This excecise aims to study the dynamics of a motor vehicle, in particular it is considered a Land Rover Defender 90. First, using appropriate software, the dynamic behavior of the vehicle was analyzed with a conventional propulsion system and, subsequently, the same model was re-analyzed with a hybrid configuration in series configuration. At a later time a FEM analysis was carry out for fatigue dimensioning of the rear propshaft of the vehicle.

1. SIMULATION OF THE DYNAMIC
MODEL OF A VEHICLE AND FEM
ANALYSIS ABOUT ITS DRIVE SHAFT
Students:
Rosario Coppolino
Pietro Foti
Antonio Frazzica
Teachers:
Prof. Antonio Galvagno
Prof. Giacomo Risitano

2. SUMMARY
• Introduction
• Aims
• Materials and methods
• Theory and calculations
 Vehicle dynamics
 Configuration with a conventional system
 Configuration with an hybrid system
• Results
 Configuration with a conventional system
 Configuration with an hybrid system
 Comparison between the two types of system
• Model setup on Ansys APDL
• Transient Analysis
• Fatigue analysis
• Conclusions

3. INTRODUCTION
This work aims to study the dynamics of a motor vehicle, in particular it is considered a Land Rover
Defender 90. First, using appropriate software, the dynamic behavior of the vehicle was analyzed
with a conventional propulsion system and, subsequently, the same model was re-analyzed with a
hybrid configuration in series configuration. At a later time a FEM analysis was carry out for
fatigue dimensioning of the rear propshaft of the vehicle.

4. AIMS
The aim of the first part was to verify that the respective propulsion systems were able
to satisfy the power demand necessary to perform some standard driving cycles.
For each driving cycle consumption and emissions were analyzed using experimental
data obtained on the test bench.
In the second part, a fatigue dimensioning was conducted by using FEM analysis data,
the rainflow counting method, the Wohler diagram and the Miner curves.

5. MATERIALS AND METHODS
The used material is the AISI 4340 Steel,
normalized, 50 mm (2 in.) round.
Elemento % Elemento %
C 0.37-0.4 Fe 95.2-96.33
Si 0.15-0.30 Mo 0.20-0.30
Mn 0.60-0.80 Ni 1.65-2.0
P 0.035 Cr 0.7-0.9
S 0.04
Densità (ρ) 7850 kg/m3
Modulo di Young (E) 200 GPa
Modulo di Poisson (�) 0.29
Tensione di snervamento (σy) 786 N/mm2
Tensione a rottura (σr) 1200 N/mm2
Durezza Vickers 361 HV

6. THEORY AND CALCULATION:
VEHICLE DYNAMIC

7. THEORY AND CALCULATION:
VEHICLE DYNAMIC

8. THEORY AND CALCULATION:
VEHICLE DYNAMIC
The Cooper's empirical formula was implemented for the
calculation of the front and rear friction coefficients.
Considering that the friction coefficient depends on:
• Tire pressure
• Aerodynamic resistance
• Relative sliding between tire and road
• Vehicle speed

9. THEORY AND CALCULATION:
VEHICLE DYNAMIC
Since the vehicle has a four-wheel drive, it was necessary to design the front and rear differential in
order to obtain an equal speed of the rear and front wheels
is the radius of the front wheels
is the radius of the rear wheels
is the front torque partition coefficient. In this case is 0.4

10. THEORY AND CALCULATION:
VEHICLE DYNAMIC
To compute the torque (power) requested from the engine shaft the formulas used was:
is the efficiency of i-th mechanical component
Torque
Angularvelocity

11. THEORY AND CALCULATION:
VEHICLE DYNAMIC

12. THEORY AND CALCULATION:
VEHICLE DYNAMIC

13. THEORY AND CALCULATION:
CONFIGURATION WITH A CONVENTIONAL SYSTEM
After obtaining the torque-time and angular-time curves required by the particular driving cycle, we choice
the thermal engine that can satisfy the power requirements at any time.
The thermal engine chosen is a Merceds
OM611 2.2 liters with 4 valves able to
erogate a maximum power of 92 kW at
4200 rpm.
Angular velocity
Maximumtorque

14. THEORY AND CALCULATION:
CONFIGURATION WITH A CONVENTIONAL SYSTEM
For each driving cycle we calculated the fuel consumption and emissions (HC, CO, NOx and PM).
Here fuel consumption and CO are reported as examples.

15. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
After the configuration with conventional
engine, the hybridization of the motor
vehicle has been carried out. The aim is to
operate a down sizing of the thermal engine
in order to reduce emissions and fuel
comsuption.
The vehicle has been made hybrid by
adopting a series configuration.

16. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
To implement in the best possible way
the control unit that can be able to
manage the power flows between the
various components, first of all it is
necessary to consider the possible
driving regimes that the vehicle can face

17. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
In the modeling of the control unit via Simulink, the
control of the electric motor, the internal combustion
engine and the batteries is carried out using the values
0.1 and 2
0 1 2
Electric motor Generation Motor Off
Internal combustion engine Off On
Batteries Discharging Recharging Off
With regards to power flows, it was decided to
consider the powers as positive and negative
according to the diagram on the side
Positive Negative
Power electric
motor
Motor Generation
Power batteries Recharging Discharging

18. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
To determine the control parameters, the control unit refers to a series of parameters:
• SOC
• Power that can be supplied by the batteries compared to the required power
• Power that can be supplied by the thermal engine compared to the required power
• Previous batteries control parameters
• Vehicle speed
• Vehicle acceleration

19. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
how the control unit chooses the control parameter for batteries in the normal operating mode

20. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
how the control unit chooses the operating mode of the vehicle

21. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
for example, for a city driving cycle, the control unit communicates the following control parameters
Torque
Speed[m/s]
Time (seconds)
Electricmotorcontrolparameter
Batterycontrolparameter
Internalcombustionenginecontrolparameter

22. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
The engine used in the hybrid configuration was imported from the FC_CI60_emis.m file. The engine in
question is a Mercedes 1.7L Diesel Engine.
A further choice made by the control unit is the
regime to which the thermal engine is to be
operated. Two different schemes are possible:
• a maximum efficiency regime;
• a maximum power regime.
This last choice is made only when
.
In this case the control unit verify if
if it is true, the thermal engine works at the maximum efficiency rotation speed (126 rad/sec).
If it is false the thermal engine works at the rotation speed of maximum power (346 rad/sec).MaximumTorque
Angular velocity

23. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
The electric motor used in the hybrid configuration was imported from the MC_AC150_Focus_draft.m file.
It can work as electric generator or as electric motor.
MaximumTorque
MaximumTorque
Angular velocityAngular velocity

24. THEORY AND CALCULATION:
CONFIGURATION WITH AN HYBRID SYSTEM
To study the behavior of the accumulators, it has been chosen a simplified schematization.
In such a schematization the battery is represented as an ideal voltage generator, which supplies a voltage
equal to the vacuum voltage of the accumulators , placed in series with the internal resistance of the energy
storage system
Both and assume different value dipending by SOC
Trought the SOC and the value of , , e la it is possible to
calculate the current erogated by the battery that
allowed to calculate the new value of SOC.
The used formula is:

25. RESULTS
CONFIGURATION WITH A CONVENTIONAL SYSTEM
For each driving cycle, the graphs relating to consumption and emissions are shown. Moreover, for each graph the
area under the curves was calculated to get an idea of engine efficiency in every situation.
The driving cycle under examination (ECE) shown in the figure has a duration of 820 seconds and, after solving the
equations of motion, requires the following torque characteristic.
Speed
Torquerequired

26. RESULTS
CONFIGURATION WITH A CONVENTIONAL SYSTEM
Fuel consumption and emissions of the 2.2 liters engine used in the conventional configuration are shown in the
graphs
Fuelconsumption

27. RESULTS
CONFIGURATION WITH A CONVENTIONAL
SYSTEM

28. RESULTS
CONFIGURATION WITH A CONVENTIONAL SYSTEM
Fuel
consumption
[km/lt]
CO
[g/km]
HC
[g/km]
Nox
[g/km]
PM
[g/km]
12.13 0.895 0.280 0.514 0.023

29. RESULTS
CONFIGURATION WITH A CONVENTIONAL SYSTEM
The driving cycle under consideration (EUDC) shown in figure has a duration of 400 seconds and, once the equations
of motion are resolved, requires the following torque characteristic
Fuel
consumption
[km/lt]
CO
[g/km]
HC
[g/km]
Nox
[g/km]
PM
[g/km]
16.15 0,095 0,037 0,073 0.004
Torquerequired
Speed

30. RESULTS
CONFIGURATION WITH A CONVENTIONAL SYSTEM
The driving cycle under examination (NEDC) shown in figure has a duration of 1220 seconds and, once the equations
of motion are resolved, requires the following torque characteristic.
Consuption
[km/lt]
CO
[g/km]
HC
[g/km]
Nox
[g/km]
PM
[g/km]
14.42 0,396 0,121 0,217 0,011
Speed
Torquerequired

31. RESULTS
CONFIGURATION WITH A HYBRID SYSTEM
The driving cycle under examination (ECE) shown in the figure has a duration of 820 seconds and, after solving the
equations of motion, requires the following torque characteristic.
Speed
Torquerequired

32. RESULTS
CONFIGURATION WITH A HYBRID SYSTEM
Fuel consumption and emissions of the 1.7 liters engine used in the hybrid configuration are shown in the graphs.
To have a right representation of the curves we have considered, after each driving cycle, the recharge of the batteries
at the SOC’s initial value.
Consumption

