Degradation Gear In

Gearbox Simulation Model

Simulation of the vibration behaviour of a gearbox under degradation

Preliminary

Load Modules

# Build In
import os
from copy import deepcopy as dc
import sys
from IPython.display import display, HTML
# Third Party
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from scipy.stats import norm
# from gearbox_functions import gearbox_functions as gf
import gearbox_functions as gf

Define Directories

wd = os.getcwd()
hd = r'####' # Gearbox Toolbox directory

Other

from matplotlib import rcParams
rcParams['figure.figsize'] = [7.4803*4, 4.62309*2]
sizefactor = 2
rcParams['ytick.labelsize'] = 8 * sizefactor
rcParams['xtick.labelsize'] = 8 * sizefactor
rcParams['axes.labelweight'] = 8 * sizefactor
rcParams['axes.titleweight'] = 8 * sizefactor
rcParams.update({'font.size': 8 * sizefactor})

Motivation

Gear Wheel Pitting

Degradation dominates at one tooth only

Operating Strategy [Gretzinger2017]

Local Stress reduction

Brief Introduction

Toolbox to simulate gearbox vibration

Virtual copy of an existing testbench

Match on Vibration Spectra
Match on Gear Degradation

No consideration of:

Transmission paths formulation (Structure Borne Acoustics)
Bearing Degradation (not seen in testbench)

State Model

Acts as a state model:

Executes for a given load cycle (must be greater than the previous)

Optional: Setting a new torque signal at the given load cycle (effecting the following load cycles)

Inputs and main Methods()

General Input Arguments:

f_i: Rotational Frequency input shaft - in revolutions per second (float)

t_i: Sample Interval - in seconds (float)

f_s: Sample Rate - in Hz (float)

seed: Random Generator Seed (integer)

Input Arguments vibrations = model.run():

n_lc: Current number of load cycle - in revolutions (float)

Input Arguments model.set():

n_lc: Current number of load cycle - in revolutions (float)

torque: Input Torque - in Nm

Torque Definition

Vibration/Degradation Output is calculated for previous given torque_p-1 argument.

Given Input Torque will be relevant for the next time steps n_lc

Definition:

Must be defined as array

Each value corresponds to a given time

Function 'get_sample_time_torque()' returns the time vector for torque

Length of the torque vector must be at least as long as it takes for running once every possible meshing

Which Torque Applies on which Gear Element

Input Torque applies on:

Vibration Influence of Gear In, Bearing 1 and Bearing 2

Load Spectre Calculation of Gear In, Bearing 1, Bearing 2 and Gear Out

Output Torque applies on:

Vibration Influence of Gear Out, Bearing 3 and Bearing 4

Load Spectre Calculation of Bearing 3 and Bearing 4

Gear Degradation strongly depends on the Gearbox Design → Both Input and Output Gear Degradation are defined for input torque!!!

Toolbox Running Example - Definition

Complete High Level Example. Details and Theory will follow.

Load Gearbox Simulation Toolbox:

# os.chdir()
os.chdir(hd)
from gearbox import Gearbox
os.chdir(wd)

Define General Input Arguments:

rotational_frequency_in = 5.2 # U/s | float
number_of_load_cycle = 0 # | Must be float in .3f
sample_interval = 1 # s | float
sample_rate = 5000 # Hz | float
seed = 4

Define Vibration Elements

GearIn = {'no_teeth': 11,                                         # Number of teeth
          'signal': 'gausspulse',                                 # Signal type for gear
          'ampl_method': 'gaussian_repeat',                       # Amplitude Method for inner gear
          'ampl_attributes': {'mu': 4, 'sigma': 0.5},             # Attributes regarding Amplitude Method for gear signal
          'noise_method': None,                             # Noise Method for inner gear
          'noise_attributes': {'mu': 0, 'sigma': 0.25},           # Attributes regarding Noise Method for gear signal
          'torq_method': None,                                    # Torque Influence Method for inner gear
          'torq_attributes': {'scale_min': 0,                     # Attributes regarding Torque Influence Method for gear signal
                              'scale_max': 0.2,
                               'value_min': 0,
                               'value_max': 50,
                              'norm_divisor': 200,
                              'exponent': 2},           
          }

GearOut = {'no_teeth': 21,                                        # Number of teeth
           'signal': 'gausspulse',                                # Signal type for gear
           'ampl_method': 'gaussian_repeat',                      # Amplitude Method for inner gear
           'ampl_attributes': {'mu': 3, 'sigma': 0.5},            # Attributes regarding Amplitude Method for gear signal
           'noise_method': None,                            # Noise Method for inner gear
           'noise_attributes': {'mu': 0, 'sigma': 0.25},          # Attributes regarding Noise Method for gear signal
           'torq_method': None,                                   # Torque Influence Method for inner gear
           'torq_attributes': {'scale_min': 0,                    # Attributes regarding Torque Influence Method for gear signal
                               'scale_max': 0.2,
                               'value_min': 0,
                               'value_max': 50,
                               'norm_divisor': 1,
                               'exponent': 4},           
          }

# General Definition of Amplitudes etc. (can be also defined separately for each Bearing)
BearingI =   {# Inner Ring Rollover
             'signal_iring': 'sine',                               # Signal type for inner cage
             'ampl_method_iring': 'const',                         # Amplitude Method for inner cage signal (Repeat methods are not working for bearings)
             'ampl_attributes_iring': {'constant': 2.5},           # Attributes regarding Amplitude Method for inner cage signal
             'noise_method_iring': 'gaussian',                     # Noise Method for inner gear
             'noise_attributes_iring': {'mu': 0, 'sigma': 0.05},   # Attributes regarding Noise Method for gear signal
             'torq_method_iring': None,                         # Torque Influence Method for rolling element
             'torq_attributes_iring': {'scale_min': 0,          # Attributes regarding Torque Influence Method for rolling element signal
                                       'scale_max': 0.1,
                                       'value_min': 0,
                                       'value_max': 50,
                                       'norm_divisor': 1,
                                       'exponent': 4},           

             # Rolling Element:
             'signal_relement': 'sine',                            # Signal type for rolling element
             'ampl_method_relement': 'const',                      # Amplitude Method for rolling element signal (Repeat methods are not working for bearings)
             'ampl_attributes_relement': {'constant': 1.2},        # Attributes regarding Amplitude Method for rolling element signal
             'noise_method_relement': 'gaussian',                  # Noise Method for rolling element
             'noise_attributes_relement': {'mu': 0, 'sigma': 0.05},# Attributes regarding Noise Method for gear signal
             'torq_method_relement': None,                         # Torque Influence Method for rolling element
             'torq_attributes_relement': {'scale_min': 0,          # Attributes regarding Torque Influence Method for rolling element signal
                                          'scale_max': 0.1,
                                          'value_min': 0,
                                          'value_max': 50,
                                          'norm_divisor': 1,
                                          'exponent': 4},
             # Outer Ring Rollover
             'signal_oring': 'sine',                               # Signal type for inner cage
             'ampl_method_oring': 'const',                         # Amplitude Method for inner cage signal (Repeat methods are not working for bearings)
             'ampl_attributes_oring': {'constant': 2.5},           # Attributes regarding Amplitude Method for inner cage signal
             'noise_method_oring': 'gaussian',                     # Noise Method for inner gear
             'noise_attributes_oring': {'mu': 0, 'sigma': 0.05},   # Attributes regarding Noise Method for gear signal
             'torq_method_oring': None,                         # Torque Influence Method for rolling element
             'torq_attributes_oring': {'scale_min': 0,          # Attributes regarding Torque Influence Method for rolling element signal
                                       'scale_max': 0.1,
                                       'value_min': 0,
                                       'value_max': 50,
                                       'norm_divisor': 1,
                                       'exponent': 4},          
            }

Bearing1 = {**{'no_elements': 11}, **BearingI}                     # Number of rolling elements
Bearing2 = {**{'no_elements': 9}, **BearingI}                     # Number of rolling elements
Bearing3 = {**{'no_elements': 13}, **BearingI}                     # Number of rolling elements
Bearing4 = {**{'no_elements': 12}, **BearingI}                     # Number of rolling elements

Define Degradation Elements

# Reference Value for PDFs is given for load defined 'Whoeler' 'torqp'

Deg_GearIn = {'Failing_Teeth': 2,                                      # Number of Teeth falling at Gear
              'Chances': {'neighbouring': 1,                           # Chance that multiple falling teeth are neighbouring
                          'opposite': 1,                               # Chance that multiple falling teeth are opposite to each other
                          'keeporder': 10},                            # Chance that multiple falling teeth are keeping order from init to eol
              'PDF_Deg_Init': {'n': norm(loc=6.875e6, scale=1.053e6),  # P(n_0) n in Load Cycles (ref: input shaft)
                               'a': norm(loc=0.450, scale=0.305)},     # P(a_0) a in %
              'PDF_Deg_EOL': {'n': norm(loc=10390000, scale=1.053e6),  # P(n_eol) n in Load Cycles (ref: input shaft)
                              'a': norm(loc=4.0, scale=0.)},           # P(a_eol) a in %
              'Woehler': {'k': 8.5,                                   # Woehler Exponent
                          'np': 10390000,                              # Woehler Reference n in Load Cycles (ref: input shaft)
                          'torqp': 200},                               # Woehler Reference sigma in Nm
              'GridSearch': {'slice_theta1': (0.0001, 0.0902, 0.01),   # Grid for function a = theta1 * exp(theta2 * n) + theta3 defined in slices
                             'slice_theta2': (0.10/1e6, 1.51/1e6, 0.2/1e6), #tbd change step to 0.02/1e6
                             'slice_theta3':(-2.0, 0.5, 0.1)}
             }

