1 Introduction Present political efforts to achieve global climate goals require efficient propulsion systems in industrial and mobile applications [DLR20]. In addition to the environmental aspects, an optimized efficiency also offers significant potential for cost savings in energy consumption. Rising prices of fossil fuels increase the need for efficiency-optimized powertrains. The concrete implementation requires the geometric and tribological utilization of the load-carrying capacity of gears flanks. The reduction in friction due to tribologically optimized slideroll contacts is beneficial for the dissipation of power losses and maximizing load carrying capacities (e.g. scuffing and micropitting sensitively depend on friction) [SNID04]. The implementation of gears with reduced friction is thus an effective action for more sustainable propulsion technology. A short-term action for efficiency optimization to the gearbox is the use of isotropic superfinished gears. Isotropic superfinishing leads to a topography with significant improvements on the frictional properties [SJÖB16; VORG23b]. An optimization in friction has already been observed in standardized tests for the scuffing load carrying capacity as well as in analogy experiments using 2-disc tribometer [SNID04; KOLL10]. The analysis regarding gear power losses conducted in this study aims to further understand this influence of the topography and confirm it for high pitch line velocities up to v t = 95 m/ s. 2 State of the art 2.1 Isotropic superfinishing of gears In conventional manufacturing, gear flanks are hard machined after heat treatment to achieve the targeted geometry [KLOC17]. The process kinematics lead to a surface texture with transverse grooves, which has functional deficits compared to surfaces used in rolling bearings. Surface topography and tribological interactions between lubricant, material, and load significantly determine the frictional effect [PRÜL15; HANS08]. The objective of isotropic superfinishing is to smooth the surface by gently removing the outer layer without additional thermomechanical stress to influence the residual stress condition. In general, the working principle involves iteratively etching the surface and subsequently removing the reactive outer layer through relative motion with grinding grits [KÖNI20]. In the context of the topographic properties, isotropic superfinishing significantly reduces the profile roughness below the capabilities of conventional profile grinding [JOAC16]. Profile ground surfaces exhibit an anisotropic topography with transverse oriented grinding grooves due to the grit of the grinding disc and the process kinematics. These grooves are often the starting condition for surface crack formation [HERG13; LOHM16; VORG19], resulting in worse wear properties. Isotropic Science and Research 5 Tribologie + Schmierungstechnik · volume 71 · issue 3/ 2024 DOI 10.24053/ TuS-2024-0012 Efficiency of high speed spur gears with an isotropic superfinishing Jaacob Vorgerd, Mathis Steinrötter, Alexander Thomas, Manuel Oehler* submitted: 12.03.2024 accepted: 15.08.2024 (peer review) Presented at the GfT Conference 2023 Gear friction is decisive for the efficiency and power density of cylindrical gears. One method to realise the highest possible efficiency is to carry out a isotropic superfinishing. In this paper, a measuring method for evaluating the gear power losses in the regime of high pitch line velocity is presented. Using this measuring method, efficiency analyses of gears with conventional profile grinding and of variants with additional isotropic superfinishing were carried out. The experimental investigations showed a significant potential in gear friction and thus efficiency due to isotropic superfinishing. The potential was confirmed independent of the gear geometry and over the entire range of pitch line velocities investigated. Keywords gear friction, isotropic superfinishing, power loss, spur gears Abstract * Dr.-Ing. Jaacob Vorgerd, Mathis Steinrötter, M.Sc., Alexander Thomas, M.Sc., Prof. Dr.-Ing. Manuel Oehler, Lehrstuhl für Antriebstechnik Ruhr-Universität Bochum Universitätsstr. 