Twice-Running-Speed Response Due to Elliptical Bearing Clearances

Yamamoto [1] examined a vertical Jeffcott rotor model with bearing clearances and showed that a small bearing “dead-band” clearance could have a dramatic influence on synchronous rotor response. Recent test results for a turbopump in a liquid-rocket-engine development program showed a twice-running-speed response (2E) on the order of 8 gs over a wide speed range, while synchronous response levels were only at an 0.5 g level. Childs [2] predicted a sharp 2E response for the Advanced Technology Development, High-Pressure Fuel Turbopump (ATD-HPFTP) of the Space Shuttle Main Engine due to bearing clearances, when the running speed was nearly one half of a housing-mode natural frequency, i.e., when the 2E frequency was close to the housing mode natural frequency. However, his model did not predict significant 2E response over a broad running-speed range. Ellipticity of the bearing dead-band clearances was suggested as a possible cause for the observed 2E phenomenon. An extension of Yamamoto’s analysis [1] is presented including bearing ellipticity to examine that proposed explanation. The analysis results show that clearance ellipticity will produce 2E response over a considerable running-speed range during which the bearing clearance is engaged; however, the predicted 2E-response amplitude corresponding to an ellipticity of 0.1 were about 10% of the synchronous levels, and the projected 2E acceleration levels were about 40% of synchronous. The predicted 2E response includes a resonance peak (that can be sharp) at speeds slightly above 25% of the rotor critical speed. The perturbation-analysis results provide an explanation for persistent, lower 2E-response levels observed in many turbopumps, but do not explain the high levels observed with this turbopump.