A Five-Axis Toolpath Corner-Smoothing Method Based on the Space of Master–Slave Movement

Local corner smoothing method is commonly adopted to smooth linear (G01) tool path segments in computer numerical control (CNC) machining to realize continuous motion at transition corners. However, because of the highly non-linear relation between the arc-length and the spline parameter, and the challenge to synchronize the tool tip position and tool orientation, real-time and high-order continuous five-axis tool path smoothing and interpolation algorithms have not been well studied. This paper proposes a real-time C3 continuous corner smoothing and interpolation algorithm for five-axis machine tools. The transition corners of the tool tip position and tool orientation are analytically smoothed in the workpiece coordinate system (WCS) and the machine coordinate system (MCS) by C3 continuous PH splines, respectively. The maximum deviation errors of the smoothed tool tip position and the tool orientation are both constrained in the WCS. An analytical synchronization algorithm is developed to guarantee the motion variance of the smoothed tool orientation related to the tool tip displacement is also C3 continuous. The corresponding real-time interpolation method is developed with a continuous and peak-constrained jerk. Simulation results verify that the maximum deviation errors caused by the tool path smoothing algorithm are constrained, and continuous acceleration and jerk of each axis are achieved along the entire tool path. Comparisons demonstrate that the proposed algorithms achieve lower amplitude and variance of acceleration and jerk when compared with existing methods. Experiments show that the proposed five-axis corner smoothing and interpolation algorithms are serially executed in real-time with 0.5-ms cycle.

Overlap classification-based and kinematically coordinated corner rounding using double asymmetrical transitions for five-axis short-segmented tool path

Feedrate blending method for five-axis linear tool path under geometric and kinematic constraints

Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end tools. Tool orientation can be specified in terms of tool inclination and tool tilt angles. For a given surface path, these aspects need to be specified for each cutter contact point along the path, because poor tool orientation choice can cause large axial acceleration of the machine tool, leading to inferior quality of the machined surface. The rotation-minimizing frame aims to reduce unnecessary frame rotation during movement. This concept has been adopted to develop tool orientation methods that allow variation in the inclination angle, the tilt angle, and both the inclination and tilt angles. The intention is to reduce unnecessary rotation of the tool frame as the tool follows a specified path. Evaluation was conducted in the context of five-axis flat-end tool machining. Based on these methods, tool orientation was planned along surface paths of a torus, sphere, and dome. Changes in tool orientation were always smooth. From the perspective of reducing tool orientation changes and axial acceleration, it was demonstrated that simultaneous variation of the inclination and tilt angles based on rotation minimization provided the best results.

Accuracy enhancement of five-axis CNC machines through real-time error compensation

The accuracy of high speed five-axis machine tool is mainly determined by the contour accuracy of machine tools. The contour accuracy evaluation and improvement of 5-axis machine tools have always been concerned. In order to simplify the calculation of five-axis contour error considering the synchronization between tool tip position and tool orientation, a novel five-axis contour evaluation index TCCE(Two-point Cutter location Contour Error) is proposed in this paper, which is based on the tool axis trajectory surface. The calculating method of the proposed index by NC servo encoder input from 5-axis machine tools is introduced. Finally, the experiment is performed to evaluate the trajectory accuracy and servo matching performance of the machine tool with the proposed contour error evaluation index and the calculating method.

This paper presents a cutter partition-based tool orientation optimization algorithm that can identify and eliminate both local and rear gouging in five-axis machining. This algorithm is developed to generate smooth gouge-free tool paths for arbitrary free-form surfaces machined by general Automatically Programmed Tools (APT) cutters. The algorithm involves an iterative process of cutter projection to compute the gouge-free cutter positions. During each iteration, the cutter partition method is used to classify the cutting portion of the cutter, which in turn determines the gouging condition. Based on the classification, the algorithm applies an optimal gouge-avoidance strategy to minimize the size of tool orientation and position changes. The proposed algorithm can handle the combination of local and rear gouging (either separately or simultaneously), guarantee front edge cutting (avoiding damage to the cutter and surface), ensure a safety clearance between the rear edge of the cutter and the machined surface, and achieve minimal interruption to tool orientation and position from gouge avoidance. Simulation and cutting experiments confirm the effectiveness of the proposed algorithm.

