As an internal gear manufacturer, we often encounter challenges in maintaining gear accuracy after heat treatment. Internal gears are critical components in various heavy-duty applications such as wind turbines, drilling platforms, and planetary gear systems. The precision of these internal gears directly impacts the performance and longevity of the entire mechanical system. In this study, we address the issue of common normal line deviation in internal gears after quenching treatment, which is a common problem faced by internal gear manufacturers worldwide.
The manufacturing of high-precision internal gears requires sophisticated processes to ensure dimensional stability. Traditional methods like gear hobbing and shaping are commonly used, but they often necessitate additional finishing operations such as grinding or honing to achieve the required accuracy. These supplementary processes increase production time and cost, making them less desirable for industrial-scale manufacturing. As an internal gear manufacturer, we sought to develop a more efficient approach that minimizes post-quenching deviations while maintaining cost-effectiveness.
Our research focuses on the precision machining of internal gears before quenching, specifically targeting the compensation of common normal line deviations. The common normal line represents the shortest distance between two parallel planes tangent to opposite tooth profiles, and its accuracy is crucial for proper gear meshing and power transmission. Through extensive testing and analysis, we discovered that differential shrinkage during quenching between the mounting and non-mounting surfaces causes significant deviations in the common normal line length.
Conventional Internal Gear Manufacturing Process
In standard internal gear manufacturing processes, the gear blank undergoes rough turning, finish turning, gear cutting (typically by shaping or hobbing), and finally quenching treatment. The conventional approach maintains parallel alignment between the tool spindle and machine spindle, resulting in equal feed rates for both mounting and non-mounting surfaces. This produces internal gears with theoretically identical common normal line lengths on both surfaces before quenching.
The mathematical relationship between feed rate and common normal line length can be expressed as follows. Consider the gear geometry where the radial feed increment directly affects the common normal line measurement. For a standard pressure angle of 20°, the relationship between feed increment (t) and common normal line difference (L₁ – L) is given by:
$$ \frac{L_1 – L}{2} = t \sin\alpha $$
Where α represents the pressure angle. Rearranging this equation gives us:
$$ t = \frac{L_1 – L}{2 \sin\alpha} = \frac{L_1 – L}{2 \sin 20^\circ} = \frac{L_1 – L}{0.684} \approx 1.46(L_1 – L) $$
This fundamental relationship forms the basis for our compensation strategy. The coefficient of 1.46 indicates that the required feed difference is approximately 1.46 times the desired common normal line difference.
To quantify the problem, we conducted measurements on internal gears produced using conventional methods. The following table shows the common normal line measurements before and after quenching for three sample gears:
| Measurement Location | Sample 1 Before Quenching (mm) | Sample 1 After Quenching (mm) | Sample 1 Variation (mm) | Sample 2 Before Quenching (mm) | Sample 2 After Quenching (mm) | Sample 2 Variation (mm) | Sample 3 Before Quenching (mm) | Sample 3 After Quenching (mm) | Sample 3 Variation (mm) |
|---|---|---|---|---|---|---|---|---|---|
| Mounting Surface Common Normal | 759.42 | 759.26 | 0.16 | 759.42 | 759.28 | 0.14 | 759.44 | 759.26 | 0.18 |
| Mounting Surface Common Normal | 759.42 | 759.24 | 0.18 | 759.44 | 759.26 | 0.18 | 759.48 | 759.30 | 0.18 |
| Mounting Surface Common Normal | 759.38 | 759.28 | 0.10 | 759.38 | 759.24 | 0.14 | 759.46 | 759.28 | 0.18 |
| Mounting Surface Common Normal | 759.40 | 759.22 | 0.18 | 759.38 | 759.24 | 0.14 | 759.44 | 759.24 | 0.20 |
| Non-Mounting Surface Common Normal | 759.42 | 759.14 | 0.28 | 759.42 | 759.14 | 0.28 | 759.44 | 759.14 | 0.30 |
| Non-Mounting Surface Common Normal | 759.42 | 759.16 | 0.26 | 759.42 | 759.14 | 0.28 | 759.46 | 759.18 | 0.28 |
| Non-Mounting Surface Common Normal | 759.38 | 759.14 | 0.24 | 759.38 | 759.12 | 0.26 | 759.42 | 759.16 | 0.26 |
| Non-Mounting Surface Common Normal | 759.38 | 759.12 | 0.26 | 759.40 | 759.14 | 0.26 | 759.42 | 759.16 | 0.26 |
The accuracy requirement specified a common normal line length between 759.21 mm and 759.33 mm. While the mounting surface measurements after quenching fell within this range (759.22-759.30 mm), the non-mounting surface measurements (759.12-759.18 mm) failed to meet the specification. This discrepancy arises from differential thermal contraction during quenching – the non-mounting surface, being smaller in diameter, experiences greater constraint resistance to contraction compared to the mounting surface, resulting in uneven shrinkage.
