modeling, simulation and correlation of drag losses in a ...1475473/...modeling, simulation and...

DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020

Modeling, Simulation and Correlation

of Drag losses in a Power Transfer

Unit of an All- Wheel Drive System

Balaji Srinivasan Venkatesan

KTH Master of Science Thesis TRITA-ITM-EX 2020:546

KTH Industrial Engineering and Management

Machine Design

SE-100 44 STOCKHOLM

i

Examensarbete TRITA-ITM-EX 2020:546

Modellering, simulering och korrelation av

dragförluster i en kraftöverföringsenhet i ett fyrhjulsdrivsystem

Balaji Srinivasan Venkatesan Godkänt

2020-09-30

Examinator

Ulf Sellgren

Handledare

Stefan Björklund

Uppdragsgivare

GKN Driveline Köping AB

Kontaktperson

Anders Sörensson

SAMMANFATTNING

En kraftöverföringsenhet (PTU) i ett fyrhjulsdriftsystem är en hypoidväxellådsöverföringsenhet som

fördelar kraften från växellådan till alla hjul i fordonet. Det rapporterade arbetet syftar till att öka

konfidensen i de analytiska beräkningsmetoderna för effektförlust genom testdatakorrelation och

genom att utveckla en 1D-simuleringsmodell som kan användas för att utvärdera dragförlusterna i

PTUn i tidiga designfaser.

För det första studeras analysmetoderna för att förutsäga friktionsförluster och plaskförluster på grund

av hypoidväxeln, rullager och tätningar nedsänkta i olja. Flera ”Drag Loss”-tester med olika

kombinationer av interna komponenter, lagerförspänningar och med / utan närvaro av olja utfördes

tidigare på PTU vid olika hastigheter och temperaturer utan pålagt moment. Effektförlusterna beräknas

i ROMAX Energy med olika analysmetoder tillgängliga i litteraturen för varje komponent i PTU. Sedan

separeras resultaten från dragförlusttesterna komponentmässigt för datakorrelation med de tidigare

utvärderade förlusterna. Baserat på datakorrelationen införs modifieringsfaktorer för alla

analysmetoder för att matcha de segregerade testresultaten.

Efterfrågan inom fordonsindustrin att minska tiden till marknaden är hög. Därför väljs simulering på

systemnivå som en lösning för att bedöma systemeffektiviteten i ett tidigt konceptdesignfas, vilket

sparar mycket tid och underlättar den detaljerade designen. 1D-simuleringsteknik används för att

studera PTUns totala effektförlust för att optimera dess design. Arbetet syftar till att utveckla en 1D-

systemmodell av PTU i ett kommersiellt verktyg som heter LMS AMESim, för att utvärdera enhetens

totala effektförlust. Inbyggda komponentmodeller från programvarubiblioteket används för att skapa

en skiss av en förenklad modell av det fysiska systemet. De totala effektförlusterna beräknade med

AMESim jämförs med effektivitetstestresultaten vid olika vridmomentnivåer och ROMAX-resultat.

Från korrelationen med testresultaten observeras att systemmodellen är korrekt och kan användas för

att förutsäga effektförlusterna i PTU i de tidiga designstadierna. Denna modell kan också användas för

att studera de viktigaste faktorerna genom känslighetsanalys av olika parametrar, vilket kan göras som

en förlängning av detta arbete.

Nyckelord: 1-D simulering, systemsimulering, ROMAX Energy, LMS AMESim, effektförlust,

hypoidväxel, kraftöverföringsenhet, effektivitet och dragförlusttester.

iii

Master of Science Thesis TRITA-ITM-EX 2020:546

Modeling, Simulation and Correlation of Drag losses in a Power Transfer Unit of an All-Wheel

Drive System


Approved

2020-09-30

Examiner

Ulf Sellgren

Supervisor

Stefan Björklund

Commissioner

GKN Driveline Köping AB

Contact person

Anders Sörensson

ABSTRACT

A Power Transfer Unit (PTU) of an All-Wheel Drive System is a hypoid gear transmission unit that

distributes the power from the vehicle transmission to all wheels of the vehicle. This thesis aims at

increasing the fidelity of the analytical power loss calculation methods through test data correlation and

develop a 1D simulation model that can be used to evaluate the drag losses in the PTU at early design

stages.

Firstly, the analytical methods to predict the frictional losses and oil churning losses due to the hypoid

gearset, rolling bearings and seals immersed in oil are studied. Several drag loss tests with different

combinations of internal components, bearing preloads and with/without the presence of oil were

previously conducted on the PTU at different speeds and temperatures at zero torque. The power losses

are computed in ROMAX Energy and Excel using different analytical methods available in the

literature for each component in the PTU. Then the results from the drag loss tests are segregated

component-wise for data correlation with the losses evaluated previously. Based on the data correlation,

modification factors are introduced for all analytical methods to match the segregated test results.

The demand in the automotive industry to reduce time to market is high. Hence, system-level simulation

was chosen as a solution to assess the system efficiency at early concept design stage, saving a lot of

time and aid the detailed design. 1D simulation technique is used to study the total power loss of the

PTU to optimize its design. The thesis is aimed at developing a 1D system model of the PTU in a

commercial tool called LMS AMESim, to evaluate the total power loss of the unit. Inbuilt component

models from the software library are used to build a sketch of a simplified lumped mass model of the

physical system. The model is simulated in a time domain temporal analysis. The total power loss

results simulated using AMESim are compared to the efficiency tests results conducted at different

torque levels and ROMAX results.

Comparisons between the simulations and test data shows that the system model is accurate and can be

used in predicting the power losses in the PTU in the early design stages. This model can also be used

to study the influential factors through sensitivity analysis of different parameters which can be done

as an extension to the current scope of this work.

Keywords: 1-D simulation, System simulation, ROMAX Energy, LMS AMESim, Power loss,

Hypoid gear, Power Transfer Unit, Efficiency and Drag Loss Tests

v

ACKNOWLEDGEMENTS

I would like to take this occasion to thank GKN Driveline Köping AB and my manager Karthik Pingle

for offering me the opportunity to carry out this work amidst COVID time. I would like to express my

gratitude to my supervisor at the company, Anders Sörensson, for being extremely supportive, helping

me to familiarize with the power loss tests, softwares and give constant feedback with my work. I would

like to thank the entire design and gear development team for helping me with several inputs and

suggestions over the course of my thesis. I would like to thank my supervisor Stefan Björklund for his

support, inputs and feedback throughout the thesis. Finally, I would like to thank my family for keeping

my mental strength stable during the COVID lockdown time while performing the thesis.


Stockholm, September 2020

vii

TABLE OF CONTENTS

SAMMANFATTNING ..................................................................................................................... i

ABSTRACT ................................................................................................................................... iii

ACKNOWLEDGEMENTS ................................................................................................................. v

TABLE OF CONTENTS .................................................................................................................. vii

NOMENCLATURE ......................................................................................................................... xi

Notations ................................................................................................................................................... xi

Abbreviations ........................................................................................................................................... xvi

1 INTRODUCTION.................................................................................................................... 1

1.1 Background ......................................................................................................................................... 1

1.2 Purpose ................................................................................................................................................ 1

1.3 Delimitations ........................................................................................................................................ 2

1.4 Method ................................................................................................................................................. 2

2 FRAME OF REFERENCE..................................................................................................... 3

2.1 Power Transfer Unit ........................................................................................................................... 3

2.1.1 Hypoid Gears........................................................................................................................... 3

2.1.2 Rolling Bearings ...................................................................................................................... 4

2.1.3 Radial Shaft Seals .................................................................................................................. 4

2.2 Power Losses ...................................................................................................................................... 5

2.2.1 Load Dependent losses ......................................................................................................... 5

2.2.2 Non- Load Dependent Losses .............................................................................................. 5

2.3 Power Loss Models ............................................................................................................................ 5

2.3.1 Radial Shaft Seals .................................................................................................................. 6

2.3.1.1 ISO14179-1 ............................................................................................................. 6

2.3.1.2 ISO14179-2 ............................................................................................................. 6

2.3.1.3 Parker ....................................................................................................................... 6

2.3.1.4 Linke ......................................................................................................................... 7

2.3.2 Rolling Bearings ...................................................................................................................... 7

2.3.2.1 ISO14179-1 ............................................................................................................. 7

2.3.2.2 ISO14179-2 ............................................................................................................. 9

2.3.2.3 Palmgren ................................................................................................................ 10

2.3.2.4 SKF Frictional Method.......................................................................................... 11

2.3.3 Hypoid Gears......................................................................................................................... 14

2.3.3.1 Load Dependent Power Losses .......................................................................... 14

2.3.3.2 Non- Load Dependent Power Losses ................................................................ 17

2.4 System Level Simulation ................................................................................................................. 21

viii

2.4.1 System Model ........................................................................................................................ 21

2.5 One-Dimensional Simulation ........................................................................................................... 22

2.5.1 Models and submodels ........................................................................................................ 23

