1 Introduction Severely reducing CO 2 emissions worldwide is one of the main parts of the climate change objectives for the next 30 years [13]. Besides electrification and alternative fuels, friction reduction in powertrains to diminish overall fuel consumption is one way to meet these goals in the transportation sector. In passenger cars, about one third of the fuel energy is used to overcome friction in the powertrain [21]. Geared transmissions offer potential for loss reduction in gears, bearings, sealings and auxiliary units. Several simulation models intended to predict and optimize gearbox power losses have recently been published, e. g. [5], [25], [34] and [40]. No-load power losses are generally relevant under operating conditions with high circumferential velocities. In this context, Mauz [30] investigated the hydraulic power losses of spur gears up to circumferential velocities of 60 m/ s for both injection and dip lubrication. Neurouth et al. [36] investigated the use of splash lubrication at high circumferential velocities up to 60 m/ s for future automotive applications and showed the huge impact of oil distribution on the resulting no-load gear power losses. Polly et al. [42] varied the position of the pinion relative to its mating gear to quantify the proportion of squeezing and churning of no-load gear loss. Besides experimental investigations on no-load power losses, numerical simulations based on Computational Fluid Dynamics (CFD) have become a relevant tool for analyzing oil distribution and estimating no-load gear power losses, e. g. [6], [7], [14], [24], [27] and [45]. Under operating conditions with high input torque, load-dependent gear loss represents a high proportion of the overall power losses in a gearbox. Hence, several studies were performed to investigate gear friction, e. g. [1], [19], [23], [29], [37], [41], [44] and [51]. A practical approach to calculate load-dependent gear power losses in an early stage of the design process is based on the use of a gear loss factor [37], [50] and a mean gear coeffi- Aus Wissenschaft und Forschung 15 Tribologie + Schmierungstechnik · 66. Jahrgang · 3/ 2019 DOI 10.30419/ TuS-2019-0014 Minimizing Load-dependent Gear Losses Michael Hinterstoißer, Martin Sedlmair, Thomas Lohner, Karsten Stahl* Im Rahmen der vorliegenden Untersuchung wurden mehrere Optimierungsmaßnahmen zur Reduktion der lastabhängigen Verzahnungsverluste schrittweise auf den 6. Gang eines Pkw-Handschaltgetriebes angewendet. Im Einzelnen wurden die Einflüsse der Zahnradgeometrie, der Zahnflankenoberfläche, des Einlaufvorgangs, des Schmieröltyps sowie des Ölstandes untersucht. Um das Potenzial dieser Maßnahmen zu bewerten, wurde die Verzahnung aus dem Pkw-Handschaltgetriebe so modifiziert, dass sie in einen FZG- Stirnradwirkungsgradprüfstand passt, mit dem die Versuche durchgeführt wurden. Durch die bestmögliche Kombination aller Einzelmaßnahmen konnten die lastabhängigen Verzahnungsverluste in Summe um maximal 87 % reduziert werden. Schlüsselwörter Getriebe, Wirkungsgrad, lastabhängige Verzahnungsverluste, Verzahnungsreibungszahl, low-loss, Polyether, Einlauf, Wirkungsgradprüfstand In this study, several measures to reduce the load-dependent gear power loss were applied step by step to the 6 th gear of a passenger car manual transmission. These measures concern gear geometry, tooth flank surface, run-in process, lubricant type and oil level. To evaluate the potential of these measures, the 6 th gear of the manual transmission was modified to fit into a FZG efficiency gear test rig, where efficiency tests were performed. The measures reduced loaddependent gear power loss by a maximum of about 87 % and showed further potential for increasing gearbox efficiency. Keywords Gear, efficiency, load-dependent gear losses, coefficient of gear friction, low-loss, polyether, run-in, efficiency gear test rig Kurzfassung Abstract * Dr.-Ing. Michael Hinterstoißer Orcid-ID: https: / / orcid.org/ 0000-0002-2029-2579 Martin Sedlmair, M.Sc. Orcid-ID: https: / / orcid.org/ 0000-0002-7696-5162 Dr.-Ing. Thomas Lohner Orcid-ID: https: / / orcid.org/ 0000-0002-6067-9399, Prof. Dr.