Search Results (144)

Lubrication plays a crucial role in reducing gear surface damage and defects such as pitting, wear, and scuffing; therefore, analyzing the influence of lubrication is essential for preventing such failures in gear transmission systems. To this end, the dynamic properties of gear systems were examined, leading to the creation of a thermal elastohydrodynamic lubrication (TEHL) model for the line contact of involute spur gears. This model utilizes a multigrid method to calculate the oil film pressure and thickness. Subsequently, models for meshing stiffness, normal oil film stiffness, and overall normal stiffness were developed using energy methods and lubrication theory. Ultimately, a dynamic model of the spur gear system that incorporated lubrication effects was developed to examine how different operating conditions affect dynamic transmission error, vibration velocity, and dynamic meshing force. The findings revealed that when considering the TEHL effect, the dynamic transmission error along the gear meshing line increases, while both the vibration velocity and dynamic meshing force exhibit a decrease. Furthermore, as speed and load intensify, the amplitudes of dynamic transmission error, vibration velocity, and dynamic meshing force also rise. Notably, an increase in the initial viscosity of the lubricating oil correlates with a decrease in the fluctuation of dynamic transmission error, while the variations in vibration velocity and dynamic meshing force remain relatively insignificant. Full article

Gear transmission error (GTE) is a critical factor influencing the performance and service life of gear systems, as it directly contributes to vibration, noise generation, and premature wear. The present study introduces a combined theoretical and experimental approach to characterizing GTE in a single-stage spur gear system. A six-degree-of-freedom nonlinear dynamic model was formulated to capture coupled lateral–torsional vibrations, accounting for gear mesh stiffness, bearing and coupling characteristics, and a harmonic transmission error component representing manufacturing and assembly imperfections. Simulations and experiments were conducted under healthy and eccentricity-faulted conditions, where a controlled 890 g eccentric mass induced misalignment. Frequency domain inspection of faulty gear data showed pronounced sidebands flanking the gear mesh frequency near 200 Hz, as well as harmonics extending from 500 Hz up to 1200 Hz, in contrast with the healthy case dominated by peaks confined to 50–100 Hz. STFT analysis revealed dispersed spectral energy and localized high-intensity regions, reinforcing its role as an effective fault diagnostic tool. Experimental findings aligned with theoretical predictions, demonstrating that the integrated modelling and time–frequency framework is effective for early fault detection and performance evaluation of spur gear systems. Full article

Cylindrical gears are used extensively due to their significant advantages including high efficiency, high load-bearing capacity, and long lifespan. However, the machining accuracy of cylindrical gears is significantly affected by motion errors and force-induced errors of machine tools. In this study, a motion error model of the machine tools was established based on multi-body system theory and homogeneous coordinate transformation method, quantifying the contributions and variation patterns of 12 key errors in the A and B-axes to workpiece geometric errors. Then, by using the stiffness analytical model and the spatial meshing theory, the influence of the force-induced elastic deformation of the shaft of rolling wheel and the springback of the workpiece tooth flank on the geometric error was revealed. Finally, taking the through rolling of a spur cylindrical gear with a module of 1.75 mm, a pressure angle of 20°, and 46 teeth as an example, the force-induced elastic deformation model of the shaft was verified by the rolling tests. Results show that for 40CrNiMo steel, the total profile deviation, total helix deviation, and single pitch deviation in the X-direction caused by rolling forces are 32.48 μm, 32.13 μm, and 32.13 μm, respectively, with a maximum contact rebound is δ_c = 28.27 μm. The relative error between theoretical and measured X-direction spindle deformation is 8.26%. This study provides theoretical foundation and experimental support for improving the precision of rolling process. Full article

This study explores the application of profile shift coefficients as a design strategy to eliminate the need for stepped planet gears in a specific type of planetary gear train, referred to as the AA gear train. By appropriately selecting gear tooth numbers and applying compensating profile shifts to the two central gears, it is possible to equalize their diameters, enabling the use of simple single-step spur gears as planet gears. This significantly simplifies manufacturing, may improve power branching capabilities, and reduces the cost and volume. This paper outlines the geometric and functional limitations of this approach, including the practically allowable range of profile shift values and their impact on the tooth strength, contact ratio, and potential interference. Additionally, the influence of the planet count on assembly conditions and profile shift requirements is examined. The design may offer advantages in compactness and manufacturability (for moderate gear ratios) within a single stage. However, limitations in efficiency, power branching, and self-locking—especially at high ratios—must be considered. While the method provides a viable alternative to conventional stepped planet designs in certain cases, its applicability remains constrained by profile shift limitations and system-specific design compromises. Full article

