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Tribologie und Schmierungstechnik EDITOR IN CHIEF MANFRED JUNGK 2 _ 24 VOLUME 71 Tribology—Lubrication Friction Wear An Official Journal of Gesellschaft für Tribologie An Official Journal of Österreichische Tribologische Gesellschaft An Official Journal of Swiss Tribology Issue 2 | 2024 Volume 71 Editor in chief: Dr. Manfred Jungk Tel.: +49 (0)6722 500836 eMail: manfred.jungk@mj-tribology.com www.mj-tribology.com Editorial director: Ulrich Sandten-Ma Tel.: +49 (0)7071 97 556 56 / eMail: sandten@verlag.expert Editor: Patrick Sorg Tel.: +49 (0)7071 97 556 57 / eMail: sorg@verlag.expert Dr. rer. nat. Erich Santner Tel.: +49 (0)2289 616136 / eMail: esantner@arcor.de Contributions marked with the author’s initials or full name represent the author’s opinion, not necessarily that of the editorial office. We take no responsibility for unsolicited contributions. The author is responsible for obtaining the rights to pictures. 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ISSN 0724-3472 ISBN 978-3-381-11591-4 Imprint Tribologie und Schmierungstechnik Tribology—Lubrication Friction Wear An Official Journal of Gesellschaft für Tribologie | An Official Journal of Österreichische Tribologische Gesellschaft | An Official Journal of Swiss Tribology Editorial 1 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0006 The acronym MINT stands for Mathematics, Information Technology, Natural Science and Technology. It is used in German language to highlight the economic importance of those fields for fostering innovation. The English umbrella term for Science, Technology, Engineering and Mathematics is STEM, though it does not list Information Technology separate as it is viewed as the cross section between mathematics, technology and engineering. On the other side MINT does not specify engineering separately as it falls generally under Technology. Regardless if it is called STEM or MINT there are concerns of not having an educated work force for those fields. The German Chemical Society GDCh recently published in their newsletter a call for joint action as a shortage of STEM specialists will endanger the prosperity. The key requirements listed are - effective measures to promote students in STEM subjects (including sufficient lessons and more extracurricular activities), - making school service more attractive for STEM teachers (including financial incentives, rewards for individual commitment, career opportunities and further training opportunities), - improvements in STEM training and studies (including the removal of stereotypes and barriers, sufficient support to reduce dropout rates) - coordinated and sustainable support for the diverse initiatives and programs to promote STEM subjects. As early as October 2022, 325,290 vacant STEM positions in Germany could not be filled, as a lack of skilled workers was the biggest bottleneck. In view of the enormous tasks posed by the economic and technological challenges of climate change, the energy transition and the transition to a circular economy, this development represents a major threat to the prosperity, security of supply and social stability of Germany. The decreasing number of students starting University in STEM fields can be related to lower degrees in elementary and high schools, thus a lack of teaching. For Tribology a sound education in STEM is essential, as our field represents a cross section of natural and engineering sciences. Should we rely on a decreasing number of STEM graduates finding their way to Tribology or should we raise awareness in high schools so more pupils start STEM studies? As the general public is very rarely aware of Tribology and its potential in the sustainability discussion starting with raising the awareness with our teenagers seems to be the right way forward. STLE is organizing STEM camps along its Annual Meetings to showcase Tribology in front of local high school students. Mirjam Baese is leading the public relations working group within the GfT and the need to address our youngest generation is on the agenda. So we are looking forward for more discussions and initiatives to raising the awareness of Tribology and remember Tribology is everywhere. Your editor in chief Manfred Jungk MINT or STEM, how to raise awareness for Tribology Events 2 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 Events Date Place Event ► 17.09. - 19.09.24 Messe Düsseldorf, Lubricant Expo Europe Germany ► 23.09. - 25.09.24 Göttingen, Germany 65 th German Tribology Conference 2024 ► 14.09. - 18.09.24 Tianjin, China 7 th Asia International Conference on Tribology & 9 th China International Symposium on Tribology ► 26.09. - 28.09.24 Sofia, Bulgaria 11 th International Conference on Tribology (BALKANTRIB ’24) ► 03.10. - 04.10.24 Portorož, Slovenia 5 th International Conference on Polymer Tribology (PolyTrib 2024) ► 21.11. - 23.11.24 Kaunas, Lithuania International Tribological Conference (BALTRIB 2024) ► 22.01. - 23.01.25 Leipzig, Germany Nextlub Contents 3 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 Tribologie und Schmierungstechnik Tribology - Lubrication Friction Wear An Official Journal of Gesellschaft für Tribologie An Official Journal of Österreichische Tribologische Gesellschaft An Official Journal of Swiss Tribology Volume 71, Issue 2 August 2024 5 Marius Hofmeister, Jonas Schütz, Katharina Schmitz On the Validity of the Flow Factor Concept with Respect to Shear-thinning Fluids 14 Thomas Decker, Georg Jacobs, Christoph Paridon, Julian Röder Condition monitoring for planetary journal bearings in wind turbine gearboxes by means of acoustic measurements and machine learning 23 Merle Hanse, Christian Heinrich, Armin Lohrengel Reduction in power loss and increased safety of thrust collar bearings through profiling of the treads - Application of rolling bearing profiles and crowning on thrust collar bearings 33 Steffen Jäger, Tilmann Linde, Kai von Schulz Product Development Methodology Targeting Efficiency and Acoustics of E-Mobility Gearboxes 1 Editorial MINT or STEM, how to raise awareness for Tribology 2 Events Science and Research 42 News Gesellschaft für Tribologie Österreichische Tribologische Gesellschaft Columns Preface For authors Authors of scientific contributions are requested to submit their manuscripts directly to the editor, Dr. Jungk (see inside back cover for formatting guidelines). Anzeige 4 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 Gesundheit \ Romanistik \ Theologie \ Kulturwissenschaften \ Soziologie \ Theaterwissenschaft \ Geschichte \ Spracherwerb \ Philosophie \ Medien- und Kommunikationswiss chaft \ Linguistik \ Literaturgeschichte \ Anglistik \ Bauwesen \ Fremdsprachendidaktik \ DaF \ Germanistik \ Literaturwissenschaft \ Rechtswissenschaft \ Historische Sprachwiss chaft \ Slawistik \ Skandinavistik \ BWL \ Wirtschaft \ Tourismus \ VWL \ Maschinenbau \ Politikwissenschaft \ Elektrotechnik \ Mathematik & Statistik \ Management \ Altphilol Sport \ Gesundheit \ Romanistik \ Theologie \ Kulturwissenschaften \ Soziologie \ Theaterwissenschaft \ Geschichte \ Spracherwerb \ Philosophie \ Medien- und Kommunikatio issenschaft \ Linguistik \ Literaturgeschichte \ Anglistik \ Bauwesen \ Fremdsprachendidaktik \ DaF \ Germanistik \ Literaturwissenschaft \ Rechtswissenschaft \ Historische Spra issenschaft \ Slawistik \ Skandinavistik \ BWL \ Wirtschaft \ Tourismus \ VWL \ Maschinenbau \ Politikwissenschaft \ Elektrotechnik \ Mathematik & Statistik \ Management \ hilologie \ Sport \ Gesundheit \ Romanistik \ Theologie \ Kulturwissenschaften \ Soziologie \ Theaterwissenschaft \ Linguistik \ Literaturgeschichte \ Anglistik \ Bauwese remdsprachendidaktik \ DaF \ Germanistik \ Literaturwissenschaft \ Rechtswissenschaft \ Historische Sprachwissenschaft \ Slawistik \ Skandinavistik \ BWL \ Wirtschaft \ Touris VWL \ Maschinenbau \ Politikwissenschaft \ Elektrotechnik \ Mathematik & Statistik \ Management \ Altphilologie \ Sport \ Gesundheit \ Romanistik \ Theologie \ Kulturwiss chaften \ Soziologie \ Theaterwissenschaft \ Geschichte \ Spracherwerb \ Philosophie \ Medien- und Kommunikationswissenschaft \ Linguistik \ Literaturgeschichte \ Anglisti auwesen \ Fremdsprachendidaktik \ DaF \ Germanistik \ Literaturwissenschaft \ Rechtswissenschaft \ Historische Sprachwissenschaft \ Slawistik \ Skandinavistik \ BWL \ Wirtsc BUCHTIPP Nicole Dörr, Carsten Gachot, Max Marian, Katharina Völkel 24th International Colloquium Tribology Industrial and Automotive Lubrication Conference Proceedings 2024 1. Auflage 2024, 279 Seiten €[D] 148,00 ISBN 978-3-381-11831-1 eISBN 978-3-381-11832-8 expert verlag - Ein Unternehmen der Narr Francke Attempto Verlag GmbH + Co. KG Dischingerweg 5 \ 72070 Tübingen \ Germany Tel. +49 (0)7071 97 97 0 \ Fax +49 (0)7071 97 97 11 \ info@narr.de \ www.narr.de The conference provides an international exchange forum for the industry and the academia. Leading university researchers present their latest findings, and representatives of the industry inspire scientists to develop new solutions. Main Topics > Trends lubricants and additives > Automotive and transport industry > Industrial machine elements and wind turbine industry > Coatings, surfaces and underlying mechanisms > Test methodologies and measurement technologies > Digitalisation in tribology > Digital Tribological Services: i-TRIBOMAT > Sustainable lubrication Target Groups > Companies in the field of lubrication, additives and tribology > Research facilities Introduction The flow factor method according to Patir and Cheng is an established modification of the Reynolds equation for calculating fluid flows between rough surfaces. The method allows the consideration of roughness without having to discretize the computational domain in the same order of magnitude as the present roughness peaks. This way, it is possible to consider the influence of roughness on the flow with sufficient accuracy and moderate computing time [1 - 7]. The conventional determination of flow factors assumes that the fluid viscosity is constant [1, 2]. In case of a shear thinning fluid, this assumption is not valid. Now, the viscosity is a function of the shear rate and varies for every film thickness, which differs from the averaged film thickness and also in gap height direction. Accordingly, the viscosity is not negligible anymore and the flow factor depends on the viscosity behavior of the fluid, too. Herbst has already investigated the influence of various shear-thinning oils on the flow factors as a function of the fluid film height, but not as a function of the pressure gradient [7]. However, the flow factor according to Patir and Cheng assuming Newtonian viscosity is widely used in many branches of industry and is also applied for non-Newtonian fluids like engine oils. This contribution aims to evaluate the error introduced by neglecting the non-Newtonian viscosity behavior in the calculation of flow factors especially for different pressure gradients and the associated consequences for the design of tribological systems. In the first part of this contribution the flow factor method according to Patir and Cheng is highlighted and the approach for the derivation of the flow factors is explained. Moreover, it is demonstrated how the viscosity varies in gap heights direction for non-Newtonian fluids. To consider the described viscosity variations for the flow factor calculation, in the next section of this contribution a simulation model based on the Reynolds equation according to Dowson and Herbst’s preliminary work is presented. The mathematical principles and the used algorithm are to be discussed as well [7,8]. Subsequently, the results determined with the simulation model will be presented. Here, the error caused by neglecting non-Newtonian viscosity behavior is evaluated for different gap heights, pressure gradients and fluid properties. Finally, the consequences for the design of tribological systems arising from the obtained results will be discussed. Flow calculation for rough surfaces In various technical applications the influence of roughness on the flow between two surfaces is not negligible. This applies for example to the piston bushing contact in hydraulic machines, combustion engines or other tribological systems where the gap height is small Science and Research 5 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 unikationswissenhe Sprachwissenent \ Altphilologie Kommunikationsistorische Sprachanagement \ Alttik \ Bauwesen \ schaft \ Tourismus ie \ Kulturwissenichte \ Anglistik \ \ BWL \ Wirtschaft On the Validity of the Flow Factor Concept with Respect to Shear-thinning Fluids Marius Hofmeister, Jonas Schütz, Katharina Schmitz* submitted: 03.09.2023 accepted: 24.06.2024 (peer-review) Presented at the GfT Conference 2023 This contribution aims to determine the error introduced by assuming constant viscosities in the calculation of the flow factors for non-Newtonian fluids. For this purpose, a simulation model based on the generalized Reynolds equation according to Dowson is used to evaluate shear thinning effects for various oils as well as different technical surfaces. Keywords Dowson, flow factors, non-Newtonian fluids, simulation, generalized Reynolds equation, shear thinning effects, technical surfaces Abstract * Marius Hofmeister, M. Sc. Jonas Schütz, B. Sc. Univ.-Prof. Dr.-Ing. Katharina Schmitz Institut für fluidtechnische Antriebe und Systeme (ifas) der RWTH Aachen Campus-Boulevard 30, 52074 Aachen es on the flow factor method according to Patir and Cheng. For the determination of the flow factors, first, a representative area between the two rough surfaces is selected like shown in Figure 1. This area is discretized in the order of magnitude of the present roughness peaks. For calculating ϕ p,x , the flow in y-direction is set to zero and a pressure gradient is applied in x-direction. [1, 3] The resulting flow is calculated by means of the Reynolds equation and corresponds to the term for rough surfaces in eqn. 2. Subsequently, the flow is determined for ideally smooth surfaces and an average gap height, which equals the one of the rough gaps. Finally, the pressure flow factor is the ratio of the flow between rough surfaces and the one for ideally smooth surfaces. To account for surface irregularities, the process should be performed several times for different areas of the surface. [1, 2] eqn. 2 The pressure flow factor in y-direction is calculated analogously by changing the direction of the pressure gradient and the boundary conditions. This way, one considers roughness effects depending on the flow direction. In general, the procedure for the determination is comparable to that of the pressure flow. In contrast to the pressure flow, no pressure gradient is applied for the determination of shear flow but a relative velocity between the surfaces shown in Figure 1. Since the flow factor is a tensor, the method described should be carried out parallel or transverse to the surface orientation, as otherwise there is an coupling between the flow for xand y-direction.This contribution only focuses on the pressure flow, so that the shear flow factor is not described in detail. . p,x = 1 y T 3 12 y 0 rough surface 3 12 smooth surface Science and Research 6 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 in relation to the present roughness peaks. One possibility to consider the influence of roughness on the flow is the discretization of the entire computational domain in the order of magnitude of the present roughness peaks. Subsequently, the flow and pressure field can be calculated for defined boundary conditions by means of numeric models like the Reynolds equation or Navier Stokes equation. However, this approach is associated to a high computational effort and is therefore impracticable. One way to avoid these high computational costs is to use the flow factor method according to Patir and Cheng. This method represents the information about the influence of roughness on the flow by only two scalar values: the pressure flow factor ϕ p and the shear flow factor ϕ s . These values are integrated to the Reynolds equation for 2-dimensional" flow visible in eqn. 1 and correct the deviations in flow rate caused by the rough surface for pressure flow and shear flow. In this manner, the influence of roughness is considered without discretizing the computational domain in the order of magnitude of the present roughness peaks, which is beneficial regarding discretization and computational effort. [1, 2] eqn. 1 An alternative to the flow factor method is the homognized Reynolds equation, which is independent from effects arising from the orientation of the chosen coordinate system [9]. However, this contribution only focuss- . ( ) Pressure build up = p,x 3 12 Pressure flow s,x ,1 ,2 2 ,1 Shear flow L y L x surface 2 no flow no flow x fluid film h surface 1 p