Spiral bevel gears transmit motion between intersecting shafts through curved, obliquely oriented teeth. Their gradual engagement gives smooth operation and high load capacity, but the contact pattern is sensitive to the relative curvature of the two flanks, the mounting position, and the stiffness of the supporting structure. In a production batch of 12CrNi3A spiral bevel gears, the run-in check showed a contact patch positioned too low on the tooth and covering less than the required 40% of the tooth height, together with slight abnormal noise and vibration. Magnetic particle inspection found no tooth-root or flank cracks.
The gear was a left-hand spiral bevel gear with a midpoint normal module of 5 mm, 41 teeth, a midpoint spiral angle of 37°, a large-end transverse module of 7.349 mm, and an accuracy grade of 7. Its production route was: blank forging, rough turning, normalizing, quenching and tempering, semi-finish turning, gear milling, carburizing and quenching, shot peening, finish turning, gear grinding, grinding-in, precision grinding of the journals, and final inspection. The technical requirements called for a surface hardness of 60–63 HRC, a core hardness of 30–40 HRC, and an effective carburized case depth of 1.0–1.4 mm.
Material and heat-treatment condition
The chemical composition of the tooth material complied with the 12CrNi3 limits of GB/T 3077—2015. The measured composition is compared with the standard range in the table below; all values are in mass percent.
| Element | C | S | Si | Mn | P | Cr | Ni |
|---|---|---|---|---|---|---|---|
| Measured | 0.16 | 0.004 | 0.24 | 0.35 | 0.007 | 0.82 | 2.930 |
| GB/T 3077—2015 range | 0.10–0.17 | ≤0.025 | 0.17–0.37 | 0.30–0.60 | ≤0.025 | 0.60–0.90 | 2.75–3.15 |
Nonmetallic inclusion ratings were also acceptable: type A 0.5, type B 0, type C 0, and type D 0.5 according to GB/T 10561—2023. The material and cleanliness therefore did not provide an initiation site for the observed failure.
The carburizing cycle consisted of a boost stage and a diffusion stage, followed by high-temperature tempering after air cooling to remove non-equilibrium structures formed near the surface. The parts were then quenched in fast bright quenching oil. Because the high nickel content raises austenite stability, a cryogenic treatment at −100 °C was used to increase the degree of martensitic transformation. A φ25 mm furnace coupon treated with the same cycle reached a surface hardness of 61.0–62.5 HRC and an effective case depth of 1.560 mm, both within the process specification. This coupon result confirmed that the carburizing cycle itself was capable of producing the required case. It did not represent the final ground tooth flank, where additional stock removal changed the case-depth distribution.
Hardness and case-depth results
Tooth-tip hardness was measured as a shop-floor surrogate for surface hardness because direct flank measurement is difficult on a bevel gear with varying module, hand, and tooth height. The measured tooth-tip values ranged from 60.2 to 62.5 HRC and thus met the 60–63 HRC requirement. This result did not, however, establish that the active flank after grinding retained the required case depth or near-surface hardness.
Effective case depth was measured from the surface toward the core under a load of 9.8 N, using 550 HV1 as the boundary. Two sectioned tooth blocks were taken at the 180° position, divided into small-end, middle, and large-end sections, and measured at the left and right pitch circles, the tooth roots, and the tooth grooves. The results are summarized below in millimetres.
| Specimen | Section | Left pitch | Left root | Groove | Right pitch | Right root |
|---|---|---|---|---|---|---|
| A | Small end | 0.757 | 0.115 | 0.290 | 0.659 | 0.226 |
| A | Middle | 0.967 | 0.202 | 0.294 | 0.830 | 0.205 |
| A | Large end | 0.655 | 0.118 | 0.259 | 0.565 | 0.227 |
| B | Small end | 0.983 | 0.333 | 0.478 | 0.810 | 0.236 |
| B | Middle | 0.738 | 0.153 | 0.309 | 1.047 | 0.255 |
| B | Large end | 0.880 | 0.318 | 0.416 | 0.924 | 0.310 |
Only one of the twelve pitch-circle measurements, 1.047 mm on the right tooth at the middle of specimen B, reached the lower specification limit of 1.0 mm. The remaining pitch values were 0.565–0.983 mm. The root values were far lower, ranging from 0.115 to 0.333 mm, and the groove values ranged from 0.259 to 0.478 mm.
The root criterion is especially important because the root fillet controls bending fatigue resistance. GB/T 38805—2020 requires the root case depth to be no less than two-thirds of the pitch-circle case depth. With a design pitch minimum of 1.0 mm, the minimum acceptable root case was therefore
$$h_{\text{root,min}} \ge \frac{2}{3}h_{\text{pitch,min}} = \frac{2}{3}(1.0\ \text{mm}) = 0.67\ \text{mm}.$$
The measured root case depths were less than half of this minimum, and the minimum value of 0.115 mm indicates that the root had lost nearly the entire effective case.
Microstructure and hardness gradient
Metallographic examination at the middle of specimen A showed a pitch-circle case consisting mainly of acicular and lath martensite with fine granular carbides and retained austenite. According to the rating charts of JB/T 6141.3—1992, the martensite plus retained austenite was grade 2 and the carbide was grade 1. The core consisted of lath martensite and bainite with small blocky undissolved ferrite at grain boundaries, giving a core rating of 3. The presence of undissolved ferrite suggests that the austenitizing or holding time was marginal, although the microstructure ratings did not indicate a gross carburizing defect. At the root arc, a distinct transition zone was visible; hardness indents spaced at 0.05 mm marked the gradient, and etching contrast near 0.20 mm reflected the microstructural change across the shallow root case.