-Ing. Karsten Stahl Orcid-ID: https: / / orcid.org/ 0000-0001-7177-5207 Gear Research Centre (FZG), Technical University of Munich (TUM), 85748 Garching b. München T+S_3_2019.qxp_T+S_2018 13.06.19 11: 31 Seite 15 in eq. (1), the relative, load-dependent gear power loss ξ ZP can be determined as (4) with the gear loss factor H V , which considers the influence of gear geometry on load-dependent gear loss P VZP and therefore allows a direct comparison of the loss behavior of different gear geometries. Ohlendorf [37] assumed a well-balanced load distribution along the tooth flank to solve the integral in eq. (4). For gears with a transverse contact ratio ε α between one and two, the gear loss factor H V can be simplified to (5) This equation enables a first calculation of gear efficiency behavior in an early stage of the design process, once the gear macro geometry is fixed. Note that eq. (5) requires the pitch point C to be placed within the single contact area. Wimmer [50] extended the applicability of eq. (5) to arbitrary transverse contact ratios and positions of the pitch point C. For a transverse pitch ratio ε α less than one, eq. (5) transforms to (6) The squared influence of the addendum contact ratio of pinion (ε 1 ) and wheel (ε 2 ) causes the gear loss factor H V to decrease with the transverse contact ratio ε α . However, increasing helix angles β result in an increase of the gear loss factor H V . According to Wimmer [50], gears with a loss factor H V less than 0.1 are called highly efficient. To increase the accuracy of the calculation of the loaddependent gear loss P VZP , Wimmer [50] derived the local gear loss factor H VL based on the load distribution along the tooth flank: (7) This equation can be calculated by a numerical approximation along the plane of contact and considers not only the gear macro geometry but also its micro geometry. Influences of tooth flank modifications as well as displacements of gears and shafts can hence be considered. Due to its dependency on load, the local gear loss factor H VL has to be determined separately for each input torque. Whereas the gear loss factor H V(L) considers geometrical influences, tribological influences are allocated to the ? #$ " ! #$ <@ " ? " * +, - 1 . / - 0 2 3 456 2 AB - 78 9 4567 8 AB : 5 ; < " * +, - C ! C ! " F - 4G % 16 H I - G - JKLM A - 41 N D E % D IO % D OO 6 C PKQ 1 R D E R S C ! " F - 4G % 16 H I - G - JKLM A - 1 D E - 4D IO % D OO 6 PKQ C PKQ D E R 1 C ! ' " 1 . / B - 0 0 P 3 45U V6 2 AB - 8 9 45U V6 8 BA : 5: V ; < A WX& Aus Wissenschaft und Forschung 16 Tribologie + Schmierungstechnik · 66. Jahrgang · 3/ 2019 DOI 10.30419/ TuS-2019-0014 cient of friction [2], [10], [11], [12], [32], [35] and [47]. Optimization measures involving gear geometry, tooth flank surface and the use of DLC coatings enable significant reductions of the load-dependent power loss [20], [49], [50] and [5]. Ziegltrum et al. [52] used a simulation model for elastohydrodynamically lubricated (EHL) contacts to investigate the influence of different lubricants on load-dependent gear loss. Another approach to improve tribological contacts is surface texturing, e. g. [16], [23], [33] and [43]. Mayer [31] showed that the effect of friction reduction by laser-structured surfaces is limited to extreme boundary lubrication conditions. In this study, several measures to reduce load-dependent gear power loss are shown. Low-loss gear geometries and experimental measures [19], [49] were thereby combined and applied step by step to show the big picture for increasing gearbox efficiency. The results of this study were partly presented during a technical session at the 21 st International Colloquium Tribology 2018 [20]. 2 Gearbox Efficiency The efficiency of a gearbox is defined as the ratio of output power to input power. Therefore, its complement, the relative power loss ξ, describes the ratio of the overall power loss P V to the input power P An : (1) Overall gearbox power loss P V can be expressed as the sum of partial losses caused by gears (index Z), bearings (index L), sealings (index D) and others (index X). (2) Other losses P VX can occur e. g. in clutches, synchronizers, planet carriers or auxiliary units. The power losses of gears and bearings can be separated into no-load (index 0) and load-dependent (index P) losses. Loaddependent losses occur due to friction in tribological contacts in gears and bearings. No-load losses are mainly caused by displacing lubricant and secondary media. The load-dependent gear loss P VZP can be calculated as the integral of the local distributions of the coefficient