2.5.2 Powertrain Library ................................................................................................................. 23

2.5.3 Causuality .............................................................................................................................. 23

2.6 Drag Loss Test .................................................................................................................................. 23

2.7 ROMAX Simulations ......................................................................................................................... 24

2.7.1 Bearing Force Calculation ................................................................................................... 24

2.7.2 Efficiency Calculation ........................................................................................................... 24

2.8 AMESim Bevel Gear Assembly ...................................................................................................... 25

2.8.1 Gear Mesh Forces ................................................................................................................ 25

2.8.2 Rolling and Slipping Losses ................................................................................................ 25

3 IMPLEMENTATIONS ...........................................................................................................27

3.1 Test Data Segregation ..................................................................................................................... 27

3.1.1 Seal Friction Loss Approximation ....................................................................................... 28

3.2 ROMAX Energy Simulation ............................................................................................................. 28

3.3 Power Loss Calculation ................................................................................................................... 31

3.4 Test Data Correlation ....................................................................................................................... 32

3.5 1-D Simulation ................................................................................................................................... 32

3.5.1 Model Simplification .............................................................................................................. 32

3.5.2 Model Building ....................................................................................................................... 33

3.5.2.1 Hypoid Gears ........................................................................................................ 34

3.5.2.2 Bearings ................................................................................................................. 35

3.5.2.3 Radial Shaft Seals ................................................................................................ 37

3.5.2.4 Bearing Force Model ............................................................................................ 37

3.5.3 Parametrization ..................................................................................................................... 41

3.5.3.1 Bevel Gear Assembly Parameters ..................................................................... 41

3.5.3.2 Bearing Parameters ............................................................................................. 41

3.5.3.3 Seals Parameters ................................................................................................. 42

3.5.3.4 Inertia and Compliance Parameters ................................................................... 42

3.5.3.5 Bearing Force Calculation Parameters .............................................................. 43

3.5.4 Simulation .............................................................................................................................. 43

4 RESULTS ..............................................................................................................................45

4.1 Test Data Correlation ....................................................................................................................... 45

4.1.1 Seal Loss ............................................................................................................................... 45

4.1.2 Bearing Loss .......................................................................................................................... 47

4.1.3 Gear Loss .............................................................................................................................. 49

ix

4.2 AMESim Power Loss........................................................................................................................ 49

5 DISCUSSION AND CONCLUSIONS ..................................................................................53

5.1 Discussion ................................................................................................................................... 53

5.2 Conclusions ................................................................................................................................. 55

6 FUTURE WORK ...................................................................................................................57

7 REFERENCES ......................................................................................................................59

APPENDIX A: DETAILED PROJECT PLAN ........................................................................61

APPENDIX B: RISK ASSESMENT ........................................................................................63

xi

NOMENCLATURE

The notations and abbreviations used during this project are described in this section.

Notations

a Load constant

Ag Arrangement constant for gearing

b Diameter constant

B Bearing width [mm]

b Face width [mm]

b0 Effective width [mm]

bw Face width in contact with mating element [mm]

C1 Mesh coefficient of friction constant

C1,2 Factors

Cch Churning Torque [Nm]

Cm Dimensionless drag torque

CSp Splash oil factor

Cw Parameter used in SKF model

D OD of element for gearing windage and churning[mm]

di Bearing bore diameter [mm]

dm Bearing mean diameter [mm]

dm Central reference diameter [mm]

do Bearing outside diameter [mm]

ds Shaft diameter [mm]

dv1, dv2 Reference diameter of virtual cylindrical gear [mm]

dva1, dva2 Tip diameter of virtual cylindrical gear [mm]

eh Oil thickness [mm]

Eeq Equivalent Young’s Modulus

E1 Young’s Modulus of driving gear

E2 Young’s Modulus of driven gear

F Total face width of gear or pinion [mm]

F Tangential force [N]

f0 Bearing dip factor

f1 Coefficient of friction

xii

f2 Factor depending on bearing design and lubrication

Fa Axial bearing load [N].

fA Parameter used in SKF model

fg Slipping coefficient

fg Gear Dip Factor

Fn Normal force [N]

Fnu Normal force per length unit [N/m]

Fr Froude Number

Fr Radial Bearing Load [N]

ft Parameter used in SKF model

g Gravity Acceleration [m/s2]

ɤ Centrifugal Acceleration

g1 Factor depending on direction of load in Palmgren model

gf Length of approach [mm]

Grr Geometric and Load dependent variable for rolling moment

Gsl Geometric and Load dependent variable for sliding moment

H Oil level [mm]

ham1, ham2 Mean addendum [mm]

hc Height of point of contact above the lowest point of the immersing gear

he, max Max. Tip circle immersion depth with oil level stationary [mm]

he0 Reference value of immersion depth, he0 =10 mm

he1,e2 Tip circle immersion depth with oil level stationary [mm]

Hs Sliding ratio at start of approach

Ht Sliding ratio at end of recess

HV Loss Factor

Irw Number of ball rows

K Load Intensity[N/mm2]

Kball Ball bearing element constant

KL Roller bearing type related geometric constant

Kroll Roller bearing element constant

Krs Replenishment constant: for low level oil bath and oil jet lubrication

=3x10-8, for grease and oil-air lubrication = 6x10-8

KZ Bearing type related geometric constant

L Length of element for gearing windage and churning [mm]

l Pitch point coordinate on the action line

xiii

La Length of action [mm]

lD Parameter used in SKF model

lh Hydraulic length [mm]

M Mesh mechanical advantage

m Gear Module

M0 No-load torque of the bearing [Nm]

M1 Bearing load dependent torque [Nm]

M2 Cylindrical roller bearing axial load dependent moment [Nm]

Mdrag Frictional moment of drag losses [Nmm]

Mrr Rolling Frictional Moment [Nm]

Mseal Friction Moment of seals [Nm]

Msl Sliding Frictional Moment [Nm]

mt Transverse tooth module

Mt Transverse module

n Shaft rotational speed [rpm]

ɳoil Dynamic viscosity of oil at operating temperature [Pa.s]

p Difference between atmospheric pressure and the vaporization pressure

of the oil in Palmgren model (kg/mm2)

P0 Static equivalent bearing load in Palmgren model (kg)

P1 Bearing dynamic load [N]

PA Transmitted power [w]

PB Bearing friction losses[W]

PBi Power loss for each individual bearing [KW]

PGWI Individual gear windage and churning loss

PL Load dependent Loss [W]

PM Sum of gear Mesh Loss[W]

PN Non-load dependent losses [W]

PP Sum of all the individual oil pump loss[W]

PS Seal Friction loss[W]

Psi Power loss for each individual oil seal [W]

Pv Total power loss [W]

PVZP Load dependent gear losses of hypoid gearsets [W]

PVZP Gear Power Loss [W]

PW Sum Of all individual internal windage and oil churning in gears [W]

PWB Sum of all individual internal windage and churning in bearings[W]

xiv

Ra Arithmetic average roughness of pinion and gear wheel

Re Reynolds Number

Rf Roughness factor for gear teeth

ro1 Pinion Outside Radius[mm]

ro2 Gear Outside Radius[mm]

Rp Gear pitch radius [mm]

Rp1 Pitch radius of the driven gear [mm]

Rp1w Working pitch radius of the driven gear[mm]

Rp2w Working pitch radius of the connected gear [mm]

Rs Parameter used in SKF model

rw1 Pinion Operating Pitch Radius[mm]

rw2 Gear Operating Pitch Radius[mm]

Sm Surface area of contact between the gear and the lubricant

ßb Helix angle at base circle [degrees]

t Parameter used in SKF model

T1 Torque at port [Nm]

Ti1, Ti2 Input torque per unit force, pinion and wheel [Nmm]

To2 Output torque, wheel, per unit force mm [Nmm]

Ts Oil seal torque [Nm]

u Gear Ratio

V Pitch Line Velocity[m/s]

V0 Volume of Lubricant

Vg Total immersed volume

Vg Slipping velocity [m/s]

Vl Immersed volume of the gear

Vm Volume of oil bath

VM Drag loss factor

Vp Oil piezo viscosity coefficient

Vr Rolling velocity [m/s]

w2 Rotary velocity of the driven gear [rad]

X1 Curve radius for driven gear [mm]

X2 Curve radius for connected gear (mm)

Xeq Equivalent curve radius (mm)

XL Oil Lubricant factor

Z Number of teeth

xv

Z1 Number of teeth of the driven gear

Z2 Number of teeth of the connected gear

α Contact angle between roller element and bearing rings [degrees]

αN Normal pressure angle (according to ISO 23509) [degrees]

αn Normal pressure angle[degrees]

αT Transverse pressure angle[degrees]

αtm Operating Traverse Pressure Angle[degrees]

αTw Working transverse pressure angle [degrees]

αw Operating transverse pressure angle[degrees]

β Helix angle[degrees]

βm Operating Helix Angle[degrees]

