GMS friction model approximation

•We apply sigmoid curves in approximation of GMS friction model.•Modification enables continuous transition between stiction and sliding friction.•The M-GMS model represents all friction properties of GMS model.

The paper deals with the research of sigmoid smooth curve application to the approximation of GMS (Generalized Maxwell-Slip) friction model. The study provides an analysis of the influence of the curves on the effectiveness of friction property modelling and computational efficiency. The smooth curves have been used to replace switching instructions in the differential equation of the state variables in GMS model, thus allowing the simulation of a smooth transition between two friction regimes: stiction and sliding. The new modified friction model facilitates production of continuous derivatives and maintenance of all the GMS model friction properties. The M-GMS model can be used to solve dynamic machine systems applying the methods designed for continuous systems, e.g. during the Lyapunov exponent calculation with standard methods to determine the system chaoticity or to be applied to gradient optimization techniques.