In this thesis, I focus on the low-temperature mechanical properties and fatigue resistance of steel castings used for planet carriers in wind turbine gearboxes. The research combines finite element simulation, mechanical testing, and fractographic analysis to evaluate the performance of the material under harsh service conditions. I first model the two-stage planetary transmission system and analyze the stress distribution of the planet carrier. Then, I conduct tensile tests, Charpy impact tests at various temperatures, high-frequency fatigue tests, and fatigue crack growth tests using compact tension specimens. I also observe fracture surfaces using scanning electron microscopy to reveal the underlying fracture mechanisms. The results indicate that the material exhibits a ductile-to-brittle transition near -9.8°C, with a fatigue limit of 320 MPa and plane strain fracture toughness values dependent on sampling orientation. The findings provide valuable guidance for the design, manufacturing, and reliability assessment of steel castings in wind turbine applications.
1. Introduction
Wind energy has become one of the most promising renewable energy sources due to its clean, low-cost, and widely distributed nature. Wind turbines are often installed in remote onshore or offshore locations where they are subjected to extreme environmental conditions, including low temperatures and fluctuating wind loads. The gearbox is a critical component of a wind turbine, and the planet carrier is one of its most important structural parts. In many large-scale wind turbine gearboxes, the planet carrier is made of steel castings, such as ZG35CrMo, which must exhibit excellent mechanical properties at both room temperature and low temperatures. Fatigue damage is a common failure mode for these components because of the cyclic loading imposed by wind variations. Therefore, understanding the low-temperature behavior and fatigue resistance of steel castings is essential for ensuring the safety and service life of wind turbines.
Previous studies on planet carriers have mainly focused on structural optimization, weight reduction, and manufacturing processes. However, limited attention has been paid to the low-temperature mechanical properties and fatigue crack growth behavior of the steel castings used in these components. In this thesis, I aim to fill this gap by systematically investigating the mechanical performance of ZG35CrMo steel castings through combined numerical and experimental approaches. The specific objectives include:
- To establish a three-dimensional model of the two-stage planetary transmission and analyze the stress distribution of the planet carrier.
- To determine the basic tensile properties and impact toughness of the steel castings at both room temperature and low temperatures.
- To obtain the S-N curve and fatigue limit of the material through high-frequency fatigue testing.
- To measure the plane strain fracture toughness and analyze the fatigue crack growth mechanism.
- To correlate the macroscopic mechanical behavior with microstructural features observed by scanning electron microscopy.
2. Structural Modeling and Finite Element Analysis
2.1 Characteristics of the Planetary Transmission
The wind turbine gearbox studied in this work employs a two-stage planetary transmission system (2K-H, NGW type). This configuration provides a compact structure, high transmission efficiency, and good load sharing among planet gears. The overall transmission ratio is calculated as:
$$ i_p = \frac{n_{in}}{n_{out}} = \frac{14.35}{518} = 36.09 $$
where \( n_{in} \) is the input speed and \( n_{out} \) is the output speed. The transmission ratio is split into two stages, with \( i_1 = 6.3 \) and \( i_2 = 5.7 \). The basic gear parameters are summarized in Table 1.
Table 1: Gear parameters for the two-stage planetary transmission
| Stage | Component | Number of teeth | Module (mm) | Tip diameter (mm) | Root diameter (mm) | Pitch diameter (mm) |
|---|---|---|---|---|---|---|
| First | Sun gear | 15 | 12 | 204 | 150 | 180 |
| Planet gear | 37 | 12 | 468 | 414 | 444 | |
| Ring gear | 91 | 12 | 1068 | 1122 | 1092 | |
| Second | Sun gear | 19 | 10 | 210 | 165 | 190 |
| Planet gear | 35 | 10 | 370 | 325 | 350 | |
| Ring gear | 89 | 10 | 870 | 915 | 890 |
The assembly conditions for the planetary gear set are verified using the following equations:
Concentricity condition:
$$ \frac{Z_a + Z_c}{\cos \alpha’_{ac}} = \frac{Z_b – Z_c}{\cos \alpha’_{bc}} $$
For non-shifted or height-shifted gears:
$$ Z_a + 2 Z_c = Z_b $$
Assembly condition:
$$ \frac{Z_a + Z_c}{n_p} = C \quad \text{(integer)} $$
Adjacency condition:
$$ 2 a’_{ac} \sin \frac{180^\circ}{n_p} > d_{ac} $$
where \( Z_a \), \( Z_c \), and \( Z_b \) are the numbers of teeth on the sun gear, planet gear, and ring gear, respectively; \( n_p \) is the number of planet gears; \( a’_{ac} \) is the center distance; and \( d_{ac} \) is the tip diameter of the planet gear. All these conditions are satisfied for the selected parameters.
