# On Friction Reduction by Surface Modifications in the TEHL Cam/Tappet-Contact-Experimental and Numerical Studies

^{*}

## Abstract

**:**

## 1. Introduction

_{2}and Al

_{2}O

_{3}-coatings compared to the uncoated specimens.

## 2. Materials and Methods

#### 2.1. Experimental Methods

#### 2.1.1. Materials

_{a}≈ 0.005 μm, and ultrasonically cleaned in acetone and isopropyl alcohol.

#### 2.1.2. Microtexturing

_{a}≈ 0.005 μm) and texture depth. Thus, we set a shallow depth of around 2 μm. Lateral dimensions of each texture element were constant at 35 μm in, as well as 2 mm perpendicular to the direction of motion. Distances between the textures were 180 μm in and 1 mm perpendicular, respectively. This measure corresponded to area coverage of approximately 10%. The values were chosen as they were advantageous as described in the literature and previous studies [49,50].

#### 2.1.3. Coating

_{a}≈ 0.047 μm.

#### 2.1.4. Characterization and Tribological Testing

_{IT}and indentation modulus E

_{IT}were measured by nanoindentation using a Picodenter HM500 (HELMUT FISCHER, Sindelfingen, Germany). The H

_{IT}and E

_{IT}values of the coating were determined at a maximum load of 3 mN, ensuring indentation depths of the Vickers indenter of less than 10% of the coating thickness to minimize the influence of the substrate material [52]. A load of 500 mN was chosen for the indentation of the uncoated steel substrate. To compensate for the statistical scattering due to surface roughness and irregularities, we performed twenty indentations of which not more than four significant outliers were precluded from the evaluation.

_{a}≈ 0.2 μm) without profiling, at a width of 10 mm, a base radius of 15 mm, and a tip radius of 2.3 mm was cut out of a series camshaft, provided with cone seats and held by two shafts. The same cam which had previously been run in for 24 h was used for all tests. The test-unit, in which the tappet and valve were moving linearly, was mounted elastically at the bottom and supported by four crosswise arranged, preloaded piezoelectric force sensors at the top. Thus, the friction force within the cam/tappet-contact could be determined. For lubrication, pure mineral oil FVA 3 (kinematic viscosity 95 mm/s² at 40 °C, viscosity index 195) was used and heated to 90 °C in the hydraulics-unit. Three samples of each, polished references, as well as the microtextured and DLC-coated specimens, were tested, and the sequence was randomized. After running in for one hour at 1000 min

^{−1,}, the camshaft rotation speed was increased gradually from 200 to 2000 min

^{−1,}and each level was held for one minute. Measurement values were detected at the end of each speed level. For the evaluation, we compared the maximum friction force averaged over three samples per type and several rotations each.

#### 2.2. Numerical Methods

#### 2.2.1. Hydrodynamics

#### 2.2.2. Contact Mechanics

#### 2.2.3. Thermodynamics

#### 2.2.4. Numerical Procedure

#### 2.2.5. Load Cases, Material and Lubricant Properties

^{−1}(Moes parameters M = 9.3, L = 8.1, SRR = −2.6), 1000 min

^{−1}(M = 6.3, L = 9,7, SRR = −2.6), and 2000 min

^{−1}(M = 3.6, L = 11.5, SRR = −2.6), were studied within the scope of this manuscript.

## 3. Results and Discussion

#### 3.1. Experimental Results

_{IT}of 15.8 ± 0.5 GPa, and an indentation modulus E

_{IT}of 110.9 ± 3.3 GPa. Therefore, compared to the substrate (H

_{IT}= 8.3 ± 0.2 GPa, E

_{IT}= 216.5 ± 2.5 GPa), the coating was harder, though elastically less stiff.

