Ph.D. DEFENSE PRESENTATION — Elasto-hydrodynamic film formation in heavily loaded rolling-sliding contacts: Influence of surface topography on the transition between lubrication regimes

Elasto-hydrodynamic film formation in heavily loaded rolling-sliding contacts

Influence of surface topography on the transition between lubrication regimes

Ph.D. candidate: Jonny Hansen Subject area: Machine Elements

Opponent: Guillermo E. Morales-Espejel

Principal supervisor: Roland Larsson

Assistant supervisor: Marcus Björling

Heavy duty gear lubrication

2

Non-conformal contact

• Gear (line contact)

Background

Why is this project important?

UNFCCC: The Paris Agreement, https://unfccc.int/process-and-meetings/the-paris-agreement/the-paris-agreement

• Sustainability – pathway to the future

Heavy duty gear lubrication

3

Non-conformal contact

• Gear (line contact)

Background

Why is this project important?

UNFCCC: The Paris Agreement, https://unfccc.int/process-and-meetings/the-paris-agreement/the-paris-agreement

• Transportation sector

– Emits nearly a quarter of global carbon emissions

• Sustainability – pathway to the future

– Accounts for nearly one third of the world’s annual total energy use

– Sustainable transport – must be fossil-free by 2050

Heavy duty gear lubrication

4

Non-conformal contact

• Gear (line contact)

Background

Why is this project important?

UNFCCC: The Paris Agreement, https://unfccc.int/process-and-meetings/the-paris-agreement/the-paris-agreement

• Transportation sector

– Emits nearly a quarter of global carbon emissions

• Scania

– Have pledged to reduce emissions at the scale and pace necessary to limit global warming to 1.5°C above pre-industrial levels

• Sustainability – pathway to the future

– Accounts for nearly one third of the world’s annual total energy use – Sustainable transport – must be fossil-free by 2050

– This project aims to establish key competence in gear tribology

Industrial Ph.D. project on gear lubrication

5

Inadequate lubrication quality

The main types of failure modes connected to lubricant film breakdown are

• Wear – adhesion, abrasion and corrosion

• Plastic deformations – displacement of material in the normal and sliding (friction) direction

• Scuffing – welding of asperity junctions

• Rolling contact fatigue – subsurface originated spalling and/or surface originated micro-/macro-pitting

6

Severe abrasion

Pictures: American Gear Manufacturers Association. (1995). ANSI-AGMA 1010-E95.Appearance of Gear Teeth—Terminology of Wear and Failure.

Hansen (2015). M.Sc. Thesis

Scuffing Pitting Micro-pitting

Inadequate lubrication quality

The main types of failure modes connected to lubricant film breakdown are

• Wear – adhesion, abrasion and corrosion

• Plastic deformations – displacement of material in the normal and sliding (friction) direction

• Scuffing – welding of asperity junctions

• Rolling contact fatigue – subsurface originated spalling and/or surface originated micro-/macro-pitting

May lead to

• Noise, vibration, and harshness (NVH)

• Catastrophic failure (crack propagation, tooth breakage)

7

Severe abrasion

Pictures: American Gear Manufacturers Association. (1995). ANSI-AGMA 1010-E95.Appearance of Gear Teeth—Terminology of Wear and Failure.

Hansen (2015). M.Sc. Thesis

Scuffing Pitting Micro-pitting

Inadequate lubrication quality

The main types of failure modes connected to lubricant film breakdown are

• Wear – adhesion, abrasion and corrosion

• Plastic deformations – displacement of material in the normal and sliding (friction) direction

• Scuffing – welding of asperity junctions

• Rolling contact fatigue – subsurface originated spalling and/or surface originated micro-/macro-pitting

May lead to

• Noise, vibration, and harshness (NVH)

• Catastrophic failure (crack propagation, tooth breakage)

8

Severe abrasion

Pictures: American Gear Manufacturers Association. (1995). ANSI-AGMA 1010-E95.Appearance of Gear Teeth—Terminology of Wear and Failure.

Hansen (2015). M.Sc. Thesis

Scuffing Pitting Micro-pitting

Transmission efficiency trends

• Minimizing losses

• Weight optimization

• Lower viscosity oils

-> Thinner protective films -> Reduced lubrication quality -> Premature failure

 Controlling the tribo-

system is vital!

Fundamentals EHL

(Ch. 3-4)

9

Outlet Inlet

u 2

ω 1

u 1

The mechanism of EHL ¹⁰

u e

P

u

ω

w

Outlet Inlet

u 2

ω 1

u 1

The mechanism of EHL ¹¹

h m

h c

u e

P

u

ω

w

Rough surface EHL

12

Separation=ℎ=Lubricant oil film thickness

Surface 1

Surface 2

𝒉𝒉

Rough surface EHL

13

Surface 1

Surface 2

ℎ =?

3σ

3σ ^2σ

1σ 0 -1σ -2σ -3σ

Rough surface EHL

14

Surface 1

Refs. (in thesis)

28. Tallian, T.E.: On competing failure modes in rolling contact. ASLE Trans. 10, 418–439 (1967) 81. ISO: ISO/TS 6336-22:2018(E): Calculation of micropitting load capacity. (2018)

Surface 2

ℎ = 3𝜎𝜎

𝒉𝒉

3σ

3σ ^2σ

1σ 0 -1σ -2σ -3σ

Rough surface EHL

15

Surface 1

Refs. (in thesis)

28. Tallian, T.E.: On competing failure modes in rolling contact. ASLE Trans. 10, 418–439 (1967) 81. ISO: ISO/TS 6336-22:2018(E): Calculation of micropitting load capacity. (2018)

Surface 2

Λ = ℎ

𝜎𝜎 = 3

𝒉𝒉

3σ

3σ ^2σ

1σ 0 -1σ -2σ -3σ

Rough surface EHL

16

Surface 1

Refs. (in thesis)

28. Tallian, T.E.: On competing failure modes in rolling contact. ASLE Trans. 10, 418–439 (1967) 81. ISO: ISO/TS 6336-22:2018(E): Calculation of micropitting load capacity. (2018)