150, D-44801 Bochum lity to transfer the model to alternative topographies is not guaranteed for all models. Topography cannot be solely represented by roughness parameters and is therefore considered through empirical influence factors [PREX90; MAYE13; LÖPE15; SCHL95]. Isotropic superfinished gears are not addressed in the state of the art, so the analysis in Figure 1 considers isotropic superfinishing solely through the reduction in profile roughness to Ra = 0.1 µm. The comparison between the gear friction models shows a significant spread, with all models indicating a tendency towards decreasing coefficients of friction due to isotropic superfinishing. However, they differ in their respective weighting. 2.3 Power loss of gears Load dependent power losses P VZP are the integral of the locally dissipated frictional power (μ R · F N · v g ) in each roll angle, Eq. 1. The meshing of gears can alternatively be described by the engagement time t_E to take account for influences of elasticity on the line of action. Addressing gear geometry, the length and position of the line of action affect the formation of load dependent power loss. [VORG21; OHLE58; WIMM06] (1) In addition to the load dependent shares, the absolute gear power loss P VZ is influenced by an load independent component, Eq. 2. The load independent power loss P VZ0 results from fluid mechanical effects of the rotating gears in an air-oil environment. The primary influence factors are the pitch line velocity v_t and rheological properties of the lubricant. Furthermore, the load independent power loss is affected by the mechanical design of the gearbox components and the explicit design of the lubrication system. [MAUZ88; GREI90] (2) Science and Research 6 Tribologie + Schmierungstechnik · volume 71 · issue 3/ 2024 DOI 10.24053/ TuS-2024-0012 superfinished surfaces do not exhibit this characteristic topography. Instead, the surfaces tend to an isotropic texture with a profile roughness Ra < 0.1 µm [SOSA17; KÖNI20; JOAC16]. The time-consuming grinding process with micrometer-sized ceramic particles eliminates the profile peaks and leaves the original profile valleys from the hard machining process [NISK05]. The isotropic superfinished surface optimizes friction and relieves the surface-near stress field. Experiments on stationary disc contacts [SNID04] indicated up to Δμ = 30 % reduced friction for isotropic superfinished surfaces compared to conventionally ground surfaces. Investigations by S OSA [SOSA17] confirmed this tribological potential for gear contacts. 2.2 Gear friction Friction primarily determines the dissipation of gear power losses [NIEM03; OHLE58]. In lubricated and case-hardened gear contacts, average coefficients of friction in the range of µ m = 0.02 … 0.15 are observed [SCHO73]. The coefficient of friction depends on the local tribological condition in the gear contacts. Gears contacts are loaded by contact pressure and act under relative tangential motion. One major influence value is the pitch line velocity which relates to the relative speeds in the gear contact. During one full gear mesh the local contacts are affected by temporarily slide-roll ratios and EHL conditions. Gear friction is thus a transient phenomenon and depends on the explicit roll angle. The local tribological load, topographical condition and the lubricant formulation have the primary influence on the occurring coefficients of friction [ISO17]. In the state of the art, various models exist for calculating gear friction [SCHL95; MICH87; ISO17; JOOP18; LÖPE15; BENE61; KLEI12]. Between the models, there are significant differences under identical operating conditions. In most cases, these models are calibrated with experiments using conventionally ground gears. The abi- Legend 0 0.02 0.04 0.06 0.08 0.10 mean CoF μ m [- ] Joop [ JOOP 18b] Benedict [ BENE 61] superfinished Löpenhaus [ LÖPE 15] Klein [ KLEI 12] ISO 6336-20 [ ISO 17a] ground Löpe Klein Joop Bene ISO Δµ = - 10 % - 12 % - 35 % - 37 % - 23 %  Geometry: FZG-C  Dyn. Viscosity: η = 25 mPas Öl  Roughness: Ra = 0.5 µm (ground) Ra = 0.1 µm (superfinished) Operating point  Load: T = 200 Nm 1 v = 80 m/ s t Figure 1: Analysis regarding the influence of topography on gear friction 3 Design of experiments 3.1 Calorimetric measurement of gear power losses The conducted experiments on gear friction in this work were conducted using a setup to measure gear power losses by the calorimetric properties. This calorimetric measurement setup was integrated into a back-to-back gear test rig for high speed applications [VORG23a]. The test rig is primarily used for load-carrying investigations of spur gears, enabling pitch line velocities up to v t = 100 m/ s due to its torsionally stiff design and hydraulic load