OS-V: 1020 Nelson-Mac Vaugh Rotor Model (3D Rotor)

The Nelson-Mac Vaugh rotor model for rotor dynamics is described to determine the critical speeds at which resonance occurs. The Campbell diagram is used in to review resonance and stability.

Figure 1. Model

Figure 2. Rotor Bearing Supports

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

Benchmark Model

The model details are as follows:
  • Flexible rotor shaft supported on 2 bearings.
  • Connected to support via RBE2 and CELAS1 elements, damping is via CDAMP1.
  • ASYNC Complex Eigenvalue Analysis with Gyroscopic effects.
  • Rotor speed increments via RSPEED from 0 to 100000 RPM, in steps of 5000 RPM.


The material properties are:
Young's modulus (E)
2.08E+11 N/m2
Poisson's Ratio (NU)
Mass Density (RHO)
7806 kg/m3


Table 1. Eigen Mode Contour Plots

The Campbell diagram is one of the most crucial tools in rotor dynamic analysis for comprehending the dynamic behaviour of the rotating machines. The rotational speed (RPM) is plotted along the x-axis, while the frequency (Hz) is plotted along the y-axis. To plot the Campbell diagram in HyperGraph, import the Whirl modes, which are printed in the .out file. The observation of the critical speeds comes from the Campbell diagram. Since the analysis yields complex conjugate mode pairs, only alternate modes are plotted. The harmonic critical speeds can be observed at intersections at order = 1.0.
Figure 3. OptiStruct Results

Table 2. Reference versus OptiStruct Results
Critical Rotor Speed (RPM) Modes
Beam Model (Reference)1 OptiStruct
15501.7 15210.1 1
17168.8 17034.8 3
46950.8 46503.4 5
50254.4 49979.4 7
64039.3 63010.4 11
96365.9 96346.2 13
Figure 4. Reference versus OptiStruct Results

1 Nelson,H.D. and McVaugh, J.M. (1976) The Dynamics of Rotor-Bearing Systems Using Finite Elements, J. Eng. Ind. (ASME), 593-600