A real-time interpolator for parametric curves

Driven by the ever increasing need for the high-speed high-accuracy machining of freeform surfaces, the interpolators for parametric curves become highly desirable, as they can eliminate the feedrate and acceleration fluctuation due to the discontinuity in the first derivatives along the linear tool path. The interpolation for parametric curves is essentially an optimization problem, and it is extremely difficult to get the time-optimal solution. This paper presents 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, meanwhile, the feedrate is maintained as high as possible with minimum fluctuation. The lookahead length is dynamically adjusted to minimize the computation load. And the numerical integration error is considered during the lookahead calculation. Two typical parametric curves are selected for both numerical simulation and experimental validation, a cubic phase plate freeform surface is also machined. The numerical simulation is performed using the software (open access information is in the Acknowledgment section) that implements the proposed RTIPC, the results demonstrate the effectiveness of the RTIPC. The real-time performance of the RTIPC is tested on the in-house developed controller, which shows satisfactory efficiency. Finally, machining trials are carried out in comparison with the industrial standard linear interpolator and the state-of-the-art Position-Velocity-Time (PVT) interpolator, the results show the significant advantages of the RTIPC in coding, productivity and motion smoothness

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

Improving Contouring Accuracy in CNC Machines

Ph.DDOCTOR OF PHILOSOPH

Arc-Length Parameterized NURBS Tool Path Generation and Velocity Profile Planning for Accurate 3-Axis Curve Milling

In modern industrial CNC (Computer Numerical Control) machining processes, the pursuing of higher accuracy and efficiency has always been one of the most important tasks to be discussed and studied. A lot of proposed algorithms are developed in order to optimize the machining performance in either of the above focused domains. Nevertheless, there is forever a trade-off between gaining less machining error and providing higher feed rate. As for machining a free-shaped curve (e.g., Bezier curves, B-splines and NURBS) in a three-dimensional space, a better manner to balance out the aforementioned trade-offs turns out to be even more critical and essential. The conventional iterative function used for tool path generation could cause feed rate fluctuation during the actual machining, and it thus might lead to failure on constraining the error within the machining accuracy requirement. Another potential problem occurs when the machining process comes across into a relatively high curvature segment with the prescribed high feed rate, due to the machine axial acceleration limit, the machine may not be able to maintain the tool tip trajectory within the error tolerance. Therefore, a new approach to NURBS tool path generation for high feed rate machining is proposed. In this work, several criterions are set for checking the viability of the prescribed feed rate and adjusting it according to the actual shape of the objective curve and the capability of the machine. After the offline feed rate viability check and readjustment, a new iterative algorithm based on the arc-length re-parameterized NURBS function would be implemented to calculate the tool path in real-time. By using this proposed method, the feed rate fluctuation is diminished and the overall efficiency of the machining process would have been optimized under the condition of accuracy guaranteed

