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.

[1]  W. J. Minkowycz,et al.  Erratum: “Local Non-Similar Solutions for Natural Convection on a Vertical Cylinder” (Journal of Heat Transfer, 1974, 96, pp. 178–183) , 1975 .

[2]  Timothy J. E. Miller,et al.  Design of Brushless Permanent-Magnet Motors , 1994 .

[3]  F. Ordóñez,et al.  Scaling Laws From Statistical Data and Dimensional Analysis , 2005 .

[4]  Gilles Lefebvre,et al.  Using model size reduction techniques for thermal control applications in buildings , 2000 .

[5]  N. Ramachandran,et al.  Correlations for laminar mixed convection on vertical, inclined and horizontal flat plates with uniform surface heat flux , 1987 .

[6]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[7]  James H. Brown,et al.  The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization , 2005, Journal of Experimental Biology.

[8]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

[9]  Jack P. C. Kleijnen,et al.  Kriging Metamodeling in Simulation: A Review , 2007, Eur. J. Oper. Res..

[10]  W. Rohsenow,et al.  Handbook of Heat Transfer , 1998 .

[11]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[12]  J.A. Ortega,et al.  Moving towards a more electric aircraft , 2007, IEEE Aerospace and Electronic Systems Magazine.

[13]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[14]  Sean N. Brennan,et al.  Scaling of hybrid-electric vehicle powertrain components for Hardware-in-the-loop simulation , 2009 .

[15]  T. Simpson,et al.  Comparative studies of metamodeling techniques under multiple modeling criteria , 2000 .

[16]  Hiroyuki Ozoe,et al.  A Correlation for Laminar Free Convection From a Vertical Plate , 1973 .

[17]  Marc Budinger,et al.  Scaling-law-based metamodels for the sizing of mechatronic systems , 2014 .

[18]  Stuart W. Churchill,et al.  Correlating equations for laminar and turbulent free convection from a horizontal cylinder , 1975 .

[19]  Crispin Hales,et al.  Engineering design: a systematic approach , 1989 .

[20]  Steffen Beich,et al.  Physical And Computational Aspects Of Convective Heat Transfer , 2016 .

[21]  Giovanni Miragliotta,et al.  Physics for Managers? The power of Dimensional Analysis in production systems design , 2011 .

[22]  Glenn Murphy,et al.  Similitude in engineering , 1950 .

[23]  M Budinger,et al.  Estimation models for the preliminary design of electromechanical actuators , 2012 .

[24]  Edward S. Taylor,et al.  Dimensional analysis for engineers , 1974 .

[25]  Ching-Chih Tsai,et al.  Design and control of a brushless DC limited-angle torque motor with its application to fuel control of small-scale gas turbine engines , 2009 .

[26]  R. Le Letty,et al.  Limited angel torque actuator for fine angular positioning , 2010 .

[27]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[28]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[29]  Mohand Laïd Idoughi Extraction de modèles thermiques simplifiés des machines électriques à partir d’un calcul du champ de températures , 2011 .

[30]  Jan Wikander,et al.  Optimal selection of motor and gearhead in mechatronic applications , 2006 .

[31]  Herman Van der Auweraer,et al.  Virtual engineering at work: the challenges for designing mechatronic products , 2012, Engineering with Computers.