B p A y Figure 1: Computational Domain When deriving the pressure and shear flow factors, a constant viscosity is assumed in gap height direction and along the flow direction. This assumption is only valid for Newtonian fluids. In case of a non-Newtonian fluid, the viscosity depends on the present shear rate, which varies along the gap height and the flow direction. This phenomenon is illustrated by Figure 2. Here, two gaps with the different heights h and H are visible. The same pressure gradient is applied to both gaps. The corresponding velocity, shear and viscosity profiles are indicated by black and green arrows for a Newtonian and a non- Newtonian fluid, respectively. The viscosity of both fluids is the same for a shear rate of zero. For both gaps and the Newtonian fluid, the pressure gradient leads to a parabolic velocity profile and therefore to a linear shear profile. Since the varying shear rate along the gap height has no influence on the viscosity of the Newtonian fluid, the viscosity is constant for the entire gap height and both gaps. The shear dependent viscosity course of the non-Newtonian fluid is visible in Figure 3. In this case, the non- Newtonian fluid is shear-thinning and can be described by the Cross equation (eqn. 7). For low shear rates the Cross fluid behaves like a Newtonian fluid. For a specific shear rate, the viscosity starts to decrease rapidly until the second Newtonian plateau is reached. [10] Since the viscosity of the non-Newtonian fluid decreases with increasing shear rate, the viscosity varies along the gap, which in turn influences the velocity and the shear profiles so that maximum velocity is higher for the non- Newtonian fluid. Furthermore, the flow velocity and the maximum shear rate is higher for the gap with the greater height H. The overall higher shear rates lead to a stronger decrease of viscosity. Applied to the flow between rough surfaces, this means that the viscosity is variable in gap height direction, but also changes for each gap height in flow direction. Thus, eqn. 2 is not valid and leads to errors if the varying viscosity is not considered. Flow simulation model To avoid the errors in flow factor calculation caused by the non-Newtonian viscosity behavior, a novel simulation model is built up. Since the fluid viscosity varies along the gap height direction, as described in the previous section, the conventional Reynolds equation cannot be used. However, the Reynolds equation according to Dowson offers the possibility to discretize the viscosity course in the gap height direction. The corresponding equation is given in eqn. 3. Analogous to the common Reynolds equation, the Reynolds equation, according to Dowson, consists of a term for pressure flow, shear flow and a term for pressure build up.[8] Science and Research 7 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 1st Newtonian plateau 2nd Newtonian plateau shear rate viscosity Figure 3: Qualitative viscosity course for a Cross fluid Figure 2: Velocity, shear rate, and viscosity profiles for Newtonian/ non-Newtonian fluids and different gap heights The shear rate is derived from the flow profile. Based on an arbitrary fluid model, the viscosity profile for each volume is calculated. Any model that gives a clear relationship between viscosity and shear rate can be used as a fluid model. In the context of this contribution only shear-thinning fluids, which can be described by the Cross or Carreau equation, are considered. The viscosity values calculated based on the shear profile are used to correct the Dowson integrals and the Reynolds equation is solved again. This procedure repeats until the deviation of two flow profiles determined in consecutive cycles is below a specified limit. As mentioned before, in the context of this contribution only pressure flow is considered and no shear flow occurs. With the described algorithm it is possible to calculate the flow Q rough,η(γ ˙ ) for non-Newtonian fluids and therefore the flow factor ϕ mod,x for the same. The modified flow factor does not only depend on the gap heights and the surface properties but also on the pressure gradient and the viscosity properties of the considered fluid. eqn. 6 To evaluate the error caused by assuming constant fluid viscosity, the normalized pressure flow factor ϕ N given in eqn. 7 is used. This measure represents the ratio of the pressure flow factor ϕ p,x determined with the common method by assuming constant viscosities and the pressure flow factor ϕ mod calculated with the model introduced before. eqn. 7 Results and discussion The described algorithm is used for the calculation of the normalized pressure flow factor ϕ N for the simplified . , = rough, ( ) 3 12 , rough, ( ) = ( , ( , ), ( )) = , Science and Research 8 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 eqn. 3 For the calculation of the shear rate γ ˙ for every value of z eqn. 4 is used.[8] eqn. 4 Unlike the Reynolds equation, in eqn. 3 and eqn. 4 the viscosity is not specified explicitly, but is considered by means of the Dowson integrals mentioned in eqn. 5. The Dowson integrals result from the derivation of the Reynolds equation from the Navier Stokes equation, if a variable viscosity in gap height direction is assumed.[8] eqn. 5 Eqn. 3 is integrated in the algorithm visible in Figure 4. The algorithm starts with an initialization process. Here, the boundary conditions are defined, the computational domain is discretized and divided into a specified number of volumes in xand y-direction. Additionally, each volume is subdivided in z-direction, whereby this discretization only refers to the values for fluid viscosity. Furthermore, during the initialization process the Dowson integrals are calculated for an initially constant viscosity. In the next step, the Reynolds equation according to Dowson is solved for the entire computational domain and the pressure field is calculated. The velocity profile is determined for each volume using eqn. 4. ( ) Pressure build-up = ,4 1 2 0 Pressure flow ,1 ,2 2 1 0 ,1 Shear flow = = 1 1 0 + ,2 ,1 0 = 1 = = 1 = = flow profile shear profile viscosity profile end pressure profile Reynolds equation start Dowson integrals Initialization Dowson integrals Dowson integrals Dowson integrals Boundary Conditions Discretization max(|v -v |) j,i-1 j,i < v res no yes Figure 4: Algorithm for the calculation of flow for rough surfaces and non-Newtonian fluids rough gap visible in Figure 5. This gap consists of two areas, each with the gap height h and H, respectively. In this example, the relationship between h and H is given by the following equation: H = h + 1 μm. The height h¯ of the second gap visible in Figure 5 corresponds to the average height of the rough gap and is the mean value of h and H. The flow direction points into the drawing plane for both gaps. As the orientation of the surface roughness in this simplified gap runs exclusively in the x-direction along the pressure gradient, the calculated flow factor corresponds to that in the main axis direction. Therefore, no further components of the flow tensor away from the main axes need to be taken into account. The fluid used in the simulation is a shear-thinning oil that can be described by the Cross model and the parameters given in eqn. 8. The value r refers to the ratio of the viscosity η 0 for zero shear and the viscosity at the 2 nd Newtonian plateau. The factor m indicates how rapidly the transition between 1 st and 2 nd Newtonian plateau takes place. The K variable determines the shear rate where shear-thinning starts to be noticeable.[10] eqn. 8 The overall dimensions of the computational domain are 10 by 10 mm. The domain is divided into 20 volumes in xand y-direction. Each volume is subdivided in 51 sections in z-direction. The Dowson integrals from eqn. 5 are solved by Trapezoidal numerical integration. The corresponding results for the normalized flow factor ϕ N and the Reynolds number are visible in Figure 6. The normalized flow factor is equal to one for a pressure gradient tending towards zero and therefore equals the flow factor determined according to Patir and Cheng for constant viscosity. With increasing pressure gradient, the normalized flow factor increases rapidly and reaches a maximum. After passing the maximum, ϕ N decreases slowly. It can thus be seen that for a non-Newtonian fluid, the flow factor depends not only on the gap height but also on the pressure gradient respectively the shear rate. The Reynolds number is low for the entire set of parameters and therefore the prerequisite for using of the Reynolds equation Re ≪ 1 is true. The course of the normalized pressure flow factor ϕ N can be divided into four sections. Within the first section where the pressure gradient is nearly zero, the corresponding shear rate is also close to zero. Therefore, the shear rate has no effect on the fluid viscosity and for every gap height shown in Figure 5 the viscosity is the same. In this case, the normalized pressure flow factor = + 1 1 + ( ) ϕ N equals the flow factor according to Patir and Cheng. This phenomenon is also indicated by the circles in the viscosity diagram Figure 7. Since the gap heights differ from each other, an increased pressure gradient leads to varying shear rates for each gap height. Due to the comparably low hydraulic resistance for gap heights H, here, the shear rate is the highest and therefore the viscosity loss is the largest. This leads to a higher flow rate for H compared to h and h¯ and an increase of the normalized flow factor. If the pressure gradient increases even further, the shear thinning also starts to become noticeable for gap h¯. Accordingly, the curve begins to fall again in section III. For high pressure gradients tending to an infinite value, the viscosity for each gap has reached the second Newtonian plateau. Now, the viscosity is the same for each gap and the normalized flow factor approaches one again. Science and Research 9 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 H h h rough gap smooth gap H h B B ¹⁄ B ¹⁄ B Figure 5: Simplified rough gap Figure 7: Fluid model for fluid 1 0 10 20 30 40 50 1 1.005 1.01 1.015 0 0.00076 0.0015 0.0023 0.003 0.0038 Reynolds Number I II dp/ dx 0 → dp/ dx → 1.025 ∞ III IV Pressure gradient dp/ dx in bar/ mm Normalized Flow Factor ϕ N Figure 6: Results for the normalized flow factor s = 1,34 10 , = 0,68 = 40 mPa s, = 0,49 Besides the simplified gap from Figure 5 the technical surface visible in Figure 12 was investigated, too. The surface was measured by means of a digital microscope with a lateral resolution of 350 nm and a minimal vertical resolution of 10 nm. Figure 12 shows a section of the technical surface with the dimensions 0.5 mm by 0.5 mm. For the simulation the entire surface scan with the dimensions 1 mm by 1 mm was used. As can be seen, there are several grooves on surface 1 that are neither parallel nor transverse to the x-axis and would therefore also influence the flow in the y-direction for a pressure gradient in x-direction. However, surface 2 has a very similar surface orientation in the opposite direction, which cannot be seen in this figure as it is covered by surface 1. Overall, the surfaces are positioned in relation to each other so that the x-direction of the calculation area corresponds to the main flow direction. To represent the influence of roughness correctly, the computational domain must be meshed much finer for the measured surface in comparison to the simplified Science and Research 10 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 A further parameter investigated in the context of this paper, is the gap height, which was varied as shown in Figure 9. The gap heights is reduced stepwise until the h vanishes. The results for the gap heights variation and the same fluid parameters as used before are visible in Figure 8. The results show that ϕ N increases with decreasing gap height. In this example the highest value for ϕ N is 1.096 and is reached for h¯ = 0.5 μm. In Figure 10, the influence of different fluid parameters on the normalized pressure flow factor is evaluated. For this purpose, the m value of the Cross equation was varied as shown in Table 1. The corresponding viscosity courses are visible in Figure 11. The simulation results show that an increased m value leads to a stronger expression of the maxima for ϕ N . For example, the maximum value of ϕ N is 1.215 for fluid 3 with m = 1.34 and an average gap height h¯ of 0.5 µm. In comparison, the maximum value for fluid 1 and the same gap height is significantly smaller and is 1.044. 0 10 20 30 40 50 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 Re = 1e-5 Re = 5e-5 Re = 1e-4 Re = 2e-4 Re = 3e-4 Pressure gradient dp/ dx in bar/ mm h = 1 m μ h = 0.75 m μ h = 0.5 m μ h = 2 m μ h = 1.25 m μ h = 1.75 m μ h = 1.5 m μ Normalized Flow Factor ϕ N Figure 8: Results for different gap heights H h h rough gap smooth gap H h B B ¹⁄ B ¹⁄ B h rough gap smooth gap H B B ¹⁄ B Figure 9: Gap heights reduction 0 5 10 15 20 25 Pressure gradient in bar/ mm dp/ dx 1 1.05 1.1 1.15 1.2 1.25 Normalized Flow Factor Φ N Fluid 1 Fluid 2 Fluid 3 0.5 m μ 0.75 m μ 1 m μ 1.25 m μ 1.5 m μ 1.5 m μ 1.5 m μ 1.25 m μ 1 m μ 0.75 m μ 0.5 m μ 1.25 m μ 1 m μ 0.75 m μ 0.5 m μ Figure 10: Results for different fluid parameter 0 5 10 15 20 Shear rate in 1/ s 20 30 40 Viscosity η in mPas Fluid 1 Fluid 2 Fluid 3 Figure 11: Investigated fluid models Fluid 1 Fluid 2 Fluid 3 in Pa·s 40 0,49 0,000134 0,68 0,34 1,34 Table 1: Cross parameter for Fluid 1-3 gap. To find the optimal mesh size a, convergence analysis was conducted. The corresponding results are visible in Figure 14. As can be seen, the deviation in flow rate decreases significantly for a mesh with 80 volumes in each direction. Therefore the resolution of 300 by 300 volumes implemented for previous simulations is sufficient to map the flow between the selected surface accurately. The results for the normalized pressure flow factor ϕ N and the technical surface are visible in Figure 13. Again, the fluid properties of fluid 1 are used and the corresponding Reynolds numbers are given.The effects shown for the simplified gap can also be observed for the technical surface. The previously defined four areas in the flow factor course exist also for the technical surface. It can be seen that a decrease in the gap height leads to an increase in the maximum normalized flow factor exactly the same as in the previous examples. Differences exist essentially in the expression of the maximum values for ϕ N . Thus, the maximum value of ϕ N for the simplified gap and a gap height of 1 µm is 1.050, while for the technical surface and the same gap height only a value of 1.027 is obtained. The comparison between simplified gap and technical surface illustrates that the characteristic of the surface also has a significant impact on the normalized pressure flow factor. Summary and outlook This contribution first highlighted the concept of flow factors according to Patir and Cheng and described the derivation of the pressure flow factor. Subsequently, the variation of viscosity for non-Newtonian fluids in z-direction and for different gap height was illustrated. Furthermore, the errors caused by this viscosity variation were addressed. Science and Research 11 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 Figure 13: Results for technical rough surface 6 8 10 12 14 20 40 60 80 100 140 180 225 275 350 500 700 900 1100 1300 1500 Cells per direction 0.7 0.8 0.9 1 1.1 1.2 Normalized flow deviation to 1500 Figure 14: Convergence analysis Figure 12: Technical rough surface Nomenclature B gap width H, h gap height h¯ averaged gap height J i Dowson integral K K-constant Cross model L i length m m-constant Cross model p i pressure r r-constant Cross model t time u i velocity of surface i x,y,z x,y,z-coordinates γ ˙ shear rate η dynamic viscosity η 0 dynamic viscosity at γ ˙ = 0 ρ density ϕ N normalized pressure flow factor ϕ mod modified pressure flow factor ϕ p,x pressure flow factor x-direction ϕ s,x shear flow factor x-direction References [1] Patir, N.; Cheng, H. S., An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic. J. lubr. technol., Vol. 1, 1978, pp. 12- 17 [2] Patir, N.; Cheng, H. S.. Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces. J. lubr. technol.Vol. 2, 1979, pp. 220-229 [3] Elrod, H. G., A General Theory for Laminar Lubrication With Reynolds Roughness. J. lubr. technol., Vol. 1, 1979, pp. 8-14 [4] Harp, S. R.; Salant, R. F., An Average Flow Model of Rough Surface Lubrication With Inter-Asperity Cavitation. J. lubr. technol., Vol. 1, 2001, pp. 134-143 [5] Hasim Khan; Prawal Sinha. Thermal Elastohydrodynamic Lubrication of Line Contact Rough Surfaces Using Flow Factor Method. Contemp. Eng. Sci., Vol. 3, 2010, no. 3, pp. 113-138 [6] Kumar, R.; Azam, M. S.; Ghosh, S. K., Influence of stochastic roughness on performance of a Rayleigh step bearing operating under Thermo-elastohydrodynamic lubrication considering shear flow factor. Tribol. Int., 2019, pp. 264-280 [7] Herbst HM. Theoretical modeling of the cylinder lubrication in internal combustion engines and its influence on piston slap induced noise, friction and wear. Graz (Austria): Graz University of Technology, 2008. [8] Dowson, D., A Generalized Reynolds Equation for Fluidfilm Lubrication, Int. J. Mech. Sci., Vol. 4, 1962, pp. 159- 170 [9] Rom, M.; Müller, S., A Reduced Basis Method for the Homogenized Reynolds Equation Applied to Textured Surfaces, Commun. Comput. Phys., Vol. 24, 2018, No. 2, pp. 481-509 [10] Bukovnik, S., Thermo-elasto-hydrodynamic lubrication model for journal bearing including shear rate-dependent viscosity. Lubrication Science, Vol. 19, 2007, pp. 231-245 Science and Research 12 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 To consider the described viscosity variations for the flow factor calculation, a simulation model based on the Reynolds equation according to Dowson and preliminary works from Herbst was introduced. Mathematical principles as well as the used algorithm were discussed. To understand the fundamental mechanism influencing the flow factor calculation with respect to non-Newtonian fluids, initially, a simplified rough gap was generated. The corresponding results showed that neglecting the variable viscosity behavior of non-Newtonian fluids leads to significant errors. Furthermore, it could be shown that the error increases with decreasing gap height. The error is especially huge for fluids, whose viscosity change rapidly for varying shear rates. A further parameter influencing the error in flow factor calculation is the pressure gradient. Besides the simplified gap, a realistic technical surface was investigated, as well. Here, the same effects that were previously evaluatedcould be demonstrated. The presented method can be used to estimate the error in the flow factor calculation caused by neglecting shear thinning in the conventional method. In a further step, the phenomena and dependencies shown are to be investigated in more detail in to be able to estimate the maximum deviations from the flow factor according to Patir and Cheng as a function of surface properties, fluid properties, gap height and pressure gradient without complex simulation. This way users can estimate wether high deviation in flow factor can be expected for their specific tribological system. Since the error is especially high for small gap height, the future implementation of a contact model is desirable. This way, the gap height between the two rough surfaces can be reduced even more. Additionally, the influence of flow channel formation on the error could be investigated with an appropriate deformation model. Moreover, the investigation of further non-Newtonian fluids apart from Cross fluids is planned. In this context, the evaluation of ionic liquids that are showing strong shear thinning behavior is also feasible. This contribution only focused on the pressure flow between rough surfaces. For this reason, the simulation model shall be extended by a calculation routine for shear flow. Acknowledgement Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - Exzellenzcluster 2186 “The Fuel Science Center”. Science and Research 13 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 Further information and registration at www.tae.de/ go/ tribologie Attend our seminars, courses and conferences. Friction, wear and lubrication Lubricants and operating fluids Lubrication technology Lubricated machine elements A large part of our seminars is supported by the Ministry of Economic Affairs, Labour, and Housing of Baden-Württemberg with funds from the European Social Fund. Benefit from the ESF course funding and secure up to a 70 % subsidy on your participation fee. All information on eligibility for funding can be found at www.tae.de/ foerdermoeglichkeiten Tribology, friction, wear and lubrication Up to 70 % subsidy possible 1 Introduction and motivation Wind energy is the most important renewable power source in Germany with a share of around 20 % of the overall power production [1]. In recent years the increase of rated power output per WT and a reduced levelized cost of energy are subject to research efforts. The usage of planetary journal bearings in wind turbine gearboxes Science and Research 14 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 Condition monitoring for planetary journal bearings in wind turbine gearboxes by means of acoustic measurements and machine learning Thomas Decker, Georg Jacobs, Christoph Paridon, Julian Röder* submitted: 18.09.2023 accepted: 05.07.2024 (peer-review) Presented at the GfT Conference 2023 * Thomas Decker, M. Sc. (corresponding author) Orcid-ID: https: / / orcid.org/ 0000-0002-3296-7166 Prof. Dr.-Ing. Georg Jacobs Christoph Paridon, B. Sc. Julian Röder, M. Sc. Center for Wind Power Drives Campus Boulevard 61 52074 Aachen - Germany The use of journal bearings instead of rolling bearings as planetary bearings in wind turbine (WT) gearboxes is advantageous for the power density of the drive train. In addition, they can increase the reliability of the gearboxes as they can be operated wear-free in hydrodynamic operation, i.e. with fluid friction. The dynamic loading conditions in wind turbines, as well as special conditions such as insufficient lubrication and particle contamination, can lead to mixed friction operation and consequently to wear in the journal bearings. If mixed friction is not detected, damage and failure of the journal bearing and consequently of the WT gearbox may occur. Therefore, it is required to develop a Condition Monitoring System (CMS) to detect mixed friction in the journal bearings during operation of the WT. Preliminary investigations have shown that various friction conditions can be detected by acoustic measurements in combination with machine learning classifiers. Current investigations on CMS methods for journal bearings using acoustic measurement methods are limited to component level applications. A condition monitoring methodology for wind turbine gearbox journal bearings does not currently exist. A major challenge for CMS development for journal bearings in WT gearboxes is the transfer of methods already proven at component level to gearbox applications. In preparation for CMS application at the gearbox level, this paper presents an approach for monitoring different Abstract friction conditions of journal bearings based on acoustic measurements at a component test rig. For the classification of the friction state, different machine learning (ML)-based approaches trained on the acquired acoustic measurement data are compared with respect to the achieved classification accuracy. Knowledge of the robustness of the classification method, e.g. with respect to the distance of the sensor to the bearing, provides the necessary basis for the use of the CMS at the gearbox level. The investigations are carried out under operating conditions typical for planetary bearings in wind turbines. Classification performance is evaluated using a validated elasto-hydrodynamic simulation model. The aim of the work is to develop a method that detects friction classes in the journal bearing based on structure-borne sound measurements. Here, simulation results are used to train the algorithms. Finally, the demonstrated method will be successfully applied to a test rig for wind turbine gearbox journal bearings. Based on the results, an ML approach will be selected for application in gearboxes. Keywords wind energy, journal bearings, condition monitoring, machine learning is advantageous compared to roller bearings in terms of torque density of the planetary stage and the reliability of the drivetrain and can therefore contribute to the aforementioned goals [2]. When designed and operated correctly (i.e. in hydrodynamic conditions), journal bearings have an unlimited operating lifetime. To ensure a wear safe operation of journal bearings, mixed friction states that can lead to wear of the bearing should be avoided. Mixed friction states can be detected using condition monitoring systems (CMS). CMS typically consist of a specifically designed sensor setup measuring the operating condition of the bearing and a computing unit that automatically conducts the autonomous evaluation and interpretation of the data. CMS techniques are already established for the use in gearboxes over a broad range of different industries. However, these methods are limited to the monitoring of roller bearings and gears. A reliable CMS for planetary journal bearings in WT gearboxes does not currently exist. This paper presents an approach towards the monitoring of planetary journal bearings using acoustic measurements to detect mixed friction. The experimental investigations are carried out on a component test rig for radial journal bearings. The acoustic measurements are used to train different supervised machine learning algorithms for the classification of friction states. Previous works on tribometers and small journal bearing test rigs have shown that classification algorithms can differentiate between friction states based on Acoustic Emission (AE) measurements [3, 4] and even detect wear progression [5, 6]. Different classification algorithms perform differently on the same data sets. Therefore, this paper evaluates the classification accuracy of different algorithms. Furthermore, the transferability of the method to planetary journal bearings is demonstrated on a planetary gear stage test rig with a journal bearing. Thus, the first step towards transferring the method to a gearbox in the field is shown. 2 Methods and test infrastructure The methodological approach of this work is shown in Figure 1. Acoustic measurement data is gathered from a journal bearing on the test rig under various operating conditions and merged into one data set. This data set is divided into training and validation data. The same operating conditions from the tests are also used for elastohydrodynamic (EHD) simulations to characterize the occurring friction regime. The simulation results are summarized into four different friction states that must be detected by the CMS: “fluid friction”, “mild mixed friction”, “mixed friction” and “severe mixed friction”. The simulation results are used as labels for the training data. The labels are fed into a supervised machine learning algorithm, which is trained to differentiate between the defined friction states. In a final step the algorithm uses the test data to produce a prediction based on the learned behavior. The prediction is validated using the simulation results. a. Experimental test setup The used bearing material and lubricant are typical for gearbox applications in WTs. The bearings are loaded using a hydraulic actuator with a maximum force of 216 kN, which corresponds to a specific pressure of 60 MPa in the test bearing. For this work several test bearings are used. Their specifications are given in Table 1. Science and Research 15 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 Figure 1: Workflow of the condition monitoring method used in this work Bearing width = 30 Bearing diameter = 120 Bearing surface roughness = 0.4 Bearing material 12 2 , = 100 GPa Shaft material 42 4, = 210 GPa Radial bearing clearance = 80 Lubricant 320 Table 1: Specifications of the test setup 12 2 , = 100 GPa 42 4, = 210 GPa Figure 4 shows the AE measurement results during a test procedure with a constant sliding speed v and swelling load between 15 and 60 MPa of specific pressure p̅ and the measured friction moment F R . The bottom plot shows the so-called root mean square (RMS) U RMS and the kurtosis κ Equation 1 Equation 2 with x̅ being the moving average of the raw signal and σ being the standard deviation. U RMS and κ are characteristic signal features that in previous works have proven to be effective for the differentiation between friction states [4, 9]. Both characteristics are calculated in the time domain using a moving window with a length of N = 10 6 datapoints, which at a sampling frequency of 3 MHz corresponds to a window duration of 0.33 s. Before the extraction of the signal features the raw signal is filtered using a steep bandpass filter between 0.4 MHz and 1 MHz. This frequency range was identified as suitable for the detection of abrasive wear in journal bearings [3]. The AE signals clearly correspond to the load imposed on the bearing. The extracted U RMS (t) and κ (t) give an indication for different friction states in the journal bearing. No increase in signal amplitude occurs at the load level with the lowest pressure (p̅ =15 MPa). The load interval with the highest specific pressure (p̅ = 60 MPa) results in the highest amplitude in the AE features. Strong mixed friction is assumed for this operating point. This is examined in more detail below using simulations. c. Elasto-hydrodynamic simulation of the test bearing The used classification approaches in this work all belong in the category of supervised machine learning. This means that the classification algorithm is trained to detect the different states according to labels defined by the user. The training data consists of sensor signals recorded at different friction states. For the training process a valid information (label) about the corresponding friction state (mixed or fluid) for each section of the training data set is required. These labels are generated using an EHD simulation of the test bearing in its test rig environment. The EHD simulation consists of the flexible bodies bearing and shaft. These are created by means of the finite element method and are shown in Figure 5. Previous works have shown that EHD models can predict the friction state (mixed or fluid friction) in a journal bearing if they are parametrized correctly [10]. Mixed friction in a hydrodynamic journal bearing is characteriz- = 1 = ( ) ( 1) Science and Research 16 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 The test rig is shown in Figure 2. Radial force and speed are applied by a hydraulic actuator and an electric drive. Other than for a planetary journal bearing in a wind turbine gearbox, no tilting moment acts on the journal bearing on the component test rig. Gear influences are also neglected. The specimen is mounted inside a rotatable enclose that is connected to a force transducer. This allows for the measurement of friction moment during operation, which causes the enclosure to tilt around the rotational axis. The test rig can be heated artificially to typical wind turbine gearbox temperatures (20 °C to 100 °C). b. Acoustic Emission AE has already proven to be a suitable technology to detect different friction states and wear progression in tribological systems such as pin-on-disk tribometers [3, 4] and small journal bearings [7, 8]. In this work the AE sensor (piezoelectric transducer) is bolted to the bearing cover as close to the bearing as possible, approximately 80 mm away from the load zone of the bearing (see also Figure 3). Figure 2: Experimental setup on the journal bearing component test rig Figure 3: AE sensor mounted to the bearing cover on the component test rig ed by the occurrence of asperity contact pressure p a . The asperity contact pressure is calculated using the stochastic contact model according to Greenwood and Tripp [11]. It describes the asperity contact pressure as a function of the elasticity factor K, the average elastic modulus E of the bearing and shaft and the probability distribution for the occurring contact F(H S ) as a function of the nominal gap height H S . Equation 3 With H S being the ratio between the absolute oil film height h and the root mean square summit height σ S of the surface roughness, asperity contact occurs only when the oil film height H S falls below a minimum [11, 12]. Equation 4 The asperity contact pressure p a according to Equation 3 and Equation 4 is shown in Figure 6 with different values for the elasticity factor K chosen within the recommended range [12]. According to the given contact model the simulated asperity contact pressure p a is strongly influenced by the elastic factor K, surface roughness values and the oil film height h. The latter results from the solution of the Reynold’s equation and is strongly influenced by the operating conditions (load p̅ , speed v and temperature T). Model input parameters such as the nominal bearing clearance and the roughness values of the bearing and the shaft result from surface measurements prior to the testing. The temperature of the lubricant T is measured on the test rig as well. The elastic factor K is fitted such that the resulting friction moment in the simulation corresponds to the measurement for one selected operating point (p̅ = 45 MPa,v = 0.4 m/ s). For this work the elastic factor