Virtual testing of a technical product with respect to its acoustic behavior enables engineers to evaluate the design without the need for physical prototypes. In order to virtually test the acoustic behavior, the effects of both, the dynamic excitations of the system and the transfer behavior of sound from the excitation source to the user must be considered in simulation models. The transfer path is primarily influenced by resonance frequencies and damping. In structures connected via bolted joints, damping within the joint is the dominant source of damping along the transfer path. Therefore, appropriate structural dynamic models of bolted joint stiffness and damping are necessary. These models must represent both the normal and tangential stiffness and damping in bolted joints. Currently, experimental investigations are still required for the parameterization of bolted joint models. As an example, for the normal behavior, optical 3D measurements of the joint surfaces are conducted to obtain their topology. The surface topology is then used to identify parameters of an exponential contact law through elasto-plastic material modeling. To eliminate the need for complex measurements during model parameterization, this article presents a method for predicting the normal contact stiffness in bolted joints based on numerically generated surfaces. For this purpose, an algorithm is implemented to generate surfaces with different roughness properties. Based on these surfaces, the exponential contact law through elasto-plastic material modeling is performed. This calculation is used to determine the contact stiffness at different pressures. A Design of Experiments is conducted in which the surface roughness is varied to calculate the normal contact stiffness. Therefore, the surface parameters SA, Ssk and Sku are varied. SA describes the average roughness and thus the size of the real contact area, Ssk characterizes the asymmetry of the height distribution and provides information on load-bearing peaks or valleys, and Sku quantifies the sharpness of the distribution and thus the proportion of peaks. These properties significantly determine the microscopic deformation at the contact and therefore directly affect the stiffness and damping values of bolted joints. The resulting normal contact stiffness values are then used to create a regression model. This makes it possible, for the first time, to derive normal contact stiffness values for different surface roughnesses without performing any physical measurements. The normal contact stiffness values calculated from the regression model are used to parameterize a structural dynamic finite element model of the Brake-Reuß-Beam bolted structure. The model predicts the eigenfrequencies with a deviation of about 1.9
This paper presents a novel robust multi-objective optimization method for helical gear sets in electric vehicle (EV) transmissions. The method simultaneously addresses the conflicting objectives of gear mesh excitation and efficiency while satisfying durability constraints and meeting the accelerated time-to-market demands of modern development processes. The proposed framework employs a synergy of techniques: a high-fidelity simulation model to capture the influence of manufacturing tolerances via a robustness metric on gear performance and an adapted, surrogate-model-based Non-dominated Sorting Genetic Algorithm-II (NSGA-II) for optimization in conjunction with adaptive sampling. The paper demonstrates the effectiveness of this method through its application to the first stage of an electric vehicle transmission. The benefits of informed decision-making for both macro- and micro-geometric parameters are showcased by identifying Pareto-optimal solutions that balance NVH and efficiency in compliance with reliability requirements across the entire torque range while accounting for manufacturing variations within specified tolerances. This framework enables the design of quieter, more efficient, and reliable gear sets for EV transmissions.
Knurled interference fits (KIFs) are force- and form-locking shaft-hub connections whose torque transmission capacity results from the contact surface generated during joining of a knurled component and the softer, oversized counter body. In inner-knurled interference fits (IKIFs), the profile of the oversized shaft is formed by the knurled hub. Despite the high power density and compact design of the joint, there are currently no reliable, universally applicable design criteria for ensuring structural integrity, which limits their industrial application. This article therefore investigates the structural integrity of IKIFs under cyclic torsional loading in order to establish a correlation between the shape of the joint, the type of failure and the location of failure. Considering the residual stress states and the forming history in the calibrated finite element model, the suitability of a local verification at the expected location of damage is validated.
