Engineers of off-road equipment, on-road vehicles, pavement, and tires must assess the roughness of a terrain surface for the design of their products. The International Roughness Index (IRI), a standardized means of assessing longitudinal road roughness, quantifies roughness based on the average suspension travel for a particular vehicle at a prescribed speed. The Discrete Roughness Index (DRI) developed in this work address fundamental limitations of the IRI. Specifically, the DRI is calculated for each discretely measured location along a terrain surface and is applicable to vehicles traveling at varying speeds and using parameters other than the Golden Quarter-Car on which the IRI is based. The development of the DRI begins with a consistent discretization of the terrain surface, vehicle response, and the IRI. Next the Fractional Response Coefficient is developed, the properties of which are critical in the development of the DRI. The DRI is developed and its properties are discussed through theory and simulation of the ASTM E1926-08 profile. One important property of the average DRI is that it converges to the IRI as the distance between sampled points becomes smaller, for the particular case when the Golden Quarter-Car model is simulated at 80 kph. The DRI is not an alternative to the standard IRI, therefore, but a widely applicable roughness measure of which the standard IRI is a single specialized application. / Master of Science

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)