Pries [P1] provided an approach for the holistic modelling of transient, semi-elliptical contact areas, including head, root and edge load-bearing. Bünder [B2] complemented the load distribution model with a comprehensive representation of the contact forces. Neugebauer [N1] extended the design by adding criteria for mixed friction states and analysed the influence of deflection angle and temporal variability of the friction coefficient on typical damage patterns. Spura [S2] developed a new holistic simulation model for load distribution and investigated the wear behaviour of crowned, displaceable spline couplings. Science and Research 22 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 1 Introduction The reliability and service life of displaceable spline couplings determine the safety of many drive systems, from industrial gearboxes to wind turbines. Their characteristic crowned tooth flanks compensate for shaft misalignment, but they give rise to an oscillating Hertzian contact between a cylinder and a plane with complex frictional behaviour, in which hydrodynamic, mixed and solid-body friction alternate. Until now, design approaches have largely been confined to static press-fit analyses or to empirical metrics for individual operating conditions, while a method for early quantification of linear wear loss under varying contact conditions has been lacking. This paper links Archard’s phenomenological wear law [A1] with Kragelski’s molecularmechanical fatigue theory [K1] and Fleischer’s energybased fundamental equation [F1]. Instead of a constant wear coefficient, the reciprocal of the wear energy density derived from the elastic contact deformation is employed. Validation by means of test-rig experiments and field measurements demonstrates very good agreement with the observed wear values and provides a robust basis for the engineering design and optimisation of displaceable spline couplings. 2 State of the Art Investigations by Benkler [B1] into load distribution in toothed couplings form the basis for research on displaceable spline couplings. Heinz [H1] extended this work to the tooth kinematics under deflection, introduced the parameters pressure overlap and load-carrying number, and adapted the flash temperature hypothesis for the determination of frictional energy and tooth contact temperature. Strauß [S1] studied run-in and wear behaviour under variable operating conditions and defined a critical contact temperature as the threshold for adhesion. Wear energy density for wear prediction of displaceable spline couplings Christian Spura* Presented at GfT Conference 2025 This study presents a comprehensive predictive methodology combining the Archard wear model, Kragelski’s molecular-mechanical fatigue theory, and Fleischer’s energetic wear framework to accurately forecast linear wear depth in displaceable spline couplings. The specific crowned tooth flank geometry generates a cylinder-to-plane contact accompanied by oscillatory relative motion, which complicates traditional wear evaluation methods. To address this, the wear energy density is introduced as a key parameter, enabling a mechanistically founded quantification of wear progression. Extensive validation through dedicated test rig experiments and field trials confirms the high reliability of the model, with deviations between predicted and observed wear remaining below 9 % for flank pressures up to 900 N/ mm 2 . The presented approach facilitates early-stage wear prediction during the design process, supporting effective optimisation measures to enhance component durability and service life. Furthermore, the model’s adaptability to varying lubrication conditions and material pairings underscores its practical relevance for engineering applications involving complex contact scenarios. Keywords displaceable spline couplings, gear couplings, gear shaft connections, wear energy density, wear prediction calculation, molecular-mechanical fatigue theory, energetic wear fundamental equation Abstract * Prof. Dr.-Ing. Christian Spura Orcid-ID: https: / / orcid.org/ 0000-0001-8307-8919 FH Münster Department of Mechanical Engineering Stegerwaldstraße 39 48565 Steinfurt Archard [A1] developed the well known phenomenological wear model. Kragelski [K1] considered wear as a fatigue process at the molecular level, in which cyclic deformations lead to material removal. Fleischer [F1] supplemented these approaches with an energy balance and defined the wear energy density. Despite their different approaches, all three models can be transformed into one another. 