This study investigates the incorporation of 2D materials as solid lubricant filler, particularly MoS2 (in particle sizes of 1.5 and 12.5 μm), WS2, and Ti3C2Tx MXenes, into polylactic acid (PLA) for mechanically and tribologically enhanced polymer matrix composites (PMC) using a simplified feedstock preparation method. Thereby, dry powder-pellet mixing process followed by Fused Granular Fabrication (FGF) is employed to avoid filament extrusion, aiming for scalable and thermally efficient production. All reinforced samples exhibit improved tensile strength and hardness, attributed primarily to enhanced interlayer adhesion from improved processability. Tribological performance is filler-specific: MXene and fine MoS2 achieve substantial reductions in coefficient of friction (up to 30
In the design of gearboxes, gears without manufacturing deviations are usually assumed. Due to deviations in the manufacturing of individual components, the real, tolerance-affected system no longer corresponds to the idealized system of the design. As a result, the actual characteristics differ from the calculated target properties. Within the framework of the BMWE-funded research project Opt4E, the influence of manufacturing deviations on gearbox characteristics in terms of load capacity, efficiency, and dynamic behavior is systematically analyzed. A full factorial simulation or a meaningful analysis using design and analysis of computer experiments (DACE) methods across all tolerance bands is usually not feasible due to the exponential increase in required simulation runs with expanding tolerance dimensions and ranges. Therefore, alternative approaches are to be explored. Underlying simulations are carried out in the first step using the loaded tooth contact analysis (LTCA) program RIKOR of the research association for drive technology (FVA). These initial calculation results are subject to a global sensitivity analysis (GSA), which can determine the relevance of individual influencing factors and their interactions within the defined parameter space. The analysis identifies the dominant deviations for each performance indicator at a moderate vehicle speed, assuming uniform load sharing across the active tooth pairs. Load-carrying capacity is significantly influenced by bearing misalignments (v-direction, pinion) and helix slope deviations, while efficiency is mainly influenced by profile slope deviations. In terms of NVH behavior, bearing misalignments (v-direction, pinion) and flank twist are dominant deviations. These results of the sensitivity analysis form the basis for further investigations.
Press-fit connections are widely used shaft-hub connections in gearbox design. Rising power density and cost-efficiency requirements necessitate improved utilisation of load-bearing capacity in critical shaft regions. Deep rolling offers an effective means to introduce beneficial residual stresses and enhance fatigue strength while being easily integrated into manufacturing processes. Designing deep rolled shafts commonly relies on integral approaches such as DIN 743 or the FKM guideline, which model strengthening through the surface hardening factor KV. Differentiated approaches, particularly the FVA guideline, incorporate the actual residual stress state and therefore promise higher predictive accuracy. This study evaluates these concepts through extensive experiments on deep rolled press-fit connections with and without undercuts under rotating bending, cyclic torsion, and rotating bending with superimposed quasi-static torsion. The results show notable discrepancies between the calculation methods. The FVA guideline provides the most accurate predictions of component fatigue safety, whereas integral concepts exhibit systematic deviations due to their insufficient consideration of axial residual stresses—identified as the primary mechanism driving strength increases. Moreover, torsional loading yields significantly lower strengthening potential than rotating bending, reflecting the different effectiveness of residual stresses in the critical cross-section. The findings demonstrate the advantages of differentiated approaches for assessing deep rolled press-fit connections and provide a robust experimental basis and supporting simulation models for improving future fatigue design methodologies.
This paper investigates the influence of the roller geometry and the manufacturing tolerances on the wear behavior of a short and wide flat-belt conveyor with three rollers, using the frictional power density as a qualitative wear indicator. Previous studies mainly focus on overall belt dynamics and wear with ideal cylindrical rollers. This work emphasizes the effect of geometric deviations arising from manufacturing or intentional shaping. Building upon an existing lumped mass model of the belt and a visualization approach of the frictional power density, the model is extended by a deflection-based roller geometry that enables the analysis of concave and convex roller profiles. The study reveals that small deviations from an ideal cylindrical roller significantly influence the distribution of frictional power density across the belt width. Convex roller geometries particularly increase edge wear, while concave rollers reduce it up to a certain point before it rises again. For the investigated three-roller system, the authors therefore propose a slightly concave roller geometry with a narrow tolerance band as a pragmatic trade-off between reduced frictional power density and belt-run stability, the latter being a known effect of concave roller geometries. These insights enhance the understanding of how geometric tolerances affect belt deformation and wear behavior. They establish a consistent framework for deriving design guidelines and conducting future parameter studies involving belt tension, speed, and alternative roller geometries.
