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

An investigation of a novel LuGre-based friction force model

The LuGre friction force models are amongst the most popular and powerful approaches to treat frictional contact in modeling, simulation and control of mechanical systems. However, these friction force models have some numerical difficulties related to physical inconstancies, when the systems under analysis include frictional contacts with significant variations in the normal loads. The LuGre friction force models can exhibit some problems resulting in the ratio between the friction and normal contact forces exceeding the friction coefficients. Another limitation deals with the drift problem which might occur during sticking periods. Thus, this work is aimed at presenting a new investigation based on the LuGre friction foundation capable of overcoming those limitations. In a simple manner, the new solution for the LuGre friction force model includes a stiffness coefficient to adjust and accommodate the variations of the normal contact forces in dynamical systems. In this study, two LuGre friction force models are revisited to facilitate the description of the proposed solution. Finally, several numerical application examples regarding a block of mass on a horizontal plane are presented to compare and examine the advantages and potentials of the original, amended and proposed modelsThis work has been supported by Portuguese Foundation for Science and Technology, under the national support to R&D units grant, with the reference project UIDB/04436/2020 and UIDP/04436/2020. This research has been supported by the National Science Centre (Poland) grant no. 2018/29/B/ST8/00374