Gears are fundamental machine elements used in various industries due to their durability, ability to transmit high torques, and high precision. Modern demands for gear manufacturing involve improving production methods in order to achieve greater efficiency while maintaining the prescribed tolerances. The focus of this study is on the fast, simple, and cost-effective manufacturing of gears and the geometric analysis of gears produced in such a way. For the purpose of this research, six pairs of cylindrical spur gears with straight teeth and involute profiles were fabricated. The gears were manufactured by laser cutting on a BODOR C6 machine, using low-alloy structural steel grade S355. After production, the gears were measured using a TESA Micro-Hite coordinate measuring machine, supported by PC-DMIS Gear software, in accordance with ISO 1328-1. The measured parameters were analyzed, identifying the potential applicability of laser cutting as a viable gear production method. In conclusion, recommendations for the use of such gears are provided. Further research will include the investigation of functional parameters of laser-cut gears, such as efficiency, noise, vibration, and more. Full article

This study aims to develop a new model for windage losses, building upon existing formulation, complemented by dedicated experimental campaigns and a specific methodology designed to isolate and quantify windage losses. The model relies on an analytical approach to flow characterization, incorporating a correction factor accounting for air density reduction. The experimental investigation was carried out on a dedicated test bench and includes both spur and helical gears. The results demonstrate good agreement between the proposed model and the experimental data, with and without the presence of nearby obstacles, such as side flanges, highlighting the model’s robustness across different configurations. The proposed windage loss model reproduces the experimental results with significantly greater accuracy than the original one, yielding relative deviations below 5% compared to almost 20% for spur gears, and below 9% compared to over 21%, and in some cases up to 50%, for helical gears. Full article

Digital Twins (DTs) have become essential tools for the design, diagnostics, and prognostics of mechanical systems. In gearbox applications, DTs are often built using physics-based simulations guided by ISO standards. However, standards-based approaches may suffer from complexity, licensing limitations, and computational costs. The concept of symmetry is inherent in gear mechanisms, both in geometry and in operational conditions, yet practical applications often face asymmetric load distributions, misalignments, and asymmetric and symmetric nonlinear behaviors. In this study, we propose a hybrid method that integrates data-driven modeling with standard-based simulation to develop efficient and accurate digital twins for gear transmission systems. A digital twin of a spur gear transmission is generated using KISSsoft^®, employing ISO standards to compute safety factors across varied geometries and load conditions. An automated MATLAB-KISSsoft^® (COM-interface) enables large-scale data generation by systematically varying key input parameters such as torque, pinion speed, and center distance. This dataset is then used to train a neural network (NN) capable of predicting safety factors, with hyperparameter optimization improving the model’s predictive accuracy. Among the tested NN architectures, the model with a single hidden layer yielded the best performance, achieving maximum prediction errors below 0.01 for root and flank safety factors. More complex failure modes such as scuffing and micropitting exhibited higher maximum errors of 0.0833 and 0.0596, respectively, indicating areas for potential model refinement. Comparative analysis shows strong agreement between the NN outputs and KISSsoft^® results, especially for root and flank safety factors. Performance is further validated through sensitivity analyses across seven cases, confirming the NN’s reliability as a surrogate model. This approach reduces simulation time while preserving accuracy, demonstrating the potential of neural networks to support real-time condition monitoring and predictive maintenance in gearbox systems. Full article

The manufacture of lightweight components is one of the most important requirements in the automotive and aerospace industries. Gears, on the other hand, are among the heaviest parts in terms of their total weight. Accordingly, a spur gear was considered, the body of which was configured as a lattice structure to make it lightweight. In addition, the structure was optimized by topology optimization using ProTOP software. Subsequently, the gear was manufactured by a selective laser melting process by using a strong and lightweight material, namely Ti-6Al-4V. This study defeated the problems of manufacturing orientation, surface roughness, support structure, and bending due to the high thermal gradient in the selective laser melting process. To experimentally investigate the benefits of such a lightweight gear body structure, a new test rig with a closed loop was developed. This rig enabled measurements of strains in the gear ring, hub, and tooth root. The experimental results confirmed that a specifically designed and selectively laser-melted, lightweight cellular lattice structure in the gear body can significantly influence strain. This is especially significant with respect to strain levels and their time-dependent variations in the hub section of the gear body. Full article