Adaptive systems in engineering adjust their properties in response to changing conditions such as load, temperature, or speed. Many existing implementations achieve adaptability through mechatronic systems incorporating actuators, sensors, and control systems, which often result in increased complexity, weight, and reduced robustness. To overcome these drawbacks, systems are increasingly explored that achieve adaptability solely through their structural design and material behavior. In this work, the term ‘self-adaptive’ is used for these systems to highlight that adaptation emerges inherently from the properties of the structural elements themselves, without any external control. This leads to simpler, lighter, and more robust solutions. This review focuses on the principles and applications of self-adaptive design and machine elements, such as bearings, seals, couplings, springs, dampers, housings, gears and shafts. A classification of design elements will be presented, along with an explanation of self-adaptivity principles. Additionally, an overview of the state of the art for specific design elements will be provided, followed by current and future research directions.
The FKM guideline [1] provides a robust framework for numerical fatigue assessment, ensuring component safety against fatigue failure. Its accuracy depends critically on the underlying input parameters and their interactions. In practice, the parameters are subject to a high degree of uncertainty. Global sensitivity analysis offers a rigorous, variance-based approach to quantify the influence of individual parameters and their interactions on the output of a model. This work proposes a workflow for numerical fatigue assessment under uncertainty. The workflow integrates a latent variable Gaussian process (LVGP) surrogate that simultaneously captures the effects of continuous FKM parameters, such as the ultimate tensile strength (Rm), and the categorical influence of mesh refinement strategies. Finally, a Sobol sensitivity analysis is applied to the trained surrogate to quantify the contribution of each parameter to the variance in the utilization of the components. The methodology is demonstrated in three representative case studies, each using a different material and component. The resulting sensitivity rankings highlight the dominant role of material strength and mean stress effects under different loading ratios on the durability of components. Additionally, the results indicate that, within practical bounds, mesh discretization has a minimal impact on numerical fatigue assessment. The findings offer valuable insights for both uncertainty quantification and optimization of experimental campaigns in fatigue design, and they underscore the potential of mixed-variable surrogate-based sensitivity analysis in engineering practice.
Disturbance factors from the use context of sensory functions can have a significant impact on the reliability of the measurement data provided. To prevent costly and time-consuming iterations due to insufficient robustness in their development, a methodology for analysis and synthesis of robust sensory functions is presented. The methodology enables the systematic and comprehensive identification of critical disturbance factors and their subsequent consideration by means of suitable measures based on established approaches from Robust Design and Measurement Engineering. In the analysis part of the methodology, disturbance factors are first identified by systematically analyzing the use context of the sensory function with a disturbance factor matrix. The identified disturbance factors are then analyzed and selected in regard of their impact on the sensory function. Therefore, an abstraction on the level of physical effects is carried out. The identified disturbance factors are then evaluated in regard of their severity and significance in a modified FMEA. Based on the evaluation results, a reasoned and objective decision regarding the criticality of disturbance factors and their respective impacts on a sensory function is drawn. In the subsequent synthesis part of the methodology, measures for consideration of critical disturbance factors are first developed systematically and comprehensively. Therefore, a flow chart is used. The developed measures are then evaluated using a utility analysis and a standardized evaluation target system. Based on the evaluations results, a reasoned decision regarding the measures to be implemented is drawn. To facilitate the application of the methodology, an existing effect graph tool is taken up and functionally extended. Finally, the effectiveness of the methodology is experimentally verified using the example of an inventive sensory function for radial offset and rotational frequency measurement of a disk pack coupling. Furthermore, a user study is conducted to assess the methodology’s efficiency and usability.