Deg_GearOut = {'Failing_Teeth': 3,                                      # Number of Teeth falling at Gear
               'Chances': {'neighbouring': 2,                           # Chance that multiple falling teeth are neighbouring
                           'opposite': 2,                               # Chance that multiple falling teeth are opposite to each other
                           'keeporder': 10},                            # Chance that multiple falling teeth are keeping order from init to eol
               'PDF_Deg_Init': {'n': norm(loc=6.875e6, scale=1.053e6),  # P(n_0) n in Load Cycles (ref: input shaft)
                                'a': norm(loc=0.450, scale=0.305)},     # P(a_0) a in %
               'PDF_Deg_EOL': {'n': norm(loc=10390000, scale=1.053e6),  # P(n_eol) n in Load Cycles (ref: input shaft)
                               'a': norm(loc=4.0, scale=0.)},           # P(a_eol) a in %
               'Woehler': {'k': 8.5,                                   # Woehler Exponent
                           'np': 10390000,                              # Woehler Reference n in Load Cycles (ref: input shaft)
                           'torqp': 200},                               # Woehler Reference sigma in Nm
               'GridSearch': {'slice_theta1': (0.0001, 0.0902, 0.01),   # Grid for function a = theta1 * exp(theta2 * n) + theta3 defined in slices
                              'slice_theta2': (0.10/1e6, 1.51/1e6, 0.2/1e6), #tbd change step to 0.02/1e6
                              'slice_theta3':(-2.0, 0.5, 0.1)}
              }

Deg_Bearing1 = 'tbd'
Deg_Bearing2 = 'tbd'
Deg_Bearing3 = 'tbd'
Deg_Bearing4 = 'tbd'

Define Degradation-Vibration-Dependencie

GearDegVibDictIn = {'signal': 'gausspulse',                                 # Signal type for gear
                       'fc_factor': 4*rotational_frequency_in,                                      # fc = frequency * fc_factor (see gauspulse definition)
                       'bw_factor': 0.5,                                    # see gauspulse definition
                       'bwr_factor': -6,                                    # see gauspulse definition
                       'scale_method': 'linear',                            # Scale Method (See Torque Influence Method)
                       'scale_attributes': {'scale_min': 0,                 # Attributes regarding Scale Method for gear signal (see Torque Influence Method)
                                           'scale_max': 10,
                                           'value_min': 0,
                                           'value_max': 2,
                                           'exponent': 2},
                       'torq_influence': True,                              # If True Torque Influence will be taken into account in the same way as in vibration definition
                       'noise_method': 'gaussian',                          # Noise Method
                       'noise_attributes': {'mu': 0, 'sigma': 0.005},       # Attributes regarding Noise Method for
                       't2t_factor': 1,
                       }

GearDegVibDictOut = {'signal': 'gausspulse',                                # Signal type for gear
                       'fc_factor': 4**rotational_frequency_in,                                      # fc = frequency * fc_factor (see gauspulse definition)
                       'bw_factor': 0.5,                                    # see gauspulse definition
                       'bwr_factor': -6,                                    # see gauspulse definition
                       'scale_method': 'linear',                            # Scale Method (See Torque Influence Method)
                       'scale_attributes': {'scale_min': 0,                 # Attributes regarding Scale Method for gear signal (see Torque Influence Method)
                                           'scale_max': 10,
                                           'value_min': 0,
                                           'value_max': 2,
                                           'exponent': 2},
                       'torq_influence': True,                              # If True Torque Influence will be taken into account in the same way as in vibration definition
                       'noise_method': 'gaussian',                          # Noise Method
                       'noise_attributes': {'mu': 0, 'sigma': 0.005},       # Attributes regarding Noise Method for
                       't2t_factor': 1,
                       }

Torque Definition (Workaround)

sample_time = gf.get_sample_time_torque(rotational_frequency_in, sample_rate, GearIn['no_teeth'], GearOut['no_teeth'])
torque_in = np.sin((2 * np.pi * rotational_frequency_in * sample_time)) * 5 + 200 # Nm | array

Toolbox Running Example - Run

Instance Initialization

Initialize a new Instance:

model = Gearbox(# Vibration Arguments
                rotational_frequency_in,
                sample_interval, sample_rate,
                GearIn, GearOut,
                Bearing1, Bearing2, Bearing3, Bearing4,
                # Degradation Arguments
                Deg_GearIn, Deg_GearOut,
                Deg_Bearing1, Deg_Bearing2, Deg_Bearing3, Deg_Bearing4,
                # Shared Arguments
                seed=seed,
                fixed_start=True,
                GearDegVibDictIn=GearDegVibDictIn,
                GearDegVibDictOut=GearDegVibDictOut)

Run only Vibration

Initialize Vibration Module: init_vibration(torque)

Input Arguments:

Input Torque

Returns:

-

model.Vibration.init_vibration(torque_in)

Get Loads from Torque: get_loads(torque)

Input Arguments:

Input Torque

Returns:

Loads Dictionary

loads = model.Vibration.get_loads(torque_in)

df_loads = pd.DataFrame(loads)
df_loads.index = df_loads.index.astype(dtype='int32')
df_loads = df_loads.sort_index()

df_loads

	GearIn	GearOut	Bearing1	Bearing2	Bearing3	Bearing4
1	[200.6817258938662, 199.98264304525793, 199.96...	[200.6817258938662, 197.31505718393504, 195.49...	tbd	tbd	tbd	tbd
2	[202.62853435886845, 202.64111177836386, 202.6...	[202.62853435886845, 199.96528630540217, 197.3...	tbd	tbd	tbd	tbd
3	[204.47605246180117, 204.46872938665337, 204.4...	[204.47605246180117, 202.62643579473837, 199.9...	tbd	tbd	tbd	tbd
4	[204.88825602091026, 204.8862356892104, 204.88...	[204.88825602091026, 204.4750096988814, 202.65...	tbd	tbd	tbd	tbd
5	[203.7417678604638, 203.75305523806313, 203.74...	[203.7417678604638, 204.88858842058818, 204.47...	tbd	tbd	tbd	tbd
6	[201.42261349854877, 201.40836172680946, 201.4...	[201.42261349854877, 203.74338318244688, 204.8...	tbd	tbd	tbd	tbd
7	[198.65592789803515, 198.64161950289116, 198.6...	[198.65592789803515, 201.42498753929806, 203.7...	tbd	tbd	tbd	tbd
8	[196.29073656906985, 196.3022018523581, 196.29...	[196.29073656906985, 198.62732346333246, 201.4...	tbd	tbd	tbd	tbd
9	[195.12340552714028, 195.12118534653806, 195.1...	[195.12340552714028, 196.29237165842147, 198.6...	tbd	tbd	tbd	tbd
10	[195.50333012295354, 195.49622128638393, 195.5...	[195.50333012295354, 195.12377987024195, 196.2...	tbd	tbd	tbd	tbd
11	[197.3025887660451, 197.31505718393504, 197.30...	[197.3025887660451, 195.50231116440438, 195.12...	tbd	tbd	tbd	tbd
12	NaN	[199.98264304525793, 197.30051307870085, 195.5...	tbd	tbd	tbd	tbd
13	NaN	[202.64111177836386, 199.98016349282457, 197.2...	tbd	tbd	tbd	tbd
14	NaN	[204.46872938665337, 202.63901720696384, 199.9...	tbd	tbd	tbd	tbd
15	NaN	[204.8862356892104, 204.4676787146322, 202.636...	tbd	tbd	tbd	tbd
16	NaN	[203.75305523806313, 204.88657549807294, 204.4...	tbd	tbd	tbd	tbd
17	NaN	[201.40836172680946, 203.75466393081751, 204.8...	tbd	tbd	tbd	tbd
18	NaN	[198.64161950289116, 201.41073791519926, 203.7...	tbd	tbd	tbd	tbd
19	NaN	[196.3022018523581, 198.64400338090186, 201.41...	tbd	tbd	tbd	tbd
20	NaN	[195.12118534653806, 196.28257518840692, 198.6...	tbd	tbd	tbd	tbd
21	NaN	[195.49622128638393, 195.12155229545505, 196.2...	tbd	tbd	tbd	tbd

Get Vibration Signal: run_vibration(nolc, torque, statei=None, output=True)

Input Arguments:

nolc: current number of load cycle

torque: Input Torque

statei: current degradation state

output: if true method returns vibration signal

Returns:

vibration signal

vibration = model.Vibration.run_vibration(number_of_load_cycle, torque_in, statei=None, output=True)

plt.plot(np.arange(0, sample_interval, 1/sample_rate), vibration)
plt.xlabel('Time in seconds'), plt.ylabel('Acceleration in g'), plt.legend(['Vibration Signal'])
plt.show()

