Critical Speed Maps in Turbomachinery

For many years, one of the primary analysis techniques has been undamped critical speed analysis, and this technique is still performed today for the preliminary estimation of critical speeds and mode shape characteristics. First, let’s take a look at what this kind of analysis technique is and what it involves.

Critical speeds and their associated mode shapes are most influenced by the support (bearing and pedestal structure) stiffness magnitudes, the support locations, and the rotor’s mass and stiffness properties. Based on this, the following definition can be given. A critical speed map is a graph representing the effect of rotor support stiffness on the critical speed of the rotor. A general view of the critical speed map is shown in Figures 1-2.

Figure 1 Undamped Critical Speed Map [1]
Figure 2 Undamped Critical Speed Map in AxSTREAM RotorDynamics
Figure 2 Undamped Critical Speed Map in AxSTREAM RotorDynamics

With this definition in hand, the next question would be what is critical speed? Critical speed is the rotational speed that corresponds with a structure’s resonance frequency (or frequencies). A critical speed appears when the natural frequency is equal to the excitation frequency. The excitation may come from unbalance that is synchronous with the rotational velocity or from any asynchronous excitation. Read More

Calculation Methods for Dynamic Parameters of Rolling Element Bearings and Their Prediction Accuracy

Rolling element bearings are essential components in a vast range of rotating mechanical systems, providing rotational support and a wide range of methods for friction control. The performance of these bearings is crucial to the overall functionality of the machine. Therefore, predicting the dynamic behavior of rolling bearings accurately is vital to ensure their reliable operation. Figure 1 shows a general view of angular contact ball bearings.

Figure 1 Angular contact ball bearings, [1]
Figure 1 Angular contact ball bearings, [1]
Dynamic parameter calculation is the process of determining the bearing’s dynamic response under specific operating conditions, including load, speed, and lubrication. The calculation of these parameters is crucial for designing and selecting bearings and predicting their operating life. The main dynamic parameters are:

  • Radial and axial stiffness, which is the ability of a bearing to resist deformation when subjected to radial and axial loads. This parameter is essential in ensuring that the bearing maintains its shape and does not deform excessively under the applied load.
  • Damping, which is the ability of a bearing to absorb energy and dissipate it in the form of heat. This parameter is crucial in ensuring that the bearing does not overheat, leading to premature failure.


Moreover, bearing stiffness and damping are used for the rotor dynamic calculations of the machine supported by rolling element bearings for the accurate prediction of the rotor response under static and dynamic loads, taking into account the correct bearing characteristics. Read More

Rotor Dynamics for Turbomachinery Engineers

A rotor is a body suspended through a set of cylindrical hinges or bearings that allow it to rotate freely about an axis fixed in space. It is the most critical component of any rotating machine; often operating at high speeds and within a wide speed range (Figure 1). Rotor dynamics is the branch of engineering that studies the lateral and torsional vibrations of rotating shafts. The main purpose of rotor dynamics is to predict the rotor vibrations and keep the vibration level under an acceptable limit. To meet stringent reliability requirements, each step of the rotor design should be based on an accurate rotor dynamics prediction.

Figure 1 The components of a rotating machine
Figure 1 The components of a rotating machine, [1]
A rotor dynamics analysis should accomplish several goals. It should predict critical speeds at which vibration due to rotor unbalance is severe and should be avoided. Relatedly, it should suggest modifications that would allow designers to increase a machine’s critical speeds. Rotor dynamics analysis should also predict natural frequencies of torsional vibration, as well as amplitudes of synchronous vibration caused by rotor unbalance. In addition, the analysis should predict dynamic instability (including oil whip), and suggest design modifications to suppress it. Lastly, the analysis should recommend balance correction masses and locations from measured vibration data. Read More