23rd International Colloquium Tribology - January 2022 467 Slender EHL contacts under high sliding conditions Marko Tošić Technical University of Munich, Germany; School of Engineering & Design, Department of Mechanical Engineering, Gear Research Centre (FZG) Thomas Lohner Technical University of Munich, Germany; School of Engineering & Design, Department of Mechanical Engineering, Gear Research Centre (FZG) Roland Larsson Division of Machine Elements, Luleå University of Technology, Luleå, Sweden 1. Introduction This study deals with experimental and numerical analysis of slender elastohydrodynamically lubricated (EHL) elliptical point contacts under high sliding. Thereby, the entrainment direction is orientated along the major axis of the contact ellipse. Such contact geometries can appear in worm gears [1]. Film thick-ness measurements were carried out on an optical EHL tribometer. Numerical solutions were obtained by solv-ing the EHL contact considering non-Newtonian rheol-ogy and thermal effects. 2. Methodology For experimental investigation, an optical EHL tribometer based on thin film colorimetric interferometry is used [2]. To investigate slender EHL contacts, test specimens with a radius of curvature in gap length direction of R y =12.7 mm and gap width direction of R x =12.7 were manufactured. The steel roller was polished and paired with a glass disk. A mineral oil ISO VG 100 (MIN100) is used as a lubricant. Experiments are per-formed at a normal force resulting in a Hertzian pressure of Slender EHL contacts under high sliding conditions Marko Tošić 1)* , Thomas Lohner 1) , Roland Larsson 2) 1) Technical University of Munich, Germany; School of Engineering & Design, Department of Mechanical Engineering, Gear Research Centre (FZG) 2) Division of Machine Elements, Luleå University of Technology, Luleå, Sweden 1. Introduction This study deals with experimental and numerical analysis of slender elastohydrodynamically lubricated (EHL) elliptical point contacts under high sliding. Thereby, the entrainment direction is orientated along the major axis of the contact ellipse. Such contact geometries can appear in worm gears [1]. Film thickness measurements were carried out on an optical EHL tribometer. Numerical solutions were obtained by solving the EHL contact considering non-Newtonian rheology and thermal effects. 2. Methodology For experimental investigation, an optical EHL tribometer based on thin film colorimetric interferometry is used [2]. To investigate slender EHL contacts, test specimens with a radius of curvature in gap length direction of 𝑅𝑅 ! = 12.7 𝑚𝑚𝑚𝑚 and gap width direction of 𝑅𝑅 " = 4 𝑚𝑚𝑚𝑚 were manufactured. The steel roller was polished and paired with a glass disk. A mineral oil ISO VG 100 (MIN100) is used as a lubricant. Experiments are performed at a normal force resulting in a Hertzian pressure of 𝑝𝑝 # = 0.63 𝐺𝐺𝐺𝐺𝐺𝐺 and an oil temperature of 𝜗𝜗 $%& = 40 ± 0.5 ℃ . The entrainment speed was varied as 𝑣𝑣 ' = {0.6,1.2,1.8} 𝑚𝑚 𝑠𝑠 ⁄ and the slide-to-roll ratio as 𝑆𝑆𝑅𝑅𝑅𝑅 = ()! "#$$*)$%&&"+ )' = {0, +1.5, −1.5} . The experimental investigations are accompanied by numerical modelling. Thereby, the generalized Reynolds equation for elliptical contacts with unidirectional lubricant entrainment is considered [3]. Elastic deformation of an equivalent body is obtained by solving linear elasticity equation. Applied load and generated fluid pressure are balanced via the force-balance equation. The Vogel and Roelands model describe the pressure and temperature dependence of the considered oil and the Ree-Eyring model describes its rheological behaviour. Reynolds, energy and linear elasticity equations are written in a weak form, as a convection-diffusion type of equation. Due to high Peclet numbers, SUPG and GLS stabilization terms are applied to the Reynolds and energy equation. The equations are written in dimensionless form and solved by the finite element method, using the full-system approach for the generalized Reynolds’ equation and the linear elasticity equation with strong coupling of this system of equations with the energy equation. More details on the used equations, material properties and numerical procedure is given in references [4, 5]. 