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.
Implementation of Counseling Guidance for Children with Special Needs (Viewed from Psychological Aspects, Socio-Culture and Science and Technology Development)