Integrated Servomechanism And Process Control For Machining Processes

In this research, the integration of the servomechanism control and process control for machining processes has been studied. As enabling strategies for next generation quality control, process monitoring and open architecture machine tools will be implemented on production floor. This trend brings a new method to implement control algorithm in machining processes. Instead of using separate modules for servomechanism control and process control individually, the integrated controller is proposed in this research to simultaneously achieve goals in servomechanism level and the process level. This research is motivated by the benefits brought by the integration of servomechanism control and process control. Firstly, the integration simplifies the control system design. Secondly, the integration promotes the adoption of process control on production floor. Thirdly, the integration facilitates portability between machine tools. Finally, the integration provides convenience for both the servomechanism and process simulation in virtual machine tool environment. The servomechanism control proposed in this research is based on error space approach. This approach is suitable for motion control for complex contour. When implement the integration of servomechanism control and process control, two kinds of processes may be encountered. One is the process whose model parameters can be aggregated with the servomechanism states and the tool path does not need real time offset. The other is the process which does not have direct relationship with the servomechanism states and tool path may need to be modified real time during machining. The integration strategies applied in error space are proposed for each case. Different integration strategies would propagate the process control goal into the motion control scheme such that the integrated control can simultaneously achieve goals of both the servomechanism and the process levels. Integrated force-contour-position control in turning is used as one example in which the process parameters can be aggregated with the servomechanism states. In this case, the process level aims to minimize cutting force variation while the servomechanism level is to achieve zero contour error. Both force variation and contour error can be represented by the servomechanism states. Then, the integrated control design is formulated as a linear quadratic regulator (LQR) problem in error space. Force variation and contour error are treated as part of performance index to be minimized in the LQR problem. On the other hand, the controller designed by LQR in error space can guarantee the asymptotic tracking stability of the servomechanism for complex contour. Therefore, the integrated controller can implement the process control and the servomechanism control simultaneously. Cutter deflection compensation for helical end milling processes is used as one example in which the process cannot be directly associated with the servomechanism states. Cutter deflection compensation requires real-time tool path offset to reduce the surface error due to cutter deflection. Therefore, real time interpolation is required to provide reference trajectory for the servomechanism controller. With the real time information about surface error, the servomechanism controller can not only implement motion control for contour requirement, but also compensation for the dimensional error caused by cutter deflection. In other words, the real time interpolator along with the servomechanism controller can achieve the goals of both the servomechanism and process level. In this study, the cutter deflection in helical end milling processes is analyzed first to illustrate the indirect relationship between cutter deflection and surface accuracy. Cutter deflection is examined for three kinds of surfaces including straight surface, circular surface, and curved surface. The simulation-based deflection analysis will be used to emulate measurement from sensors and update the real-time interpolator to offset tool path. The controller designed through pole placement in error space can guarantee the robust tracking performance of the updated reference trajectory combining both contour and tool path offset required for deflection compensation. A variety of cutting conditions are simulated to demonstrate the compensation results. In summary, the process control is integrated with the servomechanism control through either direct servomechanism controller design without tool path modification or servomechanism control with real time interpolation responding to process variation. Therefore, the process control can be implemented as a module within machine tools. Such integration will enhance the penetration of process control on production floor to increase machining productivity and product quality

Hierarchical control of complex manufacturing processes

The need for changing the control objective during the process has been reported in many systems in manufacturing, robotics, etc. However, not many works have been devoted to systematically investigating the proper strategies for these types of problems. In this dissertation, two approaches to such problems have been suggested for fast varying systems. The first approach, addresses problems where some of the objectives are statically related to the states of the systems. Hierarchical Optimal Control was proposed to simplify the nonlinearity caused by adding the statically related objectives into control problem. The proposed method was implemented for contour-position control of motion systems as well as force-position control of end milling processes. It was shown for a motion control system, when contour tracking is important, the controller can reduce the contour error even when the axial control signals are saturating. Also, for end milling processes it was shown that during machining sharp edges where, excessive cutting forces can cause tool breakage, by using the proposed controller, force can be bounded without sacrificing the position tracking performance. The second approach that was proposed (Hierarchical Model Predictive Control), addressed the problems where all the objectives are dynamically related. In this method neural network approximation methods were used to convert a nonlinear optimization problem into an explicit form which is feasible for real time implementation. This method was implemented for force-velocity control of ram based freeform extrusion fabrication of ceramics. Excellent extrusion results were achieved with the proposed method showing excellent performance for different changes in control objective during the process --Abstract, page iv

Neural Network Contour Error Predictor in CNC Control Systems

Paper presented as poster presentation at MMAR 2016 conference (Międzyzdroje,Poland, 29 Aug.-1 Sept. 2016)This article presents a method for predicting contour error using artificial neural networks. Contour error is defined as the minimum distance between actual position and reference toolpath and is commonly used to measure machining precision of Computerized Numerically Controlled (CNC) machine tools. Offline trained Nonlinear Autoregressive networks with exogenous inputs (NARX) are used to predict following error in each axis. These values and information about toolpath geometry obtained from the interpolator are then used to compute the contour error. The method used for effective off-line training of the dynamic recurrent NARX neural networks is presented. Tests are performed that verify the contour error prediction accuracy using a biaxial CNC machine in a real-time CNC control system. The presented neural network based contour error predictor was used in a predictive feedrate optimization algorithm with constrained contour error

