Many researchers have investigated the performance of herringbone-grooved journal bearings (HGJBs). However, few have yet mentioned the issue of film thickness discontinuities in HGJBs with a finite number of grooves. Most studies have involved the application of a finite difference method for discretization. The present work utilizes the spectral element method to calculate the pressure distribution and dynamic coefficients of HGJBs, in which the thickness of the fluid film changes abruptly in the groove-ridge region. Conservation of mass is adopted to solve the problem. Additionally, the present method can be adopted for grooves with curvy geometry. The numerical results were compared with the analytical solution for a one-dimensional slider bearing and an HGJB. It also shows that for the case of HGJB, the numerical result by the present method is more accurate than the numerical results found in the literature (Trans. ASME 12: 518-540). Furthermore, employing the present method with the Elrod algorithm can improve the accuracy of deriving loads of HGJBs when cavitation occurs.In addition, the result displays the efficiency of the present method by observing the CPU time. Therefore, the approach can be employed to compute the critical mass of a HGJB. The influence of changing groove angle, groove depth, groove width, and the eccentricity on the critical mass are discussed. Observing the variations in critical mass shows that when the eccentricity is small, a larger groove angle, a lower groove depth, and smaller groove width correspond to a higher critical mass of the HGJB.
SPECTRAL ELEMENT ANALYSIS OF HGJBS
1117Many researchers have investigated the performance of HGJBs. In previous studies, the pressure distribution of the fluid film in the groove-ridge region was obtained by applying the narrow groove theory (NGT). NGT assumes that the number of grooves is infinite, such that the pressure distribution can be regarded as essentially linear along the grooves. Vohr and Chow [1] analyzed the herringbone-grooved gas-lubricated journal bearing using NGT, but manufacturing journals or sleeves with as many grooves as are required would be very expensive. Additionally, NGT overestimated the bearing load when the number of grooves was less than 16 [2], and when the number of grooves exceeds 16, the correct results can only be obtained at a low eccentricity. Hence, numerical methods that can be applied to bearings with a finite number of grooves must be developed.In the 1990s, the number of investigations on bearings with finite numbers of HGJBs increased rapidly. Bonneau and Absi [2] presented a numerical study of gas HGJBs that had a small number of herringbone grooves and analyzed the domain of validity of the NGT. Zirkelback and San Andrés [3] used finite element method to analyze HGJB pressure distribution and dynamic force coefficients. Faria [4] present a way to analyze HGJBs by combining the finite element method with high-order shape functions.Only a few researchers have yet mentioned the issue of film thickne...