is chosen to be K = 0.0004. Afterwards the validation of the model is carried out by a comparison of the measured and simulated friction moment for the tested procedures as shown in Figure 7. For this purpose, the force transducer of the test rig (see also Figure 2) is used to measure = ( ) ( ) = 4.4086 10 (4 ) . , < 4 0 , 4 Science and Research 17 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 Figure 5: EHD model of the component test rig Figure 4: AE measurement under dynamic load intervals and a constant sliding speed on the component test rig Figure 6: Calculated asperity contact pressure p a at different oil film heights h The occurring maximum asperity contact pressure p a,max during the swelling load procedures is given in Figure 8. Apparently, for both procedures at the first load level, no asperity contact pressure is generated. This corresponds to the signals of the AE features (see Figure 7), where no change of the AE signal amplitude can be detected in the first load level either. From that point on the level of maximum asperity contact pressure rises with each load interval. It is assumed that using the presented EHDmodel the characterization of the operating points can be done with a sufficient accuracy. Science and Research 18 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 the friction moment. Figure 7 shows two of the test procedures used in this work at 0.4 m/ s and 0.6 m/ s sliding speed. The applied load over time is equal to the procedure shown in Figure 4. The tested procedures are simulated with the EHD model and the time series of the friction moment of measurement and simulation are compared. The validation shows a qualitative agreement between simulation and measurement. For this work it is assumed that the presented parameterization and validation of the model is sufficiently accurate to demonstrate the feasibility of the CMS method shown in Figure 1. Figure 7: Comparison of the simulated and the measured friction moment Figure 8: Simulation result for the maximum asperity contact for different sliding speeds Figure 9: (a) Map of the simulated asperity contact pressure for the tested operating conditions of the bearing (Simulated bearing temperature: 55 °C) (b) Distribution of four friction states over the tested operating conditions based on the simulation results and the definition in Equation 5 (b) (a) Using the aforementioned EHD model, simulations are performed for different operating points and the resulting maximum asperity contact pressure p a,max is mapped over the specific pressure p̅ and the sliding speed v (see Figure 9 (a)). A high asperity contact pressure p a represents wear critical mixed friction, while low asperity contact pressure represent a low risk of wear. Without solid contact, pure fluid friction occurs. Using the simulation results presented above labelling of the datasets used for training and validation of the machine learning classification algorithms will be done. Therefore, the results are divided into four different classes according to the amount of asperity contact pressure p a that occurs (Figure 9 (b)). The given simulations are carried out for three different lubricant temperature levels (40 °C, 55 °C and 70 °C) to account for the temperature influence on the friction state in a typical gearbox temperature range. The simulated distribution of the friction states over the operating conditions are stored and used by the classification algorithms for the generation of labels for the training data. The training algorithm can hereby assign one of the four friction states as a training label to any operating point of the journal bearing. d. Machine learning classifiers In this work, three classification algorithms are evaluated with regard to their accuracy in detecting friction states: Support Vector Machine (SVM), Gaussian Process (GP) and Multi-Layer Perceptron (MLP) neural network. All three approaches process the same input data to ensure comparability. The input data consists of timebased signals: the extracted AE characteristics, the bearing temperature and the sliding velocity. The strengths and shortcomings of the three algorithms are discussed in the next paragraphs. With the SVM classification is achieved by defining a hyperplane that separates datapoints belonging to different classes. The hyperplane is defined such that the margin between the classes is maximized. The simple approach of the SVM is advantageous as the model’s classification decisions are comprehensible; a disadvantage resulting from the simplicity is the SVM’s limited number of adaptable parameters. Of all considered models, the SVM is the fastest to train and to run productively after training. It has already been shown that the SVM is a suitable algorithm for the detection of friction states in tribological systems [4, 9]. A GP is a probabilistic classification model. Its definition is considerably more sophisticated than for the SVM and can be found e.g. in [13]. From the user perspective, the main difference is the choice of the kernel function. The GP is comparable to the SVM in terms of time effort needed for training and execution. The MLP is a simple type of neural network. Unlike the algorithms presented before, the approach behind neural networks is not based on regression. Instead, they consist of “layers” containing multiple “neurons”. In the simple model presented here, each neuron receives input values from all neurons in the layer before, calculates the sum of all inputs plus a constant set in model training and then outputs either zero or the calculated sum, subject to whether the sum exceeds a threshold. In the final layer, the number of neurons corresponds to the number of classes to predict, and the neuron yielding the highest output value represents the predicted class. The high number of parameters configurable in training makes the MLP very adaptable to complicated relationships in the training dataset, but it also makes the model computationally expensive. All three models are evaluated with a variety of configuration parameters. Among these are multiple kernel functions for SVM and GP as well as the number of neurons and the number of layers for MLP. The performance of the best configuration of each classification algorithm is presented below. The input features are normalized to values between -1 and 1 to weight all features equally. Afterwards the samples in the dataset are randomized and split into 80 % training data and 20 % validation data. 3 Results This chapter discusses the results of the friction state classification. It has already been shown that the AE signal is speed and temperature dependent [6]. Thus, it is assumed that the classification of the friction condition can be improved if the bearing temperature and the sliding speed are included as input features in the classification algorithm. This approach does not conflict with the wind turbine application, since the necessary measurements are also available in the real application. Table 2 shows the achieved classification accuracy for all three algorithms with different input features. The given accuracy is the ratio of the number of overall correct classifications to the number of overall datapoints. The highest Science and Research 19 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 ( ) = 0 , = 0 1 , 0 < 15 2 , 15 < 45 3 , > 45 Equation 5 sliding speed used as input features are shown in Figure 10. It can be observed for all three algorithms that the friction states “fluid friction” and “severe mixed” friction can be detected relatively accurate (values above 90 %). “Mild mixed friction” is more challenging to detect (accuracy values of around 70 to 80 %) due to the very weak change in AE signal characteristics (see also Figure 4). In summary all three algorithms performed with Science and Research 20 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 accuracy is achieved by the GP classifier using AE data, bearing temperature and sliding speed as input features. This corresponds to the findings presented in [14], where the AE signals have been proven to be highly speed dependent. Overall, it should be noted that the accuracy of the classification in this work increases with the number of input features. The confusion matrices for all three classification algorithms with the AE signals, bearing, temperature and Support vector machine classifier Gaussian process classifier Multi-layer perceptron classifier Input: Accuracy [%] Accuracy [%] Accuracy [%] AE 81,6 85,6 80,7 AE + T 84,1 88,1 82,7 AE + v 86,1 90,4 87,0 AE + T + v 89,8 92,6 90,9 Table 2: Classification performance of the three implemented algorithms based on the AE measurements and different additional feature inputs Figure 10: Confusion matrices for all three algorithms with the AE signals, bearing temperature and sliding speed as input features Figure 11: (a) Planetary journal bearing test gearbox (b) AE sensor mounted to the front face of the planetary pin (a) (b) an acceptable accuracy. Since SVM and GP surpass the neural network in terms of simplicity and training effort, both approaches are favorable for the application in a CMS. a. Transfer of the method to the gearbox application The previously presented measurements result from experiments on a component test rig for radial journal bearings. To show the transferability of the presented method from component level to planetary journal bearings in wind turbine gearboxes further experiments were conducted. Figure 11 (a) shows a test rig for planetary journal bearings which allows for the examination of the bearing behavior under the influence of operating conditions typical for planetary bearings in wind turbines. The test rig consists of two parallel shafts driving a planetary gear between them. The planetary gear rotates around a fixed axis (planetary pin) with a planetary journal bearing. In contrast to the previously investigated component test rig, the planetary bearing test rig considers gear influences and planetary gear tilting. Thus, the behavior of the test bearing is more realistic to the real WT application. The AE Sensor in this test setup is mounted to the front face of the planetary pin (see also Figure 11 (b)). In this case the distance from the sensor to the center of the journal bearing is 180 mm, which is closer to the application in a gearbox in the field. There the accessibility is limited so that it is expected, that the sensor needs to be place at a significant distance to the load zone. In order to ensure comparability with the previous experiments, tests are also carried out on the planetary journal bearing test rig with constant sliding speed and different pressure levels. The bearing and gear material and lubricant are identical to those on the aforementioned component test rig. The post-processing of the measurement data was done identically to the previous experiments. The bearing temperature is measured directly under the sliding surface in the bearing sleeve. Figure 12 (a) shows an example for the conducted test runs. Both AE signal features behave similarly to the previous experiments. In addition, an amplitude modulation of the signals is noticeable that can be explained through the gear mesh influence. It is assumed that the overall effectiveness of the signal features for the classification of the friction condition is not affected by this influence and that the transfer of the signal processing developed on the component test rig is transferable to a gear stage application. In total five different sliding speeds have been examined between v = 0.1…0.3 m/ s. All tested operating points are within the range of typical load cases for planetary journal bearings in wind turbines. The results from the radial journal bearing test rig show that the gaussian process classifier achieves the best classification performance (Table 2). Figure 12 (b) shows the confusion matrix resulting from a GP classifier trained to differentiate between the same four friction states using the AE data from the planetary journal bearing. The labels for this dataset are created using an EHD model from the planetary journal bearing test gearbox with an equal parameterization to the previously shown model. The classification results show that the presented method is transferable to the planetary journal bearing application. The overall classification accuracy for the friction state “mild mixed friction” has even increased by 11 %. Science and Research 21 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 Figure 12: (a) AE measurement results on the planetary journal bearing test gearbox (b) Friction state classification with a GP classifier achieved with the AE-measurement from the planetary journal bearing test (a) (b) density with special attention to a low-noise turbine operation. In: Conference for Wind Power Drives 2019 Conference Proceedings [3] Hase, A., Mishina, H. u. Wada, M.: Correlation between features of acoustic emission signals and mechanical wear mechanisms. Wear (2021) [4] Strablegg, C., Summer, F., Renhart, P. u. Grün, F.: Prediction of Friction Power via Machine Learning of Acoustic Emissions from a Ring-on-Disc Rotary Tribometer. Lubricants 11 (2023) 2, S. 37 [5] König, F., Marheineke, J., Jacobs, G., Sous, C., Zuo, M. J. u. Tian, Z.: Data-driven wear monitoring for sliding bearings using acoustic emission signals and long shortterm memory neural networks. Wear 476 (2021), S. 203616 [6] Mokhtari, N., Guhmann, C. u. Nowoisky, S.: Approach for the Degradation of Hydrodynamic Journal Bearings based on Acoustic Emission Feature Change. In: IEEE International Conference on Prognostics and Health Management. 2018 [7] König, F., Jacobs, G., Stratmann, A. u. Cornel, D.: Fault detection for sliding bearings using acoustic emission signals and machine learning methods. IOP Conference Series: Materials Science and Engineering 1097 (2021) 1, S. 12013 [8] König, F., Sous, C., Ouald Chaib, A. u. Jacobs, G.: Machine learning based anomaly detection and classification of acoustic emission events for wear monitoring in sliding bearing systems. Tribology International 155 (2021), S. 106811 [9] Mokthari, N. u. Glühmann, C.: Classification of journal bearing friction states based on acoustic emission signals. Technisches Messen (2018) [10] König, F., Sous, C. u. Jacobs, G.: Numerical prediction of the frictional losses in sliding bearings during start-stop operation. Friction (2020) [11] Greenwood, J. A. u. Tripp, J. H.: The Contact of Two Nominally Flat Rough Surfaces. Proceedings of the Institution of Mechanical Engineers 185 (1970) 1, S. 625-633 [12] AVL: EXCITE Power Unit User Manual [13] Rasmussen, C. E. u. Williams, C. K. I.: Gaussian Processes for Machine Learning. The MIT Press 2005 [14] Mokhtari, N., Pelham, J. G., Nowoisky, S., Bote-Garcia, J.