A New Four Point Circular-Invariant Corner-Cutting Subdivision for Curve Design

A 4-point nonlinear corner-cutting subdivision scheme is established. It is induced from a special C-shaped biarc circular spline structure. The scheme is circular-invariant and can be effectively applied to 2-dimensional (2D) data sets that are locally convex. The scheme is also extended adaptively to non-convex data. Explicit examples are demonstrated

Circular Nonlinear Subdivision Schemes for Curve Design

Two new families of nonlinear 3-point subdivision schemes for curve design are introduced. The first family is ternary interpolatory and the second family is binary approximation. All these new schemes are circular-invariant, meaning that new vertices are generated from local circles formed by three consecutive old vertices. As consequences of the nonlinear schemes, two new families of linear subdivision schemes for curve design are established. The 3-point linear binary schemes, which are corner-cutting depending on the choices of the tension parameter, are natural extensions of the Lane-Riesenfeld schemes. The four families of both nonlinear and linear subdivision schemes are implemented extensively by a variety of examples

Nonlinear Compensation of Two-Dimensional Contouring Servomechanism

This paper gives a method of nonlinear compensation for a two-dimensional contouring servomechanism, by which the cornering error, or the transient error at the corner of a figure being traced, is held within given tolerance. The effect of compensation is analyzed by graphical means, using the result of model experiment and the parameters are determined so as to obtain the desirable performance. Stability analysis of the system is also given utilizing the describing function method. The result is applied to an actual automatic flame cutting machine and the practicability is proved

Surface roughness variation of thin wall milling, related to modal interactions

High-speed milling operations of thin walls are often limited by the so-called regenerative effect that causes poor surface finish. The aim of this paper is to examine the link between chatter instability and surface roughness evolution for thin wall milling. Firstly, the linear stability lobes theory for the thin wall milling optimisation was used. Then, in order to consider the modal interactions, an explicit numerical model was developed. The resulting nonlinear system of delay differential equations is solved by numerical integration. The model takes into account the coupling mode, the modal shape, the fact that the tool may leave the cut and the ploughing effect. Dedicated experiments are carried out in order to confirm this modelling. This paper presents surface roughness and chatter frequency measurements. The stability lobes are validated by thin wall milling. Finally, the modal behaviour and the mode coupling give a new interpretation of the complex surface finish deterioration often observed during thin wall milling

Toolpath dependent stability lobes for the milling of thin-walled parts

The milling of thin-walled parts can become a seriously complex problem because the parts have variable dynamics. Firstly, the dynamics evolution of the part has been calculated through Finite Element Method (FEM) analysis. Then, the 3D stability lobes have been calculated for the thin walls and the thin floor. Finally, several milling tests have been performed in order to validate the predictions made by the model

Generalized Kruithof approach for traffic matrix estimation

[Abstract]: In this paper, the traffic matrix estimation problem is formulated as an nonlinear optimization problem based on the generalized Kruithof approach which uses the Kullback distance to measure the probabilistic distance between two traffic matrices. In addition, an algorithm using the affine scaling method is provided to solve the constraint optimization problem