Campbell Diagram Part II: Backward Whirling Speed

This example shows the second part of how to find critical speeds of a rotor, i.e. finding backward whirling frequency. The ForwardWhirling example shows how to fond the forward whirling. As shown in this, the forward whirling speed of the motor is 47.2 rad/s. The same system, shown in Figure 1, is used in both examples.

Figure 1: Clamped shaft with a disk.

To identify the backward whirling speed, a static load is applied to the rotor at its resonance frequency and then released at 10 s to produce an impulse excitation that covers all frequency domains. Figure 2 shows the resulting response of the disk deflection.

Figure 2: Non-rotating disc displacements under loading and unloading.

The vibration frequencies of the disk's position on the y axis (disk.y) between time t = 10 and t = 12 are shown in an FFT (Fast Fourier Transform), which reveals values of 5.5 and 7.5 Hz, or 34.6 and 47.2 rad/s. 

Figure 3: Frequency content of the disc displacements.

According to Figure 3, the machinery's backward whirling speed is 34.6 rad/s when it runs at 47.2 rad/s. Therefore, the backward whirling speed is 34.6 rad/s, and the forward whirling speed is 47.2 rad/s.