In modern agricultural machinery, the shift toward electrification is driven by environmental concerns and climate change, leading to a growing demand for electric drive systems. As a key component, the electric drive system relies on numerous bolted connections to integrate various parts, such as motors, gearboxes, and structural frames. In a typical electric drive system, bolts can number from dozens to hundreds, with varying specifications and loading conditions. Fatigue failure accounts for approximately 90% of bolt failures, making it a critical issue in design and maintenance. Traditional bolt design involves theoretical calculations, empirical selection, 3D modeling, and finite element analysis (FEA) for verification, which is time-consuming and labor-intensive due to the multiplicity of bolt types and loads in electric drive systems. To streamline this process, I developed a bolt fatigue life prediction system that combines Ansys Workbench for parametric FEA and Matlab for BP neural network modeling. This system allows designers to quickly and accurately predict bolt fatigue life by inputting basic parameters like nominal diameter, preload, working load, and connection thickness, thereby simplifying the design and manufacturing of electric drive systems.
The core of this system lies in creating a parametric model of bolts commonly used in electric drive systems. Using Ansys Workbench’s Design Modeler module, I constructed 3D models of bolts based on GB/T 5783-2000 standards, with key design parameters defined. The primary parameters include the nominal diameter (P1), connection thickness (P2), and dimensions derived from standards, such as bolt head and nut sizes. For this study, I focused on M8, M10, and M12 bolts, with connection thicknesses ranging as shown in Table 1. The parametric approach enables automatic adjustment of bolt geometry based on input values, facilitating batch analysis for diverse electric drive system configurations.
| Nominal Diameter P1 (mm) | Connection Thickness P2 (mm) | Step Size for P2 (mm) |
|---|---|---|
| 8 | 10 to 60 | 10 |
| 10 | 15 to 75 | 15 |
| 12 | 20 to 100 | 20 |
For fatigue life analysis, I assigned material properties to the bolts and connections. The bolts are made of quenched and tempered 45# steel, with a density of 7,890 kg/m³, elastic modulus E = 209 GPa, and Poisson’s ratio of 0.269. The fatigue behavior follows the S-N curve derived from material handbooks: $$ \lg N = 14.3272 – 3.0831 \lg \sigma $$ where N is the fatigue life in cycles and σ is the fatigue strength in MPa. The connections are structural steel with default Ansys properties. Meshing was performed using tetrahedral elements for bolts and hexahedral elements for other parts, with a mesh size of 1 mm, resulting in 101,089 nodes and 34,120 elements. Contact pairs were defined between bolt, nut, and connection surfaces, with frictional contact (coefficient 0.15) for bolt-nut interfaces and bonded contacts elsewhere to simulate real interactions in electric drive systems.
Load application is crucial for simulating bolt behavior in electric drive systems. Bolts are typically preloaded to ensure tightness, with preload Qp estimated based on minor diameter and material yield strength: $$ Q_p \leq (0.6 \sim 0.7) \sigma_s A_1 $$ where $$ A_1 \approx \pi d_1^2 / 4 $$ Here, σs is the yield strength (355 MPa for 45# steel) and d1 is the minor diameter. The working load P8, representing axial forces in electric drive systems, varies sinusoidally from 0 to a peak value, mimicking cyclic operational conditions. The load ranges and steps for different bolt diameters are summarized in Table 2. In FEA, a constant preload is applied to the bolt shank, while opposing sinusoidal loads are applied to connection faces, eliminating the need for constraints and improving accuracy. The stress and strain distributions show maximum values at the first engaged thread, with stress decreasing along the thread. Fatigue life is calculated using the stress-life approach with a fatigue strength reduction factor Kf: $$ K_f = \frac{k_\sigma}{\varepsilon_\sigma \beta} $$ where kσ is the stress concentration factor, εσ is the size factor, and β is the surface factor.
| Nominal Diameter P1 (mm) | Working Load P8 (N) | Step Size for P8 (N) |
|---|---|---|
| 8 | 1,000 to 4,000 | 500 |
| 10 | 4,000 to 10,000 | 1,000 |
| 12 | 6,000 to 12,000 | 1,000 |
The fatigue life analysis revealed that bolt fatigue life is highly sensitive to load fluctuations. The stress amplitude Δσ, which drives fatigue, is related to the working load P8 through bolt and connection stiffness. The bolt load variation ΔF is given by: $$ \Delta F = \frac{C_l}{C_l + C_f} \cdot P_8 $$ where Cl is the bolt stiffness and Cf is the connection stiffness. This equation highlights how preload and system stiffness affect fatigue in electric drive systems. Using Ansys Workbench’s parameterized analysis, I computed fatigue life for 535 sample points across different combinations of P1, P2, and P8. A subset of the results is shown in Table 3, indicating fatigue life values ranging from millions to thousands of cycles, depending on loading conditions.
