Further investigation on LuGre friction force model under normal load variations

A large number of friction force models has been proposed in the literature to include the different properties and represent the frictional behavior with more detail [1, 2]. Generally, the friction models are divided into two groups, i.e., the static and dynamic models. The former group describes the steady-state behavior of friction force by enforcing a constant relationship between the relative tangential velocity and the corresponding friction force. The dynamic models are usually more complex since they consider an extra state variable, which describes the friction state, governed by a differential equation. Among the dynamic friction model, the LuGre model [3] has been gaining popularity and acceptance by the scientific community, since it presents a reasonable trade-off between easiness of implementation, range of modeled frictional phenomena, computational efficiency, and ability for parameters identification. These characteristics make LuGre model suitable for many applications in the modeling of multibody mechanical systems. Despite its wide utilization, the LuGre model presents limitations under normal load variation, which made its authors to present an amended version [4] to overcome some of those shortcomings. However, even the amended version has revealed some physical inconsistencies due to the occurrence of a drift during the sticking phase [5, 6]. In this work, a modification to the LuGre friction model is proposed to deal with normal load oscillations without presenting the shortcomings of both the original and amended versions of the model