passenger car gearbox

1. Comprehensive Reliability Model
of a
Passenger Car Gearbox
Dipl.-Ing. T. Kamper*1
Dr.-Ing. D.H. Hwang2
, Dipl.-Wirt.-Ing. B. Juretzki1
,
Stephan Neumann, M.Eng.3
, Lothar Wöll, M.Sc.3
1IME Aachen GmbH Institut für Maschinenelemente und Maschinengestaltung,
Mathieustraße 30, 52074 Aachen, Deutschland
2Hyundai Motor Company, Transmission Research Lab, Hwaseong, Südkorea
3Institut für Maschinenelemente und Maschinengestaltung, Schinkelstraße 10, 52062
Aachen, Deutschland

3. Comprehensive Reliability Model of a Passenger Car Gearbox
Contents
1 Abstract ............................................................................................................... 1
2 Introduction......................................................................................................... 1
3 Main section ........................................................................................................ 2
3.1 Load determination....................................................................................... 4
3.1.1 Dynamic model................................................................................ 5
3.1.2 Validation......................................................................................... 6
3.1.3 Gear-Shift-Test................................................................................ 7
3.2 Reliability Model ........................................................................................... 8
3.3 Results ......................................................................................................... 9
4 Summary ........................................................................................................... 10
5 Bibliography...................................................................................................... 12

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1 Abstract
The paper focusses on the development of a comprehensive reliability model of a pas-
senger car gearbox including the effect of the dynamic oscillation behavior of the sys-
tem during operation. Recently, the passenger car gearbox is getting more sophisticat-
ed to achieve more speedsteps and is operated under severe condition like higher
speed, higher torque as well as extreme load changes. Thus, there is a need to predict
the reliability of gearbox more precisely at the early stage of development which could
be crucial for saving time and cost. The consideration of the dynamic loads instead of
quasi-static loads during the examination of system’s reliability gives the advantage of
more detailed and precise results. Thus a dynamic oscillation model is built to calculate
the dynamic loads on components’ level based on driving cycles and these loads are
used as input data for the components’ reliability models. The oscillation model’s level
of detail is adapted to the amount of data, which is available during the conception of
the gearbox. Hence it is possible to predict the reliability of the system more in detail at
an early stage of the development process and thus identify conceptual weak-points or
evaluate alternative designs. The dynamic model was validated by measurements at a
passenger car manual gearbox with 6 speeds. The developed method is transferable
to other types of gearboxes though.
The modular structure of the models allows on the one hand to adapt the dynamic
model’s level of detail as soon as there is more precise data of the gearbox available,
which gives the opportunity to achieve more optimized results for the different stages
of development respectively. On the other hand the reliability model of each compo-
nent can be replaced independently in accordance with the development stage.
2 Introduction
Thinking of technical systems, their reliability is one of the most important properties
[BER04]. Thus, according to Naunheimer it is a superordinated development goal
[NAU07].
In automotive sector, frequently the breakdown statistics of automobile associations
are used to evaluate the reliability from cars. A limitation of the significance of such
statistics is, that they only count failures that lead to a breakdown. Similarly the mean-
ing of technical inspection association’s reports is limited, because they only count the
failures of safety relevant components.
The actual analysis of the CG Car-Garantie AG however gives a quite comprehensive
overview, because the company is one of the biggest car warranty insurances and can
evaluate the data of more than a million warranty contracts.

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Figure 1: Damage adjustment sum of new cars in 2015 [CAR15]
The comparison of the damage adjustment sum for different components of new cars
in 2015 (see Figure 1) shows a percentage of 13.2% of the overall damage adjustment
sum for gearbox failures. Compared to other components, the gearbox, which is in the
focus of this study, takes the third place right behind the engine and the fuel system.
This demonstrates the need for a trustworthy method to model reliability of a passen-
ger car gearbox already during development. The gearbox itself can be regarded as a
complex system of many components with different failure modes. To provide a valua-
ble output a comprehensive reliability model has to consider the loads and failure
modes of the different components to derive component’s failure probabilities that can
be combined to the system’s reliability.
3 Main section
The importance of reliability analysis on system’s level already in conceptual phase
has been shown in the previous section. The general approach of system’s reliability
analysis can be separated into the steps shown in Figure 2. For all the steps it is im-
portant to take the influence of system’s properties onto component’s level and vice
versa into account.