Surface 2

Λ = ℎ

𝑆𝑆𝑆𝑆 = 3

𝒉𝒉

2σ

2σ 3σ ^1σ 0 -1σ -2σ -3σ

Rough surface EHL

17

Surface 1

Refs. (in thesis)

28. Tallian, T.E.: On competing failure modes in rolling contact. ASLE Trans. 10, 418–439 (1967) 81. ISO: ISO/TS 6336-22:2018(E): Calculation of micropitting load capacity. (2018)

Surface 2

𝒉𝒉

Λ = ℎ

𝑆𝑆𝑆𝑆 = 2

1σ

3σ 2σ

1σ ⁰

-1σ -2σ -3σ

Rough surface EHL

18

Refs. (in thesis)

28. Tallian, T.E.: On competing failure modes in rolling contact. ASLE Trans. 10, 418–439 (1967) 81. ISO: ISO/TS 6336-22:2018(E): Calculation of micropitting load capacity. (2018)

Surface 2

𝒉𝒉

Λ = ℎ

𝑆𝑆𝑆𝑆 = 1

Surface 1

(HL)

C oF

Λ=3 Λ=1

BL ML EHL

The Stribeck curve ¹⁹

EHL

Refs. (in thesis)

123. Stribeck, R.: Eng. Characteristics of plain and roller bearings. Zeitschrift des Vereines Dtsch. Ingenieure. 46, 1341–1348, 1432–1438, 1463–1470 (1902)

16. Spikes, H.A.: Sixty years of EHL. Lubr. Sci.

18, 265–291 (2006)

Λ = ^ℎ

𝑆𝑆𝑞𝑞

+𝑆𝑆𝑞𝑞

ℎ _𝑚𝑚 ∝ 𝑢𝑢 _𝑒𝑒 𝜂𝜂 ₀ ^0.68 𝑤𝑤 ^−0.073

(HL)

C oF

Λ=3 Λ=1

BL ML EHL

The Stribeck curve ²⁰

EHL 2a

Increasing asperity contacts

Decreasing influence of roughness

Refs. (in thesis)

123. Stribeck, R.: Eng. Characteristics of plain and roller bearings. Zeitschrift des Vereines Dtsch. Ingenieure. 46, 1341–1348, 1432–1438, 1463–1470 (1902)

16. Spikes, H.A.: Sixty years of EHL. Lubr. Sci.

18, 265–291 (2006)

Λ = ^ℎ

𝑆𝑆𝑞𝑞

+𝑆𝑆𝑞𝑞

ℎ _𝑚𝑚 ∝ 𝑢𝑢 _𝑒𝑒 𝜂𝜂 ₀ ^0.68 𝑤𝑤 ^−0.073

Micro-EHL ²¹

P 0

u _d

ω _b w

Micro-EHL ²²

P 0

u _d ω _b w

u b

u d

Micro-EHL ²³

P 0

u _d ω _b w

u b

u d

u _asperity

u p _d

Classical 𝚲𝚲-ratio

• The Λ-ratio is still the most widely employed design criterion

– Problematic since it cannot accurately predict the transition between EHL and ML in general

The problem with the current design criteria ²⁴

1Dunaevsky, V.: A Proposed New Film Thickness-Roughness Ratio, z, in Rolling Bearings: Notes on an Engineer’s Experience with Surface Texture Parameters. SAE Tech. Pap. 2017-Octob, (2017).

Classical 𝚲𝚲-ratio

• The Λ-ratio is still the most widely employed design criterion

– Problematic since it cannot accurately predict the transition between EHL and ML in general

• Assuming rigid roughness is an oversimplification in many cases – excludes the micro-EHL regime

The problem with the current design criteria ²⁵

1Dunaevsky, V.: A Proposed New Film Thickness-Roughness Ratio, z, in Rolling Bearings: Notes on an Engineer’s Experience with Surface Texture Parameters. SAE Tech. Pap. 2017-Octob, (2017).

Λ = ^{ℎ 𝑚𝑚}

𝑆𝑆𝑞𝑞 ₁ ² +𝑆𝑆𝑞𝑞 ₂ ²

Classical 𝚲𝚲-ratio

• The Λ-ratio is still the most widely employed design criterion

– Problematic since it cannot accurately predict the transition between EHL and ML in general

• Assuming rigid roughness is an oversimplification in many cases – excludes the micro-EHL regime

• Wear/plastic def. mainly occurs at roughness peaks, valleys pass virtually unchanged

− Reflects poorly on the surface RMS

2σ 3σ ^1σ 0 -1σ -2σ -3σ

The problem with the current design criteria ²⁶

1Dunaevsky, V.: A Proposed New Film Thickness-Roughness Ratio, z, in Rolling Bearings: Notes on an Engineer’s Experience with Surface Texture Parameters. SAE Tech. Pap. 2017-Octob, (2017).

Wear/plastic

deformation at peaks

Classical 𝚲𝚲-ratio

• The Λ-ratio is still the most widely employed design criterion

– Problematic since it cannot accurately predict the transition between EHL and ML in general

• Assuming rigid roughness is an oversimplification in many cases – excludes the micro-EHL regime

• Wear/plastic def. mainly occurs at roughness peaks, valleys pass virtually unchanged

− Reflects poorly on the surface RMS

• Composite RMS, strictly valid only for statistically independent, random-process Gaussian surfaces

– invalidates the use of many engineering surfaces and especially those that have been used in service

• Does not account for the 3D nature of surface topographies

– same Sq=0.285 µm, different capabilliy to form a micro-EHD film

The problem with the current design criteria ²⁷

1Dunaevsky, V.: A Proposed New Film Thickness-Roughness Ratio, z, in Rolling Bearings: Notes on an Engineer’s Experience with Surface Texture Parameters. SAE Tech. Pap. 2017-Octob, (2017).

