ross.MultiRotor

ross.MultiRotor#

class ross.MultiRotor(driving_rotor, driven_rotor, coupled_nodes, gear_ratio, gear_mesh_stiffness, orientation_angle=0.0, position='above', tag=None)#

A class representing a multi-rotor system.

This class creates a system comprising multiple rotors, with the specified driving rotor and driven rotor. For systems with more than two rotors, multiple multi-rotors can be nested.

Parameters:

driving_rotorrs.Rotor: The driving rotor object.
driven_rotorrs.Rotor: The driven rotor object.
coupled_nodestuple of int: Tuple specifying the coupled nodes, where the first node corresponds to the driving rotor and the second node corresponds to the driven rotor.
gear_ratiofloat: The gear ratio between the rotors.
gear_mesh_stiffnessfloat: The stiffness of the gear mesh.
orientation_anglefloat, pint.Quantity, optional: The angle between the line of gear centers and x-axis. Default is 0.0 rad.
position{‘above’, ‘below’}, optional: The relative position of the driven rotor with respect to the driving rotor when plotting the multi-rotor. Default is ‘above’.
tagstr, optional: A tag to identify the multi-rotor. Default is None.

Returns:

rotorrs.Rotor: The created multi-rotor object.

Examples

>>> import ross as rs
>>> steel = rs.materials.steel
>>> # Rotor 1:
>>> L1 = [0.1, 4.24, 1.16, 0.3]
>>> d1 = [0.3, 0.3, 0.22, 0.22]
>>> shaft1 = [
...     rs.ShaftElement(
...         L=L1[i],
...         idl=0.0,
...         odl=d1[i],
...         material=steel,
...     )
...     for i in range(len(L1))
... ]
>>> generator = rs.DiskElement(n=1, m=525.7, Id=16.1, Ip=32.2)
>>> disk = rs.DiskElement(n=2, m=116.04, Id=3.115, Ip=6.23)
>>> gear1 = rs.GearElement(
...     n=4, m=726.4, Id=56.95, Ip=113.9,
...     pitch_diameter=1.1, pressure_angle=rs.Q_(22.5, 'deg'),
... )
>>> bearing1 = rs.BearingElement(n=0, kxx=183.9e6, kyy=200.4e6, cxx=3e3)
>>> bearing2 = rs.BearingElement(n=3, kxx=183.9e6, kyy=200.4e6, cxx=3e3)
>>> rotor1 = rs.Rotor(shaft1, [generator, disk, gear1], [bearing1, bearing2],)

>>> # Rotor 2:
>>> L2 = [0.3, 5, 0.1]
>>> d2 = [0.15, 0.15, 0.15]
>>> shaft2 = [
...     rs.ShaftElement(
...         L=L2[i],
...         idl=0.0,
...         odl=d2[i],
...         material=steel,
...     )
...     for i in range(len(L2))
... ]
>>> gear2 = rs.GearElement(
...     n=0, m=5, Id=0.002, Ip=0.004,
...     pitch_diameter=0.077, pressure_angle=rs.Q_(22.5, 'deg'),
... )
>>> turbine = rs.DiskElement(n=2, m=7.45, Id=0.0745, Ip=0.149)
>>> bearing3 = rs.BearingElement(n=1, kxx=10.1e6, kyy=41.6e6, cxx=3e3)
>>> bearing4 = rs.BearingElement(n=3, kxx=10.1e6, kyy=41.6e6, cxx=3e3)
>>> rotor2 = rs.Rotor(shaft2, [gear2, turbine], [bearing3, bearing4],)

>>> # Multi rotor:
>>> multi_rotor = rs.MultiRotor(
...     rotor1,
...     rotor2,
...     coupled_nodes=(4, 0),
...     gear_ratio=328 / 23,
...     gear_mesh_stiffness=1e8,
...     orientation_angle=0.0,
...     position="below"
... )
>>> modal = multi_rotor.run_modal(speed=0)
>>> modal.wd[0] 
74.160244...

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, ignore=[])#

Damping matrix for a multi-rotor rotor.

Parameters:

frequencyfloat: Excitation frequency.
ignorelist, optional: List of elements to leave out of the matrix.

Returns:

C0np.ndarray: Damping matrix for the multi-rotor.

Examples

>>> multi_rotor = two_shaft_rotor_example()
>>> multi_rotor.C(0)[:4, :4] / 1e3
array([[3., 0., 0., 0.],
       [0., 3., 0., 0.],
       [0., 0., 0., 0.],
       [0., 0., 0., 0.]])

G()#

Gyroscopic matrix for a multi-rotor.

For time-dependent analyses, this matrix needs to be multiplied by the rotor speed. Therefore, the gyroscopic matrix of the driven rotor is scaled by the gear ratio before being combined with the driving rotor matrix.

Returns:

G0np.ndarray: Gyroscopic matrix for the multi-rotor.

