The critical speed map can be used to evaluate the effect of changes in support stiffness upon the undamped critical speeds. The bearing stiffness curves Kxx and Kyy are sometimes superimposed on the critical speed map. Intersections of the bearing stiffness curves with the critical speed lines are approximate critical speed locations.
The vibration mode shapes associated with each critical speed are normally plotted on a scaled drawing to illustrate the relative vibration along the shaft as shown below:
This figure illustrates the vibration mode shape for a compressor shaft at the first lateral natural frequency (Mode 1). The solid and dashed lines represent the envelope of maximum motion as the shaft whirls. As shown, the maximum vibration occurs near the center impellers so this mode is most sensitive to unbalance near the shaft center.
This shaft was mathematically modeled with 88 mass stations. The added masses of the impellers, labyrinths, and coupling are shown. The compressor shaft was supported at the bearing stations 10 and 77 with a normal stiffnesses of 1,500,000 lb/in between the shaft and the ground.
