A theoretical investigation of the use of 2k factorial analysis to determine the effects of dimensional manufacturing tolerances on the stability of hydrodynamic journal bearing systems

Manufacturing tolerances and deviations from design parameters are inevitable in real hydrodynamic journal bearing systems. Normally, the stability of the system is assessed on the design parameters alone; the effects of deviations are assumed to be negligible and only the effects of gross changes are considered. In isolation, a single deviation may not demonstrate a significant effect, but in combination with other deviations, the effect may be large. This study presents a 2k factorial analysis of the effects of manufacturing tolerances on system stability. It is further used to determine which tolerance, or combination of tolerances, is the most significant. The results show that manufacturing tolerances, and combinations thereafter, do have a significant effect on system stability, and they influence the system stability in different ways. The study also identified a region where system stability is insensitive to deviations. To enable visualization of the effects, a modified Sommerfeld number and new stability map are presented. Furthermore, the overall philosophy of using a ‘design of experiments’ approach to the determination of system stability has been vindicated. A later paper will compare the results from this study to those from experimental results.