Equations For Calculation Research Articles

Versatile LCL Inverter Model for Controlled Inverter Operation in Transient Grid Calculation Using the Extended Node Method

Due to increasing decentralized power applications, power electronics are gaining importance, also in distribution grids. Since their scope of investigation is diverse, their versatile models and their use in grid calculations are important. In this work, a three-phase grid-synchronous inverter with an LCL filter is considered. It is defined as a component of the "Extended Node Method" to make it applicable in this node-based transient grid calculation method. Because the component stucture always looks the same and the construction of the grid system of equations always follows the same, straightforward process, the model can be applied easily and several times to large network calculations. Furthermore, an approach is developed for how inverter control algorithms are interconnected with the method’s results in the time domain. This allows for the fast analysis of converter control schemes in different grid topologies. To evaluate its accuracy, the developed approach is compared to equivalent calculations with Simulink and shows very good agreement, also for steep transients. In the long term, this model is intended to bridge the gap to other DC systems like electrochemical components and to gas and heating networks with the Extended Node Method.

Mechanical Properties and Numerical Modelling for Prosthetic Foot

This study uses laminated composite materials made of hybrid glass and carbon fibers to determine the mechanical characteristics of the foot. Tensile, bending, and fatigue of composite material were evaluated and applied to the ANSYS model. The volume fraction for carbon and glass fibers was 22.5% and 10.04%, respectively. The mechanical property results: σy = 40 MPa, σult = 150 MPa, and E = 1.2 GPa. The patient is a 30-year-old male with a left amputation side, 1.60 meters tall, and weighs 74 kg. The analysis was carried out for the two scenarios (toe-off and heel contact) as boundary conditions. The overall deformation, equivalent stresses, and foot safety factor have been calculated using ANSYS17.2 software. In the end, it appears that the foot is secure based on equivalent stress calculations and the Von-Mises hypothesis. The computed safety factor for the foot is constructed of a chosen composite material with the subsequent layers. When the heel (stance phase) is fixed at 1.3449, and the metatarsal (toe off) is fixed at 1.259, the safety factor for a force of 860 N is reached. The foot is secure, according to the Von-Mises hypothesis.

Research on simulation of a bullet skimming the ground by the finite element method

It is greatly complicated to research the process of bullets penetrating into the ground due to the diversity and heterogeneity of ground physical characteristics. The empirical formulas have been developed for scenarios involving deep penetration of bullets into the ground so far; however, equivalent calculations for bullets skimming the ground scenarios remain absent. This paper has established a finite element method (FEM) simulation model for deep penetration and validated it against empirical data. Leveraging this validated model, simulations have been extended to examine the bullets skimming the ground behavior of bullets. The results have delineated the impact angles at which bullets skimming the ground occur for soil with average compaction density. This methodology can be adapted to various soil types to construct a comprehensive set of parameters for bullets skimming the ground angles, thereby optimizing artillery performance.

Effect of rolling texture on bearing capacity of aircraft repair patches and replaced panels

The article combines issues related to biaxial fatigue loading, corrections for equivalent stress calculations, and the practical application of new knowledge regarding biaxial fatigue in the aviation industry. It considers the possibility and expediency of taking into account the anisotropy of metals’ mechanical characteristics in aircraft repair procedures, such as patching and replacing damaged skin panels. The biaxial loading of the skin is shown to be a significant factor that should be considered in the aircraft skin repair process. It is shown that while well-known Huber-Mises formula works well for isotropic materials, the fuselage skin made of anisotropic alloys requires corrections to the Huber-Mises method. For aircraft parts subjected to biaxial loading, the assessment of equivalent uniaxial stresses can be done by introducing the crystallographic factor into the Huber-Mises formula. This is achieved by transforming the biaxial stress components of fuselage loading due to pressurization and bending into the resolved stresses in the activated crystallographic slip systems of the dominant texture.

