Magnetorheological valves based on Herschel-Bulkley fluid model: modelling, magnetostatic analysis and geometric optimization

Magnetorheological (MR) fluids find wide application in various engineering applications. At the design stage of any MR devices, choosing a suitable rheological model for describing the flow behaviour is very critical. Since, the Herschel-Bulkley (H-B) is the most suitable model to describe the flow behaviour of MR fluids, the present study models the flow of MR fluid in the annular valve using the H-B model and does geometric optimization of the valve for three different commercially available MR fluids. The work discussed in the paper consist of three broader parts viz. (i) flow modelling, (ii) magnetostatic analysis and (iii) geometric optimization. In flow modelling, MR fluid flow is modelled using the H-B fluid model and validated by computational fluid dynamic analysis in ANSYS environment. Further, in magnetostatic analysis, for calculating the values of objective functions during the optimization process, magnetic flux density in the MR valve has been calculated using a polynomial model for the relative magnetic permeability for three different MR fluids, rather than conventionally choosing a constant value which is valid only for low ranges of current. The magnetostatic analysis has been validated through finite element modelling in ANSYS software package for different valve geometries. After defining the magnetization model for the chosen MR fluids and geometric design of the valve, variation of valve mass and performance indices such as damping force, dynamic range, inductive time constant and control energy, have been shown for all chosen fluids. In geometric optimization, the performance indices of the valve have been kept as objective functions which incorporate H-B fluid model for its definition. Such work has not been reported in the literature. Finally, a single-objective minimization problem has been formulated for the optimization with application-specific weight factors and solved using Genetic Algorithm in MATLAB (R) environment. The optimal results are then discussed and the best possible MR fluid has been suggested for the chosen applications.