In our production of wind turbine gearbox sun gears, we encountered significant issues with uneven grinding allowances and surface hardness on the tooth surfaces after heat treatment. This problem led to micro-steps at the tooth roots and unground areas in the middle section, resulting in out-of-tolerance conditions and reduced product lifespan. Through detailed data analysis and process experimentation, we implemented a gear hobbing modification technique to compensate for thermal distortions during heat treatment. This approach leverages advanced capabilities of modern gear hobbing machines to introduce tooth profile crowning during the hobbing process, effectively counteracting deformation and improving product quality.
The sun gear in question is manufactured from 18CrNiMo7-6 steel, with a module of 15 mm, 24 teeth, a pressure angle of 25°, and a tooth width of 388 mm. The required carburizing and quenching process aims for a tooth surface hardness of 58-62 HRC and an effective hardened case depth of 2.5-3.0 mm. The original process route included forging, rough and semi-finish turning, ultrasonic testing, gear hobbing, heat treatment, finish machining, deep hole drilling, outer diameter grinding, spline rolling, and finally gear grinding. However, post-heat treatment distortions caused inconsistent grinding allowances along the tooth width, leading to the aforementioned defects.
To quantify the problem, we measured the base tangent length (over 4 teeth, denoted as W4) at various positions along the tooth width after heat treatment. The data, collected at 15 mm intervals from the tooth end, with three points per circumferential section, revealed a saddle-shaped distortion pattern. The ends exhibited expansion, while the middle section contracted significantly. The maximum difference in W4 between the highest and lowest points was 0.51 mm, indicating a single-side variation of approximately 0.26 mm. This non-uniformity directly affected the grinding process and final product properties.
| Measurement Position (mm from end) | Circumferential Point 1 | Circumferential Point 2 | Circumferential Point 3 | Average |
|---|---|---|---|---|
| 15 | 164.35 | 164.34 | 164.35 | 164.35 |
| 65 | 164.20 | 164.22 | 164.23 | 164.22 |
| 115 | 164.04 | 164.04 | 164.04 | 164.04 |
| 165 | 163.94 | 163.93 | 163.91 | 163.93 |
| 215 | 163.89 | 163.88 | 163.84 | 163.87 |
| 265 | 163.95 | 163.92 | 163.90 | 163.92 |
| 315 | 164.05 | 164.03 | 164.00 | 164.03 |
| 365 | 164.14 | 164.11 | 164.10 | 164.12 |
The grinding allowance data before gear grinding further confirmed the uneven distribution. Measurements taken at upper, middle, and lower sections along the tooth height and width showed variations up to 0.06 mm in some areas, with the middle tooth width having insufficient material for grinding. This inconsistency not only caused visual defects but also led to non-uniform surface hardness and case depth, compromising the gear’s contact strength, load capacity, and fatigue life.
Heat treatment distortions primarily arise from thermal and transformational stresses. For shaft-like components such as sun gears, transformational stresses dominate due to the smaller controlling cross-section. The transformation to martensite, which has a larger specific volume, causes expansion. However, the ends, with lower heat capacity, transform more completely to martensite, leading to greater expansion compared to the middle section. This results in the characteristic saddle shape. The stress-induced deformation can be modeled using principles of thermal elasticity and phase transformation kinetics. The total strain during quenching can be expressed as:
$$ \epsilon_{total} = \epsilon_{thermal} + \epsilon_{transform} + \epsilon_{plastic} $$
where $\epsilon_{thermal}$ is the thermal strain due to temperature gradients, $\epsilon_{transform}$ is the strain from phase transformations, and $\epsilon_{plastic}$ is the plastic strain. For martensitic transformation, the volumetric strain is proportional to the fraction of martensite formed, which is a function of cooling rate and composition. The resulting distortion pattern aligns with our observations.
To address this, we evaluated several improvement strategies. Adding process extensions to the gear ends could reduce distortion by increasing thermal mass, but it raised material and machining costs. Simply increasing the grinding allowance universally exacerbated the root step and hardness non-uniformity issues. Therefore, we focused on utilizing the gear hobbing machine to introduce a compensatory crown during the hobbing process. This method involves modifying the tooth profile along the width to offset the anticipated heat treatment distortion, ensuring a more uniform grinding allowance post-treatment.
The gear hobbing process was performed on a CNC gear hobbing machine capable of profile modifications. Based on the distortion data, we determined that the maximum contraction occurred approximately 215 mm from the tooth end, with a single-side reduction of about 0.15 mm. To compensate, we programmed a symmetrical crown over a virtual tooth width of 430 mm (to account for the asymmetric distortion pattern) with a total crown amount of 0.15 mm. The crown profile was designed to be parabolic, defined by the equation:
$$ y(x) = C \left(1 – \left(\frac{2x}{L}\right)^2\right) $$
where $y(x)$ is the deviation from the nominal profile at position $x$ along the tooth width, $C$ is the maximum crown amount (0.075 mm per side for a total of 0.15 mm), and $L$ is the virtual tooth width (430 mm). This profile ensures that the post-heat treatment base tangent length becomes more uniform after grinding.
