API Reference

Assembly

class opentorsion.assembly.Assembly(shaft_elements, disk_elements=None, gear_elements=None)

Bases: object

This class assembles the multi-degree of freedom system matrices, includes functions for modal analysis and response analysis.

Attributes:

shaft_elementslist: List containing the shaft elements
disk_elementslist: List containing the disk elements
gear_elementslist: List containing the gear elements

Methods

`C_modal`(M, K[, xi])	Full damping matrix for mechanical system obtained from modal damping matrix
`E`()	Assembles the gear constraint matrix
`T`(E)	Method for determining gear constraint transformation matrix
`assemble_C`()	Assembles the damping matrix
`assemble_K`()	Assembles the stiffness matrix
`assemble_M`()	Assembles the mass matrix
`check_dof`()	Returns the number of degrees of freedom in the model
`continuous_2_discrete`(A, B, ts)	C2D computes a discrete-time model of a system (A_c,B_c) with sample time ts.
`eigenmodes`()	Solve system eigenmodes
`modal_analysis`([C])	Calculates the eigenvalues and eigenfrequencies of the assembly
`nongearK`()	Assembles the stiffness matrix when gears are not considered
`ss_response`(excitations, omegas[, C])	Calculation of the steady-state torsional response.
`state_matrix`([C])	Assembles the state matrices for eigenvalue calculation
`state_space`([C])	State space matrices of the second order system.
`undamped_modal_analysis`()	Calculates the undamped eigenvalues and eigenvectors of the assembly
`vibratory_torque`(excitations, omegas, k_shafts)	Vibratory torque calculation at one rotating speed.

C_modal(M, K, xi=0.02)

Full damping matrix for mechanical system obtained from modal damping matrix

Parameters:

Mndarray: Assembly mass matrix, included for debugging reasons
Kndarray: Assembly stiffness matrix, included for debugging reasons
xifloat, optional: Modal damping factor, default is 0

Returns:

ndarray: The full damping matrix

E()

Assembles the gear constraint matrix

Returns:

ndarray: The gear constraint matrix

T(E)

Method for determining gear constraint transformation matrix

Parameters:

Endarray: The gear constraint matrix

Returns:

ndarray: The gear constraint transformation matrix

assemble_C()

Assembles the damping matrix

Returns:

ndarray: The damping matrix assembled with component specific damping coefficients

assemble_K()

Assembles the stiffness matrix

Returns:

ndarray: The stiffness matrix

assemble_M()

Assembles the mass matrix

Returns:

ndarray: The mass matrix

check_dof()

Returns the number of degrees of freedom in the model

Returns:

int: Number of degrees of freedom of the assembly

continuous_2_discrete(A, B, ts)

C2D computes a discrete-time model of a system (A_c,B_c) with sample time ts. The function returns matrices Ad, Bd of the discrete-time system.

Parameters

A: ndarray: Continuous system state matrix A
B: ndarray: Continuous system input matrix B
ts: float: Sample time for the discrete system

Returns:

Ad: ndarray: Discrete system state matrix A
Bd: ndarray: Discrete system input matrix B

eigenmodes()

Solve system eigenmodes

Returns:

complex ndarray: Eigenmode array, columns correspond to modes left to right starting from zero

modal_analysis(C=None)

Calculates the eigenvalues and eigenfrequencies of the assembly

Returns:

ndarray: The undamped eigenfrequencies in rad/s
ndarray: The damped eigenfrequencies in rad/s
ndarray: The damping ratios

nongearK(): Assembles the stiffness matrix when gears are not considered

ss_response(excitations, omegas, C=None)

Calculation of the steady-state torsional response.

Parameters:

excitations: complex ndarray: A numpy array containing the excitationse each row corresponds to one node, and each column corresponds to one frequency.
omegas: ndarray: Angular frequencies of the excitations
C: ndarray, optional: Damping matrix, if not given, uses the default damping matrix

Returns:

complex ndarray: Displacement response
complex ndarray: Speed response

state_matrix(C=None)

Assembles the state matrices for eigenvalue calculation

Parameters:

Cndarray, optional: Damping matrix

Returns:

ndarray: The state matrix
ndarray: The input matrix

state_space(C=None)

State space matrices of the second order system.