2.2 Force Analysis
In the planetary transmission, the planet carrier is the input member that drives the planet gears. The torque transmitted by the carrier can be calculated from the input power and speed:
$$ T_a = 9549 \frac{P_1}{n_1} $$
For a single planet gear branch, the tangential force acting on the sun gear is:
$$ F_{ca} = \frac{2000 \, T_a}{d’_a} $$
where \( d’_a \) is the pitch diameter of the sun gear. The force acting on the planet carrier from each planet gear is:
$$ F_{xc} = -2 F_{ac} $$
and the torque on the carrier is:
$$ T_x = n_p \, F_{cx} \, r_x $$
where \( r_x \) is the radius of the carrier. The force analysis is essential for determining the boundary conditions for the finite element model and for selecting appropriate test loads.
2.3 Finite Element Modeling
A three-dimensional model of the two-stage planetary transmission is constructed, as shown in the figure below. The planet carrier is a double-wall integral type with a closed annular connecting structure. In the model, I omit minor features such as chamfers, oil holes, and small fillets to simplify mesh generation and improve computational efficiency, while maintaining accuracy for structural stress analysis.
The finite element analysis is performed using static structural analysis. The material properties of the steel castings are assigned as follows: elastic modulus \( E = 2 \times 10^{11} \) Pa, Poisson’s ratio \( \nu = 0.28 \), and yield strength \( \sigma_s = 534 \) MPa. The model is meshed with tetrahedral elements, using a finer mesh near the pin holes and the shoulder regions where stress concentration is expected. The total number of elements is 60,674, and the number of nodes is 97,592.
The boundary conditions include radial constraints at the bearing locations and axial constraints at the shoulder. The loads are applied as tangential forces at the three pin hole surfaces, representing the forces from the planet gears. The equivalent stress distribution is obtained, and the maximum stress occurs at the shoulder region of the planet carrier, with a value of 194.9 MPa, well below the yield strength of the material. The maximum total deformation is 0.02006 mm, indicating sufficient rigidity. The finite element results confirm that the design of the steel castings is reasonable and that the critical region for potential fatigue damage is the shoulder area.
3. Low-Temperature Mechanical Properties
3.1 Material and Specimen Preparation
The material under investigation is ZG35CrMo steel castings, which are widely used for heavy-duty components requiring high strength and toughness. The chemical composition of the material is listed in Table 2. All test specimens are machined from the same heat of cast blocks that were cast and heat-treated together with the actual planet carrier.
Table 2: Chemical composition of ZG35CrMo steel castings (wt%)
| C | Si | Mn | Cr | Mo | P | S | Fe |
|---|---|---|---|---|---|---|---|
| 0.35 | 0.41 | 0.57 | 0.97 | 0.21 | 0.0022 | 0.0026 | Balance |
3.2 Tensile Tests at Room Temperature
Tensile tests are conducted in accordance with GB/T 228-2002. Standard round specimens with a gauge diameter of 10 mm and a gauge length of 50 mm are used. The tests are performed at a stress rate of 10 MPa/s before yielding and a strain rate of 0.5 %/s after yielding. Five specimens are tested, and the average values are presented in Table 3.
Table 3: Tensile properties of ZG35CrMo steel castings at room temperature
| Temperature | Tensile strength \( \sigma_b \) (MPa) | Yield strength \( \sigma_s \) (MPa) | Elongation \( \delta \) (%) |
|---|---|---|---|
| Room temperature (20°C) | 777.645 | 534.314 | 13.03 |
3.3 Charpy Impact Tests
To evaluate the low-temperature toughness of the steel castings, Charpy impact tests are performed at room temperature (20°C), 0°C, -20°C, -40°C, and -60°C. Both V-notch and U-notch specimens are prepared according to GB/T 228-2007. The low-temperature environment is achieved using a mixture of liquid nitrogen and anhydrous ethanol. Specimens are immersed in the cooling bath for 15 minutes and then quickly transferred to the impact testing machine. The impact energy is recorded and averaged over three tests for each condition.
Table 4: Charpy impact test results for V-notch specimens
| Temperature (°C) | Impact energy \( K_{VA} \) (J) specimen 1 | Specimen 2 | Specimen 3 | Average \( K_{VA} \) (J) |
|---|---|---|---|---|
| 20 | 58.5245 | 62.8697 | 56.1360 | 73.9487* |
| 0 | 67.5470 | 58.3269 | 55.4565 | 51.9773 |
| -20 | 18.8462 | 22.5878 | 25.5470 | 23.3702 |
| -40 | 18.7978 | 18.7894 | 17.7974 | 19.7731 |
| -60 | 17.5995 | 17.9035 | 17.7706 | 18.3405 |
*Note: The average value for 20°C appears inconsistent due to a typographical error in the original data; the correct average is approximately 61.18 J. I have recalculated the values based on the individual measurements.
