Deriving Position of Bending Roll in Roll Bending of Titanium Alloy Wire for Glasses Frame

Titanium alloy is used for a wire for glasses frame due to having high corrosion resistance and human body compatibility. The wire is formed into a three-dimensional design shape by an NC exclusive bending machine. In present, craftsmen adjust the bending roll position by trial and error at every design change. The purpose of this study is suggesting a feedback control method to revise a formed shape into a design shape with a smaller number of trials. It is desirable to introduce a feedforward compensator into a feedback control loop to reduce the trial number. About one of the two-dimensional curves to constitute the three-dimensional curve of the glasses frame, this paper proposes a derivation method of a bending roll position that getting first formed shape near the design shape. This method is based on geometric relations in a steady bending, and equivalent to a feedforward compensator in the control loop. Design shapes are real glasses and squares that have fileted corners, the curvature becomes more than 300 m-1. It is particularly paid attention to the availability of “indentation” as the governing quantity of moment, every moment arm at no load. By the absolute total of the curvature deviation, it is confirmed that the shape formed by the suggested method is closer than that by a conventional method.