Effective chip control is an essential requirement of modern automatic and computer numerically controlled (CNC) machining operations. This paper asserts that the study of chip control can be divided into three branches—chip dynamics, chip kinematics, and chip breaking mechanics—each having different research emphasis. Chip kinematics is becoming a promising research area, serving as an essential bridge between the other two branches. In developing the mathematical formulation of chip kinematics, this paper introduces three patterns of chip curl, i.e., up-, side-, and lateral-curl, followed by the establishment of a Cartesian coordinate system. Chip form is measured by three geometric parameters: the resultant radius R of chip curl, the pitch P of the chip helix, and the inclined angle θ of the helical axis to the helical surface. It is revealed that the final chip form is determined by four governing variables: chip up-, side-, and lateral-curl radii (Ru, Rs, and Rl) and chip side-flow angle (ηs). The effect of Ru, Rs, Rl, and ηs on chip forms is investigated. A set of new chip kinematical equations and computer-simulated chip forms are also established in this paper.

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