-L. u. Gühmann, C.: Friction and Wear Monitoring Methods for Journal Bearings of Geared Turbofans Based on Acoustic Emission Signals and Machine Learning. Lubricants 8 (2020) 3, S. 29 Science and Research 22 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0008 4 Summary and outlook For the condition monitoring of journal bearings, a reliable detection of mixed friction is essential. This work presents an approach for a friction state detection based on AE measurements and supervised machine learning methods. The experiments for establishing the method are performed on a test bench for radially loaded journal bearings. The collected data is fed into three different classification algorithms, of which the GP proves to have the best classification accuracy. Finally, experiments on a planetary journal bearing test rig demonstrated that the method developed in this work can be applied to planetary journal bearings. As shown above the simulative distinction between different friction states strongly depends on the accuracy of the model’s parameterization. In this work the stochastic contact model according to Greenwood and Tripp is used and its parameters (e.g. elastic factor K) are fitted to represent the performed experiments. For a field application of the presented method in a real wind turbine environment the precision of the friction state labels should be further improved. The methods presented in this work will be extended in the future to feature additional metrics such as surface acoustic wave measurements from the bearing’s sliding surface and particle counting in the oil supply lines. In future work the classification software will be extended by unsupervised learning methods to enable an anomaly detection for mixed friction occurring during special events like dry-running or particle contamination. In a further step, the CMS measurement technology will be transferred to a WT gearbox with planetary journal bearings and tested on a system test bench to finally demonstrate the transferability. This will bring the CMS methods closer to the application in the field. Acknowledgement This research was funded by the German Federal Ministry of Economic Affairs and Climate Action. Literature [1] Umweltbundesamt: Erneuerbare Energien in Deutschland. Daten zur Entwicklung im Jahr 2022 (2023) [2] Lubenow, K., Schuhmann, F. u. Schemmert, S.: Requirements for wind turbine gearboxes with increased torque Nomenclature a center distance c(λ) initial lubrication gap height at the position λ c m maximum edge relief d equivalent diameter d aAR thrust ring outer diameter d aDK thrust collar outer diameter d iAR thrust ring inner diameter d iDK thrust collar inner diameter h min minimum lubrication gap height i gear ratio l t tread length l s non-profiled tread length n A number of evaluation points o overlap r crowning radius x start , y start start coordinates for profiling δ taper angle 1 Introduction Thrust collar bearings are primarily used in turbo drivetrains to increase efficiency. Thrust collars are two disks that are positioned next to the gearing, see Figure 2. In turbo drivetrains, helical gearings are usually used to reduce noise emissions and increase the transmittable torque. The helix angle leads to a parasitic axial force, which results in a tilting moment causing an additional load on the gearbox bearings. The power flow of this axial force is shown in red on the left in Figure 1. If an Science and Research 23 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 Reduction in power loss and increased safety of thrust collar bearings through profiling of the treads - Application of rolling bearing profiles and crowning on thrust collar bearings Merle Hanse, Christian Heinrich, Armin Lohrengel* submitted: 10.05.2024 accepted: 19.07.2024 (peer-review) Presented at the GfT Conference 2023 Thrust collar bearings can be used to increase the efficiency of megawatt-scaled turbo drivetrains by transferring the compressor thrust from the highspeed shaft to the low-speed shaft, where it can be efficiently supported in the low-speed bearings. This also allows the bearing on the high-speed shaft to be replaced by bearing types with lower power loss. In the following, measures to reduce the thrust collar power loss are investigated. In particular, the effect of different tread profiling is addressed. It is shown that the usual profiling of tribologically similar rolling bearings is no better suited to thrust collars than fully crowned profiles 1 . Keywords thrust collar, thrust cone, thrust bearing, turbo gearbox, compressor, variation of profile, increase in efficiency 1 This publication was published in a similar form in the conference proceedings of the “Gesellschaft für Tribologie” (GfT) in September 2023. The second publication was approved by the GfT. Abstract * Merle Hanse, M.Sc. Christian Heinrich, M.Sc. Prof. Dr.-Ing. Armin Lohrengel Institut für Maschinenwesen der TU Clausthal Robert-Koch-Straße 32 38678 Clausthal-Zellerfeld on the gearing, the rolling bearings and the impeller bearings. A key component of this concept is the use of thrust collar bearings. The package of measures is intended to halve the power loss of the entire drive train. The impeller bearing used in series production is composed of squeeze oil-damped rolling bearings. The intention is to replace it with a damping element that can be switched off and contributes to safe resonance passage. In this way, the power loss of this element can be eliminated during operation at nominal speed (above the natural frequency, damping element is switched off). The power loss of the gearing can be reduced by increasing the number of teeth and reducing the module. The resulting reduction in tooth root load capacity should be compensated for by increasing the helix angle. However, this increases the parasitic axial force, which must be supported in the bearings. This increases the power loss of the gearbox. Therefore, thrust collars are used to relieve the rolling bearings by compensating the axial force directly and transferring the compressor thrust from the fast-rotating shaft to the slow-rotating shaft, as described above. Science and Research 24 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 additional thrust collar bearing is implemented (thrust collars and thrust rings are colored grey on the right in Figure 1), the axial force is directly compensated (green power flow). The bearings are not loaded by the parasitic axial force and a tilting moment is avoided. In turbo compressors, an external axial force is added by the compressor thrust. Without thrust collar bearings, the compressor thrust is supported in the fixed bearing of the fast-rotating shaft, as shown in blue in Figure 1. With thrust collar bearings, the compressor thrust can be transferred from the fast-rotating shaft to the slow-rotating shaft, where it can be supported more efficiently in the slower rotating bearings (blue power flow on the right in Figure 1). This results in a reduction of power loss. In addition, more efficient bearing types can be selected on the output side, which do not have to support axial force, [1]. [2] [3] [4] [5] This paper was developed as part of the TurboGetEff research project. The aim of this project is to reduce the losses of turbo drivetrains without increasing the noise level or reducing the rotordynamic safety. For this purpose, a holistic concept is being developed that focuses Figure 1: Comparison of the power flow without (left) and with (right) thrust collar bearings, [2] Figure 2: Thrust collar bearing consisting of a pair of thrust surfaces (one tread on the thrust ring, the other on the thrust collar) [2] In addition, the platen rigidity of the thrust collar is to be optimized and a new type of profiling is to be developed for the thrust collar treads to increase operational reliability. This can be used in the next step to reduce the lubrication gap height to the desired level by efficiencyenhancing measures (e.g. reducing the overlap). The result is a thrust collar that causes less power loss while maintaining the same level of safety. 2 Basics of thrust collar storage and motivation for thrust collar profiling The thrust collar shown in Figure 2 is a disk that is positioned next to the pinion. Close to the pitch circle, the thrust collar tread overlaps with the thrust ring tread. This contact area is used for power transmission. Both surfaces are tapered, creating a convergent gap that enables a hydrodynamic lubrication gap to be formed with a lubricating oil. Since the contact is close to the pitch circle, the differential speed between the thrust collar and thrust ring, and therefore the power loss, is low, [2]. On the left in Figure 3, the thrust collar bearing is shown with its geometric sizes. On the right-hand side, the thrust collar tread, which is profiled in the following, is shown thicker. For dimensioning thrust collars, the minimum lubrication gap height is used, [2]. Two variables are particularly important for increasing the minimum lubrication gap height. Firstly, the lubrication gap height can be increased by selecting a favorable taper angle and secondly, the lubrication gap height can be increased by increasing the overlap, see Figure 4, [2] [7]. In order to achieve a low power loss, the overlap between thrust collar and thrust ring should be as small as possible and the tread should be close to the pitch circle of the gearing, as the differential speeds and thus the slip are low in this area. In comparison, the taper angle has less influence on power loss and lubrication gap height [7]. If thrust collars are not profiled, edge thinning can occur, as shown in Figure 5. This phenomenon is also known from rolling bearings, see [8] [9] [10]. The tread bulges in the middle and a narrowing of the lubrication gap occurs in the edge areas. Profiles that increase the lubrication gap at the edge areas by reducing the edges can have a positive effect. Science and Research 25 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 Figure 5: Problem of edge thinning without angle error Figure 3: (a) Geometric dimensions: Thrust collar outer diameter d aDK and inner diameter d iDK ; thrust ring outer diameter d aAR and inner diameter d iAR ; taper angle δ; overlap o; (b) profiled tread, [6] Figure 4: Influence of overlap and taper angle on minimum lubrication gap height and power loss, [7] height can be reduced to the permissible minimum by reducing the overlap, thus enabling a more efficient thrust collar bearing arrangement. The profiles investigated in the following are shown in Figure 7. Lundberg proposes a fully profiled tread with a logarithmic profile, see Equation 1 (notation according to [13]). He assumes elastostatic behavior and derives a profiling that by calculation leads to a uniform pressure distribution over the tread, see [12]. with Eq. 1 With the initial gap height c(λ) at the position λ, the running variable i, the maximum edge relief c m and the number of evaluation points n A , at which the geometry is defined. The maximum edge relief c m is added in comparison to the original profile according to Lundberg in order to be able to change the characteristics of the profile. Using the undeformed gap height c(λ), the profile shape can be calculated with the taper angle δ, the start coordinates x start and y start , see Equation 2. ( ) = 0,2 log , = 2 1 ; = + 1 Science and Research 26 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 In addition, errors in the manufacturing / assembly of the thrust collar can lead to taper angle errors in the order of 0,1°. Different platen rigidities of the thrust collar and thrust ring can also lead to an angular error due to deformation of the thrust collar under load, as shown on the right in Figure 6, [11]. If such a misalignment has a negative effect on the minimum lubrication gap height, this is referred to as edge wear. Here too, profiling of the tread can be advantageous. 3 Method 3.1 Profiling options Thrust collars can be fully rounded (crowned) with a radius r, [3]. A larger lubrication gap is thus initially (undeformed) present at the edges of the treads, which can reduce edge thinning and edge loading. It is known from rolling bearings that various profiles are used to avoid pressure peaks in the edge areas and thus increase the lifetime [8] [12] [13] [14]. The profiles known from rolling bearings shall be transferred to the thrust collar geometry and be optimized with regard to the largest possible minimum lubrication gap height (and thus the highest possible operational reliability). In a next step, this gap Figure 6: Problem of edge wear with an angular error of ; right: exaggerated thrust collar deformation Figure 7: Initial lubrication gap height of various profiling options; without load Eq. 2 The profile proposed by Lundberg achieves good results for cylindrical rolling bearings, therefore a similar profile is proposed in ISO/ TS 16281: 2008 or DIN 26281, [14] [8]. It can be created with the roller diameter d and the tread length l t according to Equation 3, [14]. For the application of the profile to the thrust collar, d is used as an “equivalent diameter” to optimize the profile. with Eq. 3 In addition, the profile proposed by Harris and Kotzalas [13] which produces a partially profiled tread, is investigated, see Equation 4. with Eq. 4 The variable l s corresponds to the non-profiled tread. The maximum edge relief c m and the ratio l s / l t can be optimized. There are manufacturing restrictions regarding the choice of profile. Grinded crownings are also used for gears. In Annex D of DIN 3990-1, an edge relief of between 10 µm and 40 µm plus a manufacturing tolerance of 5 to 10 µm is recommended, [15]. The flank line form deviation in DIN 3962-2 for medium gear qualities is between 4.5 µm (IT5) and 9 µm (IT8), [16]. As it must be assum- = + ( 1) , = + ( 1) , ( ) sin( ) ( ) = 0,00035 log = 2 1 ; = + 1 ( ) = = ; = + 1 ed that there is little experience in grinding thrust collars, an edge relief of 20 µm should be selected. 3.2 Simulation model To investigate the influence of tread profiling, the existing elastohydrodynamics simulation program of the Institute of Mechanical Engineering (IMW) at Clausthal University of Technology is extended to include the profiling described above. For this purpose, these are created as a 2D profile in the radial direction, tilted by the taper angle, and rotated around the rotation axis of the thrust collar. Taper angle errors, such as those caused by deformation under load or deviations during production or mounting, are considered by a profile with a modified taper angle. The tribo-solver used was originally developed as part of the DFG project Lo 1557 4-1&2 (see [1]). The Reynolds equation is solved to simulate the contact conditions. The half-space theory according to BOUSSINESQ [11] is used to consider the tread deformation. The coupling of pressure, temperature and viscosity is considered. After the end of the DFG projects, the tribosolver was extended. Besides the possibility of considering plate stiffnesses by FEM coupling (see [11]), a multigrid method stable for high pressures was implemented on the basis of [17]. This enables the simulation of highly loaded thrust collar bearings. The program provides, for example, pressure distributions and lubrication gap height distributions as shown in Figure 8. The current status of the tribosolver is described in [7]. 4 Investigation of the different tread profiles The boundary conditions used in the simulation are listed in Table 1. A typical compressor thrust for turbo compressors is selected, from which the axial force due to the helical gearing is subtracted (the helical gearing is Science and Research 27 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 Figure 8: Exemplary pressure and gap height distribution in the contact area The optimum shifts to a more pronounced profiling, as edge thinning occurs in addition to edge loading with less profiled thrust collars. The profile according to DIN 26281 has an optimum of h min = 5 µm at 6 mm replacement diameter in the case without misalignment. Below the maximum, as with the Lundberg profile, there is greater edge thinning and above it a smaller, more heavily loaded area. In this case, too, the optimum shifts towards larger replacement radii with misalignment; the optimum of h min = 3.47 µm is at d = 18.75 mm. With fully crowning, the optimum without angular error lies outside the considered range. A radius of 1 m corresponds to an edge relief of 19.5 µm, larger radii are not machinable (see above). With angular error, a maximum lubrication gap height of h min = 4.5 µm can be achieved with a crowning radius of r = 1 m. With larger radii, the thrust collar becomes more similar to the non-profiled one, resulting in edge loading. For the Harris-Kotzalas profile (partially profiled tread) without angular error, a small edge relief of 10 µm seems reasonable, but this is not machinable. With c m = 20 µm the minimum lubrication gap height is 4.5 µm. With angular error, an edge relief of 20 µm is optimal, h min is then 4.5 µm. In addition, the special case l s / l t = 0 (a profiling without a straight area in the middle) leads to the highest possible lubrication gap height and a particularly even distance between the friction partners, see purple line in Figure 11. With a nonprofiled area, this area bulges, resulting in strong edge thinning, see Figure 12. Figure 10 compares the achievable minimum lubrication gap height for the different tread profiles. A visualization of the lubrication gap profile in the latitudinal direction under load and with angular error is shown in Figure 11. The curves of the respective optimum profiling variant are shown. It can be seen that profiling the tread has a positive effect on the minimum lubrication gap height. In particular, the fully crowned and partially profiled thrust collar according to Harris and Kotzalas have an almost uniform lubrication gap. The largest minimum lubrication gap heights with angular error can be achieved with the fully crowned thrust collar. In order to reduce the remaining bulge in the geometry and achieve a more uniform gap, new tread profiles could be developed. Further research is needed here. Science and Research 28 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 aligned in such a way that the axial force of the gearing counteracts the compressor thrust). The geometric boundary conditions are known from a preliminary design of the thrust collar and the gearing. The thrust collar bearing in a compressor is designed for nominal load, as the start-up procedures occur comparatively rarely. [18] shows that the optimum profiling for rolling bearings is load-dependent. This should be taken into account for applications with widely varying loads. For a straight thrust collar without angular error with δ = 1°, the minimum lubrication gap height is 3.52 µm. With