A Real-Time C3 Continuous Tool Path Smoothing and Interpolation Algorithm for Five-Axis Machine Tools

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

In this study, the contouring control problem of a five-axis machine tool was examined. Due to the rotation axes, there are two coordinate systems involved in the five-axis machine tool, namely the workpiece coordinate system and machine coordinate system. The five-axis machine tool is required to follow a given desired path with tool orientation specified in the workpiece coordinate system. However, the system dynamics of the machine tool is described in the machine coordinates. Kinematic transformations exist between the two coordinate systems. One challenge of the problem is to design a controller in the machine coordinate system that will meet the requirements in the workpiece coordinate system. Another challenge is to minimize both the position contour error and tool orientation error. The method of equivalent errors is adopted to design the contouring controller. The desired path and tool orientation in the workpiece coordinate system are transformed into a five-dimensional hyper-curve in the machine coordinate system. A contouring controller was designed to follow the five-dimensional hyper-curve using the method of equivalent errors. Both numerical and experimental results validate the effectiveness of the proposed contouring control method.

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

The smoothing of linear toolpaths plays is critical in improving machining quality and efficiency in five-axis CNC machining. Existing corner-smoothing methods often overlook the impact of spline curvature fluctuations, which may lead to acceleration variations, hindering surface quality improvements. The paper presents a five-axis toolpath corner-smoothing method based on the space of master–slave movement (SMM), aiming to minimize curvature fluctuations in five-axis machining and improve surface quality. The concept of movement space in master–slave cooperative motion is introduced, where the tool tip position and tool orientation are decoupled into a main motion trajectory and two master–slave movement space trajectories. By deriving the curvature monotony conditions of a dual Bézier spline, a G2-continuous tool tip corner-smoothing curve with minimal curvature fluctuations is constructed in real-time. Subsequently, using the SMM and the asymmetric dual Bézier spline, a high-order continuous synchronization relationship between the tool tip position and tool orientation is established. Simulation tests and machining experiments show that with our smoothing algorithm, maximum acceleration values for each axis were reduced by 21.05%, while jerk was lowered by 22.31%. These results indicate that trajectory smoothing significantly reduces mechanical vibrations and improves surface quality.

A realtime curvature-smooth interpolation scheme and motion planning for CNC machining of short line segments

Toolpath smoothing with reduced curvature and synchronized motion for hybrid robots

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.

Tool-path smoothing is essential for ensuring continuous motion at transition corners between linear segments, since kinematic discontinuities degrade both machining efficiency and surface quality. Most existing spline-based methods achieve only G2 or C2 continuity and therefore produce discontinuous jerk, which can excite high-order structural resonances. Achieving true C3 continuity remains challenging, particularly because synchronizing tool-tip position and orientation is complicated by the nonlinear relationship between arc length and spline parameterization. This study presents an analytical Catmull–Rom (CR) spline–based method for C3-continuous tool-path smoothing in five-axis CNC milling. Transition corners are replaced by adjustable Catmull–Rom (ACR) splines, whose control points and tuning parameters are designed or optimized to constrain the deviation from the original path. The remaining linear segments are also substituted with ACR splines to enforce position–orientation synchronization, with control points that can be chosen analytically to guarantee zero synchronization error. The proposed method is fully analytical and non-iterative. Numerical simulations demonstrate that the generated tool paths satisfy prescribed geometric tolerances, produce smooth and continuous jerk profiles, and achieve exact synchronization between tool-tip position and orientation.

This paper describes a novel methodology for generating grinding tool paths, orientations and grinding parameters based on the captured trajectories of a surface finishing tool operated by the skilled operator. First, a variable frame size moving window principal component analysis is performed on the trajectories. Next, features such as the amplitude, speed of the tool centre point, direction of travel, average position, contact force and orientation of the grinder are calculated. Kernel k-means clustering is applied to the trajectory’s feature vectors for segmentation into the tool path primitives. The robotic tool path primitives would be ordered similar to the manual tool path primitives in the grinding strategy. The robotic tool path primitives are then generated based on the boundaries of the manual tool path primitive in a computer-aided manufacturing software. Anchor points are selected from the corners and at intermediate sections along the robotic tool path to inherit the orientations of the manual tool path. Using the inherited skilled operator tool orientations, spherical linear interpolation and spherical spline quaternion interpolation are used to interpolate the orientations for the robotic tool path points along the cross curves, followed by the flow curves, respectively. A finite element model of the belt grinding process is also introduced to quantify the effect of the contact wheel serrations on the material removal rate. This is to account for the difference in contact wheel design between the handheld and robotic grinding tool. The programmed robotic tool paths generated from the trajectories captured from a skilled operator were proven to be able to grind the workpiece to the desired profile within the desired tolerance in a pre-production environment.

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

Tool path generation is a fundamental problem in 5-axis CNC machining, which consists of tool orientation planning and cutter-contact (CC) point planning. The planning strategy highly depends on the type of tool cutters. For ball-end cutters, the tool orientation and CC point location can be planned separately; while for flat end cutters, the two are highly dependent on each other. This paper generates a smooth tool path of workpiece surfaces for flat end mills from two stages: Computing smooth tool orientations on the surface without gouging and collisions and then designing the CC point path. By solving the tool posture optimization problem the authors achieve both the path smoothness and the machining efficiency. Experimental results are provided to show the effectiveness of the method.

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.

Dual Drive Curve Tool Path Planning Method for 5-axis NC Machining of Sculptured Surfaces

In recent years, the productivity of machine tools have been significantly improved by using computer based CAD/CAM systems for Computer Numerical Control(CNC) program generation. There are many CAM software in the market that provide tool path programming and can be applied to different types of machining. However, in most cases the efficiency of machining in CNC is still relied on the optimization of the tool path. Hence, this present paper presents a Genetic Algorithm Tool Path Optimization (GATPO) method using to obtain the shortest tool path for three axes CNC drilling machine. A user friendly Graphical User Interface (GUI) has been developed using MATLAB to input various parameters which adapts Travelling Salesman Problem(TSP) in determining the distance took during machining. Two kinds of crossover method have been applied, i.e., single-point crossover and two-point crossover to observe the effect of them. The simulation result ascertained that our proposed GA based tool path optimization is useful to find a lower distance of tool path generation for hole drilling process.

Five-axis complex surface machining on a Computer Numerically Controlled (CNC) machine needs CAD/CAM system for the cutter location and orientation data. Since these data are defined with respect to the coordinate system of work-piece, they need to be converted to the machine’s control commands in machine coordinate system, through processing so called a CNC post-processing. In this work, a kinematic model method and a efficient algorithm for CNC post-processing have been presented for a typical five-axis milling machine of table rotating/tilting type. The proposed algorithms have been realized in our developing CNC system.