Classical 𝚲𝚲-ratio

• The Λ-ratio is still the most widely employed design criterion

– Problematic since it cannot accurately predict the transition between EHL and ML in general

• Assuming rigid roughness is an oversimplification in many cases – excludes the micro-EHL regime

• Wear/plastic def. mainly occurs at roughness peaks, valleys pass virtually unchanged

− Reflects poorly on the surface RMS

• Composite RMS, strictly valid only for statistically independent, random-process Gaussian surfaces

– invalidates the use of many engineering surfaces and especially those that have been used in service

• Does not account for the 3D nature of surface topographies

– same Sq=0.285 µm, different capabilliy to form a micro-EHD film

The problem with the current design criteria ²⁸

1Dunaevsky, V.: A Proposed New Film Thickness-Roughness Ratio, z, in Rolling Bearings: Notes on an Engineer’s Experience with Surface Texture Parameters. SAE Tech. Pap. 2017-Octob, (2017).

Pathway towards the new film criterion

29

Results

(Ch. 7-9)

30

RO 1: Explore the fundamental mechanisms of lubricant film- breakdown/-formation in rough surface, heavily loaded, and rolling-sliding EHL contacts

31

Oil from pump

Oil dispenser

Disc Motor Heater

Oil reservoir

Oil pump

Track radius Thermocouple

Thermocouple

Ball Motor I

Disc insulated from spindle

Slip ring Run-track

h

ECR=f(h)

V

u1

u2

Oil to inlet Tilt angle

Potentiometer/

Resistance measurement module

Output signals CoF and ECR

Rs DC

source

Method

32

The WAM

Mimic gear contacts by – High loads 1-3 GPa

− Mixed rolling/sliding

𝑆𝑆𝑆𝑆𝑆𝑆 = 𝑢𝑢 _𝑏𝑏 − 𝑢𝑢 _𝑑𝑑 𝑢𝑢 _𝑒𝑒 𝑢𝑢 _𝑒𝑒 = 𝑢𝑢 _𝑏𝑏 + 𝑢𝑢 _𝑑𝑑

2

Mapping of the lubrication regimes

33

Refs. (in thesis)

101. Björling, M., Habchi, W., Bair, S., Larsson, R., Marklund, P.:

Towards the true prediction of EHL friction.

Tribol. Int. 66, 19–26 (2013)

Thermoviscous Plateau

Mapping of the lubrication regimes

34

Refs. (in thesis)

101. Björling, M., Habchi, W., Bair, S., Larsson, R., Marklund, P.:

Towards the true prediction of EHL friction.

Tribol. Int. 66, 19–26 (2013)

Thermoviscous Plateau

Mapping of the lubrication regimes

35

Refs. (in thesis)

101. Björling, M., Habchi, W., Bair, S., Larsson, R., Marklund, P.:

Towards the true prediction of EHL friction.

Tribol. Int. 66, 19–26 (2013)

1. Hansen, J., Björling, M., Larsson, R.:

Mapping of the lubrication regimes in rough surface EHL contacts.

Tribol. Int. (2018), 131, 637–651

EHL

BL

ML

Onset of mixed lubrication Maximum asperity contact

Thermoviscous Plateau

Mapping of the lubrication regimes

36

Refs. (in thesis)

101. Björling, M., Habchi, W., Bair, S., Larsson, R., Marklund, P.:

Towards the true prediction of EHL friction.

Tribol. Int. 66, 19–26 (2013)

1. Hansen, J., Björling, M., Larsson, R.:

Mapping of the lubrication regimes in rough surface EHL contacts.

Tribol. Int. (2018), 131, 637–651

EHL

BL

ML

Onset of mixed lubrication Maximum asperity contact

Thermoviscous Plateau

Mapping of the lubrication regimes

37

Refs. (in thesis)

101. Björling, M., Habchi, W., Bair, S., Larsson, R., Marklund, P.:

Towards the true prediction of EHL friction.

Tribol. Int. 66, 19–26 (2013)

1. Hansen, J., Björling, M., Larsson, R.:

Mapping of the lubrication regimes in rough surface EHL contacts.

Tribol. Int. (2018), 131, 637–651

FZG LoA @ 3500 RPM

EHL

BL

ML

After

run-in Before run-in

• ECR: EHL/ML transition – Shift 10 to 1 m/s

– ℎ _𝑚𝑚 reduction >80 %

Running-in suppress the EHL-ML transition

38

After

run-in Before run-in

• ECR: EHL/ML transition – Shift 10 to 1 m/s

– ℎ _𝑚𝑚 reduction >80 %

• Surface roughness change after run-in – �𝑆𝑆𝑆𝑆 _𝑐𝑐 reduction 4 %

Running-in suppress the EHL-ML transition

39

-4 %

Surface roughness

After

run-in Before run-in

• ECR: EHL/ML transition – Shift 10 to 1 m/s

– ℎ _𝑚𝑚 reduction >80 %

• Surface roughness change after run-in – �𝑆𝑆𝑆𝑆 _𝑐𝑐 reduction 4 %

Running-in suppress the EHL-ML transition

40

• Lubrication quality

− Clear mismatch

− Λ insufficient after run-in Λ = ℎ _𝑚𝑚

𝑆𝑆𝑆𝑆 _𝑐𝑐

-4 %

Surface roughness

Topographical transformations to promote EHD lift-off

41

Λ = ℎ _𝑚𝑚

𝑆𝑆𝑆𝑆

Topographical transformations to promote EHD lift-off

42

Λ = ℎ _𝑚𝑚 𝑆𝑆𝑆𝑆

Pursuit of a more appropriate

roughness representation

ECR

CoF

EHL

BL ML

Running-in sequence

43

EHD lift-off curves

ECR

CoF

EHL

BL ML

SRR=1.0 P=1.7 GPa 𝒖𝒖 _𝒆𝒆 = 𝟏𝟏 𝐦𝐦/𝐬𝐬

Running-in sequence

44

EHD lift-off curves

Steady state

No contact

ECR

CoF

EHL

BL ML

SRR=1.0 P=1.7 GPa 𝒖𝒖 _𝒆𝒆 = 𝟏𝟏 𝐦𝐦/𝐬𝐬

Running-in sequence

45

EHD lift-off curves

Steady state No contact

Metallic shear

∆ COF=-17 %

ECR

CoF

EHL

BL ML

SRR=1.0 P=1.7 GPa 𝒖𝒖 _𝒆𝒆 = 𝟏𝟏 𝐦𝐦/𝐬𝐬

Running-in sequence

46

EHD lift-off curves

Sq [μm]