3 Simulation model and load distribution The load distribution is determined using the simulation model presented in [S2], which was developed for crowned tooth flanks. The basis is an analytical stiffness model that represents the deformations of external and internal gearing and the influence of the tooth edge. FEA-based studies provided correction factors to improve the simulation model. Real gear deviations can be taken into account to produce a realistic flank contact pressure distribution. The results provide a reliable basis for the design and optimisation of displaceable spline couplings. Figure 1 shows, as an example, the flank contact pressure distribution along the tooth width of an ideal gear according to DIN 5480 (52 × 2 × 30 × 24). Case (a) has a crowning radius of 80 mm and a deflection of 2 degrees. Case (b) has a crowning radius of 1200 mm and a deflection of 0.1 degrees. As a result of the kinematics, the contact point moves in both the tooth width and the tooth height directions, and the displacement in the tooth width direction is decisive for the loading and the wear behaviour. 4 Wear energy density The following provides a comparative discussion of the energy-based wear fundamental equation [F1, F2] and the fundamental equation of fatigue theory [K1, K2]. Both approaches are based on the assumption of a critical number of contacts and permit a description of the linear wear intensity I h for a single contact. With reference to [F3], the term frictional energy density e R is replaced in the following by the term wear energy density e V , with wear number v v = 1.0. The energy-based wear intensity is given by the ratio of frictional work to wear energy density: (1) with: friction coefficient μ, mean contact pressure p a , and wear energy density e V . Under the assumption of a run-in contact, that is equilibrium of the surface roughnesses, the fatigue theory describes the linear wear intensity I h by (2) and the associated minimum friction coefficient by (3) where C 1 is a dimensionless material factor, α H is the hysteresis coefficient, τ 0 is the shear resistance under the prevailing lubrication conditions, t is the fatigue exponent (typical range 2 to 12), k is a coefficient that depends on the internal stress distribution and on the material (typical range 3 to 7), σ B is the tensile strength, E red is the reduced elastic modulus, and β is a piezo coefficient. Equating (1) and (2) and using (3), then rearranging, yields the wear energy density (4) h = 1 ∙ H ∙ a ∙ 0 2 ⁄ ∙ � ∙ B � ∙ � 1 red � 1− 2 ⁄ = � 0 ∙ H red � 1 2 ⁄ + h = ∙ a V Science and Research 23 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 Figure 1: Flank contact pressure distribution of an ideal gear (DIN 5480: 52 × 2 × 30 × 24). a) Crowning radius 80 mm at 2° deflection; b) Crowning radius 1200 mm at 0.1° deflection. V = B 1 ∙ ∙ H ∙ 0 2 ⁄ ∙ � 1 red � ( 1− 2 ⁄ ) ∙ �� 0 ∙ H red � 1 2 ⁄ + � ( −1 ) The energetic wear model proposed by Fleischer [F1, F2], as expressed in Equation (12), relates the frictional work W R (the product of friction force F R and sliding distance s g ) to the wear volume V V via the wear energy density e V . The wear volume V V may also be determined from the nominal contact area A 0 and the linear wear depth h V . (12) A comparison of Equations (11) and (12) clearly indicates that the wear coefficient k H may be interpreted as the reciprocal of the wear energy density e V . Consequently, k H can be directly obtained from the energetic contact parameters, thereby obviating the need for a separate determination of the wear coefficient through complex tribological testing in model applications. (13) 5.1 Operational wear Based on the calculation of the wear energy density e V as given in Equation (4), the linear wear depth in the low-wear stage of the i-th tooth per revolution can be determined using Equations (12) and (13) as follows: (14) In this context, both the linear wear depth h V and the wear energy density e V are to be determined separately for the shaft tooth and the hub tooth. 5.2 Initial wear The running-in phase is typically characterised by a distinctly higher wear rate. Both the duration of this phase and the magnitude of the wear depend on the specific loading conditions and may vary significantly between different tribological systems. During the running-in process, smoothing of rough surface regions and adaptation of the macro-geometry take place. As a result, the corresponding load distribution can be approximated iteratively. According to [S2], a modified calculation based on Equation (15) is introduced to determine the linear wear depth during the running-in phase, h VE (tooth thickness reduction). This extension of Equation (14) incorporates, in addition to the previously defined parameters, the running-in time t VE (10 min to 40 min), the rotational speed n, and a dimensionless correction factor f VE (range: 10 2 to 10 4 ) to account for the increased wear rate resulting from the lower effective wear energy density: (15) Here too, the linear wear depth h VE (tooth thickness reduction) in the running-in phase is to be determined separately