Torsional Natural-Frequency Similitude Design and Experimental Assessment of a Reciprocating Air-Compressor Crankshaft

To address the complexity of the crankshaft structure in reciprocating air compressors and the high cost of prototype testing, a scaled-model design method for reproducing torsional natural-frequency characteristics is proposed based on dynamic similitude theory. Taking the crankshaft of a certain air compressor as the research object, its lumped parameter model is established and the differential equation of vibration is derived. The similitude relation for torsional natural frequency is derived using the equation analysis method, and the preservation of the retained global torsional mode shapes during model condensation is quantitatively evaluated using the Modal Assurance Criterion (MAC). By preserving the prescribed rotational inertias and torsional stiffnesses, the crankshaft system is transformed into a three-dimensional model consisting of disks and elastic shafts, and a scaled model is designed according to the similitude criteria. Finite element modal analysis compares the natural frequencies of the equivalent three-dimensional model and the scaled-down model, showing agreement with the theoretical similitude predictions. A scaled-model test rig is constructed to provide limited experimental frequency-domain evidence for the first predicted frequency characteristic. The experimentally observed frequency component consistent with the first predicted torsional natural-frequency characteristic differs from the theoretical value by 0.55%; however, this deviation is not interpreted as a quantified measure of predictive accuracy. The experiment provides only partial supporting evidence for the proposed design procedure; the second torsional natural frequency, modal shapes of the scaled physical model, modal mass, modal stiffness, and modal damping are not independently validated experimentally in the present study. The results indicate that the proposed similitude design method can reproduce the torsional natural-frequency characteristics investigated in this study with a reduced model size, and may provide a potential approach for investigating the torsional natural-frequency characteristics of crankshaft-type systems, subject to system-specific recalculation and further validation.