of friction, normal force and sliding velocity along the path of contact. As the local coefficient of friction along the path of contact is generally unknown, a mean coefficient of friction μ mz has been defined. The load-dependent gear power loss can hence be written as (3) where F N is the normal tooth force and v g the sliding velocity at a point x along the path of contact from A to E. To obtain a time-averaged gear power loss, the integral is divided by the transverse pitch p e . By inserting eq. (3) % 1 & ' % ! " ! #$ ! " ! #$ % ! #& % ! '$ % ! '& % ! ( % ! ) ! #$ " * +, - 1 . / - 0 2 3 456 - 78 9 4567: 5 ; < T+S_3_2019.qxp_T+S_2018 13.06.19 11: 31 Seite 16 mean coefficient of gear friction μ mz . Based on the empirical equation for the mean coefficient of gear friction μ mz according to Michaelis [32], Schlenk [47] introduced a factor in a modified equation to include the influence of oil type: (8) This equation considers the line load along the tooth flank F bt ⁄ b, the sum velocity at the pitch point v ΣC , the radius of relative curvature at the pitch point ρ redC , the oil viscosity at oil temperature η oil , the arithmetic mean roughness Ra and the type of lubricant (X L ). A huge advantage of this equation is the possibility to estimate the mean coefficient of friction without any preceding experimental test. Doleschel [10] derived another method to calculate the mean coefficient of friction μ mz . He developed a standardized efficiency test to determine lubricant parameters, which consider influences on tribological behavior. Based on this approach and by using the local gear loss factor H VL in eq. (7), Jurkschat et al. [22], [23] improved and extended the method for determining the mean coefficient of friction to consider influences of the driving direction of gears having unbalanced ratios of specific sliding. Besides gear power losses P VZ , bearing power losses P VL can also be divided into load-dependent and no-load losses (eq. (2)). SKF [48] released a method to calculate the bearing power losses based on an empirical approach. In terms of the load-dependent bearing loss P VLP . Schleich [46] developed a local approach based on the local load distribution and kinematics. He determined the torque loss of each rolling element, which add up to the load-dependent bearing loss P VLP . The load-dependent gear power loss P VZP results in heat dissipation along the path of contact thereby influencing the bulk temperatures ϑ M of pinion and wheel of a gear pair. The bulk temperature ϑ M is a determining factor for load-carrying capacity taking scuffing, pitting, micropitting and wear into consideration. To estimate the bulk temperature ϑ M , Oster [38] derived an empirical equation using a reference bulk temperature ϑ L at no-load, the load-dependent gear power loss P VZP , center distance a and face width b: (9) M N ( M # O H400 ) PJ ! KL E ) / Q <.R= ) F S G.T ) F : U The factors X S and X Ca consider the influences of the lubrication system and tip reliefs and are calculated according to DIN 3990 [8]. Based on [8], Otto [39] investigated the lubrication factor X S and derived the following equation: (10) Thereby, the lubrication factor X S depends on the depth of immersion e, the tip diameter d a and the parameter D, which refers to the lubricant conveying direction. The equation of Oster [38] in combination with [39] allows the bulk temperature ϑ M to be estimated using only few input parameters. Michaelis [32] and Geiger [17] derived other models to predict the gear bulk temperature ϑ M . These calculation models are based on studies by Blok [3] to split the loaddependent gear power loss between pinion and wheel. 3 FZG Gear Efficiency Test Rig To evaluate the load-dependent gear loss P VZP experimentally, investigations are performed on a modified FZG back-to-back test rig [9] with a center distance of 91.5 mm. Figure 1 shows a schematic depiction of the so-called FZG gear efficiency test rig. The following description concerns only main features of the test rig and is based on works and formulations of Doleschel [10], Hinterstoißer [19], Lohner [28] and Jurkschat et al. [23]. 0.V W F S ( 0.VI ) P X Y U Q BZ W V.H Aus Wissenschaft und Forschung 17 Tribologie + Schmierungstechnik · 66. Jahrgang · 3/ 2019 DOI 10.30419/ TuS-2019-0014 % &' ( 0.048 ) * + ,- / 1 23 ) 5 679: ; <.= ) > ? @A B<.<C ) DE <.