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

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...

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.

Methods

A(speed=0, frequency=None)#

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.

Returns

Anp.ndarray: State space matrix for the rotor.

Examples

>>> rotor = rotor_example()
>>> np.round(rotor.A()[50:56, :2])
array([[     0.,  10927.],
       [-10924.,     -0.],
       [  -174.,      0.],
       [    -0.,   -174.],
       [    -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 = rotor_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, -0.00022681,  0.        ],
       [-0.01943344,  0.        ,  0.        , -0.00022681],
       [ 0.00022681,  0.        ,  0.        ,  0.0001524 ],
       [ 0.        ,  0.00022681, -0.0001524 ,  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([[47.,  0.,  0.,  6.],
       [ 0., 46., -6.,  0.],
       [ 0., -6.,  1.,  0.],
       [ 6.,  0.,  0.,  1.]])

Kst()#

Dynamic stiffness matrix for an instance of a rotor.

Returns

Kst0np.ndarray: Dynamic stiffness matrix for the rotor. This matris IS OMEGA dependent Only useable to the 6 DoF model.

Examples

>>> rotor = rotor_example_6dof()
>>> np.round(rotor.Kst()[:6, :6]*1e6)
array([[     0., -23002.,      0.,   -479.,      0.,      0.],
       [     0.,      0.,      0.,      0.,      0.,      0.],
       [     0.,      0.,      0.,      0.,      0.,      0.],
       [     0.,      0.,      0.,      0.,      0.,      0.],
       [     0.,    479.,      0.,    160.,      0.,      0.],
       [     0.,      0.,      0.,      0.,      0.,      0.]])

M(frequency=None)#

Mass matrix for an instance of a rotor.

Returns

M0np.ndarray: Mass matrix for the rotor.

Examples

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

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.

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(**kwargs)#

Run an analyzes with rubbing.

Execute the crack defect and generates the crack object on the back-end.

Parameters

dtfloat: Time step
tIfloat: Initial time
tFfloat: Final time
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.
n_crackfloat: Element where the crack is located
speedfloat, pint.Quantity: Operational speed of the machine. Default unit is rad/s.
unbalance_magnitudearray: Array with the unbalance magnitude. The unit is kg.m.
unbalance_phasearray: Array with the unbalance phase. The unit is rad.
crack_typestring: String containing type of crack model chosed. The avaible types are: Mayes and Gasch.
print_progressbool: Set it True, to print the time iterations and the total time spent, by default False.

Examples

>>> from ross.defects.crack import crack_example
>>> probe1 = (14, 0)
>>> probe2 = (22, 0)
>>> response = crack_example()
>>> results = response.run_time_response()
>>> fig = response.plot_dfft(probe=[probe1, probe2], range_freq=[0, 100], yaxis_type="log")
>>> # fig.show()

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., 867.])

Changing output units >>> np.round(results.wd(“rpm”)) array([2590., 2868., 6074., 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]) >>> 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(coupling='flex', **kwargs)#

Run an analyzes with misalignment.

Execute the misalignment defect and generates the misalignment object on the back-end. There are two types of coupling, flexible (flex) and rigid, which have different entries. These entries are provided via **kwargs to the specific method.

Parameters

couplingstr

Coupling type. The avaible types are: flex, by default; and rigid.

**kwargs: dictionary

In the case of coupling = “flex”, **kwargs receives:

dtfloat: Time step.
tIfloat: Initial time.
tFfloat: Final time.
kdfloat: Radial stiffness of flexible coupling.
ksfloat: Bending stiffness of flexible coupling.
eCOUPxfloat: Parallel misalignment offset between driving rotor and driven rotor along X direction.
eCOUPyfloat: Parallel misalignment offset between driving rotor and driven rotor along Y direction.
misalignment_anglefloat: Angular misalignment angle.
TDfloat: Driving torque.
TLfloat: Driven torque.
n1float: Node where the misalignment is ocurring.
speedfloat, pint.Quantity: Operational speed of the machine. Default unit is rad/s.
unbalance_magnitudearray: Array with the unbalance magnitude. The unit is kg.m.
unbalance_phasearray: Array with the unbalance phase. The unit is rad.
mis_type: string: String containing the misalignment type choosed. The avaible types are: parallel, by default; angular; combined.
print_progressbool: Set it True, to print the time iterations and the total time spent. False by default.

