Introduction Crossed helical gear units with plastic gears are the current state of the art in positioning and actuating drives. The range of plastic materials with their individual material properties offers the potential to meet different application requirements safely and reliably. In addition to the geometric parameters and for the design of gears, the properties of the flank contact must be described in detail to meet specific requirements. Previous approaches to calculate contact behavior on a tribological level have concentrated on two contacting cylindrical gears. The operating behavior of a steel-plas- Science and Research 35 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005 Local considerations and experimental results on the contact behavior of crossed helical gears with general flank geometries Linda Becker, Peter Tenberge* submitted: 10.10.2023 accepted: 21.03.2024 (peer-review) Presented at the GfT Conference 2023 Schraubradgetriebe gehören zu Zahnradgetrieben mit gekreuzten Radachsen und bestehen in den meisten Anwendungen aus einer Stahl-Schnecke und einem Kunststoff-Rad. Aufgrund der hohen Übersetzung auf kleinem Bauraum werden sie in Stell-, Nebensowie in Positionierantrieben eingesetzt. Fortschritte in der Forschung zu Hochleistungspolymeren ermöglichen zunehmend leistungsstärkere Verzahnungen, die in Abhängigkeit der Eigenschaften des Kunststoffmaterials, an die Belastungsgrenzen von Stahlwerkstoffen gelangen können. Forschungen zu Schraubradgetrieben der Paarung Stahl/ Kunststoff mit geometrisch optimierten Zahnflankengeometrien bieten Effizienzsteigerungen und nachweislich Wirkungsgradpotentiale, wodurch höhere Tragfähigkeiten sowie ein Anstieg in der Lebensdauer realisierbar werden. Eine Aufschlüsselung des Kontaktverhaltens im Eingriffsgebiet ermöglicht Betrachtungen von Reibenergien und stellt die Basis für örtliche Verschleiß- und Tragfähigkeitsbewertungen. Auf dieser Grundlage lassen sich effizientere Schraubradverzahnungen mit allgemeinen Flankenformen gestalten, die infolge der Lebensdauersteigerung einen positiven Einfluss auf die Ressourcenschonung und Nachhaltigkeit haben. Schlüsselwörter Schraubradgetriebe, Freiformgeometrien, ZC, Reibung, Temperatur, Kontaktverhalten Crossed helical gears belong to gear units with crossed wheel axles and in most applications consist of a steel worm and a plastic wheel. Due to the high transmission ratio in a small installation space, they are used in actuators, auxiliary drives and positioning drives. The research into high-performance polymers is accompanied by increasingly powerful gears, depending on the properties of the plastic material, to reach the load limits of steel materials. Research on steel/ plastic crossed helical gears with geometrically optimized tooth flank geometries offers efficiency improvements and demonstrable efficiency potential, enabling higher overall load capacities and an increase in service life. A more detailed resolution of the contact behavior in the contact area allows friction energies to be considered and provides the basis for local wear and load capacity evaluations. Based on this, new crossed helical gears with general flank geometries can be designed, which have a positive influence on resource conservation and sustainability as a result of the increase in lifetime. Keywords Crossed helical gears, ZC-geometry, Friction, Temperature, Contact behavior Kurzfassung Abstract *Dr.-Ing. Linda Becker Orcid-ID: https: / / orcid.org/ 0000-0002-2183-128X Prof. Dr.-Ing. Peter Tenberge Chair of Industrial and Automotive Drivetrains Ruhr-University Bochum, D-44801 Bochum, Germany contact ellipse. The general calculation case according to [ISO17], which is recommended for gears with an axis crossing angle, such as bevel gears, converts these to virtual spur gears with modification parameters, so line contacts of the same material combination with twodimensional contact behavior are still present as the basis of the calculation. Regarding this, the assumptions according to [ISO17] are not transferable to crossed helical gears, so the development of the equations are a current research task. The consideration of the entire contact area represents an extension of the previous calculation approaches. Theoretical consideration of contact behavior For the calculation approach of ISO 6336-20 [ISO17], first it is necessary to describe the orientation of the contact ellipse on the tooth flanks and the individual velocity components. The calculation according [BECK23b] considers the contact behavior along the path of contact as a function of a parameter u, which runs from the worm root to the tip and for the wheel in the opposite direction. The contacting tooth flanks move in a certain angular position on a path through the contact ellipse, while a part of this path being sliding through. In each contact position, the velocities and directions of movement are different for general flank geometries on worm and wheel. The following section is intended to derive these parameters and to find the equations according to [ISO17] for the application of crossed helical gears for a steelplastic