#### 3.2. Numerical Results

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

a_{c} | Carreau parameter |

a_{texture} | micro-texture amplitude |

b_{Hertz} | Hertzian contact half-width |

c_{p} | specific heat capacity |

C | compliance matrix |

d_{texture} | micro-texture distance |

E | Young’s modulus |

E_{IT} | indentation modulus |

F | normal force |

F_{fluid} | fluid friction force |

F_{solid} | solid friction force |

g | zero level correction parameter |

G_{c} | critical shear stress |

h | lubricant gap |

h_{0} | rigid body motion |

H_{IT} | indentation hardness |

l | cam width in y-direction |

L | Moe’s dimensionless material properties parameter |

M | Moe’s dimensionless load parameter |

n_{c} | Carreau parameter |

p | hydrodynamic pressure |

p_{Hertz} | Hertzian contact pressure |

p_{solid} | solid contact pressure |

p_{total} | total contact pressure |

R | equivalent radius |

SRR | slide-to-roll ratio |

u_{1} | sliding velocity of body 1 |

u_{2} | sliding velocity of body 2 |

u_{m} | mean hydrodynamic velocity |

U_{z} | displacement in z-direction |

t | time |

T | temperature |

w_{texture} | micro-texture width in x-direction |

x, y, z | space coordinates |

x_{start} | starting position of the micro-texture in x-direction |

α_{p} | pressure viscosity coefficient |

β_{p} | volume expansion coefficient |

β_{η} | Roelands temperature viscosity coefficient |

δ_{elastic} | elastic deformation in z-direction |

ε | strain tensor |

η | lubricant viscosity |

η_{0} | lubricant viscosity at reference state |

λ | thermal conductivity |

μ_{solid} | solid friction coefficient |

ρ | density |

σ | stress tensor of the equivalent body |

τ_{zx} | shear stress |

υ | Poisson’s ratio |

Ω | computational domain |

## References

- Holmberg, K.; Andersson, P.; Erdemir, A. Global energy consumption due to friction in passenger cars. Tribol. Int.
**2012**, 47, 221–234. [Google Scholar] [CrossRef] - Kalghatgi, G. Is it really the end of internal combustion engines and petroleum in transport? Appl. Energy
**2018**, 225, 965–974. [Google Scholar] [CrossRef] - Serrano, J.R.; Novella, R.; Piqueras, P. Why the development of internal combustion engines is still necessary to fight against global climate change from the perspective of transportation. Appl. Sci.
**2019**, 9, 4597. [Google Scholar] [CrossRef][Green Version] - Farfan-Cabrera, L.I. Tribology of electric vehicles: A review of critical components, current state and future improvement trends. Tribol. Int.
**2019**, 138, 473–486. [Google Scholar] [CrossRef] - Holmberg, K.; Erdemir, A. Influence of tribology on global energy consumption, costs and emissions. Friction
**2017**, 5, 263–284. [Google Scholar] [CrossRef] - Kalin, M.; Velkavrh, I.; Vižintin, J.; Ožbolt, L. Review of boundary lubrication mechanisms of DLC coatings used in mechanical applications. Meccanica
**2008**, 43, 623–637. [Google Scholar] [CrossRef] - Erdemir, A.; Donnet, C. Tribology of diamond-like carbon films: Recent progress and future prospects. J. Phys. D Appl. Phys.
