Example 23 - An Overhung Rotor

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Example 23 - An Overhung Rotor#

This example is based on Example 5.9.9 from [Friswell, 2010].

An Overhung Rotor. Consider the overhung rotor shown in Figure 5.44. The shaft is 1.5m-long and the diameter is 50 mm with a disk of diameter 350mm and thickness 70 mm. The two bearings, with positions given in Figure 5.44, have a stiffness of 10 MN/m in each direction. The shaft and disk are made of steel, with material properties E = 211 GN/m², G = 81.2 GN/m² and ρ = 7,810 kg/m3. Damping is neglected. Estimate the first six natural frequencies and mode shapes between 0 and 4,000 rev/min.

import ross as rs
import plotly.graph_objects as go

# Make sure the default renderer is set to 'notebook' for inline plots in Jupyter
import plotly.io as pio

pio.renderers.default = "notebook"

Q_ = rs.Q_

steel = rs.Material("steel", E=211e9, G_s=81.2e9, rho=7810)

L = 0.25
N = 6
idl = 0
odl = 0.05

shaft = [rs.ShaftElement(L=L, idl=idl, odl=odl, material=steel) for i in range(N)]
bearings = [
    rs.BearingElement(n=0, kxx=1e7, cxx=0),
    rs.BearingElement(n=4, kxx=1e7, cxx=0),
]
disks = [
    rs.DiskElement.from_geometry(
        n=N,
        material=steel,
        width=0.07,
        i_d=odl,
        o_d=0.35,
    ),
]

rotor = rs.Rotor(shaft_elements=shaft, disk_elements=disks, bearing_elements=bearings)
rotor.plot_rotor()

campbell = rotor.run_campbell(speed_range=Q_(list(range(0, 4500, 50)), "RPM"))

campbell.plot(frequency_units="RPM", harmonics=[1, 2, 3])

modal = rotor.run_modal(speed=Q_(4000, "RPM"))

for mode in range(6):
    display(modal.plot_mode_3d(mode, frequency_units="Hz"))

for mode in range(6):
    display(modal.plot_orbit(mode, nodes=[2, 4]))

References#

[Fri10]

Michael I Friswell. Dynamics of rotating machines. Cambridge University Press, 2010.

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