Summarize Vibration: summary_vibration()

model.Vibration.summary_vibration()

Controls

Accumulated Signal

Bearing 1 Signal

Bearing 2 Signal

Bearing 3 Signal

Bearing 4 Signal

Degradation Signal

Degradation not available (probably no statei argument given)

Gear Signals

Run only Degradation

Initialize Degradation Module: init_degradation()

Input Arguments:

Returns:

statei: DataFrame containing the degradation states

statei = model.Degradation.init_degradation()

Gear in:

Running for tooth 7 failure

[================================================================================] 2000/2000

Running for tooth 3 failure

[================================================================================] 2000/2000  

\\imapc\benutzer\Mitarbeiterdaten\henss\_02_software\_08_github\Gearbox\gearbox\degradation\helper\__init__.py:181: RuntimeWarning: invalid value encountered in log
  x = np.log((y - theta3) / theta1) / theta2

Gear out:

Running for tooth 12 failure

[================================================================================] 2000/2000

Running for tooth 5 failure

[================================================================================] 2000/2000

Running for tooth 14 failure

[================================================================================] 2000/2000

pd.DataFrame(statei['GearIn'])

	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	11.0
$a_{0}$	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
$d_{0}$	NaN	NaN	NaN	NaN	NaN	NaN	-1.434069	NaN	NaN	NaN	NaN

pd.DataFrame(statei['GearOut'])

	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	...	12.0	13.0	14.0	15.0	16.0	17.0	18.0	19.0	20.0	21.0
$a_{0}$	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
$d_{0}$	NaN	NaN	NaN	NaN	-1.671099	NaN	NaN	NaN	NaN	NaN	...	-1.382792	NaN	-0.391062	NaN	NaN	NaN	NaN	NaN	NaN	NaN

2 rows × 21 columns

Summarize Vibration: summary_vibration()

model.Degradation.summary_degradation()

Degradation Gear In

State 0 Parameter (Ref. Torque: 200.000 Nm)

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.661548	5.161122e+06	7	8.760057e+06	4.0	0.0501	5.000000e-07	1.776357e-15	5.656872e+06	8.721440e+06
1	0.100020	NaN	3	1.175231e+07	4.0	0.0101	5.000000e-07	4.000000e-01	5.839910e+06	1.112036e+07

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 0)

	0
0	-1.434069
1	NaN

Legend: Row: 0 <=> Tooth: 7 | Row: 1 <=> Tooth: 3)

Pitting Growth (until load cycle 0)

	0
0	NaN
1	NaN

Legend: Row: 0 <=> Tooth: 7 | Row: 1 <=> Tooth: 3)

Degradation Gear Out

State 0 Parameter (Ref. Torque: 200.000 Nm)

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.579647	5.342086e+06	12	9.205347e+06	4.0	0.0401	5.000000e-07	1.776357e-15	4.391948e+06	9.341308e+06
1	0.551336	6.623250e+06	5	1.058666e+07	4.0	0.0201	5.000000e-07	1.776357e-15	5.441903e+06	1.073986e+07
2	0.146248	2.587852e+06	14	9.205347e+06	4.0	0.0401	5.000000e-07	1.776357e-15	5.601978e+06	9.354910e+06

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 0)

	0
0	-1.382792
1	-1.671099
2	-0.391062

Legend: Row: 0 <=> Tooth: 12 | Row: 1 <=> Tooth: 5 | Row: 2 <=> Tooth: 14)

Pitting Growth (until load cycle 0)

	0
0	NaN
1	NaN
2	NaN

Legend: Row: 0 <=> Tooth: 12 | Row: 1 <=> Tooth: 5 | Row: 2 <=> Tooth: 14)

Get Degradation Growth: run_degradation(nolc, loads)

Input Arguments:

nolc: current number of load cycle (must be greater than the previous given nolc)

loads: Dictionary regarding get_loads(torque) return

Returns:

statei

loads = {'GearIn': {'7': [200], '3': [200]},
         'GearOut': {'12': [200], '5': [200], '14': [200]}}

for nolc in np.linspace(1e6, 6e6, 50):
    statei = model.Degradation.run_degradation(nolc, loads)

pd.DataFrame(statei['GearIn'])

	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	11.0
$a_{6000000}$	NaN	NaN	NaN	NaN	NaN	NaN	1.006265	NaN	NaN	NaN	NaN
$d_{6000000}$	NaN	NaN	NaN	NaN	NaN	NaN	0.233080	NaN	NaN	NaN	NaN

pd.DataFrame(statei['GearOut'])

	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	...	12.0	13.0	14.0	15.0	16.0	17.0	18.0	19.0	20.0	21.0
$a_{6000000}$	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.193018	NaN	NaN	NaN	NaN	NaN	NaN	NaN
$d_{6000000}$	NaN	NaN	NaN	NaN	-0.878143	NaN	NaN	NaN	NaN	NaN	...	-0.56928	NaN	0.083862	NaN	NaN	NaN	NaN	NaN	NaN	NaN

2 rows × 21 columns

model.Degradation.summary_degradation()

Degradation Gear In

State 0 Parameter (Ref. Torque: 200.000 Nm)

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.661548	5.161122e+06	7	8.760057e+06	4.0	0.0501	5.000000e-07	1.776357e-15	5.656872e+06	8.721440e+06
1	0.100020	NaN	3	1.175231e+07	4.0	0.0101	5.000000e-07	4.000000e-01	5.839910e+06	1.112036e+07

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 6000000)

	0.000000e+00	1.000000e+06	1.102041e+06	1.204082e+06	1.306122e+06	1.408163e+06	1.510204e+06	1.612245e+06	1.714286e+06	1.816327e+06	...	5.081633e+06	5.183673e+06	5.285714e+06	5.387755e+06	5.489796e+06	5.591837e+06	5.693878e+06	5.795918e+06	5.897959e+06	6.000000e+06
0	-1.434069	-1.156209	-1.127856	-1.099503	-1.071151	-1.042798	-1.014445	-0.986092	-0.957739	-0.929386	...	-0.022096	0.006257	0.03461	0.062963	0.091315	0.119668	0.148021	0.176374	0.204727	0.23308
1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

2 rows × 51 columns

Legend: Row: 0 <=> Tooth: 7 | Row: 1 <=> Tooth: 3)

Pitting Growth (until load cycle 6000000)

	0.000000e+00	1.000000e+06	1.102041e+06	1.204082e+06	1.306122e+06	1.408163e+06	1.510204e+06	1.612245e+06	1.714286e+06	1.816327e+06	...	5.081633e+06	5.183673e+06	5.285714e+06	5.387755e+06	5.489796e+06	5.591837e+06	5.693878e+06	5.795918e+06	5.897959e+06	6.000000e+06
0	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	0.669038	0.704058	0.740911	0.779694	0.820506	0.863454	0.908651	0.956213	1.006265
1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

2 rows × 51 columns

Legend: Row: 0 <=> Tooth: 7 | Row: 1 <=> Tooth: 3)

Degradation Gear Out

State 0 Parameter (Ref. Torque: 200.000 Nm)

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.579647	5.342086e+06	12	9.205347e+06	4.0	0.0401	5.000000e-07	1.776357e-15	4.391948e+06	9.341308e+06
1	0.551336	6.623250e+06	5	1.058666e+07	4.0	0.0201	5.000000e-07	1.776357e-15	5.441903e+06	1.073986e+07
2	0.146248	2.587852e+06	14	9.205347e+06	4.0	0.0401	5.000000e-07	1.776357e-15	5.601978e+06	9.354910e+06

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 3142857)

	0.000000e+00	1.000000e+06	1.102041e+06	1.204082e+06	1.306122e+06	1.408163e+06	1.510204e+06	1.612245e+06	1.714286e+06	1.816327e+06	...	5.081633e+06	5.183673e+06	5.285714e+06	5.387755e+06	5.489796e+06	5.591837e+06	5.693878e+06	5.795918e+06	5.897959e+06	6.000000e+06
0	-1.382792	-1.247205	-1.233370	-1.219534	-1.205699	-1.191864	-1.178029	-1.164194	-1.150358	-1.136523	...	-0.693797	-0.679961	-0.666126	-0.652291	-0.638456	-0.624621	-0.610785	-0.596950	-0.583115	-0.569280
1	-1.671099	-1.538938	-1.525452	-1.511967	-1.498481	-1.484995	-1.471510	-1.458024	-1.444539	-1.431053	...	-0.999513	-0.986028	-0.972542	-0.959057	-0.945571	-0.932085	-0.918600	-0.905114	-0.891629	-0.878143
2	-0.391062	-0.311907	-0.303830	-0.295753	-0.287676	-0.279599	-0.271522	-0.263445	-0.255369	-0.247292	...	0.011170	0.019247	0.027324	0.035401	0.043478	0.051555	0.059631	0.067708	0.075785	0.083862

3 rows × 51 columns

Legend: Row: 0 <=> Tooth: 12 | Row: 1 <=> Tooth: 5 | Row: 2 <=> Tooth: 14)

Pitting Growth (until load cycle 3142857)