Improved Pre-Quenching Machining Methodology
To address this challenge, we developed an improved machining strategy that incorporates differential feed rates between mounting and non-mounting surfaces. The fundamental principle involves tilting the tool spindle relative to the machine spindle at a specific angle β, creating a controlled difference in common normal line lengths before quenching. This pre-compensation strategy accounts for the anticipated differential shrinkage during subsequent heat treatment.
The mathematical foundation for this approach builds upon the established relationship between feed rate and common normal line length. The required feed difference (Δt) between non-mounting and mounting surfaces can be calculated based on the observed difference in shrinkage (Δx). From our experimental data, the minimum mounting surface variation was 0.18 mm, while the maximum non-mounting surface variation was 0.30 mm, giving us Δx = 0.12 mm. Applying our derived formula:
$$ \Delta t = 1.46 \times \Delta x = 1.46 \times 0.12 = 0.1752 \text{ mm} $$
The tilt angle β can then be determined using basic trigonometric relationships with the gear height H₁:
$$ \beta = \arctan\left(\frac{0.1752}{H_1}\right) $$
This calculated angle ensures that the non-mounting surface receives greater material removal during machining, creating a longer common normal line that will shrink to the desired specification after quenching. This innovative approach represents a significant advancement in internal gear manufacturing methodology.
Experimental Verification of Improved Process
We implemented our improved manufacturing strategy using two distinct methods to verify its effectiveness across different machining platforms. Both approaches aimed to create the necessary differential in common normal line lengths before quenching to compensate for uneven shrinkage.
Conventional Gear Shaper with Spindle Adjustment
The first implementation utilized a standard gear shaper with modified spindle orientation. By adjusting the tool spindle to create the calculated angle β relative to the machine spindle, we achieved differential feed rates between mounting and non-mounting surfaces. The adjustment mechanism involved modifying the distance between the rotation handle and cam center, which tilts the tool holder accordingly.
After implementing this adjustment and processing sample internal gears, we obtained the following measurement results:
| Measurement Location | Sample 1 Before Quenching (mm) | Sample 1 After Quenching (mm) | Sample 1 Variation (mm) | Sample 2 Before Quenching (mm) | Sample 2 After Quenching (mm) | Sample 2 Variation (mm) | Sample 3 Before Quenching (mm) | Sample 3 After Quenching (mm) | Sample 3 Variation (mm) |
|---|---|---|---|---|---|---|---|---|---|
| Mounting Surface Common Normal | 759.42 | 759.26 | 0.16 | 759.42 | 759.28 | 0.14 | 759.44 | 759.26 | 0.18 |
| Mounting Surface Common Normal | 759.44 | 759.28 | 0.16 | 759.44 | 759.26 | 0.18 | 759.46 | 759.30 | 0.16 |
| Mounting Surface Common Normal | 759.40 | 759.28 | 0.12 | 759.38 | 759.24 | 0.14 | 759.46 | 759.28 | 0.18 |
| Mounting Surface Common Normal | 759.42 | 759.26 | 0.16 | 759.38 | 759.24 | 0.14 | 759.44 | 759.24 | 0.20 |
| Non-Mounting Surface Common Normal | 759.60 | 759.28 | 0.32 | 759.60 | 759.26 | 0.34 | 759.62 | 759.30 | 0.32 |
| Non-Mounting Surface Common Normal | 759.62 | 759.30 | 0.32 | 759.62 | 759.28 | 0.34 | 759.64 | 759.32 | 0.32 |
| Non-Mounting Surface Common Normal | 759.58 | 759.26 | 0.32 | 759.60 | 759.24 | 0.36 | 759.64 | 759.28 | 0.36 |
| Non-Mounting Surface Common Normal | 759.60 | 759.30 | 0.30 | 759.60 | 759.26 | 0.34 | 759.62 | 759.30 | 0.32 |
The results clearly demonstrate that all measured common normal line lengths after quenching (759.24-759.32 mm) now fall within the specified accuracy range. The pre-quenching differential successfully compensated for the uneven shrinkage, validating our improved methodology for internal gear manufacturing.
Form Milling Machine with Tapered Tooth Program
The second implementation employed a form milling machine with specialized programming to create the required common normal line differential. We utilized a tapered tooth processing program with modified tooth direction and root taper parameters. Specifically, we set the non-mounting surface tooth direction taper to zero and the mounting surface root taper to 1:243, effectively creating the necessary angle β between the tool spindle and machine spindle.
