Design, control and error analysis of a fast tool positioning system for ultra-precision machining of freeform surfaces

This thesis was previously held under moratorium from 03/12/19 to 03/12/21Freeform surfaces are widely found in advanced imaging and illumination systems, orthopaedic implants, high-power beam shaping applications, and other high-end scientific instruments. They give the designers greater ability to cope with the performance limitations commonly encountered in simple-shape designs. However, the stringent requirements for surface roughness and form accuracy of freeform components pose significant challenges for current machining techniques—especially in the optical and display market where large surfaces with tens of thousands of micro features are to be machined. Such highly wavy surfaces require the machine tool cutter to move rapidly while keeping following errors small. Manufacturing efficiency has been a bottleneck in these applications. The rapidly changing cutting forces and inertial forces also contribute a great deal to the machining errors. The difficulty in maintaining good surface quality under conditions of high operational frequency suggests the need for an error analysis approach that can predict the dynamic errors. The machining requirements also impose great challenges on machine tool design and the control process. There has been a knowledge gap on how the mechanical structural design affects the achievable positioning stability. The goal of this study was to develop a tool positioning system capable of delivering fast motion with the required positioning accuracy and stiffness for ultra-precision freeform manufacturing. This goal is achieved through deterministic structural design, detailed error analysis, and novel control algorithms. Firstly, a novel stiff-support design was proposed to eliminate the structural and bearing compliances in the structural loop. To implement the concept, a fast positioning device was developed based on a new-type flat voice coil motor. Flexure bearing, magnet track, and motor coil parameters were designed and calculated in detail. A high-performance digital controller and a power amplifier were also built to meet the servo rate requirement of the closed-loop system. A thorough understanding was established of how signals propagated within the control system, which is fundamentally important in determining the loop performance of high-speed control. A systematic error analysis approach based on a detailed model of the system was proposed and verified for the first time that could reveal how disturbances contribute to the tool positioning errors. Each source of disturbance was treated as a stochastic process, and these disturbances were synthesised in the frequency domain. The differences between following error and real positioning error were discussed and clarified. The predicted spectrum of following errors agreed with the measured spectrum across the frequency range. It is found that the following errors read from the control software underestimated the real positioning errors at low frequencies and overestimated them at high frequencies. The error analysis approach thus successfully revealed the real tool positioning errors that are mingled with sensor noise. Approaches to suppress disturbances were discussed from the perspectives of both system design and control. A deterministic controller design approach was developed to preclude the uncertainty associated with controller tuning, resulting in a control law that can minimize positioning errors. The influences of mechanical parameters such as mass, damping, and stiffness were investigated within the closed-loop framework. Under a given disturbance condition, the optimal bearing stiffness and optimal damping coefficients were found. Experimental positioning tests showed that a larger moving mass helped to combat all disturbances but sensor noise. Because of power limits, the inertia of the fast tool positioning system could not be high. A control algorithm with an additional acceleration-feedback loop was then studied to enhance the dynamic stiffness of the cutting system without any need for large inertia. An analytical model of the dynamic stiffness of the system with acceleration feedback was established. The dynamic stiffness was tested by frequency response tests as well as by intermittent diamond-turning experiments. The following errors and the form errors of the machined surfaces were compared with the estimates provided by the model. It is found that the dynamic stiffness within the acceleration sensor bandwidth was proportionally improved. The additional acceleration sensor brought a new error source into the loop, and its contribution of errors increased with a larger acceleration gain. At a certain point, the error caused by the increased acceleration gain surpassed other disturbances and started to dominate, representing the practical upper limit of the acceleration gain. Finally, the developed positioning system was used to cut some typical freeform surfaces. A surface roughness of 1.2 nm (Ra) was achieved on a NiP alloy substrate in flat cutting experiments. Freeform surfaces—including beam integrator surface, sinusoidal surface, and arbitrary freeform surface—were successfully machined