# A Virtual Prototype for Fast Design and Visualization of Gerotor Pumps

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## Abstract

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## 1. Introduction

**Implementation**. In this manuscript, we present the implementation of a virtual prototype of a Gerotor pump designed to be integrated with data measured in an experimental setup in order to improve the established design process. Our implementation does not constitute a full Digital Twin, but rather will be a step towards a fully functional Digital Twin tool that reproduces the behavior of the real pump. This virtual prototype allows for a rough design condition vs. performance appraisal, thus enabling the design and testing scenarios. Once the designer is satisfied with this approximated design vs. performance ratio, a more precise CFD simulation process would take place. An important current feature of the virtual prototype tool presented is the import and display of the sub-sequent CFD simulation results and experimental data measured in a real pump, for the benefit of the designer manufacturer and client. This feedback of the CFD simulation results might be included in a numerically oriented closed loop at the design stage. At the present time, we only report visual CFD data feedback. The implemented tool is able to use data that were measured in the experimental setup to feed the fast virtual prototype. Differences between the virtual prototype state variables and measured state variables allow for several activities: (a) to modify the pump design, (b) to control the actual pump, and (c) to feed satisfactory virtual prototype parameters into parametric or constraint-driven CAD models to obtain a full Boundary Representation of the Gerotor pump. Notice that (c) streamlines the design-for-gerotor process and avoids the need for a external CAD application.

## 2. Previous Works

#### 2.1. Fluid Mechanical Simulation

#### 2.2. Digital Twins and Virtual Prototypes in Gerotor Applications

#### 2.3. Conclusions of Literature Review

## 3. Methodology

#### 3.1. Experimental Setup

#### 3.2. Geometric Model

#### 3.3. Fluid Dynamics Module

- Input/Output flow: fluid flowing from the input port to the inside of the pump (charge) or from the inside of the pump to the output port (discharge).
- Fluid leak flow: fluid flowing from one chamber to another due to imperfect sealing that results from manufacturing defects and design constraints.

- Difference of pressure between adjacent control volumes (Poiseuille flow).
- Difference in angular speed between inner and outer rotor (Couette flow).