After implementing the crown modification in the gear hobbing process, we measured the base tangent length before heat treatment. The data confirmed the successful application of the crown, with the middle section having a larger W4 compared to the ends, as intended. The gear hobbing machine executed the profile accurately, demonstrating the precision achievable with modern CNC controls.
| Measurement Position (mm from end) | Circumferential Point 1 | Circumferential Point 2 | Circumferential Point 3 | Average |
|---|---|---|---|---|
| 15 | 164.19 | 164.20 | 164.19 | 164.19 |
| 65 | 164.22 | 164.23 | 164.23 | 164.23 |
| 115 | 164.26 | 164.26 | 164.25 | 164.26 |
| 165 | 164.29 | 164.29 | 164.29 | 164.29 |
| 215 | 164.33 | 164.33 | 164.33 | 164.33 |
| 265 | 164.28 | 164.29 | 164.29 | 164.29 |
| 315 | 164.24 | 164.24 | 164.24 | 164.24 |
| 365 | 164.19 | 164.20 | 164.20 | 164.20 |
Post-heat treatment measurements showed a significant improvement in uniformity. The maximum difference in W4 reduced to 0.14 mm, with a single-side variation of only 0.07 mm. The grinding allowances became more consistent, as evidenced by the alignment data before gear grinding. The use of the gear hobbing machine for this compensatory crowning proved highly effective in neutralizing the thermal distortions.
| Section | Position | Tooth 1 Left | Tooth 1 Right | Tooth 2 Left | Tooth 2 Right | Tooth 3 Left | Tooth 3 Right | Tooth 4 Left | Tooth 4 Right |
|---|---|---|---|---|---|---|---|---|---|
| Upper | Inner | 36 | 24 | 35 | 40 | 39 | 40 | 41 | 22 |
| Middle | 37 | 26 | 34 | 38 | 37 | 35 | 38 | 26 | |
| Outer | 36 | 27 | 35 | 36 | 38 | 30 | 36 | 30 | |
| Middle | Inner | 33 | 32 | 31 | 33 | 33 | 26 | 25 | 28 |
| Middle | 25 | 25 | 21 | 27 | 20 | 20 | 18 | 16 | |
| Outer | 22 | 21 | 16 | 24 | 18 | 16 | 17 | 20 | |
| Lower | Inner | 28 | 31 | 23 | 32 | 28 | 33 | 28 | 29 |
| Middle | 28 | 27 | 18 | 30 | 22 | 29 | 21 | 28 | |
| Outer | 25 | 22 | 20 | 28 | 19 | 23 | 18 | 25 |
The improved uniformity in grinding allowances led to consistent surface hardness and case depth after gear grinding. Hardness gradient tests showed that at a depth of 0.15 mm, the hardness was 666 HV (58.5 HRC), and at 0.3 mm, it was 660 HV (58.2 HRC), both within the specified range. This eliminated the previous issues of soft spots and non-uniform hardening. Additionally, the gear grinding time reduced from 3.6 hours to 2.6 hours, a 38% efficiency gain, due to the more predictable and even material removal.
The success of this gear hobbing-based compensation method hinges on the accurate prediction of heat treatment distortions and the precise execution of the crown profile. The relationship between the crown amount and the expected distortion can be refined using empirical data and finite element analysis. For instance, the required crown $C$ can be estimated as:
$$ C = k \cdot \Delta D $$
where $\Delta D$ is the maximum single-side distortion observed, and $k$ is a correction factor (typically between 0.8 and 1.2) derived from historical data. In our case, with $\Delta D = 0.15$ mm, we used $k=1.0$ initially and adjusted based on results.
This process improvement has been successfully applied to other shaft-like gears, especially those with slender profiles and tooth widths exceeding 300 mm. The gear hobbing machine’s flexibility allows for easy implementation of various crown profiles, making it a versatile solution for managing thermal distortions. By integrating this approach into our standard practice, we have enhanced product quality, reduced scrap rates, and extended the service life of critical components.
In conclusion, the use of gear hobbing modifications to compensate for heat treatment distortions represents a significant advancement in gear manufacturing. It addresses the root cause of uneven grinding allowances and hardness distribution without adding cost or complexity. The gear hobbing machine plays a pivotal role in this strategy, enabling precise profile control that directly counteracts thermal effects. Future work could focus on optimizing the crown profiles for different gear geometries and materials, further leveraging the capabilities of modern gear hobbing technology.