Magnetorheological Fluid in Oscillatory Shear and Parameterization with Regard to MR Device Properties

Abstract

Storage and loss moduli of an MRF submitted to a magnetic field, as measured by a plate—plate magnetorheometer versus shear amplitude in oscillatory shear, exhibit a complex non-linear response. Above a critical amplitude, the storage modulus decreases strongly, while the loss modulus passes through a distinct maximum. The periodic shear stress signal changes from sinusoidal to saw-tooth like. A mechanical analogue, consisting of a Bingham element (friction element and damper arranged in parallel) and elastic spring in series, is capable to capture the measured behaviour. Model predictions for the time-dependent shear stress and resulting moduli at agitation frequency (fundamental mode) for various amplitudes are discussed and the determination of model parameters from the experimental data is addressed. The linear radial shear strain profile in plate—plate geometry causes a smearing of the moduli and shift to higher amplitudes by about a factor of 4/3. The conversion from physical to engineering parameters for an MR device is demonstrated for disk clutches using cone—plate and plate—plate geometry. Complications due to a nonhomogeneous shear in the device are addressed. The elastic modulus of the MRF may be relevant for vibration damping and may cause some shift in the resonance frequency of the device.