Para se obter alto desempenho em máquinas-ferramenta de ultraprecisão, são necessários o desenvolvimento de sistemas de posicionamento e o controle de movimento, os quais não raramente devem operar com resolução e repetibilidade na faixa submicrométrica. A utilização das modernas técnicas de metodologia de projeto auxiliam no desenvolvimento deste tipo de sistema. Neste trabalho são discutidas e analisadas as diversas alternativas disponíveis para os elementos constituintes do sistema de posicionamento. Aspectos críticos como cinemática, acionamento, guias e apoios são estudados e confrontados usando o método de análise de valor. E baseados no resultado do estudo prévio, obtém-se um sistema híbrido para microposicionamento angular de alta rigidez e ampla largura de banda, capaz de posicionar uma superfície com resolução angular inferior a 4.\'10 POT.-5\' graus. Através das técnicas de modelagem, pode-se verificar a funcionalidade desse sistema projetado, quanto ao seu comportamento estático e dinâmico. Uma modelagem cinemática é apresentada com o objetivo de auxiliar na veracidade do projeto do posicionador angular, através da qual pretende-se observar a influência de cada ponto de apoio no posicionamento final. São apresentados os resultados obtidos em simulações numéricas, as quais constatam não só o próprio desempenho do posicionador, como também, a validade da técnica utilizada. / In order to achieve high performance in ultra-precision machine tools, appropriate capability is required of motion control and positioning systems which have to operate at resolutions and repeatability in the sub-micrometre range. Machining may reach high levels of precision through the use of suitable sensors, actuators and controllers so that the development of micro-positioner with low backlash, high bandwidth and accuracy is a crucial aspect of high precision machining technology. Modern design techniques can greatly assist in the development and design of such systems. In this work, several design options for the elements of a positioning system are discussed and analysed. Critical aspects such as kinematics, driving and bearings are studied and compared using the value analysis method. A hybrid system based upon the results of this study is proposed which combines the best characteristics of each design option. The system possesses the capability of positioning a workpiece and/or tool angularly and/or linearly (micro-tilt stage) with a resolution better than 4 \'10 POT.-5\' arc degree and high stiffness and bandwidth. Through modelling techniques, it is possible to verify the static and dynamic behaviour of the system. A kinematics model of the micro-tilt stage is presented in order to establish a relationship between the displacement of the actuators and the final position of the stage. It is anticipated that such an approach will be required in respect of interferometric feedback control. Simulations of the model are performed showing that the technique applied is valid and the system fulfils the requirements for ultra-precision design.

Para se obter alto desempenho em máquinas-ferramenta de ultraprecisão, são necessários o desenvolvimento de sistemas de posicionamento e o controle de movimento, os quais não raramente devem operar com resolução e repetibilidade na faixa submicrométrica. A utilização das modernas técnicas de metodologia de projeto auxiliam no desenvolvimento deste tipo de sistema. Neste trabalho são discutidas e analisadas as diversas alternativas disponíveis para os elementos constituintes do sistema de posicionamento. Aspectos críticos como cinemática, acionamento, guias e apoios são estudados e confrontados usando o método de análise de valor. E baseados no resultado do estudo prévio, obtém-se um sistema híbrido para microposicionamento angular de alta rigidez e ampla largura de banda, capaz de posicionar uma superfície com resolução angular inferior a 4.\'10 POT.-5\' graus. Através das técnicas de modelagem, pode-se verificar a funcionalidade desse sistema projetado, quanto ao seu comportamento estático e dinâmico. Uma modelagem cinemática é apresentada com o objetivo de auxiliar na veracidade do projeto do posicionador angular, através da qual pretende-se observar a influência de cada ponto de apoio no posicionamento final. São apresentados os resultados obtidos em simulações numéricas, as quais constatam não só o próprio desempenho do posicionador, como também, a validade da técnica utilizada. / In order to achieve high performance in ultra-precision machine tools, appropriate capability is required of motion control and positioning systems which have to operate at resolutions and repeatability in the sub-micrometre range. Machining may reach high levels of precision through the use of suitable sensors, actuators and controllers so that the development of micro-positioner with low backlash, high bandwidth and accuracy is a crucial aspect of high precision machining technology. Modern design techniques can greatly assist in the development and design of such systems. In this work, several design options for the elements of a positioning system are discussed and analysed. Critical aspects such as kinematics, driving and bearings are studied and compared using the value analysis method. A hybrid system based upon the results of this study is proposed which combines the best characteristics of each design option. The system possesses the capability of positioning a workpiece and/or tool angularly and/or linearly (micro-tilt stage) with a resolution better than 4 \'10 POT.-5\' arc degree and high stiffness and bandwidth. Through modelling techniques, it is possible to verify the static and dynamic behaviour of the system. A kinematics model of the micro-tilt stage is presented in order to establish a relationship between the displacement of the actuators and the final position of the stage. It is anticipated that such an approach will be required in respect of interferometric feedback control. Simulations of the model are performed showing that the technique applied is valid and the system fulfils the requirements for ultra-precision design.

