In this analysis, we investigate a critical failure involving cracks in the oil groove of a star gear shaft used in an air turbine starter. The gear shaft is a hollow component installed in pairs within the system, functioning as the inner raceway for needle bearings and providing support for intermediate double gears. The oil groove, a cantilevered structure at one end, collects lubricating oil from the reducer and channels it through internal passages to lubricate the bearings. During post-field testing inspections, a贯穿性crack was discovered at the transition between the inclined and horizontal surfaces of the oil groove, extending circumferentially and penetrating the wall thickness. Initial assessments identified the crack origin at the inner side of this transition area, with further analysis confirming fatigue characteristics through the presence of fatigue striations in the propagation zone.
To systematically address this gear shaft issue, a fault tree analysis was conducted with the oil groove fatigue crack as the top event. Given that the gear shaft is a stationary component and the oil groove is a cantilever structure not subjected to external loads, the crack was unlikely due to insufficient strength. Instead, potential causes were categorized into poor fatigue resistance and excessive vibrational stress. Key underlying events included insufficient transition fillet size, presence of initial defects, material deficiencies, elevated environmental temperatures, and inadequate resonance margin. After initial screening, factors such as material defects were ruled out, while transition fillet size and resonance margin were prioritized for further investigation through vibration analysis and testing.
The vibration characteristics of the gear shaft were analyzed using finite element simulations. Design reviews revealed that the transition between the inclined and horizontal surfaces of the oil groove lacked a specified fillet radius, with only a general requirement for unspecified edges to have a radius of R0.1 to R0.3 or a chamfer of C0.1 to C0.3. Actual measurements indicated fillet radii below R0.5. Simulation results highlighted this transition area as the point of maximum stress, correlating with the crack initiation site observed in the failed gear shaft components. The vibrational stress distribution was modeled under various conditions to assess the gear shaft’s behavior.
The natural frequencies of the gear shaft were computed for different states, including room temperature, elevated oil temperatures (up to 110°C and 140°C), and with or without oil collection in the groove. The results are summarized in the table below, showing how temperature and oil presence affect the gear shaft’s dynamic properties.
| Mode | Natural Frequency (Hz) at Room Temp | Natural Frequency (Hz) at 110°C | Natural Frequency (Hz) at 110°C with Oil | Natural Frequency (Hz) at 140°C with Oil |
|---|---|---|---|---|
| 1 | 5927 | 5870 | 5764 | 5744 |
| 2 | 6143 | 6084 | 5974 | 5952 |
| 3 | 18294 | 18118 | 17791 | 17727 |
Additionally, gear meshing frequencies, which act as excitation sources transmitted through the needle bearings to the gear shaft, were calculated for different operational scenarios. The table below compares these frequencies across various test conditions, indicating potential resonance risks.
| Excitation Source | Meshing Frequency (Hz) at Power Measurement Point (4300 rpm) | Meshing Frequency (Hz) at Internal Cold Run (4690 rpm) | Meshing Frequency (Hz) at Field Cold Run (3250-3900 rpm) |
|---|---|---|---|
| Drive Gear | 14778 | 16119 | 11170-13403 |
| 51-Tooth Gear | 14778 | 16119 | 11170-13403 |
| 23-Tooth Gear | 6665 | 7270 | 5037-6045 |
Comparing the natural frequencies and meshing frequencies revealed that the first-mode natural frequency of the gear shaft fell within the range of the 23-tooth gear meshing frequency during field cold-run operations, suggesting a potential for resonance. This alignment pointed to insufficient resonance margin as a probable cause of the gear shaft cracks.
To evaluate the effect of transition fillet size on the fatigue limit of the gear shaft, vibration fatigue tests were conducted on seven test specimens. Two specimens replicated the original design with small fillets, while five modified specimens featured enlarged fillet radii up to R5 at the oil groove transition. The test setup involved machining flats on the cylindrical section of the gear shaft to adjust natural frequencies and adding counterweights at the oil groove end to ensure maximum stress at the critical location. The specimens were subjected to alternating loads on a vibration table, monitored for high-cycle fatigue cracks over 10^7 cycles. The fatigue limits, representing the stress amplitude below which no failure occurs, were recorded and analyzed.