material combination with point contact. General curved surface structures also result in new contact geometries, so the assumption of two equivalent contacting cylinders are no longer permissible. The curvatures are reduced to two substitute ellipsoids in contact [BECK23b]. For general flank shapes, the contact ellipse is arranged in different angular positions in relation to the radial section of the gear. Deviating from the involute it is no longer permissible to assign the major semi axis a H to the tooth width direction. The position of the contact ellipsoid semi-axes has to be considered individually in a case distinction for each contact position and has an influence on the calculation [BECK23b]. The contact ellipse moves along a general curved contact path, as illustrated in the following ZC example (Figure 1). According to Boehme [BOEH20], the velocities are considered in individual coordinate directions. Sliding velocities in gears with crossed axes are composed of a sliding component in the tooth height direction and a component in the tooth width direction. The second one is also called helical sliding and increases with increasing axis crossing angle. The surface stress, which leads to frictional wear on the plastic gears, takes place under Science and Research 36 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005 tic pairing and a three-dimensional contact requires new calculation approaches. Recent research results [BECK23b] provide a computational algorithm that represents the contact behavior of crossed helical gears in the contact area at each contact position. In addition, this algorithm allows the variation of flank shapes, which are described by a mathematical polynomial. As a result, non-involute geometries with potentials in terms of load carrying capacity and gear life are obtained. Based on the new approach for general flank geometries, it is possible to analyze the contact behavior with regard to tribological influences in flank contact in more detail. Particularly in the case of crossed helical gears with a design-related high sliding contact on the gear surfaces, there is a research task regarding the frictional-energetic interactions in the design process. State of research The current state of research on crossed helical gears provides detailed considerations of the geometric relations in the design process as well as a description of flank pressures, efficiencies and sliding paths in the entire contact area [BECK23b]. The sliding-rolling behavior with its tribological parameter is important for the load carrying capacity, especially for plastic gears, and has not been considered very much so far. Pech [PECH11] has carried out wear investigations on practical gears for a reference gear set and described correlations for ZI geometries which reflect the maximum wear at the screw point for his geometries and material pairing. The procedure is based on geometric correlations and operating properties of worm gears, which show different effects in their operating behavior. It is shown that design criteria of crossed helical gears do not necessarily have to correspond to those of worm gears [BECK23b]. Sucker [SUCK13] has taken Pech’s approach and extended it with a thermal network. Both calculations are less focused on tribological causes for the corresponding wear amounts. In crossed helical gears, essential influences on the contact behavior are composed of the frictional effects of the contact partners in contact. This is accompanied by the specific energy transfer capacity for dissipating the contact temperature from the gear mesh. To describe these parameters, ISO 6336-20 [ISO17] deals with the calculation of the scuffing load capacity of cylindrical steel gears. Scuffing damages in steel-plastic material combinations are rare, but temperature and friction considerations have a decisive importance. The ISO guidelines refer specifically to cylindrical gears of the steel-steel material combination with a semi-elliptical flank contact, in which the contact zone is simplified to a band-shaped surface with twice the width of the minor semi-axis b H of the the sliding velocity along the path of contact in the direction of the sliding motion. To determine the sliding path orientation on the tooth flanks, the directions of the tangential velocities v t1 and v t2 of the worm and wheel are derived with reference to a coordinate system at the contact point. The geometric relationship is shown in Figure 2. The tangential velocities v t1,2 at the contact point E show the difference between the absolute and normal velocities. The indices “1” and “2” indicate the affiliation to the worm and the wheel. The velocities can be divided in the yand z-direction of the coordinate system located at the point of contact to determine the angular position. The direction results from corresponding tangential vectors [BECK23b]. As a reference position, between the angles β vt1 and β vt2 there is a horizontal auxiliary line parallel to the x-y plane through the contact point. The angles β vt1 and β vt2 are calculated according to equation (1) and (2). (1) (2) The