Internal gears are critical components in automotive transmission systems, and enhancing their surface quality is essential for reducing vibration, noise, and improving operational stability. As an internal gear manufacturer, we often face challenges in achieving high-precision surfaces through conventional methods like manual polishing, which can lead to issues such as tooth surface burning, reduced bending strength, and environmental concerns due to waste fluid disposal. Traditional machining of internal gears involves high costs, significant noise, and potential deformation, making it less efficient. To address these limitations, we explore abrasive flow machining (AFM), a advanced polishing technique that utilizes a solid-liquid two-phase flow to finish surfaces efficiently. This method offers advantages like shorter processing times, reusability of abrasive media, low noise, and uniform surface quality. In this article, I present the design and analysis of a specialized fixture for polishing internal gear tooth surfaces using AFM, focusing on numerical simulations to optimize performance. The fixture ensures precise alignment and flow guidance, enabling uniform material removal and enhanced surface geometry for internal gears. Through finite element analysis and fluid dynamics simulations, I evaluate the fixture’s structural integrity and flow characteristics under various inlet pressures, providing insights for internal gear manufacturers aiming to improve product longevity and reduce costs.
The abrasive flow machining process relies on a viscoelastic medium carrying abrasive particles, which is forced under pressure to flow reciprocally across the workpiece surface. For internal gears, this requires a fixture that securely holds the gear and directs the abrasive flow through the tooth gaps. The designed fixture, as illustrated in the context, comprises several key components: a cover plate, screws, upper and lower conical surfaces, a workpiece meshing gear plate, seals, a base plate, and support cylinders. The cover plate interfaces with the upper abrasive cylinder of the AFM machine, while the base plate connects to the lower cylinder. The conical surfaces guide the flow direction, increasing the abrasive force and processing efficiency. The workpiece meshing gear plate ensures uniform间隙 with the internal gear, promoting even abrasive distribution. Seals prevent leakage, and support cylinders enhance rigidity. This design facilitates the flow of abrasive media through the internal gear tooth surfaces, enabling effective polishing. As an internal gear manufacturer, we prioritize fixtures that maintain alignment and withstand operational stresses, which is crucial for achieving consistent results in internal gears production.
To assess the fixture’s reliability, I conducted a static structural analysis using finite element methods. Assuming the AFM machine’s rated pressure is applied uniformly, the analysis focused on overall deformation and stress distribution. The results indicate a maximum deformation of $$5.123 \times 10^{-7} \, \text{mm}$$, which is negligible and ensures that the fixture maintains precision during polishing. The stress analysis revealed minimal stress concentrations in the internal gear workpiece, confirming that the fixture meets strength requirements without compromising the gear’s integrity. This is vital for internal gear manufacturers, as any deformation could lead to inaccuracies in the final product. The deformation and stress values are summarized in the table below, highlighting the fixture’s robustness under typical operating conditions.
| Parameter | Value |
|---|---|
| Maximum Deformation | $$5.123 \times 10^{-7} \, \text{mm}$$ |
| Maximum Stress | Negligible (below yield strength) |
For the fluid analysis, I modeled the flow channel between the internal gear and the meshing gear plate, employing a structured grid for numerical simulations. The solver used was an implicit coupled approach with double precision, and the turbulence model selected was the standard k-epsilon (2eqn) model with standard wall functions. The primary phase was hydraulic oil, and the secondary phase was silicon carbide particles with a volume fraction of 0.2. Boundary conditions included pressure inlet and free outflow, with walls defined as fixed. Gravity was neglected to simplify the analysis. The governing equations for the solid-liquid two-phase flow include the continuity and momentum equations, expressed as:
Continuity equation: $$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0$$
Momentum equation: $$\frac{\partial (\rho \mathbf{v})}{\partial t} + \nabla \cdot (\rho \mathbf{v} \mathbf{v}) = -\nabla P + \nabla \cdot \mathbf{\tau} + \mathbf{F}$$
where $$\rho$$ is the density, $$\mathbf{v}$$ is the velocity vector, $$P$$ is the pressure, $$\mathbf{\tau}$$ is the stress tensor, and $$\mathbf{F}$$ represents body forces. For turbulence, the k-epsilon model involves:
Turbulent kinetic energy (k): $$\frac{\partial (\rho k)}{\partial t} + \nabla \cdot (\rho k \mathbf{v}) = \nabla \cdot \left[ \left( \mu + \frac{\mu_t}{\sigma_k} \right) \nabla k \right] + G_k – \rho \epsilon$$
Dissipation rate (ε): $$\frac{\partial (\rho \epsilon)}{\partial t} + \nabla \cdot (\rho \epsilon \mathbf{v}) = \nabla \cdot \left[ \left( \mu + \frac{\mu_t}{\sigma_\epsilon} \right) \nabla \epsilon \right] + C_{1\epsilon} \frac{\epsilon}{k} G_k – C_{2\epsilon} \rho \frac{\epsilon^2}{k}$$
Here, $$\mu_t$$ is the turbulent viscosity, calculated as $$\mu_t = \rho C_\mu \frac{k^2}{\epsilon}$$, with $$C_\mu$$, $$\sigma_k$$, $$\sigma_\epsilon$$, $$C_{1\epsilon}$$, and $$C_{2\epsilon}$$ as model constants. $$G_k$$ represents the generation of turbulent kinetic energy due to mean velocity gradients.