**2006**, 39, R311–R327. [Google Scholar] [CrossRef] - Gropper, D.; Wang, L.; Harvey, T.J. Hydrodynamic lubrication of textured surfaces: A review of modeling techniques and key findings. Tribol. Int.
**2016**, 94, 509–529. [Google Scholar] [CrossRef][Green Version] - Gachot, C.; Rosenkranz, A.; Hsu, S.M.; Costa, H.L. A critical assessment of surface texturing for friction and wear improvement. Wear
**2017**, 372–373, 21–41. [Google Scholar] [CrossRef] - Rosenkranz, A.; Grützmacher, P.G.; Gachot, C.; Costa, H.L. Surface texturing in machine elements—A critical discussion for rolling and sliding contacts. Adv. Eng. Mater.
**2019**, 86, 1900194. [Google Scholar] [CrossRef] - Grützmacher, P.G.; Profito, F.J.; Rosenkranz, A. Multi-scale surface texturing in tribology—Current knowledge and future perspectives. Lubricants
**2019**, 7, 95. [Google Scholar] [CrossRef][Green Version] - Pettersson, U.; Jacobson, S. Textured surfaces in sliding boundary lubricated contacts—Mechanisms, possibilities and limitations. Tribol. Mater. Surf. Interfaces
**2013**, 1, 181–189. [Google Scholar] [CrossRef] - Löffler, M.; Andreas, K.; Engel, U.; Schulte, R.; Groebel, D.; Krebs, E.; Freiburg, D.; Biermann, D.; Stangier, D.; Tillmann, W.; et al. Tribological measures for controlling material flow in sheet-bulk metal forming. Prod. Eng.
**2016**, 10, 459–470. [Google Scholar] [CrossRef] - Borghi, A.; Gualtieri, E.; Marchetto, D.; Moretti, L.; Valeri, S. Tribological effects of surface texturing on nitriding steel for high-performance engine applications. Wear
**2008**, 265, 1046–1051. [Google Scholar] [CrossRef] - Etsion, I. Modeling of surface texturing in hydrodynamic lubrication. Friction
**2013**, 1, 195–209. [Google Scholar] [CrossRef][Green Version] - Wos, S.; Koszela, W.; Pawlus, P. Tribological behaviours of textured surfaces under conformal and non-conformal starved lubricated contact conditions. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2015**, 229, 398–409. [Google Scholar] [CrossRef] - Grabon, W.; Koszela, W.; Pawlus, P.; Ochwat, S. Improving tribological behaviour of piston ring–cylinder liner frictional pair by liner surface texturing. Tribol. Int.
**2013**, 61, 102–108. [Google Scholar] [CrossRef] - Evans, R.D.; Cogdell, J.D.; Richter, G.A.; Doll, G.L. Traction of lubricated rolling contacts between thin-film coatings and steel. Tribol. Trans.
**2008**, 52, 106–113. [Google Scholar] [CrossRef] - Kalin, M.; Polajnar, M. The wetting of steel, DLC coatings, ceramics and polymers with oils and water: The importance and correlations of surface energy, surface tension, contact angle and spreading. Appl. Surf. Sci.
**2014**, 293, 97–108. [Google Scholar] [CrossRef] - Kalin, M.; Polajnar, M. The effect of wetting and surface energy on the friction and slip in oil-lubricated contacts. Tribol. Lett.
**2013**, 52, 185–194. [Google Scholar] [CrossRef] - Björling, M.; Larsson, R.; Marklund, P. The Effect of DLC Coating Thickness on Elstohydrodynamic Friction. Tribol. Lett.