βm1, βm2 Mean Spiral Angle [degrees]

δ Cone angle[degrees]

Δαt1, Δαt2 Change in pressure angle from pitch point to outside

ε1,2 Addendum contact ratio pinion, gear

εα Profile contact ratio

ηffc Sum of element churning efficiency

ηffl Lengthwise sliding efficiency

ηffp Profile sliding efficiency

ϑ Oil temperature [ºC]

λ Relative Film Thickness [mm]

μ Oil absolute viscosity

μbl Sliding friction coefficient in Boundary layer lubrication conditions

μEHD EHD Friction Coefficient

μEHL Sliding friction coefficient in full-film conditions

μF Solid Friction Coefficient

μm Coefficient of friction

μmz Mean coefficient of friction of the gear mesh

μsl Sliding friction coefficient

ν Oil kinematic viscosity [cst]

ν40 Lubricant kinematic viscosity at 40 deg. Celsius [cst]

νgɤ1,2 Total surface speed at tooth tip[m/s]

νgm Mean sliding speed[m/s]

νgs Helical Speed[m/s]

xvi

ξ EHD Friction fraction parameter

ρ Oil density [kg/m3]

Φbl Weighting factor for the sliding friction coefficient

Φish Inlet shear heating reduction factor

Φrs Kinematic replenishment/starvation reduction factor

ω Angular velocity of the bearing rings in relation to each other in

Palmgren model [rad/s]

Ω Rotational speed [rpm]

Abbreviations

1D One Dimension

3D Three Dimension

AMESIM Advanced Modelling Environment for performing Simulations

AWD All-Wheel Drive

CAD Computer Aided Design

CFD Computational Fluid Dynamics

DAE Differential Algebraic Equations

EHD Elasto-Hydrodynamic

FEA Finite Element Analysis

FVA Forschungsvereinigung Antriebstechnik

MPS Moving Particle Simulation

NVH Noise, Vibration and Harshness

ODE Ordinary Differential Equation

PAO Polyalphaolefin

PG Polyglycol

PTU Power Transfer Unit

RDU Rear Drive Unit

SF Solid Friction

1

1 INTRODUCTION

1.1 Background

GKN Driveline Köping AB, a part of the GKN Plc. Group specializes in electric powertrains and

intelligent all-wheel drive (AWD) systems. Their intelligent AWD gear transmission system has been

widely used in motor vehicle applications to perform a basic function of distributing the power from

the vehicle transmission to all 4 wheels. A portion of the power produced by the internal combustion

engine is lost due to the drag power loss in the form of friction and oil churning losses in these

transmission units. Hence a lot of efforts are invested to reduce the drag power loss and increase the

efficiency of these transmission units thereby reducing emissions and fuel consumption. The AWD

system consists of a PTU, a propeller shaft and a Rear Drive Unit (RDU) as shown Figure 1.1. The

PTU is coupled to the vehicle transmission and transmits power to the RDU in the rear side of the

vehicle through a propeller shaft. Transmission efficiency is important in applications in which the

primary concerns are the power consumption or maximum output torque. GKN currently uses

ROMAX Energy to find the efficiency of the PTU based on different analytical loss methods available

in the softwar+e for hypoid gear set, bearings and seals with less knowledge on their accuracy in

predicting the drag losses. Also, the existing method to predict the efficiency of the unit during the

early design stages is time consuming. The method involves creating an approximate 3D model of

the new product and create a FE model in ROMAX to simulate the efficiencies. Hence to realize an

efficient design of the PTU, 1D-simulation capabilities and its usage during the early performance

consideration stage were studied.

Figure 1.1. An All-Wheel Drive (AWD) System (Source: GKN Driveline Köping AB).

1.2 Purpose

The main goal of the project is to predict the drag losses in the PTU more accurately in the early

design stages. This is achieved through the following steps. Firstly, the fidelity of the analytical loss

prediction is improved by correlating the drag loss test data with the calculated results in ROMAX

Energy and Excel. Then, a functional 1-D simulation model of the PTU is developed in LMS

AMESim to explore the possibilities of using it in the early design stages to evaluate the drag losses

in the PTU and validate it with an existing efficiency prediction tool and the test results.

The research questions for the thesis are formulated based on the objectives and are formulated below:

1. Can the analytical models in the existing software reliably predict the losses in the PTU? 2. Can 1D simulation be used to construct a functional system model of the PTU to compute

power losses and find the efficiencies at early design stages?

2

1.3 Delimitations

The test data values segregated from the drag loss test results are approximate due to the assumptions like negligible windage losses (resistance against oil-air mixture) at low speeds,

considering pocketing losses (oil entrapment between rolling elements) as a part of the

churning losses & considering bearing friction losses caused only by the bearing preload

forces for easier data segregation lead to a less accurate data correlation.

Only a few standard analytical models were considered for data correlation in this thesis due to time constraints. Hence, there are chances of overlooking more accurate models.

The standard analytical models considered in this thesis are conducted on parallel gears and different test conditions when compared to GKN test conditions.

Non-linearities aren’t considered in the analytical methods for all components.

Gear Churning Loss model isn’t available in the inbuilt library in AMESim for evaluation.

1.4 Method

The power loss (drag loss) is evaluated using different analytical loss methods for every component of a

specific model of the Power Transfer Unit (PTU). This thesis is conducted in the following ways:

Studies of different contributors to the drag losses in PTU & available existing analytical models in the literatures and evaluate them.

Segregate the drag loss test data for comparison and conduct more tests if required.

Develop analytical models in Excel/Matlab for data correlation.

Run ROMAX Energy Simulations to compute the power losses in the PTU.

Compare and correlate the calculated test results with power loss results.

Study 1-D Simulation and its capabilities.

Develop a functional 1D system model of the PTU and simulate the power losses in the unit using Simcenter AMESim.

Analyse and validate the 1-D model with the available test results and ROMAX results.

The project plan and the risk analysis are attached in the Appendices A & B respectively.

3

2 FRAME OF REFERENCE

2.1 Power Transfer Unit

The GKN All-Wheel Drive System consists of a power transfer unit (PTU) that transfer the rotary

power from the powertrain through a propeller shaft to the Rear Drive Unit (RDU) that distributes the

power to the rear wheels. The PTU consists of a hypoid gear set, deep groove ball bearings, tapered

roller bearings and radial shaft seals that contribute to overall losses in the unit as shown in Figure

2.1.

Figure 2.1. Power Transfer Unit (Source: GKN Driveline Köping AB)

2.1.1 Hypoid Gears

Hypoid gears are a type of spiral bevel gears that have non intersecting and non-parallel axes, used to

transmit power [10]. The geometry of the hypoid gear is hyperbolic when compared to the conical

geometry of a spiral bevel gear. In a hypoid gearset, spiral angle of the pinion is larger than the gear.

Hence the diameter of the pinion is larger than that of the spiral bevel gear which provides more

contact area and better tooth strength, allowing more torque to be transmitted as well as higher gear

ratios. Since the axes are non-intersecting, bearings can be used on both sides of the gear to provide

additional rigidity. Uniform sliding along the tooth profile and longitudinal direction occurs between

pinion and gear due to difference in the spiral angle giving them a smooth-running properties and

quiet operation. Hypoid drivetrains are commonly used in automotive industry to transmit power from

the vehicle transmission to the opposite ends of the vehicle. “Below-centre” offset in a hypoid gearset

allows the driveshaft to be located lower in the vehicle allowing more cabin space. Figure 2.2. shows

a hypoid gearset with pinion and crown gears with axes offset.

4

Figure 2.2. Hypoid Gearset with pinion and crown gears with “below-center offset” (Source:[10])

2.1.2 Rolling Bearings

Rolling bearings support and guide rotating or oscillating machine elements – such as shafts, axles,

or wheels – and transfer loads between machine components with minimal friction. Rolling bearings

provide high precision and low friction and therefore enable high rotational speeds while reducing

noise, heat, energy consumption and wear. There are two types of bearings- roller and ball bearings.

Balls make point contact with the race ways while rollers make line contacts. Figure 2.3. shows an

angular contact ball bearing arrangement (left) and a tapered roller bearing arrangement (right)

mounted on the shaft.

Figure 2.3 Rolling bearing arrangements in a shaft (Source: [8])

2.1.3 Radial Shaft Seals

Radial Shaft seals protect the bearings that support a shaft in a rotating application by retaining the

bearing lubricant and keeping it clean ensuring maximum bearing life and increases the overall

service life of the equipment. Rotary shaft seals work by squeezing and maintaining the lubricant in

a thin layer between the lip and shaft as shown in Figure 2.4. Sealing is further aided by the

hydrodynamic action caused by the rotating shaft, which creates a slight pumping action [3].

Figure 2.4 Radial Shaft Seal (Source:[3])

5

2.2 Power Losses

Power loss in a Power Transfer Unit are generated by gears, bearings and seals which will be

discussed in the upcoming sections. According to [1], Equation 1 estimates the total power loss, Pv,

consisting of load dependent, PL, and non-load dependent losses, PN.

