Design optimization of external engagement cylindrical gear flowmeter under uncertainty

The purpose of this study is to determine the reasonable structural parameters of the external engagement cylindrical gear flowmeter (EGF) under the interference of random factors, so as to ensure that the EGF system has high structural reliability and robustness of performance index response. In addition to the influence of its own structural parameters (e.g., gear structure parameters, gap height), the random factors (e.g., oil viscosity, pressure, temperature and flow rate) can affect multiple performance indexes (e.g., flow pulsation, internal leakage and total power loss) in different ways, thus reducing the structural robustness of the performance response and increasing the difficulty of optimization design and subsequent accuracy compensation of the EGF. In addition, machining and assembly errors also increase the probability of structural failure of the system. In this paper, based on the Basis-adaptive polynomial chaos expansion (Basis-adaptive PCE) surrogate model technology, an uncertainty optimization design method of EGF is proposed, which improves the robustness of the performance index response while ensuring the structural reliability. Multidisciplinary modeling of the performance index of EGF is performed to derive the performance state function. Based on the design of experiments, the influence trend of random factors on performance index was analyzed. The Basis-adaptive PCE method can significantly improve the efficiency of uncertainty quantification while ensuring high calculation accuracy and can be applied to the subsequent calculation of optimization design. Based on the results of uncertainty analysis, the optimization index of EGF is determined and the uncertainty optimization design is carried out. Compared with the deterministic optimization, the results show that the uncertainty optimization strategy can significantly reduce the probability of undercutting failure of the measuring gear and the fluctuation of the internal leakage response, thus effectively improving the comprehensive performance and can be applied to the optimization design of EGF.