In the steady-state pressure analysis, I simulated inlet pressures ranging from 5 MPa to 8 MPa. The pressure distribution showed a decreasing trend from inlet to outlet, with significant pressure differences that facilitate effective polishing of internal gear tooth surfaces. This pressure drop is desirable as it ensures consistent material removal across the gear teeth. The results are summarized in the table below, illustrating how higher inlet pressures enhance the polishing capability for internal gears.
| Inlet Pressure (MPa) | Maximum Pressure (MPa) | Minimum Pressure (MPa) | Pressure Drop (MPa) |
|---|---|---|---|
| 5 | 5.0 | 0.5 | 4.5 |
| 6 | 6.0 | 0.6 | 5.4 |
| 7 | 7.0 | 0.7 | 6.3 |
| 8 | 8.0 | 0.8 | 7.2 |
Velocity vector analysis revealed that the abrasive flow accelerates at the inlet and near the tooth roots of the internal gears, with velocities increasing proportionally to inlet pressure. This relationship is crucial for internal gear manufacturers, as higher velocities correlate with greater material removal rates. The velocity magnitude can be described by the equation: $$v = \sqrt{v_x^2 + v_y^2 + v_z^2}$$, where $$v_x$$, $$v_y$$, and $$v_z$$ are the velocity components. The table below provides average velocities in the flow channel for different inlet pressures, emphasizing the benefits of optimized pressure settings for polishing internal gears.
| Inlet Pressure (MPa) | Average Velocity (m/s) | Maximum Velocity (m/s) |
|---|---|---|
| 5 | 2.1 | 4.5 |
| 6 | 2.5 | 5.2 |
| 7 | 2.9 | 5.8 |
| 8 | 3.3 | 6.5 |
The density distribution of the abrasive particles was uniform across the flow channel, indicating consistent polishing action on the internal gear tooth surfaces. This uniformity helps reduce surface roughness and waviness, which is a key quality metric for internal gear manufacturers. The density $$\rho_m$$ of the mixture can be expressed as: $$\rho_m = \alpha \rho_p + (1 – \alpha) \rho_f$$, where $$\alpha$$ is the volume fraction of particles, $$\rho_p$$ is the particle density, and $$\rho_f$$ is the fluid density. For silicon carbide in hydraulic oil, this ensures stable flow behavior.
Turbulent kinetic energy (TKE) analysis showed peak values at the tooth tips of the internal gears, suggesting enhanced polishing in these regions due to higher energy dissipation. The TKE is given by: $$k = \frac{1}{2} \left( \overline{u’^2} + \overline{v’^2} + \overline{w’^2} \right)$$, where $$u’$$, $$v’$$, and $$w’$$ are fluctuating velocity components. The table below lists TKE values for varying inlet pressures, demonstrating how increased pressure boosts turbulence and polishing efficiency for internal gears.
| Inlet Pressure (MPa) | Maximum TKE (m²/s²) | Average TKE (m²/s²) |
|---|---|---|
| 5 | 0.15 | 0.05 |
| 6 | 0.18 | 0.06 |
| 7 | 0.22 | 0.07 |
| 8 | 0.25 | 0.08 |
Turbulent viscosity analysis indicated a decrease with rising inlet pressure, which improves the flowability of the abrasive media and enhances polishing performance. The turbulent viscosity $$\mu_t$$ is related to the flow characteristics by: $$\mu_t = \rho C_\mu \frac{k^2}{\epsilon}$$. Lower viscosity at higher pressures allows for smoother flow and better surface finish on internal gears. The values are summarized in the table below, providing insights for internal gear manufacturers to optimize process parameters.
| Inlet Pressure (MPa) | Average Turbulent Viscosity (Pa·s) | Minimum Turbulent Viscosity (Pa·s) |
|---|---|---|
| 5 | 0.012 | 0.008 |
| 6 | 0.010 | 0.006 |
| 7 | 0.009 | 0.005 |
| 8 | 0.007 | 0.004 |
In conclusion, the designed fixture for polishing internal gear tooth surfaces using solid-liquid two-phase flow demonstrates excellent structural integrity and fluid dynamic performance. The static analysis confirms minimal deformation and stress, ensuring reliability during operation. Fluid simulations reveal that increasing inlet pressure enhances velocity, pressure drop, turbulent kinetic energy, and reduces turbulent viscosity, leading to superior polishing outcomes. This approach offers internal gear manufacturers a cost-effective solution to achieve high surface quality, reduce processing time, and extend the lifespan of internal gears. By integrating such fixtures into AFM processes, we can overcome traditional limitations and meet the demanding standards of automotive applications. Future work could focus on optimizing geometric parameters and exploring different abrasive media to further improve the efficiency for internal gears production.