Vibration characteristics analysis and vibration suppression of shaft system based on multivariate nonlinear factors

Shale-gas reciprocating-compressor shaft systems are subject to coupled bending-torsional vibration produced by alternating loads and interacting nonlinearities, which challenges reliable vibration prediction and safety-oriented design. This study proposes a unified multi-nonlinear bending-torsional dynamic model based on a lumped mass representation, in which variable inertia, asymmetric stiffness, interference/contact effects, rub-impact, and frictional damping are considered simultaneously. The nonlinear responses are solved using a variable-step Runge-Kutta method, and the model is validated against full-scale on-site measurements under no-load and loaded conditions in both the time and frequency domains. Sobol global sensitivity analysis is then combined with response surface methodology and NSGA-II to identify dominant structural variables and balance torsional vibration suppression against fatigue safety. The results show that incorporating interacting nonlinearities enables the model to reproduce the principal vibration and torque characteristics observed in the field. The optimized design markedly suppresses torsional fluctuation and free-end vibration under critical operating conditions while improving the fatigue safety margin. The novelty lies in integrating multi-factor nonlinear coupled modeling, full-scale field validation, global sensitivity screening, and safety-constrained multi-objective optimization within a single framework for shale gas compressor shaft systems. The proposed approach provides an engineering-oriented basis for dynamic design and vibration control under variable production conditions.