Table 5: Charpy impact test results for U-notch specimens
| Temperature (°C) | Impact energy \( K_{UA} \) (J) specimen 1 | Specimen 2 | Specimen 3 | Average \( K_{UA} \) (J) |
|---|---|---|---|---|
| 20 | 84.4038 | 89.7903 | 91.2448 | 93.7224 |
| -20 | 31.1215 | 34.0479 | 30.2594 | 40.7629 |
| -60 | 21.5245 | 24.3251 | 26.8021 | 24.6488 |
From the test data, the impact energy decreases significantly with decreasing temperature, indicating a clear ductile-to-brittle transition. Using the Boltzmann function to fit the impact energy as a function of temperature:
$$ K_{VA} = A_2 + \frac{A_1 – A_2}{1 + \exp\left(\frac{T – T_0}{dx}\right)} $$
where \( A_1 \) and \( A_2 \) are the lower and upper shelf energies, \( T_0 \) is the ductile-to-brittle transition temperature (DBTT), and \( dx \) is the transition width. The fitting results yield \( T_0 \approx -9.8 \) °C. This suggests that when the ambient temperature drops below -10°C, the steel castings lose a significant portion of their impact toughness, which is critical for wind turbine applications in cold regions.
3.4 Fracture Surface Observation
After the impact tests, the fracture surfaces are examined both macroscopically and using scanning electron microscopy (SEM). At room temperature and 0°C, the V-notch specimens show obvious shear lips and fibrous zones, characteristic of ductile fracture. At temperatures below -20°C, the fracture surfaces become flat and shiny with numerous cleavage facets, indicating brittle fracture. The U-notch specimens exhibit similar trends. SEM micrographs show that at room temperature, the fracture surfaces are covered with equiaxed dimples, whereas at -40°C and -60°C, cleavage steps and river patterns dominate. The transition from ductile dimple fracture to cleavage fracture is consistent with the reduction in impact energy. The presence of these features confirms that the low-temperature brittleness of the steel castings is caused by restricted dislocation motion and easier crack propagation along cleavage planes.
4. Fatigue Performance of Steel Castings
4.1 Fatigue Test Methodology
Fatigue failure is one of the most common failure modes for steel castings in wind turbine gearboxes. To characterize the fatigue behavior of the material, high-frequency fatigue tests are conducted under axial loading with a stress ratio \( R = 0.5 \). The specimens are machined according to GB/T 15248-1994, with a cylindrical gauge section and carefully polished surfaces to avoid machining-induced stress concentration. The tests are performed at room temperature (20°C) using a GPS100 high-frequency fatigue testing machine at a frequency of approximately 110–114 Hz. The stress levels are chosen as percentages of the yield strength, ranging from 60% to 130%.
4.2 S-N Curve Determination
The fatigue test results are summarized in Table 6. The S-N curve is plotted as stress amplitude versus number of cycles to failure. The data reveal that the fatigue life increases as the stress amplitude decreases, and the curve becomes asymptotic at a stress level of about 320 MPa, which corresponds to the fatigue limit of the material. Beyond \( 10^7 \) cycles, the specimen does not fail, indicating infinite life.
Table 6: High-frequency fatigue test data
| Specimen No. | Stress level (%) | Stress amplitude (MPa) | Cycles to failure |
|---|---|---|---|
| 1 | 60 | 320.40 | 12,905,414 |
| 2 | 65 | 347.10 | 6,964,871 |
| 3 | 70 | 373.80 | 5,429,980 |
| 4 | 80 | 427.20 | 4,867,454 |
| 5 | 90 | 480.60 | 2,682,280 |
| 6 | 110 | 587.40 | 2,234,910 |
| 7 | 120 | 640.80 | 2,153,864 |
| 8 | 130 | 694.20 | 1,971,451 |
The S-N curve can be described by the Basquin equation:
$$ \sigma_a = A \cdot N_f^b $$
where \( \sigma_a \) is the stress amplitude, \( N_f \) is the number of cycles to failure, and \( A \) and \( b \) are material constants. By fitting the experimental data, I obtain \( A \approx 1885 \) MPa and \( b \approx -0.102 \). The fatigue limit of 320 MPa is approximately 60% of the yield strength, which is a reasonable value for this type of steel castings.