application. In the current test rig topology, utilizing calorimetry is recommended as the measurement principle for recording gear power losses. The physical working principle is based on the assumption that the power loss is entirely dissipated as heat. When achieving steady-state thermal conditions, the absorbed heat of the lubricant Q˙ oil corresponds to the gear power loss P VZ . The absorbed heat of the lubricating oil can be determined by measuring the inlet and outlet temperatures ϑ in and ϑ out and the volumetric flow rate V˙ oil as well as evaluating the lubricants properties c p and ρ oil , Eq. 3. (3) To separate the gear power losses from additional sources of dissipated heat such as bearings and sealings, the test gears are insulated with an additional housing, Figure 2. The test gears exhibit an individual lubrication system which can be regulated in volume flow, injection pressure and oil temperature. The insulation housing is made of a temperature-stable PEEK polymer. Both shafts are supported in the external steel housing, and thus, must be led out of the insulation housing. Small ! " # $ % # & ' ( gaps between the shafts and housing plates prevent the contact between these elements. Since all sealings of the test gearbox are contactless, only the bearings act as thermal error. The insulation housing prevents convective heat exchange between the heat sources, so the bearings and the test gears are only conductively connected through the common shafts. A thermal simulation of the measurement setup indicated that the conductive heat transfer through the shafts amounts to 5 - 8 % of the absolute heat for high speed conditions. The insulating setup around the test gears allows for the evaluation of the energetic state of the circulating lubricant. Due to the separated oil systems, the change in enthalpy is representative for the gear power loss. The temperature sensors used are positioned as close as possible to the injection and the returning pipe. In the inlet of the spray bars the measurement of ϑ in is carried out with a PT100-sensor embedded in the pipe. The returning oils flows back towards the tank with ambient pressure. To measure the temperature of a representative oil volume ϑ out , a siphon-like pipe connection is employed. Another PT100-sensor is immersed in the accumulated oil level. Additionally, a flow meter for measuring the oil volume flow V˙ oil is integrated into the inlet pipe, Figure 2. The conducted experiments regarding efficiency include a series of measurements in which a combination of influencing factors (pitch line velocity, topography, lubricant temperature, volume flow and gear geometry) is tested with a load spectrum of multiple loads. Figure 3 illustrates the methodology for evaluating the gear power losses. The runtime per load level is based on the time until a steady-state temperature condition is established in the test gearbox. The adjustment of load levels is automated without turning off the test rig. For each Science and Research 7 Tribologie + Schmierungstechnik · volume 71 · issue 3/ 2024 DOI 10.24053/ TuS-2024-0012 ϑ in ϑ out V oil P VZ tank measurement setup temperatur volume flow pressure pump oil properties oil density ρ [kg/ l] t ϑ emperatur oil [°C] heat capacity c p [kJ/ kg K] Figure 2: Schematic representation of the experimental setup and the measurement principle In the manufacturing of the test specimens, the gears were conventionally hard machined using the profile grinding process after case hardening. The hard machining resulted in a profile roughness Ra = 0.32 µm with a symmetric formation of valleys and peaks in the abbot curve. The achieved surface is characteristic for profile ground gears in the industrial gearbox sector [JOAC16]. The subsequent isotropic superfinishing led to a substantial reduction in the profile height. The resulting gear flanks exhibited profile roughness Ra < 0.10 µm. In the abbot curve, the surfaces indicate an isotropic, valley-dominated topography without significant profile heights, Figure 4. 