angle β Ha indicates the orientation of the major semi-axis a H to the horizontal auxiliary line. According to this, it is possible to transfer the consideration of the tangential velocity directions for worm and wheel to the position of the major semi-axis, according to the procedure in [ISO17]. = tan ( ) ( ) = ( ) ( ) Science and Research 37 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005 Path of contact Contact ellipse u Path of contact Contact ellipse u Contact ellipse u Path of contact Start of contact End of contact Middle contact are Figure 1: Change of orientation of the contact ellipse along a ZC path of contact n q(u) v t1 v t2 β vt2 β vt1 Horizontal Line parallel to the x-y plane E Tangent vector 1 at the generating profile Tangent vector 2 at the generating profile termv2z(u) termv1z(u) termv1y(u) termv2y(u) xt2q u ( ) yt2q u ( ) zt2q u ( ) xt1q u ( ) yt1q u ( ) zt1q u ( ) v t1 v t2 E a H b H Contact ellipse β Ha β vt1 β vt2 n q(u) a) b) Figure 2: Derivation of the angular positions of the tangential vectors on the worm for the tangential velocities v t at the contact point E, a) representation of the vector components, b) related to a contact point E Path of contact β Ha Horizontal auxillary line X Y Z a H s ellipse2 b H φ slide2 Tangential velocity worm v t1 β vt2 The sliding path of the contact partners through the contact ellipse is critical in terms of friction energy. Due to the three-dimensional velocity conditions, the path s ellipse is neither equally oriented nor equally long for worm and wheel, so the consideration must be carried out separately. The directions of the sliding motions φ slide1,2 result from the consideration of the orientation β vt1,2 of the tangential velocities as well as the angle β Ha to the major semi-axis a H . Figure 3 illustrates the relationships between the parameters. Figure 3: Orientation of tangential velocities and sliding movements in the radial section of the wheel B M and the contact time of the heat source T k . Equation (5) describes the increasing flash temperature θ fl according to the approach from Blok for local point contacts of crossed helical gears. (5) The maximum contact temperature at the tooth flank surface θ max results from the constant bulk temperature θ m and the flash temperature θ fl , which depends on the location on the contact path. (6) The specific contact energy E k describes the temperature-independent frictional energy input that finally leads to the heat in the contact point [LOOS15]; [STUH22]. The distribution of the partial heat flows is carried out under the assumption that equal contact temperatures result at the contacting surfaces. For crossed helical gears, the distribution of the partial heat fluxes is unevenly distributed among the contacting partners, since the steel worm has a better thermal conductivity than the plastic gear. The coefficient γ Ek describes the distribution of the heat flux among the contact partner and considers the different distances of the flanks through the contact ellipse. Again, there is a reference to the contact time. (7) Considering the heat flux distribution between the contacting teeth, the specific contact energy E k is given by equation (8). (8) The different heat flux leads to a change of the first equation term from γ Ek to (1-γ Ek ) in the calculation of the counterpart, so the energy input per area as a function of time for the wheel is obtained analogously. The influence of the lubricant as an intermediate medium in the contact is focused in further investigations with regard to the influence of the lubricating film thickness in a crossed helical gear flank contact. Application of the calculation to consider the contact behavior Based on gear examples of previous research work [BECK23b], calculations for a ZI, ZC and ZC-S geometry modification should be implemented to verify the calculation approach. At the same time, it should be de- ( ) = _ ( ) ( ) ( ) ( ) ( ) ( ) = + ( ) ( ) = ( ) ( ) ( ) = ( ) _ ( ) ( ) ( ) ( ) ( ) Science and Research 38 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005 Considering the sliding direction φ slide1,2 , the contact body-dependent path s ellipse1,2 through the contact ellipse results, which, combined with the tangential velocity, leads to the contact time T k1,2 . The sliding path results from the product of the sliding velocity v g with the contact time T k1,2 and represents a first parameter for the friction behavior of the contacting gears. For the further local consideration of the sliding rolling contact, knowledge about the tooth friction coefficient during the contact is necessary. In the first step, an approach by Pech [PECH11] is selected for the following consideration. According to equation (3), the local tooth friction is composed of a basic friction coefficient μ 0T and a load coefficient μ 1T . These quantities depend on the sliding velocity, the resulting tooth normal force in contact and dimensional coefficients. (3) The tribological effects in the contact zone depend decisively on the maximum temperature increase. The flash temperature according to Blok is the relevant parameter