=C ) F # % F # ( G.0 F # ( 0.H % Polyalphaolefin: Polyether: % F # ( 0.8 F # ( 0.I % Mineral oil: F Polyglycol: F Figure 1: FZG gear efficiency test rig The gear pairs in the test gearboxes are connected by two shafts so that they form a closed power circuit, in which the transmitted torque is applied via a load clutch. The test rig design allows efficiency tests at high loads by using only a small electric engine to supply the necessary loss torque. The transmitted load is measured with a torque meter directly on the wheel shaft inside the power circle. The total power loss P V of the back-to-back configuration can be directly measured by a torque meter shaft between the electric motor and the power circle. The chosen concept and measuring equipment allow an accuracy T+S_3_2019.qxp_T+S_2018 13.06.19 11: 31 Seite 17 tional gear design with high teeth and a contact ratio of just over two. While maintaining the number of teeth, pressure angle and helix angle, all lengths were increased to match the center distance of the FZG gear efficiency test rig of a = 91.5 mm (Table 1, left). Tooth micro geometry also was adapted accordingly. The reference flank surface was transversally ground to an arithmetic mean roughness of Ra = 0.30 µm. The profile method was used for all surface roughness measurements in the involute direction with a measurement length of L t = 4 mm and a cut-off wavelength of λ C = 0.8 mm. To quantify the saving potential of individual measures, a set of reference operating conditions was defined. In accordance with [10], a Hertzian pressure of p C = 1287 N/ mm 2 was chosen as reference, which requires a pinion torque of T 1 = 208 Nm for the conventional gear design. All tests were performed at pitch line velocities of v t = {0.5,1.0,2.0,5.0,8.3,15.0,20.0} m/ s. Dip lubrication at an oil sump temperature of ϑ oil = 90 °C with a reference oil level 20 mm below the shaft center was applied. The reference lubricant is mineral oil ISO VG 100 with 4 % sulfur-phosphorous additive Anglamol A99 (Table 2, left) [15]. For run-in, the standard process was performed for four hours at a load torque of T 1 = 423 Nm, a pitch line velocity of v t = 0.5 m/ s and an oil sump temperature of ϑ oil = 90 °C. 4.2 Influence of Gear Geometry In a first step, a moderate low-loss geometry with a transverse contact ratio of ε α = 1.1 was derived based on the conventional gear design of the reference. In addition to the reduction of the transverse contact ratio ε α , the module m n was reduced and the pressure angle α n was increased. The tooth width b is increased to meet the load-carrying capacity of the conventional reference design. The calculated load-dependent relative gear power loss ξ ZP of these moderate low-loss gears is according to eq. (5) and (8) for conditions at medium load and velocity about Aus Wissenschaft und Forschung 18 Tribologie + Schmierungstechnik · 66. Jahrgang · 3/ 2019 DOI 10.30419/ TuS-2019-0014 of 0.08 Nm for the measured loss torque and 3 Nm for the load torque [19]. Both test gearboxes are dip-lubricated with controlled oil sump temperature. During all efficiency tests, the load torque, loss torque, shaft speeds and oil sump temperatures are measured and recorded. Due to the symmetrical structure of the power circle, the measured total power loss P V can be divided equally to the test gearboxes. To evaluate the load-dependent gear loss P VZP (eq. (2)), the measured total power loss P V is reduced by the no-load power loss P V0 and the loaddependent bearing loss P VLP . The no-load power losses of gears, bearings and sealings (P V0 ) are measured on the same test rig in a separate test run at no-load. The load-dependent bearing losses are measured separately in a FZG bearing power loss test rig [19]. This gear efficiency test rig hence enables the load-dependent gear power loss and the mean coefficient of friction in the gear mesh to be determined. 4 Efficiency Optimization Measures Based on a reference (section 4.1), measures to reduce the load-dependent gear loss were applied step by step (Figure 2). These measures involve the gear geometry, tooth flank surface and run-in process, oil type and oil level. The local gear loss factor H VL in eq. (7) is taken into consideration for all operating conditions to allow detailed investigations into the efficiency behavior of the test gears. The mean coefficient of friction μ mz can be calculated based on H VL and the experimentally determined load-dependent gear power loss P VZP according to section 3. At constant load, H VL only changes due to a variation of the gear geometry. Assuming a constant local gear loss factor H VL , changes in the loaddependent gear loss P VZP are attributable to a different coefficient of friction μ mz . 