VM-WB-MECH-091

VM-WB-MECH-091
Unbalanced Harmonic Response of a Shaft Carrying Single Rotor with Damping

Overview

Reference:

Any basic vibration analysis book.

Solver(s):

Ansys Mechanical

Analysis Type(s):

Harmonic

Element Type(s):

Beam

Test Case

A disc with mass of 5 kg is mounted midway on a simply supported shaft of diameter 0.01 m and length 0.5 m. All bodies are cylindrical. The center of gravity of the disc is 5 x 10-3 m away from the geometric center. The equivalent viscous damping at the center of the disc is 40 N⋅sec/m. The shaft rotates axially at 740 RPM. Find the frequency response in the Y direction at the midpoint of the shaft.

Figure 122: Schematic

Schematic

Material PropertiesGeometric PropertiesLoading
E = 2 x 1011 Pa
ρ = 1 x 10-14 kg/m3
Length of shaft, L = 0.5 m
Diameter of shaft, D = 0.01 m
Point Mass at midpoint of shaft, m = 5 kg
Rotating radius (eccentricity), e = 5 x 10-3 m
Rotating force, (m x e) = 2.5 x 10-2 kg⋅m

Analysis Assumptions and Modeling Notes

Static deflection of shaft,
Weight of shaft,
Stiffness of shaft,
Critical speed,
Critical damping coefficient,
Damping ratio,

The amplitude of vibration is therefore:

where

= eccentricity
= speed of shaft
= damping coefficient
= mass of shaft

Results Comparison

ResultsTargetMechanicalError (%)
Frequency response (Y) at the midpoint of the shaft @ 740 RPM (12.333 Hz) (m)0.0180240.0180390.083

Figure 123: Bode Plot

Bode Plot