ross.Rotor

ross.Rotor#

class ross.Rotor(shaft_elements, disk_elements=None, bearing_elements=None, point_mass_elements=None, min_w=None, max_w=None, rated_w=None, tag=None)#

A rotor object.

This class will create a rotor with the shaft, disk, bearing and seal elements provided.

Parameters:

shaft_elementslist: List with the shaft elements
disk_elementslist: List with the disk elements
bearing_elementslist: List with the bearing elements
point_mass_elements: list: List with the point mass elements
tagstr: A tag for the rotor

Attributes:

evaluesarray: Rotor’s eigenvalues.
evectorsarray: Rotor’s eigenvectors.
wnarray: Rotor’s natural frequencies in rad/s.
wdarray: Rotor’s damped natural frequencies in rad/s.

Returns:

A rotor object.

Examples

>>> #  Rotor without damping with 2 shaft elements 1 disk and 2 bearings
>>> import ross as rs
>>> steel = rs.materials.steel
>>> z = 0
>>> le = 0.25
>>> i_d = 0
>>> o_d = 0.05
>>> tim0 = rs.ShaftElement(le, i_d, o_d,
...                        material=steel,
...                        shear_effects=True,
...                        rotary_inertia=True,
...                        gyroscopic=True)
>>> tim1 = rs.ShaftElement(le, i_d, o_d,
...                        material=steel,
...                        shear_effects=True,
...                        rotary_inertia=True,
...                        gyroscopic=True)
>>> shaft_elm = [tim0, tim1]
>>> disk0 = rs.DiskElement.from_geometry(1, steel, 0.07, 0.05, 0.28)
>>> stf = 1e6
>>> bearing0 = rs.BearingElement(0, kxx=stf, cxx=0)
>>> bearing1 = rs.BearingElement(2, kxx=stf, cxx=0)
>>> rotor = rs.Rotor(shaft_elm, [disk0], [bearing0, bearing1])
>>> modal = rotor.run_modal(speed=0)
>>> modal.wd[0]
215.3707...

Methods

A(speed=0, frequency=None, synchronous=False)#

State space matrix for an instance of a rotor.

Parameters:

speed: float, optional: Rotor speed. Default is 0.
frequencyfloat, optional: Excitation frequency. Default is rotor speed.
synchronousbool, optional: If True a synchronous analysis is carried out. Default is False.

Returns:

Anp.ndarray: State space matrix for the rotor.

Examples

>>> rotor = rotor_example()
>>> np.round(rotor.A()[75:83, :2]) + 0.
array([[     0.,  10927.],
       [-10924.,      0.],
       [     0.,      0.],
       [  -174.,      0.],
       [     0.,   -174.],
       [     0.,      0.],
       [     0.,  10723.],
       [-10719.,      0.]])

C(frequency)#

Damping matrix for an instance of a rotor.

Parameters:

frequencyfloat: Excitation frequency.

Returns:

C0np.ndarray: Damping matrix for the rotor.

Examples

>>> rotor = compressor_example()
>>> rotor.C(0)[:4, :4]
array([[0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]])

G()#

Gyroscopic matrix for an instance of a rotor.

Returns:

G0np.ndarray: Gyroscopic matrix for the rotor.

Examples

>>> rotor = rotor_example()
>>> rotor.G()[:4, :4]
array([[ 0.        ,  0.01943344,  0.        , -0.00022681],
       [-0.01943344,  0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ],
       [ 0.00022681,  0.        ,  0.        ,  0.        ]])

K(frequency)#

Stiffness matrix for an instance of a rotor.

Parameters:

frequencyfloat, optional: Excitation frequency.

Returns:

K0np.ndarray: Stiffness matrix for the rotor.

Examples

>>> rotor = rotor_example()
>>> np.round(rotor.K(0)[:4, :4] / 1e6)
array([[ 4.700e+01,  0.000e+00,  0.000e+00,  0.000e+00],
       [ 0.000e+00,  4.600e+01,  0.000e+00, -6.000e+00],
       [ 0.000e+00,  0.000e+00,  1.657e+03,  0.000e+00],
       [ 0.000e+00, -6.000e+00,  0.000e+00,  1.000e+00]])

Ksdt()#

Dynamic stiffness matrix for an instance of a rotor.

Stiffness matrix associated with the transient motion of the shaft and disks. It needs to be multiplied by the angular acceleration when considered in time dependent analyses.

Returns:

Ksdt0np.ndarray: Dynamic stiffness matrix for the rotor.

Examples

>>> rotor = rotor_example_6dof()
>>> np.round(rotor.Ksdt()[:6, :6] * 1e3, 2)
array([[  0.  , -23.  ,   0.  ,   0.48,   0.  ,   0.  ],
       [  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ],
       [  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ],
       [  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ],
       [  0.  ,  -0.48,   0.  ,   0.16,   0.  ,   0.  ],
       [  0.  ,   0.  ,   0.  ,   0.  ,   0.  ,   0.  ]])

M(frequency=None, synchronous=False)#

Mass matrix for an instance of a rotor.

Parameters:

synchronousbool, optional: If True a synchronous analysis is carried out. Default is False.

Returns:

M0np.ndarray: Mass matrix for the rotor.

Examples

>>> rotor = rotor_example()
>>> rotor.M(0)[:4, :4]
array([[ 1.42050794,  0.        ,  0.        ,  0.        ],
       [ 0.        ,  1.42050794,  0.        , -0.04931719],
       [ 0.        ,  0.        ,  1.27790826,  0.        ],
       [ 0.        , -0.04931719,  0.        ,  0.00231392]])

__init__(shaft_elements, disk_elements=None, bearing_elements=None, point_mass_elements=None, min_w=None, max_w=None, rated_w=None, tag=None)#

add_nodes(new_nodes_pos)#

Add nodes to rotor.

This method returns the modified rotor with additional nodes according to the positions of the new nodes provided.

Parameters:

new_nodes_poslist: List with the position of the new nodes.

Returns:

A rotor object.

Examples

>>> import ross as rs
>>> rotor = rs.rotor_example()
>>> new_rotor = rotor.add_nodes([0.62, 1.11])
>>> shaft_elements = new_rotor.shaft_elements
>>> len(shaft_elements)
8
>>> round(shaft_elements[3].L, 2)
0.13
>>> round(shaft_elements[6].L, 2)
0.14

convergence(n_eigval=0, err_max=0.01)#

Run convergence analysis.

