Lijia Luo

A derivative-free algorithm for nonlinear equations and its applications in multibody dynamics

Local floating coordinate system is used to represent the deployment motion of each rigid and flexible body of multibody system dynamics. Normal substructure modes are employed to describe the flexibility of a flexible body. Constraint equations establish the linkage between different bodies, part of them to specify positions and the others to specify orientations. Systems governing equations are then derived using generalized coordinates by Lagrange methods. The resulting differential-algebraic equations are transformed to algebraic equations using backward differential formula corrector method, thus highly coupled nonlinear equations are obtained. However, Jacobian matrix of the nonlinear equations is hard to calculate, and then a quasi-Newton method based on Broyden–Fletcher–Goldfarb–Shanno update approach for the solution of the nonlinear equations is proposed. And a suitable line search approach is combined with the Broyden–Fletcher–Goldfarb–Shanno method to improve its efficiency. Some numerical results are reported to show efficiency of the proposed method. Afterwards, the Broyden–Fletcher–Goldfarb–Shanno method is integrated into multibody dynamics method. A rigid multibody case and a rigid-flex multibody case are further studied to show the efficiency of the proposed multibody solver.

Reliability Analysis of Spring Operated Pressure Relief Valve

Pressure relief valve (PRV) is an important automatic overpressure protection system in the process industry. Because of the operating characteristics, the performance of PRV is supposed to be proved by the proof test. However, it’s difficult to determine the proof test intervals and the availability of the PRV between two proof tests. Based on stochastic Petri nets (SPN), the reliability modeling and analysis procedure of spring operated full lift pressure relief valve which is the most widely used PRV is depicted in this paper.Firstly, the FMECA method is used to analyze the causes and effects of the typical six failure modes of the PRV, such as vibration, leakage, frequency hopping, unable to open, open before the settings and the low back seat pressure. Second, the corresponding fault tree (FT) models of the PRV are built through the multi-component failure analysis. Third, the SPN models of the PRV are established by employing the logical relations in the FT models. Based on the collected failure data of the PRVs, the steady state and transient reliability index are calculated by Monte Carlo simulation based on the SPN software SPN@. Last, the idea about PRV reliability data collection in domestic process industries is proposed.The result of the reliability analysis can provide the basis for determination the proof test intervals of the PRV, and the proposed procedure also bears significance in its application in the reliability analysis of general system in process industry.Copyright