Extension of Vectorial Tolerances for Coordinate Measurement Analysis

In recent years, vectorial tolerancing has emerged as a new alternative of representing workpiece tolerances. In contrast with conventional geometric tolerances that originated from hard gauging practice, vectorial tolerancing follows the working principle of coordinate measuring machines and CAD/CAM systems. Moreover it provides feedback from measurement directly to manufacturing process control. Many believe it is a better tolerancing method to tie design, manufacturing, and measurement together. However, current proposal of vectorial tolerancing has several limitations. First, the current orientation vector is inadequate for representing true 3D orientation. As a result, the orientation of a free form surface can not be properly established. Second, there has not been much discussion on the subject of vectorial tolerance evaluation. This paper proposes a new orientation vector which provides a more general mathematical basis for representing vectorial tolerances. It enables true 3D orientation representation and relates tolerances to functional requirement. With the mathematical definition, a systematic evaluation approach becomes possible for both analytical geometric elements and free form surfaces. Computer simulation and real-world application were studied to validate this new approach.