Function to analyze the eigenvalues convergence through the number of shaft elements. Every new run doubles the number os shaft elements.

Parameters:

n_eigvalint: The nth eigenvalue which the convergence analysis will run. Default is 0 (the first eigenvalue).
err_maxfloat: Maximum allowable convergence error. Default is 1e-02

Returns:

resultsAn instance of ConvergenceResults class, which is used to post-process

results. Attributes stored:

el_numarray: Array with number of elements in each iteraction
eigv_arrarray: Array with the n’th natural frequency in each iteraction
error_arrarray: Array with the relative error in each iteraction

classmethod from_section(leng_data, idl_data, odl_data, idr_data=None, odr_data=None, material_data=None, disk_data=None, brg_seal_data=None, min_w=None, max_w=None, rated_w=None, nel_r=1, tag=None)#

Build rotor from sections.

This class is an alternative to build rotors from separated sections. Each section has the same number (n) of shaft elements.

Parameters:

leng_datalist

List with the lengths of rotor regions.

idl_datalist

List with the inner diameters of rotor regions (Left Station).

odl_datalist

List with the outer diameters of rotor regions (Left Station).

idr_datalist, optional

List with the inner diameters of rotor regions (Right Station). Default is equal to idl_data (cylindrical element).

odr_datalist, optional

List with the outer diameters of rotor regions (Right Station). Default is equal to odl_data (cylindrical element).

material_dataross.material or list of ross.material

Defines a single material for all sections or each section can be defined by a material individually.

disk_datadict, optional

Dict holding disks datas. Example : disk_data=DiskElement.from_geometry(n=2,

material=steel, width=0.07, i_d=0, o_d=0.28 )

*See ‘disk_element.py’ docstring for more information*

brg_seal_datadict, optional

Dict holding lists of bearings and seals datas. Example : brg_seal_data=BearingElement(n=1, kxx=1e6, cxx=0,

kyy=1e6, cyy=0, kxy=0, cxy=0, kyx=0, cyx=0)

*See ‘bearing_seal_element.py’ docstring for more information*

nel_rint, optional

Number or elements per shaft region. Default is 1.

tagstr

A tag for the rotor

Returns:

A rotor object

Raises:

ValueError: Error raised if lists size do not match.
AttributeError: Error raised if the shaft material is not defined.

gravitational_force(g=-9.8065, direction='y', M=None, num_dof=None)#

Compute the gravitational force vector for the system.

Parameters:

gfloat, optional: Acceleration due to gravity. Default is -9.8065 m/s².
direction{“x”, “y”, “z”}, optional: Direction in which gravity acts. Default is “y”.
Mndarray, optional: Mass matrix of the system. If None, the internal mass matrix is used.
num_dofint, optional: Number of degrees of freedom per node. If None, the internal value is used.

Returns:

forcendarray: Gravitational force (weight) vector of shape (ndof,).

Examples

>>> rotor = compressor_example()
>>> force = rotor.gravitational_force()
>>> force[:4]
array([ 0.        , -3.12941854,  0.        ,  0.01851573])

init_ambs_for_integrate(**kwargs)#

integrate_system(speed, F, t, **kwargs)#

Time integration for a rotor system.

This method returns the time response for a rotor given a force, time and speed based on time integration with the Newmark method.

Parameters:

speedfloat or array_like

Rotor speed.

Fndarray

Force array (needs to have the same length as time array).

tndarray

Time array.

**kwargsoptional

Additional keyword arguments can be passed to define the parameters of the Newmark method if it is used (e.g. gamma, beta, tol, …). See newmark for more details. Other optional arguments are listed below.

model_reductiondict, optional

When model_reduction is provided, the corresponding reduction method is initialized. Dict keys:

methodstr, optional
Reduction method to use, e.g., “guyan” or “pseudomodal”. Defaults to “guyan”.

num_modesint, optional
Number of modes to reduce the model to, if pseudo-modal method is considered.

include_nodeslist of int, optional
List of the nodes to be included, if Guyan reduction method is considered.

dof_mappinglist of str, optional
List of the local DOFs to be considered when using Guyan reduction method. Valid values are: ‘x’, ‘y’, ‘z’, ‘alpha’, ‘beta’, ‘theta’, corresponding to:

‘x’ and ‘y’: lateral translations

‘z’: axial translation

‘alpha’: rotation about the x-axis

‘beta’: rotation about the y-axis

‘theta’: torsional rotation (about the z-axis)

Default is [‘x’, ‘y’].

include_dofs (list of int, optional):
Additional degrees of freedom (DOFs) to include in the reduction, such as DOFs with applied forces or probe locations when using Guyan reduction method.

add_to_RHScallable, optional

An optional function that computes and returns an additional array to be added to the right-hand side of the equation of motion. This function should take the time step number as argument, and can take optional arguments corresponding to the current state of the rotor system, including the displacements disp_resp, velocities velc_resp, and acceleration accl_resp. It should return an array of the same length as the degrees of freedom of the rotor system rotor.ndof. This function allows for the incorporation of supplementary terms or external effects in the rotor system dynamics beyond the specified force input during the time integration process.

Returns:

tndarray: Time values for the output.
youtndarray: System response.

Examples

>>> import ross as rs
>>> rotor = rs.compressor_example()
>>> size = 10000
>>> node = 3
>>> speed = 500.0
>>> accel = 0.0
>>> t = np.linspace(0, 10, size)
>>> F = np.zeros((size, rotor.ndof))
>>> F[:, rotor.number_dof * node + 0] = 10 * np.cos(2 * t)
>>> F[:, rotor.number_dof * node + 1] = 10 * np.sin(2 * t)
>>> t, yout = rotor.integrate_system(speed, F, t)
Running direct method
>>> yout[:, rotor.number_dof * node + 1]
array([0.00000000e+00, 2.07239823e-10, 7.80952429e-10, ...,
       1.21848307e-07, 1.21957287e-07, 1.22065778e-07])

classmethod load(file)#

Load rotor from toml file.

Parameters:

filestr or pathlib.Path: String or Path for a .toml file.

Returns:

rotorross.rotor.Rotor

magnetic_bearing_controller(step, magnetic_bearings, time_step, disp_resp, **kwargs)#

Compute control forces for Active Magnetic Bearings (AMBs).

This method calculates the magnetic control forces generated by active magnetic bearings (AMBs) at each time step using a PID control law. The forces are based on the measured displacements and can optionally include external disturbances for sensitivity analysis.