The test results are summarized in the following table, indicating that increasing the fillet radius did not significantly enhance the fatigue limit, as some modified specimens showed similar or only marginally improved performance compared to the original gear shaft design.
| Specimen Type | Specimen ID | Frequency (Hz) | Fatigue Limit (MPa) | Remarks |
|---|---|---|---|---|
| Original | 1 | 2260 | 230.4 | Crack observed |
| Original | 2 | 2290 | 205.7 | Crack observed |
| Modified | 3 | 2279 | 206.2 | No failure |
| Modified | 4 | 2279 | 204.8 | No failure |
| Modified | 5 | 2267 | 292.3 | Fracture at clamping area |
| Modified | 6 | 2418 | 254.2 | Fracture at clamping area |
| Modified | 7 | 2434 | 238.5 | Crack observed |
Sweep frequency and resonance dwell tests were performed on the complete assembly to confirm resonance occurrence during cold-run conditions. Strain gauges attached to the back of the oil groove measured dynamic stresses as the starter speed increased. The original gear shaft exhibited a resonance peak at 3747 rpm (5807 Hz) with an amplitude of 357 microstrain, within the field cold-run speed range of 3250-3900 rpm. In contrast, the modified gear shaft resonated at 4171 rpm (6465 Hz) with a lower amplitude of 68.6 microstrain. A dwell test at 3747 rpm for 13 minutes and 30 seconds resulted in a fatigue crack in the original gear shaft at the same location as the field failure, while the modified version remained intact. This demonstrated that resonance under field conditions directly caused the gear shaft cracks.
The underlying failure mechanism involves the first-mode natural frequency of the gear shaft oil groove structure coinciding with the meshing frequency of the 23-tooth gear during field cold-run operations. The persistent meshing excitation transferred to the gear shaft induced first-mode resonance, generating oscillatory stresses that initiated and propagated fatigue cracks at the stress concentration point. The vibrational stress amplitude can be modeled using the relationship for resonant response: $$ \sigma = \frac{F}{k} Q $$ where $\sigma$ is the stress amplitude, $F$ is the excitation force, $k$ is the stiffness, and $Q$ is the quality factor. For the gear shaft, the stress concentration at the transition fillet exacerbates this effect, leading to reduced fatigue life. The fatigue life under resonant conditions can be estimated using the Basquin’s equation: $$ N_f = C \sigma_a^{-b} $$ where $N_f$ is the number of cycles to failure, $\sigma_a$ is the stress amplitude, and $C$ and $b$ are material constants. In this case, the resonant vibrations significantly accelerated crack initiation in the gear shaft.
To mitigate the issue, structural modifications were implemented to increase the natural frequency of the gear shaft oil groove and avoid resonance. Changes included raising the oil groove height, shortening its length, adding larger chamfers at the end, and increasing the transition fillet radius. These adjustments enhanced the stiffness and shifted the natural frequency away from critical excitation ranges. Post-modification simulations indicated a first-mode natural frequency of 8386 Hz at room temperature, substantially higher than previous values. Validation tests on the updated gear shaft showed peak strain amplitudes reduced to 63.3 microstrain at the original resonance speed, with no cracks detected after prolonged operation. Field inspections of modified units confirmed the effectiveness of these changes in preventing gear shaft failures.
In conclusion, the fatigue cracks in the gear shaft oil groove were primarily caused by resonance under specific operational conditions. The transition fillet size had minimal impact on fatigue performance, whereas resonance avoidance through design improvements proved critical. This analysis underscores the importance of comprehensive vibration assessments for stationary components like the gear shaft in aerospace applications to prevent resonant failures and ensure reliability.