The causes of hub fracture of the sun gear in the planetary gear transmission system were analyzed through chemical composition, mechanical properties, macroscopic characteristics, microscopic structure, simulation and experimental methods. Due to the low nickel content in the gear material, the absence of fillet at the root of the internal spline teeth, and the thickness of the thin hub (which led to severe stress concentration), fatigue cracks began to form in the stress-concentrated area of the internal spline teeth root. The fatigue fracture of the sun gear hub is caused by the initiation of fatigue cracks at the root of the spline teeth under cyclic bending and torsional loads and their propagation along the thickness direction of the thin-rimmed hub. The fundamental reasons for its failure are gear materials with inadequate chemical composition, excessive stress concentration and overly thin hubs. Improvement measures for preventing and avoiding fatigue failure of the sun gear were proposed. A simulation analysis model for the strength of the planetary transmission sun gear was established, and fatigue tests before and after structural improvement were carried out, good consistency was achieved with the on-site fatigue crack initiation and propagation path. After the improvement, the fatigue strength and service life of the sun gear were significantly enhanced.
Rolling element bearings are critical components in aerospace, automotive, renewable energy, and precision manufacturing systems, where performance and reliability are strongly governed by the surface quality of raceways. Even minor irregularities such as grinding marks or waviness compromise elastohydrodynamic lubrication, increase friction, accelerate wear, and initiate rolling contact fatigue cracks. Conventional finishing methods like grinding, honing, lapping, and superfinishing improve surfaces to some extent but remain limited to sub-micrometer finishes and often introduce tensile residual stresses or embedded abrasives. In this study, hardened SAE 52100 steel bearing races were subjected to magnetorheological (MR) nano-finishing to evaluate its capability for producing ultra-smooth surfaces and enhancing functional performance. Experimental results demonstrated a dramatic reduction in surface roughness from 0.20 µm Ra in ground races to below 0.015 µm, representing a > 92
Der vorliegende Beitrag umfasst die Untersuchung und Simulation des Einflusses von Pressverbänden auf das Anregungsverhalten und die Zahnfußspannung von schrägverzahnten Stirnrädern mit kegelförmiger und zylindrischer Pressverbandgeometrie. Voruntersuchungen zeigten einen Einfluss des Pressverbands auf die Zahnfußspannungen und die Zahnflankengeometrie in Form einer Profillinien-Winkelabweichung. Die Beanspruchung im Zahnfuß gefügter Stirnräder umfasst neben den Spannungen resultierend aus der Belastung der Verzahnung ebenfalls die durch den Pressverband induzierte Spannung. Hierbei hat die Gestaltung der Radkörpergeometrie einen Einfluss auf den resultierenden Spannungszustand im Zahnfuß gefügter Stirnräder. Den genormten Berechnungsverfahren werden vereinfacht tendenziell steife Radkränze zugrunde gelegt, ohne die komplexe Geometrie des Radkranzes und steifigkeitsverändernde Randeffekte zu berücksichtigen. Das Leichtbaupotenzial und die Leistungsdichte gefügter Zahnräder werden aufgrund fehlender Berücksichtigung beliebiger Pressverbandgeometrien auf die Zahnbelastung unzureichend ausgeschöpft. Um diese Modellierungslücke zu schließen, wird eine Finite-Elemente-Berechnungsmethodik entwickelt, die den Einfluss dünnwandiger, geometrisch flexibler Querpressverbände auf die Zahnbelastung abbildet. Der Fokus der Methode liegt auf der Erfassung der Zahnfußspannung unter Berücksichtigung des Pressverbandeinflusses mit freien Radkörpergeometrien. Mit der Berechnungsmethode wird neben dem Einsatzverhalten gefügter Stirnräder zudem die Mikrogeometrieänderung der Zahnflanke infolge des Pressverbandes realitätsnah abgebildet.
This study presents a comprehensive analysis of the size effect on the bending fatigue strength of gears with a normal module below 5 mm, focusing on both case-carburized and nitrided variants. While the size effect in case-carburized gears has been extensively investigated and quantified through empirical studies, the corresponding data for nitrided gears remain limited. By aggregating and evaluating experimental results from various sources, this work identifies trends in size-dependent fatigue performance and compares them to general mechanical size effect models. The findings reveal that current standards, such as ISO 6336, underestimate the fatigue strength of small-sized gears. The study highlights the need for a distinct and reliable size factor also for nitrided gears to fully exploit their load-carrying potential in modern engineering applications.