If sensitivity analysis is enabled via keyword arguments, the method injects a known disturbance at a specific DoF and logs excitation, disturbed, and sensor signals for post-processing.

Parameters:

stepint: Current time step index in the simulation.
magnetic_bearingslist: List of MagneticBearingElement objects used for force computation.
time_stepfloat: Time increment used in the numerical integration scheme (in seconds).
disp_respndarray: Displacement response vector of the rotor at the current time step. The size must match the number of rotor DoFs.

Returns:

magnetic_forcendarray: Force vector containing control forces applied by each magnetic bearing in the rotor system. Has the same length as self.ndof.

Other Parameters:

sensitivity_compute_dofint, optional

Index of the DoF where a disturbance signal is applied (for sensitivity analysis).

sensitivity_disturbancendarray, optional

Disturbance signal array (e.g., chirp) to be injected at the specified DoF.

sensitivity_result_valuesdict, optional

Dictionary to store the time history of:

“excitation_signal”
“disturbed_signal”
“sensor_signal”

for post-processing in sensitivity computations.

Notes

The control forces are applied in both x and y directions at each AMB location.
The actual PID computation is delegated to the compute_pid_amb function.
If sensitivity_compute_dof is provided, the excitation is applied to that DoF only.

Examples

>>> import ross as rs
>>> import numpy as np
>>> rotor = rs.rotor_amb_example()
>>> dt, speed, step = 1e-4, 1000, 1
>>> t = np.arange(0, 5 * dt, dt)
>>> node = [27, 29]
>>> mass = [10, 10]
>>> F = np.zeros((len(t), rotor.ndof))
>>> for n, m in zip(node,mass):
...     F[:, 6 * n + 0] = m * np.cos((speed * t))
...     F[:, 6 * n + 1] = (m-5) * np.sin((speed * t))
>>> response = rotor.run_time_response(speed, F, t, method = "newmark")
Running direct method
>>> magnetic_bearings = [brg for brg in rotor.bearing_elements if isinstance(brg, rs.bearing_seal_element.MagneticBearingElement)]
>>> magnetic_force = rotor.magnetic_bearing_controller(step, magnetic_bearings, dt, response.yout[-1,:])
>>> np.nonzero(magnetic_force)[0]
array([ 72,  73, 258, 259])
>>> magnetic_force[np.nonzero(magnetic_force)[0]]
array([-7.24276404e-04, -1.42153354e-05, -1.17641699e-04,  2.39844354e-05])

plot_rotor(nodes=1, check_sld=False, length_units='m', **kwargs)#

Plot a rotor object.

This function will take a rotor object and plot its elements representation using Plotly.

Parameters:

nodesint, optional: Increment that will be used to plot nodes label.
check_sldbool: If True, checks the slenderness ratio for each element. The shaft elements which has a slenderness ratio < 1.6 will be displayed in yellow color.
length_unitsstr, optional: length units to length and diameter. Default is ‘m’.
kwargsoptional: Additional key word arguments can be passed to change the plot layout only (e.g. width=1000, height=800, …). *See Plotly Python Figure Reference for more information.

Returns:

figplotly.graph_objects.Figure: The figure object with the rotor representation.

run_amb_sensitivity(speed, t_max, dt, disturbance_amplitude=1e-05, disturbance_min_frequency=0.001, disturbance_max_frequency=150, amb_tags=None, sensors_theta=0.7853981633974483, verbose=1)#

Run Active Magnetic Bearing (AMB) sensitivity analysis.

This method performs a frequency-domain sensitivity analysis of the rotor system equipped with active magnetic bearings (AMBs). The analysis uses a logarithmic chirp excitation applied as an external disturbance force to compute the system’s frequency response at the AMB-controlled degrees of freedom (DoFs). The results provide magnitude and phase sensitivity functions for each AMB in both x and y directions.

Parameters:

speedfloat: Rotational speed of the rotor in rad/s.
t_maxfloat: Total time duration of the simulation in seconds.
dtfloat: Time step for the simulation in seconds.
disturbance_amplitudefloat, optional: Amplitude of the excitation chirp signal applied as a disturbance. Default is 10e-6.
disturbance_min_frequencyfloat, optional: Minimum frequency (in Hz) of the logarithmic chirp signal used for excitation. The chirp sweeps from this frequency up to disturbance_max_frequency. Default is 1e-3 Hz.
disturbance_max_frequencyfloat, optional: Maximum frequency (in Hz) of the logarithmic chirp signal used for excitation. Default is 150 Hz.
amb_tagslist of str, optional: List of magnetic bearing tags to include in the sensitivity analysis. If None or empty, all MagneticBearingElement instances in the rotor are used. If provided, only the AMBs matching the specified tags will be analyzed. Raises a RuntimeError if no AMB with the given tag is found.
sensors_thetafloat, optional: Angular position of the Active Magnetic Bearing (AMB) sensors, in radians. This angle defines the orientation of the sensor coordinate system (v, w) relative to the global coordinate system (x, y). A positive angle corresponds to a counter-clockwise rotation. Default is 45 degrees (π/4 rad).
verboseint, optional: Controls the verbosity of the method. If 1 or greater, both the simulation time and the forces produced by the AMBs are presented. If 0, no output is shown. Default is 1.

Returns:

resultsSensitivityResults: Object containing sensitivity magnitude, phase, and frequency vectors for each magnetic bearing tag and direction (‘x’, ‘y’). Also includes the excitation, disturbed, and sensor signals used in the computation.

Notes

The excitation is a logarithmic chirp sweeping from disturbance_min_frequency to disturbance_max_frequency (Hz).
The excitation is applied individually to each DoF controlled by an AMB.
The method assumes that the rotor contains MagneticBearingElement instances.
A Newmark time integration scheme is used internally via run_time_response().

Examples

>>> import ross as rs
>>> rotor = rs.rotor_amb_example()

>>> # Run sensitivity for all magnetic bearings in the rotor (default sweep)
>>> sensitivity_results = rotor.run_amb_sensitivity(speed=314.16, t_max=5e-4, dt=1e-4)
Running direct method...

>>> # Run sensitivity only for a specific AMB tag (e.g., "Magnetic Bearing 0")
>>> sensitivity_results = rotor.run_amb_sensitivity(
...     speed=314.16, t_max=5e-4, dt=1e-4, amb_tags=["Magnetic Bearing 0"]
... )
Running direct method...