	0.000000e+00	1.000000e+06	1.102041e+06	1.204082e+06	1.306122e+06	1.408163e+06	1.510204e+06	1.612245e+06	1.714286e+06	1.816327e+06	...	5.081633e+06	5.183673e+06	5.285714e+06	5.387755e+06	5.489796e+06	5.591837e+06	5.693878e+06	5.795918e+06	5.897959e+06	6.000000e+06
0	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	0.151754	0.155864	0.160086	0.164422	0.168875	0.173449	0.178147	0.182972	0.187928	0.193018

3 rows × 51 columns

Legend: Row: 0 <=> Tooth: 12 | Row: 1 <=> Tooth: 5 | Row: 2 <=> Tooth: 14)

loads = {'GearIn': {'7': [200], '3': [200]},
         'GearOut': {'12': [188], '5': [194], '14': [200]}}

for nolc in np.linspace(6.1e6, 10e6, 40):
    statei = model.Degradation.run_degradation(nolc, loads)

pd.DataFrame(statei['GearIn'])

	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	11.0
$a_{10000000}$	NaN	NaN	NaN	NaN	NaN	NaN	7.435351	NaN	NaN	NaN	NaN
$d_{10000000}$	NaN	NaN	NaN	NaN	NaN	NaN	1.344519	NaN	NaN	NaN	NaN

pd.DataFrame(statei['GearOut'])

	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	...	12.0	13.0	14.0	15.0	16.0	17.0	18.0	19.0	20.0	21.0
$a_{10000000}$	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	0.550255	NaN	NaN	NaN	NaN	NaN	NaN	NaN
$d_{10000000}$	NaN	NaN	NaN	NaN	-0.494206	NaN	NaN	NaN	NaN	NaN	...	-0.286066	NaN	0.400478	NaN	NaN	NaN	NaN	NaN	NaN	NaN

2 rows × 21 columns

model.Degradation.summary_degradation()

Degradation Gear In

State 0 Parameter (Ref. Torque: 200.000 Nm)

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.661548	5.161122e+06	7	8.760057e+06	4.0	0.0501	5.000000e-07	1.776357e-15	5.656872e+06	8.721440e+06
1	0.100020	NaN	3	1.175231e+07	4.0	0.0101	5.000000e-07	4.000000e-01	5.839910e+06	1.112036e+07

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 10000000)

	0.000000e+00	1.000000e+06	1.102041e+06	1.204082e+06	1.306122e+06	1.408163e+06	1.510204e+06	1.612245e+06	1.714286e+06	1.816327e+06	...	9.100000e+06	9.200000e+06	9.300000e+06	9.400000e+06	9.500000e+06	9.600000e+06	9.700000e+06	9.800000e+06	9.900000e+06	1.000000e+07
0	-1.434069	-1.156209	-1.127856	-1.099503	-1.071151	-1.042798	-1.014445	-0.986092	-0.957739	-0.929386	...	1.094445	1.122231	1.150017	1.177803	1.205589	1.233375	1.261161	1.288947	1.316733	1.344519
1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

2 rows × 91 columns

Legend: Row: 0 <=> Tooth: 7 | Row: 1 <=> Tooth: 3)

Pitting Growth (until load cycle 10000000)

	0.000000e+00	1.000000e+06	1.102041e+06	1.204082e+06	1.306122e+06	1.408163e+06	1.510204e+06	1.612245e+06	1.714286e+06	1.816327e+06	...	9.100000e+06	9.200000e+06	9.300000e+06	9.400000e+06	9.500000e+06	9.600000e+06	9.700000e+06	9.800000e+06	9.900000e+06	1.000000e+07
0	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	4.740989	4.984065	5.239603	5.508243	5.790657	6.08755	6.399666	6.727783	7.072724	7.435351
1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

2 rows × 91 columns

Legend: Row: 0 <=> Tooth: 7 | Row: 1 <=> Tooth: 3)

Degradation Gear Out

State 0 Parameter (Ref. Torque: 200.000 Nm)

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.579647	5.342086e+06	12	9.205347e+06	4.0	0.0401	5.000000e-07	1.776357e-15	4.391948e+06	9.341308e+06
1	0.551336	6.623250e+06	5	1.058666e+07	4.0	0.0201	5.000000e-07	1.776357e-15	5.441903e+06	1.073986e+07
2	0.146248	2.587852e+06	14	9.205347e+06	4.0	0.0401	5.000000e-07	1.776357e-15	5.601978e+06	9.354910e+06

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 5238095)

	0.000000e+00	1.000000e+06	1.102041e+06	1.204082e+06	1.306122e+06	1.408163e+06	1.510204e+06	1.612245e+06	1.714286e+06	1.816327e+06	...	9.100000e+06	9.200000e+06	9.300000e+06	9.400000e+06	9.500000e+06	9.600000e+06	9.700000e+06	9.800000e+06	9.900000e+06	1.000000e+07
0	-1.382792	-1.247205	-1.233370	-1.219534	-1.205699	-1.191864	-1.178029	-1.164194	-1.150358	-1.136523	...	-0.349789	-0.342709	-0.335629	-0.328548	-0.321468	-0.314388	-0.307307	-0.300227	-0.293147	-0.286066
1	-1.671099	-1.538938	-1.525452	-1.511967	-1.498481	-1.484995	-1.471510	-1.458024	-1.444539	-1.431053	...	-0.580592	-0.570994	-0.561395	-0.551797	-0.542198	-0.532600	-0.523001	-0.513403	-0.503805	-0.494206
2	-0.391062	-0.311907	-0.303830	-0.295753	-0.287676	-0.279599	-0.271522	-0.263445	-0.255369	-0.247292	...	0.329239	0.337154	0.345070	0.352985	0.360901	0.368816	0.376731	0.384647	0.392562	0.400478

3 rows × 91 columns

Legend: Row: 0 <=> Tooth: 12 | Row: 1 <=> Tooth: 5 | Row: 2 <=> Tooth: 14)

Pitting Growth (until load cycle 5238095)

	0.000000e+00	1.000000e+06	1.102041e+06	1.204082e+06	1.306122e+06	1.408163e+06	1.510204e+06	1.612245e+06	1.714286e+06	1.816327e+06	...	9.100000e+06	9.200000e+06	9.300000e+06	9.400000e+06	9.500000e+06	9.600000e+06	9.700000e+06	9.800000e+06	9.900000e+06	1.000000e+07
0	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	0.434707	0.446242	0.458083	0.470239	0.482717	0.495527	0.508676	0.522174	0.536031	0.550255

3 rows × 91 columns

Legend: Row: 0 <=> Tooth: 12 | Row: 1 <=> Tooth: 5 | Row: 2 <=> Tooth: 14)

Run All Vibration and Degradation

Initialize Degradation Module: initialize(torque)

Input Arguments:

torque: input torque

Returns:

model.initialize(torque_in)

Initialize Degradation

Gear in:

Running for tooth 8 failure

[================================================================================] 2000/2000

Running for tooth 6 failure

[================================================================================] 2000/2000

Gear out:

Running for tooth 9 failure

[================================================================================] 2000/2000

Running for tooth 18 failure

[================================================================================] 2000/2000

Running for tooth 21 failure

[================================================================================] 2000/2000

Initialize Vibration

Done

Run Vibration and Degradation: run(nolc, output=True)

Input Arguments:

nolc: current number of load cycle (must be greater than the previous given nolc)

output: if true returns vibration signal

Returns:

vibration (if output is True)

Set Torque for upcoming cycles: set(nolc, torque)

Input Arguments:

nolc: current number of load cycle (must be equal to the previous nolc in run())

torque: input torque

Returns:

for nolc in np.linspace(6.1e6, 9e6, 10):
    vibration = model.run(nolc, output=True)
    model.set(nolc, torque_in)

Load Cycle 6100000 done

Load Cycle 6422222 done

Load Cycle 6744444 done

Load Cycle 7066666 done

Load Cycle 7388888 done

Load Cycle 7711111 done

Load Cycle 8033333 done

Load Cycle 8355555 done

Load Cycle 8677777 done

Load Cycle 9000000 done

Summarize Vibration and Degradation: summary()

model.summary()

Summary Degradation

Degradation Gear In

State 0 Parameter (Ref. Torque: 200.000 Nm)

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.661548	5.161122e+06	8	8.760057e+06	4.0	0.0501	5.000000e-07	1.776357e-15	5.656872e+06	8.721440e+06
1	0.100020	1.827980e+06	6	9.205347e+06	4.0	0.0401	5.000000e-07	1.776357e-15	5.839910e+06	9.181707e+06

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 9000000)

	0.000000e+00	6.100000e+06	6.422222e+06	6.744444e+06	7.066667e+06	7.388889e+06	7.711111e+06	8.033333e+06	8.355556e+06	8.677778e+06	9.000000e+06
0	-1.434069	-0.041508	0.032052	0.105611	0.179171	0.252731	0.326290	0.399850	0.473410	0.546969	0.620529
1	-0.247782	0.642824	0.689869	0.736914	0.783959	0.831003	0.878048	0.925093	0.972138	1.019182	1.066227

Legend: Row: 0 <=> Tooth: 8 | Row: 1 <=> Tooth: 6)