4 Experimental results on gear efficiency and power losses 4.1 Results on gear power losses The conducted experiments on the influence of the topography confirm the hypothesis from the state of the art Science and Research 8 Tribologie + Schmierungstechnik · volume 71 · issue 3/ 2024 DOI 10.24053/ TuS-2024-0012 test combination, the data points represent the absolute power loss depending on torque. To separate the loaddependent and load-independent components, the data points are linearly regressed. The ordinate indicates the load-independent power loss. The difference between the absolute power loss and the load-independent component yields the load-dependent power loss. 3.2 Test specimens The efficiency measurements were conducted with two variants of test gears, Table 1. To minimize gear dynamics in the regime of high pitch line velocities, both variants were designed with a deep tooth form exhibiting a normal overlap of ε α = 2. Additionally, both variants are profile modified to reduce the impacts of elasticity and premature contact. In the design of variant Geom B, a positive profile shift was implemented to concentrate the main load events in the recess contact. In the experimental investigations, a synthetic ester-based oil was used. Preheating oil system on targeted temperature Evaluation of load dependent power loss (P = P - P ) VZP VZ VZ0 Preloading of power loop T = 500 Nm 2 Running up test rig Loading power loop acc. to load scheme Test duration 10 / 15 min (thermally steady state) through linear regression independent power loss P VZ0 Evalautaion of load n = n + 1 Increase load stage Ls 1 Ls 2 Ls 3 Ls n (Heating of components) 15 min / T = LS 2 1 10 min / T = LS 2 2 10 min / T = LS 2 3 10 min / T = LS 2 n torque T [Nm] 2 gear power loss [ kW] P VZ P VZ0 Regression Load scheme regression line data points confidence interval P VZP Figure 3: Test methodology to evaluate gear power losses Tabelle 1: Test gear geometry Denomination Symbol Unit Geom A Geom B Normale modulus m n mm 4.825 5.625 Number of teeth z 1 / z_ - 35 / 39 30 / 42 Active tooth width b 1 / b 2 mm 22 / 20 16 / 14 Normale pressure angle α n ° 22.5 20.0 Helix angle β ° 5 5 Profile shift x 1 / x 2 - 0.2000 / -0.2195 0.3000 / -0.2899 Overlap ε α - 2.00 2.00 Active tip circle d a1 / d a2 mm 183.93 / 247.69 187.04 / 248.17 that isotropic superfinishing reduces the absolute gear power losses. Figure 5-a shows the absolute gear power loss as for variant Geom A with pitch line velocities v t = 65 m/ s and v t = 80 m/ s. The respective linearity constants of the regression lines are smaller for the isotropic superfinishing samples compared to profile ground gears. On the other hand, the load independent power loss for both topography conditions is identical. Thus, topography significantly affects gear friction in the gear contacts, while the load independent shares remain unaffected. With increasing rotational speed, the load dependent components generally increase, as more gear mesh cycles accumulate per unit of time. This relationship is also evident in the measurement results. The experimental results on absolute gear power loss for variant Geom B are qualitatively similar, Figure 5-b). At both presented pitch line velocities v t = 40 m/ s and v t = 80 m/ s, the isotropic superfinished samples exhibit lower load dependent power losses. Comparing the two geometry variants at the operating point v t = 80 m/ s, the variation in oil volume flow affects the magnitude of the load independent power losses. The load independent share of variant Geom B is smaller due to the lower oil volume flow. Overall, the results for the investigated pitch line velocities indicate that load independent components constitute a significant portion of the absolute power losses. Science and Research 9 Tribologie + Schmierungstechnik · volume 71 · issue 3/ 2024 DOI 10.24053/ TuS-2024-0012 Legend Test conditions  Oil temperature: 100 °C  Oil volume flow: 14 l/ min ( ) Geom A 12 l/ min ( ) Geom B ground superfinished 0 1000 2000 3000 4000 torque T 2 [Nm] 0 5 10 15 gear power loss [kW] P V Z v = 80 m/ s t v = 65 m/ s t Objective  Gear power loss P VZ = P + P VZP VZ0 0 1000 2000 3000 4000 torque T 2 [Nm] 0 5 10 15 gear power loss P V Z [kW] b) Geom B v = 80 m/ s t v = 40 m/ s t a) Geom A Figure 5: Experimental results on gear power losses Figure 4: Resulting topography of the test gears friction. The efficiency of the isotropic superfinished samples are consistently higher than those of the profile ground samples across the entire parameter range. Furthermore, the measurement results show no significant influence of the load on efficiency. In both geometry and topography variants, constant efficiencies result for a given pitch line velocity, Figure 6-b) and Figure 6-d). The efficiencies of both geometry variants are in a similar range. 