0.686\) were obtained from the Hopkinson pressure – bar test. To prevent stress – wave oscillation, the target material damping \(\alpha = 6\times10^{6}\) s⁻¹ was set. Table 4 summarizes the material parameters.
| Material | Parameter | Value |
|---|---|---|
| Projectile | Young’s Modulus | 210 GPa |
| Poisson’s Ratio | 0.3 | |
| Density | 7800 kg/m³ | |
| Yield Strength | 1400 MPa | |
| Target (9310 Carburized and Quenched Steel) | Young’s Modulus | 210 GPa |
| Poisson’s Ratio | 0.3 | |
| Density | 7800 kg/m³ | |
| \(A\) (Johnson – Cook Model) | 1234.38 | |
| \(B\) (Johnson – Cook Model) | 881 | |
| \(C\) (Johnson – Cook Model) | 0.018 | |
| \(n\) (Johnson – Cook Model) | 0.238 | |
| \(m\) (Johnson – Cook Model) | 0.686 | |
| Material Damping | \(6\times10^{6}\) s⁻¹ |
3.2.3 Projectile Impact Information
The impact angle, velocity, and number of projectiles were determined by the calculation results in Section 3.1.2. According to the size standard of ASH110 – type projectiles, the projectiles were set as spherical with a diameter of 0.3 mm. Considering the random distribution of projectile impact positions in actual situations, Python language programming was used in the simulation. The Random function was used to generate random positions, and the impact center points of the projectiles were all within Area I shown in Figure 4.
4. Results and Discussion
4.1 Comparison between Simulation and Experimental Results
To verify the accuracy of the simulation model, the same process parameters as in the experiment were set in the established shot peening process simulation model. Figure 5 shows the measured and simulated three – dimensional topography of point b on the convex surface after shot peening. The three – dimensional roughness \(S_{a}\) value was calculated by the formula \(S_{a}=\frac{1}{n}\sum_{i = 1}^{n}|Z_{i}|\), where \(n\) is the number of data points and \(Z_{i}\) is the height value of the \(i\) – th node. The measured value was 0.35 μm, and the simulated result was 0.386 μm, with an error of 10.3%. In the \(x\) and \(y\) directions, the resolution of the simulation result was lower than that of the measured result because the sampling interval of the measured data was 0.5 μm, while the target plate mesh size of the finite – element model was 10 μm×10 μm.
Table 5 compares the measured and simulated residual stress values in the tooth – height direction on the tooth surface. The positions of points a, b, and c are consistent with those marked in Figure 1. The results show that the surface residual stress of each point on the tooth is between – 800 and – 880 MPa, and the calculation error is within 6%. Figure 6 shows the measured and simulated residual stress distributions along the depth direction of points b on the convex and concave surfaces. After shot peening, the residual stress change trends of the convex and concave surfaces of the tooth are consistent, and the residual compressive stress value of the concave surface is slightly greater than that of the convex surface. The residual stress distributions in the tooth – width and tooth – height directions are similar, with the surface residual stress being approximately – 800 to – 850 MPa and the maximum residual compressive stress value being between 1200 and 1300 MPa at a depth of about 20 – 30 μm. Table 6 summarizes the surface residual compressive stress and maximum residual compressive stress values on the tooth surface. The errors between the measured values and the simulation results are all less than 10%, indicating that the simulation model can accurately predict the residual stress field on the tooth surface layer of spiral bevel gears after shot peening.