Pitting Growth (until load cycle 9000000)

	0.000000e+00	6.100000e+06	6.422222e+06	6.744444e+06	7.066667e+06	7.388889e+06	7.711111e+06	8.033333e+06	8.355556e+06	8.677778e+06	9.000000e+06
0	NaN	NaN	0.700825	0.800012	0.913236	1.042485	1.190027	1.358449	1.550709	1.770178	2.020709
1	NaN	1.071208	1.274202	1.515663	1.802882	2.144528	2.550916	3.034316	3.609319	4.293286	5.106864

Legend: Row: 0 <=> Tooth: 8 | Row: 1 <=> Tooth: 6)

Degradation Gear Out

State 0 Parameter (Ref. Torque: 200.000 Nm)

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.579647	4.518059e+06	9	8.709422e+06	4.0	0.0501	5.000000e-07	1.000000e-01	4.391948e+06	8.721440e+06
1	0.551336	6.623250e+06	18	1.058666e+07	4.0	0.0201	5.000000e-07	1.776357e-15	5.441903e+06	1.073986e+07
2	0.146248	2.587852e+06	21	9.205347e+06	4.0	0.0401	5.000000e-07	1.776357e-15	5.601978e+06	9.181707e+06

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 4714285)

	0.000000e+00	6.100000e+06	6.422222e+06	6.744444e+06	7.066667e+06	7.388889e+06	7.711111e+06	8.033333e+06	8.355556e+06	8.677778e+06	9.000000e+06
0	-1.077945	-0.304016	-0.263134	-0.222253	-0.181371	-0.140489	-0.099608	-0.058726	-0.017845	0.023037	0.063918
1	-1.671099	-0.852686	-0.809455	-0.766223	-0.722992	-0.679761	-0.636530	-0.593298	-0.550067	-0.506836	-0.463604
2	-0.391062	0.099115	0.125008	0.150900	0.176793	0.202686	0.228579	0.254471	0.280364	0.306257	0.332150

Legend: Row: 0 <=> Tooth: 9 | Row: 1 <=> Tooth: 18 | Row: 2 <=> Tooth: 21)

Pitting Growth (until load cycle 4714285)

	0.000000e+00	6.100000e+06	6.422222e+06	6.744444e+06	7.066667e+06	7.388889e+06	7.711111e+06	8.033333e+06	8.355556e+06	8.677778e+06	9.000000e+06
0	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	0.603372	0.648399
1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2	NaN	0.203009	0.221168	0.240951	0.262504	0.285985	0.311566	0.339436	0.369798	0.402876	0.438913

Legend: Row: 0 <=> Tooth: 9 | Row: 1 <=> Tooth: 18 | Row: 2 <=> Tooth: 21)

Summary Vibration

Controls

Accumulated Signal

Bearing 1 Signal

Bearing 2 Signal

Bearing 3 Signal

Bearing 4 Signal

Degradation Signal

Gear Signals

Details and Theory

Module Structure

GearBox Simulation Toolbox is structured in Modules

Top Modules are accessing lower Modules

Helper-Module is used by Modules on the same level

Modules consisting of several Module Methods

Vibration Element Definition

Gear Element

Keyword Attributes:

no_teeth: Number of teeth
signal: Nonstationary Signals
ampl_method: Method to create Signal Amplitude
ampl_attributes: Attributes regarding the Method to create Signal Amplitude
noise_method: Method to create Signal Noise (repeat methods are not working)
noise_attributes: Attributes regarding the Method to create Signal Noise
torq_method: Method to create Signal Noise (repeat methods are not working)
torq_attributes: Attributes regarding the Method to create Signal Noise

Gear Element:

Gear = {'no_teeth': 10,                                         # Number of teeth
        'signal': 'gausspulse',                                 # Signal type for gear
        'ampl_method': 'gaussian_repeat',                       # Amplitude Method for inner gear
        'ampl_attributes': {'mu': 4, 'sigma': 0.5},             # Attributes regarding Amplitude Method for gear signal
        'noise_method': None,                                   # Noise Method for inner gear
        'noise_attributes': {'mu': 0, 'sigma': 0.25},           # Attributes regarding Noise Method for gear signal
        'torq_method': None,                                    # Torque Influence Method for inner gear
        'torq_attributes': {'scale_min': 0,
                            'scale_max': 0.2,
                            'value_min': 0,
                            'value_max': 50,
                            'norm_divisor': 200,
                            'exponent': 2},
        }

Modelling:

The chosen Non-Stationary Signal is repeated every tooth mesh

Repeat Methods are modeling the same amplitude at tooth i

Using const_repeat argument constant must be a list of length no_teeth

Bearing Element

Keyword Attributes:

no_elements: Number of rolling elements
signal_*: Nonstationary Signals
ampl_method_*: Method to create Signal Amplitude
ampl_attributes_*: Attributes regarding the Method to create Signal Amplitude
noise_method_*: Method to create Signal Noise (repeat methods are not working)
noise_attributes_*: Attributes regarding the Method to create Signal Noise
torq_method_*: Method to create Signal Noise (repeat methods are not working)
torq_attributes_*: Attributes regarding the Method to create Signal Noise

*: Can be 'iring' (inner ring), 'relement' (rolling element) or 'oring' (outer ring)

Bearing =   {'no_elements': 11,                                    # Number of Rolling Elements
             # Inner Ring Rollover
             'signal_iring': 'sine',                               # Signal type for inner cage
             'ampl_method_iring': 'const',                         # Amplitude Method for inner cage signal (Repeat methods are not working for bearings)
             'ampl_attributes_iring': {'constant': 2.5},           # Attributes regarding Amplitude Method for inner cage signal
             'noise_method_iring': 'gaussian',                     # Noise Method for inner gear
             'noise_attributes_iring': {'mu': 0, 'sigma': 0.05},   # Attributes regarding Noise Method for gear signal
             'torq_method_iring': None,                         # Torque Influence Method for rolling element
             'torq_attributes_iring': {'scale_min': 0,          # Attributes regarding Torque Influence Method for rolling element signal
                                       'scale_max': 0.1,
                                       'value_min': 0,
                                       'value_max': 50,
                                       'norm_divisor': 1,
                                       'exponent': 4},           

             # Rolling Element:
             'signal_relement': 'sine',                            # Signal type for rolling element
             'ampl_method_relement': 'const',                      # Amplitude Method for rolling element signal (Repeat methods are not working for bearings)
             'ampl_attributes_relement': {'constant': 1.2},        # Attributes regarding Amplitude Method for rolling element signal
             'noise_method_relement': 'gaussian',                  # Noise Method for rolling element
             'noise_attributes_relement': {'mu': 0, 'sigma': 0.05},# Attributes regarding Noise Method for gear signal
             'torq_method_relement': None,                         # Torque Influence Method for rolling element
             'torq_attributes_relement': {'scale_min': 0,          # Attributes regarding Torque Influence Method for rolling element signal
                                          'scale_max': 0.1,
                                          'value_min': 0,
                                          'value_max': 50,
                                          'norm_divisor': 1,
                                          'exponent': 4},
             # Outer Ring Rollover
             'signal_oring': 'sine',                               # Signal type for inner cage
             'ampl_method_oring': 'const',                         # Amplitude Method for inner cage signal (Repeat methods are not working for bearings)
             'ampl_attributes_oring': {'constant': 2.5},           # Attributes regarding Amplitude Method for inner cage signal
             'noise_method_oring': 'gaussian',                     # Noise Method for inner gear
             'noise_attributes_oring': {'mu': 0, 'sigma': 0.05},   # Attributes regarding Noise Method for gear signal
             'torq_method_oring': None,                         # Torque Influence Method for rolling element
             'torq_attributes_oring': {'scale_min': 0,          # Attributes regarding Torque Influence Method for rolling element signal
                                       'scale_max': 0.1,
                                       'value_min': 0,
                                       'value_max': 50,
                                       'norm_divisor': 1,
                                       'exponent': 4},          
            }

Modelling:

The frequencies for the chosen Stationary Signal are estimated by VDI 3832 (Estimation without geometrical dimensions)

Repeat Methods are not working

As approximation factor 0.425 is chosen

Vibration Methods and Theory

Module Methods Structure:

Required Inputs:

General Input Arguments (previous slides)

Vibration Method Definition for each Element (see following slides)

State of Degradation (given by degradation model)

Methods and Returns:

run(): Vibration Signal (for state s_p = n_lc based on previous torque_p-1)

set(): Loads per tooth/bearing (based on current torque_p)

Element Method

Creating Base Signals for Bearing and Gear Elements

Amplitude of +-1

For Bearing choose any stationary signal: 'sine'

For Gear choose any non-stationary signal: 'gausspulse'

Example Non-Stationary Sine Signal

from scipy.signal import gausspulse
fi, fs = 5, 100
time_vector = gf.get_sample_time_torque(fi, fs, 21, 41)
element_signal = gausspulse(np.linspace(-max(time_vector)/2, max(time_vector)/2, time_vector.size), fc=fi, bw=0.5, bwr=-6, tpr=-60, retquad=False, retenv=False) # Nm | array

plt.plot(time_vector, element_signal)
plt.xlabel('Time in seconds'), plt.ylabel('Acceleration in g'), plt.legend(['Example Element Signal'])
plt.show()