Rapid Identification of Virtual CNC Drives

Virtual manufacturing has gained considerable importance in the last decade. To obtain reliable predictions in a virtual environment, the factors that influence the outcome of a manufacturing operation need to be carefully modeled and integrated in a simulation platform. The dynamic behavior of the Computer Numerical Control (CNC) system, which has a profound influence on the final part geometry and tolerance integrity, is among these factors. Classical CNC drive identification techniques are usually time consuming and need to be performed by an engineer qualified in dynamics and control theory. These techniques require the servo loop or the trajectory interpolator to be disconnected in order to inject the necessary identification signals, causing downtime to the machine. Hence, these techniques are usually not practical for constructing virtual models of existing CNC machine tools in a manufacturing environment. This thesis presents an alternative strategy for constructing virtual drive models with minimal intervention and downtime to the machinery. The proposed technique, named “rapid identification”, consists of executing a short G-code experiment and collecting input/output data using the motion capture feature available on most CNC controllers. The data is then processed to reverse engineer the equivalent tracking and disturbance transfer functions and friction characteristics of the machine. It is shown that virtual drive models constructed this way can be used to predict the real machine’s contouring performance for large class of drive systems, controlled with different control techniques. In the proposed scheme, the excitation is delivered by smoothly interpolated motion commands. Hence, convergence of parameters to their true values is not guaranteed. When the real system contains pole-zero cancellations, namely due to feedforward control action, this also results in a loss of identifiability. In order to guarantee the stability of the identified drive models, the pole locations are constrained with frequency and damping ratio limits. Hence, the rapid identification task is cast as a constrained minimization problem. Two solution strategies have been developed. In the first approach, Lagrange Multipliers (LM) technique is applied, which yields successful estimation results. However, implementation of LM is computationally intensive and requires the use of a dedicated symbolic solver. This limits the portability for industrial implementation. In the second approach, a Genetic Algorithm (GA) search technique is developed, which is a more practical but slightly approximate alternative. The GA allows parameter bounds to be incorporated in a natural manner and converges to 2-3% vicinity of the LM solution in one-tenth of the computation time. The GA solution can be easily ported to different computation platforms. Both LM and GA identification techniques were validated in simulations and experiments conducted on virtual and real machine tool drives. It is shown that although the parameters estimated using the rapid identification scheme do not always match their true values, the key tracking and disturbance rejection characteristics of the drives are successfully captured in the frequency range of the CNC motion commands. Therefore, the drive models constructed with rapid identification can be used to predict the contouring accuracy of real machine tools in a virtual process planning environment. This thesis presents an alternative strategy for constructing virtual drive models with minimal intervention and downtime to the machinery. The proposed technique, named “rapid identification”, consists of executing a short G-code experiment and collecting input/output data using the motion capture feature available on most CNC controllers. The data is then processed to reverse engineer the equivalent tracking and disturbance transfer functions and friction characteristics of the machine. It is shown that virtual drive models constructed this way can be used to predict the real machine’s contouring performance for large class of drive systems, controlled with different control techniques. In the proposed scheme, the excitation is delivered by smoothly interpolated motion commands. Hence, convergence of parameters to their true values is not guaranteed. When the real system contains pole-zero cancellations, namely due to feedforward control action, this also results in a loss of identifiability. In order to guarantee the stability of the identified drive models, the pole locations are constrained with frequency and damping ratio limits. Hence, the rapid identification task is cast as a constrained minimization problem. Two solution strategies have been developed. In the first approach, Lagrange Multipliers (LM) technique is applied, which yields successful estimation results. However, implementation of LM is computationally intensive and requires the use of a dedicated symbolic solver. This limits the portability for industrial implementation. In the second approach, a Genetic Algorithm (GA) search technique is developed, which is a more practical but slightly approximate alternative. The GA allows parameter bounds to be incorporated in a natural manner and converges to 2-3% vicinity of the LM solution in one-tenth of the computation time. The GA solution can be easily ported to different computation platforms. Both LM and GA identification techniques were validated in simulations and experiments conducted on virtual and real machine tool drives. It is shown that although the parameters estimated using the rapid identification scheme do not always match their true values, the key tracking and disturbance rejection characteristics of the drives are successfully captured in the frequency range of the CNC motion commands. Therefore, the drive models constructed with rapid identification can be used to predict the contouring accuracy of real machine tools in a virtual process planning environment