an angular error of 0.1, solid contact is present due to edge loading, see Figure 6. Figure 9 shows the results of a parameter variation of all profiles. In each case, the minimum lubrication gap height h min is plotted against the corresponding profile parameter (r, d, c m ). Figure 10 shows that all profiling options improve the minimum lubrication gap height compared to the straight thrust collar. In the case of an angle error, profiling can reduce edge loading and prevent the solid contact that occurs without a profile. In addition, it can be determined that the minimum lubrication gap height with angular misalignment is lower for all profiles than without angular misalignment, see Figure 9. The reason for this is the reduced utilization of the contact surface due to the misalignment, see Figure 11. In order to design thrust collar bearings safely, a calculation must always be performed under the maximum possible misalignment. In contrast to other machine elements, consideration of a safety factor is not sufficient, as an angular error can result in high lubrication gap reductions. For example, the lubrication gap height with angular error in the Lundberg-Sjövall profile is only 30 % of the lubrication gap height without error if the optimum of c m = 20 µm is selected. For the Lundberg-Sjövall profile without angular error, it is advantageous to select an edge relief between 20 and 30 µm, resulting in an h min of 4.7 µm for the selected boundary conditions. Smaller edge reliefs cannot be machined (see above) and lead to an increasingly straighter thrust collar, resulting in edge thinning. With larger edge reliefs, the load-bearing area becomes smaller, as edge areas with a large initial lubrication gap height do not contribute to the load-bearing pressure. For simulation with angular error, the optimum lies in the range between 70 and 90 µm of edge relief, h min is reduced to 2.9 µm. Axial force 23.5 kN Output speed 15000 1/ min Gear ratio 5 overlap 12.5 mm center distance 295 mm Thrust collar inner diameter 107.7 mm Oil ISO VG 32 @ 70°C Table 1: Boundary conditions of the Thrust collar simulation Science and Research 29 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 Figure 9: Parameter variation of the profiles with and without angle error Without taper angle error Lundberg-Sjövall-Profile Profile acc. to DIN 26281 Fully crowned Harris-Kotzalas-Profile 0,1° taper angle error height. Running surface profiles with a profiled central area that does not bulge under load are advantageous. If the overlap of the profiled thrust collar is now reduced until the same minimum lubrication gap height is achieved as with the straight thrust collar, the potential for saving power loss through profiling becomes evident. For example, to achieve a minimum lubrication gap height of 1.9 µm with a non-profiled thrust collar without angular misalignment, an overlap of 9.7 mm is required. With a crowned thrust collar, 6 mm overlap and an optimum crowning radius of 0.5 m are required, see Figure 13 (a). This reduces the power loss from 245 W (straight thrust collar) by 47 % to 129 W (crowned thrust collar). With an angular error, an overlap of 7 mm and a crowning radius of 0.375 m would have to be selected to ensure safe operation, see Figure 13 (b). If the thrust collar, designed with angular error, is operated without angular error, the resulting minimum lubrication gap height would be 2.3 μm, resulting in a power loss of 150 W. Furthermore, there is a noticeable shift in the optimum crowning radius depending on the overlap. The reason Science and Research 30 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 The common rolling bearing profiles are therefore no better suited to thrust collar treads than full crowning. One reason for this is the lower angular error in rolling bearing arrangements in the range of 0,005° to 0,05° ([19] and [10]) and thus the lower potential for edge loading. With high angular errors, which can occur at the thrust collar, mainly the profile at the edge of the contact area is relevant; profiling in the center has less effect on the pressure or lubrication gap profile. In addition, the maximum pressure of rolling bearings exceeds that of thrust collars by an order of magnitude and is therefore the relevant variable for the operationally stable design. Rolling bearings are therefore profiled in such a way that the pressure curve over the rolling element is as uniform as possible. When applying a typical rolling bearing profile to the thrust collar tread, a very constant pressure profile over the overlap width can be obtained, see Figure 12 (top). However, the associated lubrication gap height profile shows a clear edge thinning (Figure 12, bottom). [19] describes the lubrication gap height distribution in rolling bearing arrangements as a “dog bone” profile. Such a narrowing of the lubrication gap is disadvantageous for thrust collar bearings, as they are dimensioned against the minimum lubrication gap Figure 11: Gap height in latitudinal direction under load; taper angle 1°; taper angle error 0.1° Figure 10: Minimum gap height of the optimized profiles in (a) without and in (b) with taper angle error, normalized in (a) to the DIN profile and in (b) to the fully crowned profile for this is the reduced force-transmitting surface available for forming the parallel gap. This results in edge loading if the crowning radius is too large. 5 Conclusion Non-profiled thrust collars tend to edge thinning and, if there is an additional taper angle error (caused by errors in manufacturing / assembly or different plate rigidities of the thrust collar and thrust ring), edge wear can occur. In these cases, the lubrication gap in the edge area of the contact is significantly reduced, which can lead to failure of the thrust collar bearing. It has been shown that profiling thrust collars with and without taper angle errors is an effective measure against edge wear and edge thinning. All investigated profiles (Lundberg-Sjövall profile, profile according to DIN 26281, Harris-Kotzalas profile and fully crowned thrust collars) can significantly increase the minimum lubrication gap height compared to the non-profiled thrust collar and therefore increase the operational reliability of thrust collars. Typical rolling bearing profiles are no more suitable than complete crowning for thrust collars. When designing rolling bearings, the aim is to achieve the most uniform pressure profile possible; this can be achieved with the proven rolling bearing profiles. The target design for thrust collars is to achieve the largest possible lubrication gap height through a lubrication gap as uniform as possible. This is obtained by complete crowning. Furthermore, it was shown that when selecting the tread profile, the design should consider the possible angular Science and Research 31 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 Figure 13: Minimum gap height as a function of the crowning radius and the overlap in (a) without taper angle error and in (b) with 0,1° taper angle error Figure 12: Pressure distribution with use of a typical rolling bearing profile (based on [10], l s / l t = 0.6; c m = 20 µm; δ = 1°) and lubrication gap height profile with significant edge thinning [6] C. Heinrich, „Auslegung und Konstruktion einer Druckkammlagerung für ein Schienenfahrzeuggetriebe,“ Master thesis, Technische Universität Clausthal - Not publicly accessible, 2018. [7] C. Heinrich und A. Lohrengel, „Simulation von hoch belasteten Druckkammlagerungen,“ Mitteilungen des Instituts für Maschinenwesen, 2023. [8] L. Tudose und C. Tudose, „Roller profiling to increase rolling bearing performances,“ IOP Conference Series: Materials Science and Engineering, 2018. [9] X. Chen, X. Shen, W. Xu und J. Ma, „Elastohydrodynamic lubrication studies on effects of crowning value in roller bearings,“ Jornal of Shanghai University (English Edition), Bd. 5, pp. 76-81, 2001. [10] H. Fujiwara und T. Kawase, „Logarithmic Profiles of Rollers in Roller Bearings and Optimization of the Profiles,“ NTN Technical Review, Bd. 75, pp. 140-148, 2007. [11] C. Heinrich, „Druckkammsimulation unter Berücksichtigung der Platten- und Wellensteifigkeit,“ 17. Gemeinsames Kolloquium Konstruktionstechnik, pp. 126-137, 2019. [12] G. Lundberg, „Elastische Berührung zweier Halbräume,“ Forschung auf dem Gebiete des Ingenieurwesens, Bd. 10, pp. 201-211, 1939. [13] T. Harris und M. Kotzalas, Advanced Concepts of Bearing Technology in Rolling Bearing Analysis, Boca Raton: CRC Press, 2006. [14] DIN 26281: 2010-11, Wälzlager - Dynamische Tragzahlen und nominelle Lebensdauer - Berechnung der modifizierten nominellen Referenz-Lebensdauer für Wälzlager. [15] DIN 3990-1: 1987-12, Tragfähigkeitsberechnung von Stirnrädern Einführung und Einflußfaktoren. [16] DIN 3962-2: 1978-08, Toleranzen für Stirnradverzahnungen, Toleranzen für Flankenlinienabweichungen. [17] C. H. Venner und A. A. Lubrecht, Multilevel methods in lubrication, Amsterdam ; New York: Elsevier, 2000, p. 379. [18] F. B. Oswald, E. V. Zaretsky und J. V. Poplawski, „Effect of Roller Geometry on Roller Bearing Load-Life Relation,“ Tribology Transactions, pp. 928-938, 2014. [19] T. J. Park, „Effect of Roller Profile and Misalignment in EHL of Finite Line Contacts,“ ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Bd. 1, pp. 395-401, 2010. [20] M. Heß, „Einsatz von Druckkämmen zur Effizienzsteigerung von schrägverzahnten Getrieben,“ Dissertation, Technische Universität Clausthal, 2018. Science and Research 32 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0009 error. A design based solely on a safety factor is not sufficient, as an angular error can lead to large losses in lubrication gap height. The optimum profile shape is also different with and without an angular error, and because an angular error cannot always be avoided, the optimum profile shape should be selected with the maximum possible taper angle error. By selecting an optimum crowning radius, the minimum lubrication gap height and therefore the operational reliability can be increased compared to the non-profiled thrust collar. In the next design step, the operational reliability achieved is lowered to the minimum permissible lubrication gap height by reducing the overlap between the thrust collar and thrust ring. Due to the smaller contact area, the power loss can be reduced. In a comparison with and without profiling, a reduction potential of 47 % could be shown by profiling. Acknowledgments The work was funded by the Bundesministerium für Wirtschaft und Klimaschutz (BMWK) as part of the TurboGetEff project (FKZ: 03EN4037A-B). The authors thank the BMWK for the financial support. References [1] C. Heinrich und A. Lohrengel, „Druckkammlagerung: Eingrenzung der Verlustleistungsreduktion bei optimaler Wälzlagerwahl,“ Mitteilungen aus dem Institut für Maschinenwesen der Technschen Universität Clausthal, Bd. 46, pp. 91-100, 2021. [2] M. Heß, „Einsatz von Druckkämmen zur Effizienzsteigerung von schrägverzahnten Getrieben,“ Doctoral thesis, Technische Universität Clausthal, 2018. [3] F. Barragan de Ling, „Lubrication of Thrust Cones,“ Doctoral thesis, University of Wales, 1993. [4] T. Kerr, Experimental and Numerical Study of Oil Lubrication on a Thrust Collar for Use in an Integrally Geared Compressor, Dissertation: A&M University, 2020. [5] M. Heß und A. Lohrengel, „Thrust cone bearings provide increased efficiency for helical gear units at moderate speed levels,“ Forschung im Ingenieurwesen, Bd. 81, pp. 135-143, 2017. Introduction Improving the efficiency of vehicle powertrains remains a key focus for the automotive industry. There are several methods for achieving an optimized powertrain configuration that addresses both efficiency [1] and customer requirements [2,3]. The use of gearboxes enables the utilization of lighter electric motors with higher maximum speeds. However, both the high speeds and the lack of acoustic masking in internal combustion engines lead to an increase in the actual gear noise and its perception by the driver. In particular, the tooth mesh and its behaviour are a noise source that must be considered during the development process. Both the macroand micro-geometry of the teeth can be optimized to achieve improved acoustic characteristics [4]. Efforts are made to keep the transmission error as low as possible, as it is a significant factor in noise emission [5]. This is being attempted through profile modifications, which also impact mesh stiffness and load distribution and are currently under investigation [6]. These modifications (e.g. tip relief) can be used to improve the dynamic behaviour of gears and reduce occurring vibrations [7-9]. Furthermore, specific modifications of the teeth’s surface will also be discussed [10]. Established analytical models are used to describe the influence of profile shifts on the mesh stiffness of spur gears [11]. Additionally, the vibration and acoustic radiation of gearbox housings based on 3D-simulations will be studied in detail, as well as the influence of different gearbox macro-designs on efficiency and vibration at high speeds [12-14]. While methods for creating optimized gears regarding the acoustics and designing gears for improved efficiency are well established, there is a distinct lack of a comprehensive view of the interaction between efficiency and noise characteristics in the early stages of product development. Validation is the main activity of the product development to generate knowledge and to fulfil the characteristics of the product customers expect. Using a mixed physical-virtual validation environment allows for early studies of product behaviour [15]. The X-in-the-Loop framework (XiL) supports the validation activities and the development of validation environments, leading to a faster and more efficient product development [16]. A top-down validation approach is the basis of the paper and is described below. XiL is used to validate product properties over a wide range of development stages without the need for a complete system prototype. Validation is viewed as a multi-layer activity, where the X represents the system in question at the spe- Science and Research 33 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 Product Development Methodology Targeting Efficiency and Acoustics of E-Mobility Gearboxes Steffen Jäger, Tilmann Linde, Kai von Schulz* Submitted: 10.01.2024 accepted: 12.07.2024 (peer review) Presented at the GfT Conference 2023 This paper presents an approach for physical/ virtual coupled product development and validation. A method for studying the influence of tooth geometry on the efficiency and acoustics of an electric vehicle’s powertrain will be presented. To achieve improved acoustic characteristics the micro geometry of the teeth will be optimized. The modified gears were analysed on a gear test rig under load and at high speeds and evaluated with regard to their acoustic properties. Established analytical models are used to describe the influence of profile modifications on the gear stiffness of helical gears. The authors’ approach is to calculate the dynamic system behaviour of the gearbox using a 1D simulation. Based on this, studies of the entire gearbox will be performed. For this, the results of the 1D simulation are coupled with 3D FEA analyses. This enables acoustic calculations (structure-borne and airborne sound) to be carried out. Keywords tooth geometry, acoustics, electric vehicle, powertrain, 1D simulation, 3D FEA analyses Abstract * Prof. Dr.