From a03bd47566a0603327e2eee901d6db99c766f31d Mon Sep 17 00:00:00 2001 From: Andrea Blengino Date: Sat, 18 Nov 2023 14:19:32 +0100 Subject: [PATCH] DOC: add second usage example in documentation --- docs/source/examples/index.rst | 3 +- .../examples/structural_analysis/README.md | 260 ++++++++++++++++++ .../structural_analysis/images/plot_1.png | Bin 0 -> 240214 bytes .../structural_analysis/images/plot_2.png | Bin 0 -> 130237 bytes .../structural_analysis/images/plot_3.png | Bin 0 -> 124453 bytes .../structural_analysis/images/scheme.png | Bin 0 -> 8070 bytes .../examples/structural_analysis/index.rst | 11 + .../structural_analysis.py | 160 +++++++++++ 8 files changed, 433 insertions(+), 1 deletion(-) create mode 100644 docs/source/examples/structural_analysis/README.md create mode 100644 docs/source/examples/structural_analysis/images/plot_1.png create mode 100644 docs/source/examples/structural_analysis/images/plot_2.png create mode 100644 docs/source/examples/structural_analysis/images/plot_3.png create mode 100644 docs/source/examples/structural_analysis/images/scheme.png create mode 100644 docs/source/examples/structural_analysis/index.rst create mode 100644 docs/source/examples/structural_analysis/structural_analysis.py diff --git a/docs/source/examples/index.rst b/docs/source/examples/index.rst index 58562af..45d7b0c 100644 --- a/docs/source/examples/index.rst +++ b/docs/source/examples/index.rst @@ -4,4 +4,5 @@ Usage Examples .. toctree:: - example_1/index + simple_transmission_chain/index + structural_analysis/index diff --git a/docs/source/examples/structural_analysis/README.md b/docs/source/examples/structural_analysis/README.md new file mode 100644 index 0000000..2ff2d97 --- /dev/null +++ b/docs/source/examples/structural_analysis/README.md @@ -0,0 +1,260 @@ +### System in Analysis + +The mechanical transmission to be studied is reported in the image below: + +![](images/scheme.png) + +A *flywheel* and the *gear 1* are connected to the *DC motor* output +shaft and rotate with it. The *gear 2* mates with *gear 1* and is +connected to *gear 3* through a rigid shaft, so *gear 2* and *gear 3* +rotate together. The *gear 3* mates with *gear 4*, to which is connected +to the external load. +The first step is the analysis of transmission elements kinematics and +torques, then the focus is set to structural strength of the gear teeth. +The teeth of all gears must be verified for static bending and contact +stress with a safety factor 1.5. + + +### Model Set Up + +As a first step, we instantiate the components of the mechanical +transmission: + +```python +from gearpy.mechanical_object import DCMotor, SpurGear, Flywheel +from gearpy.units import AngularSpeed, InertiaMoment, Length, Torque, Stress + +motor = DCMotor(name = 'motor', + no_load_speed = AngularSpeed(2000, 'rpm'), + maximum_torque = Torque(200, 'mNm'), + inertia_moment = InertiaMoment(5, 'gm^2')) +flywheel = Flywheel(name = 'flywheel', + inertia_moment = InertiaMoment(30, 'gm^2')) +gear_1 = SpurGear(name = 'gear 1', + n_teeth = 10, + inertia_moment = InertiaMoment(10, 'gm^2'), + module = Length(1, 'mm'), + face_width = Length(5, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_2 = SpurGear(name = 'gear 2', + n_teeth = 80, + inertia_moment = InertiaMoment(80, 'gm^2'), + module = Length(1, 'mm'), + face_width = Length(5, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_3 = SpurGear(name = 'gear 3', + n_teeth = 10, + inertia_moment = InertiaMoment(10, 'gm^2'), + module = Length(1, 'mm'), + face_width = Length(5, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_4 = SpurGear(name = 'gear 4', + n_teeth = 60, + inertia_moment = InertiaMoment(60, 'gm^2'), + module = Length(1, 'mm'), + face_width = Length(5, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +``` + +All gears are assumed to be equal, with 1 mm module, 5 mm face width, +made in steel. The steel yield stress is 250 MPa. +Then it is necessary to specify the types of connection between the +components. We choose to study a non-ideal transmission so, in order to +take into account power loss in matings due to friction, we specify a +gear mating efficiency below `$100\%$`: + +```python +from gearpy.utils import