for the shaft tooth and the hub tooth. R = R ∙ g = ∙ N ∙ g = V ∙ V = V ∙ 0 ∙ ℎ V H = V ℎ V , i = i ∙ N , i ∙ g V ∙ 0 , i ℎ VE , i = VE ∙ i ∙ N , i ∙ g ∙ ∙ VE V ∙ 0 , i Science and Research 24 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 Thus the wear energy density can be determined from the physical and mechanical material properties, the shear resistance, the hysteresis coefficient and the loading. The remaining quantities are defined as follows: (5) (6) (7) (8) (9) with: Young’s modulus E, Poisson’s ratio ν, and flank contact pressure σ Fl . The energy-based wear fundamental equation [F1] relates the wear energy density e V and the linear wear intensity I h via the frictional shear stress τ R : (10) Note that the calculation of the wear energy density e V and of the linear wear intensity I h must be carried out separately for each of the two contacting bodies. 5 Wear prediction calculation It should be noted that the present calculation refers exclusively to the low-wear stage and does not account for the subsequent progressive high-wear stage. Initial wear can, in practice, be quantified; however, it results from several superimposed wear mechanisms, making an unambiguous attribution of the causes impracticable. The Archard wear model [A1, A2], given in Equation (11), describes the volumetric wear V V as a function of the normal force F N , the sliding distance s g , and the wear coefficient k. Depending on the model variant, the hardness H of the material is either explicitly included in the denominator of Equation (11) or already incorporated within the wear coefficient k H . The ranges of k or k H vary considerably with the underlying tribological system and must be established by means of experimental investigation. (11) red = 1 1 − 12 1 + 1 − 22 2 1 = 0,12 ∙ 16 �2∙ 5 � 2,6 � −5 4� = 1,5 ∙ � 4 ∙ ( 1 − − 2 ) + ( 1 − 2 ∙ ) 2 2 = − Fl ∙ H 1,45 ∙ red 0 = Fl 2 ∙ H 2,1 ∙ red ℎ = = ∙ Fl V = ∙ N ∙ g = H ∙ N ∙ g 5.3 Wear compensation calculation Using Equations (14) and (15) to determine the linear wear depth in the low-wear stage as well as during the running-in phase, an iterative wear compensation calculation can be performed. For each tooth pair, the linear material loss is successively added to the existing single pitch deviations, and on this basis, the resulting load distribution is recalculated iteratively. This process is first carried out for the running-in phase, followed by the operational wear in the low-wear stage. To adequately represent the running-in dynamics, five to ten iterations are usually sufficient. Running-in wear leads, on the one hand, to a reduction in tooth thickness and thus to a change in gear stiffness, and, on the other hand, compensates for pitch errors. Both effects improve the load distribution and consequently reduce flank pressure. Furthermore, according to [D1, K3], the compensation of pitch errors through running-in wear improves gear quality by one to two tolerance grades. Similar mechanisms apply to operational wear, although with significantly less impact than during the running-in phase. Figure 2 illustrates the normalised flank pressure distributions for two different types of misalignment-tolerant spline teeth. Figure 2a shows the results for a gear coupling with a tooth profile according to DIN ISO 21771 (analogous to a running gear profile). In this case, the tall and slender tooth profile provides high compliance, enabling pitch errors along the tooth circumference to be compensated and ensuring an even load distribution across all tooth pairs. The maximum flank pressure remains comparatively low even when individual pitch deviations are taken into account. Figure 2b presents the pressure distributions for a spline connection with a tooth profile according to DIN 5480. The short and stiff tooth profile leads to a more pronounced load concentration. This imbalance causes increased running-in wear in the initial stage. As a result of the running-in wear, the tooth flanks adapt to the actual load, increasing the number of load-carrying tooth pairs from 21 to 24. Consequently, the maximum pressure decreases to about 68 % of its original value, and the load distribution becomes noticeably more uniform. In the gear coupling, running-in wear is less pronounced, as all available tooth pairs are already involved in load sharing before the running-in phase. As a result, flank pressure is reduced to around 94 % of the initial value. This confirms, from a computational standpoint, that running-in wear achieves a compensation of pitch errors equivalent to an improvement in gear quality by one to two tolerance grades, as described in [D1, K3]. 