In internal gear power honing processes, residual stress generated on workpiece surfaces critically impacts gear fatigue strength and operational reliability. This study establishes a comprehensive methodology combining parametric modeling, dynamic simulation, and experimental validation to analyze residual stress distribution under varying honing parameters. The workflow integrates MATLAB for geometric modeling, SolidWorks for 3D reconstruction, and ANSYS/LS-DYNA for finite element analysis, providing insights into how honing parameters influence residual stress formation.
Parametric Modeling of Internal Honing Wheel
Mathematical representation of gear tooth surfaces forms the foundation for accurate simulation. For external helical workpieces, the tooth surface coordinates in the workpiece coordinate system are defined as:
$$
\begin{cases}
x_1 = r_{b1} \cos(\sigma_0 + \theta + \lambda) + r_{b1} \lambda \sin(\sigma_0 + \theta + \lambda) \\
y_1 = r_{b1} \sin(\sigma_0 + \theta + \lambda) – r_{b1} \lambda \cos(\sigma_0 + \theta + \lambda) \\
z_1 = \theta p
\end{cases}
$$
where $r_{b1}$ is base circle radius, $\sigma_0$ denotes tooth surface starting angle, $\theta$ represents helix increment angle, $p$ is workpiece lead, and $\lambda$ signifies involute increment angle. Coordinate transformation yields the internal honing wheel’s tooth surface equation:
$$
\begin{cases}
x_2 = x_1(\cos\phi_1\cos\phi_2 + \sin\phi_1\sin\phi_2\cos\Sigma) + \\
\ \ \ \ y_1(-\sin\phi_1\cos\phi_2 + \cos\phi_1\sin\phi_2\cos\Sigma) + \\
\ \ \ \ z_1\sin\phi_2\sin\Sigma + a\cos\phi_2 \\
y_2 = x_1(-\cos\phi_1\sin\phi_2 + \sin\phi_1\cos\phi_2\cos\Sigma) + \\
\ \ \ \ y_1(\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Sigma) + \\
\ \ \ \ z_1\cos\phi_2\sin\Sigma – a\sin\phi_2 \\
z_2 = -x_1\sin\phi_1\sin\Sigma – y_1\cos\phi_1\sin\Sigma + z_1\cos\Sigma
\end{cases}
$$
Using the gear parameters in Table 1, MATLAB generates discrete data points mapped to the honing wheel’s tooth surface. SolidWorks converts these points into 3D geometry through surface lofting, creating the complete internal gear power honing model.
| Component | Parameter | Value |
|---|---|---|
| Common Parameters | Module (mm) | 2.25 |
| Normal Pressure Angle (°) | 17.5 | |
| Number of Teeth | 73 | |
| Workpiece Gear | Helix Angle (°) | 33 |
| Face Width (mm) | 27 | |
| Honing Wheel | Number of Teeth | 123 |
| Helix Angle (°) | 41.722 | |
| Face Width (mm) | 30 |
Honing Force Mechanics
During internal gear power honing, three-dimensional force decomposition occurs along tangential ($F_s$), radial ($F_r$), and axial ($F_n$) directions:
$$
\begin{cases}
F_r = F_a \cos\beta \tan\alpha_t \\
F_s = F_a \sin\alpha_n \\
F_n = F_a \cos\beta
\end{cases}
$$
where $F_a$ is resultant honing force, $\beta$ represents workpiece helix angle, and $\alpha_n$ denotes normal pressure angle. Radial force magnitude serves as the primary process control parameter in gear honing operations.
