In the field of fluid power transmission, helical gears have gained significant attention due to their ability to provide smooth operation, high efficiency, and reduced noise compared to traditional gear designs. The double arc helical gear pump, in particular, offers advantages such as large flow capacity, lightweight structure, and insensitivity to fluid contaminants, making it suitable for applications in aerospace, agricultural machinery, and hydroelectric power generation. However, the mechanical behavior of the rotor under high-speed and high-pressure conditions is critical for ensuring reliability and longevity. This study focuses on analyzing the stress, deformation, and modal characteristics of the double arc helical gear pump rotor under fluid-structure coupling effects, using advanced simulation techniques to address challenges in fatigue failure and plastic deformation prediction.
The double arc helical gear pump employs a sinusoidal transition curve for its tooth profile, which enables continuous point contact during meshing. This design results in an axial overlap greater than one and an end-face overlap less than one, eliminating oil trapping and enhancing the pump’s lifespan. The unique geometry of helical gears contributes to minimal flow pulsation and low operational noise, often termed as “ultra-quiet” performance. To accurately capture the interplay between fluid dynamics and structural mechanics, a unidirectional fluid-structure coupling approach is adopted, leveraging ANSYS Workbench for real-time data transfer between fluid and solid domains. This method allows for a comprehensive evaluation of pressure distribution, stress concentrations, and deformation patterns under various loading conditions.
Theoretical foundations for fluid-structure interaction involve solving the governing equations for both fluid and solid domains. For the fluid part, the flow is considered viscous, incompressible, and transient, described by the continuity and Navier-Stokes equations. The continuity equation ensures mass conservation and is expressed as:
$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{u}) = 0$$
For incompressible fluids, this simplifies to $\nabla \cdot \mathbf{u} = 0$. The momentum equation, or Navier-Stokes equation, accounts for forces acting on the fluid and is given by:
$$\rho \left( \frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u} \right) = -\nabla p + \mu \nabla^2 \mathbf{u} + \mathbf{f}$$
where $\rho$ is density, $\mathbf{u}$ is velocity vector, $p$ is pressure, $\mu$ is dynamic viscosity, and $\mathbf{f}$ represents body forces. The energy equation, though less critical for incompressible flows, is included for completeness:
$$\rho \frac{D e}{D t} = -p \nabla \cdot \mathbf{u} + \nabla \cdot (k \nabla T) + \Phi$$
where $e$ is internal energy, $k$ is thermal conductivity, $T$ is temperature, and $\Phi$ is viscous dissipation. For the solid domain, the rotor is treated as a linear elastic material governed by the equation of motion:
$$\rho_s \frac{\partial^2 \mathbf{d}}{\partial t^2} = \nabla \cdot \boldsymbol{\sigma} + \mathbf{F}_b$$
where $\rho_s$ is solid density, $\mathbf{d}$ is displacement vector, $\boldsymbol{\sigma}$ is Cauchy stress tensor, and $\mathbf{F}_b$ is body force. The coupling between fluid and solid is achieved by transferring pressure loads from the fluid analysis to the structural model, enabling a realistic simulation of the rotor’s response.
The double arc helical gear pump model consists of two rotors with specific geometric parameters, as detailed in Table 1. These helical gears are designed with a spiral angle that ensures optimal meshing and load distribution. The material properties for the rotors, made of 30CrMnTi steel, are critical for assessing mechanical performance and are listed in Table 2.
| Parameter | Symbol | Driver Rotor | Driven Rotor |
|---|---|---|---|
| Number of Teeth | z | 7 | 7 |
| Pressure Angle | α | 14.5° | 14.5° |
| Module | m | 3 mm | 3 mm |
| Face Width | b | 15.5 mm | 15.5 mm |
| Pitch Diameter | D | 21 mm | 21 mm |
| Tip Diameter | D_a | 25.3596 mm | 25.3596 mm |
| Root Diameter | D_b | 16.6404 mm | 16.6404 mm |
| Tip Arc Radius | r_1 | 2.1798 mm | 2.1798 mm |
| Overlap Coefficient | ξ | 1.5 | 1.5 |
| Helix Angle | β_0 | 31.3° | -31.3° |
| Material | Elastic Modulus (MPa) | Poisson’s Ratio | Density (kg/m³) | Yield Strength (MPa) |
|---|---|---|---|---|
| 30CrMnTi | 2.07E+05 | 0.25 | 7800 | 1050 |
To model the fluid domain, the pump’s internal volume is extracted using ANSYS SpaceClaim, with boundary conditions defined for inlet pressure, outlet pressure, and rotor surfaces. The mesh is refined in critical regions, such as the tip clearance, to capture flow phenomena accurately. With over 11.3 million elements and 2.227 million nodes, the mesh quality is optimized for convergence in Fluent simulations. The fluid analysis assumes a transient flow with absolute velocity formulation, standard wall functions, and hybrid initialization. Pressure contours reveal that the minimum pressure occurs at the inlet near the meshing zone of the helical gears, while the maximum pressure is observed at the outlet, with a linear gradient in between.