𝑃𝑉 = ∑(𝑃𝐿 + 𝑃𝑁) (1)

The power losses in general are called as drag losses at GKN which contradicts the terms available in

the literatures.

2.2.1 Load Dependent losses

Load-dependent power losses are induced by friction due the sliding and rolling components in the

gear and bearing contacts. These losses depend on the transmitted load, coefficient of friction and

sliding velocity in the contact areas of the components.The load dependent losses are comprised of

the sum of all the individual bearing friction losses, PB, and the sum of all the individual gear mesh

losses, PM which is determined by Equation 2:

𝑃𝐿 = ∑(𝑃𝐵 + 𝑃𝑀) (2)

For a transmission unit at nominal speeds and torque, load-dependent losses dominate.

2.2.2 Non- Load Dependent Losses

The non-load dependent or load independent power losses are due to viscous effects of the lubricant

and are influenced largely by the lubrication method employed. They include drag losses in the form

of oil churning or air windage losses depending on the type of fluid medium, and pocketing losses at

the gear mesh interface due to pumping of the oil or air. Pocketing losses are of a lower order of

magnitude when compared to churning and windage losses. Churning power losses are predominant

under high speed and low torque conditions. Equation 3 estimates the non-load dependent losses

which is the sum of all the individual oil seal losses, PS, the sum of all the individual internal windage

and oil churning losses for the gears and bearings, PW and PWB, respectively, and the sum of all the

individual oil pump losses, PP [1]:

𝑃𝑁 = ∑(𝑃𝑆 + 𝑃𝑊 + 𝑃𝑊𝐵 + 𝑃𝑃) (3)

2.3 Power Loss Models

Different ISO standards containing the analytical formulas for load dependent/ non-load dependent

losses and proposed empirical formulas based on experiments will be used for correlation with the

data from the experiments conducted on PTU. ISO 14179-1 & ISO 14179-2 are used to evaluate load

dependent and load independent power losses for bearings, gears and seals. ISO 14179-1 is the

American proposal that utilizes an analytical heat balance model to calculate the thermal transmittable

power for a single or multiple stage gear drive lubricated by mineral oil. It presents the means for

determining the thermal load carrying capacity of gears that includes measurement on original gear

units under practical conditions. This takes the form of either measurement of the power loss, heat

dissipation or both, or, in the case of splash-lubricated gear units, the determination of the quasi-

stationary temperature in the oil sump [1]. ISO/TR 14179-2 is based on a German proposal whereby

the thermal equilibrium between power loss and dissipated heat is calculated. From this equilibrium,

the expected gear oil sump temperature for a given transmitted power, as well as the maximum

6

transmittable power for a given maximum oil sump temperature, can be calculated. The following

sections will give an overview of some of the models available in literature that many researchers

validated and altered them for special cases.

2.3.1 Radial Shaft Seals

The power loss of radial shaft seals is due to the friction between the sealing lip and the rotating shaft

as shown in Figure 2.5. Different ISO standards (ISO14719-1 & ISO14179-2) & approaches by Linke

and Parker were considered to evaluate the seal power loss. Different seal designs, rubber compounds,

fluids, fluid levels, temperatures, shaft textures, pressures, and time in service each affect friction, so

there is no exact calculation to predict torque [3].

Figure 2.5. Friction between Radial Shaft Seal lip and rotating shaft (Source:[3])

2.3.1.1 ISO14179-1

According to [1], contact lip oil seal losses are a function of shaft speed, shaft size, oil sump

temperature, oil viscosity, depth of submersion of the oil seal in the oil and oil seal design. Seal power

loss (in Watts) and seal loss torque (in Nm) can be estimated by Equation 4 and 5 respectively.

𝑃𝑠 =𝑇𝑆 𝑛

9549 (4)

The seal torque (in Nm) can be calculated using the Equation 5 for seals made of Viton material.

𝑇𝑠 = 3.737 𝑑𝑠 10−3

(5)

2.3.1.2 ISO14179-2

According to [2], power loss (in Watts) of a radial shaft seals can be estimated by Equation 6.

𝑃𝑠 = 7.69 𝑑𝑠2𝑛 10−6 (6)

2.3.1.3 Parker

According to [4], power losses (in Watts) or energy consumption from an elastomer radial shaft seals

can be estimated by Equation 7.

𝑃𝑠 = 7.47𝑑𝑠2𝑛4/310−7 (7)

The underlip temperature increase is due to the friction between the shaft and seal lip. Torque is the

frictional force the shaft must overcome to rotate in the seal. For dry running conditions, power loss

is 2 to 3 times the above equation.

7

2.3.1.4 Linke

According to [4], power losses (in Watts) of a radial shaft seals can be estimated by Equation 8.

𝑃𝑠 = [145 − 1.6 𝜗 + 350 × 𝑙𝑜𝑔(𝑙𝑜𝑔(𝜈40 + 0.8))]𝑑𝑠2𝑛10−7 (8)

2.3.2 Rolling Bearings

Rolling element bearing is a critical part in supporting the rotating components in a mechanical system

and provides additional damping to stabilize the system. In comparison to plain bearings, it is more

difficult to model the rolling bearing as a whole due to the complicated coupling between the

interactions of internal components (i.e., rolling elements, cages, and rings) of rolling bearings [5].

Drag Losses in rolling bearings can be split into load-dependent and load independent losses. Figure

3 shows six different types of load-dependent losses in a rolling contact bearing [6]:

1. Rolling and sliding friction between rolling element and bearing rings (1 and 2) 2. Sliding friction between cage bar and bearing rings (3) 3. Sliding friction between cage and rolling element front surface (4) 4. Sliding friction between rolling element and outer ring (5) 5. Friction between cage and rolling element (6)

Figure 2.6. Friction between Radial Shaft Seal lip and rotating shaft (Source:[6])

In an oil bath lubrication method, bearings are partially submerged or, in special situations,

completely submerged. A small quantity lubricant creates a thin fluid film between the rolling

elements as shown in Figure 2.6. Load-independent bearing churning losses occur due to the

resistance of the rolling elements moving through the oil. The following sections will brief the

analytical models considered for correlating the power losses in the rolling bearings.

2.3.2.1 ISO14179-1

• LOAD DEPENDENT LOSS TORQUE:

[1] provides a method for calculating drag losses in the bearings based on SKF General Catalogue

4000, USA, 1991. Equation 9 gives the value for the torque on each bearing as a function of the

applied load. Values for 𝑓1are described in Table 2.1.

8

𝑀1 =𝑓1𝑃1

𝑎𝑑𝑚𝑏

1000 (9)

Table 2.1: Factors for calculating 𝑴𝟏 [1]

Friction Power loss of a rolling bearing is determined by Equation 10.

𝑃𝐵𝑖 =(𝑀1+𝑀2)𝑛

9549 (10)

For cylindrical roller bearings supporting an additional axial load, the Equation 11 determines the

additional frictional moment M2, which depends on the axial load:

𝑀2 =𝑓2𝐹𝑎𝑑𝑚

1000 (11)

Values of f2 are given in Table 2.2.

Table 2.2: Factors f2 cylindrical roller bearings [1]

Assumptions for 𝑓2-

• viscosity ratio K ≥ 1,5.

• (Fa/Fr) must not exceed 0,5 for EC design and single-row full complement bearings, 0,4 for

the other bearings with cage, or 0,25 for double-row full complement bearings.

• NON-LOAD DEPENDENT LOSS TORQUE:

[1] describes methods based on SKF General Catalogue 4000, USA, 1991 to determine the non-load

dependent frictional moment, M0 in a rolling bearing with the Equations 12 and 13. The kinematic

viscosity, 𝜈, is a function of sump temperature.

If ν n < 2000; 𝑀𝑜 = 1.6𝑓0𝑑𝑚310−8 (12)

If ν n ≥ 2000; 𝑀𝑜 = 10−10𝑓0( 𝜈 𝑛)2/3

𝑑𝑚3 (13)

9

Factor f0 adjusts the torque based on the amount that the bearing dips in the oil and varies from f0(min)

to f0(max). Equation 14 determines f0 and the values for f0 (min) and f0 (max) can be found in Table

2.3 in the appendix.

𝑓0 = 𝑓0(𝑚𝑖𝑛) + (𝑓0(𝑚𝑎𝑥) − 𝑓0(𝑚𝑖𝑛))𝐻

𝐷𝑂𝑅 (14)

Table 2.3: Bearing dip factor, f0 [1]

Pocketing losses are assumed null by Mauz in ISO 14179-1.

2.3.2.2 ISO14179-2


[2provides a method for calculating load dependent losses based on ESCHMANN, P.u.a.Die

Wälzlagerpraxis. Oldenbourg München-Wien, 1978. Equation 15 & 16 estimate the load-dependent

bearing loss torques TVLP1 & TVLP2.

