VM261

VM261
Rotating Beam with Internal Viscous Damping

Overview

Reference:

E.S. Zorzi, H.D. Nelson, "Finite element simulation of rotor-bearing systems with internal damping", ASME Journal of Engineering for Power, Vol. 99, 1976, pg 71-76.

Analysis Type(s):

Modal Analysis (ANTYPE = 2)

Element Type(s):

3–D 2 node beam (BEAM188)

2–D spring damper elements (COMBI214)

Input Listing:

vm261.dat

Test Case

A beam with internal viscous damping is simply supported by means of two isotropic undamped bearings. Modal analysis is performed with multiple load steps to determine the critical speeds and logarithmic decrement of the system.

Figure 451: Rotating Beam With Internal Viscous Damping

Material Properties

Geometric Properties

Loading

Beam model

E = 2.10E11 Pa

GXY = 2.10E14 Pa

DENS = 7800 Kg/m³

Nu = 0.3

Bearing stiffness

Kyy = 1.75E+07 N/m

Kzz = 1.75E+07 N/m

Beam length = 1.27m

Beam diameter = 0.1016m

Rotational velocity

1^st load step = 0 rpm

2^nd load step = 1241.409 rpm

3^rd load step = 2492.366 rpm

4^th load step = 3743.324 rpm

5th load step = 5149.458 rpm

6^th load step = 6245.240 rpm

7^th load step = 7496.198 rpm

8^th load step = 8747.156 rpm

9^th load step = 9998.114 rpm

10^th load step = 11249.071 rpm

11^th load step = 12500.029 rpm

12^th load step = 13789.184 rpm

13^th load step = 14992.396 rpm

Analysis Assumptions and Modeling Notes

The beam is modeled as an assembly of five equal length finite elements and meshed with BEAM188 elements. Internal viscous damping is included in the model as a material property using MP,BETD command. Modal analysis is performed using QR Damp eigensolver. Axial motion and rotation are suppressed to avoid any torsion or traction related displacements.

Separate element material attribute pointer is assigned to bearing elements to avoid material property of beam being carried over to the bearing elements. Gyroscopic damping and rotating damping are activated by using CORIOLIS command turned on in a stationary reference frame.

The critical speeds for a synchronous excitation (slope = 1) and logarithmic decrements of the first two unstable frequencies after first and second critical speeds are determined and compared against reference values of case1 (a). The logarithmic decrement values are obtained from Figure 3.

Results Comparison

	Target	Mechanical APDL	Ratio
1^st forward critical speed (rpm)	4950	5107.3538	1.032
2^nd forward critical speed (rpm)	10500	10693.6863	1.018
Logarithmic decrement for 1^st unstable frequency after critical speed	0.0010	0.0010	0.989
Logarithmic decrement for 2^nd unstable frequency after critical speed	0.0103	0.0099	0.964