33. RESULTS
CONFIGURATION WITH A HYBRID SYSTEM

34. RESULTS
CONFIGURATION WITH A HYBRID SYSTEM
As can be seen from the graphs, compared to those relating to the conventional configuration, these are
much more regular and have less variations with respect to time.
Consumption
[km/lt]
CO
[g/km]
HC
[g/km]
Nox
[g/km]
PM
[g/km]
29.28 0,007 0,002 0,039 0,001

35. RESULTS
CONFIGURATION WITH A HYBRID SYSTEM
The driving cycle under consideration (EUDC) shown in figure has a duration of 400 seconds and, once the equations
of motion are resolved, requires the following torque characteristic
Consumption
[km/lt]
CO
[g/km]
HC
[g/km]
Nox
[g/km]
PM
[g/km]
16.86 0,020 0,006 0,057 0,002
Speed
Torquerequired

36. RESULTS
CONFIGURATION WITH A HYBRID SYSTEM
The driving cycle under examination (NEDC) shown in figure has a duration of 1220 seconds and, once the equations
of motion are resolved, requires the following torque characteristic.
Consumption
[km/lt]
CO
[g/km]
HC
[g/km]
Nox
[g/km]
PM
[g/km]
19.91 0,015 0,005 0,051 0,002
Speed
Torquerequired

37. RESULTS
COMPARISON BETWEEN THE TWO TYPES OF SYSTEM
Consumption
[g/kW]
CO [g/kW] HC[g/kW] NOx [g/kW] PM [g/kW]
Termic
config.
12.13 0.895 0.280 0.514 0.023
Hybrid conf. 29.28 0.007 0.002 0.039 0.001
Delta % -58.5 99.2 99.3 92.4 95.7
Consumption
[g/kW]
CO [g/kW] HC[g/kW] NOx [g/kW] PM [g/kW]
Termic
config.
16.51 0.095 0.037 0.073 0.004
Hybrid conf. 16.86 0.020 0.006 0.057 0.002
Delta % -2.1 78.9 83.8 21.9 50
Consumption
[g/kW]
CO [g/kW] HC[g/kW] NOx [g/kW] PM [g/kW]
Termic
config.
14.42 0.396 0.121 0.217 0.011
Hybrid conf. 19.91 0.015 0.005 0.051 0.002
Delta % -27.6 98.7 95.9 76.5 81.8
City driving cycle
Suburban driving cycle
Mixed driving cycle

38. MODEL SETUP ON ANSYS
Parametric model building.

39. MODEL SETUP ON ANSYS
Parametric model building.

40. MODEL SETUP ON ANSYS
Parametric model building.

41. MODEL SETUP ON ANSYS
SOLID 186:
• 20 nodes
• DOF: UX, UY, UZ.
Choice of elements type used for the mesh.
MASS 21:
1 nodes
DOF: UX, UY, UZ ,ROTX, ROTY, ROTZ.

42. MODEL SETUP ON ANSYS
Details of the mesh on the propshaft model.

43. MODEL SETUP ON ANSYS
Loads and constraints on the propshaft model.

44. MODEL SETUP ON ANSYS
Number of
elements
Von Mises
Stress [MPa]
189503 57,634
405354 57,489
685315 57,466
1028477 57,457
1405181 57,448
1879321 57,439
2340562 57,439
Results of sensitivity analysis.

45. TRANSIENT ANALYSIS
Torque and Von Mises tensions values
by cycle NEDC from 52 to 178 seconds.
Von Mises Stress
Torque

46. TRANSIENT ANALYSIS
Von Mises stress at time of 5 seconds.

47. TRANSIENT ANALYSISDetails of von Mises stress propshaft.

48. FATIGUE ANALYSIS
The counting cycle method used for the fatigue analysis is the rainflow (tankflow).

49. FATIGUE ANALYSIS
The fatigue life of the propshaft was verified trought Miner
and Manson curve.
VonMisesstress[MPa]

50. FATIGUE ANALYSIS
The propshaft can last for 250000 km.
Cycles
VonMisesstress[MPa]

51. CONCLUSIONS
The hybrid configuration was convenient in terms of fuel consumption and emissions compared to the
conventional configuration.
The only exception is due to the consumption of the extra-urban cycle where the difference between the
configurations is very low.
This can be explained by the fact that in an extra-urban cycle the power required to the thermal engine is more
regular, which translates into better efficiency. In this case the hybrid is disadvantaged due to multiple energy
conversions.
FEM analysis was carry out for fatigue dimensioning of the rear propshaft of the vehicle. It was
possible by using FEM analysis data, the rainflow counting method, the Wohler diagram and the
Miner curves.
Given the results of the fatigue check it is advisable to upsize the component

52. THANKS FOR
THE ATTENTION