5.4 Wear-related service life prediction The wear-related service life can be determined directly from the maximum permissible linear wear depth h V,zul , the applied loads, the wear energy density e V , and a sta- Science and Research 25 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 Figure 2: Normalised flank pressure distribution of the splines with module m = 2 mm, number of teeth z = 24, crowned circle radius r B = 1200 mm, angular misalignment ε = 0.07°, torque T = 1700 Nm, and quality grades 8 (shaft) and 10 (hub). Tooth profile according to: a) DIN ISO 21771; b) DIN 5480. The shaft and hub materials employed were 18CrNi- Mo7 - 6 and 42CrMo4, respectively. A closed-loop oil circulation system, equipped with filtration and temperature monitoring, ensured consistent and reproducible lubrication conditions. Three lubricants of identical viscosity were tested: a mineral oil, a polyalphaolefin, and an ester-based oil. The experimental objectives encompassed the verification of load-bearing capacity criteria related to pitting and scoring resistance, as well as the determination of safe threshold values for flank pressure and mixed friction regimes. Furthermore, the influence of pressure overlap on lubricant supply and resultant wear was investigated, supplementary load-bearing criteria were identified, and the predicted linear wear depth in the low-wear stage was validated. Additional studies addressed the impact of lubricant type, maintaining constant viscosity, and facilitated the classification of observed wear mechanisms. 6.1 Results of experimental investigations and wear prediction calculations The test points were selected to encompass a broad spectrum of flank pressure, specific frictional power, and sliding velocity, as illustrated in Figure 3. A region characterised by pronounced low-wear stage was utilised for the direct validation of the model predictions. Test specimens exhibiting consistent mild wear and maintaining the low-wear stage were classified as successful runs, whereas specimens without a low-wear stage or showing signs of scoring, pitting, and flank breakouts were categorised as failures. Science and Research 26 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 tistical correction factor. In the basic formula presented in [F4]: (16) the proportion of frictional energy α 1,2 is explicitly specified, and the maximum sliding velocity v g,max is used. As shown in [S2], α 1,2 may be omitted if e V is determined using Equation (4) and v g,max is replaced by the sliding distance per revolution s g and the rotational speed n. This yields the service life L h , which is to be calculated separately for each counterbody (shaft or hub): (17) with: quantile C x (for 90 % survival probability = -1.28; for 50 % = 0), coefficient of variation C v (range for steel-steel pairings: 0.1 to 0.6). 6 Experimental investigations The validation of the wear prediction model was conducted on a machining test rig designed in accordance with DIN 51354, featuring a maximum torsional moment of 1750 Nm, a maximum rotational speed of 1500 min −1 , and a deflection angle capability of up to 2°. The setup comprises two test shafts, each equipped with two independently adjustable gearing sequences, enabling the simultaneous evaluation of four distinct geometry configurations per test cycle. Deflection angles are precisely controlled by a mechanical adjustment mechanism. h = 10 −3 ∙ V ∙ �ℎ V , zul − ℎ VE � R ∙ g ∙ ∙ ( 1 − x ∙ v ) ∙ 60 + VE = V ∙ �ℎ V , zul − ℎ VE � 3600 ∙ 1 , 2 ∙ R ∙ � g , max � ∙ ( 1 − x ∙ v ) + VE h Figure 3: Results of the experimental investigations. The normalised experimental results for the linear wear depth, presented in Figure 4, demonstrate the high accuracy of the computational models introduced in Sections 4 and 5. For enhanced comparability, all measured values were normalised to the respective maximum wear depth. Deviations of up to 9 % were observed under very high flank pressures in the range of 500 N/ mm 2 to 916 N/ mm 2 , which is considered acceptable given the extreme load conditions. For flank pressures typically encountered in practical applications, up to 500 N/ mm 2 , the discrepancy between experimental data and model predictions is 6 % or less, thereby confirming the excellent predictive capability of the wear prognosis calculation. The parameters utilised for the wear prediction calculations are listed in Table 1. 