Investigation of shear mechanical behaviors of geogrid-coral sand interfaces

Geogrid-reinforced coral sand (GRCS) effectively enhances the strength and stability of marine geo-structures in island and coastal areas. The complex interaction and underlying mechanism of the geogrid-coral sand interface potentially determine the mechanical properties of the GRCS. In this study, large-scale interfacial shear tests were carried out to investigate the mechanical behaviors of geogrid-coral sand interfaces under the coupled influence of grain size, geogrid properties, and stress level. Comparisons with siliceous sand indicate that the mechanical properties of the geogrid-coral sand interface are excellent but suffer from more complex influences originating from particle properties. The interfacial friction angle is more sensitive to grain size, whereas the pseudo cohesion is more sensitive to aperture properties. The shear interface shows a general evolution trend of “contraction-dilation-contraction”, with the maximum and final dilation becoming more prominent as the aperture size and stress level decrease. The increase in grain size, vertical stress and geogrid apertures induces a thicker interface with more particle crushing. Given the microscopic geogrid-coral sand interaction, the force characteristics of the aperture are further analyzed, and an equivalent additional stress calculation method is developed to quantitatively characterize the effects of grain size, geogrid properties, and stress level.

Equivalent calculation and characterization of the thermoplasmonics effect of Au nanoparticle arrays

Equivalent calculation and characterization of the thermoplasmonics effect of Au nanoparticle arrays

Impacts of Calculation Grid Spacing and Statistical Uncertainty of Monte Carlo Algorithm on Stereotactic Radiosurgery Planning With Volumetric-Modulated Arcs for Single Brain Metastases Using the Monaco® System.

Purpose In linac-based stereotactic radiosurgery (SRS) utilizing a multileaf collimator (MLC) for brain metastases (BMs), a volumetric-modulated arc (VMA) technique is indispensable for generating a suitable dose distribution with efficient planning and delivery. However, the optimal calculation grid spacing (GS) and statistical uncertainty (SU) of the Monte Carlo algorithm for VMA optimization have yet to be determined. This planning study aimed to examine the impacts of GS and GU settings on VMA-based SRS planning and to find the optimal combination for templating. Materials and methods Thirty clinical BMs with a gross tumor volume (GTV) of 0.08-48.09 cc (median 9.81 cc) were included. The treatment platform included a 5-mm leaf-width MLC Agility® (Elekta AB, Stockholm, Sweden) and a planning system Monaco® (Elekta AB). The prescribed dose was uniformly assigned to the GTV D V-0.01 cc, the minimum dose of GTV minus 0.01 cc, i.e.,D >95% for GTV >0.20 cc or to the GTV D 95% for GTV ≤0.20 cc, to minimize the uncovered GTV to the equivalent of a 3 mm diameter lesion. Five combinations of GS and SU per plan were examined for 12 selected GTVs (median 17.41 cc): GS of 2 mm and SU of 3% (G2U3), 2 mm and 2% (G2U2), 2 mm and 1% (G2U1), 1 mm and 2% (G1U2), and 1 mm and 1% (G1U1). Otherwise, the same arc arrangement and optimization method were uniformly used to prioritize the GTV dose conformity and the steepness of the dose gradient outside the GTV without dose constraints inside the GTV boundary. Further comparisons were conducted using 30 GTVs between the two groups with the highest plan quality. Results The G2U3 and G2U2 resulted in the equivalent total calculation time (tCT) and exactly the same plan quality. The overall plan quality was significantly superior in the G1U2 and G1U1 than in the G2U1 and G2U2, although the tCT was significantly longer in the G1U1 and G1U2 than in the G2U1 and G2U2. In the comparison of the G1U2 and G1U1, the concentric lamellarity of dose gradients 2 mm outside and 2-4 mm inside the GTV boundary was significantly superior in the G1U1 than in the G1U2, while there was no significant difference in the other parameters. The tCT tended to be longer in the G1U1 than in the G1U2. Conclusions The initial settings of GS and SU have significant impacts on the plan quality and tCT. The settings with GS of 1 mm and SU of 1% per plan are recommended to create the most suitable dose distribution for single BMs, especially for irregularly shaped and/or large lesions, although the tCT is long. In addition to common evaluation metrics, the coverage values of 2 mm outside and 2-4 mm inside the GTV surface by the D eIIV, the minimum dose to cover the irradiated isodose volume equivalent to each target volume, are valuable for in-depth plan comparison.

