Smooth trajectory generation for 5-axis CNC machine tools

This thesis is presented in the alternative thesis format. The first paper presents an accurate machining feedrate prediction technique by modeling the trajectory generation behaviour of modern CNC machine tools. Typically, CAM systems simulate machines’ motion based on the commanded feedrate and the path geometry. Such approach does not consider the feed planning and interpolation strategy of the machine’s numerical control (NC) system. In this study, trajectory generation behaviour of the NC system is modelled and accurate cycle time prediction for complex machining toolpaths is realized. NC system’s linear interpolation dynamics and commanded axis kinematic profiles are predicted by using Finite Impulse Response (FIR) based low-pass filters. The corner blending behaviour during non-stop interpolation of linear segments is modeled, and for the first time, the minimum cornering feedrate, that satisfies both the tolerance and machining constraints, has been calculated analytically for 3-axis toolpaths of any geometry. The proposed method is applied to 4 different case studies including complex machining tool-paths. Experimental validations show actual cycle times can be estimated with 90% accuracy, greatly outperforming CAM-based predictions. It is expected that the proposed approach will help improve the accuracy of virtual machining models and support businesses decision making when costing machining processes. The second paper presents a novel real-time interpolation technique for 5-axis machine tools to attain higher speed and accuracy. To realize computationally efficient real-time interpolation of 6DOF tool motion, a joint workpiece-machine coordinate system interpolation scheme is proposed. Cartesian motion of the tool centre point (TCP) is interpolated in the workpiece coordinate system (WCS), whereas tool orientation is interpolated in the machine coordinate system (MCS) based on the FIR filtering. Such approach provides several advantages: i) it eliminates the need for complex real-time spherical interpolation techniques, ii) facilitates efficient use of slower rotary drive kinematics to compensate for the dynamic mismatch between Cartesian and rotary axes and achieve higher tool acceleration, iii) mitigates feed fluctuations while interpolating near kinematic singularities. To take advantage of such benefits and realize accurate joint WCS-MCS interpolation scheme, tool orientation interpolation errors are analysed. A novel approach is developed to adaptively discretize long linear tool moves and confine interpolation errors within user set tolerances. Synchronization errors between TCP and tool orientation are also characterized, and peak synchronization error level is determined to guide the interpolation parameter selection. Finally, blending errors during non-stop continuous interpolation of linear toolpaths are modelled and confined. Advantages of the proposed interpolation scheme are demonstrated through simulation studies and validated experimentally. Overall, proposed technique can improve cycle times up to 10% while providing smooth and accurate non-stop real-time interpolation of tool motion in 5-axis machining. The third paper proposes a novel online interpolation method for 3 and 5-axis machine tools to reduce machining cycle times. Previous Finite Impulse Response filtering based methods for numerically controlled machining used the maximum feedrate command within a part program for selecting the FIR filter time constant resulting in sub-optimal kinematic performance for toolpaths with varying feedrates. This paper presents an On-The-Fly (OTF) method of NC interpolation capable of kinematically optimising each individual G01 command. The method adaptively changes the FIR filter time constant along the toolpath maximising the kinematic performance for each G01 command without violating the constraints thereby reducing the overall machining cycle time. The tool centre point and orientation blending errors during continuous machining are controlled using an Overlap-Add (OLA) method of signal reconstruction. The OLA method is analytically calculated to confine interpolation errors within user set tolerances. The reduction in machining cycle times compared to standard FIR based interpolation methods is demonstrated through simulation studies. The proposed OTF method of NC interpolation can reduce continuous and P2P machining cycle times by up to 5% and 7% respectively while generating accurate online adaptively interpolated 3 and 5-axis reference trajectories. Finally, Finite Impulse Response filtering is increasingly becoming the interpolation method of choice in modern computer numerically controlled (CNC) machining centres. The method offers significant computational advantages over polynomial based methods. Most published methods use fixed FIR filter time constants to smooth the input signal. Recently, On-The-Fly interpolation was presented using Direct Convolution methods to adaptively change and optimise the FIR filter time constant throughout the toolpath online. Direct convolution in the time domain is an efficient method of implementing FIR interpolation online, however, computational advantages can be gained by using frequency domain methods instead. This research introduces a novel on-the-fly CNC interpolation method using Fast Fourier Transforms (FFTs). The presented OTF FFT method demonstrates an order increase in computational speed than the direct convolution OTF method. The effectiveness of the proposed method is validated in simulation based case studies.