3. Results and Discussion Fig. 1 shows exemplarily for v m = 1.8 m/ s experimental and numerical results for the film thickness along the gap length direction (top) and film thickness interferograms (bottom) for different sliding conditions. Fig. 2 shows the corresponding calculated temperature and dynamic viscosity contours for 𝑆𝑆𝑅𝑅𝑅𝑅 = −1.5 and SRR = 1.5. Fig. 3 shows the derived results for h m and h c over the entrainment speed v m . In general, the experi- 0 1µm 0.05 0.85µm 0 1µm 0.05 0.85µm 0 1µm 0.05 0.85µm Figure 1. Experimental and numerical results for film thickness along the gap length direction (top) and film thickness 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm v_m_exp=1.8 m/ s v_m_num=1.8 m/ s 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm vm_exp=1.8 m/ s vm_num=1.8 m/ s 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm vm_exp=1.8 m/ s vm_num=1.8 m/ s SRR=-1.5 v m =1.8 m/ s SRR=0 v m =1.8 m/ s SRR=-1.5 v m =1.8 m/ s SRR=0 v m =1.8 m/ s v m =1.8 m/ s SRR=1.5 SRR=1.5 v m =1.8 m/ s b) a) c) v m|exp = 1.8 m/ s v m|num = 1.8 m/ s v m|exp = 1.8 m/ s v m|num = 1.8 m/ s v m|exp = 1.8 m/ s v m|num = 1.8 m/ s and an oil temperature of Slender EHL contacts under high sliding conditions Marko Tošić 1)* , Thomas Lohner 1) , Roland Larsson 2) 1) Technical University of Munich, Germany; School of Engineering & Design, Department of Mechanical Engineering, Gear Research Centre (FZG) 2) Division of Machine Elements, Luleå University of Technology, Luleå, Sweden 1. Introduction This study deals with experimental and numerical analysis of slender elastohydrodynamically lubricated (EHL) elliptical point contacts under high sliding. Thereby, the entrainment direction is orientated along the major axis of the contact ellipse. Such contact geometries can appear in worm gears [1]. Film thickness measurements were carried out on an optical EHL tribometer. Numerical solutions were obtained by solving the EHL contact considering non-Newtonian rheology and thermal effects. 2. Methodology For experimental investigation, an optical EHL tribometer based on thin film colorimetric interferometry is used [2]. To investigate slender EHL contacts, test specimens with a radius of curvature in gap length direction of 𝑅𝑅 ! = 12.7 𝑚𝑚𝑚𝑚 and gap width direction of 𝑅𝑅 " = 4 𝑚𝑚𝑚𝑚 were manufactured. The steel roller was polished and paired with a glass disk. A mineral oil ISO VG 100 (MIN100) is used as a lubricant. Experiments are performed at a normal force resulting in a Hertzian pressure of 𝑝𝑝 # = 0.63 𝐺𝐺𝐺𝐺𝐺𝐺 and an oil temperature of 𝜗𝜗 $%& = 40 ± 0.5 ℃ . The entrainment speed was varied as 𝑣𝑣 ' = {0.6,1.2,1.8} 𝑚𝑚 𝑠𝑠 ⁄ and the slide-to-roll ratio as 𝑆𝑆𝑅𝑅𝑅𝑅 = ()! "#$$*)$%&&"+ )' = {0, +1.5, −1.5} . The experimental investigations are accompanied by numerical modelling. Thereby, the generalized Reynolds equation for elliptical contacts with unidirectional lubricant entrainment is considered [3]. Elastic deformation of an equivalent body is obtained by solving linear elasticity equation. Applied load and generated fluid pressure are balanced via the force-balance equation. The Vogel and Roelands model describe the pressure and temperature dependence of the considered oil and the Ree-Eyring model describes its rheological behaviour. Reynolds, energy and linear elasticity equations are written in a weak form, as a convection-diffusion type of equation. Due to high Peclet numbers, SUPG and GLS stabilization terms are applied to the Reynolds and energy equation. The equations are written in dimensionless form and solved by the finite element method, using the full-system approach for the generalized Reynolds’ equation and the linear elasticity equation with strong coupling of this system of equations with the energy equation. More details on the used equations, material properties and numerical procedure is given in references [4, 5]. 