𝑢𝑢

[m/s]

EHL/ML transition

Λ

0.3 1 0.61 Pre Post 0.35

>12 0.52

Steady state No contact

Metallic shear

∆ COF=-17 %

ECR

CoF

EHL

BL ML

SRR=1.0 P=1.7 GPa 𝒖𝒖 _𝒆𝒆 = 𝟏𝟏 𝐦𝐦/𝐬𝐬

Running-in sequence

47

EHD lift-off curves

Sq [μm]

𝑢𝑢

[m/s]

EHL/ML transition

Λ

0.3 1 0.61 Pre Post 0.35

>12 0.52

Steady state No contact

Metallic shear

∆ COF=-17 %

Well-off 𝚲𝚲 = 𝟑𝟑

Why?

Asperity deformations

48

0.1 mm I

I

Pre

Post

Hertzian contact

diameter

Sliding

Asperity deformations

49

0.1 mm I

I

Pre

Post

Hertzian contact

diameter

Sliding

Asperity deformations

50

0.1 mm I

I

Pre

Post

Hertzian contact

diameter

Sliding

Asperity deformations

51

0.1 mm I

I

Pre

Post

Hertzian contact

diameter

Sliding

10 μm

Micro-EHL regime

52

Refs. (in thesis)

3. Hansen, J., Björling, M., Larsson, R.: Lubricant film formation in rough surface non-conformal conjunctions subjected to GPa pressures and high slide-to-roll ratios. Sci. Rep. 10, 1–16 (2020)

𝒖𝒖 _𝒆𝒆

10 μm

Micro-EHL regime

53

Refs. (in thesis)

197. Choo JW, Glovnea RP, Olver A V., Spikes H a. The Effects of Three- Dimensional Model Surface Roughness Features on Lubricant Film Thickness in EHL Contacts. J Tribol 2003;125:533.

3. Hansen, J., Björling, M., Larsson, R.: Lubricant film formation in rough surface non-conformal conjunctions subjected to GPa pressures and high slide-to-roll ratios. Sci. Rep. 10, 1–16 (2020)

ℎ _𝑎𝑎 = ℎ _𝑐𝑐 × 𝑟𝑟 _𝑥𝑥 𝑆𝑆 _𝑥𝑥

0.464

𝒖𝒖 _𝒆𝒆

micro-horseshoe

𝒖𝒖 _𝒆𝒆

Plastic deformation

→ Asperity blunting

→ lowering in asperity peaks

→ increase to asperity radii

The mechanism of running-in ⁵⁴

Interference plane

Plastic deformation

→ Asperity blunting

→ lowering in asperity peaks

→ increase to asperity radii

The mechanism of running-in ⁵⁵

Interference plane

Plastic deformation

→ Asperity blunting

→ lowering in asperity peaks

→ increase to asperity radii

w

δ

The mechanism of running-in ⁵⁶

Interference plane

Plastic deformation

→ Asperity blunting

→ lowering in asperity peaks

→ increase to asperity radii

w

δ

The mechanism of running-in ⁵⁷

Interference plane

Omni-directional

plastic flow

w

δ r _x,0

r _x,1

The mechanism of running-in

Plastic deformation

→ Asperity blunting

→ lowering in asperity peaks

→ increase to asperity radii

58

Interference plane

Omni-directional

plastic flow

Undeformed asperity at inlet

Asperity in micro-EHL

r

z 0

h a

u a

u d

h c

x z

w

δ r _x,0

r _x,1

The mechanism of running-in

Plastic deformation

→ Asperity blunting

→ lowering in asperity peaks

→ increase to asperity radii

59

Omni-directional plastic flow ℎ _𝑎𝑎 = ℎ _𝑐𝑐 × 𝑟𝑟 _𝑥𝑥

𝑆𝑆 _𝑥𝑥

0.464

Refs. (in thesis)

26. Fein, R.S., Kreuz, K.L.: “Discussion on boundary lubrication”, Inter-disciplinary approach to friction and wear. In: NASA SP-181 (1967) 20. Hamrock, B.J., Dowson, D.: Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part III - Fully Flooded Results. J. Tribol. 99, 264–275 (1977).

197. Choo, J.W., Glovnea, R.P., Olver, A. V., Spikes, H. a.: The Effects of Three-Dimensional Model Surface Roughness Features on Lubricant Film Thickness in EHL Contacts. J. Tribol. 125, 533 (2003)

3. Hansen, J., Björling, M., Larsson, R.: Lubricant film formation in rough surface non-conformal conjunctions subjected to GPa pressures and high slide-to-roll ratios. Sci. Rep. 10, 1–16 (2020)

Surface metrology

Height and curvature

60

Λ = ℎ _𝑚𝑚 𝑆𝑆𝑆𝑆

0.

I

Post

Hertzian contact diameter Sliding

0.1 mm I

Pre

Post

Refs. (in thesis)

2. Hansen, J., Björling, M., Larsson, R.: Topography transformations due to running-in of rolling- sliding non-conformal contacts. Tribol. Int. 144, 106126 (2020).

3. Hansen, J., Björling, M., Larsson, R.: Lubricant film formation in rough surface non-conformal conjunctions subjected to GPa pressures and high slide-to-roll ratios. Sci. Rep. 10, 1–16 (2020)

Surface metrology

Height and curvature

More sensitive for film formation

• 𝑆𝑆𝑆𝑆 → 𝑆𝑆𝑆𝑆𝑆𝑆 (plastic def. mild wear)

• 𝑟𝑟 (𝑆𝑆𝑆𝑆𝑆𝑆) → micro-EHL

61

Λ = ℎ _𝑚𝑚 𝑆𝑆𝑆𝑆

0.