Finite Element Simulation Methodology
Dynamic simulation of the gear honing process requires accurate material definitions and contact physics. The material properties for simulation are defined as:
| Component | Density (kg/m³) | Elastic Modulus (GPa) | Poisson’s Ratio |
|---|---|---|---|
| Workpiece (20CrMnTi) | 7,800 | 207 | 0.25 |
| Honing Wheel (Microcrystalline Corundum) | 3,120 | 70 | 0.07 |
The simulation incorporates automatic surface-to-surface contact with static and dynamic friction coefficients of 0.35 and 0.40, respectively. Residual stress calculation follows a two-step approach: first, obtaining equivalent stress distribution under honing loads, then solving residual stresses after load removal using the initial stress field. The equivalent stress formulation is:
$$
\sigma = \sqrt{\frac{1}{2} \left[ (\sigma_{11} – \sigma_{22})^2 + (\sigma_{22} – \sigma_{33})^2 + (\sigma_{33} – \sigma_{11})^2 + 6(\sigma_{12}^2 + \sigma_{23}^2 + \sigma_{31}^2) \right]}
$$
Residual Stress Analysis
Simulation results demonstrate consistent compressive residual stresses across all tooth surface positions. Parameter studies reveal three key relationships in gear honing operations:
1. Honing Speed Effect: Residual stress decreases with increasing rotational speed (Figure 1). Higher speeds reduce abrasive-workpiece contact duration, diminishing plastic deformation depth.
| Node | 60.08 rad/s (MPa) | 90.12 rad/s (MPa) | 120.16 rad/s (MPa) | 150.20 rad/s (MPa) | 180.24 rad/s (MPa) |
|---|---|---|---|---|---|
| 56621 | -725 | -550 | -490 | -420 | -385 |
| 56586 | -450 | -362 | -325 | -295 | -255 |
| 56606 | -1320 | -1200 | -1075 | -925 | -850 |
2. Radial Force Effect: Residual stress magnitude increases proportionally with radial honing force (Figure 2). Higher forces intensify abrasive penetration depth and plastic deformation.
| Node | 150N (MPa) | 300N (MPa) | 450N (MPa) | 600N (MPa) | 750N (MPa) | 1000N (MPa) |
|---|---|---|---|---|---|---|
| 56621 | -550 | -610 | -705 | -850 | -940 | -1085 |
| 56586 | -362 | -410 | -485 | -555 | -625 | -745 |
| 56606 | -1200 | -1390 | -1550 | -1735 | -1920 | -2250 |
3. Shaft Angle Effect: Residual stress decreases with increasing shaft intersection angle (5-16° range). Larger shaft angles reduce normal force components while increasing sliding velocity.
| Node | 8° (MPa) | 10° (MPa) | 12° (MPa) | 14° (MPa) | 16° (MPa) |
|---|---|---|---|---|---|
| 56621 | -550 | -510 | -465 | -420 | -375 |
| 56586 | -362 | -340 | -315 | -290 | -265 |
| 56606 | -1200 | -1105 | -1010 | -915 | -820 |
Experimental Validation
X-ray diffraction measurements using a Rigaku D/MAX 2550 diffractometer (Cu-Kα radiation, λ=0.15406nm) validate simulation results. The gear honing parameters for test specimens match simulation conditions: shaft angle 8.722°, workpiece speed 90.12 rad/s, honing wheel speed 151.67 rad/s, and radial force 150N. Measurement positions correspond to simulation nodes with maximum error of 13.6% (Table 6), confirming model accuracy for gear honing residual stress prediction.
| Node | Simulation (MPa) | Experiment (MPa) | Error (%) |
|---|---|---|---|
| 56621 | -550 | -625 | 13.6 |
| 56586 | -362 | -367 | 1.4 |
| 56606 | -1200 | -1152 | 4.2 |
| 56926 | -950 | -1074 | 13.1 |
| 56326 | -605 | -684 | 13.1 |
| 55286 | -510 | -572 | 12.2 |
Conclusions
This investigation establishes that internal gear power honing consistently generates compressive residual stresses on workpiece surfaces. The magnitude demonstrates parametric dependencies: residual stress decreases with higher honing speeds (reduced contact duration), increases with radial force (greater plastic deformation), and decreases with larger shaft angles (altered force vectors). The integrated simulation approach combining MATLAB, SolidWorks, and ANSYS/LS-DYNA predicts residual stress distributions with maximum 13.6% deviation from experimental measurements. These findings enable optimized gear honing parameter selection for desired residual stress profiles, enhancing gear fatigue performance while minimizing experimental iterations. Future work will investigate abrasive grain geometry effects and develop multi-objective optimization algorithms for precision gear honing applications.