Magnetorheological Damper: Field-Controlled Yield Stress

Electromagnet

Coil current I 0.00 A

Road Excitation

Frequency f 1.2 Hz

Amplitude A 8 mm

Live Readouts

Damper force

0 N

Piston velocity

0 mm/s

Mass displacement (rel. equilibrium)

0.0 mm

How it works

A magnetorheological (MR) fluid is a carrier oil loaded with micron-scale iron particles. With no field the particles drift freely and the fluid behaves like an ordinary viscous liquid. Switching on a magnetic field polarises the particles, which snap into chains along the field lines in milliseconds — the fluid develops a controllable yield stress and behaves as a Bingham plastic:

Bingham plastic shear stress:
  τ = τ_y(B)·sign(γ̇) + η·γ̇

Damper force (Bingham-plastic model):
  F_d = F_y(I)·tanh(v_rel / v_ε) + c₀·v_rel

Quarter-car equation of motion:
  m·z̈ = -k·(z - r(t)) - F_d(v_rel)
  v_rel = ż - ṙ(t)

τ_y(B) — yield stress, roughly proportional to B² at low field then saturating as the particle chains max out; here it is driven by coil current I.
tanh(v_rel/v_ε) — a smoothed sign function standing in for the Coulomb-friction-like yield term, avoiding the numerical stiffness of a true discontinuity.
c₀ — the fluid's field-independent viscous (post-yield) damping coefficient, always present even with the field off.
Raising I widens the low-velocity "stuck" region where the damper resists motion almost rigidly, then lets the piston slip once the force exceeds the yield force — visible as a flatter, boxier force-velocity response than a passive viscous damper's straight line.

Real-world relevance: this exact controllable-yield-stress principle runs semi-active shock absorbers (e.g. Lord Corporation dampers used on some production cars) and vibration-isolation mounts — a control loop reads the road/vibration state and adjusts coil current tens of times per second to retune the damping force on the fly.

Iron particle chains Field coil (glow ∝ current) Sprung mass

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