Efficient Simulation of a Dynamic System With LuGre Friction

Abstract

Friction is a difficult phenomenon to model and simulate. One promising friction model is the LuGre model, which captures key frictional behavior from experiments and from other friction laws. While displaying many modeling advantages, the LuGre model of friction can result in numerically stiff system dynamics. In particular, the LuGre friction model exhibits very slow dynamics during periods of sticking and very fast dynamics during periods of slip. This paper investigates the best simulation strategies for application to dynamic systems with LuGre friction. Several simulation strategies are applied including the explicit Runge-Kutta, implicit Trapezoidal, and implicit Radau-IIA schemes. It was found that both the Runge-Kutta and Radau-IIA methods performed well in simulating the system. The Runge-Kutta method had better accuracy, but the Radau-IIA method required less integration steps.

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

“…In these models, both stiction and sliding regimes are unified and governed by the same equations. At a price of introducing additional differential equations, some drawbacks of smoothed Coulomb models are overcome, and more realistic results are gained [8,17,18]. This article points out that in the stiction regime and its neighborhood, the multibody model behavior is highly sensitive to changes of some less important parameters (often hardly measurable) of the model of joint friction.…”

“…Moreover, particularly when the approximating curve is steep in the region of zero velocity of sliding, numerical properties of these models are poor [17,18]. These drawbacks may be diminished by introducing additional state variables, as it is done in the LuGre model of joint friction and other state-variable friction models [12,17].…”

“…1a), various functions of the velocity of sliding are used. Some of them, for example, saturation [8,17], hyperbolic tangent [7,18], or arctangent [27] do not differ static and kinetic friction coefficients (Fig. 1b).…”

“…Encountered difficulties most often pertain to numerical stiffness of equations of motion [12,17]. It can be shown, however, that when friction is present in joints of a closed-loop rigid body mechanism, problems of completely different type, namely problems with uniqueness of solution, may emerge.…”

“…In practical applications, the constraint addition-deletion approach is seldom used since discontinuity at zero relative joint velocity causes a number of analytical and computational problems [17,18]. More frequently employed models treat both stiction and sliding regimes uniformly, that is, the same friction model is used in both regimes, and no additional constraints are imposed during the stiction phase.…”