Tool path optimization in layered manufacturing

Abstract

There are several manufacturing applications in which a tool needs to move along a prescribed path performing machining operations. The path is typically described by a sequence of curves. For the entire process, the tool must move along each curve exactly once. For typical paths, significant lime may be wasted in the movement between the end point of one curve to the start vertex of the next one along which the tool must operate. Normally, this non-machining motion is a straight-line motion. A good process plan would minimize the time wasted on such motion. An excellent application of this problem is found in the increasingly popular Layered Manufacturing (LM) methods. We first introduce a Genetic Algorithm (GA)-based approach to solve this problem. Next, we present a new strategy using a combination of the Asymmetric Traveling Salesman Problem and Integer Programming (TSP-IP) to solve it. Based on the pros and cons of these approaches, two enhanced GA formulations are developed. We compare the performance of the different techniques, with a view to their application to real-time path planning in LM applications.

A review of cutting path algorithms for laser cutters

“…Wah et al [65] consider a cutting path optimization problem for "layered manufacturing processes," such as selective laser sintering, laminated object manufacturing, and fused deposition modeling. An endpoint cutting model is used where only air move times are relevant.…”

“…Manber and Israni [64] H P, I, CC, Pi, Br Wah et al [65] G A P , A Moreira et al [66] H P , I , C C Imahori et al [67] H P , I , C C Rodriguez and Soeiro [68] MA P ,A Kolakowska et al [70] CP P, A, Timed constraints Sherif et al [69] S A P , A Dewil et al [ [78] H / G A P , A , ( B r )…”

Deriving the Minimum Traversal Function of Three Circles

“…Direct substitution in Equation (5) Fig. 4 contains one circles C with its radius length equal to 2 and two points A and B with their coordinates (-3, 4) and (4,5), respectively. Observe that the shape of the discrete curve is approximately sin-like wave.…”

“…Let f(xp, yp) be the distance function of the real variables xp and yp. It is defined by the equation C(X,YP) =J(XA XP) + (YA YP)2 + V(XB XP) + (YB YP) (5) If we introduce the polar coordinates x,.= recosO yp r sin 0 then e(xp,yp) becomes e(r,0) Since the radius r in the proposed paper is a constant, the function C(r, 0) can then be denoted as ((0). Direct substitution in Equation (5) Fig.…”

“…For each scanning layer, a laser beam scans along the contours in the layer to solidify the cross-section of the object. The path planning [4] for the scanning each layer is therefore a traversal optimization problem on geometric entities in a two dimensional plane [5], [6]. Fig.…”