Karnopp's model- Stick-Slip Friction Dynamics in Simulink

A Simulink block diagram of Karnopp's model for representing dynamic mechanical systems with stick-slip motion

Karnopp's model is among the most computationally-efficient methods to simulate stick-slip motion. Karnopp's approach is to compare a virtual velocity signal with a dead-zone (around zero) to determine the state transitions between stuck and sliding [1]. The velocity dead-zone represents the unmodelled pre-sliding regime wherein the sliding body may undergo microscopic sliding but is macroscopically stationary.

The block diagram is structured for a single body undergoing two-dimensional motion based on Figure 2 from the original paper [1].The key inputs include the driving force, the velocity dead-zone, the friction vs. velocity relationship, and the static friction saturation. A Stribeck subroutine is included in the block-diagram to represent a generic friction-velocity relationship as described by Andersson [2]. The model performance is demonstrated in the figures below.

Enjoy!

-Kirk

References:

[1]Karnopp, D., Computer Simulation of Stick-Slip Friction in Mechanical Dynamic Systems. Journal of Dynamic Systems, Measurement, and Control, 1985. 107(1): p. 100-103.

[2]Andersson, S., 4 - Friction and wear simulation of the wheel–rail interface, in Wheel–Rail Interface Handbook, R. Lewis and U. Olofsson, Editors. 2009, Woodhead Publishing. p. 93-124.

Figure 1: Comparison of the displacement (output) and sinusoidal driving force (input) for a mass undergoing stick-slip motion with a velocity deadzone of ±2 m/s.

Figure 2: Visualization of the velocity deadzone concept for the mass undergoing stick-slip motion from Figure 1. The 'virtual' Karnopp velocity i.e. control signal, is overlayed with the actual sliding velocity and the deadzone (horizontal lines), denoted as 'DV' in the original paper [1] .

Figure 3: Static (Fstick) and kinetic (Fslip) components of friction for the mass undergoing stick-slip motion from Figure 1. The static signal is saturated to 1N and kinetic friction is represented by a generic Stribeck curve.