The hardness gradient provides a direct explanation for the loss of flank performance. At 0.1 mm below the surface, the converted microhardness was below 60.0 HRC at all tested positions. At the left and right teeth of specimen A and the left tooth of specimen B, it was below 58.0 HRC. Even at the one pitch location that reached 1.047 mm case depth, where the zone with hardness of at least 57.0 HRC occupied about 50% of the case, the 0.1 mm hardness remained below the tooth-tip value. This is the characteristic signature of grinding through the hardest outer case into a lower-hardness inner region: total case depth decreases, and the functional surface is shifted to a less hard part of the gradient.
Grinding removal as the dominant cause
The gear-milling operation left a nominal grinding allowance of 0.30 mm per flank on the common normal. To achieve the specified tooth form after carburizing and quenching, however, the actual stock removal reached nearly 1.0 mm at the tooth groove, and the grinding-wheel and cutter geometry increased removal at the root. The nominal allowance therefore did not represent the real amount of case removed from the pitch circle, root, and groove.
This explains the apparent contradiction between the acceptable coupon and the unacceptable finished part. The coupon reached 1.560 mm case depth, but the finished pitch-circle values fell to 0.565–1.047 mm, and the root and groove values fell much lower. The loss was caused by mechanical removal of the case during grinding, not by a failure of the carburizing atmosphere. No grinding cracks were found, which is consistent with dimensional stock removal rather than cracking as the primary damage mode.
The consequences are different at the two critical locations. At the pitch circle, a thin case and reduced near-surface hardness lower contact fatigue resistance and allow local plastic deformation or wear under the high Hertzian pressure of a bevel gear mesh. At the root, where bending stress is highest, the near-complete loss of case removes the hard, wear-resistant layer and much of the beneficial compressive residual stress. The root result is therefore more severe than the pitch-circle result, even though the pitch-circle values are easier to compare with the drawing requirement.
Tooth geometry and contact pattern
Three single teeth spaced at 120° were measured on a Z6 gear measuring center, with both flanks inspected over five profile points and nine lead points. The maximum profile and lead deviations were −21.5, −19.6, and −20.6 μm, with a maximum absolute deviation of about 21.6 μm. These values complied with the grade 7 requirement of GB/T 11365—2019. A gross machining error large enough to displace the contact pattern would normally appear in these profile and lead traces; no such error was present.
The low contact position therefore points away from a simple grinding error and toward the theoretical tooth-profile parameters used at the design and simulation stage. If the conjugate flank curvature or the profile correction is defined incorrectly, the gear can meet its drawing tolerance and still place the contact ellipse too low on the tooth. The result is a contact patch that covers less than the required 40% of the tooth height and sits closer to the root, where the bending stress is highest. This design-stage profile error contributed to the abnormal contact pattern, while the grinding-induced case loss contributed to the abnormal noise and vibration.
Failure mechanism
The failure was not caused by a single metallurgical defect. The material composition, inclusion content, and case microstructure ratings were acceptable, and the carburizing cycle produced adequate case on a coupon. The dominant process failure was excessive grinding after carburization. The 0.30 mm nominal allowance was exceeded to the point that the pitch-circle case fell below 1.0 mm at eleven of twelve measurement positions, the root case fell to 0.115–0.333 mm, and the near-surface hardness at 0.1 mm dropped below 60.0 HRC. Tooth-tip hardness remained within specification because the tip did not represent the ground flank, so the shop-floor hardness check did not detect the loss of effective case.
Two effects then combined. First, the low contact patch reduced the effective contact area and concentrated load toward the root, increasing bending stress and altering the mesh stiffness cycle. Second, the thin and softened case at the pitch circle and root reduced the surface’s resistance to contact fatigue, plastic deformation, and wear. Under running load, these effects are consistent with the observed slight vibration and abnormal noise. The case-depth loss is the more direct material cause, while the design-stage tooth-profile error is the more direct geometric cause of the low contact position.
Corrective actions
Several changes follow directly from the measured case-depth distribution and the process chain.
- Restore case-depth margin before grinding. The boost and diffusion stages should each be extended by about 1–2 h, targeting a pre-grind pitch-circle case depth of at least 1.70 mm. With the intended 0.30 mm allowance, this provides margin above the 1.0 mm final lower limit. The target is only effective if actual stock removal is also brought back toward the nominal allowance; otherwise the additional case is simply ground away.
- Control actual grinding stock removal. The milling tooth form, heat-treatment distortion, and grinding-wheel profile should be reconciled so that removal at the pitch circle, root, and groove stays close to the designed allowance. The root and groove must be monitored separately because wheel geometry can remove much more material there than at the pitch circle.
- Adjust the austenitizing or holding time. The small blocky undissolved ferrite in the core indicates incomplete homogenization and supports a moderate extension of the holding time before quenching.
- Correct the design-stage tooth-profile parameters. The theoretical flank curvature and profile correction should be rechecked against the intended contact pattern, and the corrected design should be verified by a contact-pattern test rather than by profile and lead tolerances alone.
- Replace tooth-tip hardness as the sole acceptance check. For carburized and ground bevel gears, flank case-depth and near-surface hardness audits at the pitch circle, root, and groove are needed on representative sectioned parts. Tooth-tip hardness can remain a supplementary check, but it cannot confirm that the active flank has retained its case.
The broader lesson is that a carburized spiral bevel gear can pass material, microstructure, and tooth-tip hardness checks while its functional flank has been weakened by grinding. Effective process control must connect the carburizing case depth, the actual grinding allowance, and the design-stage contact pattern. When those three elements are not reconciled, a gear that meets its drawing tolerances can still develop a low contact patch and a case too thin to support the intended load.