**2014**, 55, 353–362. [Google Scholar] [CrossRef][Green Version] - Björling, M.; Habchi, W.; Bair, S.; Larsson, R.; Marklund, P. Friction Reduction in Elastohydrodynamic Contacts by Thin-Layer Thermal Insulation. Tribol. Lett.
**2014**, 53, 477–486. [Google Scholar] [CrossRef][Green Version] - Björling, M.; Isaksson, P.; Marklund, P.; Larsson, R. The Influence of DLC Coating on EHL Friction Coefficient. Tribol. Lett.
**2012**, 47, 285–294. [Google Scholar] [CrossRef][Green Version] - Bobzin, K.; Brögelmann, T.; Stahl, K.; Michaelis, K.; Mayer, J.; Hinterstoißer, M. Friction reduction of highly-loaded rolling-sliding contacts by surface modifications under elasto-hydrodynamic lubrication. Wear
**2015**, 328–329, 217–228. [Google Scholar] [CrossRef] - Elsharkawy, A.A.; Hamrock, B.J. EHL of Coated Surfaces: Part I—Newtonian Results. J. Tribol.
**1994**, 116, 29. [Google Scholar] [CrossRef] - Habchi, W. A numerical model for the solution of thermal elastohydrodynamic lubrication in coated circular contacts. Tribol. Int.
**2014**, 73, 57–68. [Google Scholar] [CrossRef] - Bobach, L.; Bartel, D.; Beilicke, R.; Mayer, J.; Michaelis, K.; Stahl, K.; Bachmann, S.; Schnagl, J.; Ziegele, H. Reduction in EHL Friction by a DLC Coating. Tribol. Lett.
**2015**, 60, 1270. [Google Scholar] [CrossRef] - Ebner, M.; Ziegltrum, A.; Lohner, T.; Michaelis, K.; Stahl, K. Measurement of EHL temperature by thin film sensors—Thermal insulation effects. Tribol. Int.
**2018**, 105515. [Google Scholar] [CrossRef] - Choo, J.W.; Olver, A.V.; Spikes, H.A. The influence of transverse roughness in thin film, mixed elastohydrodynamic lubrication. Tribol. Int.
**2007**, 40, 220–232. [Google Scholar] [CrossRef] - Choo, J.W.; Olver, A.V.; Spikes, H.A.; Dumont, M.-L.; Ioannides, E. The Influence of Longitudinal Roughness in Thin-Film, Mixed Elastohydrodynamic Lubrication. Tribol. Trans.
**2006**, 49, 248–259. [Google Scholar] [CrossRef] - Ehret, P.; Dowson, D.; Taylor, C.M. Waviness Orientation in EHL Point Contact. In The Third Body Concept Interpretation of Tribological Phenomena; Elsevier: Amsterdam, The Netherlands, 1996; pp. 235–244. ISBN 9780444825025. [Google Scholar]
- Venner, C.H.; Lubrecht, A.A. Numerical Simulation of a Transverse Ridge in a Circular EHL Contact Under Rolling/Sliding. J. Tribol.
**1994**, 116, 751. [Google Scholar] [CrossRef] - Cusano, C.; Wedeven, L.D. The Effects of Artificially-Produced Defects on the Film Thickness Distribution in Sliding EHD Point Contacts. J. Lubr. Technol.
**1982**, 104, 365. [Google Scholar] [CrossRef][Green Version] - Ai, X.; Cheng, H.S. The Influence of Moving Dent on Point EHL Contacts. Tribol. Trans.
**1994**, 37, 323–335. [Google Scholar] [CrossRef] - Mourier, L.; Mazuyer, D.; Lubrecht, A.A.; Donnet, C. Transient increase of film thickness in micro-textured EHL contacts. Tribol. Int.
**2006**, 39, 1745–1756. [Google Scholar] [CrossRef] - Mourier, L.; Mazuyer, D.; Ninove, F.-P.; Lubrecht, A.A. Lubrication mechanisms with laser-surface-textured surfaces in elastohydrodynamic regime. Proc. Inst. Mech. Eng. Part. J J. Eng. Tribol.
