Example 2 - Effect of varying slenderness ratio

In this example, we use the rotor seen in Example 5.8.2 from [Friswell, 2010].

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

steel = rs.materials.steel

number_of_elements = [2, 3, 4, 5, 6, 7, 8]

def create_rotor(n_el, R, shear_effects=False, rotary_inertia=False):
    """Create example rotor with given number of elements and R ration."""
    L_total = 1
    D = R * L_total

    shaft = [
        rs.ShaftElement(
            1.0 / (n_el),
            idl=0,
            odl=D,
            material=steel,
            shear_effects=shear_effects,
            rotary_inertia=rotary_inertia,
        )
        for i in range(n_el)
    ]

    bearings = [
        rs.BearingElement(0, kxx=1e15, cxx=0),
        rs.BearingElement(n_el, kxx=1e15, cxx=0),
    ]

    return rs.Rotor(shaft_elements=shaft, bearing_elements=bearings)

# create reference rotor with 80 elements
n_eigen = 8
R = 0.04
rotor_80 = create_rotor(80, R)
modal_80 = rotor_80.run_modal(speed=0, num_modes=2 * n_eigen)

errors = np.zeros([len(number_of_elements), n_eigen])

for i, n_el in enumerate(number_of_elements):
    rotor = create_rotor(n_el, R)
    modal = rotor.run_modal(speed=0, num_modes=2 * n_eigen)
    errors[i, :] = abs(
        100 * (modal.wn[:n_eigen] - modal_80.wn[:n_eigen]) / modal_80.wn[:n_eigen]
    )

fig = go.Figure()
for i in range(n_eigen):
    fig.add_trace(go.Scatter(x=number_of_elements, y=errors[:, i], name=f"Mode {i}"))
fig.update_layout(
    xaxis=dict(title="Number of elements"),
    yaxis=dict(title="Natural Frequency error(%)", type="log"),
)

# create reference rotor with 80 elements
n_el = 6
R_list = np.linspace(1e-4, 0.15, 10)

n_eigen = 6
errors = np.zeros([len(R_list), n_eigen])

for i, R in enumerate(R_list):
    rotor_ref = create_rotor(100, R, shear_effects=True, rotary_inertia=True)
    modal_ref = rotor_ref.run_modal(speed=0)

    rotor = create_rotor(n_el, R)
    modal = rotor.run_modal(speed=0, num_modes=2 * n_eigen)
    errors[i, :] = abs(
        100 * (modal.wn[:n_eigen] - modal_ref.wn[:n_eigen]) / modal_ref.wn[:n_eigen]
    )

fig = go.Figure()
for i in range(n_eigen):
    fig.add_trace(go.Scatter(x=R_list, y=errors[:, i], name=f"Mode {i}"))
fig.update_layout(
    xaxis=dict(title="Slenderness ratio"),
    yaxis=dict(title="Natural Frequency error(%)", type="log"),
)

References

Fri10

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