3 - Gear Structural Analysis

System in Analysis

The complete example code is available here.
The mechanical powertrain to be studied is the one described in the 2 - Complex External Torque example.
The teeth of all gears must be verified for static bending and contact stress with a safety factor 1.5.

Model Set Up

We want to deep dive the analysis on gears structural strength. In order to take into account these computation, we have to edit the gear definitions, to include some required data:

from gearpy.units import Length, Stress

gear_1 = SpurGear(name = 'gear 1',
                  n_teeth = 10,
                  inertia_moment = InertiaMoment(1, 'gcm^2'),
                  module = Length(1, 'mm'),
                  face_width = Length(10, 'mm'),
                  elastic_modulus = Stress(200, 'GPa'))
gear_2 = SpurGear(name = 'gear 2',
                  n_teeth = 80,
                  inertia_moment = InertiaMoment(3100, 'gcm^2'),
                  module = Length(1, 'mm'),
                  face_width = Length(10, 'mm'),
                  elastic_modulus = Stress(200, 'GPa'))
gear_3 = SpurGear(name = 'gear 3',
                  n_teeth = 10,
                  inertia_moment = InertiaMoment(4, 'gcm^2'),
                  module = Length(1.5, 'mm'),
                  face_width = Length(10, 'mm'),
                  elastic_modulus = Stress(200, 'GPa'))
gear_4 = SpurGear(name = 'gear 4',
                  n_teeth = 60,
                  inertia_moment = InertiaMoment(5000, 'gcm^2'),
                  module = Length(1.5, 'mm'),
                  face_width = Length(10, 'mm'),
                  elastic_modulus = Stress(200, 'GPa'))
gear_5 = SpurGear(name = 'gear 5',
                  n_teeth = 10,
                  inertia_moment = InertiaMoment(12, 'gcm^2'),
                  module = Length(2, 'mm'),
                  face_width = Length(10, 'mm'),
                  elastic_modulus = Stress(200, 'GPa'))
gear_6 = SpurGear(name = 'gear 6',
                  n_teeth = 50,
                  inertia_moment = InertiaMoment(7600, 'gcm^2'),
                  module = Length(2, 'mm'),
                  face_width = Length(10, 'mm'),
                  elastic_modulus = Stress(200, 'GPa'))

See SpurGear for more details on instantiation parameters.
Structural analysis is also available for HelicalGear and WormWheel (bending stress only).
All gears are made in steel, which yield stress is 250 MPa.
The remaining set up of the model stay the same.

Results Analysis

We can get a snapshot of the system at a particular time of interest:

powertrain.snapshot(target_time = Time(10, 'sec'),
                    torque_unit = 'mNm',
                    driving_torque_unit = 'mNm',
                    load_torque_unit = 'mNm')

Mechanical Powertrain Status at Time = 10 sec
          angular position (rad)  angular speed (rad/s)  angular acceleration (rad/s^2)  torque (mNm)  driving torque (mNm)  load torque (mNm) tangential force (N) bending stress (MPa) contact stress (MPa)  pwm
motor               11510.286813            1375.840709                        5.011918      0.058805              1.241126           1.182321                                                                 1.0
flywheel            11510.286813            1375.840709                        5.011918      0.058805              1.241126           1.182321
gear 1              11510.286813            1375.840709                        5.011918      0.058805              1.241126           1.182321             0.236464             0.117644            15.128545
gear 2               1438.785852             171.980089                        0.626490      0.423395              8.936107           8.512712             0.223403             0.051239            14.704783
gear 3               1438.785852             171.980089                        0.626490      0.423395              8.936107           8.512712             1.135028              0.37646            27.559369
gear 4                239.797642              28.663348                        0.104415      2.286335             48.254979          45.968644             1.072333             0.169807            26.787411
gear 5                239.797642              28.663348                        0.104415      2.286335             48.254979          45.968644             4.596864             1.143499            48.712974
gear 6                 47.959528               5.732670                        0.020883     10.288508            217.147407         206.858899             4.342948             0.532224            47.348488

We can get a more general view of the system by plotting the time variables and focus the plot only on interesting elements and variables. We can also specify a more convenient unit to use when plotting torques:

powertrain.plot(figsize = (10, 10),
                elements = [gear_1, gear_2, gear_3, gear_4, gear_5, gear_6],
                angular_position_unit = 'rot',
                torque_unit = 'mNm',
                variables = ['driving torque', 'load torque', 'torque', 'tangential force', 'bending stress',
                             'contact stress'])

We can appreciate how the torques, forces and stresses vary over time, and in particular there is a peak in some variables at the beginning of the simulation.
We can see that the torques, forces and stresses are low in the first gears, and increase in the last gears, so we can draw a more clean plot and focus on the last two gears only:

powertrain.plot(figsize = (8, 8),
                elements = [gear_5, gear_6],
                angular_position_unit = 'rot',
                torque_unit = 'mNm',
                variables = ['driving torque', 'load torque', 'torque', 'tangential force', 'bending stress',
                             'contact stress'])

The maximum contact stress is about 135 MPa on the gear 6 resulting in a safety factor about 1.85, higher than the target 1.5. The bending stresses are even lower on all gears.
We can consider these gears correctly designed for the considered application.