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Figure 2: Steps in Reliability Modeling Process
The tasks to be performed to analyze system’s reliability can be arranged into two
groups named “Load” and “Reliability”. The aim of the whole process is to estimate the
system’s failure probability based on system’s properties such as the designated use
and the design. Thus based on the input data a suitable load cycle has to be chosen
and local loads acting on the components have to be determined from a system analy-
sis to take into account all interdependencies between the components. These loads
are used to derive load collectives that are the input data for the reliability analysis on
component’s level. The resulting failure probabilities for the components are combined
to the system’s failure probability in the last step.
For the particular tasks of the process, different methods can be applied dependent on
the available data and the required detail level. Figure 3 shows an overview of exem-
plary methods in a Morphological Box.
Figure 3: Morphological Box – System’s Reliability Analysis
The presented method follows a modular approach, which gives the opportunity to ex-
change single modules with respect to:
 the necessary accuracy of the results
 the development status of the gearbox and thus the available amount of data
 the latest state of the art of the different methods

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The chosen methods are marked in Figure 3 and will be introduced in the following
sections.
The approach was applied to the example of a passenger car manual gearbox with 6
speeds which was also available for a measurement campaign on a dynamic test rig at
IME. Thus it was possible to validate the approach, in particular in the first part of load
determination.
3.1 Load determination
There are different methods available for the task of load determination. They can be
grouped in experimental methods, simulative methods and analytical methods. Fur-
thermore there are approaches, which combine the different methods. For example
global loads can be measured on system’s level. These measurements can then pro-
vide input data for analytical methods, which are used to derive the local loads on
component’s level. This is a common approach, because the measurement of loads on
component’s level would lead to high effort due to the amount and costs of required
sensors and telemetry. The calculation of quasi static component’s load based on
global loads using analytical methods however is quite fast.
The choice of the suitable method depends on:
 Expected results (input for component’s reliability models)
 Status in design process (available database, prototype)
In this case the expected results are dynamic loads on component’s level at an early
stage in the design process, were it has to be assumed that no prototype and only a
rough design is available. Thus a simulative approach was chosen. Among the simula-
tive methods different levels of detail are available:
 Torsional vibration analysis (1 DOF rotation)
 Torsional vibration analysis with bearings-extension (1 DOF rotation, 4 DOF tilt-
ing and radial displacement)
 Multibody Simulation (complete 6 DOF rotation and displacement)
 Elastic Multi-Body-Simulation (complete 6 DOF, elastic bodies by FE-extension)
Since the main excitation in the gearbox is in the rotational degree of freedom but still
the dynamic loads at the bearing should be investigated, the torsional vibration analy-
sis with bearings-extension was chosen.
This approach has a low amount of necessary data and the modeling process is fast.
Due to a lumped-mass approach, which is the usual modelling approach for torsional
vibration models, the model is geometrically independent and the effect of variations of
stiffness or inertia can be evaluated easily. This is an important benefit for analysis
during early design stage.
The dynamic model is described in section 3.1.1. Section 3.1.2 gives information about
the measurement campaign as well as the validation of the results.

