Five axis milling machines

We propose a new framework for toolpath generation for five-axis machining of part surfaces represented by the StereoLithography (STL) format. The framework is based on flattening the STL part and generation of adaptive curvilinear toolpaths. The corresponding cost functions, designed to represent the accuracy and the efficiency of the toolpath, are scalar functions, such as the curvature, kinematic error, rotation angles, machining strip or material removal rate or a vector field when the tool moves along a curvilinear path partly or even entirely aligned with directions considered to be optimal. The adaptive toolpath exploits grid generation methods and biased space-filling curves, combined with adaptation to the boundary and the domain decomposition. The proposed methodology of the adaptive curvilinear toolpath (ACT) has been tested on a variety of STL surfaces, including a case study of STL dental parts. Machining crowns/ implants for four basic types of human teeth, molar, premolar, canine and incisor, has been considered and analysed. The reference methods are the standard iso-parametric path, MasterCam toolpath, and advanced methods of NX9 (former UG). The experiments show that there is no universal sequence of steps applicable to every surface. However, a correct choice of the tools available within the proposed ACT-framework always leads to a substantial improvement of the toolpath, in terms of its length and the machining time.

We propose a new framework for toolpath generation for five-axis machining of part surfaces represented by the StereoLithography (STL) format. The framework is based on flattening the STL part and generation of adaptive curvilinear toolpaths. The corresponding cost functions, designed to represent the accuracy and the efficiency of the toolpath, are scalar functions, such as the curvature, kinematic error, rotation angles, machining strip or material removal rate or a vector field when the tool moves along a curvilinear path partly or even entirely aligned with directions considered to be optimal. The adaptive toolpath exploits grid generation methods and biased space-filling curves, combined with adaptation to the boundary and the domain decomposition. The proposed methodology of the adaptive curvilinear toolpath (ACT) has been tested on a variety of STL surfaces, including a case study of STL dental parts. Machining crowns/implants for four basic types of human teeth, molar, premolar, canine and incisor, has been considered and analysed. The reference methods are the standard iso-parametric path, MasterCam toolpath, and advanced methods of NX9 (former UG). The experiments show that there is no universal sequence of steps applicable to every surface. However, a correct choice of the tools available within the proposed ACT-framework always leads to a substantial improvement of the toolpath, in terms of its length and the machining time.

Matching a five-axis toolpath and a vector field (VF) of preferred directions (VFPD) is increasingly popular in the five-axis machining industry. However, surfaces represented by industrial formats often produce irregular non-homogeneous VFPD. The current methods are often unable to match such complicated VFs. We propose a new technique based on an enhanced vector flow (EVF), similar to the gradient flow by Xu and Prince (1998. "Generalized Gradient Vector Flow External Forces for Active Contours." Signal Processing 71 (2): 131-139) for image processing. The EVF keeps the high-rank vectors unchanged while extending them to unimportant regions, using a diffusion process based on a system of parabolic equations. The resulting enhanced vector field of statistically significant directions (EVFSD) is close to the original VFPD but is characterised by better continuity and regularity. Our second contribution is the clustering of the EVFSD using a prescribed library of templates by means of complex moments. The library includes three basic patterns: 'parallel'-zigzag, 'circular'-contour, and 'star'-radial patterns. The toolpaths are generated by an extension of transfinite interpolation (TFI). Virtual and real machining shows the advantages of EVFSD with reference to the standard iso-parametric paths and several state-of-the-art VF-based methods. The experiments have been performed on a five-axis machining centre, Haas VF-2TR. A video, illustrating the proposed procedure is at https://drive.google.com/open?id = 1qCrLZSSNKOpURs0JmbGpqV2oeJEUhBmT.

This paper presents a new grid generation method for tool path planning for five-axis machining based on minimization of the kinematics error. First, the procedure constructs a space-filling curve so that the scallops between the resulting tracks of the tool do not exceed a prescribed tolerance. At the second stage (which is the subject of this paper) a one-dimensional grid along the space-filling curve is generated using direct minimization of the kinematics error. A closed form representation of the kinematics error as a function of locations cutter contact points is derived from the inverse kinematics transformations associated with a particular five-axis machine and obtained through automatic symbolic calculations. The grid of cutter location points is generated so that it minimizes the kinematics error. Numerical and cutting experiments demonstrate that the proposed procedure outperforms distribution of points based on the equi-arc-length principle. Finally, we show that our optimization routine requires less points than that based on sequential point insertion and numerical evaluation of the cost function, such as bisection.

Reducing the kinematic errors is an important problem in five-axis machining. Errors of this type substantially affect the quality of the five-axis manufacturing. In this paper, we propose and analyse a new numerical algorithm to reduce the kinematic errors of a five-axis tool path using minimisation of the variation of the rotation angles. Our algorithm finds the locations of the cutter contact points (CC points) in the angular space and the orientation/location of the target surface relative to the mounting table that minimise the angle variation. We show through the numerical experiments and cutting simulations that the proposed method is efficient and accurate.

