Inverse design techniques in the area of fluid mechanics are normally conducted for continuous flow turbomachines rather than positive displacement devices. However, the work in this article is concerned with a class of rotary positive displacement device referred to as the limaçon-to-limaçon machine. The rotors and housings of these machines are manufactured of limaçon profiles, and are likely to suffer from interference if the rotors are not carefully profiled. Published literature indicates that solutions proposed to tackle the interference problem in these machines will adversely affect their efficiency figures. This notion motivated the work presented in this article, which first introduces the relevant mathematical models of the limaçon-to-limaçon machine and then uses these models to construct an inverse geometric design problem formulation. The proposed model has been coded in a computer program that utilises a Marquardt-Levenberg technique to converge to the required geometric parameters. Case studies are presented at the end of the article to verify the validity of the proposed inverse design model.
Multiple-point defects and abraded surfaces in rotary machinery induce complex vibration signatures, and have a tendency to mislead defect diagnosis models. A challenging problem in machine defect diagnosis is to model and study defect signature dynamics in the case of multiple-point defects and surface abrasion. In this study, a multiple-point defect model (MPDM) that characterizes the dynamics of n-point bearing defects is proposed. MPDM is further extended to model degradation in a rotating machine as a special case of multiple-point defects. Analytical and experimental results for multiple-point defects and abrasions show that the location of the fundamental defect frequency shifts depending upon the relative location of the defects and width of the abrasive region. This variation in the defect frequency results in a degradation of the defect detection accuracy of the defect diagnostic model. Based on envelope detection analysis, a modification in existing defect diagnostic models is recommended to nullify the impact of multiple-point defects, and general abrasion in machine components.