𝑇𝑉𝐿𝑃1 =𝑓1𝑃1

𝑎𝑑𝑚𝑏

1000 (15)

𝑇𝑉𝐿𝑃2 =𝑓2𝐹𝑎𝑑𝑚

1000 (16)

Table 2.4 gives the value of the factor f1 which depends on Static Load Rating and Equivalent static load rating found from the supplier catalog.

Table 2.4: Coefficient, f1, and equivalent bearing load, P1 [2]

For cylindrical roller bearings supporting an additional axial load, the Equation 17 determines the

additional frictional moment M2, which depends on the axial load:

𝑀2 =𝑓2𝐹𝑎𝑑𝑚

1000 (17)

Values of f2 are given in Table 2.5.

10

Table 2.5: Factors f2 cylindrical roller bearings [2]


Non-Load Dependent Torque or load independent loss torque depends on the bearing design, the type of lubrication, the viscosity of the lubricant and the bearing speed which is estimated by the Equations 18 & 19.

If ν n < 2000 mm2/s min; 𝑀𝑜 = 1.6𝑓0𝑑𝑚310−8 (18)

If ν n ≥ 2000 mm2/s min; 𝑀𝑜 = 10−10𝑓0( 𝜈 𝑛)

2/3𝑑𝑚

3 (19)

Table 2.6 gives the value of the factor f0 which depends on bearing type and bearing lubrication.

Table 2.6: Bearing dip factor, f0 [2]

2.3.2.3 Palmgren


According to Palmgren [7], Equation 20 and 21 can be used to calculate load dependent loss of roller

bearings.

𝑀1 = 0.0098𝑓1𝑔1𝑃0𝑑𝑚 (20)

𝑔1𝑃0 = 0.8𝐹𝑎𝑐𝑜𝑡𝛼 ≥ 𝐹𝑟 (21)


According to Palmgren [7], the non-load dependent torque loss is given by the Equations 22 & 23.

If 𝜔 𝑛

𝑝 < 2×10-6 ; 𝑀𝑜 = 1.5572𝑓0𝑝𝑑𝑚

310−6 (22)

If 𝜔 𝑛

𝑝 ≥ 2×10-6 ; 𝑀𝑜 = 9.81 × 10−3𝑓0(

𝜔 𝑛

𝑝)

2/3𝑝𝑑

𝑚3 (23)

11

In a grease lubrication system, the non-load dependent losses are estimated by the Equation 24.

If ν n ≥ 2000 mm2/s min ; 𝑀𝑜 = 9.81 × 10−11𝑓0( 𝜈 𝑛)2/3𝑑𝑚

3 (24)

2.3.2.4 SKF Frictional Method

The SKF model calculates the total frictional moment considering rolling frictional moment, sliding

frictional moment, frictional moment of seals and frictional moment of drag losses (churning,

splashing etc.,) [8]. The amount of friction depends on the load and on several other factors (bearing

type and size, the operating speed, the properties of the lubricant and the quantity of lubricant).

Equation 25 estimates the total frictional moment.

𝑀1 = 𝑀𝑟𝑟 + 𝑀𝑠𝑙 + 𝑀𝑠𝑒𝑎𝑙 + 𝑀𝑑𝑟𝑎𝑔 (25)

The SKF model is derived from more advanced computational models developed by SKF

Application conditions for this model is given in Table 2.7.

Table 2.7: Requirements of SKF model [9]

• SLIDING FRICTIONAL MOMENT:

The sliding frictional moment in the bearings is calculated by Equation 26 to 28

𝑀𝑠𝑙 = 𝐺𝑠𝑙𝜇𝑠𝑙 (26)

𝜇𝑠𝑙 = 𝛷𝑏𝑙𝜇𝑏𝑙 + (1 − 𝛷𝑏𝑙)𝜇𝐸𝐻𝐿 (27)

𝛷𝑏𝑙 =1

𝑒2.6×10−8(𝜈 𝑛)

1.4𝑑𝑚 (28)

Table 2.8 & 2.9 gives the analytical formulas to compute geometric and load dependent variables, &

geometric constants for sliding moment in Angular contact ball bearings and Tapered roller bearings.

Axial Load factor (Y) can be found in the product tables in manufacturer’s catalog.Values for μbl is

0.12 (speed≠0) & μEHL is 0.02 for cylindrical roller bearings and 0.002 for tapered roller bearings.

12

Table 2.8: Geometric & load dependent variables for sliding frictional moments –radial bearings [8]

Table 2.9: Geometric constants for sliding frictional moments of roller bearings [8]

• ROLLING FRICTIONAL MOMENT:

The Rolling frictional moment in the bearings is calculated by Equation 29 to 31.

𝑀𝑠𝑙 = 𝛷𝑖𝑠ℎ𝛷𝑟𝑠𝐺𝑟𝑟(𝜈 𝑛)0.6 (29)

𝛷𝑖𝑠ℎ =1

1+1.84×10−9(𝑛𝑑𝑚)1.28

𝜈 0.64 (30)

𝛷𝑏𝑙 =1

𝑒[𝐾𝑟𝑠𝜈 𝑛(𝑑+𝐷)√

𝐾𝑍

2(𝐷−𝑑) (31)

Table 2.10 & 2.11 gives the analytical formulas to compute geometric and load dependent variables,

& geometric constants for rolling moment in Angular contact ball bearings and Tapered roller

bearings. Kz is 4.4 and 6 for Angular contact ball bearings and Tapered roller bearings, respectively.

Krs is 3×10-8 low level oil bath lubrication.

13

Table 2.10: Geometric & load dependent variables for rolling frictional moments –radial bearings [8]

Table 2.11: Geometric constants for rolling frictional moments of roller bearings [8] • DRAG LOSSES:

The drag losses occur when the bearing is rotating in an oil bath. The influencing factors are bearing

speed, oil viscosity, oil level, size, geometry of the oil reservoir and external oil agitation from the

mechanical elements. The SKF model for calculating drag losses in oil bath lubrication considers the

resistance of the rolling elements moving through the oil and includes the effects of the oil viscosity

[8]. Equations 32 to 41 estimates the drag loss torque and the variables and functions used in the

equations for the frictional moment of drag losses.

For Ball Bearings,

For Roller Bearings,

(32)

(33)

14

Rolling element related constants:

Equations 36 to 41 estimates the variables and functions used in the equations for the frictional

moment of drag losses.

2.3.3 Hypoid Gears

Gear losses can be split up into load dependent torque and load independent torque [11]. Different

ISO standards[1,2,23] and FVA 345[15] are considered to evaluate load dependent losses, and ISO

standards[1,2], formulas proposed by Changenet [12],[13] and Terekhov [14] to evaluate load

independent churning losses in the gears.

2.3.3.1 Load Dependent Power Losses

Torque dependent losses occur when two gear surfaces which are under pressure move relatively to

each other. These losses depend on the force, sliding speed and the friction coefficient (which is, in

turn, depending on the lubrication) in the contact area. Loss models considered to evaluate these

losses are discussed in the following sections.

• ISO 14179-1 According to [1], Mesh losses are a function of the mechanics of tooth action and the coefficient of

friction. Tooth action involves some sliding with the meshing teeth separated by an oil film. The mesh

efficiency is expressed as a function of the sliding ratios and the mesh coefficient of friction. The gear

tooth mesh losses can be expressed by Equation 42. This equation contains the mesh coefficient of

(34)

(35)

(36)

(37)

(38)

(39)

(40)

(41)

15

friction, fm, which is a function of the applied load and the mesh mechanical advantage, M, which

describes the mechanics of the tooth action which must be solved before solving Equation 42.

The equation for mesh mechanical advantage is given by equation 43

The transverse pressure angle αw is given by the equation 44.

The sliding ratios Hs and Ht are given by the equations 45 & 46 respectively.

The gear design parameters like mean cone distances, addendum and face angle can be evaluated

from ISO 23509.

If the pitch line velocity, V, is 2 m/s < V < 25 m/s and the K-factor is 1,4 N/mm2 < K < 14 N/mm2,

then fm can be estimated using Equation 47. Outside these limits, the values for fm must be determined

by experience.

The K-factor is given by the equation 48.

• ISO 14179-2 ISO 14179-2 [2 estimates the gear mesh power loss based on coulomb law which is given by Equation

49.

(42)

(43)

(48)

(44)

(45)

(46)

(47)

(49)

16

The average sliding speed νgm is given by the Equation 50

As the coefficient of friction only changes slightly with the variable operating conditions on the

path of contact, it is possible for the purpose of approximation to assume an average coefficient of

friction. This can be determined for hypoid gears according to the Equation 51.

• ISO TR 22489 The mesh efficiency (considering tooth profile and lengthwise sliding and churning), ηff, expressed

as a percentage, is calculated using Equation 52 [23].

The calculation of profile sliding is based on virtual cylindrical gears defined in the mean transverse

plane by the Equation 53.

Lengthwise Sliding calculation is made in the mean pitch plane and given by the Equation 54.

