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