Epicyclic gear trains are widely used in modern automatic transmissions due to their compactness, high power density, and ability to provide multiple speed ratios. Among compound planetary systems, Lepelletier gear trains offer an efficient architecture for achieving multiple forward and reverse gears with reduced structural complexity. However, their design remains a challenging multi-objective problem involving strict geometric feasibility, compactness, manufacturing simplicity, and high kinematic accuracy. This study presents a Pareto-based multi-objective framework for the constraint-driven synthesis of a Lepelletier multi-speed transmission. Symbolic expressions for velocity ratios are derived by decomposing the transmission into fundamental gear entities, ensuring exact kinematic representation under all coupling conditions. These formulations are integrated into a multi-objective genetic algorithm (MOGA) to determine discrete gear tooth numbers that satisfy predefined target ratios while enforcing geometric, angular, and structural constraints. The method generates a set of feasible integer solutions forming a Pareto front that captures the trade-off between ratio accuracy and structural complexity. Since multiple solutions can satisfy the same kinematic requirements, selection is performed based on engineering criteria including minimal ratio deviation, compactness, and smooth ratio progression. Accordingly, the proposed framework focuses on identifying and selecting feasible discrete configurations rather than quantifying improvement relative to a predefined baseline design. The selected configuration achieves eleven forward and one reverse operating modes with high accuracy and consistent ratio distribution. The obtained results confirm that the synthesized configurations achieve a very close agreement with the predefined target velocity ratios, with minimal deviation across all operating modes, demonstrating the effectiveness of the proposed constraint-driven synthesis approach. Integer refinement confirms the stability of the solution and convergence toward a discrete optimum. The results demonstrate that the proposed framework operates as a design-oriented synthesis tool, enabling systematic identification and selection of feasible Lepelletier transmission configurations under strict design constraints.
Vibroacoustic Metamaterials (VAMM) are composed of periodically arranged unit cells, each consisting of a section of the base structure and a resonator. The virtual negative stiffnesses or masses resulting from the local resonance effect create a stop band in which no free wave propagation is possible. This stop band can be tuned in terms of its bandwidth, amplitude reduction, and position in the frequency range by adjusting the properties of the resonators. Metamaterials are often manufactured using 3D printing processes. However, for the production of large quantities, other manufacturing methods are required. Stamping, laser cutting, or waterjet cutting are common mass-production-compatible processes for producing sheet structures and are also suitable for manufacturing VAMM. Therefore, this contribution presents various unit cell designs that can be manufactured using the aforementioned processes and describes their advantages and disadvantages. For example, some designs allow the integration of multiple resonances into a single unit cell within the relevant frequency range, leading to multiple or wider stop bands. The potential of sheet-based VAMM is demonstrated on a grinding machine stand, an inverter cover of an electric drive, and a sound-absorbing noise barrier and a saw blade. Vibration reductions of up to 20 dB are achieved.
Digital twins offer significant potential for optimizing engineering processes, yet their application across industries remains uneven. This study combines a PRISMA-guided publication-based literature review with an expert survey to analyze the current use and perceived potential of digital twin technologies. The literature review consists of two parts: the first provides a normative analysis of definitions and conceptual distinctions between digital twins and simulations based on international standards and foundational literature; the second applies a PRISMA-based screening and analysis of peer-reviewed publications to examine modeling approaches, interaction concepts, and application contexts. While conceptual distinctions between simulations and digital twins are well established in standards and prior research, a clear research gap remains regarding their process-related role within engineering development workflows and their perceived relevance in industrial practice. To address this gap, a total of 56 professionals from sectors such as automotive, IT, and research participated in an online survey. The survey investigates the opportunities and challenges associated with implementing digital twins in various industrial domains in the region of southern Germany. In addition to the empirical analysis, the paper provides a process-oriented classification of simulations, virtual testing, and digital twins along the V‑Model, building on established definitions rather than proposing a new conceptual distinction. Although the data indicate strong future interest, barriers such as limited user experience and implementation costs remain. By linking a structured state-of-the-art analysis with practitioner perceptions, the study contributes a process-oriented perspective on digital twins that connects existing definitions with their practical adoption.