5 Conclusion and outlook In this work, a calorimetric measurement method was introduced, which is integrated into a high-speed gear test rig and is capable of determining the gear power loss of high-speed gears. Based on this method, experimental analyses were conducted to investigate the influence of isotropic superfinished gears on efficiency and gear power losses. The investigations cover the range of high pitch line velocities up to v t = 95 m/ s. Overall, the measurements confirmed the potential in efficiency achievable through a tribologically optimized topography. The efficiency benefits were also evident in the regime of high pitch line velocities. Isotropic superfinishing provides the opportunity to optimize the efficiency of propulsion systems from the perspective of manufacturing. Ultimately, an economic evaluation is Science and Research 10 Tribologie + Schmierungstechnik · volume 71 · issue 3/ 2024 DOI 10.24053/ TuS-2024-0012 4.2 Results on gear efficiency The preceding analysis results confirm that the load dependent power loss is dependent on gear friction and consequently attributable to the local tribological conditions in the gear contacts. Subsequently, the absolute power loss is corrected for the load independent components. For a qualitative influence analysis of torque and pitch line velocity on the load dependent power loss P VZP , these results are related to the mechanical power P mech . This ratio relates to the load dependent gear efficiency η VZ according to Eq. 4. The efficiency represents both the geometric conditions and the tribological conditions. (4) Figure 6 shows the experimental results on the influence of topography and gear geometry on the gear efficiency. For comparative purposes between both variants, the load is referenced to the Hertzian contact pressure at the nominal pitch point p H,C . Both geometry variants show a progressively increasing efficiency with increasing pitch line velocities, Figure 6-a) and Figure 6-c). Increasing the pitch line velocity leads to higher hydrodynamic velocities in the gear contacts and thus improves the EHL condition [DOWS68]. Increasing the fluid film thickness is beneficial for the resulting coefficient of ) * % ( ( +,-. Legend  Oil temperature: 100 °C  Geometry: Geom A  Oil volume flow: 14 l/ min Test conditions  Efficiency = 1 - P / P VZP mech η VZ Objective ground superfinished Test conditions  Geometry: Geom B  Oil volume flow: 12 l/ min  Oil temperature: 80 °C 0 50 100 pitch line velocity v [m/ s] t 99 99.2 99.4 99.6 99.8 100 p = 1250 MPa H,C 500 1000 1500 2000 Hertzian pressure p H C , [MPa] 99 99.2 99.4 99.6 99.8 100 v = 40 m/ s t 500 1000 1500 2000 Hertzian pressure p [MPa] H C , 99 99.2 99.4 99.6 99.8 100 0 50 100 pitch line velocity v t [m/ s] 99 99.2 99.4 99.6 99.8 100 gear efficiency V Z [% ] η p = 1000 MPa H,C v = 65 m/ s t a) Geom A b) Geom A c) Geom B d) Geom B gear efficiency V Z [% ] η gear efficiency VZ [%] η gear efficiency VZ [%] η Figure 6: Experimental results on gear efficiency necessary to determine whether the additional manufacturing costs offset potential additional expenses due to higher energy consumption. Funding This work is being carried out jointly with Rolls-Royce Germany as part of the KOVOHLG research project (funding number: 20T1912). The authors would like to thank Rolls- Royce Germany for their support during the project and for the opportunity to publish this work and the Federal Ministry of Economics and Climate Action (BMWK) for providing the financial resources. Abbreviations Latin symbols c P [J/ kgK] Spec. heat capacity n [rpm] Rotational speed t E [ms] Engagement time v t [m/ s] Pitch line velocity v g [m/ s] Sliding speed z [-] Number of teeth F N [N] Normal force F R [N] Friction force P VZ [W] Gear power loss P VZP [W] Load independent power loss P VZ0 [W] Load dependent power loss Q˙ oil [W] Absorbed heat (lubricant) T [Nm] Torque V˙ oil [l/ min] Oil volume flow Greek symbols η VZ [-] Gear efficiency μ R [-] Coefficient of friction ρ oil [kg/ m 3 ] Oil density ϑ out [°C] Outlet temperature ϑ ein [°C] Inlet temperature ϑ oil [°C] Oil temperature References [BENE61] Benedict, G. H.; Kelley, B. W.: Instantaneous Coefficients of Gear Tooth Friction, In: ASLE Trans. 4 (1961), S. 59-70 [DLR20] Deutsches Zentrum für Luft- und Raumfahrt (DLR): Zero emission aviation - emissionsfreie Luftfahrt. 2020 [DOWS68] Dowson, D.: Elastohydrodynamics, In: Proc.Inst. Mech. 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