Toolpath Smoothing using Clothoids for High Speed CNC Machines

As a result of this research, new methods for CNC toolpath smoothing were developed. Utilising these methods can increase the speed, decrease vibrations and improve the cut quality of a CNC machine. In the developed techniques, Euler spirals have been used to smooth the corners

Smooth and Time-Optimal Trajectory Generation for High Speed Machine Tools

In machining complex dies, molds, aerospace and automotive parts, or biomedical components, it is crucial to minimize the cycle time, which reduces costs, while preserving the quality and tolerance integrity of the part being produced. To meet the demands for high quality finishes and low production costs in machining parts with complex geometry, computer numerical control (CNC) machine tools must be equipped with spline interpolation, feedrate modulation, and feedrate optimization capabilities. This thesis presents the development of novel trajectory generation algorithms for Non Uniform Rational B-Spline (NURBS) toolpaths that can be implemented on new low-cost CNC's, as well as, in conjunction with existing CNC's. In order to minimize feedrate fluctuations during the interpolation of NURBS toolpaths, the concept of the feed correction polynomial is applied. Feedrate fluctuations are reduced from around 40 % for natural interpolation to 0.1 % for interpolation with feed correction. Excessive acceleration and jerk in the axes are also avoided. To generate jerk-limited feed motion profiles for long segmented toolpaths, a generalized framework for feedrate modulation, based on the S-curve function, is presented. Kinematic compatibility conditions are derived to ensure that the position, velocity, and acceleration profiles are continuous and that the jerk is limited in all axes. This framework serves as the foundation for the proposed heuristic feedrate optimization strategy in this thesis. Using analytically derived kinematic compatibility equations and an efficient bisection search algorithm, the command feedrate for each segment is maximized. Feasible solutions must satisfy the optimization constraints on the velocity, control signal (i.e. actuation torque), and jerk in each axis throughout the trajectory. The maximized feedrates are used to generate near-optimal feed profiles that have shorter cycle times, approximately 13-26% faster than the feed profiles obtained using the worst-case curvature approach, which is widely used in industrial CNC interpolators. The effectiveness of the NURBS interpolation, feedrate modulation and feedrate optimization techniques has been verified in 3-axis machining experiments of a biomedical implant

Time-Optimal Feedrate Planning for Freeform Toolpaths for Manufacturing Applications

Optimality and computational efficiency are two desired yet competing attributes of time-optimal feedrate planning. A well-designed algorithm can vastly increase machining productivity, by reducing tool positioning time subject to limits of the machine tool and process kinematics. In the optimization, it is crucial to not overload the machining operation, saturate the actuators’ limits, or cause unwanted vibrations and contour errors. This presents a nonlinear optimization problem for achieving highest possible feedrates along a toolpath, while keeping the actuator level velocity, acceleration and jerk profiles limited. Methods proposed in literature either use highly elaborate nonlinear optimization solvers like Sequential Quadratic Programming (SQP), employ iterative heuristics which extends the computational time, or make conservative assumptions that reduces calculation time but lead to slower tool motion. This thesis proposes a new feedrate optimization algorithm, which combines recasting of the original problem into a Linear Programming (LP) form, and the development of a new windowing scheme to handle very long toolpaths. All constraint equations are linearized by applying B-spline discretization on the kinematic profiles, and approximating the nonlinear jerk equation with a linearized upper bound (so-called ‘pseudo-jerk’). The developed windowing algorithm first solves adjacent portions of the feed profile with zero boundary conditions at overlap points. Afterwards, using the Principle of Optimality, connection boundary conditions are identified that guarantee a feasible initial guess for blending the pre-solved adjacent feed profiles into one another, through a consecutive pass of LP. Experiments conducted at the sponsoring company of this research, Pratt & Whitney Canada (P&WC), show that the proposed algorithm is able to reliably reduce cycle time by up to 56% and 38% in two different contouring operations, without sacrificing dynamic positioning accuracy. Benchmarks carried out with respect to two earlier proposed feedrate optimization algorithms, validate both the time optimality and also drastic (nearly 60 times) reduction in the computational load, achieved with the new method. Part quality, robustness and feed drive positioning accuracy have also been validated in 3-axis surface machining of a part with 1030 waypoints and 10,000 constraint checkpoints

Toolpath algorithm for free form irregular contoured walls / surfaces with internal deflecting connections.