As a crucial mechanical fastener, nuts are widely employed in various engineering applications, including mechanical equipment, building structures, transportation systems, and other related fields. However, conventional nuts exhibit an uneven load distribution among the threads under external forces, resulting in significant stress concentration at the thread roots, which adversely affects their load-bearing capacity and fatigue life. To improve the stress state at the thread root, this study addresses the issue of load uniformity in suspension nuts subjected to dynamic loading by proposing a parameter optimization method based on a combination of Genetic Algorithm and finite element co-simulation. With uniform load distribution as the optimization objective, a mathematical model is established with maximum equivalent stress and deformation as constraints, and the genetic algorithm is employed for the optimization process. The optimized results are validated through static simulations using ANSYS Workbench. The result demonstrates that the maximum stress of the optimized suspension nut represents a decrease of 28.1
Bearing fault diagnosis is critical for the predictive maintenance of industrial equipment. However, existing deep learning methods frequently encounter bottlenecks, such as feature extraction degradation and insufficient generalization capability, when operating under complex working conditions and severe noise interference. To address these issues, this paper proposes a novel dual-branch collaborative fault diagnosis network, termed C‑SwinNet, which integrates a Convolutional Neural Network (CNN) and a Swin Transformer. In the data preprocessing stage, a multi-modal RGB image generation strategy is proposed. By fusing the Continuous Wavelet Transform (CWT), Short-Time Fourier Transform (STFT), and Recurrence Plot (RP), this strategy deeply aligns the physical attributes of time-frequency signals with the channel perception mechanisms of deep vision networks, thereby providing the model with highly efficient, feature-complementary inputs. To overcome the technical challenges associated with architectural fusion and severe noise, C‑SwinNet deeply integrates three core mechanisms. First, to mitigate strong noise interference, the Swin Transformer branch incorporates a Multi-Dimensional Spatial Channel Attention (MDSCA) module, which effectively filters local high-frequency noise and enhances the robust capturing capability of global information. Second, a Fusion Block is designed to achieve rigorous spatial alignment of cross-modal features via pyramid pooling and cross-attention mechanisms, successfully bridging the semantic gap between local details and global contexts. Third, a dynamic routing module, DynamicGLU, is introduced at the terminal stage of the network. Utilizing a three-weight gating mechanism, it adaptively adjusts the collaborative proportion of the dual-branch features based on real-time operating conditions. Comprehensive experiments conducted on five datasets, including CWRU, MFPT, JNU, Ottawa, and a laboratory self-built dataset, demonstrate that C‑SwinNet achieves a macro-averaged accuracy of 98.7 ± 0.5
After the failure of the lubrication system of the helicopter main drive, the spiral bevel gear transmission system will experience normal lubrication and starved-oil lubrication, and finally enter the extreme working state of dry running operation. The time-varying backlash, time-varying friction and time-varying meshing stiffness caused by thermal deformation, wear and elastic deformation between meshing tooth surfaces will directly affect the dynamic characteristics and stability of the transmission system. Therefore, it is necessary to carry out research on the full backlash dynamics of spiral bevel gears considering lubrication change. Firstly, a time-varying full backlash calculation model considering thermal deformation, elastic deformation and wear of spiral bevel gear pair is proposed. Based on the principle of thermoelastic mechanics, Hertz contact theory and Archard wear model, the time-varying full backlash under different lubrication conditions is acquired. Secondly, the friction coefficient between the meshing tooth surfaces of the spiral bevel gear pair under different lubrication conditions is obtained by means of the friction characteristic test, and then the time-varying friction force and friction torque at the meshing point under different lubrication conditions are obtained. Thirdly, a time-varying meshing stiffness model considering elastic contact stiffness, temperature stiffness and oil film stiffness is established. Then, the lumped parameter method is used to establish an 8‑degree-of-freedom nonlinear dynamic model of the spiral bevel gear bending-torsion-axis coupling with time-varying full backlash, time-varying friction and time-varying meshing stiffness. The nonlinear dynamic response of the spiral bevel gear transmission system under different lubrication conditions is solved and analyzed. Finally, the correctness of the dynamic model in this paper is indirectly verified by experiments.