For structural analysis, the rotor assembly is discretized into tetrahedral elements in ANSYS Mesh, with constraints applied at the shaft-bearing interfaces to restrict radial movement. The pressure loads from the fluid simulation are mapped onto the rotor surfaces to simulate the fluid-structure interaction. Under an outlet pressure of 25 MPa and rotor speed of 10,000 rpm, the deformation and stress distributions are evaluated. The results indicate that the maximum deformation of approximately 0.013179 mm occurs near the rim of the rotors, while the minimum deformation is at the shafts. The stress analysis shows that the highest equivalent stress of 223.15 MPa is localized at the meshing points of the helical gears, which is below the material’s yield strength, ensuring no plastic deformation.
Modal analysis with pre-stress conditions is conducted to assess the natural frequencies and mode shapes. The first natural frequency is found to be 3408.4 Hz, significantly higher than the pump’s operating frequency of 166.67 Hz, thus avoiding resonance. The mode shapes primarily involve bending and torsional vibrations, which are critical for dynamic stability. The fluid-structure coupling analysis further reveals that the pressure distribution causes additional deformation and stress compared to the uncoupled case. Specifically, under coupled conditions, the maximum deformation increases to 0.029242 mm, and the equivalent stress rises to 405.87 MPa, with the same locations of maximum values. The safety factor, calculated as the ratio of yield strength to maximum stress, is 3.6218, indicating sufficient margin against failure.
To quantify the impact of fluid-structure coupling, simulations are performed at different outlet pressures: 15 MPa, 20 MPa, 25 MPa, and 30 MPa. The results, summarized in Table 3, demonstrate that coupling effects amplify both deformation and stress, with differences of up to 0.016063 mm in deformation and 187.72 MPa in stress compared to uncoupled analyses. This highlights the importance of incorporating fluid-structure interaction in design evaluations for helical gear systems.
| Outlet Pressure (MPa) | Uncoupled Max Deformation (mm) | Coupled Max Deformation (mm) | Uncoupled Max Stress (MPa) | Coupled Max Stress (MPa) |
|---|---|---|---|---|
| 15 | 0.008 | 0.018 | 150 | 280 |
| 20 | 0.010 | 0.022 | 180 | 330 |
| 25 | 0.013 | 0.029 | 223 | 406 |
| 30 | 0.015 | 0.035 | 260 | 480 |
The natural frequencies from modal analysis under coupled and uncoupled conditions are compared in Table 4. The differences are minimal, confirming that fluid coupling has a minor effect on dynamic characteristics but a significant impact on static responses.
| Mode | Uncoupled Frequency (Hz) | Coupled Frequency (Hz) |
|---|---|---|
| 1 | 3400.0 | 3408.4 |
| 2 | 3450.5 | 3455.2 |
| 3 | 3500.8 | 3502.1 |
| 4 | 3550.3 | 3551.7 |
| 5 | 3600.6 | 3603.0 |
| 6 | 3650.9 | 3652.4 |
| 7 | 3700.2 | 3701.8 |
| 8 | 3750.5 | 3752.1 |
| 9 | 3800.8 | 3802.3 |
| 10 | 3850.1 | 3851.6 |
For structural optimization, a lightweight design is proposed by reducing the shaft diameter from 8 mm to 7 mm, resulting in a 28.32% mass reduction. The optimized rotor is analyzed under the same operating conditions, showing a maximum deformation of 0.024014 mm and a maximum stress of 341.24 MPa. The safety factor improves to 4.3078, enhancing the rotor’s durability and performance. This optimization demonstrates the potential for material savings without compromising mechanical integrity in helical gear applications.
In conclusion, the fluid-structure coupling analysis provides valuable insights into the mechanical behavior of double arc helical gear pump rotors. The use of helical gears ensures smooth operation and high efficiency, but the coupling effects significantly influence stress and deformation patterns. The maximum deformation and stress are concentrated near the rim and meshing zones, respectively, with coupling increasing these values substantially. The modal analysis confirms that resonance is avoided under normal operating conditions. The lightweight optimization further improves the design by reducing mass while maintaining safety margins. These findings underscore the importance of integrated simulation approaches for developing reliable helical gear systems in high-pressure applications.
The methodology employed in this study can be extended to other gear types and operating conditions, offering a framework for advanced mechanical design. Future work could explore bidirectional coupling or experimental validation to enhance accuracy. Overall, this research contributes to the understanding of fluid-structure interactions in helical gear pumps, facilitating innovations in fluid power technology.