The mechanical connection between a transmission system and an electric motor gives rise to a strong interaction between their respective dynamics. In particular, the coupling between an electric motor and a nonlinear spur gear transmission significantly influences the overall dynamic behavior of the integrated system. This study presents a detailed investigation into the electromechanical coupling effects between a permanent magnet synchronous machine (PMSM) and a nonlinear spur gear transmission. To focus on these effects, three configurations are analyzed: (i) a standalone gear pair model without motor interaction, (ii) a combined gear–motor system without dynamic coupling, and (iii) a fully coupled electromechanical system where the mechanical feedback influences motor control. The dynamic interaction between the motor’s torsional vibrations and the gear transmission is captured using the derivative of the transmission error as a feedback signal, enabling a closed-loop electromechanical model. Numerical simulations highlight the critical role of this coupling in shaping system dynamics, offering insights into the stability and performance of electric drive–gear transmission systems under different operating conditions. It also underscores the limitations of traditional modeling approaches that neglect feedback effects from the mechanical subsystem. The findings contribute to a more accurate and comprehensive understanding of coupled motor–gear dynamics, which is essential for the design and control of advanced electromechanical transmission systems in high-performance applications. Full article

Early failure detection in gear systems reduces unplanned downtime and associated maintenance costs in rotating machinery. Although numerous indicators can be extracted from vibration signals, selecting the most relevant ones remains challenging. This study proposes a methodology for selecting time-domain features to classify fault severity levels in spur gearboxes. Vibration signals are acquired using six accelerometers and processed to extract 64 statistical condition indicators (CIs). The most informative subset of CIs is identified and selected through a wrapper-based selection approach and artificial intelligence tools. The selected features are then evaluated based on the classification accuracy and the area under the curve (AUC) in receiver operating characteristic (ROC) achieved using Random Forest (RF) and K-nearest neighbours (K-NN) models, with performance exceeding 98%. Additionally, the effect of sensor position and inclination on signal quality and classification performance is analysed using factorial analysis of variance (ANOVA) and multiple comparison tests. The results confirm the robustness of the selected CIs and the minimal influence of sensor placement variability, supporting the practical applicability of the proposed approach in industrial settings. The methodology offers a structured framework for selecting condition indicators in vibration signals, experimentally validated using multiple sensors and fault severity levels, and it is both automated and straightforward to implement. Full article

In this paper, we are looking for the answer to the following question: what geometric deviations do polymer gears made by 3D printing have from the theoretical geometry? From a practical point of view, the question is whether the currently installed injection-molded gear can be replaced by a 3D-printed gear. Thus, the measurements are also carried out on the sample gear and the comparison is made with this data as well. Knowing the data of the existing gear wheel, the CAD model was created, and based on this, samples of the gear were printed using various 3D printing machines. The printed gears were then subjected to geometrical analysis. During the inspection, we performed the measurement of the chordal thickness of the gear wheel using a gear tool caliper, instead of pin measurement and span measurement using a special micrometer, and 3D scanning and analysis. A surface roughness measurement was carried out as well. By conducting measurements on the injection-molded and 3D-printed samples, this research seeks to evaluate the reliability and limitations of the 3D-printed gears, providing insights into their industrial use. This study aims to determine whether 3D printing technologies can produce gears with sufficient accuracy and surface quality for practical applications. Based on the conducted analysis, general conclusions were drawn regarding the potential applicability of the 3D-printed gears. The experimental results indicate notable differences in dimensional accuracy between gears manufactured using Fused Deposition Modeling (FDM) and Selective Laser Sintering (SLS). In terms of chordal thickness measurements, FDM gears exhibited a mean relative error of 1.96 mm, whereas SLS gears showed a significantly higher average deviation of 5.64 mm. For the pin measurement, the relative error averaged 0.193 mm in the case of FDM gears, compared to 0.616 mm for SLS gears. Similarly, the span over four teeth measurements resulted in an average deviation of 0.153 mm for FDM gears, while SLS gears demonstrated a markedly higher mean error of 0.773 mm. With regard to surface roughness, it can be concluded that SLS-manufactured gears exhibit superior performance compared to FDM gears, with an average Ra value of 2.65 µm versus 9.28 µm, although their surface quality remains inferior to that of the injection-molded gear. In light of the higher relative errors observed in SLS gears compared to FDM gears, the dimensions of the theoretical model should be refined to improve the manufacturing accuracy of SLS-produced gears. Full article

