Friction in Machines and Mechanisms

A historical review of structural and mechanical systems with friction is given by Feeny et al. [10]. Their paper starts from the first human experiences in fire making and early inventions of the ancient cultures to the works of Leonardo da Vinci, and expands to the modern-day scientific advances in friction utilization and prevention. 

An essential part of any study on the behavior of a dynamical system with friction is to appropriately account for the friction effects using a sufficiently accurate friction model. There are numerous works found in the literature on the various friction models for simulation and analysis of dynamical systems. In one of the first survey papers on friction modeling by Armstrong-Helouvry et al. [11], various friction models are studied. These models can be divided into the following two categories  

The latter category is the subject of numerous works as can be seen in review papers by Ibrahim [4], Awrejcewicz and Olejnik [5], and Berger [12]. As reported in these works, friction can be considered dependent on any of the following factors relative sliding velocity, acceleration, friction memory, pre-slip displacement, normal load, dwell time, temperature, etc. 

The friction models used in the dynamic modeling of systems can be further divided into static models and dynamic models. In the dynamic friction models such as the so-called LuGre model [13], the friction force is dependent on additional state variables that are governed by nonlinear differential equations stemming from the model for the average deflection of the contacting surfaces. At the price of increased complexity of the overall system dynamics, these models are capable of reproducing various features of friction such as velocity and acceleration dependence, pre-slip displacement, and hysteresis effect 

Depending oti the specific problem being investigated, an appropriate friction model should be chosen that reflects the relevant features of the physical system. The simplest approximate friction model may be given by (see, e.g., [11, 12]) 

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