A mathematical model for simulating and manufacturing ball end mill
The performance of ball end mill cutters in cutting operations is influenced by the configuration of the rake and clearance faces in the ball component. From the mathematical design of a cutting edge curve, the rake face can be defined by the rake angle and the width of the rake face at each cross section along the cutting edge. We propose the fundamental conditions that must govern the engagement between the grinding wheel and the designed rake face in order to avoid interference while machining a ball end mill. As a result, a new mathematical model for determining the wheel location and a software program for simulating the generation of the rake face of a ball end mill are proposed. In addition, methods for grinding the clearance face in both concave and flat-shapes are introduced. The flute surface generated by a disk wheel during the grinding process is determined on the basis of a tangency condition. The results of the experiment and the simulation are compared to validate the proposed model.
A novel CNC grinding method for the rake face of a taper ball-end mill with a CBN spherical grinding wheel
A novel method using a CBN spherical grinding wheel to grind the rake face of a taper ball-end mill and the configuration of corresponding CNC tool grinder are presented. This method utilizes the self-adaptation characteristics of a sphere to decrease the number of simultaneous cooperative axes of a CNC tool grinder and to smooth the rake face on the transition area between the taper and the ball-end of the mill. In order to obtain an accurate normal rake angle, which is one of the key factors affecting tool cutting performance, a moving coordinate system based on the required normal rake angle and the cutting edge was established. Then, by the proposed moving coordinate system, an algorithm to determine the position and orientation of a spherical grinding wheel, the basis of CNC code generation, is proposed and the relevant formulations are deduced. The 3D simulation of rake face grinding for a taper ball-end mill with constant helical angle indicates that the number of simultaneous cooperative axes of the CNC tool grinder is decreased from five to four and the smooth transition of the rake face is realized by the proposed method herein.
AMERICAN WESTS: PREFACE TO A GEOGRAPHICAL INTERPRETATION
ABSTRACT Geographers might make a very significant contribution to the interpretation of the American West and of the American nation by a systematic investigation of the West as a set of dynamic regions. The outline offered suggests a focus upon four categories of regional features (population, circulation, political areas, and culture) to be examined as complexes changing through four recognizable stages (nuclear, regional, regional-national, metropolitan-national) from initial European colonization to the present with projections into the future.