-Ing. Steffen Jäger M.Sc. Tilmann Linde M.Sc. Kai von Schulz Furtwangen University Institute of Product and Service Engineering Robert-Gerwig-Platz 1 78120 Furtwangen, Germany working on solutions to optimize powertrain units, the driver’s experience of vibration and noise remains at the focus and must be considered at all levels of validation. Therefore, the top-level vehicle tests are planned as set out in figure 1. Stripping the chassis, the wheels, the side shafts, and the battery from the real vehicle - and transferring these to the virtual remaining system - results in the second validation layer (layer 2, see figure 2). Within that layer, the motor-gearbox-unit is the physical unit under test, forming a powertrain test rig. Reducing this system by the traction motor leads to a gearbox test environment on the third validation layer. The fourth validation layer examines the tooth mesh as the physical unit under test, cf. figure 2. Planning the validation in a top-down order clearly defines all the validation layers as well as the system interfaces. The start of implementation activities on the fourth validation layer leads to a gear mesh study with the objective of generating results for gears optimized in terms of both sound emission and efficiency. Here, a model-based validation environment is established as shown in figure 3. It shows the content of both the virtual and physical domains as well as the interfaces between them. The objective is to achieve validated models of the gear mesh. Therefore, the detailed toothing data are calculated by an industry project partner using specialized software for gear calculations. These parameters are used as input for the virtual domain as well as manufacturing parameters in the physical domain. Science and Research 34 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 cific validation layer. Independently of the layer at which a system is validated, the user and its environment are an essential part of the XiL framework. This can be shown particularly clearly in the validation of vehicles, since, here, the driver closely interacts with the system as well as the environment, which includes factors such as routes chosen, weather conditions, etc.; cf. figure 1. One of the major challenges is to develop virtual models that need to be validated by physical testing. These virtual models will be used to evaluate both acoustic and efficiency characteristics in the early stages of the product development process. Validation Framework Planning the validation from the top-level, in this particular setting, leads here to a four-layer environment (with the complete vehicle on the first layer). When Figure 1: System layout, vehicle-in-the-loop Figure 2: XiL system layout Virtual Model Implementation To assess the dynamic system behaviour and efficiency of the gear pair, a 1D simulation software is used (SimulationX). Subsequently, the housing’s dynamic excitation forces are transferred to a Finite Element Analysis (FEA), where, firstly, the structural behaviour of the ideal gearbox housing geometry is considered. By combining the structural behaviour and the excitation forces calculated by the 1D simulation, the vibrational characteristics of the gearbox and the sound emissions, including both air-borne and structure-borne sound, can be estimated. This study will evaluate a set of helical gears in a simplified gearbox (cf. figure 9). A contact analysis is conducted by the gear calculation software (KISSsoft ® ) in order to determine the respective mesh stiffness of the gears under given load conditions. The stiffness calculation is based on the Weber/ Banaschek method and includes wheel body deformation, bending and Hertzian contact stiffness. This method of calculating mesh stiffness allows modifications to the gears to be taken into account. Additional transmitted data to the 1D simulation include contact ratio as well as friction coefficients. An excerpt of the gear pair data is shown in section Result Discussion. The entire powertrain system parameters, including the inertia of the engine and gearbox shafts as well as the stiffness of the couplings, are also represented. In the simulation model, the electric motors used on the test rig are considered as torque sources at the input and output of the gearbox. In accordance with the test Science and Research 35 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 Figure 3: Model implementation Figure 4: Layout of the gearbox system lation of the gear software as previously stated. Figure 5a presents details of the rotational system in the 1D simulation software. Two translational part models are utilized to represent each shaft, encompassing the equilibrium of both moment and force, along with the geometric characteristics that form the foundation of the test rig. These characteristics include the pitch diameter of the gears and the distances between the bearings and the tooth mesh. Figure 6 shows the simulation model used to calculate the forces acting on the bearing of a gear shaft, including the forces F a , F r and F t from gear element as shown in Figure 5a. The internal forces of the spring-damper elements will be utilized for the finite element analyses described below. The efficiency of the system is mostly affected by the efficiency of the teeth. The tooth contact losses are loaddependent and are calculated using friction coefficients. As the measurements obtained from the actual test rig contains not only gear losses themselves but also additional factors such as bearing losses, it is necessary to factor these in when comparing the results of the simulation models with the measured values. The bearing losses are implemented using rolling friction, sliding friction, as well as frictional torques due to seals and flow losses. Additionally, the eigenfrequencies and their shapes of the test rig components are analysed to achieve a comprehensive understanding of the system, according to the model implementation depicted in figure 3. This includes the motor mount, the test bed, the gearbox housing and the shafts with gears. To verify these virtual results, which have been accomplished through the utilization of simulations, subsequent experiments have been conducted on actual physical components; see next sec- Science and Research 36 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 rig, the control of the torque sources is regarded to be a speed-torque control. The simulation thus contains rotational and translational components, the latter being used to calculate the bearing reaction forces based on the forces generated by the tooth mesh. The bearings are implemented as springdamper elements and contain stiffness values determined by means of a bearing calculation software. The internal forces within the spring-damper models include the resulting forces in x-/ yand z-direction. In this model, particularly, the effect of the mesh stiffness on the overall system is examined. Periodic changes in the mesh stiffness result in irregularities of the output rotational speed and thus in a dynamic response of the system. With this approach, the excitations calculated through the tooth mesh are transmitted to the gearbox housing via the bearing points. An overview of the implemented system is shown in figure 4. The dynamic equations of the gear system can be expressed as: where M represents the matrix comprising the values of masses and inertias, D represents the damping matrix, and C denotes the stiffness matrix; q is the displacement vector and F the vector encompassing the forces. The tooth mesh is assumed to be a spring-damper, with the spring stiffness being equivalent to the mesh stiffness, which is determined as the specific tooth contact stiffness in relation to the normalized meshing length, see figure 5b. The figure shows two stiffness curves based on the same gear data, but differing in micro-modifications. The stiffness values are based on the calcu- [M]{q̈ } + [D]{q̇ } + [C]{q} = {F(t)} Figure 5: (a) Rotational system of the 1D simulation; (b) specific tooth stiffness for the mesh stiffness calculation for two slightly different gear pairs (a) (b) tion. The most important test rig components’ frequencies are plotted in figure 7 in a Campbell diagram, so that possible interferences can be seen. These include eigenfrequencies of the gearbox housing, certain modes of the shafts and the motor mounts. Speed-dependent frequencies include rollover frequencies of the bearings as well as the gear meshing frequency including higher orders. The knowledge about the frequencies at which possible interferences can occur, simplifies the determination of their causes during the physical validation of the test rig. Many of the eigenfrequencies will not directly affect measurement results or may also depend on the location of the measurement. It is therefore important to know the eigenfrequencies of the components for the subsequent experiments, which are discussed in the section Result Discussion. However, the amplitude at a specific frequency can only be calculated using a structure-borne sound simulation. In a subsequent 3D finite element calculation, the harmonic response of the gearbox housing is examined using the dynamic loads at the bearing points. Based on a modal analysis, a harmonic (frequency) response analysis with modal superposition is performed. This, together with the previous performed calculation of the eigenfrequencies and their shapes, determines the structural behaviour of the housing. These results can then be compared with structure-borne noise sensor data measured on the test rig. This is accomplished by determining the surface velocities at each sensor point. A sample result of the harmonic response analysis is shown in figure 8. The eigenfrequencies, which are fed by the bearings’ dynamic forces, are indicated by higher amplitudes in the velocity amplitude spectrum (right) for a specific gearbox housing surface. An example of the deformation of the gearbox housing at a specific eigenfrequency is shown in figure 8a. In order to come from the structural dynamic behaviour to an acoustic evaluation (in particular the air-borne sound emission), an acoustic simulation can be carried out in the next step. For this purpose, the surface speeds calculated in the harmonic response analysis are used to determine Science and Research 37 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 Figure 6: Translational systems for computing the bearing forces in zand y-direction (left), and x-direction (right) Figure 7: Campbell diagram of the test rig components the test rig components. The gearbox housing, the motor mounts and the entire test setup were examined. Exemplarily, table 1 shows the results for the modal analysis of the gearbox housing. Since the differences between the virtual and physical analyses are in a realistic range, the virtual gearbox model is considered valid. The test rig is designed to measure the effects caused by slightest changes in the gear’s flanks surface (in sub-micrometre range). To ensure that the clamping of the gears does not affect the measurement results, it needs to be very precise and reproducible. Therefore, the gears are clamped onto the shaft by means of a conical clamping sleeve developed for this particular application. To enable the remaining system simulation as shown in figure 2, the motors are controlled by a real-time capable controller. Therefore, both stationary operating points and complex manoeuvres can be approached. Appropriate software systems, data acquisition modules for data recording and processing as well as a field bus system are implemented. Data acquisition requires accurate sensors, so each shaft is equipped with a torque sensor and two speed sensors. One located at the end of the Science and Research 38 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 the sound pressure level. This will then be compared to microphone measurements. Phsical Validation To validate the virtual model implemented as shown in the previous section, the physical model is realized, cf. figure 9. Here, the aim is to obtain a valid virtual model of the tooth mesh layer as well as getting information about the quality of both the efficiency and acoustic simulation. The test rig used is a real-time capable two-motor system with a maximum drive speed of 20,000 rpm and a maximum load torque of 45 Nm at 5,000 rpm. To realize the physical domain according to figure 3, various virtual models are implemented. These are necessary to get both geometry and predictions about the dynamic behaviour of the components. By further developing the virtual domain and parallel realizing the physical test rig, the validation as shown in figure 3 can be achieved. To validate the eigenfrequencies’ simulation results (cf. figure 7), physical tests were performed for Figure 8: (a) FEA deformation result of the harmonic response analysis; (b) velocity amplitude spectrum Figure 9: Gear pair test rig (a) (b) Value 38, 61 1.5 20 32 shaft close to the gear and the other integrated within the motor. There are also two temperature sensors located in the bearing seats. The speed and torque sensors acquire data to calculate the efficiency of the tooth mesh and detect rotational irregularities. In addition, four structureborne sound sensors are attached to the gearbox housing. In order to obtain reliable measured values, the positions for the structure-borne sound sensors are determined based on the dynamic behaviour of the gearbox housing (see section Virtual Model Implementation). The efficiency is calculated by using data from both the torque and speed sensors mounted on the shaft ends. It is then calculated according to where Μ out is the torque and ω out is the angular speed of the output shaft. M in is the torque and ω in the angular speed of the input shaft. The total efficiency η tot results of multiplying the tooth mesh efficiency η tooth and the bearing efficiency η bearing . As the bearing losses cannot be measured isolated currently, both the tooth mesh efficiency and the efficiency of the bearings are included in η tot . Result Discussion Here, two helical gearsets are compared, both of which are provided by an industry partner. The first gearset is defined as the reference set. The second comes with a modified flank surface resulting due to an adjustment of manufacturing process parameters. The approach outlin- = · = Μ · · ed in the section Virtual Model Implementation was developed to simulate the possible effects of micro-modifications on the gears. However, in contrast to what is described in the section Virtual Model Implementation, no micro-modifications have been made to the pair presented in the following. Instead, only modifications have been made to the manufacturing process for this gear pair, which cannot be reflected in its macroscopic geometry. The different behaviour is therefore based solely on different surface properties of the tooth flanks. This leads to the hypothesis that the impact on the dynamics occurs mainly at low torques where the surface deformation due to the load is low. The two gear pairs’ parameters are shown in table 2. Further test parameters are a static torque of 22.5 Nm and speed ramps ranging from 0 to ± 5,000 rpm. For tests with the specified parameters, vibration signals were recorded from the sensors and plotted in Campbell diagrams, cf. figure 10. Both speed-dependent frequencies (diagonal beams) and speed-independent frequencies (horizontal beams) can be recognised for each diagram. The amplitude (coloured representation) is a measure of the structure-borne noise intensity, shown in power-spectral-density. The manufacturing adjustment in the modified gear pair (right) has a measurable effect, particularly in the higher orders of tooth mesh frequencies. The recorded Campbell diagram and the simulated one in, shown in figure 7, mostly correspond. The modified gear pair leads to a significantly lower excitation of the system’ structure compared to the reference gear pair. This is presumably attributed to a change in surface waviness due to the adjustment of the process parameters. Science and Research 39 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 Mode No. Calculated Eigenfrequency in Hz Measured Eigenfrequency in Hz Difference in % Mode Shape 1 549.7 520.0 5.4 Vibration in x-direction 2 924.3 824.3 10.8 Vibration in y-direction 3 948.7 946.1 0.3 Vibration in z-direction 4 1258.7 1192.8 5.2 Torsion y-axis 5 1308.3 1187.1 9.3 1st order membrane oscillation 6 1734.0 1795.5 3.5 Torsion z-axis 7 2437.0 2229.3 8.6 2nd order membrane oscillation 8 2803,3 2674.7 4.6 3rd order membrane oscillation Table 1: Results of modal analyses (physical/ virtual) for the gearbox housing Parameter Symbol No. of teeth (-) , Normal module (mm) m Face width (mm) b Helix angle (°) β Table 2: Gear pair data electric drive unit. Using an appropriate combination of software tools allows virtual dynamic and vibration analysis. For the physical validation of the simulations’ results, a test rig has been developed. The potential of the gear test rig is demonstrated using an example in which the influence of changes in gear manufacturing parameters is shown. Furthermore, the efficiency of the tooth mesh was determined using the recorded measured values. The reduced excitation of the modified gear pair and the resulting lower vibrations on the gearbox housing indicate improved acoustic performance. However, this must be further investigated and verified in future work. Moreover, the results outlined represent only a limited sample, as the measurements were taken at a constant torque and at a maximum speed of 5000 rpm. Changing the test parameters, the effects could be reflected in a different behaviour, resulting in a modified interaction between efficiency and acoustics. Science and Research 40 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 As previously stated the efficiency has also been determined and is within a plausible range, see figure 11. The changes made to the second gear pair have a noticeable effect on the efficiency. For all relevant speeds, the modified gear pair (red line) shows improved efficiency compared to the reference gear pair (blue line). This may be attributed to higher power dissipation of the reference gear pair, especially at higher frequencies, which in turn results in a greater energy input into the housing structures. Conclusion The purpose of this paper is the presentation of a validation approach which combines physical and virtual domains. System in question is a helical gear pair from an Figure 10: Campbell diagram of the reference gear pair (left) and the modified gear pair (right) Figure 11: Gearbox efficiency plot Acknowledgments The authors are very grateful for the financial support from BMBF (Federal Ministry of Education and Research) of Germany (Grant No. 13FH527KA9). References [1] Kwon, K.; Jo, J.; Min, S. Multi-objective gear ratio and shifting pattern optimization of multi-speed transmissions for electric vehicles considering variable transmission efficiency. Energy 2021, 236, 121-419, doi: 10.1016/ j.energy.2021.121419. [2] Eghtessad, M.; Meier, T.; Rinderknecht, S.; Küçükay, F. Antriebsstrangoptimierung von Elektrofahrzeugen. ATZ Automobiltech Z 2015, 117, 78-85, doi: 10.1007/ s35148- 015-0089-3. [3] Esser, A.; Eichenlaub, T.; Schleiffer, J.