本研究之動機為利用轉速區間內若干個轉速的不平衡振動反應，在一次試運轉狀況之下，鑑別出軸承係數。一次試運轉的情形下鑑別出軸承係數，其優點為不必停機做第二次不平衡配重配置之調整，故適合進行線上鑑別軸承係數之作業。在較寬之轉速區間中，軸承係數曲線可能呈現 2次彎曲之走勢，且在所選取的轉速區間內可能遇到系統之共振轉速。本文以三階多項式（可呈現 2次彎曲之走勢）近似軸承係數曲線，由不平衡振動反應直接計算出該多項式的係數。遇到系統之共振轉速時，本文方法依然可相當精確地估算出軸承係數。本文方法同時可降低雜訊效應，又有利於內插法求取不同轉速下之軸承係數。

This study aims at identifying the speed-dependent bearing coefficients in only one test run using the unbalance responses measured at different rotating speeds within a specific speed range. The merits of identification with one test run are that it does not require the rotating machines to stop for the setting of independent unbalance configurations and is suitable for on-line identification of bearing coefficients. In a wider range of operating speeds, the curves of bearing coefficients may have two bends, as well as the critical speeds may occur within the speed range. Third order polynomials, which can follow the two-bend trends, are used to approximate the curves of bearing- coefficients in this paper. The coefficients of the polynomials are calculated from the unbalance responses directly. The effectiveness of the method around critical speeds is also justified. In addition, this approach has the noise reduction effects and the bearing coefficients at different speeds can be obtained easily by interpolations.