6.2 Effects of pressure overlap The pressure overlap factor λ σ is a key parameter characterising the lubrication condition in the tooth contact. It describes the ratio between the Hertzian contact width 2a and the contact path length s k along the tooth flank, thereby providing information on lubricant supply and the development of the hydrodynamic lubricating film. If λ σ < 1.0, the contact path fully covers the contact width, which promotes the formation of a load-bearing lubricating film. For λ σ > 1.0, an overlap of contact regions occurs, potentially impairing lubricant supply. Under such conditions, both material stress and adhesion tendencies increase, leading to local mixed or boundary lubrication regimes that promote scuffing. The characteristic W-shaped wear profile appears at λ σ < 1, with the highest wear located at the reversal point of the contact motion, as shown in Figure 5a. At these reversal points, the lubricating film is absent, resulting in solid contact with abrupt transitions between static and sliding friction. Even at low sliding speeds below approximately 100 mm/ s, scuffing initiates due to micro-welds producing rough particles that accelerate wear. At elevated temperatures above approximately 150 °C, scuffing may also occur, causing severe damage to the tooth flanks. If λ σ > 1.0, a U-shaped wear profile develops, as illustrated in Figure 5b. A permanent region of the tooth flanks remains in continuous contact, which restricts lubricant supply and only permits a limited lubricating film. Mixed Science and Research 27 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 Figure 4: Comparison of normalised linear wear depth h V in the low-wear stage between calculated predictions and experimental results. Material 18CrNiMo7-6 750 0,02 7,93 0,20 18CrNiMo7-6 (case-hardened) 1150 0,02 7,90 0,24 42CrMo4 800 0,02 8,04 0,20 42CrMo4 (nitrided) 1000 0,02 8,00 0,22 Table 1: Parameters used for the wear prediction calculations. Figure 6. Despite differing wear profiles (U-shaped vs. W-shaped), the values of wear energy density and linear wear intensity within the respective low-wear stages fall within the same range. 6.4 Wear phenomena and damage patterns The following section describes and characterises the wear mechanisms and associated damage patterns observed on the test rig. The results correspond closely to those reported from field tests. Science and Research 28 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 friction alternates with areas of intensified solid contact, and the maximum wear is concentrated in the overlap zone. Scuffing also occurs here, as the material surface is subjected to persistently high shear and adhesion forces. 6.3 Wear energy density and linear wear intensity The experimental results reveal distinct running-in and operational regions for the wear energy density e V and the corresponding linear wear intensity I h , as shown in Figure 5: Wear profile as a function of the pressure overlap factor: a) λ σ < 1.0, b) λ σ > 1.0. Figure 6: Ranges of wear energy density e V and linear wear intensity I h for the running-in and operational regions (low-wear stage). • Scoring: Linear grooves oriented along the sliding direction over the tooth width. They result from abrasive loading when asperities of the harder partner, hardened wear particles, or hard foreign particles penetrate the softer contact partner. These grooves are often superimposed with local plastic indentations. • Indentations: Appear as shallow depressions frequently surrounded by ring-shaped material buildup at their edges. They arise from the impact of flat particles (contaminants or wear debris) that do not embed into the substrate. Indentations often coincide with scoring and are difficult to detect macroscopically; thus, SEM or optical microscopy is recommended for reliable identification. • Scuffing: Characterised by sharply defined material tears bordered by fine scoring patterns. It occurs under insufficient lubrication and high flank pressures when welding of contact points happens and subsequent sliding causes material removal. • Pitting: Small, circular depressions formed by particle accumulation on the contact surface combined with minor relative motion. They are frequently accompanied by plastic deformation or scoring at their edges due to locally elevated contact pressures. • Scars, dimples, ripples (vibrational wear): Manifest in three closely related forms: scars (associated with irregular vibration amplitude), dimples (from twodimensional oscillation), and ripples (from one-dimensional oscillation). Common features include local accumulation of wear debris resulting in irregular surface patches, circular depressions, or periodic transverse structures. Transitions and mixed forms among these types are frequently observed. • Shear cracks: Linear microcracks oriented transverse to the sliding direction, sometimes branching. They develop when the local shear strength of the material is exceeded due to pointwise overload and are mainly found near scuffing sites or scuffing grooves. • Surface fragmentation: Under oscillatory motion with small deflection angles, fine crack networks and severely notch-inducing fragmentation occur. The combination of high local stresses and insufficient debris removal leads to a rugged surface topography often accompanied by abrasive marks. • Worm tracks: Appear as elongated breakouts perpendicular to the sliding direction, often displaying characteristic discoloration. They