The use of high-precision automated equipment is steadily increasing due in part to the progressively smaller sizes of electronic circuits. Currently, piezoelectric transducers (piezos) dominate as the actuation device for high precision machines, but shape memory alloys (SMA) may be a viable alternative to reduce monetary costs. This work explores the implementation of a low-cost linear macro-micro positioning system. The system consists of a modified printer carriage to provide long range, macro scale linear motion (approximately 200 mm range and 200 µm precision) and a micro scale system (approximately 4 mm range and 5 µm target precision) that uses an SMA actuator. A detailed description of the design and implementation of the system is given in this research. A model of the macro-stage is then generated by first identifying and inverting a simple friction model to linearize the system, thereby allowing for modified least squares (MLS) identification of a linear model. Various controllers are attempted for the macro-stage and compared with an experimentally tuned nonlinear PD controller that is implemented in the final design. A model of the micro-stage is derived through analysis of the SMA actuator. The model for the actuator is separated into two portions, an electro-thermal model, and a hysteresis model. The hysteresis model is derived using the Preisach model, and the electro-thermal model through MLS identification. To control the micro-stage, a PI controller with antiwindup is developed experimentally. The two stages are then executed together in closed loop and the resulting coupling between the two stages is briefly examined. Experimental data used for the modelling and design is presented, along with results of the final macro-micro linear positioning system.

The use of high-precision automated equipment is steadily increasing due in part to the progressively smaller sizes of electronic circuits. Currently, piezoelectric transducers (piezos) dominate as the actuation device for high precision machines, but shape memory alloys (SMA) may be a viable alternative to reduce monetary costs. This work explores the implementation of a low-cost linear macro-micro positioning system. The system consists of a modified printer carriage to provide long range, macro scale linear motion (approximately 200 mm range and 200 µm precision) and a micro scale system (approximately 4 mm range and 5 µm target precision) that uses an SMA actuator. A detailed description of the design and implementation of the system is given in this research. A model of the macro-stage is then generated by first identifying and inverting a simple friction model to linearize the system, thereby allowing for modified least squares (MLS) identification of a linear model. Various controllers are attempted for the macro-stage and compared with an experimentally tuned nonlinear PD controller that is implemented in the final design. A model of the micro-stage is derived through analysis of the SMA actuator. The model for the actuator is separated into two portions, an electro-thermal model, and a hysteresis model. The hysteresis model is derived using the Preisach model, and the electro-thermal model through MLS identification. To control the micro-stage, a PI controller with antiwindup is developed experimentally. The two stages are then executed together in closed loop and the resulting coupling between the two stages is briefly examined. Experimental data used for the modelling and design is presented, along with results of the final macro-micro linear positioning system.

Ultraprecision single point diamond turning is required to produce parts with sub-nanometer surface roughness and sub-micrometer surface profiles tolerances. These parts have applications in the optics industry, where tight form accuracy is required while achieving high surface finish quality. Generally, parts can be polished to achieve the desired finish, but then the form accuracy can easily be lost in the process rendering the part unusable. Currently, most mid to low spatial frequency surface finish errors are inspected offline. This is done by physically removing the workpiece from the machining fixture and mounting the part in a laser interferometer. This action introduces errors in itself through minute differences in the support conditions of the over constrained part on a machine as compared to the mounting conditions used for part measurement. Once removed, the fixture induced stresses and the part’s internal residual stresses relax and change the shape of the generally thin parts machined in these applications. Thereby, the offline inspection provides an erroneous description of the performance of the machine. This research explores the use of a single, high resolution, capacitance sensor to quickly and qualitatively measure the low to mid spatial frequencies on the workpiece surface, while it is mounted in a fixture on a standard ultraprecision single point diamond turning machine after a standard facing operation. Following initial testing, a strong qualitative correlation exists between the surface profiling on a standard offline system and this online measuring system. Despite environmental effects and the effects of the machine on the measurement system, the capacitive system with some modifications and awareness of its measurement method is a viable option for measuring mid to low spatial frequencies on a workpiece surface mounted on an ultraprecision machine with a resolution of 1nm with an error band of ±5nm with a 20kHz bandwidth. / Thesis / Master of Applied Science (MASc)