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

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

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

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

Machine Learning Techniques on Multidimensional Curve Fitting Data Based on R- Square and Chi-Square Methods

Curve fitting is one of the procedures in data analysis and is helpful for prediction analysis showing graphically how the data points are related to one another whether it is in linear or non-linear model. Usually, the curve fit will find the concentrates along the curve or it will just use to smooth the data and upgrade the presence of the plot. Curve fitting checks the relationship between independent variables and dependent variables with the objective of characterizing a good fit model. Curve fitting finds mathematical equation that best fits given information. In this paper, 150 unorganized data points of environmental variables are used to develop Linear and non-linear data modelling which are evaluated by utilizing 3 dimensional ‘Sftool’ and ‘Labfit’ machine learning techniques. In Linear model, the best estimations of the coefficients are realized by the estimation of R- square turns in to one and in Non-Linear models with least Chi-square are the criteria.

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

Piecewise Arc-Length Parameterized NURBS Tool Paths Generation for 3-Axis CNC Machining of Accurate, Smooth Sculptured Surfaces

In current industrial applications many engineering parts having complex shapes are designed using sculptured surfaces in CAD system. Due to the lack of smooth motions and accurate machining of these surfaces using standard linear and circular motions in conventional CNC machines, new commercial CNC systems are equipped with parametric curve interpolation function. However, in some applications these surfaces can be very complex that are susceptible to gouging and due to the approximation of; CL-path in CAM system and path parameter in real –time, high machining accuracy, smooth kinematic and feed-rate profiles, are difficult to achieve. This dissertation focuses on developing algorithms that generate tool paths in NURBS form for smooth, high speed and accurate sculptured surface machining. The first part of the research identifies and eliminates gouge cutter location (CL) point from the tool path. The proposed algorithm uses global optimization technique (Particle Swarm Optimization) to check all the CC-points along a tool-path with high accuracy, and only gouging free CC-points are used to generate the set of valid CL-points. Mathematical models have been developed and implemented to cover most of the cutter shapes, used in the industry. In the second phase of the research, all valid CL-points along the tool-path are used to generate CL-path in B-spline form. The main contribution of this part is to formulate an error function of the offset approximation and to represent it in NURBS form to globally bound the approximation errors. Based on this error function, an algorithm is proposed to generate tool-paths in B-spline from with; globally controlled accuracy, fewer control points and low function degree, compared to its contemporaries. The proposed approach thus presents an error-bounded method for B-spline curve approximation to the ideal CL-path within the accuracy. This part of research has two components, one is for 2½- axis (pocket) and the other one is for 3-axis (surface) CNC machining. The third part deals with the problem of CL-path parameter estimation during machining in real time. Once the gouging free CL-path in NURBS form with globally controlled accuracy is produced, it is re-parameterized with approximate arc-length in the off-line stage. The main features of this work are; (1) sampling points and calculating their approximate arc-lengths within error bound by decomposing the input path into Bezier curve segments, (2) fitting the NURBS curve with approximate arc-length parameter to the sample points until the path and parameterization errors are within the tolerance, and (3) segment the curve into pieces with different feed rates if during machining the cutter trajectory errors are beyond the tolerance at highly curved regions in the NURBS tool path

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

Optimized NURBS Curve Based G-Code Part Program for CNC Systems

Indiana University-Purdue University Indianapolis (IUPUI)Computer Numerical Control (CNC) is widely used in many industries that needs high speed machining of the parts with high precision, accuracy and good surface finish. In order to avail this the generation of the CNC part program size will be immensely big and leads to an inefficient process, which increases the delivery time and cost of products. This work presents the automation of high-accuracy CNC tool trajectory planning from CAD to G-code generation through optimal NURBs surface approximation. The proposed optimization method finds the minimum number of NURBS control points for a given admissible theoretical cord error between the desired and manufactured surfaces. The result is a compact part program that is less sensitive to data starvation than circular and spline interpolations with potential better surface finish. The proposed approach is demonstrated with the tool path generation of an involute gear profile and a topologically optimized structure is developed using this approach and then finally it is 3D printed

Smooth Trajectory Generation for Machine Tools and Industrial Robots

This thesis presents accurate and time-optimal smooth reference trajectory generation techniques for manufacturing equipment such as high-speed machine tools (MT) and industrial robots (IR). Typical machining tool-paths for MTs and IRs are defined as a series of discrete linear moves. Although Point-to-Point (P2P) feed motion can be generated by interpolating each linear segment with high-order velocity profiles, the continuous and accurate transition between consecutive segments is necessary to realize a non-stop contouring motion for efficient manufacturing. To generate continuous feed motion along sharp cornered tool-paths, most numerical control (NC) systems blend (smooth) corners locally using various curves and splines. The feed (speed) is reduced around the blend sections so that the motion system’s kinematic limits are respected. This thesis proposes 2 novel techniques to enable modern MT and IR to generate non-stop rapid motion along discrete tool-paths. Firstly, a Kinematic Corner Smoothing (KCS) technique has been proposed to generate time-optimal (minimum time) motion trajectories in a real-time within axis kinematic limits. A novel real-time interpolation technique based on Finite Impulse Response (FIR) filtering has also been proposed to suppress residual vibrations for high positioning accuracy of machine tools and motion systems as well. These two techniques are tailored for Cartesian structured motion systems such as 2-3 axis machine tools. Finally, a decoupled FIR filtering technique has been developed to synchronously interpolate tool position and orientation for accurate motion generation for 5-axis MTs and IRs. These techniques are computationally lightweight and suitable for real-time implementation on modern NC systems. Simulation and experimental validation on Cartesian and 5-axis machine tools are presented to validate the effectiveness of the developed algorithms to interpolate along with discrete commands for high-speed and high-accuracy motion