3. Results and Discussion Fig. 1 shows exemplarily for v m = 1.8 m/ s experimental and numerical results for the film thickness along the gap length direction (top) and film thickness interferograms (bottom) for different sliding conditions. Fig. 2 shows the corresponding calculated temperature and dynamic viscosity contours for 𝑆𝑆𝑅𝑅𝑅𝑅 = −1.5 and SRR = 1.5. Fig. 3 shows the derived results for h m and h c over the entrainment speed v m . In general, the experi- 0 1µm 0.05 0.85µm 0 1µm 0.05 0.85µm 0 1µm 0.05 0.85µm Figure 1. Experimental and numerical results for film thickness along the gap length direction (top) and film thickness 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm v_m_exp=1.8 m/ s v_m_num=1.8 m/ s 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm vm_exp=1.8 m/ s vm_num=1.8 m/ s 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm vm_exp=1.8 m/ s vm_num=1.8 m/ s SRR=-1.5 v m =1.8 m/ s SRR=0 v m =1.8 m/ s SRR=-1.5 v m =1.8 m/ s SRR=0 v m =1.8 m/ s v m =1.8 m/ s SRR=1.5 SRR=1.5 v m =1.8 m/ s b) a) c) v m|exp = 1.8 m/ s v m|num = 1.8 m/ s v m|exp = 1.8 m/ s v m|num = 1.8 m/ s v m|exp = 1.8 m/ s v m|num = 1.8 m/ s . The entrainment speed was varied as 2) Division of Machine Elements, Luleå University of Techno 1. Introduction This study deals with experimental and numerical analysis of slender elastohydrodynamically lubricated (EHL) elliptical point contacts under high sliding Thereby, the entrainment direction is orientated along the major axis of the contact ellipse. Such contact geometries can appear in worm gears [1]. Film thickness measurements were carried out on an optical EHL tribometer. Numerical solutions were obtained by solving the EHL contact considering non-Newtonian rheology and thermal effects. 2. Methodology For experimental investigation, an optical EHL tribometer based on thin film colorimetric interferometry used [2]. To investigate slender EHL contacts, test specimens with a radius of curvature in gap length direction of 𝑅𝑅 ! = 12.7 𝑚𝑚𝑚𝑚 and gap width direction of 𝑅𝑅 " = 4 𝑚𝑚𝑚𝑚 were manufactured. The steel roller was polished and paired with a glass disk. A mineral oil ISO VG 100 (MIN100) is used as a lubricant. Experiments are performed at a normal force resulting in Hertzian pressure of 𝑝𝑝 # = 0.63 𝐺𝐺𝐺𝐺𝐺𝐺 and an oil temperature of 𝜗𝜗 $%& = 40 ± 0.5 ℃ . The entrainment speed was varied as 𝑣𝑣 ' = {0.6,1.2,1.8} 𝑚𝑚 𝑠𝑠 ⁄ and the slide-to-roll ratio as 𝑆𝑆𝑅𝑅𝑅𝑅 = ()! "#$$*)$%&&"+ )' = {0, +1.5, −1.5} . The experimental investigations are accompanied by numerical modelling. Thereby, the generalized Reynolds equation for elliptical contacts with unidirectional lubricant 0 1µm 0.05 0.85µm 0 Figure 1. Experimental and numerical results for film thickness along the gap length direction (top) and film thickness interferograms (bottom) for 𝑆𝑆𝑅𝑅𝑅𝑅 = −1.5 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm v_m_exp=1.8 m/ s v_m_num=1.8 m/ s 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 h in µm Gap length direction x in mm SRR=-1.5 v m =1.8 m/ s SRR=-1.5 SRR=0 v m =1.8 m/ s v m =1.8 m/ s b) a) v m|exp = 1.8 m/ s v m|num = 1.8 m/ s and the slide-to-roll ratio as Slender EHL contacts under high sliding conditions Marko Tošić 1)* , Thomas Lohner 1) , Roland Larsson 2) 1) Technical University of Munich, Germany; School of Engineering & Design, Department of Mechanical Engineering, Gear Research Centre (FZG) 2) Division of Machine Elements, Luleå University of Technology, Luleå, Sweden 1. Introduction This study deals with experimental and numerical analysis of slender elastohydrodynamically lubricated (EHL) elliptical point contacts under high sliding. Thereby, the entrainment direction is orientated along the major axis of the contact ellipse. Such contact geometries can appear in worm gears [1]. Film thickness measurements were carried out on an optical EHL tribometer. Numerical solutions were obtained by solving the EHL contact considering non-Newtonian rheology and thermal effects. 