according to [ISO17]. Blok [BLOK37] provides an analytical model which is able to calculate the maximum flash temperature below the heat-affected zone of the moving heat source. The temperature increase results from the diffusion of frictional heat due to contact stress under relative velocity. Local frictional energy is introduced into the contact zone and thermally dissipated from the contact zone into the substrate [WIŚN00]. The thermal depth effect largely depends on the material parameters thermal conductivity λ M , density ρ M and heat capacity c P and is described with the thermal contact coefficient B M . Due to the different material behavior of the different materials, the thermal contact coefficient must be calculated individually for both contact bodies using equation (4). (4) The theory of Blok [BLOK37] considers the tangential movement of the heat source along the contact path through the contact surface. During tooth contact, the contact force resulting from the torque is distributed to multiple teeth in contact. Locally, the contact pressure σ Hκ transmitted under relative motion v g and frictional influence μ z_contact leads to a frictional energy input. The model includes the simplification that the planar heat-affected zone is approximated with the help of a point heat source. The shape parameter A Form transforms the two-dimensional consideration into a point-shaped equivalent. As a result of the axis crossing angle, the path through the ellipse is unequal for the worm and wheel. Regarding this, the contact times T k1,2 , in which frictional energy is introduced into the surfaces, are different for the two contact partners. The effective distribution of the heat input is determined by the thermal contact coefficient _ ( ) = ( ) + ( ) = monstrated that non-involute crossed helical gear geometries offer potential in load-carrying capacity. Table 1 lists the gear parameters. Due to the different contact locations on the tooth flanks, the graphs in the following diagrams are offset. The local contact points of the start of contact A and end of contact E (on the tooth flanks) are compared in absolute terms in the parameter values. The observation is made along the parameter u in the whole contact area. Within the graphs, the steps visualize the change between the numbers of teeth in contact. The sliding velocity is similar for all three geometries due to the comparable dimensions of the gear teeth. The starting point of the optimization process was the ZI reference gear according to Pech [PECH11], which should be optimized by modifying the flank curvatures. The position and size of the contact ellipse can be influenced through design of the curvatures. Therefore the tribological potential is mainly related to the flank pressure, as shown in Figure 4-b. Figure 5 compares the different contact times of the worm and the wheel. While the worm flank is in contact for a very short time, the plastic wheel remains in contact significantly longer. In particular, the ZC contact end shows a long contact time, while the values of ZI and ZC-S are comparable. With regard to the coefficients of friction according to Figure 6-a, the difference between the individual contact points is small. While the tooth friction coefficient for ZI is constant in the contact area, the values for the ZC and ZC-S geometry decreases along the path of contact. Combined with the sliding velocity and the flank Science and Research 39 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005 g y ZI ZC ZC-S Normal section Center distance a 30 mm Number of tooth z 1 / z 2 1 / 40 Normal pressure angle n 20° 5° 15° Normal modulus m n 1.25 mm Helical angle 1 / 2 82.493° / 7.507° Tip diameter d a1 / d a2 12.068 mm / 52.932 mm 9.818 mm / 55.182 mm 10.250 mm / 54.750 mm Reference diameter d 1 / d 2 9.568 mm / 50.432 mm Center diameter d m1 / d m2 9.568 mm / 50.432 mm 10 mm / 50 mm Root diameter d f1 / d f2 6.443 mm / 47.307 mm 4.193 mm / 49.557 mm 4.625 mm / 49.125 mm Tooth thickness facto s mx * 0.5 0.3 0.25 Contact ratio 1.837 2.247 1.708 Operating point n 1 / T 2 1500 1/ min -1 / 8 Nm Table 1: Parameter sizes of the ZI, ZC and ZC-S geometry modification [BECK23a] Figure 4: Comparison of the a) sliding velocity and b) flank pressure in the contact area u two thirds of the contact area, which, however, experience an exponential increase towards the contact end. The ZC-S geometry shows lower flash temperatures in the entire contact area. Science and Research 40 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005 pressure in multiple tooth contact, the flash temperature of Blok is obtained according to Figure 6-b. The ZI geometry is used as the initial point for the comparison. The ZC geometry shows the lowest flash temperatures in Figure 5: Contact time of the tooth flanks along the path of contact for a) worm and b) wheel Figure 6: Path of a) tooth friction coefficient in the contact area and b) flash temperature in the tooth contact as local temperature increase according to Blok Figure 7: Change in the Hertzian contact area A K For the consideration of the specific contact energy, the area