To leverage this data for predictive modeling, I employed a BP neural network in Matlab. The input parameters are P1, P2, P8, and preload, while the output is fatigue life P10. Data preprocessing involved normalization using min-max scaling: $$ P_i’ = \frac{P_i – \min P_i}{\max P_i – \min P_i} $$ for i = 1, 2, 8, 9 (where P9 represents preload). From the 535 samples, 30 were randomly selected for validation (6 per bolt diameter), and the rest were used for training. The neural network architecture consists of an input layer with 4 neurons, 4 hidden layers with 20 neurons each, and an output layer with 1 neuron. The training function is the BFGS quasi-Newton backpropagation algorithm, with TANSIG activation functions and mean squared error (MSE) as the performance metric. After training, the network achieved a correlation coefficient R = 0.99309 between predicted and target values, demonstrating excellent fit for electric drive system applications.
| P1 (mm) | P2 (mm) | P8 (N) | Fatigue Life P10 (cycles) |
|---|---|---|---|
| 8 | 10 | 1,000 | 10,000,000 |
| 8 | 10 | 1,312.5 | 9,829,120 |
| 8 | 10 | 1,625 | 7,856,616 |
| 8 | 10 | 1,937.5 | 5,884,112 |
| 8 | 10 | 2,250 | 3,911,608 |
| 10 | 10 | 4,000 | 10,000,000 |
| 10 | 10 | 4,400 | 10,000,000 |
| 10 | 10 | 4,800 | 9,323,360 |
| 10 | 10 | 5,200 | 8,590,837 |
| 10 | 10 | 5,600 | 7,858,314 |
| 12 | 15 | 6,000 | 6,639,872 |
| 12 | 15 | 6,600 | 5,492,496 |
| 12 | 15 | 7,200 | 4,345,120 |
| 12 | 15 | 7,800 | 3,197,744 |
| 12 | 15 | 8,400 | 2,050,367 |
Validation of the BP network was conducted using the reserved 30 samples. The normalized input parameters were fed into the network, and predictions were denormalized for comparison with FEA results. As shown in Table 4, the relative errors between predicted and simulated fatigue lives range from -5.97% to 4.58%, with most errors within ±3%. This indicates that the network can accurately predict bolt fatigue life for various electric drive system conditions. The maximum error of 5.97% occurs for an M10 bolt with high working load, but overall accuracy is sufficient for design purposes. The system’s speed is notable: predictions are generated almost instantaneously, compared to hours required for FEA simulations, offering a significant efficiency boost in electric drive system development.
| P1 (mm) | P2 (mm) | P8 (N) | Simulated Life (cycles) | Predicted Life (cycles) | Error (%) |
|---|---|---|---|---|---|
| 8 | 10 | 1,937.5 | 5,884,112 | 5,856,012 | -0.48 |
| 8 | 20 | 3,500 | 8,142,378 | 8,240,961 | 1.21 |
| 8 | 30 | 4,125 | 1,903,019 | 1,990,084 | 4.58 |
| 8 | 40 | 2,875 | 8,951,482 | 8,967,168 | 0.18 |
| 8 | 60 | 2,875 | 7,854,439 | 8,009,238 | 1.97 |
| 8 | 70 | 3,812.5 | 3,828,343 | 3,786,813 | -1.08 |
| 10 | 10 | 7,600 | 4,195,699 | 4,105,271 | -2.16 |
| 10 | 20 | 8,400 | 647,841 | 645,014 | -0.44 |
| 10 | 40 | 9,200 | 957,222 | 934,841 | -2.34 |
| 10 | 60 | 4,400 | 8,374,292 | 8,535,073 | 1.92 |
| 10 | 70 | 10,000 | 742,250 | 697,964 | -5.97 |
| 10 | 90 | 6,400 | 179,357 | 175,282 | -2.27 |
| 12 | 15 | 9,600 | 915,357 | 938,498 | 2.53 |
| 12 | 30 | 7,200 | 86,324 | 82,001 | -5.01 |
| 12 | 45 | 8,400 | 9,139,929 | 9,104,733 | -0.39 |
| 12 | 75 | 6,000 | 93,179 | 92,108 | -1.15 |
| 12 | 90 | 7,200 | 4,388,483 | 4,293,151 | -2.17 |
| 12 | 105 | 12,000 | 8,720 | 8,552 | -1.93 |
The development of this prediction system addresses several challenges in electric drive system design. Firstly, it reduces computational burden by replacing repetitive FEA with a neural network model, saving time and resources. Secondly, it enhances design flexibility, allowing engineers to explore multiple bolt configurations quickly for optimal electric drive system performance. Thirdly, the system’s accuracy ensures reliability in fatigue life estimation, which is critical for safety and durability in agricultural machinery. The integration of Ansys and Matlab demonstrates a practical approach to leveraging simulation data for machine learning, applicable beyond bolts to other components in electric drive systems. Future work could expand the parameter ranges, include more bolt types, or incorporate multiaxial loading conditions to further refine predictions for complex electric drive system environments.
In conclusion, I have successfully created a bolt fatigue life prediction system for electric drive systems using parametric FEA and BP neural networks. This system simplifies the design process by enabling rapid and accurate fatigue life predictions based on key input parameters. Validation shows that the neural network achieves high precision, with most errors within acceptable limits. By streamlining bolt selection and analysis, this tool can significantly improve the efficiency of electric drive system development, contributing to the advancement of electric agricultural machinery. The methodology can be extended to other mechanical systems, underscoring its versatility in engineering design.