4.1 Reference The design of the 6 th gear from a passenger car manual transmission is chosen as a reference [18]. It is a conven- Figure 2: Reference and measures to reduce the load-dependent gear loss investigated step by step T+S_3_2019.qxp_T+S_2018 13.06.19 11: 31 Seite 18 67 % lower compared to the conventional gear design. In a further step, an extreme low-loss geometry was designed to show the maximum potential of power loss reduction. Its transverse contact ratio ε α was chosen to be well below one, its pressure angle α n was further increased and its module m n further reduced. The tooth width was further increased to achieve a load-carrying capacity resembling that of the conventional reference design. For this extreme low-loss gear design, the load-dependent relative gear loss ξ VZP calculated according to eqs. (5) and (8), shows savings of about 85 % compared to the conventional gear design for medium load and velocity. The geometry of all three gear pairs is shown in Table 1. The load-dependent gear loss of each of the three gear designs were experimentally measured at the FZG efficiency test rig. The derived relative gear power loss ξ VZP is shown in Figure 3. Due to the chosen constant load torque of T 1 = 208 Nm for all three gear designs, the Hertzian pressure at the pitch point is with p C = 913 N/ mm 2 for the moderate low-loss and p C = 788 N/ mm 2 for the extreme low-loss lower compared to the conventional gear design (section 4.1, p C = 1287 N/ mm 2 ). All investigated gear designs show a decreasing trend for ξ VZP along the pitch line velocity v t due to low lubricant film thickness and mixed lubrication at low pitch line velocities and higher lubricant film thickness and approach of fluid film lubrication at high pitch line velocities. For T 1 = 208 Nm, the moderate low-loss gear design results in power loss savings of 56 % on average for all tested operating conditions compared to the conventional gear design. The extreme low-loss gear design shows an even higher average saving of 75 %. The experimental investigations essentially confirmed the preliminary calculation results. 4.3 Influence of Flank Surface and Run-in Besides the gear geometry, the flank surface strongly influences the lubricated gear contact and provides optimization potential for reducing the load-dependent power loss. To evaluate this potential, the moderate low-loss design with the reference Aus Wissenschaft und Forschung 19 Tribologie + Schmierungstechnik · 66. Jahrgang · 3/ 2019 DOI 10.30419/ TuS-2019-0014 Parameter Symbol Unit Conventional gear design Moderate low-loss Extreme low-loss Geometry plot - - Normal pressure angle 𝛼 ° 16.0 27.0 36.0 Normal module 𝑚 mm 2.30 1.92 1.81 Number of teeth pinion 𝑧 - 29 34 39 Number of teeth wheel 𝑧 - 39 46 52 Helix angle 𝛽 ° 31.5 33.0 25.0 Transverse contact ratio 𝜀 - 2.10 1.10 0.65 Overlap ratio 𝜀 - 1.27 2.10 2.08 Face width 𝑏 mm 17.6 23.3 28.0 Center distance 𝑎 mm 91.5 91.5 91.5 Local gear loss factor (T 1 = 208 Nm) 𝐻 - 0.2006 0.0852 0.0405 Table 1: Geometry data and local gear loss factor of considered test gears Figure 3: Influence of gear geometry on the load-dependent gear losses T+S_3_2019.qxp_T+S_2018 13.06.19 11: 31 Seite 19 ses to 7 % on average after the additional run-in process - compared to the 13 % shown above after the first runin. However, at high pitch line velocities with higher lubricant film thickness, the load-dependent power losses tend to almost the same level. Both investigated gear sets show the highest saving potential at low pitch line velocities, where boundary lubrication dominates. Taking all performed tests into consideration, the superfinished flank surface shows a maximum power loss reduction by about 20 % compared to the transverse ground variant after the reference run-in. Supplementing a run-in with the lower viscous mineral oil ISO VG 32 enables the load-dependent power loss to be reduced by up to 35 % for low pitch line velocities although the Ra-value shows no further decrease. Hence, the additional saving potential is due to a change of the gear flank surface not noticed by the Ra-value. 