selection of written reports
Thesis: Design of Piezoelectrically Controlled Active Flexure Joints for Vibration Control and Disturbance Rejection
With the aim of allowing a compliant mechanism to benefit both from the large force and range of motion provided by a traditional actuator, as well as the precise control of small-amplitude, high- frequency motion offered by a piezoelectric actuator, this project aims to develop a proof-of-concept flexure joint that incorporates piezoelectric vibration dampening directly within the mechanism. This is done using Macro Fibre Composites, flexible and high specific strength piezos, that are bonded in antagonistic pairs to the top and bottom of a cantilever plate, providing a proof-of-concept on a simple geometry that can be expanded to different flexure joints in the future. The project further aims to fabricate two active flexure joints, one with a naive central actuator configuration along its length, and one with a hypothesised improved placement at the clamped edge of the cantilever, where the greatest amount of modal strain energy at lower frequencies is concentrated. (continued in full text)
A Study of Aerocapture using Numerical MODELLING
The physical problem of a spacecraft’s trajectory when approaching Titan using Aerocapture is ana- lyzed and simplified to be subject only to a drag force and the force of gravity. Using vector notation, a second order ODE is formulated and split into two coupled first order ODEs in terms of the space- craft’s velocity and position relative to the center of Titan. Numerical methods are implemented to solve these ODEs, using the resulting state vector to classify when the spacecraft has reached its apogee and minimum altitude. The apogee is considered reached when the component of the velocity vector in the direction of the vector pointing from the center of Titan to the spacecraft transitions from positive to negative. The minimum altitude is updated every time the current altitude is the lowest it has been thus far, with updates being prevented if the apogee has been passed to stop a crash from registering as the lowest altitude. The system is then further modeled in three dimensions, where the velocity of Titan’s atmosphere relative to the spacecraft applies a drag force in the z direction, which is found to have only limited impacts on the computed optimal altitude α. Finally, improvements to the performance of the program through early loop breaking are implemented, along with some aesthetic elements.
Design of a Decade Counter and Combinational Logic to Simulate a Stoplight
Stoplights need to be absolutely predictable and fail-proof to be used during driving, the leading cause of death for people ages 15 to 29 in Britain [1]. This means that every aspect of the system’s behaviour needs to be accounted for. By nature, a stoplight’s behaviour is dependent on its current state, meaning that it must consist of a sequential logic circuit. The design of this circuit must account for any hazards and must allow the stoplight to run autonomously, rectifying any glitches on its own. The circuit will consist of a counting circuit (known as a modulo counter / register) and combinational logic to interpret said counter’s output into stoplight behaviour. This report therefore investigates methods for constructing such a counter, methods for translating counter outputs into a combination of red, amber, and green colour outputs, and any hazards and glitches that need to be accounted for or considered.
MODELLING Conductive Heat Flow Through a Space Shuttle Insulating Silica Ceramic Tile
A 1-dimensional model for thermal conduction through a space shuttle thermal tile is proposed. Four finite difference methods, two explicit and two implicit, are analyzed for stability in space and time, highlighting the Crank-Nicolson method as the most appropriate. Two functions are implemented to optimize the number of time steps and spatial steps for accuracy and efficiency. These are used with the Crank-Nicolson method and the shooting method to optimize tile thickness, keeping the space shuttle aluminium hull below 200◦F without wasting material. The effects of an optimized thickness on plots of temperature through time and distance through tile are shown. Limitations of the model are identified as neglecting lateral heat conduction, and disregarding the effect of temperature on the tile’s material properties. Validation of the results is suggested through the analytical solution to the Heat Equation. Finally, a third order accurate in time forward differencing method is derived and analyzed for stability, proving to be unconditionally unstable despite an attempt to rectify this.
Flow of a Free Air Jet
The interactions of a free air jet with its surrounding medium and environment are investigated through quantitative analysis of stream velocity and volumetric flow rate, providing insight into jet structure and fluid-fluid shear induced turbulence. A pitot-static tube and manometer measure fluid velocity at discrete points about the jet centerline at three distances from the nozzle. By plotting these velocity profiles to scale with the nozzle, the core and mixing regions of the jet, along with their boundary to the free stream, are identified and investigated for their structure. Velocity measurements are used to calculate volumetric flow rate at four distances from the nozzle. Together with the scaled velocity profiles, it depicts and explains how shear between the jet and ambient air form a conically growing stream with a growing volumetric flow rate and decreasing velocity. Errors in the method are discerned as being simplifications in the manometer equation, parallax and measurement error, and suboptimal data fidelity from large spatial steps resulting in unclear structural boundaries.