Interference-free tool path generation for 5-axis sculptured surface machining using rational Bézier motions of a flat-end cutter

Abstract

This paper presents a new approach that uses rational Be´zier motions to generate 5-axis tool path for sculptured surface machining (finish cut) with a flat-end cutter. By using dual quaternion to represent a spatial displacement, the representation of kinematic motions for the cutter bottom circle of the flat-end cutter is formulated. Based on that, a new approach for tool path generation using rational Be´zier cutter motions is described, in which key issues such as interference avoidance and surface accuracy requirement are addressed. First, a set of cutter contact points on an iso-parametric curve of the designed surface is obtained based on a given fitting tolerance. The associated cutter locations (CLs) are then obtained by finding the suitable cutter orientations that avoid any gouging. The conversion from the CLs to dual quaternion representation is carried out and the rational Be´zier dual quaternion curve for cutter motion is generated. The entire tool path is therefore established based on the cutter undergoing the rational Be´zier motion. Next, the whole tool path is checked to find (1) if there is any interference between the cutter and the designed surface, and (2) whether the deviation between the surface generated by the cutter motion and the designed surface is larger than the given tolerance. The problematic CLs, which cause either gouging or accuracy problem, are then modified. The process of tool path checking ! CLs modification ! tool path regeneration continues until the whole tool path is interference-free and satisfies the accuracy requirement. Furthermore, a more accurate representation of the effective cutting shape is proposed, which is used to evaluate the scallop height between adjacent tool paths. A method for constructing the adjacent tool path has been developed by considering the allowable scallop height. Finally, computer implementation and an illustrative example are presented to demonstrate the efficacy of the approach.

Using geometric algebra to represent and interpolate tool poses

“…For both R and T , the result of the map is again a point, and, since RR = T T = 1, the presence of unity as the part not involving ε in equation A3is preserved. As with other formulations, combining control points, given as dual quaternions, using Bézier and B-spline techniques can be used to create motions along free-form curves or across free-form surfaces (Purwar and Ge 2005, Zhang et al 2005.…”

An Analytical Decoupled Corner Smoothing Method for Five-Axis Linear Tool Paths

“…Based on this idea, Wang et al [6] realized a double NURBS curve based interpolator and integrated it to an open CNC system. Zhang et al [7] generated smooth tool path using…”

Singularities in five-axis machining: Cause, effect and avoidance

“…The addition of two rotary axes in five-axis machining offers the extra capability to control orientation of the cutter. This added flexibility can be utilised to machine more complex geometries, reduce the number of setups, achieve higher material-removal rates, improve surface finish and thus increase productivity [1].…”