>>> # Run sensitivity with a custom chirp band (0.1 Hz to 200 Hz)
>>> sensitivity_results = rotor.run_amb_sensitivity(
...     speed=314.16, t_max=5e-4, dt=1e-4,
...     disturbance_min_frequency=0.1, disturbance_max_frequency=200.0
... )
Running direct method...

>>> # Accessing maximum absolute sensitivities for "Magnetic Bearing 0"
>>> max_sens_bearing_0_x = sensitivity_results.max_abs_sensitivities["Magnetic Bearing 0"]["x"]
>>> max_sens_bearing_0_y = sensitivity_results.max_abs_sensitivities["Magnetic Bearing 0"]["y"]

>>> # Plotting the sensitivities for all AMBs and axes
>>> fig = sensitivity_results.plot(
...     frequency_units="Hz", phase_unit="degree",
...     magnitude_scale="decibel", xaxis_type="log"
... )

>>> # Plotting the time results used in sensitivity calculation
>>> fig = sensitivity_results.plot_time_results()

run_campbell(speed_range, frequencies=6, frequency_type='wd', torsional_analysis=False)#

Calculate the Campbell diagram.

This function will calculate the damped natural frequencies for a speed range.

Available plotting methods:: .plot()

Parameters:

speed_rangearray, pint.Quantity: Array with the speed range in rad/s.
frequenciesint, optional: Number of frequencies that will be calculated. Default is 6.
frequency_typestr, optional: Choose between displaying results related to the undamped natural frequencies (“wn”) or damped natural frequencies (“wd”). The default is “wd”.
torsional_analysisbool, optional: If True, performs a separate torsional analysis and returns the respective modes in the Campbell diagram. In this case, a system with only torsional degrees of freedom is considered, thus disregarding coupled modes (lateral + torsional). Default is False.

Returns:

resultsross.CampbellResults: For more information on attributes and methods available see: ross.CampbellResults

Examples

>>> import ross as rs
>>> rotor1 = rs.rotor_example()
>>> speed = np.linspace(0, 400, 11)

Diagram with undamped natural frequencies >>> camp = rotor1.run_campbell(speed, frequency_type=”wn”)

Diagram with damped natural frequencies >>> camp = rotor1.run_campbell(speed)

Plotting Campbell Diagram >>> fig = camp.plot()

run_crack(n, depth_ratio, node, unbalance_magnitude, unbalance_phase, speed, t, crack_model='Mayes', cross_divisions=None, **kwargs)#

Run analysis for the rotor system with crack given an unbalance force.

Crack object is instantiated and system’s time response is simulated.

Parameters:

nfloat: Element number where the crack is located.
depth_ratiofloat: Crack depth ratio related to the diameter of the crack container element. A depth value of 0.1 is equal to 10%, 0.2 equal to 20%, and so on.
nodelist, int: Node where the unbalance is applied.
unbalance_magnitudelist, float, pint.Quantity: Unbalance magnitude (kg.m).
unbalance_phaselist, float, pint.Quantity: Unbalance phase (rad).
speedfloat or array_like, pint.Quantity: Rotor speed.
Farray: Force array (needs to have the same number of rows as time array). Each column corresponds to a dof and each row to a time.
tarray: Time array.
crack_modelstring, optional: String containing type of crack model chosed. The available types are: “Mayes”, “Gasch”, “Flex Open” and “Flex Breathing”. Default is “Mayes”.
cross_divisions: float, optional: Number of square divisions into which the cross-section of the cracked element will be divided in the analysis conducted for the Flex Breathing model.
**kwargsoptional: Additional keyword arguments can be passed to define the parameters of the Newmark method if it is used (e.g. gamma, beta, tol, …). See ross.utils.newmark for more details. Other keyword arguments can also be passed to be used in numerical integration (e.g. model_reduction). See Rotor.integrate_system for more details.

Returns:

resultsross.TimeResponseResults: For more information on attributes and methods available see: ross.TimeResponseResults

Examples

>>> import ross as rs
>>> from ross.probe import Probe
>>> from ross.units import Q_
>>> rotor = rs.rotor_example_with_damping()
>>> n1 = rotor.disk_elements[0].n
>>> n2 = rotor.disk_elements[1].n
>>> results = rotor.run_crack(
...    n=18,
...    depth_ratio=0.2,
...    node=[n1, n2],
...    unbalance_magnitude=[5e-4, 0],
...    unbalance_phase=[-np.pi / 2, 0],
...    crack_model="Mayes",
...    speed=Q_(1200, "RPM"),
...    t=np.arange(0, 0.5, 0.0001),
...    model_reduction={"num_modes": 12},  # Pseudo-modal method
... )
Running with model reduction: pseudomodal
>>> probe1 = Probe(14, 0)
>>> probe2 = Probe(22, 0)
>>> fig1 = results.plot_1d([probe1, probe2])
>>> fig2 = results.plot_dfft(
...     [probe1, probe2],
...     frequency_range=Q_((0, 200), "Hz"),
...     yaxis_type="log",
... )

run_critical_speed(speed_range=None, num_modes=12, rtol=0.005)#

Calculate the critical speeds and damping ratios for the rotor model.

This function runs an iterative method over “run_modal()” to minimize (using scipy.optimize.newton) the error between the rotor speed and the rotor critical speeds (rotor speed - critical speed).

Differently from run_modal(), this function doesn’t take a speed input because it iterates over the natural frequencies calculated in the last iteration. The initial value is considered to be the undamped natural frequecies for speed = 0 (no gyroscopic effect).

Once the error is within an acceptable range defined by “rtol”, it returns the approximated critical speed.

With the critical speeds calculated, the function uses the results to calculate the log dec and damping ratios for each critical speed.

Parameters:

speed_rangetuple, optional, pint.Quantity: Tuple (start, end) with the desired range of frequencies (rad/s). The function returns all eigenvalues within this range.
num_modesint, optional: The number of eigenvalues and eigenvectors to be calculated using ARPACK. If sparse=True, it determines the number of eigenvalues and eigenvectors to be calculated. It must be smaller than Rotor.ndof - 1. It is not possible to compute all eigenvectors of a matrix with ARPACK. If speed_range is not None, num_modes is overrided. Default is 12.
rtolfloat, optional: Tolerance (relative) for termination. Applied to scipy.optimize.newton. Default is 0.005 (0.5%).