The churning losses are calculated based on the formulas proposed in ISO TR 14179-1 [1] which will

be discussed in the next section.

• FVA345 Power loss in a transmission is strongly related to the properties of the gear lubricant [15]. A test

method was developed to evaluate the frictional properties of candidate transmission lubricants in

relation to a mineral reference oil ISO VG 100 with a typical Sulphur phosphorus additive package.

The test results can be expressed in simple correlation factors for no-load, EHD and boundary

lubrication conditions, in comparative steady-state temperature development for given mean values

of operating conditions, and in a ranking scale of different candidates. The test results can be applied

to any gear in practice at any operating conditions for any gear geometry. The load dependent gear

losses of hypoid gearsets can be calculated from Equation 55.

The geometrical loss factor HV is calculated from the Equation 56.

The friction contact is split into a fraction with solid body friction μF and a fraction with EHD friction

μEHD. The mean value of the coefficient of friction μmz is given by the following equations 57-60.

(50)

(51)

(52)

(53)

(54)

(55)

(56)

17

The reference conditions for the calculation of the coefficient of friction for EHD are set to PR = 1000

N/mm², VR,EHD = 8.3 m/s and ηR = 20 mPas and for solid body friction to PR = 1000 N/mm², VR,EHD =

0.2 m/s. The fraction of EHD friction ξ can be evaluated according to Equation 61 as a function of

the relative film thickness λ with the assumption of EHD conditions for λ > 2. The relative film

thickness λ is evaluated from the Equation 62 as the relation between the mean film thickness

according to Ertel/Grubin.

2.3.3.2 Non- Load Dependent Power Losses

Load independent gear churning losses are caused when the gears move through the lubricant where

the lubricant is entrapped between the gear mesh.

• ISO 14179-1 [1] gives the equations for gear windage and churning power loss derived from the equations proposed

by Dudley. Gear windage and churning losses encompass three types of loss. Equation 63 estimates

losses associated with a smooth outside diameter, such as the outside diameter of a shaft. Equation

64 estimates the losses associated with the smooth sides of a disc, such as the faces of a gear and

includes both sides of the gear. Equation 65 estimates losses associated with the tooth surfaces, such

as the outside diameter of a gear or pinion.

(57)

(58)

(59)

(60)

(61)

(62)

18

The roughness factor Rf in the power loss equation for the tooth surface given by the Equation 66.

The dip factor fg is based on the amount of dip that the element has in the oil. when the element does

not dip in the oil, fg = 0 and when the element is fully submerged in the oil, fg = 1. When the element

is partly submerged in the oil, linearly interpolate between fg = 0 and fg = 1.

• ISO 14179-2 The total hydraulic loss torque, TH, of a gear stage system loss are determined according to Mauz

using Equation 67.

The factors C1 and C2 state the effect of the tooth width and the immersion depth are determined

using the Equations 68 & 69. The splash oil factor, Csp, given by the Equation 70 considers the effect

of the splash oil supply, dependent on the immersion depth.

(63)

(64)

(65)

(66)

(67)

(68)

(69)

(70)

19

• Changenet 2007 Changenet and Velex (2007) suggested the empirical equation for churning losses of a pair of meshing

gears considering parameters such as gear module, gear diameter, gear face width, rotational speed

and lubricant viscosity [12]. Equation 71 gives the churning loss of a gear pair.

Equation 72 gives the normalized churning torque which is expressed in terms of seven groups of

dimensionless quantities.

Table 2.12 shows the values of the dimensionless quantities for low and high speeds.

Table 2.12: Dimensionless quantities used in churning loss equation

At low-medium speeds, gear geometry is influential via the submerged surface area only while tooth

number and face width play a negligible. At high speeds, churning power losses are found to be

largely independent of oil viscosity (Re=0) and the inertia forces become much more significant than

the viscous ones. The Reynolds and Froudes number are given by the following equations 73 & 74

respectively.

Depending on the sense of rotation, very different trends have been found in the experimental results.

The churning losses during the anti-clockwise rotation of the pinion gear is higher than the clockwise

rotation. The difference is probably due to the trapping of lubricant by the meshing teeth and by a

swell effect which dissipates energy and increases the immersion depth on the pinion. The variation

in churning power loss ΔP is expressed in terms of a dimensionless variation of churning torque ΔCm

by the equation 75 and ΔCm by the Equation 76.

(71)

(72)

(73)

(74)

(75)

(76)

20

• Changenet 2011 Changenet investigated the various fluid flow regimes generated by a pinion running partly immersed

in an oil bath and the corresponding churning power losses. Based on some new measurements for

transient operating conditions, it has been found that the separation in two regimes may be not

accurate enough for wide-faced gears and high temperatures. An extended formulation is therefore

proposed which, apart from viscous forces, introduces the influence of centrifugal effects [13].

Equation 77 gives the value of churning power loss.

A new parameter analogous to centrifugal acceleration has therefore been introduced to characterize

this additional regime and broaden the range of application of dimensional analysis. Equation 78 gives

the value of centrifugal acceleration.

Based on a large experimental data base, the following equations 79-82 of Cm have been derived:

• Terekhov Terekhov (1991) conducted several experiments on rotating single and meshing spur gears with high

viscosity lubricant and low rotational speed [14]. The calculation of the torque coefficient is deduced

from dimensional analysis based on the flow regime and the rotating direction of a pair of gears. The

churning torque Cch and a dimensionless torque Cm is given by Equation 83 & 40 respectively. In

Terekhov‟s analysis, however, neither the gear tooth geometry nor the immersed surface area is not

considered.

(77)

(78)

(83)

(79)

(80)

(81)

(82)

21

Table 2.13 shows the values of the dimensionless quantities for different flow regimes.

Table 2.13: Exponential coefficients for Terekhov's empirical equation

2.4 System Level Simulation

System simulation involves simulating a physical system and analyzing its behaviour [18]. It is a part

of the broader system engineering discipline, which aims to model, analyze and simulate physical

systems. The first step in system simulation is to create a mathematical model of the physical system

using existing physical laws. This model is a set of differential equations, which represent the physics

of the system or capture the dynamics of system [18]. Solving these equations at various instants of

time gives the response of the system with respect to time. Thus, system engineering allows the

following study to be carried out [19]:

• Study the transient response of the system for varying inputs • Study the stability and steady response of the system • Modify the given system to behave in the desired manner using control mechanism

With an increasing demand in the automotive industry to reduce the time to market, a lot of impetus

is placed on reducing the dependence on physical tests with calculations and by identification of

system performance at an early stage. modern products are becoming increasingly multi-disciplinary

and a tool which can predict the system behaviour earlier in the product life cycle will significantly

reduce the design iteration process. System simulation bridges this gap between concept and

prototype since it does not require detailed design information but gives a good estimate of the system

response.

2.4.1 System Model

Traditionally, the system analysis was carried out using the physical system subjected to test input

signals, observing its corresponding response. Nevertheless, this is not always feasible, since either

the extent to which the parameters of the physical system can be varied is very limited or there are

imposed restrictions to the application of these input tests (i.e. system analysis in human physiology).

To overcome these problems, a simplified representation of the physical system under analysis is

developed instead, what is called system model which are a set of governing equations [19].

The system model may be either mental, when expressed through an abstract description of the

relationships among the system variables, or formal model, when using graphs, diagrams, and

mathematical equations derived from the mental model used to describe the system behavior [18].

System models can be classified as [19]-

(84)

22

1. Linear/Non-linear - depending on whether the principle of superposition is applicable or not to the

system dynamic equations

2. Distributed/Lumped - depending on the dependence of the variables on spatial coordinates

3. Time-varying/Stationary - depending on variation of system model parameters in time

4. Continuous/Discrete - depending on the continuous or discrete range definition of Variables

2.5 One-Dimensional Simulation

1D-Simulation is a system level simulation that represents the entire design of a system and the

interaction of different components within the system. System Simulation is used to validate design

proposals and quantifies the potential benefits before making a design recommendation. 1D

simulation is excellent for optimizing the design of an entire system, while 3D simulation is great for

optimizing individual components [21]. Advanced Modelling Environment for performing

Simulations of engineering systems (LMS AMESim) 2019.1 is used for system simulation to model

multi-physics systems and components. This tool is based on the bond graph theory, where the

interactions between elements in the physical dynamic sdystem are modelled as power transactions.

The architecture of LMS AMESim can be seen in figure 2.7.

Figure 2.7: Architecture of LMS AMESim simplied (Source:[20])

The software architecture allows exibility to aid the design process of the system V-cycle. There are

four major modes to be followed sequentially while building a model:

• Sketch mode

• Submodel mode

• Parameter mode

• Simulation mode

The sketch mode involves building the model using components of physical systems available in the

AMESim libraries or using custom built components. The submodel mode involves assigning suitable

submodels or mathematical equations to these components. The parameter mode involves assigning

the parameters in the equations defined in the submodel mode. The simulation mode is the final step

23

where a simulation of the model built is performed. It can be a simulation with respect to time when

a temporal analysis is chosen or it can be a linear analysis to study the frequency domain

characteristics [18].