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3.1.1 Dynamic model
In this section, an overview of the model is given. As mentioned above, the target sys-
tem is modeled using a torsional vibration model with bearings extension. This type of
model includes the elasticity of shafts only in rotational degree of freedom but their
mass moments of inertia and masses are considered in all directions. Furthermore the
gear mesh forces are calculated in three directions and the bearings’ stiffnesses are
included in the model. Thus the shafts are allowed to tilt in the bearing seat. With this
approach it is possible to evaluate the dynamic loads on the bearings. For the model
the Software DRESP (DrehSchwingungsProgram) was used [JAC09]. Figure 4 shows
the DRESP model of the transmission used in this study.
Figure 4: Dynamic Model
Since the dynamic model focusses on the extraction of dynamic loads on the compo-
nents, the major excitations, which cause the vibration in the transmission, have to be
considered. As well known, there are basically two vibration sources in the transmis-
sion of the vehicle, namely the intermittent combustion of the engine and periodical
variation of the stiffness of the gear mesh.
To simulate the excitation of the combustion engine, a generic four-stroke four cylinder
engine model is used. The engine model is controlled with respect to a time dependent
target speed which is given by the NEDC driving mode. The model is loaded with ap-
proximate vehicle inertia and a speed-dependent driving resistance.
The excitation caused by the variable gear mesh stiffness is characterized with Fourier
coefficients gained from an external calculation based on a finite-elements-approach
dependent on the geometry of teeth and gear body.

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The bearing stiffness is calculated according to PALMGREN and HARRIS [PAL64,
HAR91] using an internal module of the software DRESP.
The shafts are modeled as lumped mass models with a torsional stiffness. In other di-
rections they remain rigid. The inertia is modeled in all directions though.
A friction element is applied to simulate the clutch and the synchronizers which ena-
bles the smooth start at the beginning of the driving and also for the gear shift respec-
tively.
The gearbox model includes the six speed gear pairs, the differential gear set and
eight bearings in total.
Overall, the input data is the target speed and the output is the resulting torque and
forces in the drivetrain. To provide data for the reliability calculations (see section 3.2),
local rotational speeds, torques and the forces acting on the bearings are exported.
3.1.2 Validation
To validate the output of the dynamic model a measurement campaign was conducted
on a 250 kW electrical driven test rig. The experimental set up is shown in Figure 5.
Figure 5: Experimental set up
Beside of the external loads and system responses like torque and rotational speed on
both input and output-shaft, gearbox-internal values like rotational speeds of two gears
as well as the strain of one gearwheel were measured. Furthermore, the temperature
was measured at nine positions inside the gearbox. Additionally the acceleration in
three directions was recorded at 4 positions, which were located on the gearbox hous-
ing close to the bearings (see Figure 6).
The measurement campaign included run ups for all gears at three different load levels
as well as constant operating points of the gearbox. In addition, gear shift tests were

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performed (see section 3.1.3). In order to realize this tests, a hydraulic system to acti-
vate the clutch and an actuator for the gear shift was installed on the test rig.
To ensure comparability of measurement and simulation the dynamic model of the
gearbox (see section 3.1.1) had to be included into a dynamic model of the test rig in-
stead of the car model which is used for the load determination.
Figure 6: Run up measurement 50% maximal torque
Figure 6 gives an example of the validation campaign. The torsional eigenfrequencies,
that can be identified in the measured run up show a good fit with the simulated tor-
sional eigenfrequencies. Beyond the eigenfrequencies, the system response was vali-
dated using amplitudes of internal and external rotational speeds. The results of the
validated dynamic model are used as an input for the reliability model described in sec-
tion 3.2.
3.1.3 Gear-Shift-Test
Since not all dynamic effects of the gearbox can be included in the model with reason-
able effort, specified load measurements can offer an added value the simulated loads.
In this case the dynamic torque during gear shift was measured. In order to get the
most valuable results, strain gages were applied on the gear body of gear 3. Since the
place of the gear mesh changes in relation to the place of strain measurement, the
strain results show a periodic variation during rotation of the gear loaded with constant
torque. Thus the calibration factor K, which is used to calculate the dynamic torque
based on the strain, shows also periodic variation depending on the angle of rotation of
the wheel. The calibration factor was measured for 12 positions of the gear and the
result was refined by means of a Finite-Elements-Model of the gear. The rotational po-
sition of the gear was measured using an inductive proximity sensor.