Example Stationary Sine Signal

fi, fs = 5, 100
time_vector = gf.get_sample_time_torque(fi, fs, 21, 41)
element_signal = np.sin((2 * np.pi * fi * time_vector)) # Nm | array

plt.plot(time_vector, element_signal)
plt.xlabel('Time in seconds'), plt.ylabel('Acceleration in g'), plt.legend(['Example Element Signal'])
plt.show()

Amplitude Method

Scaling the Base Signals

Various methods can be chosen (depending on Element)

Depending on the chosen Method, different Attributes must be given

'repeat' Methods create a pattern which will be repeated

Methods:

None: Method not used

'const': Constant Amplitude for all teeth and all tooth mesh repetitions (attributes: 'constant' (scalar))

'const_repeat': Constant Amplitude for each tooth (list), and unchanging over all tooth mesh repetitions (attributes: 'constant' (list, tuple))

'gaussian': Gaussian Random Amplitude for all teeth and all tooth mesh repetitions (attributes: 'mu' (scalar), 'sigma' (scalar))

'gaussian_repeat': Gaussian Random Amplitude for each tooth, and unchanging over all tooth mesh repetitions (attributes: 'mu' (scalar), 'sigma' (scalar))

Example Stationary Sine Signal * const Amplitude

const = 5
amplitude_signal = element_signal * const

plt.plot(time_vector, element_signal, time_vector, amplitude_signal)
plt.xlabel('Time in seconds'), plt.ylabel('Acceleration in g'), plt.legend(['Example Element Signal', 'Amplitude Signal'])
plt.show()

Noise Method

Adds noise to the signal

Based on the Amplitude Methods Toolbox (repeat methods are not working)

General use: Adding Gaussian Noise

Methods:

None: Method not used

'const': Constant Amplitude for all teeth and all tooth mesh repetitions (attributes: 'constant' (scalar))

~~'const_repeat': Constant Amplitude for each tooth (list), and unchanging over all tooth mesh repetitions (attributes: 'constant' (list, tuple))~~

'gaussian': Gaussian Random Amplitude for all teeth and all tooth mesh repetitions (attributes: 'mu' (scalar), 'sigma' (scalar))

~~'gaussian_repeat': Gaussian Random Amplitude for each tooth, and unchanging over all tooth mesh repetitions (attributes: 'mu' (scalar), 'sigma' (scalar))~~

Example Stationary Sine Signal * const Amplitude + noise

noise = np.random.randn(time_vector.size)*0.5
noised_signal = amplitude_signal + noise

plt.plot(time_vector, element_signal, time_vector, amplitude_signal, time_vector, noised_signal)
plt.xlabel('Time in seconds'), plt.ylabel('Acceleration in g'), plt.legend(['Example Element Signal', 'Amplitude Signal', 'Noised Signal'])
plt.show()

Torque Method

Scales Signal s regarding the torque s_t

1. s_t = s_t/s_norm, norm signal by s_norm

2. s_t = f(s_t), while f can be linear, polynomial and exponential

3. s_t = scale(s_t), scale into range scale_min-scale_max while scale_min corresponds to value_min and scale_max to value_max

4. s_t = s_t + 1, add one to retain original signal and add torque on top

5. s = s * s_t

Methods:

None: Method not used

'linear': f in step 2 is a linear transformation (no transformation)

'polynomial': f in step 2 is polynomial with given exponent argument

'exponential': f in step 2 is exponential

Example Torque Signal 200 Nm +- 5 Nm

torque = np.sin((2 * np.pi * fi /10 * time_vector))*5 + 200 # Nm | array

plt.plot(time_vector, torque)
plt.xlabel('Time in seconds'), plt.ylabel('Torque in Nm'), plt.legend(['Torque'])
plt.show()

Define Scale Arguments

scale_min = 0                   
scale_max = 0.2
value_min = 1-0.01
value_max = 1.01
norm_divisor = 200
exponent = 2

1. s_t = s_t/s_norm, norm signal by s_norm

torque_1 = torque / norm_divisor

plt.plot(time_vector, torque_1)
plt.xlabel('Time in seconds'), plt.ylabel('Torque'), plt.legend(['Normed Torque'])
plt.show()

2. s_t = f(s_t), while f can be linear, polynomial and exponential

torque_2 = np.power(torque_1, exponent)

plt.plot(time_vector, torque_1, time_vector, torque_2)
plt.xlabel('Time in seconds'), plt.ylabel('Torque'), plt.legend(['Normed Torque', 'f(Torque)'])
plt.show()

3. s_t = scale(s_t), scale into range scale_min-scale_max while scale_min corresponds to value_min and scale_max to value_max

from sklearn.preprocessing import MinMaxScaler

scaler = MinMaxScaler(feature_range=(scale_min, scale_max))
scaler.fit(np.array([value_min, value_max]).reshape(-1, 1))
torque_3 = scaler.transform(torque_2.reshape(-1, 1))

plt.plot(time_vector, torque_1, time_vector, torque_2, time_vector, torque_3)
plt.xlabel('Time in seconds'), plt.ylabel('Torque'), plt.legend(['Normed Torque', 'f(Torque)', 'scale(f(Torque))'])
plt.show()

4. s_t = s_t + 1, add one to retain original signal and add torque on top

torque_4 = torque_3 + 1

plt.plot(time_vector, torque_1, time_vector, torque_2, time_vector, torque_3, time_vector, torque_4)
plt.xlabel('Time in seconds'), plt.ylabel('Torque'), plt.legend(['Normed Torque', 'f(Torque)', 'scale(f(Torque))', '+1'])
plt.show()

5. s = s * s_t

(Example Stationary Sine Signal * const Amplitude + noise) * Torque

final_signal = noised_signal * torque_4.reshape(-1)

plt.plot(time_vector, element_signal, time_vector, amplitude_signal, time_vector, noised_signal, time_vector, final_signal)
plt.xlabel('Time in seconds'), plt.ylabel('Acceleration in g'), plt.legend(['Example Element Signal', 'Amplitude Signal', 'Noised Signal', 'Final Signal'])
plt.show()

Degradation Element Definition

Gear Element

Keyword Attributes:

Failing Teeth: Number of teeth failing at given Gear
Chances: Various chances influencing the teeth failing order
PDF_Deg_Init: PDF for pitting_size and load_cycles @ pitting initialization
PDF_Deg_EOL: PDF for pitting_size and load_cycles @ pitting end of life
Woehler: Woehler Definition
GridSearch: Slices for exp.-function Parameters to be determined in Gridsearch

Deg_Gear = {'Failing_Teeth': 2,                                      # Number of Teeth falling at Gear
            'Chances': {'neighbouring': 1,                           # Chance that multiple falling teeth are neighbouring
                        'opposite': 1,                               # Chance that multiple falling teeth are opposite to each other
                        'keeporder': 10},                            # Chance that multiple falling teeth are keeping order from init to eol
            'PDF_Deg_Init': {'n': norm(loc=6.875e6, scale=1.053e6),  # P(n_0)
                             'a': norm(loc=0.450, scale=0.305)},     # P(a_0)
            'PDF_Deg_EOL': {'n': norm(loc=10390000, scale=1.053e6),  # P(n_eol)
                            'a': norm(loc=4.0, scale=0.)},           # P(a_eol)
            'Woehler': {'k': 8.5,                                   # Woehler Exponent
                        'np': 10390000,                              # Woehler Reference n
                        'torqp': 200},                               # Woehler Reference sigma in Nm
            'GridSearch': {'slice_theta1': (0.0001, 0.0902, 0.01),   # Grid for function a = theta1 * exp(theta2 * n) + theta3 defined in slices
                           'slice_theta2': (0.10/1e6, 1.51/1e6, 0.2/1e6), #tbd change step to 0.02/1e6
                           'slice_theta3':(-2.0, 0.5, 0.1)}
           }

Bearing Element

Keyword Attributes:

TBD

Degradation Methods

Module Methods Structure:

Load the Gear Degradation Module for demonstration purposes

# os.chdir()
os.chdir(hd)
from gearbox.degradation.gear import Gear_Degradation
os.chdir(wd)

Chances

Chances are describing how many times more likely it is that an event occurs compared to the event does not occur

Events:

neighbouring: The next failing tooth is a neighbour of an already fallen one

opposite: The next failing tooth is opposite of an already fallen one

keeporder: The teeth are keeping the same order in initialization and end of life (first tooth with initialization is also the first reaching end of life

Random Pitting Initialization

Deg_Gear['Chances'] = {'neighbouring': 1, 'opposite': 1, 'keeporder': 1}  
deg_model = Gear_Degradation(17, Deg_Gear, 1)
deg_model.get_initial_values()

deg_model.state0.head()

	a0	n0	tooth	neol	aeol
0	0.122745	5.716048e+06	13	1.130127e+07	4.0
1	0.895943	5.889635e+06	17	7.966480e+06	4.0
2	0.945425	5.950615e+06	8	9.833835e+06	4.0
3	0.397409	5.984998e+06	4	9.985591e+06	4.0
4	0.332863	6.146681e+06	11	8.220672e+06	4.0

