add_worm_gear_mating¶

add_worm_gear_mating(master: WormGear | WormWheel, slave: WormGear | WormWheel, friction_coefficient: float | int) → None¶

It creates a gear mating between a worm gear and a worm wheel. This mating is used to compose the Powertrain.

The master gear is closest to the motor and transfers a fraction of the driving torque to the slave one, based on the mating efficiency, which depends on the friction_coefficient: the higher the friction_coefficient, the lower the fraction of transferred driving torque.

Parameters¶

masterWormGear or WormWheel: Driving gear. It must be an instance of WormGear or WormWheel, but different from slave.
slaveWormGear or WormWheel: Driven gear. It must be an instance of WormGear or WormWheel, but different from master.
friction_coefficientfloat or int: Static friction coefficient of the gear mating. It must be a float or an int between 0 and 1.

Raises

TypeError

If master is not an instance of WormGear or WormWheel,
if slave is not an instance of WormGear or WormWheel,
if both master and slave are instances of WormGear,
if both master and slave are instances of WormWheel,
if friction_coefficient is not a float or an int.

ValueError

If friction_coefficient is not within 0 and 1,
if master and slave have different values for pressure_angle (see WormGear.pressure_angle or WormWheel.pressure_angle)

Notes

The gear ratio of the mating can be computed with the following relationship, regardless of master or slave roles:

\[\tau = \frac{n_z}{n_s}\]

where:

\(\tau\) is the gear ratio, the ratio between the worm gear angular speed and the worm wheel angular speed,
\(n_z\) is the worm wheel number of teeth,
\(n_s\) is the worm gear number of starts.

If the WormGear is the master and the WormWheel is the slave, then the gear mating efficiency can be computed with the relationship:

\[\eta = \frac{\cos \alpha - f \, \tan \beta}{\cos \alpha + \frac{f}{\tan \beta}}\]

otherwise, if the WormGear is the slave and the WormWheel is the master, then the gear mating efficiency can be computed with the relationship:

\[\eta = \frac{\cos \alpha - \frac{f}{\tan \beta}}{\cos \alpha + f \, \tan \beta}\]

where:

\(\eta\) is the gear mating efficiency,
\(\alpha\) is the gear pressure angle, equal for both worm gear and worm wheel (WormGear.pressure_angle or WormWheel.pressure_angle),
\(f\) is the friction_coefficient,
\(\beta\) is the gear helix angle (WormGear.helix_angle or WormWheel.helix_angle).

The mating self-locking condition can be checked as:

\[f > \cos \alpha \, \tan \beta\]