I

Post

Hertzian contact diameter Sliding

0.1 mm I

Pre

Post

Refs. (in thesis)

2. Hansen, J., Björling, M., Larsson, R.: Topography transformations due to running-in of rolling- sliding non-conformal contacts. Tribol. Int. 144, 106126 (2020).

3. Hansen, J., Björling, M., Larsson, R.: Lubricant film formation in rough surface non-conformal conjunctions subjected to GPa pressures and high slide-to-roll ratios. Sci. Rep. 10, 1–16 (2020)

62

Results

(Ch. 9)

63

RO 2: Develop a new improved film parameter that much more accurately estimates the

lubrication quality in rough surface EHL contact than offered by the classical approach (the Λ-ratio)

Ball

Disc x z

y

Inlet

Mathematical foundation ⁶⁴

Ball

Disc

Deformed asperity

Undeformed asperity x

z y

Inlet

Mathematical foundation

Deformed asperity height:

𝑧𝑧

= 𝑧𝑧

− ℎ

(1)

65

Ball

Disc

Deformed asperity

Undeformed asperity x

z y

Inlet

Mathematical foundation

Deformed asperity height:

𝑧𝑧

= 𝑧𝑧

− ℎ

(1)

The available space at the contact outlet zone

ℎ

= Δℎ + 𝑧𝑧

(2)

66

Ball

Disc

Deformed asperity

Undeformed asperity x

z y

Inlet

Mathematical foundation

Deformed asperity height:

𝑧𝑧

= 𝑧𝑧

− ℎ

(1)

The available space at the contact outlet zone

ℎ

= Δℎ + 𝑧𝑧

(2)

Eq. (1) in (2) and rearranging, we get:

Δℎ = ℎ

− 𝑧𝑧

= ℎ

− (𝑧𝑧

− ℎ

) (3) Rearranging and considering contact

Δℎ = (ℎ

+ ℎ

) − 𝑧𝑧

= ℎ

− 𝑧𝑧

= 0 (4)

67

Ball

Disc

Deformed asperity

Undeformed asperity x

z y

Inlet

Mathematical foundation

Deformed asperity height:

𝑧𝑧

= 𝑧𝑧

− ℎ

(1)

The available space at the contact outlet zone

ℎ

= Δℎ + 𝑧𝑧

(2)

Eq. (1) in (2) and rearranging, we get:

Δℎ = ℎ

− 𝑧𝑧

= ℎ

− (𝑧𝑧

− ℎ

) (3) Rearranging and considering contact

Δℎ = (ℎ

+ ℎ

) − 𝑧𝑧

= ℎ

− 𝑧𝑧

= 0 (4) A micro-EHL film parameter can then be expressed

Λ

=

0

=

0

(5)

With the transition to FF-EHL when Λ

≥ 1

68

• From the ratio of the micro/-macro-scale D-H (and D-C) equ.

𝑓𝑓 _𝑞𝑞 = ^𝑟𝑟 _𝑅𝑅

^𝜒𝜒 × ^1−𝜅𝜅

^×𝑒𝑒 _1−𝜅𝜅

1

×𝑒𝑒

Refs. (in thesis)

26. Fein, R.S., Kreuz, K.L.: “Discussion on boundary lubrication”, Inter- disciplinary approach to friction and wear. In: NASA SP-181 (1967)

20. Hamrock, B.J., Dowson, D.: Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part III - Fully Flooded Results. J. Tribol. 99, 264–275 (1977).

245. Guangteng, G., Cann, P.M., Olver, A. V, Spikes, H.A.: Lubricant Film Thickness in Rough Surface, Mixed Elastohydrodynamic Contact, (2000)

67. Jacobson, B.: Nano-Meter Film Rheology and Asperity Lubrication. J.

Tribol. 124, 595 (2002)

197. Choo, J.W., Glovnea, R.P., Olver, A. V., Spikes, H. a.: The Effects of Three-Dimensional Model Surface Roughness Features on Lubricant Film Thickness in EHL Contacts. J. Tribol. 125, 533 (2003)

215. Choo, J.W., Olver, A. V., Spikes, H. a., Dumont, M.-L.E.L., Ioannides, E.: The Influence of Longitudinal Roughness in Thin-Film, Mixed Elastohydrodynamic Lubrication. Tribol. Trans. 49, 248–259 (2006) 214. Choo, J.W., Olver, A. V., Spikes, H.A.: The influence of transverse roughness in thin film, mixed elastohydrodynamic lubrication. Tribol. Int.

40, 220–232 (2007)

A generalized equation for hemispherical bumps and ridges

Surface

roughness lay Ratio of film thickness

equation 𝛘𝛘 𝛋𝛋

𝛋𝛋

𝛋𝛋

Isotropic &

Transversal D-H 0.464 0.61 0.75 2/𝜋𝜋

Longitudinal D-C

0.466 1 1.23 2/3

a246. Chittenden, R.J., Dowson, D., Dunn, J.F., Taylor, C.M.: A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. I. Direction of lubricant entrainment coincident with the major axis of the Hertzian contact ellipse. Proc. R. Soc. - a. 397, 245–269 (1985)

The computation of 𝒉𝒉 _𝒂𝒂 69

4. Hansen, J., Björling, M., Larsson, R.: A new film parameter for rough surface EHL contacts with anisotropic and with isotropic structures. Tribol.

Lett. (in review)

• From the ratio of the micro/-macro-scale D-H (and D-C) equ.