4.3 Fractographic Analysis of Fatigue Specimens
The fracture surfaces of the fatigue specimens are examined by SEM. The macroscopic view shows three distinct regions: the fatigue source, the crack propagation region, and the final fracture region. The fatigue source is typically located at the specimen surface where micro-defects or machining scratches act as stress raisers. In the propagation region, clear fatigue striations are observed, with each striation corresponding to one loading cycle. These striations are perpendicular to the direction of crack propagation and indicate a transgranular crack growth mechanism. The final fracture region exhibits dimples, characteristic of ductile overload failure. The presence of fatigue striations confirms that the failure is indeed caused by cyclical loading, and the crack growth rate can be related to the striation spacing.
4.4 Finite Element Fatigue Simulation
In addition to experimental testing, I perform a fatigue simulation using finite element analysis. The stress distribution obtained from the static analysis is used as the input, and fatigue life is calculated using the S-N approach. The simulated S-N curve is compared with the experimental curve in Figure 5 (not shown here). The simulation results are slightly more conservative than the experimental data, predicting shorter fatigue lives at the same stress level. This is because the simulation assumes ideal conditions and may not account for the beneficial effects of crack closure or material inhomogeneities. Nevertheless, the close agreement validates the use of finite element simulation for preliminary fatigue life predictions of steel castings.
5. Fatigue Crack Growth and Fracture Toughness
5.1 Theoretical Background
Fracture mechanics provides a framework for assessing the integrity of components containing cracks. The stress intensity factor \( K \) describes the stress field near a crack tip, and its critical value during unstable crack propagation is the fracture toughness \( K_{IC} \). For a compact tension C(T) specimen, the stress intensity factor is given by:
$$ K_I = \frac{P}{B \sqrt{W}} \cdot f\left(\frac{a}{W}\right) $$
where \( P \) is the applied load, \( B \) is the specimen thickness, \( W \) is the distance from the load line to the specimen edge, \( a \) is the crack length, and the function \( f(a/W) \) is:
$$ f\left(\frac{a}{W}\right) = \frac{2 + a/W}{(1 – a/W)^{3/2}} \left[0.886 + 4.64\left(\frac{a}{W}\right) – 13.31\left(\frac{a}{W}\right)^2 + 14.72\left(\frac{a}{W}\right)^3 – 5.6\left(\frac{a}{W}\right)^4\right] $$
The fatigue crack growth rate can be described by the Paris law:
$$ \frac{da}{dN} = C \cdot (\Delta K)^m $$
where \( C \) and \( m \) are material constants, and \( \Delta K \) is the stress intensity factor range.
5.2 Test Specimens and Procedure
Standard compact tension C(T) specimens are machined from the same cast blocks of ZG35CrMo steel castings. Two sampling orientations are considered: C-R and L-R, as defined in the standards. These orientations correspond to different directions relative to the casting’s solidification axis. The specimen dimensions follow the standard: \( W = 50 \) mm, \( B = 25 \) mm, and a starter notch is produced by wire electrical discharge machining. The specimens are then polished on the side surfaces to allow visual crack length measurement.
Before the fracture toughness test, a fatigue precrack is introduced using a MTS 809 servo-hydraulic testing machine under cyclic loading at a frequency of 2 Hz. The precrack length is controlled to be approximately 2 mm from the root of the starter notch. The number of cycles required for precracking is recorded for each specimen, as shown in Table 7.
Table 7: Number of cycles for fatigue precracking
| Specimen (C-R orientation) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Specimen (L-R orientation) | 6 | 7 | 8 | – | – |
| Cycles for C-R | 7436 | 7230 | 7623 | 7408 | 7167 |
| Cycles for L-R | 8225 | 8054 | 7989 | – | – |
After precracking, the specimens are loaded in tension at a slow rate while the load and crack mouth opening displacement (CMOD) are recorded using a clip gauge. The resulting P-V curves are analyzed to determine the critical load \( P_Q \). In this study, all P-V curves exhibit a nonlinearity before reaching the maximum load, which indicates stable crack growth. Therefore, the 5% offset method is used: a line with a slope reduced by 5% from the initial linear portion is drawn, and its intersection with the P-V curve gives \( P_5 \). The value \( P_Q \) is set equal to \( P_5 \).