2.5.1 Models and submodels

In Simcenter Amesim the set of equations defining the behavior of the engineering system and its

implementation as code is referred to as the model of the system. The model is built up from equations

(and the corresponding code) for each component within the system. These are referred to as

submodels. Simcenter Amesim contains large libraries of icons and submodels of components. When

models are developed, assumptions and simplifications are made. In this case it is normal to reduce

any partial differential equations to ordinary differential equations. This leads to models with either

ordinary differential equations (ODEs) or differential algebraic equations (DAEs) [20].

2.5.2 Powertrain Library

The Powertrain library contains a large set of submodels dedicated to the modeling and the simulation

of both basic and advanced vehicle transmission systems. The library can be used both to model the

complete Powertrain or Driveline and sophisticated, fast acting or controlled components such as

manual transmission (MT), automatic transmission (AT), powershift transmission with dual clutch

(DCT), Continuously Variable Transmission (CVT), hydrostatic power splitting transmissions

(Hydro mechanical), Dual Mass Flywheel (DMF) and torque vectoring devices [20].

2.5.3 Causuality

[18] Causality refers to the compatibility between components and is important in building a model

in LMS AMESim. The multi-port physical modelling approach in AMESim means every component

has a set of ports where data exchange takes place. The effort and flow variables are exchanged across

these ports and the output at one port of a component corresponds with the input at the connecting

port of the other component. This must be maintained in order to build a model in AMESim [20].

2.6 Drag Loss Test

The purpose of a drag torque test is to study the power losses at specific speeds and oil temperatures

when no load is applied. The other type of tests conducted at GKN are the efficiency tests conducted

at non- zero torque levels to find the efficiency of the product. The test object is filled with oil and

fitted to a fixture. The tubular shaft is connected to Motor 1 as shown in the figure 2.8. The tubular

shaft is connected to the test rig (input) with universal joints to reduce alignment forces from the

electrical motor. Prior to the drag loss test the unit is first subjected to a break-in cycle. That cycle is

typically running for several hours at various pinion speeds and pinion torques maintained at a

particular oil temperature. The drag loss investigation is performed with a specified number of test

units, which are tested three separate times for statistical purposes. The three repetitions are carried

out for each combination of speed and temperature.

24

Figure 2.8. Schematic figure of the test rig setup (Source: GKN Driveline Köping AB).

2.7 ROMAX Simulations

ROMAX software is a product simulation platform for integrating whole-system design end-to-end,

and simulation, analysis, and optimization for NVH, efficiency and durability, of mechanical or of

transmissions and drivelines.

2.7.1 Bearing Force Calculation

Standard method for calculating shear force and bending moment in a shaft doesn’t include the tilt

stiffness when compared to the detailed ROMAX shaft/bearing model. Rolling element bearing

stiffnesses depend on many parameters. Some of these are associated with the component - bearing

type, internal clearance, number of rolling elements, rolling element dimensions. Additionally, for

each bearing, the stiffness is non-linear as it increases with the applied load. This introduces an

additional complexity to the analysis. The solution needs to be iterative, as it needs to find a

compatible set of forces and deflections and the analysis includes the true behaviour of the bearing.

The analysis now includes the ability to assess the effect of changing the bearing internal geometry.

ROMAX bearing model includes the following features to calculate the bearing forces-

ROMAX works by matching the stiffness of the shaft and shaft supports

Bearings are modelled by evaluating the individual bearing rolling elements accounting for loads, deflections and misalignments.

ROMAX can model bearing pre-load, end play, housing stiffnesses, internal clearance and housing misalignments.

Shaft Deflections and slopes are calculated.

Advanced modules are available to investigate load distribution, profiling and other detailed modifications on individual elements within a particular bearing.

2.7.2 Efficiency Calculation

ROMAX Energy is an efficiency prediction tool for automotive transmissions. Encompassing

advanced tribological models, ROMAX Energy calculates power losses, fuel consumption and

emissions for a given drive cycle, and to investigate the impact of different bearing and gear designs

on system efficiency [11].

25

2.8 AMESim Bevel Gear Assembly

The forces acting on each gear (in the tangential, radial and axial directions) are not strictly opposite

as in the case of a bevel gear. It possible to choose with the parameter "load output" the gear for which

the forces are output at port 3, 4, 5. Figure 2.9 shows the forces in the output port based on the load

output parameter chosen.

Figure 2.9. Forces in Port 3,4 &5 based on load output. (Source:[20]).

2.8.1 Gear Mesh Forces

The axial, radial and tangential forces in a bevel gear assembly sub model in AMESim are calculated

using the Equations 85 to 87 respectively.

Tangential Force:

𝐹𝑡1 =2𝑇1

𝑑𝑚1

Axial Force:

𝐹𝑥1 =𝐹𝑡

𝑐𝑜𝑠 𝛽 (𝑡𝑎𝑛𝛼 𝑠𝑖𝑛𝛿 + 𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛿)

Radial Force:

𝐹𝑟1 =𝐹𝑡

cos 𝛽(𝑡𝑎𝑛𝛼 𝑐𝑜𝑠𝛿+𝑠𝑖𝑛𝛽.𝑠𝑖𝑛𝛿)

2.8.2 Rolling and Slipping Losses

The power dissipated by the teeth slip is calculated by a lineic integration of the slipping power on the action line using the Equation 88 [16].

𝑃𝑔 =1

𝐿𝑎∫ 𝐹𝑛𝑓𝑔𝑉𝑔𝑑𝑙

𝐿𝑎0

Where:

𝐹𝑛 =𝐹

𝑐𝑜𝑠𝛼𝑁𝑐𝑜𝑠 𝛽

(85)

(86)

(87)

(88)

(89)

26

𝑓𝑔 = 0.0127 𝑙𝑜𝑔 (0.02912 𝐹𝑛𝑢

𝜌𝜇𝑉𝑔𝑉𝑟2 )

𝑉𝑔(𝑙) = 𝜔2|𝑙 − 𝑔𝑓| (1 +𝑍1

𝑍2)

The power dissipated by the teeth roll is calculated by a lineic integration of the rolling power on the action line using the Equation 92 [16]. The change in viscosity under mechanical

pressure is called as piezo-viscous effect. The coefficient of viscosity under piezo-viscous

effect is the piezo-viscosity coefficient (Vp). This is predominant under mixed and EHD

lubrication conditions.

Pr =1

La∫ FrVrdl

La0

Where:

𝐹𝑟 =9 × 107𝑒ℎ𝑏0

𝑐𝑜𝑠𝛽

𝑉𝑟 = 2𝜔2𝑅𝑝1 sin(𝛼𝑇𝜔) + 𝜔2|𝑙 − 𝑔𝑓| (1 −𝑍1

𝑍2)

𝑒ℎ = 𝑋eq2.65 (𝜇𝑉𝑟

2𝐸𝑒𝑞𝑋𝑒𝑞)

0.7

(𝑉𝑝𝐸𝑒𝑞)0.54 (

𝐹𝑛𝑢𝐸𝑒𝑞𝑋𝑒𝑞

)

−0.13

𝐸𝑒𝑞 =2

1 − 𝜈12

𝐸1+

1 − 𝜈22

𝐸2

𝑋𝑒𝑞 =𝑋1𝑋2

𝑋1 + 𝑋2

(90)

(91)

(92)

(93)

(94)

(95)

(96)

(97)

27

3 IMPLEMENTATIONS

3.1 Test Data Segregation

As discussed in the frame of reference section, the internal components of PTU include pinion shaft

with pinion gear and tapered roller bearings, and the tubeshaft with ring gear and angular contact ball

bearings. Multiple exclusive drag loss tests with a different combination of internal components in

the PTU, bearing preload and lubricant presence were conducted to segregate the power losses to the

component level. Since it’s impossible to replicate the same arrangements in the efficiency tests, the

idea is to understand the behaviour of component-wise load dependent and independent losses at zero

torque level and extend it to the non-zero torque levels. Figure 3.1 shows the tests and green box

represent the losses that occurs in each test, respectively.

Figure3.1. Segregation of losses to the component level

Total Power losses from each test are recorded from the test rig. The following explains different

types of tests conducted:

• Test 1 is conducted on PTU with all components and in the presence of bearings preloads and lubricant.

• Test 2 is conducted in the presence of the lubricant and with no preloads on the tapered roller bearings.

• Test 3 is conducted in the presence of the lubricant, with no preloads on the angular contact ball bearings and no pinion shaft.

• Test 4 is conducted in the presence of the lubricant and without the pinion shaft. • Test 5 is conducted in the absence of the lubricant and without the pinion shaft. • Test 6 is conducted in the absence of the lubricant and without the pinion shaft.

