ross.Mesh

ross.Mesh#

class ross.Mesh(driving_gear, driven_gear, gear_mesh_stiffness=None, square_varying_stiffness={'amplitude_ratio': 0, 'enable': False}, backlash={'enable': False, 'error_amp': 0.0, 'initial_value': 0.0, 'sigma': 10000.0, 'smooth_operator': False}, damping_ratio=0.07, orientation_angle=0)#

A class representing the meshing behavior between two gears in contact, including stiffness and contact ratio calculations.

Parameters:

driving_gearGearElement

The driving gear object used in the gear pair.

driven_gearGearElement

The driven gear object used in the gear pair.

gear_mesh_stiffnessfloat, optional

Directly specify the stiffness of the gear mesh. If not provided, it can be calculated automatically when using GearElementTVMS instead of GearElement. Default is None.

square_varying_stiffnessdict, optional

Dictionary to enable and configure a square-shaped time-varying mesh stiffness. Keys are:

enablebool
If True, a square-shaped time-varying mesh stiffness is used. Default is False.
amplitude_ratiofloat
Ratio of the stiffness amplitude based on the mean value of the mesh stiffness.

Default is {“enable”: False, “amplitude_ratio”: 0}.

backlashdict, optional

Dictionary to enable and configure the backlash model between the coupled gears. Keys are:

enablebool
If True, the backlash model is used. Default is False.
initial_valuefloat
Initial backlash of the gear pair (m). Default is 0.0.
error_ampfloat
Error amplitude used in the backlash force model. Default is 0.0.
smooth_operatorbool
If True, a smooth (hyperbolic tangent) approximation is used for the backlash force. Default is False.
sigmafloat
Parameter related to the regularization of the smooth approach. Default is 1e4.

Default is {“enable”: False, “initial_value”: 0.0, “error_amp”: 0.0, “smooth_operator”: False, “sigma”: 1e4}.

damping_ratiofloat, optional

Damping ratio used to compute the mesh damping when the backlash model is enabled. Default is 0.07.

orientation_anglefloat, pint.Quantity, optional

The angle between the line of gear centers and x-axis. Default is 0.0 rad.

Attributes:

driving_gearGearElement: The driving_gear object, which contains information about the geometry and properties of the driving gear.
driven_gearGearElement: The driven gear object, which contains information about the geometry and properties of the wheel gear.
gear_ratiofloat: The transmission ratio, defined as the ratio of the number of teeth between the driving and driven gears.
pressure_anglefloat: The pressure angle of the gear mesh (rad).
contact_ratiofloat: The contact ratio of the gear pair.
stiffnessfloat: The (constant or mean) mesh stiffness of the gear pair (N/m).
backlashBacklash or None: The backlash model of the gear pair, if enabled. None otherwise.

Examples

>>> from ross.materials import steel
>>> driving = GearElementTVMS(
...    n=0,
...    material=steel,
...    width=0.02,
...    bore_diameter=0.0175 * 2,
...    module=0.002,
...    n_teeth=62,
...    pr_angle=0.349066
... )
>>> driven = GearElementTVMS(
...    n=2,
...    material=steel,
...    width=0.02,
...    bore_diameter=0.0175 * 2,
...    module=0.002,
...    n_teeth=62,
...    pr_angle=0.349066
... )
>>> mesh = Mesh(driving, driven)
>>> mesh.stiffness
419603831.338...

Methods

__init__(driving_gear, driven_gear, gear_mesh_stiffness=None, square_varying_stiffness={'amplitude_ratio': 0, 'enable': False}, backlash={'enable': False, 'error_amp': 0.0, 'initial_value': 0.0, 'sigma': 10000.0, 'smooth_operator': False}, damping_ratio=0.07, orientation_angle=0)#

compute_contact_ratio()#

Calculate the contact ratio of the gear pair.

Returns:

contact_ratiofloat: The calculated contact ratio.

generate_stiffness_table(stiffness_type=None, n_points=200)#

Generate a table of stiffness values for a gear pair.

Parameters:

stiffness_typestr, optional: Type of stiffness to compute. Available options are: - “square”: square varying stiffness - “equivalent”: variable equivalent stiffness Default is None, which uses the stiffness type defined in the Mesh object.
n_pointsint, optional: Number of data points to evaluate for the stiffness profile. Default is 200.

Returns:

theta_rangenp.ndarray: Array of angular positions (rad).
contact_ratio_rangenp.ndarray: Array of contact ratios.
stiffness_tablenp.ndarray: Array of stiffness values corresponding to each angular position and contact ratio.

get_square_varying_stiffness(theta_range, contact_ratio)#

Calculate the square varying stiffness of a gear pair.

Parameters:

theta_rangearray-like: Angular positions at which to calculate the stiffness (rad).
contact_ratiofloat: The contact ratio of the gear pair.

Returns:

stiffness_rangearray-like: Stiffness values at the given angular positions (N/m).

get_stiffness_for_mesh_period(stiffness_type='constant', n_mesh_period=1, n_points=1000)#

Compute the mesh stiffness profile over a specified number of gear mesh periods.

Parameters:

stiffness_typestr, optional: Type of stiffness to compute. Available options are: - “square”: square varying stiffness - “equivalent”: variable equivalent stiffness otherwise, a constant stiffness is used.
n_mesh_periodint, optional: Number of mesh periods to evaluate. Default is 1.
n_pointsint, optional: Number of angular sample points to compute within the total range. Default is 1000.

Returns:

theta_rangenp.ndarray: Array of angular positions (rad) spanning the specified mesh periods.
stiffness_rangelist of float: List of stiffness values corresponding to each angular position.

get_variable_equivalent_stiffness(angular_position, contact_ratio)#

Calculate the variable equivalent stiffness of a gear pair.

This method computes the equivalent stiffness of a gear mesh at a given angular position, taking into account the periodic nature of the meshing process and the contact ratio of the gear pair. It is assumed constant rotor speed.

Parameters:

angular_positionfloat: Gear angular position for which the meshing stiffness is calculated (rad).
contact_ratiofloat: The contact ratio of the gear pair.

Returns:

stiffnessfloat: The total equivalent meshing stiffness at the given angular position.

interpolate_stiffness(angular_position)#

Interpolate the mesh stiffness value at a given angular position.

Parameters:

angular_positionfloat or array-like: Angular position(s) at which to evaluate the stiffness (rad).

Returns:

stiffnessfloat or np.ndarray: Interpolated stiffness value(s) in N/m.

plot_stiffness_profile(n_mesh_period=1, n_points=1000, angle_units='rad', stiffness_units='N/m', stiffness_type=None, **kwargs)#

Plot the gear mesh stiffness profile over one or more meshing periods.

Parameters:

n_mesh_periodint, optional: Number of mesh periods to plot. Default is 1.
n_pointsint, optional: Number of data points to evaluate for the stiffness profile. Default is 1000.
angle_unitsstr, optional: Units for the angular position axis. Default is ‘rad’.
stiffness_unitsstr, optional: Units for the stiffness axis. Default is ‘N/m’.
stiffness_typestr, optional: Type of stiffness to compute. Available options are: - “constant”: constant stiffness - “square”: square varying stiffness - “equivalent”: variable equivalent stiffness Default is None, which uses the stiffness type defined in the Mesh object.
**kwargsdict, optional: Additional keyword arguments passed to plotly.graph_objects.Figure.update_layout for customizing the figure (e.g., title, font, size, legend settings, etc.).

Returns:

figgo.Figure: Figure object.

ross.Mesh

Contents

ross.Mesh#