𝑓𝑓 _𝑞𝑞 = ^𝑟𝑟 _𝑅𝑅

^𝜒𝜒 × ^1−𝜅𝜅

^×𝑒𝑒 _1−𝜅𝜅

1

×𝑒𝑒

• The inlet induced micro-EHL separation is then simply ℎ _𝑎𝑎 = ℎ _𝑐𝑐 × 𝑓𝑓 _𝑞𝑞

• Or given from the chart

A generalized equation for hemispherical bumps and ridges

Surface

roughness lay Ratio of film thickness

equation 𝛘𝛘 𝛋𝛋

𝛋𝛋

𝛋𝛋

Isotropic &

Transversal D-H 0.464 0.61 0.75 2/𝜋𝜋

Longitudinal D-C

0.466 1 1.23 2/3

a246. Chittenden, R.J., Dowson, D., Dunn, J.F., Taylor, C.M.: A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. I. Direction of lubricant entrainment coincident with the major axis of the Hertzian contact ellipse. Proc. R. Soc. - a. 397, 245–269 (1985)

The computation of 𝒉𝒉 _𝒂𝒂 70

4. Hansen, J., Björling, M., Larsson, R.: A new film parameter for rough surface EHL contacts with anisotropic and with isotropic structures. Tribol.

Lett. (in review)

Extension to engineering roughness

Step 1. Determine a representative 𝒓𝒓

• A convenient method is by means of motif analysis (ISO 25178)

71

Extension to engineering roughness

Step 1. Determine a representative 𝒓𝒓

• A convenient method is by means of motif analysis (ISO 25178)

• Segment the surface into significant peaks and valleys

72

Extension to engineering roughness

Step 1. Determine a representative 𝒓𝒓

• A convenient method is by means of motif analysis (ISO 25178)

• Segment the surface into significant peaks and valleys

– Determine a representative (mean) peak height (𝑧𝑧 _𝑎𝑎 ) and width (𝑏𝑏 _𝑎𝑎 )

73

Extension to engineering roughness

Step 1. Determine a representative 𝒓𝒓

• A convenient method is by means of motif analysis (ISO 25178)

• Segment the surface into significant peaks and valleys

– Determine a representative (mean) peak height (𝑧𝑧 _𝑎𝑎 ) and width (𝑏𝑏 _𝑎𝑎 ) – Compute 𝑟𝑟 by means of trigonometry

𝑟𝑟 = 𝑆𝑆 _{𝑥𝑥/𝑦𝑦,𝑎𝑎} = 𝑏𝑏 _{𝑥𝑥/𝑦𝑦,𝑎𝑎} ² 8𝑧𝑧 _𝑎𝑎

74

Extension to engineering roughness

Step 1. Determine a representative 𝒓𝒓

• A convenient method is by means of motif analysis (ISO 25178)

• Segment the surface into significant peaks and valleys

– Determine a representative (mean) peak height (𝑧𝑧 _𝑎𝑎 ) and width (𝑏𝑏 _𝑎𝑎 ) – Compute 𝑟𝑟 by means of trigonometry

𝑟𝑟 = 𝑆𝑆 _{𝑥𝑥/𝑦𝑦,𝑎𝑎} = 𝑏𝑏 _{𝑥𝑥/𝑦𝑦,𝑎𝑎} ² 8𝑧𝑧 _𝑎𝑎

– Then, from the chart, determine 𝑓𝑓 _𝑞𝑞 for computation of ℎ _𝑎𝑎 = ℎ _𝑐𝑐 × 𝑓𝑓 _𝑞𝑞

75

Extension to engineering roughness

Step 2. The selection of a representative height

• The Spk is highly sensitive for film formation

• Free of the Gaussian constrain (two-sided roughness)

76

Extension to engineering roughness

Step 2. The selection of a representative height

• The Spk is highly sensitive for film formation

• Free of the Gaussian constrain (two-sided roughness)

• Thus, consider 𝑧𝑧 ₀ = 𝑆𝑆𝑆𝑆𝑆𝑆 in equation (4)

Δℎ = (ℎ _𝑚𝑚 + ℎ _𝑎𝑎 ) − 𝑆𝑆𝑆𝑆𝑆𝑆 = ℎ ^∗ − 𝑆𝑆𝑆𝑆𝑆𝑆

77

Extension to engineering roughness

Step 2. The selection of a representative height

• The Spk is highly sensitive for film formation

• Free of the Gaussian constrain (two-sided roughness)

• Thus, consider 𝑧𝑧 ₀ = 𝑆𝑆𝑆𝑆𝑆𝑆 in equation (4)

Δℎ = (ℎ _𝑚𝑚 + ℎ _𝑎𝑎 ) − 𝑆𝑆𝑆𝑆𝑆𝑆 = ℎ ^∗ − 𝑆𝑆𝑆𝑆𝑆𝑆

• A general micro-EHL film parameter can then be expressed

𝚲𝚲 ^∗ = ^{𝒉𝒉 𝒎𝒎} _{𝑺𝑺𝑺𝑺𝑺𝑺} ^{+𝒉𝒉 𝒂𝒂} , with FF-EHL when 𝚲𝚲 ^∗ ≥ 𝟏𝟏

78

The complete model ⁷⁹

𝚲𝚲 ^∗ = 𝒉𝒉 _𝒎𝒎 + 𝒉𝒉 _𝒂𝒂

𝒛𝒛 _𝟎𝟎 = 𝒉𝒉 _𝒎𝒎 + [𝒉𝒉 _𝒄𝒄 × 𝒇𝒇 _𝒒𝒒 ]

𝑺𝑺𝑺𝑺𝑺𝑺 = 𝒉𝒉 ^∗ 𝑺𝑺𝑺𝑺𝑺𝑺

A new film parameter accounting for

• Isotropic-/anisotropic-roughness with either Gaussian/non-Gaussian height distribution

• The inlet induced roughness deformation that enables micro-EHL

Smooth disc

c) b)

Area 1

Minimum slope with 40% window

Smr2 Smr1

z [µm ]

Area 2

Material ratio [%]

a) Representative micro-EHD roughness feature

Undeformed ball roughness

Experimental validation

Possible by

• Running-in sequence to promote FF-EHL from ML

• Surface re-location techniques to determine 𝑟𝑟 and 𝑆𝑆𝑆𝑆𝑆𝑆 very precisely

80

Experimental validation

Possible by

• Running-in sequence to promote FF-EHL from ML

• Surface re-location techniques to determine 𝑟𝑟 and 𝑆𝑆𝑆𝑆𝑆𝑆 very precisely

81

Experimental validation

Possible by

• Running-in sequence to promote FF-EHL from ML

• Surface re-location techniques to determine 𝑟𝑟 and 𝑆𝑆𝑆𝑆𝑆𝑆 very precisely

82

Topography 𝒓𝒓/𝑹𝑹

[-] 𝒉𝒉

[µm] Spk

[µm] 𝚲𝚲

[-] 𝚲𝚲

[-] ECR

[%]