add_gear_mating, add_fixed_joint + +add_fixed_joint(master = motor, slave = flywheel) +add_fixed_joint(master = flywheel, slave = gear_1) +add_gear_mating(master = gear_1, slave = gear_2, efficiency = 0.9) +add_fixed_joint(master = gear_2, slave = gear_3) +add_gear_mating(master = gear_3, slave = gear_4, efficiency = 0.9) +``` + +We have to define the external load applied to *gear 4*. The torque +taken into account has 6 Nm constant component and a variable component +dependent on the angular position of the last gear: + +```python +def ext_torque(time, angular_position, angular_speed): + return Torque(value = 6 + 0.5*np.sin(2*np.pi/10*angular_position.to('rad').value), + unit = 'Nm') + +gear_4.external_torque = ext_torque + ``` + +Finally, it is necessary to combine all components in a transmission +object: + +```python +from gearpy.transmission import Transmission + +transmission = Transmission(motor = motor) +``` + +### Simulation Set Up + +Before performing the simulation, it is necessary to specify the initial +condition of the system in terms of angular position and speed of the +last gear in the mechanical transmission. In this case we can consider +the *gear 4* stop in the reference position: + +```python +from gearpy.units import AngularPosition + +gear_4.angular_position = AngularPosition(0, 'rad') +gear_4.angular_speed = AngularSpeed(0, 'rad/s') +``` + +Finally, we have to set up the simulation parameters: the time +discretization for the time integration and the simulation time. Now we +are ready to run the simulation:: + +```python +from gearpy.units import TimeInterval +from gearpy.solver import Solver + +solver = Solver(time_discretization = TimeInterval(0.1, 'sec'), + simulation_time = TimeInterval(100, 'sec'), + transmission = transmission) +solver.run() +``` + +### Results Analysis + +We can get a snapshot of the system at a particular time of interest: + +```python +from gearpy.units import Time + +transmission.snapshot(target_time = Time(50, 'sec')) +``` + +```text +Mechanical Transmission Status at Time = 50 sec + angular position (rad) angular speed (rad/s) angular acceleration (rad/s^2) torque (Nm) driving torque (Nm) load torque (Nm) tangential force (N) bending stress (MPa) contact stress (MPa) +motor 2221.559697 48.412745 5.886017 0.036284 0.153769 0.117485 NaN NaN NaN +flywheel 2221.559697 48.412745 5.886017 0.036284 0.153769 0.117485 NaN NaN NaN +gear 1 2221.559697 48.412745 5.886017 0.036284 0.153769 0.117485 23.497094 23.380193 218.540109 +gear 2 277.694962 6.051593 0.735752 0.167255 1.107138 0.939884 27.678462 12.696542 237.189281 +gear 3 277.694962 6.051593 0.735752 0.167255 1.107138 0.939884 187.97675 187.041543 629.467458 +gear 4 46.384583 1.02089 0.122915 0.339245 5.978548 5.639303 199.284927 94.672174 648.124502 +``` + +We can get a more general view of the system by plotting the time +variables of each element with respect to time: + +```python +transmission.plot(figsize = (10, 12)) +``` + +![](images/plot_1.png) + +After few seconds from the simulation start, the driving torque +applied on *gear 4* is almost equal to the load torque on it. After +about 10 seconds the transient is finished and the system is in a +stationary regime, where the periodicity of the external load is clearly +visible. +The kinematics of the transmission is clear, but gears stresses deserve +more attention, so we can generate a plot focused on structural time +variables of the gears: + +```python +transmission.plot(elements = ['gear 1', 'gear 2', 'gear 3', 'gear 4'], + variables = ['angular position', 'torque', 'driving torque', 'load torque', + 'tangential force', 'bending stress', 'contact stress'], + angular_position_unit = 'rot', + figsize = (8, 6)) +``` + +![](images/plot_2.png) + +The computed stresses on gears teeth are to high, in particular the +contact stress, even higher than the steel yield stress, so we have to +improve the strength of the teeth by increasing the module and face +width. As a consequence of the increased module and face width, the gear +size will be higher, so the inertia moment increases too. + + +### Improved Model Set Up + +The transmission elements are updated as follows: + +```python +motor = DCMotor(name = 'motor', + no_load_speed = AngularSpeed(2000, 'rpm'), + maximum_torque = Torque(200, 'mNm'), + inertia_moment = InertiaMoment(5, 'gm^2')) +flywheel = Flywheel(name = 'flywheel', + inertia_moment = InertiaMoment(30, 'gm^2')) +gear_1 = SpurGear(name = 'gear 1', + n_teeth = 10, + inertia_moment = InertiaMoment(10, 'gm^2'), + module = Length(1.25, 'mm'), + face_width = Length(10, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_2 = SpurGear(name = 'gear 2', + n_teeth = 80, + inertia_moment = InertiaMoment(80, 'gm^2'), + module = Length(1.25, 'mm'), + face_width = Length(10, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_3 = SpurGear(name = 'gear 3', + n_teeth = 10, + inertia_moment = InertiaMoment(40, 'gm^2'), + module = Length(2.5, 'mm'), + face_width = Length(20, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_4 = SpurGear(name = 'gear 4', + n_teeth = 60, + inertia_moment = InertiaMoment(240, 'gm^2'), + module = Length(2.5, 'mm'), + face_width = Length(20, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +``` + +Note that *gear 1* and *gear 2* must have the same value of module to +make the mating possible, as well as *gear 3* and *gear 4*. +The other parameters of the simulation remain the same as before. + + +### Improved Model Result Analysis + +We can get a snapshot at the same time of interest as before: + +```python +transmission.snapshot(target_time = Time(50, 'sec')) +``` + +```text +Mechanical Transmission Status at Time = 50 sec + angular position (rad) angular speed (rad/s) angular acceleration (rad/s^2) torque (Nm) driving torque (Nm) load torque (Nm) tangential force (N) bending stress (MPa) contact stress (MPa) +motor 2217.156919 47.314348 5.4848 0.036905 0.154818 0.117913 NaN NaN NaN +flywheel 2217.156919 47.314348 5.4848 0.036905 0.154818 0.117913 NaN NaN NaN +gear 1 2217.156919 47.314348 5.4848 0.036905 0.154818 0.117913 18.866154 7.508917 123.849929 +gear 2 277.144615 5.914293 0.6856 0.171383 1.114691 0.943308 22.29381 4.090607 134.631358 +gear 3 277.144615 5.914293 0.6856 0.171383 1.114691 0.943308 75.464616 7.508917 126.122595 +gear 4 46.290493 0.997237 0.115219 0.359483 6.019329 5.659846 80.257717 3.812718 130.066249 +``` + +We can also get the same plot as before, in order to make a complete +comparison: + +```python +transmission.plot(elements = ['gear 1', 'gear 2', 'gear 3', 'gear 4'], + variables = ['angular position', 'torque', 'driving torque', 'load torque', + 'tangential force', 'bending stress', 'contact stress'], + angular_position_unit = 'rot', + figsize = (8, 6)) +``` + +![](images/plot_3.png) + +As desired, all stresses are decreased, the maximum contact stress is +about 153 MPa on the *gear 2* resulting in a safety factor about 1.63, +higher than the target 1.5. 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F@*jPlaEkx{ literal 0 HcmV?d00001 diff --git a/docs/source/examples/structural_analysis/index.rst b/docs/source/examples/structural_analysis/index.rst new file mode 100644 index 0000000..aafaac0 --- /dev/null +++ b/docs/source/examples/structural_analysis/index.rst @@ -0,0 +1,11 @@ +Structural Analysis +=================== + + +.. mdinclude:: README.md + + +.. toctree:: + :hidden: + + README diff --git a/docs/source/examples/structural_analysis/structural_analysis.py b/docs/source/examples/structural_analysis/structural_analysis.py new file mode 100644 index 0000000..6713526 --- /dev/null +++ b/docs/source/examples/structural_analysis/structural_analysis.py @@ -0,0 +1,160 @@ +# Import required packages, classes and functions + +from gearpy.mechanical_object import DCMotor, SpurGear, Flywheel +from gearpy.units import AngularSpeed, InertiaMoment, Length, Torque, AngularPosition, TimeInterval, Time, Stress +from gearpy.utils import add_gear_mating, add_fixed_joint +from gearpy.transmission import Transmission +from gearpy.solver import Solver +import numpy as np + + +# Model Set Up + +motor = DCMotor(name = 'motor', + no_load_speed = AngularSpeed(2000, 'rpm'), + maximum_torque = Torque(200, 'mNm'), + inertia_moment = InertiaMoment(5, 'gm^2')) +flywheel = Flywheel(name = 'flywheel', + inertia_moment = InertiaMoment(30, 'gm^2')) +gear_1 = SpurGear(name = 'gear 1', + n_teeth = 10, + inertia_moment = InertiaMoment(10, 'gm^2'), + module = Length(1, 'mm'), + face_width = Length(5, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_2 = SpurGear(name = 'gear 2', + n_teeth = 80, + inertia_moment = InertiaMoment(80, 'gm^2'), + module = Length(1, 'mm'), + face_width = Length(5, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_3 = SpurGear(name = 'gear 3', + n_teeth = 10, + inertia_moment = InertiaMoment(10, 'gm^2'), + module = Length(1, 'mm'), + face_width = Length(5, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_4 = SpurGear(name = 'gear 4', + n_teeth = 60, + inertia_moment = InertiaMoment(60, 'gm^2'), + module = Length(1, 'mm'), + face_width = Length(5, 'mm'), + elastic_modulus = Stress(210, 'GPa')) + + +add_fixed_joint(master = motor, slave = flywheel) +add_fixed_joint(master = flywheel, slave = gear_1) +add_gear_mating(master = gear_1, slave = gear_2, efficiency = 0.9) +add_fixed_joint(master = gear_2, slave = gear_3) +add_gear_mating(master = gear_3, slave = gear_4, efficiency = 0.9) + + +def ext_torque(time, angular_position, angular_speed): + return Torque(value = 6 + 0.5*np.sin(2*np.pi/10*angular_position.to('rad').value), + unit = 'Nm') + +gear_4.external_torque = ext_torque + + +transmission = Transmission(motor = motor) + + +# Simulation Set Up + +gear_4.angular_position = AngularPosition(0, 'rad') +gear_4.angular_speed = AngularSpeed(0, 'rad/s') + + +solver = Solver(time_discretization = TimeInterval(0.1, 'sec'), + simulation_time = TimeInterval(100, 'sec'), + transmission = transmission) +solver.run() + + +# Result Analysis + +transmission.snapshot(target_time = Time(50, 'sec')) + + +transmission.plot(figsize = (10, 12)) + +transmission.plot(elements = ['gear 1', 'gear 2', 'gear 3', 'gear 4'], + variables = ['angular position', 'torque', 'driving torque', 'load torque', + 'tangential force', 'bending stress', 'contact stress'], + angular_position_unit = 'rot', + figsize = (8, 6)) + + +# # Improved Model Set Up + +motor = DCMotor(name = 'motor', + no_load_speed = AngularSpeed(2000, 'rpm'), + maximum_torque = Torque(200, 'mNm'), + inertia_moment = InertiaMoment(5, 'gm^2')) +flywheel = Flywheel(name = 'flywheel', + inertia_moment = InertiaMoment(30, 'gm^2')) +gear_1 = SpurGear(name = 'gear 1', + n_teeth = 10, + inertia_moment = InertiaMoment(10, 'gm^2'), + module = Length(1.25, 'mm'), + face_width = Length(10, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_2 = SpurGear(name = 'gear 2', + n_teeth = 80, + inertia_moment = InertiaMoment(80, 'gm^2'), + module = Length(1.25, 'mm'), + face_width = Length(10, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_3 = SpurGear(name = 'gear 3', + n_teeth = 10, + inertia_moment = InertiaMoment(40, 'gm^2'), + module = Length(2.5, 'mm'), + face_width = Length(20, 'mm'), + elastic_modulus = Stress(210, 'GPa')) +gear_4 = SpurGear(name = 'gear 4', + n_teeth = 60, + inertia_moment = InertiaMoment(240, 'gm^2'), + module = Length(2.5, 'mm'), + face_width = Length(20, 'mm'), + elastic_modulus = Stress(210, 'GPa')) + + +add_fixed_joint(master = motor, slave = flywheel) +add_fixed_joint(master = flywheel, slave = gear_1) +add_gear_mating(master = gear_1, slave = gear_2, efficiency = 0.9) +add_fixed_joint(master = gear_2, slave = gear_3) +add_gear_mating(master = gear_3, slave = gear_4, efficiency = 0.9) + + +def ext_torque(time, angular_position, angular_speed): + return Torque(value = 6 + 0.5*np.sin(2*np.pi/10*angular_position.to('rad').value), + unit = 'Nm') + +gear_4.external_torque = ext_torque + + +transmission = Transmission(motor = motor) + + +# Simulation Set Up + +gear_4.angular_position = AngularPosition(0, 'rad') +gear_4.angular_speed = AngularSpeed(0, 'rad/s') + + +solver = Solver(time_discretization = TimeInterval(0.1, 'sec'), + simulation_time = TimeInterval(100, 'sec'), + transmission = transmission) +solver.run() + + +# Improved Model Result Analysis + +transmission.snapshot(target_time = Time(50, 'sec')) + + +transmission.plot(elements = ['gear 1', 'gear 2', 'gear 3', 'gear 4'], + variables = ['angular position', 'torque', 'driving torque', 'load torque', + 'tangential force', 'bending stress', 'contact stress'], + angular_position_unit = 'rot', + figsize = (8, 6))