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

Singular configurations of five-axis machines have long been observed. Machining near to such singularities drastically affects the behaviour of machine axes movements. Singularities have been linked to the kinematic chain of the machine configuration but not necessarily machine axes movement. The first contribution of this paper is a link between cutter motion in workpiece and machine coordinate systems. This leads to a description for the machine axes movements for a given tool path. Unstable machine axes movements are discovered near singular configurations of the rotary axes. By relating these configurations to orientations in the workpiece coordinate system, a simple approach that avoids singularities by reorienting the workpiece is proposed. Machining tests verify the effectiveness of this approach.

This paper presents a new optimization model designed to minimize kinematics error introduced by the initial setup of a five-axis milling machine. An initial setup consists of the position and orientation of the workpiece with respect to the mounting table and, optionally, the machine's initial configuration. Given a set of cutter contact points and tool orientations, a least-squares optimization procedure finds the optimal setup parameters. Since the set of optimization parameters depends on the machine's characteristics, three basic types of five-axis kinematics are introduced. The classification into types depends on the sequence of positions of the machine's rotary axes in its kinematics chain. For each type, sets of invariant and dependent variables are identified, a corresponding system of nonlinear equations is constructed, and then the system is solved numerically. The method is not only efficient, but also provides tangible accuracy increases in tests on practic...

In this paper, we propose two new algorithms to correct the trajectories of the tool tip of a five-axis milling machine by adjusting the rotation angles in such a way that the kinematics error is reduced. The first algorithm is based on the shortest-path optimization with regards to feasible rotations of the inverse kinematics. The cost function is represented in terms of the total angle variation. We show that such an optimization increases the accuracy of machining and is the most appropriate in the case of a rough cut. The shortest-path procedure applies to either the entire set of trajectories or to only the most inappropriate undercuts inside the workpiece. In the latter case, the algorithm generates an interesting family of solutions characterized by smaller undercuts obtained at the expense of increased overcuts. The second algorithm also exploits the idea of the minimization of the angle variation. It is based on the uniform distribution of the cutter contact points with regards to the rotation angles. The method inserts additional tool positions by numerically finding a grid of points distributed uniformly in the angular space. We prove that the proposed algorithm in the neighborhood of stationary points requires 3-4 times fewer additional points than the conventional scheme. Also, if a maximum angular speed has been exceeded, the controller detects this event and reduces the angular speed. Our correction algorithms minimize the total angle variation, thus, reducing the probability of such an event. Finally, the efficiency of the two algorithms has been verified by a five-axis machine MAHO600E at the CIM Lab of the Asian Institute of Technology of Thailand and HERMLE UWF920H at the

The kinematic error (KE) of a five-axis milling machine is an important measure of the accuracy. The proposed software allows to interactively position the cutter contact (CC) points to reduce the KE. The system helps to optimize the tool path by a trial and error approach and provides a learning experience for the users of five-axis machines. The code works with the STL and OFF files as well as with parametric surfaces.The Interactive system (IS) was offered to unexperienced users as a game with a goal to reduce visible kinematic errors while keeping the number of available CC points. The users were able to achieve a decrease of of the maximum KE by 91.73% and of the average KE by 43.70%. The program has been verified with a post processor from HAAS VF-2TR machining center (Trunnion VMCs).

Reducing the kinematic errors is an important problem in five-axis machining. Errors of this type substantially affect the quality of the five-axis manufacturing. In this paper, we propose and analyse a new numerical algorithm to reduce the kinematic errors of a five-axis tool path using minimisation of the variation of the rotation angles. Our algorithm finds the locations of the cutter contact points (CC points) in the angular space and the orientation/location of the target surface relative to the mounting table that minimise the angle variation. We show through the numerical experiments and cutting simulations that the proposed method is efficient and accurate.

This paper presents a new optimization model designed to minimize kinematics error introduced by the initial setup of a five-axis milling machine. An initial setup consists of the position and orientation of the workpiece with respect to the mounting table and, optionally, the machine's initial configuration. Given a set of cutter contact points and tool orientations, a least-squares optimization procedure finds the optimal setup parameters. Since the set of optimization parameters depends on the machine's characteristics, three basic types of five-axis kinematics are introduced. The classification into types depends on the sequence of positions of the machine's rotary axes in its kinematics chain. For each type, sets of invariant and dependent variables are identified, a corresponding system of nonlinear equations is constructed, and then the system is solved numerically. The method is not only efficient, but also provides tangible accuracy increases in tests on practical machining problems. q

This paper presents a new optimization model designed to minimize kinematics error introduced by the initial setup of a five-axis milling machine. An initial setup consists of the position and orientation of the workpiece with respect to the mounting table and, optionally, the machine's initial configuration. Given a set of cutter contact points and tool orientations, a least-squares optimization procedure finds the optimal setup parameters. Since the set of optimization parameters depends on the machine's characteristics, three basic types of five-axis kinematics are introduced. The classification into types depends on the sequence of positions of the machine's rotary axes in its kinematics chain. For each type, sets of invariant and dependent variables are identified, a corresponding system of nonlinear equations is constructed, and then the system is solved numerically. The method is not only efficient, but also provides tangible accuracy increases in tests on practical machining problems.