The response of an overhung unbalanced rotor accelerated through a critical speed

Includes bibliographical references (page 54)Modern high performance machinery almost always operates at a\ud speed in excess of at least one critical speed. In many cases, the\ud vibrations of important components are difficult or impossible to\ud damp at a critical, yet the machinery must be brought up to the\ud operating point with safety and reliability.\ud Studies have been made during the last 50 years mathematically\ud quantifying the fact that rapid acceleration in rotational speed\ud through a critical does not allow time for destructive vibrations to\ud build up beyond a permissible limit.\ud Previous investigators have largely confined their mathematical\ud investigations to the Jeffcott Rotor, that is, the simple straddle\ud mounted rotor mass between two simple supports.\ud This investigation extends the above results to the case of the\ud overhung rotor, such as is commonly encountered in turbines. As a departure from the Jeffcott Rotor, whose natural frequency\ud is obtained in dynamics of machinery, three kinds of methods were\ud used to deal with the general critical speed and deflection problem,\ud with the effects of gyroscopic, empirical formulas, a deduced quadratic\ud equation, and analytical solutions all being employed. The\ud second is recommended, emphatically. It is shown that considerable Gyroscopic stiffening is possible\ud in the case of forward synchronous precession, and that the consequent\ud elevation of the apparent critical speed and suppression of amplitude\ud buildup can be related to proportions and unbalance by the results of\ud a computer solution of several simultaneous non-linear differential\ud equations. These results are presented in non-dimensional form, in\ud simple curves to guide design