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Figure 7: Torque Measured During Gear Shift on Gear Body
Figure 7 shows the evaluated measurement. The measured torque is normalized using
the maximal torque provided by the engine. Clearly the time of gear shift as well as the
time of clutching in can be identified in the graph. It is easy to see that the process of
clutching in causes a relevant load peak in the drive-train.
3.2 Reliability Model
The results of the dynamic load determination described in the previous chapter (see
section 3.1) are the input data for the reliability model, which will be discussed in the
following section. The overall result of the reliability model is a Failure Distribution F(t)
that describes the likelihood of system’s failure after a certain period of time.
In a first step the failure distributions for the different components of the system have
to be evaluated. For this study using the example of a passenger’s car gearbox bear-
ings, seals, gears, shafts and synchronizers are taken into account because other
components are not considered relevant for the reliability of the system [NAU07]. The
dynamic model is used to evaluate the dynamic loads acting on these components.
For every component to be considered there are different failure models existent ex-
cept for clutches respective synchronizers and seals. Although for these component
are no verified methods available, the lifetime of synchronizers can be estimated by
calculating the wear volume of the friction surfaces which depends on the performed
friction work. By predefining a bearable wear volume, the lifetime can be determined
[HEN10].
For seals, the lifetime is hard to quantify due to the very complex tribological system.
As a rough estimate the lifetime is approximated by using an unverified method only
considering thermal degradation [HAA10].
In contrast to the previous mentioned components lifetime prediction for bearings,
gears and shafts is available and fairly straightforward. Bearings are the only mechani-
cal component that has its lifetime calculation, as well as the distribution available di-

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rectly from a standardized calculation [ISO281]. Therefore the reliability calculation of
bearings is considered the most assured of all components.
Failure of gears can arise to due to tooth fractures, pitting or scuffing. Scuffing is not
considered in this calculation as they usually don’t occur within the predefined operat-
ing conditions [BOO11]. Pitting affects both tooth sides. The calculation of a gear’s
bearable load is documented in the DIN standard [DIN3990].
Guided by the standard [DIN743] the fatigue calculation of shafts is available as well.
By utilizing the Miner linear damage accumulation hypothesis, the calculation of the
damage and the lifetime is achievable.
To evaluate the reliability of the entire system, the failure distributions of the compo-
nents need to be combined by a system theory. To do so, the general conditions have
to be defined to choose a suitable system theory among the available theories that
differ depending on the system structure, failure behavior and whether the components
are repaired or replaced in case of a failure during their lifetime. For the approach in
this paper Boole’s System Theory was chosen as repair or replacement of components
is not intended. Furthermore the failures of all components are described by the
Weibull Distribution, because it was shown that this distribution fits the failure distribu-
tion of mechanical components best [BER04]. With those assumptions the require-
ments for the application of the chosen system theory are met and the system’s relia-
bility can be calculated by Eq. 1, as long as no component is used redundantly, were n
is the number of failure distributions of all components.
𝐹𝑆𝑦𝑠 = 1 − ∏(1 − 𝐹𝑖)
𝑛
𝑖=1
Eq. 1
In the course for the evaluation of the reliability of the examined car transmission an
easy-to-adapt modular simulation tool was created. The simulation model is divided to
represent all gear steps. Eventually the damages caused by each gear step are accu-
mulated individually for each component and the lifetime and reliability are calculated.
3.3 Results
To give an example of how the consideration of dynamic effects influences the predict-
ed lifetime of the gearbox, one has to choose a representative load cycle. The NEDC
(New European Driving Cycle) applies to all cars and light commercial vehicles and is
used for the verification of compliance with emission limits and the determination of
consumption values. It is chosen in this study as an example of a standardized load
cycle.
Figure 8 demonstrates the importance of the consideration of dynamic effects following
the method introduced in this study for accurate results in reliability analysis. The com-
parison of the lifetime prediction according to the new developed method with the life-

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time prediction using quasi static loads shows a significant influence of the dynamic
loads on the overall lifetime of the system.
Figure 8: Comparison of lifetime-results
To evaluate the highest relevant frequency for dynamic loading, a convergence study
was conducted with increasing sampling frequency. Figure 9 shows a big increase of
accuracy raising the sampling frequency from 10 Hz to 1000 Hz. Above 5000 Hz no
gain of accuracy can be detected. The predicted lifetime in Figure 9 is normalized us-
ing the lowest value.
Figure 9: Convergence study
4 Summary
The current paper discusses the development of a comprehensive reliability model of a
passenger car gearbox including the effect of the dynamical behavior of the system
during the operation.