**2010**, 224, 697–711. [Google Scholar] [CrossRef] - Krupka, I.; Hartl, M. The effect of surface texturing on thin EHD lubrication films. Tribol. Int.
**2007**, 40, 1100–1110. [Google Scholar] [CrossRef] - Krupka, I.; Vrbka, M.; Hartl, M. Effect of surface texturing on mixed lubricated non-conformal contacts. Tribol. Int.
**2008**, 41, 1063–1073. [Google Scholar] [CrossRef] - Rosenkranz, A.; Szurdak, A.; Gachot, C.; Hirt, G.; Mücklich, F. Friction reduction under mixed and full film EHL induced by hot micro-coined surface patterns. Tribol. Int.
**2016**, 95, 290–297. [Google Scholar] [CrossRef] - Marian, M.; Grützmacher, P.; Rosenkranz, A.; Tremmel, S.; Mücklich, F.; Wartzack, S. Designing surface textures for EHL point-contacts—Transient 3D simulations, meta-modeling and experimental validation. Tribol. Int.
**2019**, 137, 152–163. [Google Scholar] [CrossRef] - Beilicke, R.; Bobach, L.; Bartel, D. Transient thermal elastohydrodynamic simulation of a DLC coated helical gear pair considering limiting shear stress behavior of the lubricant. Tribol. Int.
**2016**, 97, 136–150. [Google Scholar] [CrossRef] - Ziegltrum, A.; Lohner, T.; Stahl, K. TEHL Simulation on the Influence of Lubricants on the Frictional Losses of DLC Coated Gears. Lubricants
**2018**, 6, 17. [Google Scholar] [CrossRef][Green Version] - Kano, M. Super low friction of DLC applied to engine cam follower lubricated with ester-containing oil. Tribol. Int.
**2006**, 39, 1682–1685. [Google Scholar] [CrossRef] - Dobrenizki, L.; Tremmel, S.; Wartzack, S.; Hoffmann, D.C.; Brögelmann, T.; Bobzin, K.; Bagcivan, N.; Musayev, Y.; Hosenfeldt, T. Efficiency improvement in automobile bucket tappet/camshaft contacts by DLC coatings—Influence of engine oil, temperature and camshaft speed. Surf. Coat. Technol.
**2016**, 308, 360–373. [Google Scholar] [CrossRef] - Yu, C.; Meng, X.; Xie, Y. Numerical simulation of the effects of coating on thermal elastohydrodynamic lubrication in cam/tappet contact. Proc. Inst. Mech. Eng. Part. J J. Eng. Tribol.
**2017**, 231, 221–239. [Google Scholar] [CrossRef] - Meng, X.; Yu, C.; Xie, Y.; Mei, B. Thermal insulation effect on EHL of coated cam/tappet contact during start up. Ind. Lubr. Tribol.
**2018**, 70, 917–926. [Google Scholar] [CrossRef] - Gangopadhyay, A.; McWatt, D.G. The Effect of Novel Surface Textures on Tappet Shims on Valvetrain Friction and Wear. Tribol. Trans.
**2008**, 51, 221–230. [Google Scholar] [CrossRef] - Krupka, I.; Hartl, M.; Zimmerman, M.; Houska, P.; Jang, S. Effect of surface texturing on elastohydrodynamically lubricated contact under transient speed conditions. Tribol. Int.
**2011**, 44, 1144–1150. [Google Scholar] [CrossRef] - Marian, M.; Tremmel, S.; Wartzack, S. Microtextured surfaces in higher loaded rolling-sliding EHL line-contacts. Tribol. Int.
**2018**, 127, 420–432. [Google Scholar] [CrossRef] - Tremmel, S.; Marian, M.; Zahner, M.; Wartzack, S.; Merklein, M. Friction reduction in EHL contacts by surface microtexturing—Tribological performance, manufacturing and tailored design. Ind. Lubr. Tribol.