To investigate the mechanisms of unexpected failures in a multi-stage gear transmission system under a relatively low load, a rigid–flexible coupled multi-body dynamics model with 10 spur gears and 12 helical gears is established. The dynamic condensation theory is applied to improve computational efficiency. The construction of this model incorporates critical nonlinear factors, ensuring high precision and reliability. Based on the proposed model, four critical dynamic parameters, including acceleration, mesh stiffness, dynamic transmission error, and vibration displacement, are analyzed. This research systematically reveals the nonlinear dynamic mechanism under the multi-gear coupling effect. The spectrum of the gears exhibits prominent low-frequency peaks at 320 Hz and 750 Hz. Notably, alternate load-dominated gears show a shift in prominent low-frequency peaks. The phenomenon of marked oscillations in mesh stiffness suggests a potential risk of localized weakening in the system’s load-carrying capacity. Critically, alternating torques induce periodic double-tooth contact regions in the gear at specific time points (0.115 s and 0.137 s), which are identified as critical factors leading to gear transmission system failures. The variation characteristics of the dynamic transmission error (DTE) demonstrate that the DTE is strongly correlated with the meshing state. The analysis of vibration displacement further indicates that the alternating external loads are the dominant excitation source of vibrations, noise, and failures in the gear transmission system. Full article

In this paper, the time-varying mesh stiffness (TVMS) of a gear is meticulously derived using the potential energy method (PEM) and an analytical expression for it is obtained. Subsequently, calculations are performed to determine the effects of crack depth and crack angle on the TVMS. The validation is carried out using the finite element method (FEM). Then, a discussion is carried out on the dynamic characteristics of a spur gear system with a crack. Moreover, uncertainty is an objective reality in gear systems, arising from various factors such as the material properties and working environment. To enable a more reasonable evaluation of the dynamic characteristics of the spur gear system, this paper presents a deviation of an uncertainty interval analysis method based on Chebyshev polynomials. A dynamic model of the spur gear system with uncertain parameters is then proposed. The dynamic response of a gear transmission system with these uncertain parameters is investigated in detail. Additionally, the interval response of a gear system with root cracks under uncertainty is further investigated. The experimental results confirm the inherent presence of uncertainty in the gear system and validate the effectiveness of the proposed uncertainty analysis method. Full article

Noise, vibration and harshness analyses are of great interest for the latest developments of the gearboxes of electric vehicles. Gearboxes are now the main source of vibrations, since electric powertrains are much quieter than internal combustion engines. Traditionally, the simulation of the non-linear gear dynamics is studied by first performing a series of preliminary static analyses to compute the static transmission error (STE). The STE (i.e., in the form of varying mesh stiffness) is then accepted as the system’s excitation source to compute the dynamic transmission error (DTE). This paper presents a novel approach to analyze the non-linear dynamics of gears which does not require any preliminary static analyses. The method consists of a frequency–domain approach based on the Harmonic Balance Method (HBM) and the Alternating Frequency–Time (AFT) scheme, allowing for much faster simulations when compared to the widely used direct–time integration (DTI). The contact between the teeth is modeled as intermittent and penalty based with a varying gap. The time–varying gap between the teeth is initially approximated to a step function that guarantees the design contact ratio. The methodology introduced is tested on a lumped parameter model of a spur–gear pair already proposed and simulated in the literature. The results obtained with the novel approach are compared with the DTI simulation of the model as a reference. The excellent match between the different approaches validates the reliability of developed methodology. Full article

Spalling alters a gear’s time-varying meshing stiffness (TVMS), thereby affecting its vibration characteristics. However, most studies focus on single-spalling gears and overlook the possibility of multi-spalling gears. Additionally, because most spalls are irregular, traditional analytical models neglect the torsional effects that are caused by asymmetric spalling. In this study, a shape-independent model for calculating the TVMS of multi-spalling gears, which considers torsional stiffness, was developed. A 16-degree-of-freedom dynamic model was established to analyze the dynamic response, incorporating the multi-spalling TVMS. The model was then validated through experiments. The results show that the proposed method accurately calculates the TVMS of a multi-spalling spur-gear system. Changes in the relative position of the spalling can significantly affect the TVMS. Multiple-tooth spalling influences the TVMS over several meshing cycles, while single-tooth multiple spalling affects the TVMS based on the specific spalling parameters. Different spalling patterns lead to substantial differences in the system’s dynamic behavior. Multiple spalling teeth generate several pulses, whereas a single tooth with multiple spalls only generates one significant pulse. This study provides a solid foundation for understanding the dynamic behavior of spalled gear systems, revealing their dynamic characteristics and failure mechanisms. Full article