Stanislav S. Makhanov

Optimization of rotations of a five-axis milling machine near stationary points

Abstract We consider a new algorithm designed for five-axis milling to minimize the kinematics error near the stationary points of the machined surface. Given the tool orientations, the algorithm optimizes the required rotations on the set of the solutions of the corresponding inverse kinematics equations. We solve the problem by means of the shortest path scheme based on minimization of the kinematics error. We present an application of the proposed algorithm to tool-path planning and demonstrate the efficiency of the proposed scheme verified by practical machining.

Tool path generation for five-axis NC machining using adaptive space-filling curves

We present the concept of an adaptive space-filling curve for tool path planning for five-axis NC machining of sculptured surfaces. Generation of the adaptive space-filling curves requires three steps: grid construction, generation of the space-filling curve, and tool path correction. The space-filling curves, adapted to the local optimal cutting direction, produce shorter tool paths. Besides, the tool path correction stage makes it possible to eliminate the effect of sharp angular turns which characterize standard space-filling curve patterns. Our space-filling curve method is endowed with a new modification of techniques for computing the machining strip width along with a modified formula for the minimum tool inclination angle to avoid gouging. Finally, we show that the adaptive space-filling curves are more efficient compared with the traditional iso-parametric scheme. The numerical experiments are complemented by real machining as well as by test simulations on Unigraphics 18.

Optimization and correction of the tool path of the five-axis milling machine

We introduce three algorithms for optimization of a tool path of a numerically controlled five-axis milling machine. The unifying idea is a flexible geometric structure which adapts itself to a certain cost function defined on the required part surface. Algorithm 1 is based on the variational grid generation, Algorithm 2 is based on a new modification of the space filling curves techniques. Algorithm 3 is based on construction of vector fields composed of optimal cutting directions. The algorithms verified by numerical experiments as well as by practical machining display a priority with the reference to the standard methods.

Parameter-free optic disc detection

The paper presents a simple, parameter-free method to detect the optic disc in retinal images. It works efficiently for blurred and noisy images with a varying ratio OD/image size. The method works equally well on images with different characteristics which often cause standard methods to fail or require a new round of training. The proposed method has been tested on 214 infant and adult retinal images and has been compared against hand-drawn ground truths generated by experts. It displays consistently high OD detection rates without any prior training or adjustment of the parameters.

A family of quadratic snakes for road extraction

The geographic information system industry would benefit from flexible automated systems capable of extracting linear structures from satellite imagery. Quadratic snakes allow global interactions between points along a contour, and are well suited to segmentation of linear structures such as roads. However, a single quadratic snake is unable to extract disconnected road networks and enclosed regions. We propose to use a family of cooperating snakes, which are able to split, merge, and disappear as necessary. We also propose a preprocessing method based on oriented filtering, thresholding, Canny edge detection, and Gradient Vector Flow (GVF) energy. We evaluate the performance of the method in terms of precision and recall in comparison to ground truth data. The family of cooperating snakes consistently outperforms a single snake in a variety of road extraction tasks, and our method for obtaining the GVF is more suitable for road extraction tasks than standard methods.

Grid generation as applied to optimize cutting operations of the five-axis milling machine

Optimization of cutting operations is an active area of research in the CNC-based manufacturing. The limited capabilities of the CAD/CAM systems require development of a new software and new numerical methods verified by practical machining. First, we outline the recent methods of tool-path planning of industrial milling robots. Next, we present some introductory examples to demonstrate that the concept of adaptive curvilinear grid contains almost all the basic ingredients of tool-path planning, such as: adaptation to regions of large milling errors, conventional zigzag/spiral patterns and constraints related to the scallop height. Therefore, we formulate the problem of toolpath optimization in terms of interpolation of the required part surface in the curvilinear coordinate system associated with the cutter location points. In order to solve the problem numerically we introduce a variational grid generator based on minimization of the Dirichlet-type functional subjected to constraints related to the maximum allowed scallop between the consecutive tracks of the tool. The corresponding variational problem is then solved numerically by the quasi Newtonian scheme combined with a penalty-type iterative algorithm. We present an application of the algorithm to tool-path planning of the complex shaped parts and demonstrate the efficiency of the proposed scheme by methodological examples verified by real machining. Finally, we show that grid generation may constitute a basic component of a system of mathematical models for part optimization.

Curvilinear space-filling curves for five-axis machining

The paper presents a new combination of two methods for tool path generation for five-axis machining proposed earlier by the authors. The first method is based on the grid generation technologies whereas the second method exploits the space-filling curve approach. Combination of the two techniques is superior with regard to the conventional methods and with regard to the case when the two methods are applied independently. In particular the algorithm allows us to generate tool paths for workpieces with complex boundaries as well as when the scallop and gouging constraints are changing sharply and irregularly. In this case the conventional methods are inefficient, whereas the proposed algorithms construct the required tool path and reduce the length of the path and the time of the machining. The numerical experiments are complemented by the real machining as well as by the test simulations on the Unigraphics 18.

Optimization and correction of the tool path of the five-axis milling machine: Part 2: Rotations and setup

Abstract We present two new algorithms (which supplement Algorithms 1, 2 and 3 presented in part 1) to optimize the tool path of the five-axis numerically controlled milling machine. Algorithm 4 optimizes a set of feasible rotations. Algorithm 5 presents a least-square optimization with regard to a setup of the machine

Continuous force field analysis for generalized gradient vector flow field

We propose a modification of the generalized gradient vector flow field techniques based on a continuous force field analysis. At every iteration the generalized gradient vector flow method obtains a new, improved vector field. However, the numerical procedure always employs the original image to calculate the gradients used in the source term. The basic idea developed in this paper is to use the resulting vector field to obtain an improved edge map and use it to calculate a new gradient based source term. The improved edge map is evaluated by new continuous force field analysis techniques inspired by a preceding discrete version. The approach leads to a better convergence and better segmentation accuracy as compared to several conventional gradient vector flow type methods.

Numerical experiments on the accuracy of rotation moments invariants

Rotationally invariant moments constitute important techniques applicable to a versatile number of pattern recognition applications. Although the moments are invariant with regard to spatial transformations, in practice, due to the finite screen resolution, the spatial transformation themselves affect the invariance. This phenomenon jeopardizes the quality of pattern recognition. Therefore, this paper presents an experimental analysis of the accuracy and efficiency of discrimination under the impact of the most important spatial transformations such as rotation and scaling. We evaluate experimentally the impact of the noise induced by the spatial transformations on the most popular basis functions such as Zernike polynomials, Mellin polynomials and wavelets. The analysis reveals that the wavelet based moment invariants constitute one of the best choices to construct noise resistant features.