with optical-grade quality. Ideas for future improvements were proposed in the end of this thesis.Freeform surfaces are widely found in advanced imaging and illumination systems, orthopaedic implants, high-power beam shaping applications, and other high-end scientific instruments. They give the designers greater ability to cope with the performance limitations commonly encountered in simple-shape designs. However, the stringent requirements for surface roughness and form accuracy of freeform components pose significant challenges for current machining techniques—especially in the optical and display market where large surfaces with tens of thousands of micro features are to be machined. Such highly wavy surfaces require the machine tool cutter to move rapidly while keeping following errors small. Manufacturing efficiency has been a bottleneck in these applications. The rapidly changing cutting forces and inertial forces also contribute a great deal to the machining errors. The difficulty in maintaining good surface quality under conditions of high operational frequency suggests the need for an error analysis approach that can predict the dynamic errors. The machining requirements also impose great challenges on machine tool design and the control process. There has been a knowledge gap on how the mechanical structural design affects the achievable positioning stability. The goal of this study was to develop a tool positioning system capable of delivering fast motion with the required positioning accuracy and stiffness for ultra-precision freeform manufacturing. This goal is achieved through deterministic structural design, detailed error analysis, and novel control algorithms. Firstly, a novel stiff-support design was proposed to eliminate the structural and bearing compliances in the structural loop. To implement the concept, a fast positioning device was developed based on a new-type flat voice coil motor. Flexure bearing, magnet track, and motor coil parameters were designed and calculated in detail. A high-performance digital controller and a power amplifier were also built to meet the servo rate requirement of the closed-loop system. A thorough understanding was established of how signals propagated within the control system, which is fundamentally important in determining the loop performance of high-speed control. A systematic error analysis approach based on a detailed model of the system was proposed and verified for the first time that could reveal how disturbances contribute to the tool positioning errors. Each source of disturbance was treated as a stochastic process, and these disturbances were synthesised in the frequency domain. The differences between following error and real positioning error were discussed and clarified. The predicted spectrum of following errors agreed with the measured spectrum across the frequency range. It is found that the following errors read from the control software underestimated the real positioning errors at low frequencies and overestimated them at high frequencies. The error analysis approach thus successfully revealed the real tool positioning errors that are mingled with sensor noise. Approaches to suppress disturbances were discussed from the perspectives of both system design and control. A deterministic controller design approach was developed to preclude the uncertainty associated with controller tuning, resulting in a control law that can minimize positioning errors. The influences of mechanical parameters such as mass, damping, and stiffness were investigated within the closed-loop framework. Under a given disturbance condition, the optimal bearing stiffness and optimal damping coefficients were found. Experimental positioning tests showed that a larger moving mass helped to combat all disturbances but sensor noise. Because of power limits, the inertia of the fast tool positioning system could not be high. A control algorithm with an additional acceleration-feedback loop was then studied to enhance the dynamic stiffness of the cutting system without any need for large inertia. An analytical model of the dynamic stiffness of the system with acceleration feedback was established. The dynamic stiffness was tested by frequency response tests as well as by intermittent diamond-turning experiments. The following errors and the form errors of the machined surfaces were compared with the estimates provided by the model. It is found that the dynamic stiffness within the acceleration sensor bandwidth was proportionally improved. The additional acceleration sensor brought a new error source into the loop, and its contribution of errors increased with a larger acceleration gain. At a certain point, the error caused by the increased acceleration gain surpassed other disturbances and started to dominate, representing the practical upper limit of the acceleration gain. Finally, the developed positioning system was used to cut some typical freeform surfaces. A surface roughness of 1.2 nm (Ra) was achieved on a NiP alloy substrate in flat cutting experiments. Freeform surfaces—including beam integrator surface, sinusoidal surface, and arbitrary freeform surface—were successfully machined with optical-grade quality. Ideas for future improvements were proposed in the end of this thesis