Returns:

resultsross.CriticalSpeedResults: For more information on attributes and methods available see: ross.CriticalSpeedResults

Examples

>>> import ross as rs
>>> rotor = rs.rotor_example()

Finding the first Nth critical speeds >>> results = rotor.run_critical_speed(num_modes=8) >>> np.round(results.wd()) array([ 92., 96., 271., 300.]) >>> np.round(results.wn()) array([ 92., 96., 271., 300.])

Finding the first critical speeds within a speed range >>> results = rotor.run_critical_speed(speed_range=(100, 1000)) >>> np.round(results.wd()) array([271., 300., 636., 774., 867.])

Changing output units >>> np.round(results.wd(“rpm”)) array([2590., 2868., 6074., 7394., 8278.])

Retrieving whirl directions >>> results.whirl_direction # doctest: +ELLIPSIS array([…

run_forced_response(force=None, speed_range=None, modes=None, cluster_points=False, num_modes=12, num_points=10, rtol=0.005, unbalance=None)#

Forced response for a mdof system.

This method returns the unbalanced response for a mdof system given magnitude and phase of the unbalance, the node where it’s applied and a frequency range.

Available plotting methods:: .plot() .plot_magnitude() .plot_phase() .plot_polar_bode() .plot_deflected_shape() .plot_bending_moment() .plot_deflected_shape_3d() .plot_deflected_shape_2d()

Parameters:

forcelist, array, pint.Quantity: Unbalance force in each degree of freedom for each value in omega
speed_rangelist, array, pint.Quantity: Array with the desired range of frequencies
modeslist, optional: Modes that will be used to calculate the frequency response (all modes will be used if a list is not given).
unbalancearray, optional: Array with the unbalance data (node, magnitude and phase) to be plotted with deflected shape. This argument is set only if running an unbalance response analysis. Default is None.
cluster_pointsbool, optional: boolean to activate the automatic frequency spacing method. If True, the method uses _clustering_points() to create an speed_range. Default is False
num_pointsint, optional: The number of points generated per critical speed. The method set the same number of points for slightly less and slightly higher than the natural circular frequency. It means there’ll be num_points greater and num_points smaller than a given critical speed. num_points may be between 2 and 12. Anything above this range defaults to 10 and anything below this range defaults to 4. The default is 10.
num_modes: The number of eigenvalues and eigenvectors to be calculated using ARPACK. It also defines the range for the output array, since the method generates points only for the critical speed calculated by run_critical_speed(). Default is 12.
rtolfloat, optional: Tolerance (relative) for termination. Applied to scipy.optimize.newton to calculate the approximated critical speeds. Default is 0.005 (0.5%).

Returns:

resultsross.ForcedResponseResults: For more information on attributes and methods available see: ross.ForcedResponseResults

Examples

>>> rotor = rotor_example()
>>> speed = np.linspace(0, 1000, 101)
>>> force = rotor._unbalance_force(3, 10.0, 0.0, speed)
>>> resp = rotor.run_forced_response(force=force, speed_range=speed)
>>> abs(resp.forced_resp)
array([[0.00000000e+00, 5.06073311e-04, 2.10044826e-03, ...

Using clustered points option. Set cluster_points=True and choose how many modes the method must search and how many points to add just before and after each critical speed.

>>> response = rotor.run_forced_response(
...     force=force, cluster_points=True, num_modes=12, num_points=5
... )
>>> response.speed_range.shape
(61,)

run_freq_response(speed_range=None, modes=None, cluster_points=False, num_modes=12, num_points=10, rtol=0.005, free_free=False)#

Frequency response for a mdof system.

This method returns the frequency response for a mdof system given a range of frequencies and the modes that will be used.

Available plotting methods:: .plot() .plot_magnitude() .plot_phase() .plot_polar_bode()

Parameters:

speed_rangearray, optional, pint.Quantity: Array with the desired range of frequencies. Default is 0 to 1.5 x highest damped natural frequency.
modeslist, optional: Modes that will be used to calculate the frequency response (all modes will be used if a list is not given).
cluster_pointsbool, optional: boolean to activate the automatic frequency spacing method. If True, the method uses _clustering_points() to create an speed_range. Default is False
num_pointsint, optional: The number of points generated per critical speed. The method set the same number of points for slightly less and slightly higher than the natural circular frequency. It means there’ll be num_points greater and num_points smaller than a given critical speed. num_points may be between 2 and 12. Anything above this range defaults to 10 and anything below this range defaults to 4. The default is 10.
num_modes: The number of eigenvalues and eigenvectors to be calculated using ARPACK. It also defines the range for the output array, since the method generates points only for the critical speed calculated by run_critical_speed(). Default is 12.
rtolfloat, optional: Tolerance (relative) for termination. Applied to scipy.optimize.newton to calculate the approximated critical speeds. Default is 0.005 (0.5%).
free_freebool, optional: If True, the method will consider the rotor system as free-free. Default is False.

Returns:

resultsross.FrequencyResponseResults: For more information on attributes and methods available see: ross.FrequencyResponseResults

Examples

>>> import ross as rs
>>> rotor = rs.rotor_example()
>>> speed =np.linspace(0, 1000, 101)
>>> response = rotor.run_freq_response(speed_range=speed)

Return the response amplitude >>> abs(response.freq_resp) # doctest: +ELLIPSIS array([[[0.00000000e+00, 1.00261725e-06, 1.01076952e-06, …

Return the response phase >>> np.angle(response.freq_resp) # doctest: +ELLIPSIS array([[[…

Using clustered points option. Set cluster_points=True and choose how many modes the method must search and how many points to add just before and after each critical speed.

>>> response = rotor.run_freq_response(cluster_points=True, num_points=5)
>>> response.speed_range.shape
(61,)

Selecting the disirable modes, if you want a reduced model: >>> response = rotor.run_freq_response(speed_range=speed, modes=[0, 1, 2, 3, 4]) >>> abs(response.freq_resp) # doctest: +ELLIPSIS array([[[0.00000000e+00, 1.00261725e-06, 1.01076952e-06, …

Plotting frequency response function: >>> fig = response.plot(inp=13, out=13)

To plot velocity and acceleration responses, you must change amplitude_units from “[length]/[force]” units to “[speed]/[force]” or “[acceleration]/[force]” respectively

Plotting velocity response >>> fig = response.plot(inp=13, out=13, amplitude_units=”m/s/N”)

Plotting acceleration response >>> fig = response.plot(inp=13, out=13, amplitude_units=”m/s**2/N”)

run_level1(n=5, stiffness_range=None, num=5, **kwargs)#

Plot level 1 stability analysis.