The measurement results from internal gears produced using this method are presented below:
| Measurement Location | Sample 1 Before Quenching (mm) | Sample 1 After Quenching (mm) | Sample 1 Variation (mm) | Sample 2 Before Quenching (mm) | Sample 2 After Quenching (mm) | Sample 2 Variation (mm) | Sample 3 Before Quenching (mm) | Sample 3 After Quenching (mm) | Sample 3 Variation (mm) |
|---|---|---|---|---|---|---|---|---|---|
| Mounting Surface Common Normal | 759.44 | 759.28 | 0.16 | 759.40 | 759.26 | 0.14 | 759.46 | 759.26 | 0.20 |
| Mounting Surface Common Normal | 759.46 | 759.30 | 0.16 | 759.38 | 759.24 | 0.14 | 759.44 | 759.30 | 0.14 |
| Mounting Surface Common Normal | 759.44 | 759.26 | 0.18 | 759.36 | 759.22 | 0.14 | 759.46 | 759.28 | 0.18 |
| Mounting Surface Common Normal | 759.42 | 759.26 | 0.16 | 759.38 | 759.24 | 0.14 | 759.44 | 759.24 | 0.20 |
| Non-Mounting Surface Common Normal | 759.62 | 759.30 | 0.32 | 759.58 | 759.26 | 0.32 | 759.64 | 759.30 | 0.34 |
| Non-Mounting Surface Common Normal | 759.64 | 759.32 | 0.32 | 759.56 | 759.26 | 0.30 | 759.62 | 759.32 | 0.30 |
| Non-Mounting Surface Common Normal | 759.62 | 759.28 | 0.34 | 759.54 | 759.22 | 0.32 | 759.64 | 759.28 | 0.36 |
| Non-Mounting Surface Common Normal | 759.60 | 759.26 | 0.34 | 759.58 | 759.26 | 0.32 | 759.62 | 759.30 | 0.32 |
These results confirm that the form milling implementation also successfully produced internal gears meeting the accuracy specifications after quenching, with all common normal line measurements falling between 759.22 mm and 759.32 mm. The consistency across both manufacturing methods demonstrates the robustness of our improved approach for internal gear production.
Comprehensive Analysis and Discussion
The successful implementation of our improved manufacturing process highlights several important aspects of internal gear production. The fundamental relationship between feed rate and common normal line length provides a mathematical foundation for precision compensation. For internal gear manufacturers, this relationship can be generalized as:
$$ t = k(L_1 – L) $$
Where k represents a gear-specific constant derived from the pressure angle and gear geometry. For standard 20° pressure angle gears, k ≈ 1.46 as established in our research. However, this constant may vary for different gear specifications, and internal gear manufacturers should calculate the appropriate value for their specific applications.
The thermal behavior during quenching plays a crucial role in the differential shrinkage observed in internal gears. The non-mounting surface, typically having smaller dimensions, experiences different cooling rates and constraint conditions compared to the mounting surface. This differential thermal response creates uneven contraction that must be anticipated and compensated during machining. Our approach effectively addresses this fundamental challenge in internal gear manufacturing.
For internal gear manufacturers implementing this methodology, several practical considerations emerge. The accuracy of the spindle angle adjustment directly impacts the effectiveness of compensation. Precise calibration using dial indicators and test bars is essential to achieve the required angular alignment. Additionally, the stability of the machining setup must be maintained throughout the production process to ensure consistent results.
The versatility of our approach allows implementation across different machining platforms, as demonstrated by our successful trials with both gear shapers and form milling machines. This flexibility makes the methodology accessible to various internal gear manufacturers regardless of their specific equipment configurations. The programming modifications required for form milling machines represent a software-based solution that can be easily integrated into existing manufacturing processes.
Conclusion and Industrial Implications
Our research demonstrates that implementing differential feed rates between mounting and non-mounting surfaces during pre-quenching machining effectively compensates for common normal line deviations in internal gears after heat treatment. The mathematical relationship between feed increment and common normal line difference provides a precise foundation for calculating the required compensation parameters.
The successful verification using both conventional gear shapers with spindle adjustment and form milling machines with tapered tooth programming confirms the methodology’s effectiveness across different manufacturing platforms. All tested internal gears produced using our improved process met the specified accuracy requirements after quenching, with common normal line measurements consistently falling within the acceptable range of 759.21-759.33 mm.
For internal gear manufacturers, this research offers significant practical benefits. The improved process eliminates the need for additional finishing operations after quenching, reducing production time and cost while maintaining high precision. The methodology can be readily implemented using existing equipment with minimal modifications, making it accessible to manufacturers of various scales.
The principles established in this study can be extended to other gear types and manufacturing scenarios where differential thermal effects impact dimensional accuracy. Internal gear manufacturers can adapt the fundamental compensation approach to address similar challenges in their specific applications, potentially expanding beyond common normal line compensation to other critical gear parameters.
In conclusion, our research provides internal gear manufacturers with an effective and precise approach to producing high-quality hardened internal gears. By incorporating pre-quenching compensation based on mathematical relationships between machining parameters and gear geometry, manufacturers can achieve consistent accuracy while optimizing production efficiency. This advancement represents a significant contribution to the field of precision gear manufacturing and offers practical solutions to longstanding challenges in internal gear production.