Visualization of Pitting Size at Initialization

gf.plot_gear_polar(deg_model.state0, kind='pitting', key='a0')

Pitting Order Visualization

gf.plot_gear_polar(deg_model.state0, kind='order')

Neighbouring favoured Pitting Initialization

Deg_Gear['Chances'] = {'neighbouring': 100, 'opposite': 1, 'keeporder': 1}  
deg_model = Gear_Degradation(17, Deg_Gear, 1)
deg_model.get_initial_values()
gf.plot_gear_polar(deg_model.state0, kind='order')

Opposite favoured Pitting Initialization

Deg_Gear['Chances'] = {'neighbouring': 1, 'opposite': 100, 'keeporder': 1}  
deg_model = Gear_Degradation(17, Deg_Gear, 1)
deg_model.get_initial_values()
gf.plot_gear_polar(deg_model.state0, kind='order')

Neighbouring and Opposite favoured Pitting Initialization

Deg_Gear['Chances'] = {'neighbouring': 100, 'opposite': 100, 'keeporder': 1}  
deg_model = Gear_Degradation(17, Deg_Gear, 1)
deg_model.get_initial_values()
gf.plot_gear_polar(deg_model.state0, kind='order')

Keeporder favoured Initialization

Deg_Gear['Chances'] = {'neighbouring': 1, 'opposite': 1, 'keeporder': 100}  
deg_model = Gear_Degradation(17, Deg_Gear, 1)
deg_model.get_initial_values()

deg_model.state0.head()

	a0	n0	tooth	neol	aeol
0	0.122745	5.716048e+06	13	7.966480e+06	4.0
1	0.895943	5.889635e+06	17	8.220672e+06	4.0
2	0.945425	5.950615e+06	8	9.231814e+06	4.0
3	0.397409	5.984998e+06	4	9.260164e+06	4.0
4	0.332863	6.146681e+06	11	1.222729e+07	4.0

PDF Degradation

Probability Density Function for Degradation Initialization

n: Initialization Load Cycle PDF - P(n₀)

a: Initialization Pitting Size PDF - P(a₀)

Probability Density Function for Degradation End of Life

n: EOL Load Cycle PDF - P(n_eol)

a: EOL Pitting Size PDF - P(a_eol)

PDF can be defined as any continuous distribution function available on 'Scipy Stats'

PDFs are valid for a reference torque, defined by woehler

P(n₀) and P(n_eol)

P_n0, P_neol= norm(loc=6.875e6, scale=1.053e6), norm(loc=10390000, scale=1.053e6)
n0, neol = np.linspace(P_n0.ppf(0.01), P_n0.ppf(0.99), 100), np.linspace(P_neol.ppf(0.01), P_neol.ppf(0.99), 100)

plt.plot(n0, P_n0.pdf(n0), neol, P_neol.pdf(neol))
plt.xlabel('Load Cycles N'), plt.ylabel('p(N)'), plt.legend(['PDF Initialization Load Cycle', 'PDF EOL Load Cycle'])
plt.show()

P(a₀) and P(a_eol)

P_a0, P_aeol= norm(loc=0.450, scale=0.305), norm(loc=4.0, scale=0.1)
a0, aeol = np.linspace(P_a0.ppf(0.01), P_a0.ppf(0.99), 100), np.linspace(P_aeol.ppf(0.01), P_aeol.ppf(0.99), 100)

plt.plot(a0, P_a0.pdf(a0), aeol, P_aeol.pdf(aeol))
plt.xlabel('Pitting Size a'), plt.ylabel('p(a)'), plt.legend(['PDF Initialization Pitting Size', 'PDF EOL Pitting Size'])
plt.show()

Woehler Curve

Definition of Woehler Curve for EOL

k: Woehler exponent (measure for gradien)

np: Reference Load Cycle on Woehler Curve - pair (np, torquep)

torquep: Reference Torque on Woehler Curve - pair (np, torquep)

The definition of the reference points (np, torquep) also determines the probability of failure Px for which the Woehler line applies.

Woehler Curve Plot

k, n_p, torq_p = 10.5, 10390000., 200.
torq = np.linspace(torq_p*0.5, torq_p*1.5, 10)
N = n_p * np.power((torq / torq_p), -1*k)

plt.plot(N, torq), plt.scatter(n_p, torq_p, c='r')
plt.xscale('log'), plt.yscale('log'), plt.xlabel('Load Cyvles log(N)'), plt.ylabel('Torque log(T)'), plt.legend(['Woehler Curve', 'Reference'])
plt.show()

GridSearch

Definition of Slices for Exponential Function Parameters θ

Function: a = θ₁ * exp(θ₂ * n) + θ₃

Two points Given: (a₀, n₀) and (a_eol, n_eol)

GridSearch for best fit

Only failing teeth

The definition of the reference points (np, torquep) also determines the probability of failure Px for which the Woehler line applies.

Deg_Gear['GridSearch'] = {'slice_theta1': (0.0001, 0.0902, 0.01),
                          'slice_theta2': (0.10/1e6, 1.51/1e6, 0.2/1e6),
                          'slice_theta3':(-2.0, 0.5, 0.1)}

Degradation Theory

How Degradation Simulation Works

Running Example for one tooth

1. Define Degradation Dictionary

Deg_Gear = {'Failing_Teeth': 2,                                      # Number of Teeth falling at Gear
            'Chances': {'neighbouring': 1,                           # Chance that multiple falling teeth are neighbouring
                        'opposite': 10,                               # Chance that multiple falling teeth are opposite to each other
                        'keeporder': 1},                            # Chance that multiple falling teeth are keeping order from init to eol
            'PDF_Deg_Init': {'n': norm(loc=6.875e6, scale=1.053e6),  # P(n_0)
                             'a': norm(loc=0.450, scale=0.305)},     # P(a_0)
            'PDF_Deg_EOL': {'n': norm(loc=10390000, scale=1.053e6),  # P(n_eol)
                            'a': norm(loc=4.0, scale=0.)},           # P(a_eol)
            'Woehler': {'k': 8.5,                                   # Woehler Exponent
                        'np': 10390000,                              # Woehler Reference n
                        'torqp': 200},                               # Woehler Reference sigma in Nm
            'GridSearch': {'slice_theta1': (0.00, 0.09, 0.01),   # Grid for function a = theta1 * exp(theta2 * n) + theta3 defined in slices
                           'slice_theta2': (0.30/1e6, 0.61/1e6, 0.005/1e6), #tbd change step to 0.02/1e6
                           'slice_theta3':(-.1, 0.4, 0.01)}
           }
no_teeth = 10
seed = 4

2. Draw (tooth, a₀, n₀, a_eol, n_eol) Pairs for all teeth considering chances

deg_model = Gear_Degradation(no_teeth, Deg_Gear, seed)
deg_model.get_initial_values()

deg_model.state0.head()

	a0	n0	tooth	neol	aeol
0	0.322418	5.656872e+06	6	1.102030e+07	4.0
1	0.252449	6.235948e+06	1	9.181707e+06	4.0
2	0.602485	6.782350e+06	8	8.721440e+06	4.0
3	0.100020	6.923581e+06	3	1.044324e+07	4.0
4	0.661548	7.224863e+06	2	9.707965e+06	4.0

3. GridSearch for all failing teeth to get individual degradation function

If Failing_Teeth is n --> First n teeth are considered

!! Value Pairs will be adjusted to fit on Degradation Function !!

deg_model = Gear_Degradation(no_teeth, Deg_Gear, seed)
deg_model.init_gear_degradation()

Running for tooth 6 failure

[================================================================================] 27900/27900

Running for tooth 1 failure

[================================================================================] 27900/27900

	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0
$a_{0}$	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
$d_{0}$	-0.944191	NaN	NaN	NaN	NaN	-1.028415	NaN	NaN	NaN	NaN

Results:

deg_model.state0

	a0	n0	tooth	neol	aeol	theta1	theta2	theta3	n0_old	neol_old
0	0.322418	5.588442e+06	6	1.102248e+07	4.0	0.02	4.800000e-07	0.03	5.656872e+06	1.102030e+07
1	0.252449	4.477089e+06	1	9.218807e+06	4.0	0.02	5.750000e-07	-0.01	6.235948e+06	9.181707e+06

Gear Visualization:

gf.plot_gear_polar(deg_model.state0, kind='pitting_growth', no_teeth=no_teeth, key1='a0', key2='aeol')

Degradation Function Visualization:

deg_model.plot_state0()

4. Transform Degradation to Damage D

Under constant torque load degradation starts at n₀ and ends at n_eol

D(n₀) = 0

D(n_eol) = 1

Assumption: Linear Damage Accumulation

Draw D(n₀) = 0 and D(n_eol) = 1

fig = plt.figure()
legend = []
for i, row in deg_model.state0.iterrows():
    plt.scatter([row['n0'], row['neol']], [0, 1])
    legend.append('Tooth %i' % (row['tooth']))
plt.xlabel('Load Cyvles N'), plt.ylabel('Damage (D)'), plt.legend(legend)
plt.show()