of the Hertzian contact ellipse must be determined first (Figure 7). The contact area A k represents the zone of influence in which the heat flow diffuses into the material during the contact time. The larger the area, the better the heat can be dissipated from the tooth contact. However, a balance must be found with the increasing sliding paths. From the comparison, ZI and ZC-S have similar contact areas with only minor differences along the area of contact. The ZC geometry has an advantageously large contact area at the beginning, but it becomes small at the end of contact. Combined with the high contact velocities, increased wear tendencies are expected in practice at the corresponding locations on the wheel flank. Considering the distribution of the heat flux between the worm and the wheel as well as their heat absorption capacity in the zone of influence A k during the contact time T k1,2 , the specific contact energy E k is obtained according to Figure 8. Both at the wheel and the worm, compared to ZI, the ZC geometry shows a lower energy input in the first half of contact, which is, however, dominated by an increase at the end of contact. The ZC geometry provides a noticeable improvement in contact behavior, but experience a high surface stress at the contact end due to large sliding friction. The plastic teeth have been designed to be significantly thicker than the ZI geometry and will better resist increased frictional wear. For the ZC-S geometry, the calculation results in the contact area are more favorable than for ZI and, in combination with the likewise positive development of the flash temperature θ fl , indicate a complete gear optimization. Verification of the theoretical consideration with test rig results After the theoretical calculation, practical tests of the ZI and ZC geometry are used to verify the approach. Typically, a grease lubrication is used for applications with crossed helical gears, so the test examples are lubricated with equal grease (Klübersynth LI 44-22). In a first step, it is assumed that all three geometries have a similar lubricant-influence and therefore the lubricant film analysis is outsourced to further investigations. The test rigs have speed and torque measurement in front of and behind the test gearbox. A temperature measurement is included directly under the tooth contact [BECK23b]. The previously described calculations show that there is a significant difference in the surface stress of the plastic wheel between the ZI and ZC geometry, especially at the contact end. While the coefficient of friction and the local flash temperature according to Blok are lower in a large range than with ZI, increased surface stress follows due to high sliding friction and high contact times in a small contact area at the ZC contact end. As a result of the increased flash temperature and specific contact energy at ZC, higher wear can be expected at the contact end for the same load. Additionally to the influence in wear, the heat development results in a reduction in the strength of the gear wheel material and leads to an increase in plastic deformation. The intensity depends on the plastic material and is currently taken into account in FEM simulations. The thicker ZC plastic teeth prove to be advantageous here [BECK23b] . After the test, the plastic gears were dismounted at defined time steps. The material removal is determined by measuring the surface contour with the Alicona Infinite- Focus G4 optical measuring system. Figure 9 shows the results. The operating point corresponds to Table 1. Due to the favorable contact conditions, the wear pattern at the wheel tip shows less material removal at the start of contact. Because of the worsening contact behavior at the contact end, wear increases and a visible growth of the contact surface occurs in the root area of the ZC wheel (magenta area, Figure 9). In addition, the increased surface stress leads to a roughening of the material surface. The results prove that a high sliding path at the contact end and an increased flash temperature and specific contact energy lead to higher wear at the ZC tooth root. The reduction in pressure and optimized curvature in the remaining contact area lead to less wear overall. A detailed description of the test operation is given in [BECK23b]. Additionally to wear, the operating behavior was examined. Because of the geometry optimization of a ZI geo- Science and Research 41 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005 Figure 8: Specific contact energy in the contact area at the worm (a) and at the wheel (b) Summary Based on new calculation approaches for the design and consideration of general crossed helical gear geometries in the entire contact area, it is possible to analyze the sliding-rolling behavior in terms of friction energy more precisely. With a detailed breakdown of the contact behavior, it is possible to transfer the temperature approaches of ISO 6336-20 [ISO17] from spur gears to general crossed helical gears with point contact and a threedimensional contact motion. The modification relates to the Hertzian pressure taking into account