Example 14 - Uncertainties on material properties#

In this example, we use the rotor seen in Example 5.9.4 from .

This system is the same as that of Example 3, but now we’ll work with uncertainties on material properties, representing a defect in the shaft. We will apply the uncertainties at the central elements.

import ross as rs
import ross.stochastic as srs
import numpy as np

# Deterministic Shaft Elements
Steel = rs.steel
shaft = [rs.ShaftElement(L=0.25, material=Steel, idl=0, odl=0.05) for i in range(4)]

# Material with random properties
size = 50
E = np.random.uniform(low=190e9, high=210e9, size=size)
rho = np.random.uniform(low=7000, high=7810, size=size)
G_s = np.random.uniform(low=70.5e9, high=81.2e9, size=size)
rand_mat = srs.ST_Material(name="Steel", rho=rho, E=E, G_s=G_s)

# Stochastic Shaft Elements
rand_el = srs.ST_ShaftElement(
L=0.25,
idl=0,
odl=0.05,
material=rand_mat,
is_random=["material"],
)

# Inserting stochastic elements to the shaft elements list
shaft.insert(2, rand_el)
shaft.insert(3, rand_el)

# Deterministic Disk Elements
disk1 = rs.DiskElement.from_geometry(
n=2,
material=Steel,
width=0.07,
i_d=0.05,
o_d=0.28,
)

disk2 = rs.DiskElement.from_geometry(
n=4,
material=Steel,
width=0.07,
i_d=0.05,
o_d=0.35,
)
disks = [disk1, disk2]


In this example, let’s consider an uniform distribuition for the coefficients. Because it’s a demonstrative example, we’ll not use too many samples, to avoid taking too long to run the simulation.

We can use numpy.random package to generate random values for our variables.

Stochastic Bearing Elements#

# random variables must have the same size
bearing1 = rs.BearingElement(n=0, kxx=1e6, cxx=2e2)
bearing2 = rs.BearingElement(n=6, kxx=1e6, cxx=2e2)
bearings = [bearing1, bearing2]

# Building random instances for a rotor model

rand_rotor = srs.ST_Rotor(
shaft_elements=shaft, disk_elements=disks, bearing_elements=bearings
)

# Number of samples
print("Number of samples:", len(list(iter(rand_rotor))))

Number of samples: 50


Plotting a random sample#

We can use numpy.random.choice to take a random rotor object. Then, we can use the same functions than to Rotor class.

sample = np.random.choice(list(iter(rand_rotor)))
fig = sample.plot_rotor()
fig.show()


Running Stochastic Campbell Diagram#

speed_range = np.linspace(0, 600, 31)
camp = rand_rotor.run_campbell(speed_range)


Plotting Stochastic Campbell Diagram#

# choose the desirable percentiles or confidence intervals
fig1 = camp.plot_nat_freq(conf_interval=[95], width=950, height=700)
fig1.show()

# choose the desirable percentiles or confidence intervals
fig2 = camp.plot_log_dec(conf_interval=[95], width=950, height=700)
fig2.show()


References#

Fri10

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