True Lubrication

State

Transversal Pre 0.0144 0.0482 0.312 0.61 0.50 0.06 Interference

Post 0.0341 0.0717 0.220 0.97 0.73 99.7 FF-EHL

Longitudinal Pre 0.0185 0.0286 0.208 0.82 0.50 0.11 Interference

Post 0.0331 0.0411 0.169 1.1 0.63 99.6 FF-EHL

Isotropic Pre 0.0260 0.0450 0.272 0.69 0.52 0.17 Interference

Post 0.0480 0.0597 0.196 1.0 0.58 99.6 FF-EHL

Experimental validation

Possible by

• Running-in sequence to promote FF-EHL from ML

• Surface re-location techniques to determine 𝑟𝑟 and 𝑆𝑆𝑆𝑆𝑆𝑆 very precisely

83

Experimental validation

Possible by

• Running-in sequence to promote FF-EHL from ML

• Surface re-location techniques to determine 𝑟𝑟 and 𝑆𝑆𝑆𝑆𝑆𝑆 very precisely

84

EHL-ML transition

Results

(Ch. 10)

85

Running-in for improved micro-EHL

• Why not just run-in surface as harsh as possible?

– Maximize reduction to 𝑆𝑆𝑆𝑆𝑆𝑆, and increase to 𝑟𝑟

86

Refs. (in thesis)

5. Hansen, J., Björling, M., Minami, I., Larsson, R.:

Performance and mechanisms of silicate tribofilm in heavily loaded rolling/sliding non-conformal contacts.

Tribol. Int. 123, 130–141 (2018)

Running-in for improved micro-EHL

• Why not just run-in surface as harsh as possible?

– Maximize reduction to 𝑆𝑆𝑆𝑆𝑆𝑆, and increase to 𝑟𝑟 – Scuffing

87

Refs. (in thesis)

5. Hansen, J., Björling, M., Minami, I., Larsson, R.:

Performance and mechanisms of silicate tribofilm in heavily loaded rolling/sliding non-conformal contacts.

Tribol. Int. 123, 130–141 (2018)

Running-in for improved micro-EHL

• Why not just run-in surface as harsh as possible?

– Maximize reduction to 𝑆𝑆𝑆𝑆𝑆𝑆, and increase to 𝑟𝑟 – Scuffing

• Running-in agent (P-SiSO, novel IL-additive technology) – Improve scuffing performance

– Excellent running-in characteristics (𝑆𝑆𝑆𝑆𝑆𝑆, 𝑟𝑟)

88

Refs. (in thesis)

5. Hansen, J., Björling, M., Minami, I., Larsson, R.:

Performance and mechanisms of silicate tribofilm in heavily loaded rolling/sliding non-conformal contacts.

Tribol. Int. 123, 130–141 (2018)

Running-in for improved micro-EHL

• Why not just run-in surface as harsh as possible?

– Maximize reduction to 𝑆𝑆𝑆𝑆𝑆𝑆, and increase to 𝑟𝑟 – Scuffing

• Running-in agent (P-SiSO, novel IL-additive technology) – Improve scuffing performance

– Excellent running-in characteristics (𝑆𝑆𝑆𝑆𝑆𝑆, 𝑟𝑟)

• Can the running-in agent promote a surface’s micro-EHD film forming capability?

– Very harsh running-in sequence (Λ = 0.05)

89

Refs. (in thesis)

5. Hansen, J., Björling, M., Minami, I., Larsson, R.:

Performance and mechanisms of silicate tribofilm in heavily loaded rolling/sliding non-conformal contacts.

Tribol. Int. 123, 130–141 (2018)

Run-in agent Paper 4

(Λ = 0.05) (Λ = 0.5)

Micro-EHD improvement ⁹⁰

Run-in agent Paper 4

(Λ = 0.05) (Λ = 0.5)

Micro-EHD improvement ⁹¹

Increased 𝒓𝒓

for micro-EHL

(Λ = 0.05) (Λ = 0.5) Paper 4 Run-in agent

Micro-EHD improvement ⁹²

Run-in agent Paper 4

(Λ = 0.05)

(Λ = 0.5)

(Λ = 0.05) (Λ = 0.5) Paper 4 Run-in agent

Micro-EHD improvement ⁹³

(Λ = 0.05) (Λ = 0.5) Paper 4 Run-in agent

Micro-EHD improvement ⁹⁴

Superior micro-EHD performance

Conclusions

• The classical design criterion Λ critically assessed

95

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

96

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged

97

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

98

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML

99

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

100

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

– 𝑆𝑆𝑆𝑆𝑆𝑆 much more sensitive to film formation (plastic def. wear) than 𝑆𝑆𝑆𝑆

101

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

– 𝑆𝑆𝑆𝑆𝑆𝑆 much more sensitive to film formation (plastic def. wear) than 𝑆𝑆𝑆𝑆 – 𝑟𝑟 the most sensitive, provides local elasticity to the roughness

102

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

– 𝑆𝑆𝑆𝑆𝑆𝑆 much more sensitive to film formation (plastic def. wear) than 𝑆𝑆𝑆𝑆 – 𝑟𝑟 the most sensitive, provides local elasticity to the roughness

– Enables for the micro-EHL regime

103

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

– 𝑆𝑆𝑆𝑆𝑆𝑆 much more sensitive to film formation (plastic def. wear) than 𝑆𝑆𝑆𝑆 – 𝑟𝑟 the most sensitive, provides local elasticity to the roughness