In the case of coupling = “rigid”, **kwargs receives:

dtfloat: Time step.
tIfloat: Initial time.
tFfloat: Final time.
eCOUPfloat: Parallel misalignment offset between driving rotor and driven rotor along X direction.
TDfloat: Driving torque.
TLfloat: Driven torque.
n1float: Node where the misalignment is ocurring.
speedfloat, pint.Quantity: Operational speed of the machine. Default unit is rad/s.
unbalance_magnitudearray: Array with the unbalance magnitude. The unit is kg.m.
unbalance_phasearray: Array with the unbalance phase. The unit is rad.
print_progressbool: Set it True, to print the time iterations and the total time spent. False by default.

Examples

>>> from ross.defects.misalignment import misalignment_flex_parallel_example
>>> probe1 = (14, 0)
>>> probe2 = (22, 0)
>>> response = misalignment_flex_parallel_example()
>>> results = response.run_time_response()
>>> fig = response.plot_dfft(probe=[probe1, probe2], range_freq=[0, 100], yaxis_type="log")
>>> # fig.show()

run_modal(speed, num_modes=12, sparse=True)#

Run modal analysis.

Method to calculate eigenvalues and eigvectors for a given rotor system. Tthe natural frequencies and dampings ratios are calculated for a given rotor speed. It means that for each speed input there’s a different set of eigenvalues and eigenvectors, hence, different natural frequencies and damping ratios are returned. This method will return a ModalResults object which stores all data generated and also provides so methods for plotting.

Available plotting methods:: .plot_mode_2d() .plot_mode_3d()

Parameters

speedfloat: Speed at which the eigenvalues and eigenvectors will be calculated.
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 sparse=False, num_modes does not have any effect over the method. Default is 12.
sparsebool, optional: If True, ARPACK is used to calculate a desired number (according to num_modes) or eigenvalues and eigenvectors. If False, scipy.linalg.eig() is used to calculate all the eigenvalues and eigenvectors. Default is True.

Returns

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

Examples

>>> import ross as rs
>>> rotor = rs.rotor_example()
>>> modal = rotor.run_modal(speed=0, sparse=False)
>>> modal.wn[:2]
array([91.79655318, 96.28899977])
>>> modal.wd[:2]
array([91.79655318, 96.28899977])
>>> # Plotting 3D mode shape
>>> mode1 = 0  # First mode
>>> fig = modal.plot_mode_3d(mode1)
>>> # Plotting 2D mode shape
>>> mode2 = 1  # Second mode
>>> fig = modal.plot_mode_2d(mode2)

run_rubbing(**kwargs)#

Run an analyzes with rubbing.

Execute the rubbing defect and generates the rubbing object on the back-end.

Parameters

**kwargs: dictionary

**kwargs receives:

dtfloat: Time step.
tIfloat: Initial time.
tFfloat: Final time.
deltaRUBfloat: Distance between the housing and shaft surface.
kRUBfloat: Contact stiffness.
cRUBfloat: Contact damping.
miRUBfloat: Friction coefficient.
posRUBint: Node where the rubbing is ocurring.
speedfloat, pint.Quantity: Operational speed of the machine. Default unit is rad/s.
unbalance_magnitudearray: Array with the unbalance magnitude. The unit is kg.m.
unbalance_phasearray: Array with the unbalance phase. The unit is rad.
torquebool: Set it as True to consider the torque provided by the rubbing, by default False.
print_progressbool: Set it True, to print the time iterations and the total time spent, by default False.

Examples

>>> from ross.defects.rubbing import rubbing_example
>>> probe1 = (14, 0)
>>> probe2 = (22, 0)
>>> response = rubbing_example()
>>> results = response.run_time_response()
>>> fig = response.plot_dfft(probe=[probe1, probe2], range_freq=[0, 100], yaxis_type="log")
>>> # fig.show()

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)#

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: 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.

Returns

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

Examples

>>> rotor = rotor_example()
>>> speed = 500.0
>>> size = 1000
>>> node = 3
>>> probe1 = (3, 0)
>>> t = np.linspace(0, 10, size)
>>> F = np.zeros((size, rotor.ndof))
>>> F[:, 4 * node] = 10 * np.cos(2 * t)
>>> F[:, 4 * node + 1] = 10 * np.sin(2 * t)
>>> response = rotor.run_time_response(speed, F, t)
>>> dof = 13
>>> response.yout[:, dof] 
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.
numint: Number of steps in the range. Default is 20.
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.
synchronousbool: If True a synchronous analysis is carried out and the frequency of the first forward model will be equal to the speed. 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, float, pint.Quantity: Array 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=[(probe_node, probe_angle, 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=[(probe_node, probe_angle, 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=[(probe_node, probe_angle)], … amplitude_units=”m/s” … )

Plotting acceleration response >>> fig = response.plot( … 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)#

Time response for a rotor.

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

Parameters

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).

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, ...

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

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

Returns

Hmatrix: System transfer matrix

ROSS

ross.Rotor

ross.Rotor#