2. Methodology For experimental investigation, an optical EHL tribometer based on thin film colorimetric interferometry is used [2]. To investigate slender EHL contacts, test specimens with a radius of curvature in gap length direction of 𝑅𝑅 ! = 12.7 𝑚𝑚𝑚𝑚 and gap width direction of 𝑅𝑅 " = 4 𝑚𝑚𝑚𝑚 were manufactured. The steel roller was polished and paired with a glass disk. A mineral oil ISO VG 100 (MIN100) is used as a lubricant. Experiments are performed at a normal force resulting in a Hertzian pressure of 𝑝𝑝 # = 0.63 𝐺𝐺𝐺𝐺𝐺𝐺 and an oil temperature of 𝜗𝜗 $%& = 40 ± 0.5 ℃ . The entrainment speed was varied as 𝑣𝑣 ' = {0.6,1.2,1.8} 𝑚𝑚 𝑠𝑠 ⁄ and the slide-to-roll ratio as 𝑆𝑆𝑅𝑅𝑅𝑅 = ()! "#$$*)$%&&"+ )' = {0, +1.5, −1.5} . The experimental investigations are accompanied by numerical modelling. Thereby, the generalized Reynolds equation for elliptical contacts with unidirectional lubricant entrainment is equivalent body is obtained by solving linear elasticity equation. Applied load and generated fluid pressure are balanced via the Roelands model dependence of the considered oil model descr Reynolds, energy and linear elasticity written in a of equation. Due to high Peclet numbers, SUPG GLS stabilization terms are applied energy equation. The equations are sionless form and solved by the using the full olds’ equation and the strong coupling of this system of equations with the energy equation terial properties and numerical procedure is given in erences [4, 5 3. Results and Discussion Fig. 1 shows exemplarily for and numerical results for the film thickness along the gap length direction (top) and film thickness interferograms (bottom) for shows the corresponding calculated temperature and dynamic viscosity contours for SRR = 1.5. h c over the entrainment speed v 0 1µm 0.05 0.85µm 0 1µm 0.05 0.85µ Figure 1. Experimental and numerical results for film thickness along the gap length direction (top) and film thickness interferograms (bottom) for 𝑆𝑆𝑅𝑅𝑅𝑅 = −1.5 (a), 𝑆𝑆𝑅𝑅𝑅𝑅 = 0 (b) and 𝑆𝑆 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm v_m_exp=1.8 m/ s v_m_num=1.8 m/ s 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 -0,2 -0,1 0,0 0,1 0,2 h in µm Gap length direction x in mm vm_exp=1.8 m/ s vm_num=1.8 m/ s SRR=-1.5 v m =1.8 m/ s SRR=0 v m =1.8 m/ s SRR=-1.5 SRR=0 v m =1.8 m/ s v m =1.8 m/ s b) a) v m|exp = 1.8 m/ s v m|num = 1.8 m/ s v m|exp = 1.8 m/ s v m|num = 1.8 m/ s . The experimental investigations are accompanied by numerical modelling. Thereby, the generalized Reyn-olds equation for elliptical contacts with unidirectional lubricant entrainment is considered [3]. Elastic deformation of an equivalent body is obtained by solving linear elasticity equation. Applied load and generated fluid pressure are balanced via the force-balance equation. The Vogel and Roelands model describe the pressure and temperature dependence of the considered oil and the Ree-Eyring model describes its rheological behaviour. Reynolds, energy and linear elasticity equations are written in a weak form, as a convection-diffusion type of equation. Due to high Peclet numbers, SUPG and GLS stabilization terms are applied to the Reynolds and energy equation. The equations are written in di-mensionless form and solved by the finite element method, using the full-system approach for the general-ized Reynolds’ equation and the linear elasticity equa-tion with strong coupling of this system of equations with the energy equation. More details on the used equations, material properties and numerical procedure is given in references [4, 5]. 