**2018**, 0306. [Google Scholar] [CrossRef] - Marian, M.; Weikert, T.; Tremmel, S. Numerical and experimental studies on friction reduction by surface modification in TEHL contacts. In Proceedings of the STLE 2019—74th Annual Meeting and Exhibition of the Society of Tribologists and Lubrication Engineers, Nashville, TN, USA, 19–23 May 2019. [Google Scholar]
- ISO 14577-1:2015. Metallic Materials—Instrumented Indentation Test for Hardness and Materials Parameters—Part. 1: Test, Method; International Organization for Standardization: Geneva, Switzerland, 2015. [Google Scholar]
- Habchi, W.; Demirci, I.; Eyheramendy, D.; Morales-Espejel, G.; Vergne, P. A finite element approach of thin film lubrication in circular EHD contacts. Tribol. Int.
**2007**, 40, 1466–1473. [Google Scholar] [CrossRef] - Yang, P.; Wen, S. A Generalized Reynolds Equation for Non-Newtonian Thermal Elastohydrodynamic Lubrication. J. Tribol.
**1990**, 112, 631–636. [Google Scholar] [CrossRef] - Marian, M.; Weschta, M.; Tremmel, S.; Wartzack, S. Simulation of Microtextured Surfaces in Starved EHL Contacts Using Commercial FE Software. Mater. Perform. Charact.
**2017**, 6, 165–181. [Google Scholar] [CrossRef] - Liu, S.; Peyronnel, A.; Wang, Q.J.; Keer, L.M. An extension of the Hertz theory for 2D coated components. Tribol. Lett.
**2005**, 18, 505–511. [Google Scholar] [CrossRef] - Zhao, Y.; Maietta, D.M.; Chang, L. An Asperity Microcontact Model Incorporating the Transition from Elastic Deformation to Fully Plastic Flow. J. Tribol.
**2000**, 122, 86. [Google Scholar] [CrossRef] - Masjedi, M.; Khonsari, M.M. Film Thickness and Asperity Load Formulas for Line-Contact Elastohydrodynamic Lubrication With Provision for Surface Roughness. J. Tribol.
**2012**, 134, 11503. [Google Scholar] [CrossRef] - Habchi, W. Finite Element Modeling of Elastohydrodynamic Lubrication Problems; John Wiley & Sons Incorporated: Newark, NJ, USA, 2018; ISBN 978-1119225126. [Google Scholar]
- Tan, X.; Goodyer, C.E.; Jimack, P.K.; Taylor, R.I.; Walkley, M.A. Computational approaches for modelling elastohydrodynamic lubrication using multiphysics software. Proc. Inst. Mech. Eng. Part. J J. Eng. Tribol.
**2012**, 226, 463–480. [Google Scholar] [CrossRef] - Lohner, T.; Ziegltrum, A.; Stemplinger, J.-P.; Stahl, K. Engineering Software Solution for Thermal Elastohydrodynamic Lubrication Using Multiphysics Software. Adv. Tribol.
**2016**, 2016, 1–13. [Google Scholar] [CrossRef][Green Version] - Weschta, M. Untersuchungen zur Wirkungsweise von Mikrotexturen in elastohydrodynamischen Gleit/Wälz-Kontakten. Ph.D. Thesis, Friedrich-Alexander-Universität, Erlangen-Nürnberg, Germany, 2017. urn:nbn:de:bvb:29-opus4-91095. [Google Scholar]
- Sadeghi, F.; Sui, P.C. Thermal Elastohydrodynamic Lubrication of Rolling/Sliding Contacts. J. Tribol.
**1990**, 112, 189–195. [Google Scholar] [CrossRef] - Bair, S. A Rough Shear-Thinning Correction for EHD Film Thickness. Tribol. Trans.
**2004**, 47, 361–365. [Google Scholar] [CrossRef] - Dowson, D.; Higginson, G.R. Elasto-Hydrodynamic Lubrication, SI ed.; Pergamon Press: Oxford, UK, 1977; ISBN 0080213022. [Google Scholar]