4.4 Influence of the Oil Type The measures discussed so far focused on optimizing the gear geometry and flank surface to reduce the loaddependent gear power loss. The lubricant provides another potential for improving the gear efficiency. Experi- Aus Wissenschaft und Forschung 20 Tribologie + Schmierungstechnik · 66. Jahrgang · 3/ 2019 DOI 10.30419/ TuS-2019-0014 transversally ground surface was compared experimentally to an additionally superfinished one. As summarized in Figure 4, the additional superfinishing decreases the measured Ra-value in the involute direction from 0.30 µm to 0.19 µm. After the standard run-in with mineral oil ISO VG 100 (section 4.1), the arithmetic mean roughness decreased to Ra = 0.22 µm for the transverse ground and to Ra = 0.15 µm for the superfinished flank surface. Following this run-in process, both variants were investigated on the efficiency test rig to evaluate the loaddependent gear power loss. Figure 5 shows the subsequently derived mean coefficient of gear friction μ mz for the transverse ground and superfinished gear sets after the standard run-in with ISO VG 100. The superfinished flank surface reduces the mean coefficient of gear friction μ mz by 13 % on average for all tested operating conditions compared to transverse grinding. Especially under operating conditions with low pitch line velocities, where boundary lubrication dominates, the reduction of μ mz shows up to 19 %. After these efficiency tests, both gear sets were subjected to another, special run-in under the same operating conditions with mineral oil but with a lower viscosity level of ISO VG 32 (Figure 4). This resulted in a further reduction of the Ra-value for the transverse ground flank to 0.19 µm and left it unchanged at 0.15 µm for the superfinished flank. Following these two special run-ins, both variants were again investigated on the efficiency test rig to evaluate the load-dependent gear power loss. Independently of the previous run-in process, all efficiency tests were performed with the same mineral oil ISO VG 100 according to 4.1 to evaluate just the influence of the surface. Due to the special run-in process, the gear sets gain another decrease of the load-dependent gear power loss P VZP of about 21 % for the transverse ground variant and 15 % for the superfinished variant on average for all tested operating conditions. That shows a higher impact of the special run-in process with the lower viscous mineral oil ISO VG 32 for the transverse ground flank surface. Hence, the difference between the superfinished and the transverse ground variant decrea- Figure 4: Run-in procedures and measured Ra-values of the transverse ground and superfinished moderate low-loss gear sets Figure 5: Influence of flank surface and run-in on the mean coefficient of friction T+S_3_2019.qxp_T+S_2018 13.06.19 11: 31 Seite 20 mental investigations are hence extended to the two base oil types: polyalphaolefin and polyether. The investigations are based on the superfinished moderate low-loss geometry previously run-in with the low viscous oil (section 4.3). The kinematic viscosities of the polyalphaolefin and the polyether are about 10 mm 2 / s at 100 °C and therefore adjusted to the ISO VG 100 mineral oil considered so far (Table 2). Due to the considered oil temperature of ϑ oil = 90 °C, the viscosity levels of the three oils are comparable for all investigations. Therefore, the influence of the oil type can be evaluated almost separately from the viscosity influence. Figure 6 shows the mean coefficient of gear friction derived from investigations on the gear efficiency test rig for the three base oil types. The maximum reduction of the mean coefficient of gear friction μ mz is 62 % for polyether under mixed lubrication conditions. This correlates with previous studies on a twindisc test rig [31], as polyalphaolefin and polyether lubricants feature much lower coefficients of friction than mineral oil at the same viscosity level. On average for all tested operating conditions, polyalphaolefin decreases the load-dependent gear power loss by 36 %, whereas polyether decreases the load-dependent gear power loss P VZP by 46 % compared to mineral oil. The greatest loss saving potential for polyalphaolefin and polyether