Friction Hysteresis in Simulink - Dahl's Model

A Simulink block diagram for Dahl’s model of hysteretic friction

Dahl’s model is widely used to represent hysteretic friction at micron-scale displacements, which resembles stress-strain curves for solid materials. Hysteretic friction refers to the time-history dependence of friction in the pre-sliding regime which arises due to microscopic sliping of the surface asperities [1]. This type of friction can be visualized as the stretching of 'soft springs' between surfaces in relative motion; the springs are linearly elastic at small micro-displacements and yield plastically at larger displacements [2]. The Dahl model utilizes a friction slope function with ‘rest stiffness’ and ‘shape/exponential’ parameters to represent material-specific force-deflection properties [2]. The provided Simulink block diagram represents equation #2 from Dahl's original paper [2]. A representative simulation is shown below.

Enjoy!

-Kirk

References:

[1] Al-Bender, F. Fundamentals of Friction Modeling. 2010. ASPE- The American Society of Precision Engineering.

[2] Dahl, P.R., Solid Friction Damping of Mechanical Vibrations.AIAA Journal, 1976. 14(12): p. 1675-1682.