Brushes consist of a body with fixed highly flexible filaments and can be used for deburring and surface finishing operations. During the brushing process, axial and tangential deflections of the highly flexible filaments lead to an adaptation to the shape of the workpiece and interaction between the filaments. The described complex contact behavior has been insufficiently investigated so far.

For a better understanding of the contact between a brush and the workpiece surface, this paper presents a model based on physical principles. The model describes the dynamic behavior of a brush in contact with different workpiece geometries and consists of separate physical descriptions for the filaments of the brush, the workpiece surface and the occurring contacts. A description of a single filament is given by a multi-body system of rigid links. The rigid links are connected by joints which approximate the material behavior of the filaments. To approximate different geometries, the workpiece surface is specified by a polynomial. Contact can occur between the filaments and the workpiece surface as well as between the filaments. For the description of the occurring contacts, Hertz’s theory of elastic contact and Coulomb’s law of friction are used. The aforementioned physical descriptions are included in the Lagrange’s equations to obtain a system of equations of motion that calculates the deflection of the filaments of the brush and the acting forces during the contact with the workpiece surface. A numerical solution to the system of equations of motion was calculated by using experimentally determined material and contact properties of the filament. A comparison of the calculated forces with experimentally determined values shows good correlations for different workpiece surfaces and process parameters. In this context, the developed model calculates the progression and the maximum value of the acting contact forces. The results show a shorter contact length of the filament lc for a circular surface compared to a plane surface, and a rise of the maximum normal force Fn with the depth of cut ae. Furthermore, consideration of the filament interactions leads to a more accurate approximation of the brush-workpiece contact. Based on the findings, the developed model can be used to calculate predictions for different brushing processes which reduce the number of time-consuming preliminary tests for the process design.

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