Abstract
To perform manufacturing tasks with sufficient accuracy, the position of the tool tip should be measured accurately. We developed a measurement system that detects the tool tip position by image processing. This study uses ray tracing simulations to examine the error in the tool tip position of square end mills versus the numerical apertures of the optical system used for illumination. The system consists of a telecentric illumination system and a telecentric imaging system. The diameters of the standard model for comparison and of the square end mill are φ0.1mm. The square end mill and an object used as a standard model were compared. For the standard model, the tool edge obtained by the simulation exhibits dilation relative to the original 3D model as the numerical aperture increases. This phenomenon causes refraction on the flat bottom surfaces of the standard model. On the other hand, for the square end mill, the tool edge obtained by the simulation exhibits erosion relative to the original 3D model as the numerical aperture increases. The absolute values of the errors are one-fourth those of the standard model because the bottom surface of the square end mill has a clearance angle.
