Dwell time algorithm in deterministicpolishing of free-form surface based oncontinuous tool influence function

2021 ◽  
Author(s):  
Lei Zhang ◽  
Qizhi Zhao ◽  
Cheng Fan
Keyword(s):  
Influence Function ◽  
Dwell Time ◽  
Time Algorithm ◽  
Free Form ◽  
Tool Influence Function ◽  
Free Form Surface

FREE-FORM SURFACE PARTITION IN 3-D

2011 ◽  
Vol 21 (06) ◽  
pp. 609-634 ◽  
Author(s):  
DANNY Z. CHEN ◽  
EWA MISIOŁEK
Keyword(s):  
Time Algorithm ◽  
Point Of View ◽  
Free Form ◽  
Convex Polygons ◽  
Geometric Problem ◽  
Surface Machining ◽  
Insertions And Deletions ◽  
Surface Partitioning ◽  
Free Form Surface ◽  
Free Form Surfaces

We present a theoretical study of a problem related to optimal free-form surface partitioning, which arises in surface machining in manufacturing. In particular, we consider partitioning a free-form surface in 3-D into two subsurfaces subject to a global objective function. As a key subroutine, we develop new algorithms for the geometric problem of processing an off-line sequence of insertions and deletions of convex polygons alternated with point membership/proximity queries on the common intersection of the polygons. We show how this subroutine can be used to solve surface 2-partitioning. Our algorithm for the 2-partitioning problem takes [Formula: see text] time, where m is the number of polygons of size O(n) each. This improves the asymptotic time complexity of the previous best-known O(m2n2)-time algorithm. Our algorithms may be applicable to other accessibility and partition problems involving free-form surfaces in computer graphics and manufacturing. From the computational geometry point of view, our method combines nontrivial data structures, geometric observations, and algorithmic techniques that may be used to solve other geometric problems. For example, our algorithm can process O(n) insertions and deletions of convex polygons (of size O(n) each) and queries on their intersections in O(n2 log log n) time, improving the "standard" O(n2 log n) time solution.

scholarly journals An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing

Micromachines ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 471
Author(s):  
Yajun Wang ◽  
Yunfei Zhang ◽  
Renke Kang ◽  
Fang Ji
Keyword(s):  
Dwell Time ◽  
Convergence Rates ◽  
Rotational Symmetry ◽  
Time Algorithm ◽  
Two Dimensions ◽  
Efficient Computation ◽  
Deconvolution Problem ◽  
Ultra Precision ◽  
Computer Controlled Optical Surfacing ◽  
Computer Controlled

The dwell time algorithm is one of the key technologies that determines the accuracy of a workpiece in the field of ultra-precision computer-controlled optical surfacing. Existing algorithms mainly consider meticulous mathematics theory and high convergence rates, making the computation process more uneven, and the flatness cannot be further improved. In this paper, a reasonable elementary approximation algorithm of dwell time is proposed on the basis of the theoretical requirement of a removal function in the subaperture polishing and single-peak rotational symmetry character of its practical distribution. Then, the algorithm is well discussed with theoretical analysis and numerical simulation in cases of one-dimension and two-dimensions. In contrast to conventional dwell time algorithms, this proposed algorithm transforms superposition and coupling features of the deconvolution problem into an elementary approximation issue of function value. Compared with the conventional methods, it has obvious advantages for improving calculation efficiency and flatness, and is of great significance for the efficient computation of large-aperture optical polishing. The flatness of φ150 mm and φ100 mm workpieces have achieved PVr150 = 0.028 λ and PVcr100 = 0.014 λ respectively.

A Golay3 sparse aperture optical system of primary mirror with free-form surface

2021 ◽  
Vol 28 (1) ◽  
pp. 113-118
Author(s):  
Bin Chen ◽  
Quanying Wu ◽  
Junliu Fan
Keyword(s):  
Optical System ◽  
Free Form ◽  
Primary Mirror ◽  
Sparse Aperture ◽  
Free Form Surface

Tool Path Generation for Five-Axis Controlled Machining of Free-Form Surface Using Barrel Tool: Control of Contact Point on Cutting Edge

2020 ◽  
Author(s):  
Tomonobu Suzuki ◽  
Koichi Morishige
Keyword(s):  
Tool Path ◽  
Contact Point ◽  
Cutting Edge ◽  
Free Form ◽  
End Mill ◽  
Ball End Mill ◽  
Surface Machining ◽  
Free Form Surface ◽  
The Cost ◽  
Five Axis

Abstract This study aimed to improve the efficiency of free-form surface machining by using a five-axis controlled machine tool and a barrel tool. The barrel tool has cutting edges, with curvature smaller than the radius, increasing the pick feed width compared with a conventional ball end mill of the same tool radius. As a result, the machining efficiency can be improved; however, the cost of the barrel tool is high and difficult to reground. In this study, a method to obtain the cutting points that make the cusp height below the target value is proposed. Moreover, a method to improve the tool life by continuously and uniformly changing the contact point on the cutting edge is proposed. The usefulness of the developed method is confirmed through machining simulations.

Application of Convex Hull for Tool Interference Avoidance in 5-Axis CNC Machining

1996 ◽  
Author(s):  
Yuan-Shin Lee ◽  
Tien-Chien Chang
Keyword(s):  
Convex Hull ◽  
Tool Path ◽  
Correction Method ◽  
Nc Machining ◽  
Cnc Machining ◽  
Free Form ◽  
Interference Avoidance ◽  
Tool Interference ◽  
Free Form Surface ◽  
Free Form Surfaces

Abstract In this paper, a methodology of applying convex hull property in solving the tool interference problem is presented for 5-axis NC machining of free-form surfaces. Instead of exhausted point-by-point checking for possible tool interference, a quick checking can be done by using the convex hull constructed from the control polygon of free-form surface modeling. Global tool interference in 5-axis NC machining is detected using the convex hull of the free-form surface. A correction method for removing tool interference has also been developed to generate correct tool path for 5-axis NC machining. The inter-surface tool interference can be avoided by using the developed technique.

Creation and Manipulation of Complex Displacement Features During the Conceptual Phase of Design

1996 ◽  
Author(s):  
P. A. van Elsas ◽  
J. S. M. Vergeest
Keyword(s):  
Boundary Conditions ◽  
Surface Feature ◽  
Free Form ◽  
Shape Design ◽  
Surface Model ◽  
Test Results ◽  
Base Surface ◽  
Feature Design ◽  
Data Explosion ◽  
Free Form Surface

Abstract Surface feature design is not well supported by contemporary free form surface modelers. For one type of surface feature, the displacement feature, it is shown that intuitive controls can be defined for its design. A method is described that, given a surface model, allows a designer to create and manipulate displacement features. The method uses numerically stable calculations, and feedback can be obtained within tenths of a second, allowing the designer to employ the different controls with unprecedented flexibility. The algorithm does not use refinement techniques, that generally lead to data explosion. The transition geometry, connecting a base surface to a displaced region, is found explicitly. Cross-boundary smoothness is dealt with automatically, leaving the designer to concentrate on the design, instead of having to deal with mathematical boundary conditions. Early test results indicate that interactive support is possible, thus making this a useful tool for conceptual shape design.

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