Tolerance Mathematical Model Based on the Variation of Control Points of Geometric Element

Abstract

A new tolerance model by representing the position variation of control points of geometric element is proposed.The control points of point,line and plane geometric element are defined as point itself,two end points of line,any three vertices of bounding box of plane and the interior constituting points of line and plane,which are used to present the dimensional error,the position error,the orientation error and the form error.The tolerance coordinate system of target geometric element is established according to the geometric type of target geometry and datum geometry,the relative position between target geometry and datum geometry,and the precedence of datum reference frames.The degree of freedoms(DOFs) of geometry element are classified and defined under the tolerance coordinate system.The bounding box of plane is set up at the tolerance coordinate system and the variation direction of control points is defined along translational DOF of geometry element,and the variation combination of all control points are used to represent various error of geometric element.The variation of control points is controlled to follow the error probability distribution of geometric element and the definitional domain of variation parameter of control point is the tolerance zone,the restrict relationship among the control points of target element are used to represent the interaction relationship between position and orientation tolerance,and the relationship between the variation parameters of control point of target and datum element are used to represent the tolerance principles.The model is compatible with the tolerance standards and practice rules,it also suits the mathematical analysis method of many applications such as tolerance analysis,tolerance allocation and verification.