Get Linear Damage over Load Cycle Dependency

N = np.linspace(0, 1.5e7, 10)
for i, row in deg_model.state0.iterrows():
    m = (1)/(row['neol'] - row['n0'])
    b = 0 - m * row['n0']
    plt.scatter([row['n0'], row['neol']], [0, 1])
    plt.plot(N, (m * N + b))
plt.xlabel('Load Cyvles N'), plt.ylabel('Damage (D)'), plt.legend(legend)
plt.show()

5. Pitting Size and Damage Dependency

Both Pitting Size a and Damage D are a function of Load Cycles N, so it follows:

D(a₀) = 0

D(a_eol) = 1

In General: a(D(N)) = a_d

6. Defining State0

Assumption: Linear Damage Accumulation

All values are valid for the reference load (torque) given in woehler curve definition

At State0 (Initialization) the following is known:

Degradation Function: a(N) = a_N
Damage Function: D(N) = d_N
Damage Pitting Dependency: a(D(N)) = a_d

Values @ State0

print('Load Cycle:                 %i' % (deg_model.nolc[0]))
print('Failing teeth:              %s' % ('|'.join(['   %i   ' % (tooth) for tooth in deg_model.state0['tooth']])))
print('Corresponding Damage:       %s' % ('|'.join(['%.4f' % (damage) for damage in deg_model.damage[-1]])))
print('Corresponding Pitting Size: %s' % ('|'.join(['  %.4f  ' % (ps) if np.isnan(ps) else '%.4f' % (ps) for ps in deg_model.pitting_size[-1]])))

Load Cycle:                 0
Failing teeth:                 6   |   1   
Corresponding Damage:       -1.0284|-0.9442
Corresponding Pitting Size:   nan  |  nan

7. Calculating ΔD

Given:

List of loads applied on tooth i
Load Cycles n_p and n_p-1
Previous Damage D_{p-1, i}

Searched:

ΔD = D(n_p - n_p-1)
Current Damage D_{p, i}

ΔD will be computed for all full Load Cycles (e.g. considering gear_ratio for output gear -> 10,5 Load Cycles will be considered as 10 Load Cycles)

Definition of Given

loads = [195, 200, 205]
curr_cycle = 73

From State0

idx = 0 # Tooth ID
prev_cycle = deg_model.nolc[-1]
tooth_i = deg_model.state0['tooth'].to_list()[idx]
prev_damage = deg_model.damage[-1][idx]
prev_pitting = deg_model.pitting_size[-1][idx]
n0, neol = deg_model.state0['n0'][idx], deg_model.state0['neol'][idx]
T1, k = Deg_Gear['Woehler']['torqp'], Deg_Gear['Woehler']['k']

Define Woehler for Damage tooth_i

N1 = neol - n0
torq = np.linspace(T1*0.5, T1*1.5, 10)
N = N1 * np.power((torq / T1), -1*k)

plt.plot(N, torq), plt.scatter(N1, T1, c='r')
plt.xscale('log'), plt.yscale('log'), plt.xlabel('$Load Cyvles log(N_{EOL}-N_0)$'), plt.ylabel('Torque log(T)'), plt.legend(['Woehler Curve', '$N_{EOL} - N_{0}$'])
plt.show()

Get Damage Equivalent D* for all loads

damage_equivalents = []
for load in loads:
    N2 = N1 * np.power((load / T1), -1*k)
    damage = 1/N2
    damage_equivalents.append(damage)
print('Loads:  %s' % ('|'.join(['  %.3f  ' % (load) for load in loads])))
print('D\'s:    %s' % ('|'.join([' %.3e ' % (de) for de in damage_equivalents])))

Loads:    195.000  |  200.000  |  205.000  
D's:     1.411e-07 | 1.840e-07 | 2.385e-07

Repeat Damage Equivalent D* for ΔN load cycle

delta_n = int(np.floor(curr_cycle - prev_cycle))
repeated_damage_equivalent = gf.repeat2no_values(np.array(damage_equivalents), delta_n)

print('\u0394N = %i' % (delta_n))
print('D* Shape: %s' % (str(repeated_damage_equivalent.shape)))

ΔN = 73
D* Shape: (73,)

Calculate ΔD = ∑D*

delta_d = np.sum(repeated_damage_equivalent)
print('\u0394D = \u2211 D* = %.3e for \u0394N = %i load cycles' % (delta_d, delta_n))

ΔD = ∑ D* = 1.367e-05 for ΔN = 73 load cycles

8. Calculating current D

D_p = D_p-1 + ΔD

curr_damage = prev_damage + delta_d
print('D(p) = D(p-1) + \u0394D = %.3e' % (curr_damage))

D(p) = D(p-1) + ΔD = -1.028e+00

9. Calculating a_p

Using: Damage Pitting Dependency: a(D(N))

a(D(N)) is given for each tooth

Degradation-Vibration Dependency Element Definition

Module Methods Connection Vibration and Degradtion:

Getting Loads from Torque Signal for Gear Degradation

Translating Pitting Size into Vibration

Gear Element

Keyword Attributes:

signal: Nonstationary Signals
fc_factor: Nonstationary Signals
bw_factor: Nonstationary Signals
bwr_factor: Nonstationary Signals
scale_method: Scale Method to scale Amplitude based on pitting size(see Torque Influence Method as reference)
scale_attributes: Attributes regarding Scale Method to (see Torque Influence Attributes as reference)
torq_influence: If True Torque Influence will be taken into account in the same way as in vibration definition
noise_method: Method to create Signal Noise (repeat methods are not working)
noise_attributes: Attributes regarding the Method to create Signal Noise
t2t_factor: If 1 loads are calculated without any overlap between two tooh and all loads are considered. If t2t_factor > 1 there is a overlap of loads considered for each tooth

GearDegVibDict = {'signal': 'gausspulse',                                # Signal type for gear
                   'fc_factor': 2*rotational_frequency_in,                                      # fc = frequency * fc_factor (see gauspulse definition)
                   'bw_factor': 0.5,                                    # see gauspulse definition
                   'bwr_factor': -6,                                    # see gauspulse definition
                   'scale_method': 'linear',                            # Scale Method (See Torque Influence Method)
                   'scale_attributes': {'scale_min': 0,                 # Attributes regarding Scale Method for gear signal (see Torque Influence Method)
                                       'scale_max': 1,
                                       'value_min': 0,
                                       'value_max': 4,
                                       'exponent': 2},
                   'torq_influence': True,                              # If True Torque Influence will be taken into account in the same way as in vibration definition
                   'noise_method': 'gaussian',                          # Noise Method
                   'noise_attributes': {'mu': 0, 'sigma': 0.005},       # Attributes regarding Noise Method for
                   't2t_factor': 1
                   }

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__pictures		__pictures
gearbox		gearbox
.gitignore		.gitignore
LICENSE		LICENSE
README.ipynb		README.ipynb
README.md		README.md
gearbox_functions.py		gearbox_functions.py

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Controls

Accumulated Signal

Bearing 1 Signal

Bearing 2 Signal

Bearing 3 Signal

Bearing 4 Signal

Degradation Signal

Gear Signals

Degradation Gear In

State 0 Parameter (Ref. Torque: 200.000 Nm)

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 0)

Pitting Growth (until load cycle 0)

Degradation Gear Out

State 0 Parameter (Ref. Torque: 200.000 Nm)

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 0)

Pitting Growth (until load cycle 0)

Degradation Gear In

State 0 Parameter (Ref. Torque: 200.000 Nm)

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 6000000)

Pitting Growth (until load cycle 6000000)

Degradation Gear Out

State 0 Parameter (Ref. Torque: 200.000 Nm)

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 3142857)

Pitting Growth (until load cycle 3142857)

Degradation Gear In

State 0 Parameter (Ref. Torque: 200.000 Nm)

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 10000000)

Pitting Growth (until load cycle 10000000)

Degradation Gear Out

State 0 Parameter (Ref. Torque: 200.000 Nm)

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 5238095)

Pitting Growth (until load cycle 5238095)

Degradation Gear In

State 0 Parameter (Ref. Torque: 200.000 Nm)

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 9000000)

Pitting Growth (until load cycle 9000000)

Degradation Gear Out

State 0 Parameter (Ref. Torque: 200.000 Nm)

State 0 Degradation Model Plot (Ref. Torque: 200.000 Nm)

Damage Accumulation (until load cycle 4714285)

Pitting Growth (until load cycle 4714285)

Controls

Accumulated Signal

Bearing 1 Signal

Bearing 2 Signal

Bearing 3 Signal

Bearing 4 Signal

Degradation Signal

Gear Signals

Gear Element

Bearing Element

Element Method

Amplitude Method

Noise Method

Torque Method

Gear Element

Bearing Element

Chances

PDF Degradation

Woehler Curve

GridSearch

1. Define Degradation Dictionary

2. Draw (tooth, a0, n0, aeol, neol) Pairs for all teeth considering chances

3. GridSearch for all failing teeth to get individual degradation function

4. Transform Degradation to Damage D

5. Pitting Size and Damage Dependency

6. Defining State0

2. Draw (tooth, a₀, n₀, a_eol, n_eol) Pairs for all teeth considering chances

9. Calculating a_p