Examples

>>> multi_rotor = two_shaft_rotor_example()
>>> multi_rotor.G()[:4, :4]
array([[ 0.        ,  0.17162125,  0.        ,  0.1403395 ],
       [-0.17162125,  0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ],
       [-0.1403395 ,  0.        ,  0.        ,  0.        ]])

K(frequency, ignore=[])#

Stiffness matrix for a multi-rotor.

Parameters:

frequencyfloat, optional: Excitation frequency.
ignorelist, optional: List of elements to leave out of the matrix.

Returns:

K0np.ndarray: Stiffness matrix for the multi-rotor.

Examples

>>> multi_rotor = two_shaft_rotor_example()
>>> multi_rotor.K(0)[:4, :4] / 1e10
array([[ 4.7609372 ,  0.        ,  0.        ,  0.        ],
       [ 0.        ,  4.7625872 ,  0.        , -0.23712736],
       [ 0.        ,  0.        , 14.63196778,  0.        ],
       [ 0.        , -0.23712736,  0.        ,  0.09416119]])

Ksdt()#

Dynamic stiffness matrix for a multi-rotor.

Stiffness matrix associated with the transient motion of the shaft and disks. For time-dependent analyses, this matrix needs to be multiplied by the angular acceleration. Therefore, the stiffness matrix of the driven rotor is scaled by the gear ratio before being combined with the driving rotor matrix.

Returns:

Ksdt0np.ndarray: Dynamic stiffness matrix for the multi-rotor.

Examples

>>> multi_rotor = two_shaft_rotor_example()
>>> multi_rotor.Ksdt()[:6, :4]
array([[  0.        , -74.43218395,   0.        ,   0.6202682 ],
       [  0.        ,   0.        ,   0.        ,   0.        ],
       [  0.        ,   0.        ,   0.        ,   0.        ],
       [  0.        ,   0.        ,   0.        ,   0.        ],
       [  0.        ,  -0.6202682 ,   0.        ,   0.08270243],
       [  0.        ,   0.        ,   0.        ,   0.        ]])

M(frequency=None, synchronous=False)#

Mass matrix for a multi-rotor.

Parameters:

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

Returns:

M0np.ndarray: Mass matrix for the multi-rotor.

Examples

>>> multi_rotor = two_shaft_rotor_example()
>>> multi_rotor.M(0)[:4, :4]
array([[18.55298224,  0.        ,  0.        ,  0.        ],
       [ 0.        , 18.55298224,  0.        , -0.16179571],
       [ 0.        ,  0.        , 18.37831702,  0.        ],
       [ 0.        , -0.16179571,  0.        ,  0.10074262]])

__init__(driving_rotor, driven_rotor, coupled_nodes, gear_ratio, gear_mesh_stiffness, orientation_angle=0.0, position='above', 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

check_speed(node, omega)#

Adjusts the speed for the specified node based on the rotor configuration.

This method checks if the given node belongs to the driven rotor. If so, the rotation speed is multiplied by the gear ratio.

Parameters:

nodeint: The node index where the speed check is being applied.
omegafloat or np.ndarray: The original rotation speed of the driving rotor in rad/s.

Returns:

speedfloat or np.ndarray: The adjusted rotation speed for the specified node.

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

coupling_matrix()#

Coupling matrix of two coupled gears.

Returns:

coupling_matrixnp.ndarray: Dimensionless coupling matrix of two coupled gears

Examples

>>> multi_rotor = two_shaft_rotor_example()
>>> multi_rotor.coupling_matrix()[:4, :4]
array([[0.14644661, 0.35355339, 0.        , 0.        ],
       [0.35355339, 0.85355339, 0.        , 0.        ],
       [0.        , 0.        , 0.        , 0.        ],
       [0.        , 0.        , 0.        , 0.        ]])

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.

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.
num_modesint, optional: If num_modes is passed as argument, the pseudo-modal method is applied reducing the model to the chosen number of modes.
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

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_campbell(speed_range, frequencies=6, frequency_type='wd')#

Calculate the Campbell diagram.

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

Available plotting methods:: .plot()

Parameters:

speed_rangearray: 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”.

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', **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 avaible types are: “Mayes” and “Gasch”. Default is “Mayes”.
**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. num_modes). 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),
...    num_modes=12, # Pseudo-modal method
... )
Running pseudo-modal method, number of modes = 12
>>> 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: 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: Unbalance force in each degree of freedom for each value in omega
speed_rangelist, array: 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)#

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: 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%).

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([[[1.00000000e-06, 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([[[2.00154633e-07, 2.02422522e-07, 2.09522044e-07, …

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. num_modes). 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,
...    num_modes=12,  # Pseudo-modal method
... )
Running pseudo-modal method, number of modes = 12
>>> 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. num_modes). 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),
...    num_modes=12,  # Pseudo-modal method
... )
Running pseudo-modal method, number of modes = 12
>>> 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()

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.

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

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: 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. num_modes, 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([[ 0.00000000e+00, …

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. num_modes, 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

Attributes

run_modal

ross.MultiRotor

Contents

ross.MultiRotor#