This method will plot the stability 1 analysis for a given stiffness range.

Parameters:

nint: Number of steps in the range. Default is 5.
stiffness_rangetuple, optional: Tuple with (start, end) for stiffness range. This will be used to create an evenly numbers spaced evenly on a log scale to create a better visualization (see np.logspace).
kwargsoptional: Additional key word arguments can be passed to change the plot layout only (e.g. width=1000, height=800, …). *See Plotly Python Figure Reference for more information.

Returns:

resultsross.Level1Results: For more information on attributes and methods available see: ross.Level1Results

run_misalignment(node, unbalance_magnitude, unbalance_phase, speed, t, coupling='flex', **kwargs)#

Run analysis for the rotor system with misalignment given an unbalance force.

Misalignment object is instantiated and system’s time response is simulated. There are two types of coupling: flexible (flex) and rigid, each with distinct parameters. These parameters are passed to the respective method through **kwargs.

Parameters:

nodelist, int

Node where the unbalance is applied.

unbalance_magnitudelist, float, pint.Quantity

Unbalance magnitude (kg.m).

unbalance_phaselist, float, pint.Quantity

Unbalance phase (rad).

speedfloat or array_like, pint.Quantity

Rotor speed.

Farray

Force array (needs to have the same number of rows as time array). Each column corresponds to a dof and each row to a time.

tarray

Time array.

couplingstr

Coupling type. The avaible types are: “flex” and “rigid”. Default is “flex”.

**kwargsdictionary

If coupling = “flex”, **kwargs receives:

nfloat: Number of shaft element where the misalignment is ocurring.
mis_type: string: Name of the chosen misalignment type. The avaible types are: “parallel”, “angular” and “combined”.
mis_distance_xfloat, pint.Quantity: Parallel misalignment distance between driving rotor and driven rotor along X direction.
mis_distance_yfloat, pint.Quantity: Parallel misalignment distance between driving rotor and driven rotor along Y direction.
mis_anglefloat, pint.Quantity: Angular misalignment angle.
radial_stiffnessfloat, pint.Quantity: Radial stiffness of flexible coupling.
bending_stiffnessfloat, pint.Quantity: Bending stiffness of flexible coupling. Provide if mis_type is “angular” or “combined”.
input_torquefloat, pint.Quantity: Driving torque. Default is 0.
load_torquefloat, pint.Quantity: Driven torque. Default is 0.

If coupling = “rigid”, **kwargs receives:

nfloat: Number of shaft element where the misalignment is ocurring.
mis_distancefloat, pint.Quantity: Parallel misalignment distance between driving rotor and driven rotor.
input_torquefloat, pint.Quantity: Driving torque. Default is 0.
load_torquefloat, pint.Quantity: Driven torque. Default is 0.

Additional keyword arguments can be passed to define the parameters of the Newmark method if it is used (e.g. gamma, beta, tol, …). See ross.utils.newmark for more details. Other keyword arguments can also be passed to be used in numerical integration (e.g. model_reduction). See Rotor.integrate_system for more details.

Returns:

resultsross.TimeResponseResults: For more information on attributes and methods available see: ross.TimeResponseResults

Examples

>>> import ross as rs
>>> from ross.probe import Probe
>>> from ross.units import Q_
>>> rotor = rotor_example_with_damping()
>>> n1 = rotor.disk_elements[0].n
>>> n2 = rotor.disk_elements[1].n
>>> results = rotor.run_misalignment(
...    node=[n1, n2],
...    unbalance_magnitude=[5e-4, 0],
...    unbalance_phase=[-np.pi / 2, 0],
...    speed=Q_(1200, "RPM"),
...    t=np.arange(0, 0.5, 0.0001),
...    coupling="rigid",
...    n=0,
...    mis_distance=2e-4,
...    input_torque=0,
...    load_torque=0,
...    model_reduction={"num_modes": 12},  # Pseudo-modal method
... )
Running with model reduction: pseudomodal
>>> probe1 = Probe(14, 0)
>>> probe2 = Probe(22, 0)
>>> fig1 = results.plot_1d([probe1, probe2])
>>> fig2 = results.plot_dfft(
...     [probe1, probe2],
...     frequency_range=Q_((0, 200), "Hz"),
...     yaxis_type="log",
... )

run_rubbing(n, distance, contact_stiffness, contact_damping, friction_coeff, node, unbalance_magnitude, unbalance_phase, speed, t, torque=False, **kwargs)#

Run analysis for the rotor system with rubbing given an unbalance force.

Rubbing object is instantiated and system’s time response is simulated.

Parameters:

nint: Number of shaft element where rubbing is ocurring.
distancefloat, pint.Quantity: Distance between the housing and shaft surface.
contact_stiffnessfloat, pint.Quantity: Contact stiffness.
contact_dampingfloat, pint.Quantity: Contact damping.
friction_coefffloat: Friction coefficient.
nodelist, int: Node where the unbalance is applied.
unbalance_magnitudelist, float, pint.Quantity: Unbalance magnitude (kg.m).
unbalance_phaselist, float, pint.Quantity: Unbalance phase (rad).
speedfloat or array_like, pint.Quantity: Rotor speed.
Farray: Force array (needs to have the same number of rows as time array). Each column corresponds to a dof and each row to a time.
tarray: Time array.
torquebool, optional: If True a torque is considered by rubbing. Default is False.
**kwargsoptional: Additional keyword arguments can be passed to define the parameters of the Newmark method if it is used (e.g. gamma, beta, tol, …). See ross.utils.newmark for more details. Other keyword arguments can also be passed to be used in numerical integration (e.g. model_reduction). See Rotor.integrate_system for more details.