– Enables for the micro-EHL regime

• A more general film parameter was introduced

104

𝚲𝚲 ^∗ = 𝒉𝒉 _𝒎𝒎 + 𝒉𝒉 _𝒂𝒂

𝒛𝒛 _𝟎𝟎 = 𝒉𝒉 _𝒎𝒎 + [𝒉𝒉 _𝒄𝒄 × 𝒇𝒇 _𝒒𝒒 ]

𝑺𝑺𝑺𝑺𝑺𝑺

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

– 𝑆𝑆𝑆𝑆𝑆𝑆 much more sensitive to film formation (plastic def. wear) than 𝑆𝑆𝑆𝑆 – 𝑟𝑟 the most sensitive, provides local elasticity to the roughness

– Enables for the micro-EHL regime

• A more general film parameter was introduced

– Valid for isotropic-/anisotropic-structure and Gaussian/non-Gaussian height distribution

105

𝚲𝚲 ^∗ = 𝒉𝒉 _𝒎𝒎 + 𝒉𝒉 _𝒂𝒂

𝒛𝒛 _𝟎𝟎 = 𝒉𝒉 _𝒎𝒎 + [𝒉𝒉 _𝒄𝒄 × 𝒇𝒇 _𝒒𝒒 ]

𝑺𝑺𝑺𝑺𝑺𝑺

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

– 𝑆𝑆𝑆𝑆𝑆𝑆 much more sensitive to film formation (plastic def. wear) than 𝑆𝑆𝑆𝑆 – 𝑟𝑟 the most sensitive, provides local elasticity to the roughness

– Enables for the micro-EHL regime

• A more general film parameter was introduced

– Valid for isotropic-/anisotropic-structure and Gaussian/non-Gaussian height distribution – Accounts for the micro-EHL regime

106

𝚲𝚲 ^∗ = 𝒉𝒉 _𝒎𝒎 + 𝒉𝒉 _𝒂𝒂

𝒛𝒛 _𝟎𝟎 = 𝒉𝒉 _𝒎𝒎 + [𝒉𝒉 _𝒄𝒄 × 𝒇𝒇 _𝒒𝒒 ]

𝑺𝑺𝑺𝑺𝑺𝑺

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

– 𝑆𝑆𝑆𝑆𝑆𝑆 much more sensitive to film formation (plastic def. wear) than 𝑆𝑆𝑆𝑆 – 𝑟𝑟 the most sensitive, provides local elasticity to the roughness

– Enables for the micro-EHL regime

• A more general film parameter was introduced

– Valid for isotropic-/anisotropic-structure and Gaussian/non-Gaussian height distribution – Accounts for the micro-EHL regime

− Convenient since it requires only well established EHL theory and surface metrology as input

107

𝚲𝚲 ^∗ = 𝒉𝒉 _𝒎𝒎 + 𝒉𝒉 _𝒂𝒂

𝒛𝒛 _𝟎𝟎 = 𝒉𝒉 _𝒎𝒎 + [𝒉𝒉 _𝒄𝒄 × 𝒇𝒇 _𝒒𝒒 ]

𝑺𝑺𝑺𝑺𝑺𝑺

Conclusions

• The classical design criterion Λ critically assessed

– Only valid for Gaussian surface (before running-in)

– Sq is not a sufficient representation of roughness height

• Running-in reflects poorly on RMS since valleys pass virtually unchanged – Neglects micro-EHL

• Running-in was used to promote topographical transformation to establish FF-EHL from ML – Improved micro-conformity, i.e., increased summit curvature and height

– 𝑆𝑆𝑆𝑆𝑆𝑆 much more sensitive to film formation (plastic def. wear) than 𝑆𝑆𝑆𝑆 – 𝑟𝑟 the most sensitive, provides local elasticity to the roughness

– Enables for the micro-EHL regime

• A more general film parameter was introduced

– Valid for isotropic-/anisotropic-structure and Gaussian/non-Gaussian height distribution – Accounts for the micro-EHL regime

− Convenient since it requires only well established EHL theory and surface metrology as input

− Can be used in design to promote the transition to FF-EHL

108

𝚲𝚲 ^∗ = 𝒉𝒉 _𝒎𝒎 + 𝒉𝒉 _𝒂𝒂

𝒛𝒛 _𝟎𝟎 = 𝒉𝒉 _𝒎𝒎 + [𝒉𝒉 _𝒄𝒄 × 𝒇𝒇 _𝒒𝒒 ]

𝑺𝑺𝑺𝑺𝑺𝑺

Acknowledgements

Financial support

This work was funded by the Swedish Foundation for Strategic Research (SSF), the Swedish Research Council (VR), Norrbottens Research Council and Scania CV AB.

Special thanks to

• Wedeven Associates Inc., Edgemont, PA, USA. This work would not have been possible without their creativity and dedication in developing the patterned balls.

• Marika Torbacke at Agrol Lubricants in Sweden for providing the PAO oil.

Thank you for listening! Thank you for listening! ¹¹⁰

Future work

• Define the BL and ML regimes for Λ

• Examine the influence of ‘two-sided-roughness’

• Incorporate an equally easy-to-use measure that accounts for the stress history – a life-rating model

• Analyze Λ

by means of a fully deterministic EHL solver

• Examine how the P-SiSO compound can withstand RCF

112

Body 1

Body 3 Body 2

Non-conformal contact Conformal

contact

Contact classifications

Lubrication of rotating machinery ¹¹³

• Conformal

− MPa pressures

− Insignificant elastic deformation

− HL

− Journal bearings, thrust bearings, piston-cylinder liners etc.

• Non-conformal

− GPa pressures

− Significant elastic deformation

− EHL

− Gears, cam-followers, rolling

element bearings etc.

Body 1

Body 3 Body 2

Non-conformal contact Conformal

contact

Contact classifications

Lubrication of rotating machinery ¹¹⁴

• Conformal

− MPa pressures

− Insignificant elastic deformation

− HL

− Journal bearings, thrust bearings, piston-cylinder liners etc.

• Non-conformal

− GPa pressures

− Significant elastic deformation

− EHL

− Gears, cam-followers, rolling

element bearings etc.