Example 28 - Rigid rotor on isotropic bearings

This example is based on Example 6.2.1 page 239 from [Friswell, 2010].

A uniform rigid rotor is shown in figure 3.8. The rotor has length of 0.5 m and a diameter of 0.2 m, and it is made from steel with a density of 7810 kg/m³. The rotor is supported at the ends by bearings. The horizontal and vertical stiffness are 1 MN/m at bearing 1 and 1.3 MN/m at bearing 2. The damping values in the horizontal and vertical supports are 10 Ns/m at bearing 1 and 13 Ns/m at bearing 2. This rotor is the same as that described in Example 3.5.3(b). Find the response to a mass eccentricity of 0.1 mm and plot the Campbell diagram.

import ross as rs
import plotly.graph_objects as go
import plotly.io as pio
import numpy as np

Q_ = rs.Q_
pio.renderers.default = "notebook"

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

Creating rotor

N = 6
L = 0.5 / N
idl = 0
odl = 0.2

shaft = [rs.ShaftElement(L=L, idl=idl, odl=odl, material=steel) for i in range(N)]
bearings = [
    rs.BearingElement(n=0, kxx=1e6, kyy=1.5e6, cxx=20, cyy=30),
    rs.BearingElement(n=6, kxx=1.3e6, kyy=1.8e6, cxx=26, cyy=36),
]
disks = []

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

Campbell Diagram

fig = rotor.run_campbell(speed_range=Q_(list(range(0, 3500, 50)), "RPM"), frequencies=4)
fig.plot().show()
print(
    "Wn [Hz] at 0 rpm =",
    np.round((rotor.run_modal(speed=0 * np.pi / 30, num_modes=8).wn) / (2 * np.pi), 2),
)

Wn [Hz] at 0 rpm = [21.5  25.93 35.84 42.82]

# Calculating equivalent unbalance mass
e = 0.1e-3
shaft_radius = 0.1
m_unb = (rotor.m * e) / shaft_radius

print(f"Rotor mass = {round(rotor.m, 2)} kg")
print(f"Unbalance mass = {round(m_unb, 2)} kg")

Rotor mass = 122.68 kg
Unbalance mass = 0.12 kg

Bode Plot

n1 = 3  # position of the unbalance mass in the center of the rotor
m1 = m_unb * (odl / 2)
p1 = 0  # unbalance mass phase
speed = Q_(np.linspace(0, 3500, 60), "RPM")
results_case1 = rotor.run_unbalance_response([n1], [m1], [p1], speed)

probe1 = (3, 0)
results_case1.plot(
    probe=[probe1],
    probe_units="degrees",
    frequency_units="RPM",
    amplitude_units="µm pkpk",
    phase_units="degrees",
)

Mode Shapes

speed = 3500 * np.pi / 30
modal = rotor.run_modal(speed)

for i in np.arange(0, 3.1, 1):
    modal.plot_mode_3d(mode=int(i), frequency_units="RPM").show()

for mode in range(4):
    display(modal.plot_orbit(mode, nodes=[0, 3, 6]))