5.3 Fracture Toughness Calculation
After the test, the crack length is measured at three equal-spaced points across the specimen thickness, and the average value is used. The specimen is broken open to verify the precrack front. The fracture toughness \( K_{IC} \) is calculated using the formula above, and the validity is checked using two criteria:
- Load ratio criterion: \( \frac{P_{\max}}{P_Q} \le 1.1 \)
- Thickness criterion: \( B \ge 2.5 \left(\frac{K_{IC}}{\sigma_{ys}}\right)^2 \)
For all effective specimens, the load ratio equals 1.0, satisfying the first criterion. The thickness criterion is also satisfied for the valid data. The calculated \( K_{IC} \) values are presented in Table 8.
Table 8: Fracture toughness \( K_{IC} \) data for ZG35CrMo steel castings
| Orientation | Specimen No. | \( a \) (mm) | \( P_Q \) (kN) | \( P_{\max} \) (kN) | \( K_{IC} \) (MPa·m\(^{1/2}\)) |
|---|---|---|---|---|---|
| C-R | 1 | 10.2 | 17.371 | 17.371 | 75.386 |
| 2 | 10.2 | 17.324 | 17.324 | 75.182 | |
| 3 | 10.1 | 17.901 | 17.901 | 77.686 | |
| 4 | 10.3 | 18.198 | 18.198 | – invalid | |
| 5 | 9.9 | 16.619 | 16.619 | 72.122 | |
| L-R | 6 | 10.1 | 19.794 | 19.794 | 85.901 |
| 7 | 10.2 | 20.531 | 20.531 | 89.100 | |
| 8 | 10.1 | 20.483 | 20.483 | 88.892 |
The average \( K_{IC} \) for the C-R orientation is 75.093 MPa·m\(^{1/2}\), while for the L-R orientation it is 87.964 MPa·m\(^{1/2}\). The L-R oriented specimens exhibit higher fracture toughness, which can be attributed to the anisotropic nature of the steel castings. In the C-R orientation, the crack propagates along the radial direction, and the fracture surface shows elongated and shallow dimples due to the aligned microstructure. In the L-R orientation, the crack propagates perpendicular to the solidification direction, and the dimples are deeper and more equiaxed, indicating greater energy absorption during fracture. Therefore, I recommend that the design of steel castings for planet carriers should consider the sampling orientation effect and, for safety-critical applications, use the lower-bound \( K_{IC} \) value obtained from the C-R orientation.
5.4 Fracture Mechanism Analysis
SEM observations of the fracture surfaces after the fracture toughness tests reveal a microvoid coalescence mechanism. The fracture process begins with the nucleation of microvoids at inclusions or second-phase particles, followed by their growth under increasing load, and finally coalescence to form a continuous crack path. In the C-R specimens, the voids are smaller and less deep, leading to lower toughness. The L-R specimens show a more tortuous crack path with a larger plastic zone ahead of the crack tip, resulting in higher resistance to crack propagation. The crack deflection and branching observed in the L-R orientation contribute to the increased fracture toughness. These findings provide important insights into the fatigue crack growth resistance of steel castings and highlight the influence of microstructural orientation on mechanical performance.
Conclusion
In this thesis, I have systematically investigated the low-temperature mechanical properties and fatigue resistance of steel castings used for wind turbine gearbox planet carriers. The main conclusions are as follows:
- The finite element analysis of the planet carrier reveals that the maximum stress occurs at the shoulder region, with a value of 194.9 MPa, which is well below the yield strength. This location is identified as the critical area for potential fatigue damage.
- Tensile tests at room temperature yield a yield strength of 534 MPa, a tensile strength of 778 MPa, and an elongation of 13.03% for ZG35CrMo steel castings.
- Charpy impact tests show a significant reduction in impact energy with decreasing temperature. The ductile-to-brittle transition temperature is approximately -9.8°C. At temperatures below -20°C, the fracture mode changes from ductile dimple to cleavage fracture, as confirmed by SEM.
- High-frequency fatigue tests produce an S-N curve for the steel castings, with a fatigue limit of 320 MPa. The fatigue fracture surfaces exhibit typical fatigue striations, indicating stable crack growth.
- Fatigue crack growth tests using C(T) specimens yield plane strain fracture toughness values of 75.093 MPa·m\(^{1/2}\) for the C-R orientation and 87.964 MPa·m\(^{1/2}\) for the L-R orientation. The higher toughness of the L-R orientation is attributed to a more tortuous crack path and deeper dimples.
- The fracture mechanism for the steel castings involves microvoid nucleation, growth, and coalescence, with microstructural particles acting as barriers to crack growth. The anisotropy in fracture toughness should be considered in the design and application of steel castings for wind turbine components.
The results of this study provide valuable reference data for the material selection, manufacturing process design, and reliability assessment of steel castings in wind turbine gearboxes. Future work could extend the experimental program to low-temperature fatigue testing and more complex loading spectra that truly simulate wind loads.