is seen at medium pitch line velocities. However, with increasing pitch line velocities the curves of the mean coefficients of gear friction μ mz rise for these two oil types. This contrasts with mineral oil, which shows a steady decrease of mean coefficient of gear friction μ mz . For the considered lowloss gear design, the decrease is less pronounced compared to a conventional gear design. This is because the increase of bulk temperature with increasing pitch line velocity v t is much lower and because local thermal effects along the much shorter path of contact of low-loss gears are not as strong as e. g. discussed in [53]. For polyalphaolefin and polyether with much lower viscosity-temperature and viscositypressure dependency than mineral oil, this results in Stribeck-like behavior. Hence for high-speed applications, using lower viscous lubricants can be proposed to minimize the rise of load-dependent power loss P VZP at high pitch line velocities v t . Simulation studies like those in [52], [53] can be performed to further analyze the influence of different base oil types and gear geometries on the thermo-elastohydrodynamic contact along the path of contact of gears. 4.5 Influence of Oil Level The measures discussed pertaining to low-loss gear geometry, superfinished flank surface, run-in with low viscous oil and the use of the polyether oil have already significantly decreased the load-dependent power loss P VZP . Reduced heat dissipation from the gear contact also causes the resulting bulk temperatures of pinion and wheel to decrease. This effect can be used for reduction of oil level until the bulk temperature is equal to the one of the conventional reference design in Figure 3. To estimate the corresponding new oil level for the moderate low-loss gear design, eq. (9) can be solved using the same bulk temperature ϑ M and the load-dependent gear power loss P VZP . The resulting lubrication factor X S allows the new oil level to be directly determined according to eq. (10). The calculation predicts a depth of immersion 78 % lower than the conventional oil level of the reference. Aus Wissenschaft und Forschung 21 Tribologie + Schmierungstechnik · 66. Jahrgang · 3/ 2019 DOI 10.30419/ TuS-2019-0014 Figure 6: Influence of oil type on the mean coefficient of friction ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! : ; *#/ <".&' -./ &' 5/ .%#",' +/ ,' ! +,)",7 =>"+,%7 ? / .' ! +,)7 %&>%#' Q#0.@&(! -&! 3C! 2K! R1S%T! <<C! <A8! 366; ! U@0#%-&@H! G@.H$.@&(! -&! A6! 2K! %%VS.! ; A5C! 4958! A754! U@0#%-&@H! G@.H$.@&(! -&! 366! 2K! %%VS.! ; 5<! ; 5; ! 3653! W@.H$.@&(! @0: #E! +! 88! 3A6! 79C! ! ! ! ! ! ! ! ! ! ! Table 2: Viscosity and density of the investigated lubricants T+S_3_2019.qxp_T+S_2018 13.06.19 11: 31 Seite 21 gear contact. On average, the load-dependent power loss saving potential realized by lowering the oil level is 24 %. 4.6 Impact of Combined Measures All measures presented above for reducing the loaddependent power loss - low-loss gear geometry, superfinished flank surface, special run-in with low viscous oil, use of a polyether oil and lower oil level - are summarized in Figure 8. Using low-loss gears results in the highest loss savings. A moderate low-loss design enabled load-dependent gear power loss savings of 56 % on average for all tested operating conditions according to 4.1. Using an extreme low-loss design enabled savings of up to 75 % on average with at most 79 % at low pitch line velocities to be realized. Superfinishing the tooth flank further decreased the load-dependent gear power loss by about 13 % on average, at low pitch line velocities even 19 % was possible. A run-in with a low viscous mineral oil enabled further savings of 15 % on average and maximal 26 % at low pitch line velocities. Replacing the mineral oil with a polyether oil nearly halved the remaining load-dependent gear power loss. At medium pitch line velocities, the power loss could be reduced by up to 62 %. Lowering the oil level by 23 mm to achieve the original reference bulk temperature enabled further savings of 24 % on average with a maximum of 47 % at high pitch line velocities. The last Aus Wissenschaft und Forschung 22 Tribologie + Schmierungstechnik · 66. Jahrgang · 3/ 2019 DOI 10.30419/ TuS-2019-0014 Several efficiency tests were done at different oil levels to validate the new oil-level calculation. The