result from adhesive welding at elevated temperatures and insufficient lubrication, where repeated sliding tears local welds and fatigue progressively forms breakout structures. Microstructural analyses often reveal tribo-martensite and temperature peaks up to approximately 800 °C. • Profile alteration: If wear progresses continuously after the running-in phase, macroscopic steps and material buildup form on the tooth profile. This wear progression exceeds permissible profile tolerances and may ultimately lead to plastic deformation or tooth fracture. Countermeasures generally include: (a) optimisation of lubricant selection (CLP oils with EP additives, high viscosity), (b) minimisation of lubrication deficiencies and particle contamination, (c) use of appropriate materials and heat treatments (nitriding, case hardening), (d) reduction of contact pressures and vibration amplitudes, and (e) avoidance of steel-on-steel contact via surface coatings. In summary, a combination of design measures and appropriate lubrication has proven to be an effective approach to counteract the complex and superimposed wear mechanisms in misalignment-tolerant spline couplings. 7 Conclusions The presented results demonstrate that the combined model of Archard, Kragelski, and Fleischer provides a reliable prediction of linear wear depth even under varying contact conditions, thereby offering a robust basis for design modifications and service life optimisation. The model was validated for flank pressures up to 900 N/ mm 2 and commonly used lubricants. Mean deviations between simulation and experimental data are 6 % for flank pressures up to 500 N/ mm 2 and 9 % up to 900 N/ mm 2 . Future work will focus on investigating additional lubricant types and viscosities as well as alternative material pairings. The integration of real-time data from condition monitoring systems could further enhance the model’s accuracy. In conclusion, the combined model delivers a dependable approach for the early quantification of linear wear depth and makes a valuable contribution to the structural optimisation of displaceable spline couplings. Literature [A1] J. F. Archard: Contact and Rubbing of Flat Surfaces. Journal of Applied Physics, 24 (8), 1953, S. 981-988. https: / / doi.org/ 10.1063/ 1.1721448 [A2] J. F. Archard, W. Hirst: The wear of metals under unlubricated conditions. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 236 (1206), 1956, S. 397-410. https: / / doi.org/ 10.1098/ rspa.1956.0144 [B1] Benkler, H.: Der Mechanismus der Lastverteilung an bogenverzahnten Zahnkupplungen. Diss., TH Darmstadt, 1970. [B2] Bünder, C.: Analyse der Beanspruchungen der Verzahnungen von Zahnkupplungen. Diss., TU Dresden, 2000. Science and Research 29 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 [K1] I. W. Kragelski: Reibung und Verschleiss. VEB Verlag Technik Berlin, 1968. [K2] I. W. Kragelski, G. Fleischer, W. S. Kombalov, U. Winkelmann: Vereinigung der Ermüdungstheorie und des energetischen Ansatzes zur Berechnung des Verschleißes. Schmierungstechnik, 10 (5), 1979, S. 132-136. ISSN 0036-6226 [K3] Kollmann, F. G.: Welle-Nabe-Verbindungen - Gestaltung, Auslegung, Auswahl. Springer-Verlag, Berlin Heidelberg New York, 1984. ISBN 3-540-12215-X [N1] Neugebauer, H.: Verzahnungsbeanspruchbarkeit. FVA Forschungsvorhaben Nr. 307/ II, FVA-Heft 712, Frankfurt a. M., 2003. [P1] Pries, M.: Geometrie und Kinematik von Bogenzahnkupplungen. Diss., TU Dresden, 1991. [S1] Strauß, E.: Einsatzgrenzen und Einlaufverhalten von nichtgehärteten Zahnkupplungen. Diss., TH Darmstadt, 1984. [S2] Spura, C.: Tragfähigkeitsberechnung und Verschleißanalyse von bombierten Zahnwellenverbindungen. Dissertation, RWTH Aachen, 2012. Science and Research 30 Tribologie + Schmierungstechnik · volume 72 · issue 3-4/ 2025 DOI 10.24053/ TuS-2025-0015 [D1] Dietz, P.: Die Berechnung von Zahn- und Keilwellenverbindungen. Erschienen im Selbstverlag des Verfassers, Büttelborn, 1978. [F1] G. Fleischer: Energetische Methode der Bestimmung des Verschleißes. Schmierungstechnik, 4 (9), 1973, S. 269- 274. ISSN 0036-6226 [F2] G. Fleischer: Energiebilanzierung der Festkörperreibung als Grundlage zur energetischen Verschleißberechnung. Teil 1: Schmierungstechnik, 7 (8), 1976, S. 225-230, Teil 2: Schmierungstechnik, 7 (9), 1976, S. 271-279, Teil 3: Schmierungstechnik, 8 (2), 1977, S. 49-58. ISSN 0036-6226 [F3] Fleischer, G.: 40 Jahre Bewertung von Reibung und Verschleiß mit Hilfe der Energiedichte. Tribologie und Schmierungstechnik, 51. Jahrgang, 3/ 2004, S. 5-11. ISSN 0036-6218 [F4] Fleischer, G.: Bereitstellung tribologischer Kennwerte von Reibpaarungen zur Beurteilung und Prognose der Lebensdauer. Schmierungstechnik, 12 (1981) 8, S. 233- 235. ISSN 0036-6218 [H1] Heinz, R.: Untersuchung der Kraft- und Reibungsverhältnisse in Zahnkupplungen für grosse Leistungen. Diss., TH Darmstadt, 1977.