This paper presents a toolpath generation method to efficiently machine free form irregular contoured walls / surfaces (FIWS) containing internal deflecting connections (IDC’s). The toolpath generation method is based on a series of identifications and calculations, where initially a ‘Main Computable Zone (MCZ)’ in the Machinable Areas (Ma’s) of FIWS is identified based on the Tool track dimensions (Td). Then the MCZ’s are divided into Split Computable Zones (SCZ’s) and Split Computable Zones for Internal Connections (SCZI’s) which are subsequently sub divided as ‘Categorized Computable Zones’ (CCZ) with simple-medium-high complexity. The identification of CCZ’s is based on the 10 different types of FIWS representations developed for this study. From the CCZ’s categorization of complexity, they are further split into smaller ‘Machinable Zones (MZ’s)’ using a 4-step algorithm. In the algorithm, the first step calculates a common plane (CP) to cut the steep areas in the CCZ’s where the tool cannot have full access for machining. Once the CP is identified, the second step is to extend it by moving them along the CCZ’s and calculate the necessary ‘Machinable Zones (MZ’s)’ in the next stage. This is done by finding the intersection of CP with the FIWS through a point to point / line plane intersection concept. After this step, the MZ’s are re-iterated by including the open and closed surface criteria and is analyzed for the IDC’s to be combined in the fourth stage. This is achieved by adding up the IDC’s with the existing MZ’s computed by the algorithm. At every stage, the algorithm considers tool collision avoidance and tool rubbing in the CCZ’s and MZ’s . This is by an automatic computation based on the height to fixture clearance for safer neck length which avoids collision and rubbings in the final toolpaths. Finally, a combined tool path is generated for all the MZ’s and has been verified / tested for a sample part and impeller containing similar shapes using UG NX / STEP –NC software

Optimized normal and distance matching for heterogeneous object modeling

This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material governing features for designing a heterogeneous object. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into equal number of segments, a series of intermediate piecewise curves are generated to represent the material metamorphosis between the governing material features. Alternatively, a dynamic programming approach developed in our earlier work is presented for comparison purposes. Result and computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper

Real-Time Jerk Limited Feedrate Profiling and Interpolation for Linear Motor Multiaxis Machines Using NURBS Toolpaths

In this article, a NURBS toolpath feedrate profile generation algorithm for a biaxial linear motor control system is presented. High achievable velocities and accelerations of linear motor machines present new computational challenges in implementing feedrate generation and toolpath interpolation algorithms in real-time controllers. The proposed algorithm is capable of online generation of the feedrate profile with axial acceleration and jerk constraints. Each stage of the feedrate profiling algorithm is described with attention being given to both performance and implementation aspects. Furthermore, an alternative to the commonly used Taylor series interpolation method is also tested to ensure minimal interpolation errors. The feedrate profiling and interpolation algorithms’ implementation in a PC-based controller with real-time Linux kernel is described. Experimental results are presented that confirm that the algorithm is capable of limiting acceleration and jerk in the machine’s axes and it is low computation time enables real-time on-line operation in a PC-based CNC controller

Novel control approaches for the next generation computer numerical control (CNC) system for hybrid micro-machines

