Dynamic behavior of pumps: an efficient approach for fast robust design optimization


Classical design optimization procedures rely on the application of optimization algorithms upon system simulations. These algorithms need a large number of samples to converge on the optimal point. Hence design optimization needs large simulation time since each simulation has to be performed many times. In this paper an original and useful methodology to study and optimize mechanical systems is presented. The proposed methodology combines different techniques such as design of experiments, response surface models and evolutionary algorithms leading to larger time reduction with respect to the classical design optimization approach. On the one hand the proposed methodology gives the optimal combination of variables and on the other hand provides important results to understand the influence of each input to the system outputs. Moreover, a robust design process has been carried out in order to consider the manufacturing tolerances of the real mechanical system and assess their effect on the system performance. The results offer important information and design insights that would be very difficult to obtain without such a procedure. In order to demonstrate the methodology effectiveness, two case studies have been accounted: the optimization of the vibration level of a vane pump and a gear pump. To simulate the dynamical behaviour of the two pumps, mathematical models have been used. These models have been developed and validated by the authors in previous works. The mathematical models include the main important phenomena involved in the pumps operation and they have been validated on the basis of experimental data. The main operational and geometrical input variables have been taken into account in the optimization procedure of such pumps.

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This work has been developed within the Advanced Mechanics Laboratory (MechLav) of Ferrara Technopole, realized through the contribution of Regione Emilia-Romagna—Assessorato Attività Produttive, Sviluppo Economico, Piano telematico–POR-FESR 2007-2013, Activity I.1.1.

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Correspondence to Emiliano Mucchi.



In this “Appendix” the main geometrical and operational parameters of the vane pump and gear pump being studied are listed.

Vane pump
Symbol Value Description
B oil 1700 MPa Oil bulk modulus
μ 14 mPa s Lubricant dynamic viscosity
ρ 854 kg/m3 Lubricant density in std conditions
N 11 Number of vanes
Ws 20 mm Pressure ring width
rs 30 mm Pressure ring inner radius
rr 25 mm Rotor shaft radius
tvb 2.2 mm Vane thickness at the base
tvh 0.3 mm Vane thickness at the head
vm 0.003 kg Vane mass
Gear pump
Value for gear 1 Value for gear 2 Description
a = 14.65 mm Centre distance of gear pair
b 1 = 12.1 mm b 2 = b 1 Gear face width
E = 210 × 109 Pa Young’s modulus
ν = 0.3 Poisson’s ratio
J 1 = 4.0714 × 10−7 kg m2 J 2 = 3.9564 × 10−7 kg m2 Moment of inertia
K T  = 8.053 × 102 Nm/rad Torsional stiffness of the driving shaft
m 1 = 0.0333 kg m 2 = 0.0216 kg Mass
\( \hat{m} = 1. 1 50 \) mm Gear module
r b1 = 6.484 mm r b2 = r b1 Base radius
\( \hat{x}_{1} = *** \) \( \hat{x}_{2} {\kern 1pt} = {\kern 1pt} \hat{x}_{1} \) Addendum modification coefficient (*** confidential)
z 1 = 12 z 2 = z 1 Number of teeth
α = 20 deg Pressure angle
α w  = 27.727° Pressure angle in working condition
B oil  = 1400 MPa Oil Bulk modulus
μ = 14 mPa s Lubricant dynamic viscosity

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Tosi, G., Mucchi, E., d’Ippolito, R. et al. Dynamic behavior of pumps: an efficient approach for fast robust design optimization. Meccanica 50, 2179–2199 (2015). https://doi.org/10.1007/s11012-015-0142-z

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  • Optimization
  • Response surface modelling
  • DOE
  • Pump dynamics