Investigation on the sampling size optimisation in gear tooth surface measurement using a Co-ordinate Measuring Machine

Co-ordinate Measuring Machines (CMMs) are widely used in gear manufacturing industry. One of the main issues for contact inspection using a CMM is the sampling technique. In this paper the gear tooth surfaces are expressed by series of parameters and inspection error compensation and initial value optimisation method are presented. The minimum number of measurement points for 3D tooth surfaces are derived. If high precision is required, more points need to be inspected. The sampling size optimisation is obtained from the criterion equation. The surface form deviation and initial values are optimised using the minimum zone method and Genetic Algorithms. A feature based inspection system for spur/helical gears is developed and trials and simulations demonstrated the developed method is very effective and suitable

Stochastic and epistemic uncertainty propagation in LCA

Purpose: When performing uncertainty propagation, most LCA practitioners choose to represent uncertainties by single probability distributions and to propagate them using stochastic methods. However the selection of single probability distributions appears often arbitrary when faced with scarce information or expert judgement (epistemic uncertainty). Possibility theory has been developed over the last decades to address this problem. The objective of this study is to present a methodology that combines probability and possibility theories to represent stochastic and epistemic uncertainties in a consistent manner and apply it to LCA. A case study is used to show the uncertainty propagation performed with the proposed method and compare it to propagation performed using probability and possibility theories alone. Methods: Basic knowledge on the probability theory is first recalled, followed by a detailed description of hal-00811827, version 1- 11 Apr 2013 epistemic uncertainty representation using fuzzy intervals. The propagation methods used are the Monte Carlo analysis for probability distribution and an optimisation on alpha-cuts for fuzzy intervals. The proposed method (noted IRS) generalizes the process of random sampling to probability distributions as well as fuzzy intervals, thus making the simultaneous use of both representations possible

A systematic approach to the modelling of measurements for uncertainty evaluation

The evaluation of measurement uncertainty is based on both, the knowledge about the measuring process and the quantities which influence the measurement result. The knowledge about the measuring process is represented by the model equation which expresses the interrelation between the measurand and the input quantities. Therefore, the modelling of the measurement is a key element of modern uncertainty evaluation. A modelling concept has been developed that is based on the idea of the measuring chain. It gets on with only a few generic model structures. From this concept, a practical stepwise procedure has been derived