Parameters:

C: ndarray, optional: Damping matrix, if not given, uses the default damping matrix

Returns:

A_sys: ndarray: State matrix A
B_sys: ndarray: Input matrix B

undamped_modal_analysis()

Calculates the undamped eigenvalues and eigenvectors of the assembly

Returns:

complex ndarray: The eigenvalues of the undamped assembly
complex ndarray: The eigenvectors of the undamped assembly

vibratory_torque(excitations, omegas, k_shafts, C=None)

Vibratory torque calculation at one rotating speed.

Parameters:

excitations: complex ndarray: A numpy array containing the excitationse each row corresponds to one node, and each column corresponds to one frequency.
omegas: ndarray: Angular frequencies of the excitations
k_shafts: ndarray: Stiffness values of the shafts
C: ndarray, optional: Damping matrix, if not given, uses the default damping matrix

Returns:

ndarray: Vibratory torque at each shaft resulting from each excitation

Shaft element

class opentorsion.elements.shaft_element.Shaft(nl, nr, L=None, odl=None, idl=0, G=80000000000.0, E=200000000000.0, rho=8000, k=None, I=0.0, c=0.0)

Bases: object

A 2-degree of freedom shaft object A shaft with a constant circular cross-section can be defined using length and diameter values. Other types of shafts are defined using stiffness and moment of inertia values. Giving either the stiffness or inertia value overrides the given geometry.

Methods

`C`()	Damping matrix of a shaft element
`K`()	Stiffness matrix of a shaft element
`M`()	Mass matrix of a shaft element

C(): Damping matrix of a shaft element

K(): Stiffness matrix of a shaft element

M(): Mass matrix of a shaft element

Disk element

class opentorsion.elements.disk_element.Disk(node, I, c=0, k=0)

Bases: object

A disk object

Methods

`C`()	Damping matrix of a disk element
`K`()	Stiffness matrix of a disk element
`M`()	Mass Matrix of 1 DOF disk element

C()

Damping matrix of a disk element

Returns:

C: ndarray: Damping matrix of disk element

K()

Stiffness matrix of a disk element

Returns:

K: ndarray: Stiffness matrix of the disk element

M()

Mass Matrix of 1 DOF disk element

Returns:

M: ndarray: Mass matrix of the disk element

Gear element

class opentorsion.elements.gear_element.Gear(node, I, R, parent=None)

Bases: object

A gear object Gears consist of two parts, parent gear and child gear. One gear can have multiple children, but only one parent. Either radius or teeth count can be used, as long as the the use is constant.

Methods

`C`()	Damping matrix of a gear element.
`K`()	Stiffness matrix of a gear element.
`M`()	Mass Matrix of 1 DOF gear element.

C()

Damping matrix of a gear element. Gears are assumed to have no damping.

Returns:

M: ndarray: Mass matrix of the gear element

K()

Stiffness matrix of a gear element. Gears are assumed to be rigid.

Returns:

M: ndarray: Mass matrix of the gear element

M()

Mass Matrix of 1 DOF gear element.

Returns:

M: ndarray: Mass matrix of the gear element

Excitation models

class opentorsion.excitation.SystemExcitation(dofs, omegas, shape=None, harmonic=True, transient=False)

Bases: object

This class is for building system excitation matrices.