**Figure 1.**(

**a**) Laser scanning microscopy image and a sectional view of a microtextured sample; (

**b**) FIB-milled cross-section of a DLC-coated specimen; (

**c**) Cam/bucket tappet component test-rig.

**Figure 2.**Mean change of friction force in the cam/tappet-contact for the microtextured and DLC-coated specimens at different cam rotation speeds compared to the polished references (

**a**) at the first speed level and (

**b**) at each speed level.

**Figure 3.**Coefficient of friction of the reference and DLC-coated specimens under dry conditions (

**a**) over the sliding distance of one exemplary test-run and (

**b**) as the averaged value.

**Figure 4.**(

**a**) Computed solid and fluid friction force for the reference, microtextured, and DLC-coated case, normalized total, hydrodynamic and solid contact pressure, lubricant gap, temperature, and viscosity change for the (

**b**) reference, (

**c**) microtextured, and (

**d**) DLC-coated case.

**Table 1.**Deposition parameters of layers of the amorphous carbon coating according to the order of deposition.

Coating Layer | Duration in s | Arc Current of Cr-Target in A | Sputtering Power of WC-Target in W | Bias Voltage in V (Operating Mode) | Acetylene Gas Flow in sccm | Argon Gas Flow in sccm | HMDSO Gas Flow in sccm | Temperature in °C |
---|---|---|---|---|---|---|---|---|

Cr | 280 | 70 | − | −100 (DC) | − | 70 | − | 140 |

WC | 1080 | − | 1200 | −50 (DC) | − | 195 | − | 110 |

a-C:H:W | 2267 | − | 1200 | −130 (DC) | 28 | 180 | − | 100 |

a-C:H | 1155 | − | − | −450 (bipolar pulsed) | 250 | 100 | − | 100 |

a-C:H:SiO | 2050 | − | − | −575 (unipolar pulsed) | 250 | 100 | 6 | 100 |

Parameter | Cam(100Cr6) | Tappet (16MnCr5) | Coating (a-C:H:SiO) |
---|---|---|---|

Young’s/indentation modulus E in MPa | 209,000 ^{1} | 216,000 ^{2} | 110,000 ^{2} |

Poisson’s ratio ν | 0.3 ^{1} | 0.3 ^{1} | 0.3 ^{1} |

density ρ in kg/m³ | 7850 ^{1} | 7760 ^{1} | 4655 ^{1} |

thermal conductivity λ in W/(m∙K) | 47 ^{1} | 44 ^{1} | 1.1 ^{1} |

specific heat capacity c_{p} in J/(kg∙K) | 460 ^{1} | 431 ^{1} | 8263 ^{1} |

dry coefficient of friction against 100Cr6 μ_{solid} | − | 0.5 ^{2, 3} | 0.2 ^{2,3} |

^{1}based upon literature [41,42].

^{2}based upon measurements, see Section 3.1.

^{3}conservative estimation compared to measurement results in Section 3.1.

**Table 3.**Lubricant properties [62].

Base Density at 90 °C ρ in kg/m³ | 840 |

Base Viscosity at 90 °C η_{0} in Pa∙s | 0.03 |

Pressure Viscosity Coefficient α_{p} in Pa^{−1,} | 1.31∙10^{−8} |

Roelands Temperature Coefficient β_{η} | 0.042 |

Critical Shear Stress G_{c} | 0.2 η_{0} |

Carreau Parameter a_{c} | 2.2 |

Carreau Parameter n_{c} | 0.8 |

Thermal Conductivity λ in W/(m∙K) | 0.14 |

Specific Heat Capacity c_{p} in J/(kg∙K) | 2000 |

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**MDPI and ACS Style**

Marian, M.; Weikert, T.; Tremmel, S. On Friction Reduction by Surface Modifications in the TEHL Cam/Tappet-Contact-Experimental and Numerical Studies. *Coatings* **2019**, *9*, 843.
https://doi.org/10.3390/coatings9120843

**AMA Style**

Marian M, Weikert T, Tremmel S. On Friction Reduction by Surface Modifications in the TEHL Cam/Tappet-Contact-Experimental and Numerical Studies. *Coatings*. 2019; 9(12):843.
https://doi.org/10.3390/coatings9120843

**Chicago/Turabian Style**

Marian, Max, Tim Weikert, and Stephan Tremmel. 2019. "On Friction Reduction by Surface Modifications in the TEHL Cam/Tappet-Contact-Experimental and Numerical Studies" *Coatings* 9, no. 12: 843.
https://doi.org/10.3390/coatings9120843