A simpler method to calculate instability threshold speed of hydrodynamic journal bearings

In this study, a simpler method is proposed to study the instability threshold speed of journal bearing. State vector is chose as c = [ ε φε̇φ̇ ], not [ X YẊẎ ] in previous discussions, and coordinate transformation (between (ε, φ) and (X, Y)) is avoided. For the short bearing, a simpler expression is obtained without accuracy reducing and the calculation process is simplified. While for the long bearing, the instability threshold speed is expressed analytically by the eccentricity ratio εs, the attitude angle φs and the Sommerfeld number S2. The results agree well with the numerical results in previous studies. It is confirmed that, this method is more effective than the methods used in previous studies.