results show that the oil level can be reduced to 43 mm below the axle center while ensuring the same bulk temperature at the pinion as that of the conventional reference design in Figure 3. This results in a new depth of immersion at the wheel of 11 mm, which corresponds to an immersion reduction of 67 %. This validates the calculated potential of 78 % well. While the pinion also was directly lubricated by the oil sump at the conventional oil level, it no longer submerges into the oil for the lowered oil level. Besides the efficiency test at a pinion torque of T 1 = 208 Nm, an efficiency test at no-load was also done to determine the load-dependent power loss savings realized from lowering the oil level. As expected, the no-load power losses rise with higher pitch line velocities, but the decreased oil level results in fewer no-load power losses at high pitch line velocities. The influence of the reduced oil level on load-dependent power loss is shown in Figure 7. Especially at high pitch line velocities, the load-dependent power loss could be significantly reduced due to a lower increasing mean coefficient of gear friction. In accordance with the discussion in section 4.4, this is mainly due to the more significant increase in bulk temperature and the consequently stronger reduction of effective lubricant viscosity in the Figure 7: Influence of oil level on the mean coefficient of friction Figure 8: Impact of combined measures on relative load-dependent gear losses T+S_3_2019.qxp_T+S_2018 13.06.19 11: 31 Seite 22 measure simultaneously decreases the no-load power loss significantly. Combining all investigated measures results in an average reduction of the load-dependent gear power loss P VZP by 87 % for all efficiency tests performed. 5 Conclusion In an experiment-based study, several optimization measures to reduce load-dependent gear power loss were investigated and evaluated on the FZG gear efficiency test rig: low-loss gear geometry, superfinished flank surface, special run-in process with low viscous oil, synthetic lubricant types and a lowered oil level. These measures were applied consecutively to a gearbox to determine step by step the saving potential of each. The greatest reduction of load-dependent gear loss was achieved by using the low-loss gear design and synthetic oil types with low shear resistance like polyether. All investigated optimization measures combined ultimately resulted in a reduction of the load-dependent gear loss by 87 % on average under all operating conditions tested. Acknowledgements The „CO 2 -Sonderforschungsprogramm“ of the Forschungsvereinigungen Antriebstechnik e.V. (FVA) und Verbrennungskraftmaschinen e.V. (FVV) sponsored the work presented. The results shown in this work were taken from the results of the research project FVV 609811. Special gratitude is owed to the active members of the attendant working team for the joint research work. Nomenclature Symbols a Center distance mm A Begin of contact b Face width mm C Pitch point - D Conveying factor e Depth of immersion mm d a Tip diameter mm E End of contact - F bt Circumferential force at base circle N f N Line load along the tooth flank N/ mm F N Normal tooth force N H V Gear loss factor - H VL Local gear loss factor - L t Length for roughness measurements mm m n Normal module mm p C Hertzian pressure at the pitch point N/ mm 2 p e Transverse pitch mm P An Input power W P V Power loss W P VD Sealing power loss W P VL Bearing power loss W P VX Other power loss W P VZ Gear power loss W Ra Arithmetic mean roughness µm T Torque Nm u Gear ratio v bt Circumferential velocity at base circle m/ s v g Sliding velocity m/ s v t Pitch line velocity m/ s x Point on the path of contact mm X Ca Modification factor - X L Lubricant factor - X S Lubrication factor z Number of teeth α n Normal pressure angle ° β b Helix angle at base circle ° ε Contact ratio ε α Transverse contact ratio η Gearbox efficiency η oil Dynamic viscosity at oil temperature Pa·s ϑ L Reference bulk temperature °V ϑ M Bulk temperature °C ϑ oil Oil temperature °C λ C Cut-off wavelength nm μ mz Mean coefficient of friction ξ Relative power loss ξ Z Relative gear power loss - Indices 0 No-load 1 Pinion 2 Wheel P Load-dependent References [1] Anderson, N.E.; Loewenthal, S.H.: Design of Spur Gears for Improved Efficiency. 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