Difference between the power losses computed from tests 1 and 2 gives the total friction losses due

to the bearing preloads of the tapered roller bearings (Head and Tail bearings) mounted on the pinion

shaft. Difference between the power losses computed from tests 3 and 4 gives the total friction losses

due to the bearing preloads of the angular contact ball bearings mounted on the tube shaft. Difference

between the power losses computed from tests 5 and 6 gives the total tube shaft seal friction losses.

The losses are evaluated for four different speeds (150,300,500 and 780 rpm) and two different

temperatures (50 deg and 100 deg celsius) based on the customer requirements.

1 2 3 4 5 6

Component Force

Original

Unit

100% oil.

1st RUN

WO

pinion

preload.

100% oil.

2nd RUN

Tube WO

preload.

Pinion

removed

. 100%

oil.

Tube

preloade

d. Pinion

removed

. 100%

oil.

Tube

preloade

d. Pinion

removed

. NO oil.

Tube

preloade

d. Pinion

removed

. No ube

seals. NO

oil.

Gear Mesh

Pinion Churning

Ring Churning

bearing friction Preload BB

bearing friction Preload TRB

Bearing Drag BB

Bearing Drag TRB

Pinion Seal loss

Ring Seal Loss

Bearing

Gear

Seals

28

3.1.1 Seal Friction Loss Approximation

From the tests conducted at GKN, only the total seal losses were able to be found. Based on the tests

conducted by the seal supplier exclusively for radial shaft seals with different diameters, a diameter

correlation of the seal friction losses was made through linear interpolation. A modification factor

was computed for the losses varying with diameter and the pinion shaft seal losses were found from

the tube shaft seal losses and the modification factor. Table 3.1 shows the modification factor

computed for the diameter correlation.

Table 3.1: Modification Factor for Diameter Correlation

Modification factors were computed for tube shaft rotational speeds (150,300,500 and 780 rpm) and

oil temperatures (50ºC & 100ºC). The following equation estimates pinion shaft seal friction loss from

tube shaft seal friction losses.

Pinion Shaft Seal Loss = Tube Shaft Seal Loss

Modification Factor

3.2 ROMAX Energy Simulation The purpose of using ROMAX energy is to evaluate the component wise drag losses using the inbuilt

power loss models for easier correlation with the test data. The primary steps involved in the

efficiency simulations are-

Modelling - FE models of the pinion and tube shafts, and housing were imported from SIMLAB to ROMAX. Then the bearing nodes were connected to the shaft nodes uniformly

distributed around the shaft via a series of rigid body elements to locate the bearings. The

model is condensed in ROMAX to define the stiffness and mass matrices for the FE model.

Similarly, the radial shaft seals are placed on the shaft. Figure 3.2 shows the PTU model in

ROMAX with all internal components like gears, bearings and seals. Lubricant BOT750B

used in the PTU is defined and added to the lubricant database and based on the immersion

height of the bearing, the lubricant level is calculated from the 2D drawing and defined for

the model in ROMAX.

Figure 3.2. PTU model in ROMAX (ROMAX Energy)

Speed Factor 50 deg Factor 100 deg

150 3.39 9.86

300 1.98 3.65

500 2.15 2.89

780 2.16 2.63

29

Figure 3.3. Defining a lubricant in ROMAX (ROMAX Energy)

Figure 3.3 shows the definition of lubricant in the lubricant database. FVA 345 factors were

also given as an input while defining the lubricant which will be discussed in the power loss

calculation section.

Loading - Define Duty Cycles for temperatures (50ºC & 100ºC) and load cases for four different speeds (150,300,500 and 780 rpm) to create efficiency maps. Figure 3.4 shows the

duty cycle and load cases considered for the Efficiency simulations.

Figure 3.4. Duty Cycle and Load cases (ROMAX Energy)

30

Analysis – Simulations to calculate the load dependent and non-load dependent power losses in each component using the predefined analytical calculation models. The simulations are

run for the defined duty cycles and load cases for correlation with the test results. Table 3.2

shows the analytical models available with ROMAX. The details of the models are discussed

in the frame of reference section.

Table 3.2: Analytical Models in ROMAX

The models are chosen in the analysis settings and simulated for the duty cycles and the load

cases. Figure 3.5 shows the analysis results from the efficiency simulation. The report shows the

component wise total power loss (load dependent and non-load dependent losses). A delimitation

is that the software doesn’t give the breakup of different bearing friction and churning losses

separately. To extract the churning losses simulations were run with and without the presence of

the lubricant and the difference in the total bearing power losses obtained from both cases were

assumed as the bearing churning losses.

Figure 3.5. Load case Efficiency report (ROMAX Energy Report)

31

3.3 Power Loss Calculation

Few other models considered for calculations apart from the inbuilt ROMAX models are changenet

2007 [12], Changenet 2011[13], Terekhov [14] models for Gear churning losses, and Parker [3] and

Linke [4] models for seal friction losses.. The loss models were computed in excel. The gear input

parameters, lubricant viscosity and lubricant level were given as an input and output power loss were

calculated. Figure 3.6 shows the excel calculations for changenet 2007 model.

Figure 3.6. Changenet 2007 model in excel

Since experiments in FVA345 [15] are conducted only for FVA lubricants, interpolation using

regression techniques were used to find friction coefficients and exponents of pressure, viscosity, and

speed for BOT750B lubricant. Four different types of FVA lubricants that were considered in [15]

include synthetic, PAO (polyalphaolefin), PG (polyglycol) and mineral oils. The lubricant used in the

PTU had viscosity and density properties like synthetic oils. Hence, power regression model was

applied based on synthetic oil factors to evaluate the factors for BOT750B. Figure 3.7 shows an

example of how regression technique applied to find friction coefficient in Elasto-hydrodynamic layer

friction (EHD) condition. Similarly, regression was applied to evaluate other factors.

Figure 3.7. Regression technique to evaluate friction coefficient in FVA 345 method

Wheel Pinion

module m 3.5279 3.5279 mm

face qidth b 31 33.4704 mm

subm. Perc h% 0.276533333 0.133333333 mm

oil vol V0 540000 540000 mm3

outer pitch dia Dp 156.5482 71.5546 mm

speed n 780 2014.74

temp T 100 100 °C

kin. Visc ν 9.58 9.58 mm2/s

density ρ 810.9 810.9 kg/m3

gear ratio u 2.583 2.583

Immersion depth h 43.29079557 9.540613333 mm

m/Dp 0.022535551 0.049303609

b/Dp 0.198022079 0.467760284

h/Dp 0.276533333 0.133333333

V0/(Dp)3 0.140750363 0.140750363

W 81.68140899 210.9830794 rad/s

Re 20688.90418 26372.4564

Fr 53234.78651 162343.0904

Sm 0.049 0.012 m2

Cm 0.000111417 8.06219E-05

∆Cm 23.05339303

Cch 0.007082464 0.000799631 Nm

Pch 0.57850564 0.16870856 W

Input

Calc

32

After evaluating the factors, these are given as input to ROMAX to evaluate the gear friction power

losses which was discussed earlier in the modelling section.

3.4 Test Data Correlation

After segregating the test data and extracting the simulation results from ROMAX and excel, the

results were plotted with the drag loss test results. Modification factors were introduced for every

analytical method after correlating with the test results to match the calculated results with the test

results. Data correlation was done for the following analytical methods-

• Seal Friction Loss- ISO14179-1, ISO14179-2, Parker and Linke • Bearing Friction and Churning Loss- ISO14179-1, ISO14179-2, Palmgren and SKF friction

Method

• Gear Friction Loss- ISO14179-1, ISO14179-2, ISOTR22849 & FVA 345. • Gear Churning Loss- ISO14179-1, ISO14179-2, Terekhov, Changenet 2007, Changenet 2011.

Addition and multiplication factors were introduced for all analytical methods to modify the original

equations to correlate with the test results. These factors after validation with different products can

be used in ROMAX and AMESim. The following equation shows the general formula for the

modified equation.

Modified Value = Multiplication 𝐹𝑎𝑐𝑡𝑜𝑟 ∗ 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 + 𝐴𝑑𝑑𝑖𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟

3.5 1-D Simulation

This section describes the methodology of developing a system model of the PTU in AMESim. A

system model is built with the sub models having an inbuilt power loss models for gears and bearings,

and custom-built power loss models for seals representing each component of the PTU. This model

is simulated to evaluate power losses at four different speeds and two different temperatures discussed

earlier. The purpose of this model is to estimate the total power losses of PTU in the early design

stages and customise the components to understand the influence of different factors affecting the

efficiency. The following describe the basic steps involved in building the model and simulating the

power losses [18]-

• Model Simplification- discretization of the components that represent the physical model of the PTU, to build the system model.

• Model Building- Build the system model by building the sketch from the inbuilt libraries and

associate the right sub models depending on the objectives for the simulation. • Parametrization- Assigning values to the geometrical and dynamic parameters to the sub models

based on the actual physical model. • Simu

modeling, simulation and correlation of drag losses in a ...1475473/...modeling, simulation and...

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