Returns:

resultsross.TimeResponseResults: For more information on attributes and methods available see: ross.TimeResponseResults

Examples

>>> import ross as rs
>>> from ross.units import Q_
>>> from ross.probe import Probe
>>> rotor = rotor_example_with_damping()
>>> n1 = rotor.disk_elements[0].n
>>> n2 = rotor.disk_elements[1].n
>>> results = rotor.run_rubbing(
...    n=12,
...    distance=7.95e-5,
...    contact_stiffness=1.1e6,
...    contact_damping=40,
...    friction_coeff=0.3,
...    torque=False,
...    node=[n1, n2],
...    unbalance_magnitude=[5e-4, 0],
...    unbalance_phase=[-np.pi / 2, 0],
...    speed=Q_(1200, "RPM"),
...    t=np.arange(0, 0.5, 0.0001),
...    model_reduction={"num_modes": 12},  # Pseudo-modal method
... )
Running with model reduction: pseudomodal
>>> probe1 = Probe(14, 0)
>>> probe2 = Probe(22, 0)
>>> fig1 = results.plot_1d([probe1, probe2])
>>> fig2 = results.plot_dfft(
...     [probe1, probe2],
...     frequency_range=Q_((0, 200), "Hz"),
...     yaxis_type="log",
... )

run_static()#

Run static analysis.

Static analysis calculates free-body diagram, deformed shaft, shearing force diagram and bending moment diagram.

Available plotting methods:: .plot_deformation() .plot_bending_moment() .plot_shearing_force() .plot_free_body_diagram()

Attributes:

shaft_weight: float: Shaft total weight
disk_forces_nodaldict: Relates the static force at each node due to the weight of disks
bearing_forces_nodaldict: Relates the static force at each node due to the bearing reaction forces.
bearing_forces_tagdict: Indicates the reaction force exerted by each bearing.
disk_forces_tagdict: Indicates the force exerted by each disk.
displacement_y: array: The shaft static displacement vector,
Vx: array: Shearing force vector
Bm: array: Bending moment vector

Returns:

resultsross.StaticResults: For more information on attributes and methods available see: ross.StaticResults

Raises:

ValueError: Error raised if the rotor has no bearing elements.

run_time_response(speed, F, t, method='default', **kwargs)#

Calculate the time response.

This function will take a rotor object and calculate its time response given a force and a time.

Available plotting methods:: .plot_1d() .plot_2d() .plot_3d()

Parameters:

speedfloat or array_like, pint.Quantity: Rotor speed. Automatically, the Newmark method is chosen if speed has an array_like type.
Farray: Force array (needs to have the same number of rows as time array). Each column corresponds to a dof and each row to a time.
tarray: Time array.
methodstr, optional: The Newmark method can be chosen by setting method=’newmark’.
**kwargsoptional: Additional keyword arguments can be passed to define the parameters of the Newmark method if it is used (e.g. gamma, beta, tol, …). See ross.utils.newmark for more details. Other keyword arguments can also be passed to be used in numerical integration (e.g. model_reduction, add_to_RHS). See Rotor.integrate_system for more details.

Returns:

resultsross.TimeResponseResults: For more information on attributes and methods available see: ross.TimeResponseResults

Examples

>>> from ross.probe import Probe
>>> rotor = rotor_example()
>>> speed = 500.0
>>> size = 1000
>>> node = 3
>>> probe1 = Probe(3, 0)
>>> t = np.linspace(0, 10, size)
>>> F = np.zeros((size, rotor.ndof))
>>> F[:, rotor.number_dof * node + 0] = 10 * np.cos(2 * t)
>>> F[:, rotor.number_dof * node + 1] = 10 * np.sin(2 * t)
>>> response = rotor.run_time_response(speed, F, t)
>>> response.yout[:, rotor.number_dof * node + 1]
array([ 0.00000000e+00,  1.86686693e-07,  8.39130663e-07, ...
>>> # plot time response for a given probe:
>>> fig1 = response.plot_1d(probe=[probe1])
>>> # plot orbit response - plotting 2D nodal orbit:
>>> fig2 = response.plot_2d(node=node)
>>> # plot orbit response - plotting 3D orbits - full rotor model:
>>> fig3 = response.plot_3d()

run_ucs(stiffness_range=None, bearing_frequency_range=None, num_modes=16, num=20, synchronous=False, **kwargs)#

Run Undamped Critical Speeds analyzes.

This method will run the undamped critical speed analyzes for a given range of stiffness values. If the range is not provided, the bearing stiffness at rated speed will be used to create a range.

Parameters:

stiffness_rangetuple, optional: Tuple with (start, end) for stiffness range in a log scale. In linear space, the sequence starts at base ** start (base to the power of start) and ends with base ** stop (see endpoint below). Here base is 10.0.
bearing_frequency_rangetuple, optional: The bearing frequency range used to calculate the intersection points. In some cases bearing coefficients will have to be extrapolated. The default is None. In this case the bearing frequency attribute is used.
num_modesint, optional: Number of modes to be calculated. This uses scipy.sparse.eigs method. Default is 16. In this case 4 modes are plotted, since for each pair of eigenvalues calculated we have one wn, and we show only the forward mode in the plots.
numint: Number of steps in the range. Default is 20.
synchronousbool, optional: If True a synchronous analysis is carried out according to []. Default is False.

Returns:

resultsross.UCSResults: For more information on attributes and methods available see: ross.UCSResults

run_unbalance_response(node, unbalance_magnitude, unbalance_phase, frequency=None, modes=None, cluster_points=False, num_modes=12, num_points=10, rtol=0.005)#

Unbalanced response for a mdof system.

This method returns the unbalanced response for a mdof system given magnitide and phase of the unbalance, the node where it’s applied and a frequency range.

Available plotting methods:: .plot() .plot_magnitude() .plot_phase() .plot_polar_bode() .plot_deflected_shape() .plot_bending_moment() .plot_deflected_shape_3d() .plot_deflected_shape_2d()

Parameters:

nodelist, int: Node where the unbalance is applied.
unbalance_magnitudelist, float, pint.Quantity: Unbalance magnitude (kg.m).
unbalance_phaselist, float, pint.Quantity: Unbalance phase (rad).
frequencylist, pint.Quantity: List with the desired range of frequencies (rad/s).
modeslist, optional: Modes that will be used to calculate the frequency response (all modes will be used if a list is not given).
cluster_pointsbool, optional: boolean to activate the automatic frequency spacing method. If True, the method uses _clustering_points() to create an speed_range. Default is False
num_pointsint, optional: The number of points generated per critical speed. The method set the same number of points for slightly less and slightly higher than the natural circular frequency. It means there’ll be num_points greater and num_points smaller than a given critical speed. num_points may be between 2 and 12. Anything above this range defaults to 10 and anything below this range defaults to 4. The default is 10.
num_modes: The number of eigenvalues and eigenvectors to be calculated using ARPACK. It also defines the range for the output array, since the method generates points only for the critical speed calculated by run_critical_speed(). Default is 12.
rtolfloat, optional: Tolerance (relative) for termination. Applied to scipy.optimize.newton to calculate the approximated critical speeds. Default is 0.005 (0.5%).