468 23rd International Colloquium Tribology - January 2022 Slender EHL contacts under high sliding conditions Figure 1: Experimental and numerical results for film thickness along the gap length direction (top) and film thickness interferograms (bottom) for SRR = -1.5 (a), SRR = 0 (b) and SRR = 1.5 (c) for v m = 1.8 m/ s Figure 2: Numerical results for temperature distribution and viscosity for (a) and (b) for vm = 1.8 m/ s 3. Results and Discussion Fig. 1 shows exemplarily for v m = 1.8 m/ s experimental and numerical results for the film thickness along the gap length direction (top) and film thickness interferograms (bottom) for different sliding conditions. Fig. 2 shows the corresponding calculated temperature and dynamic viscosity contours for SRR = -1.5 and SRR = 1.5. Fig. 3 shows the derived results for h m and h c over the entrainment speed v m . In general, the experimental and numerical results for the considered slender EHL contacts are in good accordance. By comparing all three graphs shown in Fig. 1 (top), it can be concluded that there is the highest film thickness at pure rolling with SRR=0, which is expected since there is no significant oil shearing and consequently temperature generation inside the oil film. Additionally, it can be seen that at SRR = 0 and SRR = -1.5, the film thickness in the central contact region has a flat shape, while at SRR = 1.5 it shows a decreasing trend along the gap length direction. The film thickness interferograms in Fig. 1 (bottom) show that at SRR = 0 and SRR = -1.5 the film thickness in the central contact region has a “U-shape”, while at SRR = 1.5 the shape reminds more of a “V-shape”. Figure 3: Experimental and numerical results for h m and h c over entrainment speed v m for SRR = -1.5 and SRR = 1.5 23rd International Colloquium Tribology - January 2022 469 Slender EHL contacts under high sliding conditions This shape of the film thickness in the central region is mainly caused by very different thermal effusivities. Since glass has a much lower thermal effusivity than steel, in both positive and negative sliding conditions the glass surface has a higher temperature than the steel one, resulting in more viscous oil in the vicinity of the steel surface (see Fig. 2). When the steel surface moves faster than the glass surface (SRR = -1.5), the viscous oil is moved through the contact with higher speed, resulting in lower central film thickness. When the steel surface moves slower than the glass surface (SRR = 1.5), the viscous oil “accumulates” in the contact, causing an obstacle for passing the oil through the contact, increasing the side flow and ultimately changing the film thickness shape in the central region. The trends of minimum and central film thickness h m and h c over the entrainment speed v m in Fig. 3 show that h c is higher and increases stronger with v m at SRR = 1.5 than at SRR = -1.5. On the other hand, h m is higher and increases faster with v m at SRR = -1.5 than at SRR = 1.5. In fact, it seems that at SRR = -1.5 increasing v m has almost no effect on h m . This means that in slender EHL contacts with positive SRR, increasing entrainment speed cannot help much in preventing very low values of h m and eventually lubricant breakdown, particularly if the ratio of R x and R y is more severe than considered in this study. 4. Conclusion The results presented in this study show for the considered slender EHL contacts with high positive sliding a continuous decrease of the lubricant film thickness in the central contact region. This is in context with the different thermal effusivity of the rolling-sliding pairing considered. The influence of the entrainment speed on the minimum film thickness is small. References [1] Sharif K et al.; Journal of Mechanical Engineering Science, 215(7), 831: 46; https: / / doi. org/ 10.1243/ 0954406011524180 (2001) [2] Yilmaz M et al.; Lubricants, 7(5), 46; https: / / doi. org/ 10.3390/ lubricants7050046 (2019) [3] Habchi W. ISBN: 978-1-119-22512-6. Wiley, Chichester, UK. 2018. [4] Ziegltrum A. et al.; Lubricants, 6(1), 17; https: / / doi. org/ 10.3390/ lubricants6010017 (2018) [5] Ziegltrum A. et al.; Tribology Letters, 68: 71; https: / / doi.org/ 10.1007/ s11249-020-01309-6 (2020)