Scaling laws based metamodels for the selection of the cooling strategy of electromechanical actuators in the early design stages

Abstract : The integration of electromechanical actuation systems for aerospace applications requires additional thermal stress considerations during the preliminary design, which were not necessary within the hydraulic technology. The favored models during this design phase are simple, continuous and explicit mathematical expressions to enable easy analytical manipulations or implementations in worksheets or optimization loops. The paper shows how such models can be obtained for the desired applications, illustrating the example of a Limited Angle Torque Motor (LATM) with different cooling strategies. The used method for gathering the models is a regression process on data obtained by finite element simulations. The originality of the method stands in the physical insight of the regression function which is based on scaling laws and dimensional analysis. An example of preliminary design of a LATM illustrates the use of the obtained models for the comparison of two possible architectures intended to minimize the mass of the actuator by implementing different cooling strategies. Abbreviations 3D three-dimensional DDV Direct Drive Valve DoE Design of Experiments LATM Limited Angle Torque Motor RMS Root Mean Square SLAWMM Scaling-LAW-based MetaModels Nomenclature β air thermal expansion coefficient [1/K] ∆θ difference between the winding temperature and bulk temperature of the fluid [K] λ fluid thermal conductivity [W/mK] µ fluid dynamic viscosity [kg/ms] π i dimensionless numbers [−] ρ fluid density [kg/m 3 ] ρ Cu copper density [kg/m 3 ] ρ el electrical resistivity [Ωm] τ copper volume fraction in the copper-resin mixture [−] θ temperature [ • C] or [K] ϕ heat flow rate density [W/m 2 ] * Corresponding author. Tel.: +33 (0)5 67048823; fax: +33 (0)5 61559950 Email address: ion.hazyuk@insa-toulouse.fr (Ion Hazyuk) B r remanent induction of the permanent magnet [T ] C p fluid specific heat capacity [J/kgK] D motor diameter [m] d i geometric dimensions [m] e air gap of the motor [m] g gravitational acceleration [m/s 2 ] Gr Grashof number [−] h global convective heat transfer coefficient [W/m 2 K] J current density [A/m 2 ] L motor length [m] M mass [kg] Nu Nusselt number [−] Pr Prandtl number [−] Q heat flow rate [W] Re Reynolds number [−] S motor external surface [m 2 ] T electromagnetic torque [Nm] T L linear electromagnetic torque [N] U kerosene velocity in the motor air gap [m/s] V Cu volume of the copper [m 3 ]
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Mechatronics, Elsevier, 2015, 29, pp.67 - 77. 〈10.1016/j.mechatronics.2015.05.011〉
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Ion Hazyuk, Marc Budinger, Florian Sanchez, Jean-Charles Maré, Stéphane Colin. Scaling laws based metamodels for the selection of the cooling strategy of electromechanical actuators in the early design stages. Mechatronics, Elsevier, 2015, 29, pp.67 - 77. 〈10.1016/j.mechatronics.2015.05.011〉. 〈hal-01861798〉

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