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The method is presented and validated with the example of a conventional passenger
car gearbox with 6 gears. It is adaptable to other gearboxes though. The method fol-
lows a modular approach. Thus the single modules can be exchanged depending on
the given database and the stage in the gearbox’s development process respectively.
The method is separated in two main modules namely “dynamic model” and “reliability
model”. The dynamic model provides the dynamic component loads as an input for the
reliability model. For both modules the considered components, parameters and ef-
fects can be varied.
In this paper for the “dynamic model” a hybrid approach was chosen which includes
torsional vibration as well as bearing forces. For the “reliability model” the following
components are considered as relevant:
 Shafts
 Bearings
 Seals
 Gears
 Synchronizers
The study has shown the importance of the consideration of component’s dynamic
loads. In comparison to the consideration of global, quasi-static-loads according to the
state of the art, the new method shows a shorter durability. Thus it should not be ne-
glected.

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5 Bibliography
[BER04] Bertsche, B.; Lechner, G.: Zuverlässigkeit im Fahrzeug- und
Maschinenbau. Ermittlung von Bauteil- und System-
Zuverlässigkeiten. 3., überarbeitete und erweiterte Auflage.
Springer, Berlin, 2004.
[BOO11] Boog, M.: Steigerung der Verfügbarkeit mobiler Arbeitsmaschi-
nen durch Betriebslasterfassung und Fehleridentifikation an
hydrostatischen Verdrängereinheiten. Dissertation. Karlsruhe,
KIT, 2011.
[CAR15] CG Car-Garantie Versicherungs-Aktiengesellschaft: Aussen-
spiegel 2-2015,
(http://www.cargarantie.com/fileadmin/user_upload/Presse/DE/
de_de_de_aussenspiegel_2015_02.pdf)
(26.09.2016).
[DIN3990] DIN – Deutsches Institut für Normung: DIN 3990: Tragfähig-
keitsberechnung von Stirnrädern. 1987.
[DIN743] DIN – Deutsches Institut für Normung: DIN 743: Tragfähig-
keitsberechnung von Wellen und Achsen. 2012.
[DLR] German Aerospace Center (DLR), Institute of Transportation
Systems.
(http://sumo.dlr.de/userdoc/Tools/Visualization.html)
(29.09.2016).
[HAA10] Haas, W., Hörl, L., Klein, B.: Betrachtungen zur Zuverlässigkeit
und Lebensdauer von Hydraulikdichtungen. Stuttgart, 2010.
[HAR91] Harris, T. A.: Rolling Bearing Analysis, Wiley – Interscience
publication, 3rd edition, New York, 1991.
[HEN10] Hensel, M., Pflaum, H.: Lebensdauer Lamellenkupplungen.
Abschlussbericht zum Forschungsvorhaben FVA 515 I. For-
schungsvereinigung Antriebstechnik e. V., Frankfurt, 2010.

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[ISO281] ISO – International Organization for Standardization: ISO 281:
Rolling bearings – Dynamic load ratings and rating life. 2010.
[JAC09] [JAC09] Jacobs, G.; Schelenz, R.; Augustino, R.; Kube, A.; Möller,
D.: Benutzerhandbuch zum Drehschwingungsprogramm DRESP,
Programmversion DRESP 12, Aachen, (2009)
[NAU07] Naunheimer, H.; Bertsche, B.; Lechner, G.; Ryborz, J.; Novak,
W.: Fahrzeuggetriebe: Grundlagen, Auswahl, Auslegung und
Konstruktion. 2., bearbeitete und erw. Aufl., Springer, New
York, 2007.
[PAL64] Palmgren, A.: Grundlagen der Wälzlagertechnik, Franckh, 3.
Auflage, Göteborg, 1964.