It is well-recognised that micro-machining is a key enabling technology for manufacturing high value-added 3D micro-products, such as optics, moulds/dies and biomedical implants etc. These products are usually made of a wide range of engineering materials and possess complex freeform surfaces with tight tolerance on form accuracy and surface finish.In recent years, hybrid micro-machining technology has been developed to integrate several machining processes on one platform to tackle the manufacturing challenges for the aforementioned micro-products. However, the complexity of system integration and ever increasing demand for further enhanced productivity impose great challenges on current CNC systems. This thesis develops, implements and evaluates three novel control approaches to overcome the identified three major challenges, i.e. system integration, parametric interpolation and toolpath smoothing. These new control approaches provide solid foundation for the development of next generation CNC system for hybrid micro-machines.There is a growing trend for hybrid micro-machines to integrate more functional modules. Machine developers tend to choose modules from different vendors to satisfy the performance and cost requirements. However, those modules often possess proprietary hardware and software interfaces and the lack of plug-and-play solutions lead to tremendous difficulty in system integration. This thesis proposes a novel three-layer control architecture with component-based approach for system integration. The interaction of hardware is encapsulated into software components, while the data flow among different components is standardised. This approach therefore can significantly enhance the system flexibility. It has been successfully verified through the integration of a six-axis hybrid micro-machine. Parametric curves have been proven to be the optimal toolpath representation method for machining 3D micro-products with freeform surfaces, as they can eliminate the high-frequency fluctuation of feedrate and acceleration caused by the discontinuity in the first derivatives along linear or circular segmented toolpath. The interpolation for parametric curves is essentially an optimization problem, which is extremely difficult to get the time-optimal solution. This thesis develops a novel real-time interpolator for parametric curves (RTIPC), which provides a near time-optimal solution. It limits the machine dynamics (axial velocities, axial accelerations and jerk) and contour error through feedrate lookahead and acceleration lookahead operations. Experiments show that the RTIPC can simplify the coding significantly, and achieve up to ten times productivity than the industry standard linear interpolator. Furthermore, it is as efficient as the state-of-the-art Position-Velocity-Time (PVT) interpolator, while achieving much smoother motion profiles.Despite the fact that parametric curves have huge advantage in toolpath continuity, linear segmented toolpath is still dominantly used on the factory floor due to its straightforward coding and excellent compatibility with various CNC systems. This thesis presents a new real-time global toolpath smoothing algorithm, which bridges the gap in toolpath representation for CNC systems. This approach uses a cubic B-spline to approximate a sequence of linear segments. The approximation deviation is controlled by inserting and moving new control points on the control polygon. Experiments show that the proposed approach can increase the productivity by more than three times than the standard toolpath traversing algorithm, and 40% than the state-of-the-art corner blending algorithm, while achieving excellent surface finish.Finally, some further improvements for CNC systems, such as adaptive cutting force control and on-line machining parameters adjustment with metrology, are discussed in the future work section.It is well-recognised that micro-machining is a key enabling technology for manufacturing high value-added 3D micro-products, such as optics, moulds/dies and biomedical implants etc. These products are usually made of a wide range of engineering materials and possess complex freeform surfaces with tight tolerance on form accuracy and surface finish.In recent years, hybrid micro-machining technology has been developed to integrate several machining processes on one platform to tackle the manufacturing challenges for the aforementioned micro-products. However, the complexity of system integration and ever increasing demand for further enhanced productivity impose great challenges on current CNC systems. This thesis develops, implements and evaluates three novel control approaches to overcome the identified three major challenges, i.e. system integration, parametric interpolation and toolpath smoothing. These new control approaches provide solid foundation for the development of next generation CNC system for hybrid micro-machines.There is a growing trend for hybrid micro-machines to integrate more functional modules. Machine developers tend to choose modules from different vendors to satisfy the performance and cost requirements. However, those modules often possess proprietary hardware and software interfaces and the lack of plug-and-play solutions lead to tremendous difficulty in system integration. This thesis proposes a novel three-layer control architecture with component-based approach for system integration. The interaction of hardware is encapsulated into software components, while the data flow among different components is standardised. This approach therefore can significantly enhance the system flexibility. It has been successfully verified through the integration of a six-axis hybrid micro-machine. Parametric curves have been proven to be the optimal toolpath representation method for machining 3D micro-products with freeform surfaces, as they can eliminate the high-frequency fluctuation of feedrate and acceleration caused by the discontinuity in the first derivatives along linear or circular segmented toolpath. The interpolation for parametric curves is essentially an optimization problem, which is extremely difficult to get the time-optimal solution. This thesis develops a novel real-time interpolator for parametric curves (RTIPC), which provides a near time-optimal solution. It limits the machine dynamics (axial velocities, axial accelerations and jerk) and contour error through feedrate lookahead and acceleration lookahead operations. Experiments show that the RTIPC can simplify the coding significantly, and achieve up to ten times productivity than the industry standard linear interpolator. Furthermore, it is as efficient as the state-of-the-art Position-Velocity-Time (PVT) interpolator, while achieving much smoother motion profiles.Despite the fact that parametric curves have huge advantage in toolpath continuity, linear segmented toolpath is still dominantly used on the factory floor due to its straightforward coding and excellent compatibility with various CNC systems. This thesis presents a new real-time global toolpath smoothing algorithm, which bridges the gap in toolpath representation for CNC systems. This approach uses a cubic B-spline to approximate a sequence of linear segments. The approximation deviation is controlled by inserting and moving new control points on the control polygon. Experiments show that the proposed approach can increase the productivity by more than three times than the standard toolpath traversing algorithm, and 40% than the state-of-the-art corner blending algorithm, while achieving excellent surface finish.Finally, some further improvements for CNC systems, such as adaptive cutting force control and on-line machining parameters adjustment with metrology, are discussed in the future work section

Toolpath interpolation and smoothing for computer numerical control machining of freeform surfaces : a review

Driven by the ever increasing demand in function integration, more and more next generation high value-added products, such as head-up displays, solar concentrators and intra-ocular-lens, etc., are designed to possess freeform (i.e., non-rotational symmetric) surfaces. The toolpath, composed of high density of short linear and circular segments, is generally used in computer numerical control (CNC) systems to machine those products. However, the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration, which will decrease the machining efficiency and product surface finish. Driven by the ever-increasing need for high-speed high-precision machining of those products, many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry, aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods. This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications. The advantages and disadvantages of these approaches are discussed. Possible future research directions are also offered

A certification method for the milling process of free-form surfaces using a test part

International audienceIt is generally admitted that the manufacturing of free-form surfaces requires the use of a CAD-CAM system. The toolpath accuracy and the dimensional quality of the final shape have to be in accordance with the geometrical specifications. But most of the time, the final parts present deviations from the expected shape. These deviations may be due to either the toolpath calculation (CAM system) or the cutting process itself. In the paper, we propose an analysis of the whole milling process to point out the possible sources of errors. These errors generally lead to geometrical deviations and the final part does not meet the required specifications. As the errors can be linked to geometrical particularities of the shape, we propose a test part associated with check means to bring out problems. The milling of this part using two different techniques of toolpath generation shows that obviously both toolpaths are not error-free and that errors result from different geometrical particularities of the part surfaces