Attributes:

dofsint: Number of degrees of freedom of the system
omegasndarray: Array of excitation frequencies
Undarray: Array of excitation amplitudes

Methods

`add_harmonic`(node, amplitudes)	Adds a harmonic excitaiton based on the omegas and amplitudes of the excitation this method should extensively check if all of the excitations have same size of omegas
`add_sweep`(node, amplitude)	Adds a sweep excitation with the given uniform amplitude to the given node
`excitation_amplitudes`()	Excitation amplitudes for steady-state and vibratory torque analysis
`excitation_frequencies`(interval)	Excitation frequencies for steady-state and vibratory torque analysis
`time_domain_excitation`(nodes, data)	Excitation matrix for transient analysis.

add_harmonic(node, amplitudes)

Adds a harmonic excitaiton based on the omegas and amplitudes of the excitation this method should extensively check if all of the excitations have same size of omegas

Parameters:

nodeint: Node number where excitation is inputted
amplitudesndarray: Harmonic excitation amplitudes

add_sweep(node, amplitude)

Adds a sweep excitation with the given uniform amplitude to the given node

Parameters:

nodeint: Node number where excitation is inputted
amplitudendarray: Harmonic excitation amplitudes

excitation_amplitudes()

Excitation amplitudes for steady-state and vibratory torque analysis

Returns:

ndarray: The excitation amplitude matrix

excitation_frequencies(interval)

Excitation frequencies for steady-state and vibratory torque analysis

Parameters:

intervallist: Lowest and highest excitation frequency values

Returns:

ndarray: Excitation frequencies evenly spaced over the specified interval

time_domain_excitation(nodes, data)

Excitation matrix for transient analysis. The function takes as input the node numbers where excitation data is inputted and the time domain excitation data. The excitation data must be listed in the same order as the listed nodes. The excitation data arrays must be of equal length.

Parameters:

nodes: list, int: List of nodes where excitation data is inputted
data: list, ndarray: Excitation amplitudes as a list of (1 x n) shaped numpy arrays

Returns:

ndarray: Excitation matrix in time domain, containing excitation amplitudes for each time step

class opentorsion.excitation.TransientExcitations(ts, t_excite, magnitude)

Bases: object

This class is for creating transient excitations. The excitations currently availible are step and impulse.

Attributes:

tsfloat: Time step size
t_excitefloat: Time instance for applying the excitation
magnitudefloat: Excitation magnitude

Methods

`impulse_next`(t)	Calculates the next impulse excitation.
`step_next`(t)	Calculates the next step excitation.

impulse_next(t)

Calculates the next impulse excitation.

Parameters:

tfloat: Current time step

Returns:

float: Torque magnitude of the next excitation

step_next(t)

Calculates the next step excitation.

Parameters:

tfloat: Current time step

Returns:

float: Torque magnitude of the next step excitation

Plots

class opentorsion.plots.Plots(assembly)

Bases: object

This class includes plotting functions

Attributes:

assemblyopenTorsion Assembly class instance

Methods

`plot_assembly`()	Plots the given assembly as disk and spring elements
`plot_campbell`([frequency_range_rpm, ...])	Plots the Campbell diagram
`plot_eigenmodes`([modes])	Updated eigenmode plot.
`plot_on_ax`(assembly, ax[, alpha])	Plots disk and spring elements
`torque_response_plot`(omegas, T[, show_plot])	Plots forced response amplitude as a function of rotational speed.

plot_assembly(): Plots the given assembly as disk and spring elements

plot_campbell(frequency_range_rpm=[0, 1000], num_modes=5, harmonics=[1, 2, 3, 4], operating_speeds_rpm=[])

Plots the Campbell diagram

Parameters:

frequency_rangelist, optional: Analysis frequency range, default is 0 to 100 Hz
num_modesint, optional: Number of modes to be plotted
harmonicslist, optional: List containing the harmonic multipliers

plot_eigenmodes(modes=5)

Updated eigenmode plot. Geared systems not supported. The eigenvectors are plotted over the assembly schematic, and the trajectories are plotted with dashed lines. Each plotted eigenvector is rotated so that the node with maximum abs displacement has phase of 0

Parameters:

modesint: Number of eigenodes to be plotted

plot_on_ax(assembly, ax, alpha=1): Plots disk and spring elements

torque_response_plot(omegas, T, show_plot=False): Plots forced response amplitude as a function of rotational speed.