-E.; Jardin, P.; Rinderknecht, S. Comparative evaluation of powertrain concepts through an eco-impact optimization framework with real driving data. Optim Eng 2021, 22, 1001-1029, doi: 10.1007/ s11081-020-09539-2. [4] Garambois, P.; Perret-Liaudet, J.; Rigaud, E. NVH robust optimization of gear macro and microgeometries using an efficient tooth contact model. Mechanism and Machine Theory 2017, 117, 78-95, doi: 10.1016/ j.mechmachtheory.2017.07.008. [5] Davoli, P.; Gorla, C.; Rosa, F.; Rossi, F.; Boni, G. Transmission Error and Noise Emission of Spur Gears. Proceedings of the ASME 2007 10th ASME International Power Transmission and Gearing Conference 2007. [6] Sánchez, M.B.; Pleguezuelos, M.; Pedrero, J.I. Influence of profile modifications on meshing stiffness, load sharing, and trasnsmission error of involute spur gears. Mechanism and Machine Theory 2019, 139, 506-525, doi: 10.1016/ j.mechmachtheory.2019.05.014. [7] Ma, H.; Pang, X.; Feng, R.; Wen, B. Evaluation of optimum profile modification curves of profile shifted spur gears based on vibration responses. Mechanical Systems and Signal Processing 2016, 70-71, 1131-1149, doi: 10.1016/ j.ymssp.2015.09.019. [8] Ghosh, S.S.; Chakraborty, G. On optimal tooth profile modification for reduction of vibration and noise in spur gear pairs. Mechanism and Machine Theory 2016, 105, 145-163, doi: 10.1016/ j.mechmachtheory.2016.06.008. [9] Bahk, C.-J.; Parker, R.G. Analytical investigation of tooth profile modification effects on planetary gear dynamics. Mechanism and Machine Theory 2013, 70, 298-319, doi: 10.1016/ j.mechmachtheory.2013.07.018. [10] Geradts, P.; Brecher, C.; Löpenhaus, C.; Kasten, M. Reduction of the tonality of gear noise by application of topography scattering. Applied Acoustics 2019, 148, 344- 359, doi: 10.1016/ j.apacoust.2018.12.039. [11] Wang, J.; Yang, J.; Lin, Y.; He, Y. Analytical investigation of profile shifts on the mesh stiffness and dynamic characteristics of spur gears. Mechanism and Machine Theory 2022, 167, 104-529, doi: 10.1016/ j.mechmachtheory.2021.104529. [12] Zhang, T.; Shi, D.; Zhuang, Z. Research on vibration and acoustic radiation of planetary gearbox housing. In Proceedings of inter.noise 2014. inter.noise 2014, Melbourne, Australia, 16. - 19. November, 2014. [13] Schweigert, D.; Gwinner, P.; Otto, M.; Stahl, K. Noise and Efficiency Characteristics of High-Rev Transmissions in Electric Vehicles. Proceedings of the E-Motive - Electric vehicles Drives; Stuttgart, 2018. [14] Jäger, S.; Linde, T. Topology optimization of gearbox components to reduce weight and improve the noise emission and efficiency of an eDrive with multi-speed gearbox. In Proceedings of 14th International Expert Forum: Conference on electric vehicle drives and e-mobility. Conference on electric vehicle drives and e-mobility, Wolfsburg, 21.-22.09.2022; FVA - Forschungsvereinigung Antriebstechnik e.V., Ed., 2022; pp 57-65. [15] Jäger, S.; Vogel, S. Validation of a squeeze-film-damper test rig by using multibody cosimulation. Multibody System Dynamics 2015, 34, 243-257, doi: 10.1007/ s11044- 014-9442-7. [16] Jäger, S.; Schätzle, J.; Linde, T. Top-Down Validation Framework for Efficient and Low Noise Electric-Driven Vehicles with Multi-Speed Gearbox. WEVJ 2022, 13, 228, doi: 10.3390/ wevj13120228. Science and Research 41 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0010 News 42 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 This year we are celebrating the 65 th annual conference of the German Society for Tribology GfT. Reason enough to look back, to reassure ourselves of our current status and to look ahead to future developments: because for a society like ours, 65 years is not the time to think about retirement or even just ‘shifting down a gear’, but on the contrary: the best is yet to come, tribology has never been as valuable as it is today. So we are celebrating an anniversary: well, we want to do justice to this with this year’s programme and offer some special ‘treats’, for example a plenary lecture on ‘The history of tribology in Germany and future prospects’. So let’s try to define the position of tribology in the 65 th year of the GfT: Won’t tribological research come to an ‘end’ at some point? Don’t we have to constantly ask ourselves the self-critical question of the effort involved in any further progress? Hermann Heinrich Gossen (1810 - 1858) was a German lawyer and economist who, as part of his work on consumption theory, developed two rules that became known as Gossen’s Laws. In a publication from 1854, he formulated the first ‘law of diminishing marginal utility’ as follows: ‘The size of one and the same pleasure, if we continue to prepare the pleasure without interruption, decreases continuously until satiation finally occurs.’ What does Gossen mean by ‘pleasure’? Applied to tribology, we can replace ‘pleasure’ with ‘friction reduction’, for example: ‘If we continue to reduce friction without interruption, the amount of friction reduction decreases continuously until saturation finally occurs.’ In this context, saturation means that the effort becomes greater than the benefit. Yes, of course we will always have to base our findings on the costs! Changes in the ‘general weather situation’ must also be soberly recognised: In recent years, efforts to reduce CO 2 emissions in motor vehicles have been a key driver of tribology research - the threat of CO 2 fines in conjunction with mandatory testing programmes (NEDC, WLTP, etc.) have been at the forefront. Due to electrification and changes in the political framework conditions, mobile drives are no longer at the centre of tribological interest. This makes it all the more important and promising to transfer the findings and improvements developed for mobile systems to other industrial systems: Another increasing driver of tribology is the reduction of wear in technical systems - the service life of devices, machines and systems is becoming significantly more important. In this context, we would like to draw your at- Gesellschaft für Tribologie Foreword: 65 th annual conference of the German Society for Tribology tention to the recently published GfT position paper on white etching cracks (WEC): In a joint effort of 25 representatives from research and industry, a comprehensive overview of damage patterns, development hypotheses, influencing factors, risk assessment and recommendations for action of the rolling bearing damage pattern WEC was compiled in a total of 42 meetings in the period from 2021 to the end of 2023. There is also a lot of positive news to report from other GfT working groups. The Training and Further Education Working Group has launched a new series of seminars under the overall management of Prof. Bartel and in cooperation with the Research Association for Drive Technology (FVA): The first seminar on plain bearing lubrication was successfully held in May 2024. Further events on the basics of tribology, gearbox lubrication and rolling bearing lubrication are in preparation. The Regional Working Groups in Munich, Rhine-Neckar and Berlin-Brandenburg have continued or resumed their regular lecture events with renewed vigour. One new feature is that the events are being offered in a hybrid format and therefore also offer supra-regional participation. If you say three, you have to say four: Following our 3 rd GfT study ‘Effects of tribology on CO 2 emissions in the use phase of products - contributions of tribology to defossilisation’, the Climate Protection & Sustainability Working Group has started work on a fourth study, which will include concrete examples of tribological contributions to friction reduction and defossilisation, in short: to avoided emissions. The Public Relations Working Group has launched further important initiatives to better present the GfT, its tasks and its benefits in the modern media world. The GfT’s presence in the social media is being expanded in order to reach young tribologists in particular on today’s relevant information channels. At this point, we would also like to mention that we have started regular dialogue contacts with the Austrian Tribological Society (OeTG) and SwissTribology. The Young Tribologists Working Group will be holding the 7 th Young Tribological Researcher Symposium on 22 and 23 July 2024 at the Friedrich-Alexander University Erlangen-Nuremberg. This year in particular, the GfT Annual Conference aims to offer you plenty of inspiration for new tribological approaches and solutions. In addition to already established News 43 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 In November, 65 years ago, the Gesellschaft für Schmiertechnik (GST), the predecessor organization of the GfT, was founded. Since annual conferences on the topics of friction, lubrication and wear have been held regularly from the very beginning, the German Tribology Conference can also celebrate its 65 th anniversary this autumn. On this occasion, the plenary event will begin with a look back not only at the history of GfT, but will also highlight the milestones of tribological re- Gesellschaft für Tribologie 65 th German Tribology Conference 2024 Some highlights of the 65 th Tribology Conference: Plenary Session: Monday, 23.09.2024: • 65 Years of GfT - History of Tribology in Germany and Future Prospects of the Field • C. Gachot, Vienna University of Technology: Perfect Friction in 2D - Solid Lubrication with MXenes and Transition Metal Carbo Chalcogenides • M. Marian, Leibniz Universität Hannover/ Pontificia Universidad Católica de Chile: AI think, therefore AI am a Tribologist • M. Dienwiebel, Karlsruhe Institute of Technology KIT / Fraunhofer IWM: Verständnis tribologischer Mechanismen durch Kombination multiskaliger Experimente und Simulation (Understanding tribological mechanisms by combining multiscale experiments and simulation) search in Germany over several centuries. In interviews and other contributions, however, the present and the outlook on future challenges are not neglected. As every year, the current state of the art of tribological research and development, mainly in Germanspeaking countries, is reflected by the program of the conference, which includes more than 70 lectures from almost all areas of tribology. special sessions, e.g. on the Research Field of Tribology, it includes many exciting contributions, poster and technical exhibitions and, of course, stimulating discussions ‘in between’ in the circle of the GfT family! Finally - after the GfT conference is before the Nextlub: The international tribology conference Nextlub will take place for the second time - as a joint format of Uniti, FVA and GfT - from 22 to 23 January 2025 in Leipzig. We can already reveal that there will once again be an extremely interesting and varied programme! But first: See you again in Göttingen! Rolf Luther Chairman of the Executive Board of GfT Dr. Thomas Gradt, Managing Director of GfT News 44 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 Wednesday, 25.09.2024: • Matthias Scherge, Fraunhofer KIT: Bowling, the Tribological Eldorado Closing ceremony: • Andreas Krüger, Fuchs Lubricants Germany: The Tribological Possibilities in the Interior of an Automobile Special Sessions: In 2024, the progress in the DFG priority program “Fluid-Free Lubrication Systems with High Mechanical Loads” will again be presented in a full-day session. The research field “Tribology” is also represented with its own session. The research field is funded as a part of the energy research programme of the Federal Ministry for Economic Affairs and Climate Action and thus contributes to the energy transition in Germany. The following awards and prizes will be presented during the conference: • Georg-Vogelpohl-Ehrenzeichen for personalities who have rendered outstanding services to tribology • Sponsorship awards for the best submitted bachelor’s, master’s and doctoral theses • The prize “Tribologie ist überall” (Tribolgy is everywhere) for submissions tribological everyday phenomena (donated by Werner Stehr) After the success of the last years, we can also look forward to a “Triboslam” again. The conference will again include a poster and a trade exhibition in the foyer of the conference hotel. There are still free places available for the latter. You can find out the prices and conditions at the GfT office. Further information you will find in the program: https: / / www.gft-ev.de/ wp-content/ uploads/ Programmheft_2024.pdf Gesellschaft für Tribologie News 45 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 On June 18, 2024, this year’s joint meeting of the GfT Arbeitskreis München and the DGMK Bezirksgruppe Bayern took place at OMV Deutschland Operations GmbH & Co. KG in Burghausen. Twenty participants from research and industry gathered to use the event as a forum for discussing research and application topics in tribology. Engaging interdisciplinary presentations on ‘Sustainable Fuels and Lubricants in the Context of the Energy Transition’ encouraged lively exchanges and discussions among the attendees. We are delighted with the success of the event and extend our gratitude to all participants for their enthusiastic interest and active engagement in the discussions. Details about the next meeting of the GfT Arbeitskreis München will be announced in due course. Gesellschaft für Tribologie 7 th GfT-Kolloquium Arbeitskreis München News 46 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 The presentation “Efficient and sustainable machine operation with the help of lubricant analyses” clearly showed the importance of oil analysis for sustainable machine and plant operation. The first part of the presentation focused on typical characteristic values for various oils and applications, as routinely carried out and evaluated by Oelcheck. Mr. Mitterer then used illustrative practical examples to show that regular oil analysis is not only important from an environmental point of view, but that there are also financial benefits for operators of vehicle fleets, wind turbines or paper machines if, for example, oil change intervals can be extended without risk. After an extensive discussion and question and answer session, the participants continued to talk shop in a relaxed atmosphere over drinks and pretzels. Gesellschaft für Tribologie 40 th GfT Tribology Colloquium of the Rhine-Neckar working group Many thanks to Mr. Stefan Mitterer from Oelcheck for his excellent presentation at our 40th GfT Tribology Colloquium of the Rhine-Neckar working group! News 47 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 Österreichische Tribologische Gesellschaft ! ""'(./ #) ) .0"#%&.1)#%&*+,+-2)"+'&$#2 ! ! ! ! ! ! "#$%&'()%*+'$,-,.$ ! "#$%&%'()#*)+*,-./ "()0*,)12.20"34)) ! "#$%&%'()*+),-()./ *$&-"! ! "#$%&'()*+,*-./ 0120$*+3+4* ! "#$%&'&()"*+,%-+.&/ 0#$,%(01"%2/ ,3+42516+7)"%"/ +8",029-2+ : ); 2&/ *<9='9%*>2/ 9? "+@A+@BCC+7)"%"/ +8",029-2A+D,02/ )9+ ! ! ! "#$%&'$%#(! '()! $*+"'$%,! -#,./ ! ! 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You can obtain the full open access service for a one-off article processing charge of € 1,850.00 (plus VAT). Editor in chief Dr. Manfred Jungk eMail: manfred.jungk@mj-tribology.com Publisher expert verlag Ein Unternehmen der Narr Francke Attempto Verlag GmbH + Co. KG Dischingerweg 5 D-72070 Tübingen Tel.: +49 (0)7071 97 556 0 eMail: info@verlag.expert www.expertverlag.de Editor Patrick Sorg eMail: sorg@verlag.expert Tel.: +49 (0)7071 97 556 57 Tribologie und Schmierungstechnik Tribology—Lubrication Friction Wear An Official Journal of Gesellschaft für Tribologie | An Official Journal of Österreichische Tribologische Gesellschaft | An Official Journal of Swiss Tribology We’re looking forward to your contribution! 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