Returns:

resultsross.ForcedResponseResults: For more information on attributes and methods available see: ross.ForcedResponseResults

Examples

>>> import ross as rs
>>> rotor = rs.rotor_example()
>>> speed = np.linspace(0, 1000, 101)
>>> response = rotor.run_unbalance_response(node=3,
...                                         unbalance_magnitude=10.0,
...                                         unbalance_phase=0.0,
...                                         frequency=speed)

Return the response amplitude >>> abs(response.forced_resp) # doctest: +ELLIPSIS array([[0.00000000e+00, 5.06073311e-04, 2.10044826e-03, …

Return the response phase >>> np.angle(response.forced_resp) # doctest: +ELLIPSIS array([[ 0. , 0. , 0. , …

Using clustered points option. Set cluster_points=True and choose how many modes the method must search and how many points to add just before and after each critical speed.

>>> response2 = rotor.run_unbalance_response(
...     node=3, unbalance_magnitude=0.01, unbalance_phase=0.0, cluster_points=True, num_points=5
... )
>>> response2.speed_range.shape
(61,)

plot unbalance response: >>> probe_node = 3 >>> probe_angle = np.pi / 2 >>> probe_tag = “my_probe” # optional >>> fig = response.plot(probe=[rs.Probe(probe_node, probe_angle, tag=probe_tag)])

plot response for major or minor axis: >>> probe_node = 3 >>> probe_angle = “major” # for major axis >>> # probe_angle = “minor” # for minor axis >>> probe_tag = “my_probe” # optional >>> fig = response.plot(probe=[rs.Probe(probe_node, probe_angle, tag=probe_tag)])

To plot velocity and acceleration responses, you must change amplitude_units from “[length]” units to “[length]/[time]” or “[length]/[time] ** 2” respectively Plotting velocity response >>> fig = response.plot( … probe=[rs.Probe(probe_node, probe_angle)], … amplitude_units=”m/s” … )

Plotting acceleration response >>> fig = response.plot( … probe=[rs.Probe(probe_node, probe_angle)], … amplitude_units=”m/s**2” … )

Plotting deflected shape configuration Speed value must be in speed_range. >>> value = 600 >>> fig = response.plot_deflected_shape(speed=value)

save(file)#

Save the rotor to a .toml file.

Parameters:

filestr or pathlib.Path

Examples

>>> from tempfile import tempdir
>>> from pathlib import Path
>>> # create path for temporary file
>>> file = Path(tempdir) / 'rotor.toml'
>>> rotor = rotor_example()
>>> rotor.save(file)

save_mat(file, speed, frequency=None)#

Save matrices and rotor model to a .mat file.

Parameters:

filestr, pathlib.Path
speed: float: Rotor speed.
frequency: float, optional: Excitation frequency. Default is rotor speed.

Examples

>>> from tempfile import tempdir
>>> from pathlib import Path
>>> # create path for temporary file
>>> file = Path(tempdir) / 'new_matrices'
>>> rotor = rotor_example()
>>> rotor.save_mat(file, speed=0)

summary()#

Plot the rotor summary.

This functioncreates a summary of the main parameters and attributes of the rotor model. The data is presented in a table format.

Returns:

resultsross.SummaryResults class: An instance of SumarryResults class to build the summary table

Examples

>>> rotor = rotor_example()
>>> table = rotor.summary().plot()
>>> # to display the plot use the command:
>>> # show(table)

time_response(speed, F, t, ic=None, method='default', **kwargs)#

Time response for a rotor.

This method returns the time response for a rotor given a force, time and initial conditions.

Parameters:

speedfloat or array_like: Rotor speed. Automatically, the Newmark method is chosen if speed has an array_like type.
Farray: Force array (needs to have the same length as time array).
tarray: Time array. (must have the same length than lti.B matrix)
icarray, optional: The initial conditions on the state vector (zero by default).
methodstr, optional: The Newmark method can be chosen by setting method=’newmark’.
**kwargsoptional: Additional keyword arguments can be passed to define the parameters of the Newmark method if it is used (e.g. gamma, beta, tol, …). See ross.utils.newmark for more details. Other keyword arguments can also be passed to be used in numerical integration (e.g. model_reduction, add_to_RHS). See Rotor.integrate_system for more details.

Returns:

tarray: Time values for the output.
youtarray: System response.
xoutarray: Time evolution of the state vector.

Examples

>>> rotor = rotor_example()
>>> speed = 0
>>> size = 28
>>> t = np.linspace(0, 5, size)
>>> F = np.ones((size, rotor.ndof))
>>> rotor.time_response(speed, F, t)
(array([0.        , 0.18518519, 0.37037037, ...

classmethod to_ross_only(rotor)#: Convert rotor with rsxl objects to ross only.

transfer_matrix(speed=None, frequency=None, modes=None)#

Calculate the fer matrix for the frequency response function (FRF).

Returns:

Hmatrix: System transfer matrix

unbalance_force_over_time(node, magnitude, phase, omega, t, return_all=False)#

Calculate unbalance forces for each time step.

This auxiliary function calculates the unbalanced forces by taking into account the magnitude and phase of the force. It generates an array of force values at each degree of freedom for the specified nodes at each time step, while also considering a range of frequencies.

Parameters:

nodelist, int: Nodes where the unbalance is applied.
magnitudelist, float: Unbalance magnitude (kg.m) for each node.
phaselist, float: Unbalance phase (rad) for each node.
omegafloat, np.darray: Constant velocity or desired range of velocities (rad/s).
tnp.darray: Time array (s).
return_allbool, optional: If True, returns F0, theta, omega, and alpha. If False, returns only F0. Default is False.

Returns:

F0np.ndarray: Unbalance force at each degree of freedom for each time step.
thetanp.ndarray: Angular positions for each time step.
omeganp.ndarray: Angular velocities for each time step.
alphanp.ndarray: Angular accelerations for each time step.

Examples

>>> rotor = rotor_example()
>>> t = np.linspace(0, 10, 31)
>>> omega = np.linspace(0, 1000, 31)
>>> F = rotor.unbalance_force_over_time([3], [10.0], [0.0], omega, t)
>>> F[18, :3]
array([     0.        ,   7632.15353293, -43492.18127561])

Attributes

run_modal

ross.Rotor

Contents

ross.Rotor#