Critical speed

About: Critical speed is a research topic. Over the lifetime, 2764 publications have been published within this topic receiving 31365 citations.

Fluid-structure interaction analysis of annular seals and rotor systems in multi-stage pumps

Abstract: Annular seals play an important role in determining the vibrational behavior of rotors in multi-stage pumps. To determine the critical speeds and unbalanced responses of rotor systems which consider annular seals, a fluid-structure interaction (FSI) method was developed, and the numerical method was verified by experiments conducted on a model rotor. In a typical FSI process, rotor systems are modeled based on a node-element method, and the motion equations are expressed in a type of matrix. To consider the influence of annular seals, dynamic coefficients of annular seals were introduced into the motion equations through matrix transformation. The test results of the model rotor showed good agreement with the calculated results. Based on the FSI method proposed here, the governing equations of annular seals were solved in two different ways. The results showed that the Childs method is more accurate in predicting a rotor’s critical speed. The critical speeds of the model rotor were calculated at different clearance sizes and length/diameter ratios. Tilting coefficients of long seals were added to the dynamic coefficients to consider the influence of tilting. The critical speeds reached their maximum value when the L/D ratio was around 1.25, and tilting enhanced the rotor’s stability when long annular seals were located in either end of the shaft.

A novel design for a gas-inducing impeller at the lowest critical speed

Abstract: To disperse the unreacted overhead gas phase into the liquid in an agitated reactor without gas outlet, a gas-inducing impeller is usually employed. To determine the lowest critical rotating speed, the gas-induction mechanism was reconsidered by constituting a mechanical energy conservation equation between the gas inlet orifice in the gas phase and the gas outlet orifice in the liquid phase under a certain rotational speed. According to this model, the critical speed of the gas-inducing impeller could be basically determined by the submersion depth and the radial position of the gas outlet, and a novel design was proposed by introduction of six short pipes stretched radially from the axis of the impeller. The final design of the gas-inducing impeller was obtained by an optimal combination of the gas-inducing pipes, the blades of the impeller and the baffle dimension.

On the Critical Speed of a Shaft of Sub-harmonic Oscillation

Abstract: Since single-row radial ball bearings have "small angular clearance", a shaft supported by them has a non-linear and non-symmetrical spring characteristic provided the bearing center lines of both bearing pedestals are not in alignment. In a small angular clearance, a shaft is freely supported, and the inclination angle of the deflection curve of the end of the shaft grows larger than a small angular clearance, then the shaft is not freely supported. When bearing center lines of both pedestals are not in alignment, the equilibrium position of a shaft is not located at the middle position of a small angular clearance, then the shaft has a non-symmetrical non-linearity. Therefore, sub-harmonic oscillation of order 1/2 can occur. In fact, the whirl of shaft with the mode of sub-harmonic oscillation of 1/2 appears at a rotating speed higher than the major critical speed.