multiple tooth engagement and integrates a tooth friction coefficient that changes along the contact area. The temperature increase resulting from a load-dependent frictional energy input leads to a material-dependent distribution of the Science and Research 42 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005 metry to a ZC geometry, the efficiency increases by 4 % and the sump temperatures directly under the tooth contact is reduced by 4 - 5 K (Figure 10). The results show that the ZC geometry has an advantage in terms of efficiency and sump temperature although the contact behavior at the contact end is unfavorable. Based on the test results, a non-involute crossed helical gear with completely improved load-carrying capacity and a reduction of the sliding and frictional effects at the contact end is possible to calculate. The ZC-S gear is part of current research work. Like the ZC geometry, the experimental results confirms the theoretical calculation. The critical contact situation at the end of contact no longer exists. ZI after 100 h ZC after 100 h 23,3 23,7 24,1 24,5 24,9 25,3 25,7 26,1 26,5 -200 -100 0 100 200 Transverse coordinate z [mm] 23,3 23,7 24,1 24,5 24,9 25,3 25,7 26,1 26,5 -2,0 -1,6 -1,2 -0,8 -0,4 0,0 Transverse coordinate z [mm] Transverse coordinate y [mm] 24,4 24,8 25,2 25,6 26,0 26,4 26,8 27,2 27,6 -2,0 -1,6 -1,2 -0,8 -0,4 0,0 Transverse coordinate z [mm] Transverse coordinate y [mm] 24,4 24,8 25,2 25,6 26,0 26,4 26,8 27,2 27,6 -200 -100 0 100 200 Transverse coordinate z [mm] Deviation to the real profile [ m] μ Deviation to the real profile [ m] μ ZI ZC Largest wear in the middle flank area Largest wear in the root flank area Figure 9: Wear behavior and false-color images to illustrate material removal as a function of surface stress and flank geometry, the middle pictures show the growth from 1 h, 25 h, 50 h and 100 h ZI ZC - 8 Nm Legend Efficiency η ges [%] 0 50 100 150 200 250 300 10 30 50 70 90 60 80 40 20 - 8 Nm Grease sump temperature [°C] t S Ti [h] me t 0 50 100 150 200 250 300 0 10 20 30 40 25 35 15 5 Time [h] t a) b) Figure 10: a) Measured grease sump temperature shows a reduction with b) simultaneous efficiency increase of a ZI and ZC geometry under identical operating conditions [BECK23a] heat flow into the material. Due to the low thermal conductivity of the plastic, the largest proportion of heat is dissipated via the worm. Practical tests verify the calculation algorithm and the results. The critical contact behavior at the contact end, shown in the example of the ZC geometry, is practically confirmed by increased material removal in the root area of the wheel. As a result of the thicker ZC plastic teeth, the stiffness increases, so tooth bending and flank deformation is lower. To reduce the increased wear in the root, the acting load at the contact end should be reduced. This can be achieved by profile modifications. The ZC-S geometry represents an example, which leads to a complete geometry optimization. This leads to the following summary. The ZC-S geometry is particularly suitable for performance gears with explicit speed and torque requirements. The ZC geometry is suitable for applications with less requirements for wear and a sliding motion. The design of crossed helical gears depends essentially on the requirements of the applications, so the optimum geometry needs to be selected individually. References [BECK23a] Becker, L.; Tenberge, P.: Crossed helical gears - simulative studies and experimental results on non-involute geometries, In: Forschung im Ingenieurswesen (2023), H. 87 [BECK23b] Becker, L.: Erweiterte Schraubradberechnung für allgemeine Flankenformen zur Ermittlung der örtlichen Belastungen. Dissertation Ruhr-Universität Bochum, 2023 [BLOK37] Blok, H.: Theoretical study of temperature rise at surfaces of actual contact under oiliness lubricating conditions, In: Proc. General Disc. Lubrication (1937) [BOEH20] Boehme, C.: Berechnungsverfahren zur Erweiterung der Anwendungsgrenzen und der Optimierung von Schraubradgetrieben. Dissertation Ruhr- Universität Bochum, 2020 [ISO17] Norm ISO/ TS 6336-20. Calculation of load capacity of spur and helical gears - Part 20: Calculation of scuffing load - Flash temperature method, 2017 [LOOS15] Loos, J.; Kruhöffer, W.: Einfluss der Reibbeanspruchung auf die WEC-Bildung in Wälzlagern, In: Tribologie und Schmierungstechnik (2015), H. 62 [PECH11] Pech, M.: Tragfähigkeit und Zahnverformung von Schraubradgetrieben der Werkstoffpaarung Stahl/ Kunststoff. Dissertation Ruhr-Universität Bochum, 2011 [STUH22] Stuhler, P.; Nagler, N.: Stand der Technik: Anschmierungen in Radial-Zylinderrollenlagern, In: Forschung im Ingenieurwesen (2022), H. 86, S. 1-20 [SUCK13] Sucker, J.: Entwicklung eines Tragfähigkeitsberechnungsverfahrens für Schraubradgetriebe mit einer Schnecke aus Stahl und einem Rad aus Kunststoff. Dissertation Ruhr-Universität Bochum, 2013 [WIŚN00] Wiśniewski, M.: Elastohydrodynamische Schmierung: Grundlagen und Anwendungen, Renningen-Malmsheim, expert-Verl., 2000 Science and Research 43 Tribologie + Schmierungstechnik · volume 71 · issue 1/ 2024 DOI 10.24053/ TuS-2024-0005