#### 3.4. Software Tool

## 4. Results

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LP | Lumped Parameter. |

CFD | Computational Fluid Dynamics. |

${P}_{i}$ | Pressure at chamber i. |

${A}_{i}$ | Area at chamber i. |

${V}_{i}$ | Volume at chamber i. |

${Q}_{i}$ | Net flowrate at chamber i. |

${A}_{i,out}$ | Shared area between chamber i and output port. |

${A}_{i,in}$ | Shared area between chamber i and input port. |

${C}_{d}$ | Discharge coefficient. |

${C}_{d,max}$ | Maximum discharge coefficient. |

${\beta}_{eff}$ | Effective bulk’s modulus of working fluid. |

${\rho}_{eff}$ | Effective density of working fluid. |

$\nu $ | Kinematic viscosity of working fluid. |

$\mu $ | Dynamic viscosity of working fluid. |

$Re$ | Reynold’s number. |

$R{e}_{crit}$ | Critical Reynold’s number. |

$Dh$ | Hydraulic diameter. |

${p}_{in}$ | Pressure at input port. |

${p}_{out}$ | Pressure at output port. |

$\omega $ | Angular speed of inner gear. |

## References

- Gamez-Montero, P.J.; Codina, E.; Castilla, R. A review of gerotor technology in hydraulic machines. Energies
**2019**, 12, 2423. [Google Scholar] [CrossRef] [Green Version] - Castilla, R.; Gamez-Montero, P.; Ertürk, N.; Vernet, A.; Coussirat, M.; Codina, E. Numerical simulation of turbulent flow in the suction chamber of a gearpump using deforming mesh and mesh replacement. Int. J. Mech. Sci.
**2010**, 52, 1334–1342. [Google Scholar] [CrossRef] - Houzeaux, G.; Codina, R. A finite element method for the solution of rotary pumps. Comput. Fluids
**2007**, 36, 667–679. [Google Scholar] [CrossRef] - Hsieh, C.F. Fluid and dynamics analyses of a gerotor pump using various span angle designs. J. Mech. Des.
**2012**, 134. [Google Scholar] [CrossRef] - Bae, J.H.; Kwak, H.S.; San, S.; Kim, C. Design and CFD analysis of gerotor with multiple profiles (ellipse–involute–ellipse type and 3-ellipses type) using rotation and translation algorithm. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2016**, 230, 804–823. [Google Scholar] [CrossRef] - Rundo, M.; Altare, G. Lumped Parameter and Three-Dimensional CFD Simulation of a Variable Displacement Vane Pump for Engine Lubrication. J. Fluids Eng.
**2018**, 140, 61–101. [Google Scholar] [CrossRef] - Gamez-Montero, P.J.; Castilla, R.; del Campo, D.; Ertürk, N.; Raush, G.; Codina, E. Influence of the interteeth clearances on the flow ripple in a gerotor pump for engine lubrication. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2012**, 226, 930–942. [Google Scholar] [CrossRef] - Pellegri, M.; Vacca, A.; Frosina, E.; Buono, D.; Senatore, A. Numerical analysis and experimental validation of Gerotor pumps: A comparison between a lumped parameter and a computational fluid dynamics-based approach. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2017**, 231, 4413–4430. [Google Scholar] [CrossRef] - Pellegri, M.; Vacca, A.; Devendran, R.S.; Dautry, E.; Ginsberg, B. A Lumped parameter approach for gerotor pumps: Model Formulation and experimental validation. In Proceedings of the 2016 10th International Fluid Power Conference, Dresden, Germany, 8–10 March 2016; Technische Universitat Dresden: Dresden, Germany, 2016; Volume 1, pp. 465–476. [Google Scholar]
- Shah, Y.; Vacca, A.; Dabiri, S.; Frosina, E. A fast lumped parameter approach for the prediction of both aeration and cavitation in Gerotor pumps. Meccanica
**2018**, 53, 175–191. [Google Scholar] [CrossRef] [Green Version] - Rundo, M. Models for flow rate simulation in gear pumps: A review. Energies
**2017**, 10, 1261. [Google Scholar] [CrossRef] [Green Version] - Tao, F.; Zhang, H.; Liu, A.; Nee, A.Y. Digital twin in industry: State-of-the-art. IEEE Trans. Ind. Inform.
**2018**, 15, 2405–2415. [Google Scholar] [CrossRef] - Pires, F.; Cachada, A.; Barbosa, J.; Moreira, A.P.; Leitão, P. Digital Twin in Industry 4.0: Technologies, Applications and Challenges. In Proceedings of the 2019 IEEE 17th International Conference on Industrial Informatics (INDIN), Espoo, Finland, 22–25 July 2019; IEEE: Piscataway, NJ, USA, 2019; Volume 1, pp. 721–726. [Google Scholar]
- Mejia, D.; Moreno, A.; Arbelaiz, A.; Posada, J.; Ruiz-Salguero, O.; Chopitea, R. Accelerated thermal simulation for three-dimensional interactive optimization of computer numeric control sheet metal laser cutting. J. Manuf. Sci. Eng.
**2018**, 140. [Google Scholar] [CrossRef] - Mejia-Parra, D.; Arbelaiz, A.; Ruiz-Salguero, O.; Lalinde-Pulido, J.; Moreno, A.; Posada, J. Fast Simulation of Laser Heating Processes on Thin Metal Plates with FFT Using CPU/GPU Hardware. Appl. Sci.
**2020**, 10, 3281. [Google Scholar] [CrossRef] - Gámez Montero, P.J. Caracterizacion Fluidodinamica de una Bomba Oleohidráulica de Engranajes Internos Generados por Perfiles Trocoidales; Universitat Politècnica de Catalunya: Barcelona, Spain, 2004. [Google Scholar]
- Kwon, S.M.; Kang, H.S.; Shin, J.H. Rotor profile design in a hypogerotor pump. J. Mech. Sci. Technol.
**2009**, 23, 3459–3470. [Google Scholar] [CrossRef] - Kim, S.; Murrenhoff, H. Measurement of effective bulk modulus for hydraulic oil at low pressure. J. Fluids Eng.
**2012**, 134. [Google Scholar] [CrossRef] - Simões, B.; Creus, C.; Carretero, M.d.P.; Guinea Ochaíta, A. Streamlining XR Technology Into Industrial Training and Maintenance Processes. In The 25th International Conference on 3D Web Technology; Association for Computing Machinery: New York, NY, USA, 2020. [Google Scholar] [CrossRef]
- Simões, B.; del Puy Carretero, M.; Santiago, J.M. Photorealism and Kinematics for Web-Based CAD Data. In The 25th International Conference on 3D Web Technology; Association for Computing Machinery: New York, NY, USA, 2020. [Google Scholar] [CrossRef]
- Castilla López, R.; Gámez Montero, P.J.; Raush Alviach, G.A.; Codina Macià, E. Three dimensional simulation of gerotor with deforming mesh by using OpenFOAM. In Proceedings of the Fluid Power Networks: Proceedings: 19th-21th March 2018: 11th International Fluid Power Conference, Aachen, Germany, 19–21 March 2018; pp. 260–271. [Google Scholar]

