OS-V: 1000 Complex Eigenvalue Analysis of Rotor Bearing System
Rotor Bearing system is an excellent example of rotating machines used in mechanical
engineering applications.
Analysis of this system to get unbalanced response, critical speed, resonance
frequency and vibration modes is important to evade the catastrophic failure of
these systems. Here the critical speed of a rotor bearing system using OptiStruct is verified. 1 図 1. 1D Rotor Model 図 2. 3D Representation of Beams
Benchmark Model
The finite element model, as shown in 図 1 is constrained at all the nodes. Only DOF 1
and 4 are allowed on all the nodes. The model is meshed with beam elements of
different sections (図 2). Mass is attached at node 5. An isotropic
system is assumed.
Material
The material properties are:
Property
Value
Young's modulus
207.8 GN/m2
Density
7806 kg/m3
Bearing (undamped and linear) with following stiffness matrix are used in this
model.
k22 = k33
= 4.378 x e7 N/m
k23 = k32
= 0 N/m
Two different approaches are used in OptiStruct to input
the Bearing Stiffness in the model.
DMIG
The stiffness matrix of the bearing is defined directly in the model as
multiple column entries using K2GG.
GENEL
A file (.inc) which contains the details of bearing
stiffness is imported in the model.
The problem has been solved for Complex Eigenvalue Analysis (ASYNC).
Results
The results are plotted over a range of spinspeed for 12 different modes. The
deformation of the rotor bearing system can be visualized in HyperView by importing an .h3d file. 図 3. Eigen Mode Contour Plot for Spin Speed of 1.75e5 RPM and 10th
Mode 図 4. Campbell Diagram (For Engine Orders 0.5, 1, 2 and 4)
Comparison of results at speed 70k RPM.
表 1. Whirl/Critical Speeds Comparison for Whirl Ratio 1 (Engine
Order-1X)
Here, you have verified that the critical speeds obtained by OptiStruct for various whirl ratios are a close match with
those mentioned in the Nelson McVaugh Paper.
Nomenclature
Critical Speed
The angular speed of a rotor that matches one of its natural
frequencies.
Whirl Ratio
Ratio of whirl speed to spin speed.
Campbell Diagram
The plot of natural frequencies of the system as functions of the spin
speeds.
Used for estimating the critical speed and resonance frequencies.
1 Nelson,H.D. and McVaugh, J.M. (1976) The Dynamics of Rotor-Bearing
Systems Using Finite Elements. ASME Journal of Engineering for Industry,
98,593-600