Posture-dependent stability prediction of a milling industrial robot based on inverse distance weighted method

Real-time composite smoothing interpolation for improved contour accuracy and surface quality in five-axis CNC machining

High-accuracy contouring error estimation is the premise of effective contouring error control. However, two key factors make it complex to estimate contouring error for multi-axis machines with rotary axes: the nonlinear kinematics and the synchronization requirement of the tool tip position and tool orientation. This paper proposes a generalized online estimation algorithm of multi-axis contouring errors for CNC machine tools with rotary axes. The nearest reference tool pose to the actual one is searched at first, and then the corresponding contouring error components on each axis are estimated by using linear ratio estimation, where the tool tip position and tool orientation are naturally synchronized to one same pose on the desired trajectory. The advantage of the proposed contouring error estimation algorithm is that only the interpolated reference poses and drive commands are needed in the calculation, which increases the generality of the algorithm to different trajectory types and machine topologies. On the other hand, the calculation load is reduced when compared with existing iterative multi-axis contouring error estimation approaches. Simulation results on both five- and four-axis machines show that the proposed contouring error estimation algorithm can estimate axis components of contouring errors with high accuracy. Experiment results on an in-house developed five-axis experiment platform verify the effectiveness of the proposed algorithm.

We have established the geometric theory of cutting stock with flat end mills in five-axis CNC machining and an accurate and efficient approach to 3D geometric modeling of un-deformed chips in this machining (Chang et al. Comput Aided Des 88:42–59, 2017). The work has laid a theoretical foundation for geometrical and physical simulation for five-axis milling. However, fillet and ball end mills are more popular than flat end mills. The equations of the instantaneous cutting edges of a fillet end mill are more complicated in the geometric theory, and the boundary of the area covered by the cutting edges is more difficult to determine. Therefore, this article is to formulate the instantaneous cutting edges and their critical points in five-axis milling and to illustrate how to use the boundary construction diagram to determine the boundary with two examples of the geometric and the physical simulations. This work is verified with the valid results of the examples, and the results indicate that this model can take into account the errors of cutter and machine tool. Therefore, the geometric theory is viable, and its application on the five-axis milling simulation is feasible for high-performance machining.

The discontinuities of a five-axis linear-segment toolpath result in fluctuation in the feedrate, acceleration and jerk commands that lead to machine tool vibration and poor surface finish. For path smoothing, with the global curve-fitting method it is difficult to control fitting error and the local corner-smoothing method has large curvature extreme. For path synchronization, the parameter synchronization method cannot ensure smooth rotary motion. Aiming at these problems, this paper proposes a double B-spline curve-fitting and synchronization-integrated feedrate scheduling method. Two C2-continuous and error-bounded B-spline curves are produced to fit tool-tip position and tool orientation, respectively. The fitting error is controlled by locally refining the curve segments that exceed the fitting tolerance. The tool-tip position trajectory is firstly planned to address axial kinematic constraints in the feedrate scheduling process. Then the feedrate is deformed for the tool orientation to guarantee smooth rotary motion as well as to share the same motion time with the tool-tip position segment by segment. The feasibility and effectiveness of the proposed method have been validated by simulations and experiments on the S-shape test piece. Simulations show that the proposed curve-fitting method can generate smooth toolpath and constrain fitting error. The proposed feedrate scheduling method can guarantee smooth rotary motion and keep axial motions under kinematic limits, compared with the method that does not consider axial kinematic constraints and the parameter synchronization method. Experimental results verify that the proposed curve-fitting method can generate smooth tool path under fitting tolerance, and the proposed feedrate scheduling method can produce smooth and restricted axial motions.

As many operating parameters are involved in five-axis machining and significantly affect the machining results, use of either an analytical method or an experimental method can only solve the problem to a degree. Therefore, a concept for developing a database system using a neural network as the inference mechanism for the purpose of improving the quality of five-axis machining was addressed in this research. A database system was constructed on the basis of the VERICUT cutting simulation and experimental data from previous literature. The simulation data were put into an intelligent database for automatic generation of the suitable tool inclination angle for each cutting point on the machined surface. The tool inclination angle was the dominating factor for improving the surface quality in five-axis machining. The inclination angle was further entered into a post-processor to modify the cutter location file and to generate the numerical control (NC) program file for practical machining. The input data used in the database required for this system are basic operating parameters, quality requirements and the geometry of the designed sculptured surface. In this research, an intelligent database system for ball mills was successfully established for five-axis machining.

A novel tool path smoothing algorithm of 6R manipulator considering pose-dependent dynamics by designing asymmetrical FIR filters

3½½-axis machining combines the flexibility of orientation offered by five-axis machines with the ease of programming offered by three-axis machines. In 3½½-axis machining the surface is divided into patches and the tool orientation is locked during the cutting of each patch. These regions or patches can be machined separately using a different tool orientation and feed direction. This paper presents improvements in the partitioning scheme and a method for determining an optimal tool direction and feed direction for each patch. Three different types of surface are utilised in this study, along with actual machining experiments. The results are compared to traditional three-axis machining and simultaneous five-axis machining.