**Figure 1.**Gerotor pump general architecture: (

**a**) inner and outer gear, (

**b**) inlet/outlet disposition in pump.

**Figure 3.**Experimental setup: (

**a**) testing bench and (

**b**) physical pump mounted on the test setup (translucent cover).

**Figure 4.**Parameterization of internal profile shape as in Equation (2).

**Figure 10.**Visualization of parameterized pump in the two-dimensional (2D) geometry configurator interface: (

**a**) pump with conjugated external profile and (

**b**) pump with classic external profile.

**Figure 13.**Geometry visualization: (

**a**) inner and outer gear of the pump, (

**b**) fluid chambers with transparent ports.

**Figure 15.**Volumetric data results from the virtual prototype: (

**a**) profile of geometry with highlighted chamber $\left(C{V}_{1}\right)$ and (

**b**) history of area in a z-cut for selected chamber.

**Figure 16.**Volumetric data results from the virtual prototype: (

**a**) history of intersection area between chamber $C{V}_{1}$ and input port and (

**b**) history of intersection area between chamber $C{V}_{1}$ and output port.

**Figure 18.**Pressure results from virtual prototype: (

**a**) profile of geometry with highlighted chamber $\left(C{V}_{1}\right)$, (

**b**) history of pressure in chamber $C{V}_{1}$, and (

**c**) pressure distribution in pump after a full revolution, as seen in Digital Twin (DT).

**Figure 19.**Virtual Prototype vs. computational fluid dynamics models (CFD) maximum predicted pressure in gerotor pump.

Variable | Value | Units |
---|---|---|

Pressure at input port (${p}_{in}$) | 1 | bar |

Pressure at output port (${p}_{out}$) | 4.5 | bar |

Density of fluid at 1 atm (${\rho}_{oil}$) | 1005 | kg/m${}^{3}$ |

Bulk modulus of fluid at 1 atm (${\beta}_{oil}$) | 1.4 | GPa |

Angular speed of inner rotor ($\omega $) | 100 | rad/s |

Dynamic viscosity ($\mu $) | 0.01 | Pa*s |

Pressure in chambers at $t=0$ | 1 | bar |

**Table 2.**Comparison of pre-processing and simulation times for the CFD simulation and our virtual prototype.

Task | CFD Time | Our Implementation Time |
---|---|---|

Pre-Processing of Geometry | 1 h | <5 min |

Simulation | 9 h | <5 min |

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## Share and Cite

**MDPI and ACS Style**

Pareja-Corcho, J.; Moreno, A.; Simoes, B.; Pedrera-Busselo, A.; San-Jose, E.; Ruiz-Salguero, O.; Posada, J.
A Virtual Prototype for Fast Design and Visualization of Gerotor Pumps. *Appl. Sci.* **2021**, *11*, 1190.
https://doi.org/10.3390/app11031190

**AMA Style**

Pareja-Corcho J, Moreno A, Simoes B, Pedrera-Busselo A, San-Jose E, Ruiz-Salguero O, Posada J.
A Virtual Prototype for Fast Design and Visualization of Gerotor Pumps. *Applied Sciences*. 2021; 11(3):1190.
https://doi.org/10.3390/app11031190

**Chicago/Turabian Style**

Pareja-Corcho, Juan, Aitor Moreno, Bruno Simoes, Asier Pedrera-Busselo, Ekain San-Jose, Oscar Ruiz-Salguero, and Jorge Posada.
2021. "A Virtual Prototype for Fast Design and Visualization of Gerotor Pumps" *Applied Sciences* 11, no. 3: 1190.
https://doi.org/10.3390/app11031190