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.