Optimization of Gerotor Pumps with Asymmetric Profiles through an Evolutionary Strategy Algorithm
Abstract
1. Introduction
2. General Design Theory for Gerotor Pump Profiles
3. Gerotor Dynamic Model
4. Contact Stress Estimation
5. Stochastic Optimization Algorithms
6. Profile Optimization
6.1. Cycloidal Gears Optimization
6.2. Second-Order Optimization through Asymmetric Lobes
7. Discussion and Further Work
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Crossover operator | |
Fluid bulk modulus | |
Angular pitch | |
Flow rate irregularity | |
Angular parameter for a parametric description of the lobe geometry | |
Angle between the normal to the contact point and the radial direction | |
External gear profile in its integral reference system | |
External gear profile in the inner gear reference system | |
Inner gear profile in its integral reference system | |
Angular position of the external gear | |
Angular position of the inner gear | |
Non-dimensional design parameter | |
Number of parents in the evolutionary algorithm | |
Fluid dynamic viscosity | |
Number of surviving elements at each iteration of the evolutionary algorithm | |
Poisson ratio | |
Profile parameterization | |
Fluid density | |
Curvature of the external profile | |
Curvature of the internal profile | |
Number of offspring in the evolutionary algorithm | |
Local radius of the lobe | |
Angular coordinates for lobe geometry description | |
Contact stress | |
Transmission ratio between the gears | |
Angular speed of the external gear | |
Angular speed of the inner gear | |
Profile parameterization | |
Frontal area of the chamber | |
Port area | |
Required port area | |
Characteristic dimensions of the contact area | |
Center of the lobe profile | |
Discharge coefficient | |
Distance between the gerotor axis and the contact points | |
“Parent” parameter vector belonging to the k-th generation | |
Parameter vector for the k+1 generation before mutation | |
Young’s modulus | |
Gerotor eccentricity | |
Contact force | |
Elliptic parameter | |
Safety coefficient against cavitation | |
Height of the leakage path | |
Axial length of the chambers | |
Length of the leakage path | |
Transformation matrix | |
Tooth number of the external gear | |
Normal to the external gear profile | |
Center of the external gear centrode | |
Center of the inner gear centrode | |
Mean pressure inside the i-th chamber | |
Pressure at the inlet port | |
Pressure at the port | |
Vapor tension | |
Pump total flow rate | |
Net flow rate for the i-th chamber | |
Flow rate between the i-1th and i − 1th chambers | |
Average pump flow rate | |
Flow rate from the port to the i-th variable volume chamber | |
Fitness of the optimization problem solution | |
Radius of the external gear centrode | |
Radius of the internal gear centrode | |
Limit value of the external gear radius | |
Limit value of the inner gear radius | |
Position of the generic point k in the lobe reference system | |
Driving torque | |
Volume of the i-th chamber | |
Limit speed | |
Sliding speed between mating profiles | |
Co-penetration between gears profiles | |
WRPF | Wear rate proportional factor |
Reference frame integral with the external gear | |
Fixed reference frame | |
Reference frame integral with the inner gear |
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Speed (rpm) | Objective of the First Optimization Process | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
(-) | (mm) | (-) | (-) | (mm) | (-) | (-) | (-) | (mm) | (-) | (mm) | (-) | |
5000 | 2.118 | 3.074 | 0.720 | 1.159 | 1.820 | 5.326 | 0.747 | 1.070 | 2.063 | 3.643 | 0.939 | 1.115 |
6000 | 2.046 | 2.880 | 0.753 | 1.179 | 1.932 | 4.582 | 0.834 | 1.142 | 2.041 | 3.279 | 0.879 | 1.114 |
7000 | 2.000 | 2.388 | 0.775 | 1.037 | 1.821 | 3.807 | 0.780 | 1.091 | 2.047 | 2.671 | 0.851 | 1.099 |
8000 | 2.162 | 1.829 | 0.743 | 1.179 | 1.862 | 3.537 | 0.765 | 1.028 | 2.126 | 2.558 | 0.805 | 1.041 |
9000 | 2.244 | 1.636 | 0.878 | 1.109 | 1.813 | 3.074 | 0.761 | 1.080 | 2.126 | 2.025 | 0.815 | 1.175 |
10,000 | 2.159 | 1.486 | 0.757 | 1.016 | 2.110 | 2.525 | 0.913 | 1.103 | 2.168 | 2.014 | 0.859 | 1.122 |
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De Martin, A.; Jacazio, G.; Sorli, M. Optimization of Gerotor Pumps with Asymmetric Profiles through an Evolutionary Strategy Algorithm. Machines 2019, 7, 17. https://doi.org/10.3390/machines7010017
De Martin A, Jacazio G, Sorli M. Optimization of Gerotor Pumps with Asymmetric Profiles through an Evolutionary Strategy Algorithm. Machines. 2019; 7(1):17. https://doi.org/10.3390/machines7010017
Chicago/Turabian StyleDe Martin, Andrea, Giovanni Jacazio, and Massimo Sorli. 2019. "Optimization of Gerotor Pumps with Asymmetric Profiles through an Evolutionary Strategy Algorithm" Machines 7, no. 1: 17. https://doi.org/10.3390/machines7010017
APA StyleDe Martin, A., Jacazio, G., & Sorli, M. (2019). Optimization of Gerotor Pumps with Asymmetric Profiles through an Evolutionary Strategy Algorithm. Machines, 7(1), 17. https://doi.org/10.3390/machines7010017