Optimal iso-planar cutting direction based on machine kinematic metric: A differential geometry method for freeform surface finishing tool path computation

In this paper, a 4D Lorenz-type multistable hyperchaotic system with a curve of equilibria is investigated by using differential geometry method, i.e. with KCC-theory. Due to the deviation curvature tensor and its eigenvalues, the curve of equilibria of this hyperchaotic system is proved analytically to be Jacobi unstable under a certain parameter condition, and a periodic orbit of this system is proved numerically to be also Jacobi unstable. Furthermore, the dynamics of contravariant vector field near the curve of equilibria and the periodic orbit are studied, respectively, and their results comply absolutely with the above analysis of Jacobi stability.

Download Full-text

Recognition of Freeform Surface Machining Features

Journal of Computing and Information Science in Engineering ◽

10.1115/1.3527075 ◽

2010 ◽

Vol 10 (4) ◽

Cited By ~ 10

Author(s):

Jun Wang ◽

Zhigang Wang ◽

Weidong Zhu ◽

Yingfeng Ji

Keyword(s):

Critical Points ◽

Computer Aided Design ◽

Tool Path ◽

Machining Process ◽

Freeform Surface ◽

Critical Surface ◽

Machining Features ◽

Computer Aided ◽

Freeform Surface Machining ◽

Machining Process Planning

This paper describes a method of machining feature recognition from a freeform surface based on the relationship between unique machining patches and critical points on a component’s surface. The method uses Morse theory to extract critical surface points by defining a scalar function on the freeform surface. Features are defined by region growing between the critical points using a tool path generation algorithm. Several examples demonstrate the efficiency of this approach. The recognized machining features can be directly utilized in a variety of downstream computer aided design/computer aided manufacturing (CAM) applications, such as the automated machining process planning.

Download Full-text

Automatic drawing of isostatics and separation of principal stress with the differential geometry method in photoelastic analysis.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A ◽

10.1299/kikaia.56.2116 ◽

1990 ◽

Vol 56 (530) ◽

pp. 2116-2122

Author(s):

Yoshika SUZUKI ◽

Shizuo MAWATARI ◽

Yoshiaki TOYODA ◽

Masahisa TAKASHI

Keyword(s):

Differential Geometry ◽

Principal Stress ◽

Photoelastic Analysis ◽

Geometry Method ◽

Automatic Drawing

Download Full-text

An Algorithm for Generating Multi-Axis NC Machining Tool-Path on Scattered Point Cloud

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.139-141.1322 ◽

2010 ◽

Vol 139-141 ◽

pp. 1322-1327

Author(s):

Dian Zhu Sun ◽

Jian Liu ◽

Yan Rui Li ◽

Zong Wei Niu

Keyword(s):

Differential Geometry ◽

Spanning Tree ◽

Point Cloud ◽

Tool Path ◽

Minimum Spanning Tree ◽

Reference Data ◽

Nc Machining ◽

Spatial Index ◽

Local Reference ◽

Normal Vectors

To achieve the accurate duplication of product in reverse engineering, we proposed an algorithm for generating multi-axis NC machining tool-path directly based on scattered point cloud. At first, we obtained the neighborhoods of tool-path section based on the dynamic spatial index of scattered point cloud and from which we selected the matching points. Then the tool-path section points can be obtained through intersection of the tool-path section and the lines which link the matching points, and the normal vectors of tool-path section points can be calculated based on the differential geometry property of local reference data. Finally we computed the cutter location points by means of projection method and sorted them based on the minimum spanning tree algorithm to form the tool-path. With the results of several experiments, the high precision and efficiency of this algorithm are verified.

Download Full-text

Tool Deflection Error Regularization and Compensation in End Milling of Contour Surfaces

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.217-219.1341 ◽

2012 ◽

Vol 217-219 ◽

pp. 1341-1345 ◽

Cited By ~ 1

Author(s):

Zhao Cheng Wei ◽

Min Jie Wang ◽

Wu Chu Tang ◽

Liang Wang

Keyword(s):

Tool Path ◽

End Milling ◽

Removal Rate ◽

Dominant Factor ◽

Mathematics Model ◽

Tool Deflection ◽

Peripheral Milling ◽

Dimensional Error ◽

New Approach ◽

Finishing Tool

This paper presents a new approach of tool deflection error regularization and compensation in end milling of contour surfaces. The material removal rate (MRR) is adopted as the dominant factor of surface dimensional error. A mathematics model of determining the MRR in generalized contour surfaces machining is proposed. Feedrate scheduling methodology is applied to regulate a constant MRR along curved tool path. The expectation with the constant MRR is that it will potentially produce a constant surface dimensional error. Thus, the compensation can be conveniently achieved by offsetting the nominal finishing path. The desired MRR and corresponding offsetting value of finishing tool path are determined by a peripheral milling test. Machining results obtained in this study reveal that the proposed approach can significantly reduce the surface dimensional error and the smooth variation of feedrate can get a few variation of surface dimensional error. Comparing to the existing methods, the time-consuming iterative process in error compensation is omitted.

Download Full-text