Accuracy improvement of thermal distribution analysis of 10 kV dry-type iron-core reactor

Hotspot temperature is a key factor affecting the safe operation for power equipment like reactor. The different distribution of the magnetic field in the iron-core and windings results in non-uniform distribution of the electromagnetic losses. However, the influence of non-uniform losses on the temperature distribution is rarely discussed in the previous studies. In this paper, the thermal behavior of 10 kV dry-type iron-core reactor considering the influence of non-uniform losses is studied to obtain more accurate simulation results. First, the winding model with separate coils is used instead of traditional cylinder structure, and the loss of each coil is obtained by equivalent calculation method. Then, the thermal characteristics of reactor with different winding models and loss distributions are analyzed. In addition, the effect of the above factors on windings temperature distribution is discussed. Finally, the simulation results are compared with the test results of 10 kV dry-type reactor in 110 kV indoor substation. The result indicates the simulation result considering the non-uniform losses distribution is closer to the measured result. The temperature distribution of windings in vertical direction is more consistent with the real situation as well.

Mode II fracture properties of parallel neosinocalamus affinis bamboo strand lumber

This study investigates the Mode II fracture properties in the RL and TL planes of parallel neosinocalamus affinis bamboo strand lumber. Eighty End-Notched Flexure (ENF) specimens were designed, varying pre-crack lengths and specimen widths. Digital Image Correlation (DIC) was employed to analyze strain variations during the development of the fracture process zone (FPZ) and crack propagation stages. The Compliance Based Beam Method (CBBM) and equivalent crack length calculations were used to determine the strain energy release rate (GIIC) of PNABSL. R curves and crack growth rate curves revealed that crack propagation in the RL and TL planes. The results indicated that Mode II fracture propagation in both the RL and TL planes of PNABSL predominantly exhibited self-similar cracking, though the fracture surfaces were rough and uneven, with noticeable fiber bridging. The study found that Mode II fracture propagation was less stable in the RL plane compared to the TL plane, which is attributed to the easier fracturing of thick-walled fiber cells in the RL plane. The critical strain energy release rate for PNABSL was determined, offering valuable insights into its fracture behavior.

Introduction of a free sound system design exchange format (SDE) for data from different sound systems for noise predictions with complex summation

To consider the correlated sources of sound systems from different manufacturers in noise predictions equally with complex summation, a free exchange format for sound system planning software on the one hand and environmental noise software on the other is being defined in a cooperation with d&b audiotechnik, L-Acoustics and SoundPLAN: SDE = Sound/System Design/Data Exchange/Export This paper introduces the SDE format, its motivation and structure. With increasing open-air events in urban areas, potential problems with noise also increase. Proactive noise predictions can help prevent noise from becoming a problem in the first place. Until now it has not been possible to use data from planned sound systems from different manufacturers for equivalent calculations with complex summation. Modern sound systems have high directivity, especially loudspeaker arrays. The directivity of arrays results from superposition of sound waves from all loudspeakers. This effect is used specifically with line arrays and subwoofer arrays to optimize sound and coverage in audience areas. However, the resulting emission of an entire sound system is not constant over distance. Time-of-flight and relative phase at the receiver points must be considered with complex summation.

An Efficient and Automatic Simplification Method for Arbitrary Complex Networks in Mine Ventilation

The simplification of complex networks is a research field closely related to graph theory in discrete mathematics. The existing methods are typically limited to simplifying the series sub-networks, parallel sub-networks, diagonal sub-networks, and nested simple sub-networks. From the current perspective, there are no available methods that can handle complex sub-networks and nested complex sub-networks. In this paper, we innovatively propose an efficient and automatic equivalence simplification method for arbitrary complex ventilation networks. The method enables, for the first time, the maximum possible equivalence simplification of nested simple sub-networks and nested complex sub-networks. In order to avoid the NP-hard problem caused by the searching of simplifiable sub-networks, it is necessary to analyze the intrinsic topology relationship between simplifiable sub-networks and spanning sub-graphs to optimize the searching process. One of our main contributions is that we present an efficient searching method for arbitrarily nested reducible sub-networks based on the bidirectional traversal process of a directed tree. The method optimizes the searching process for simplifiable node pairs by combining the characteristics of a directed tree with the judgment rules of simplifiable sub-networks. Moreover, by deriving the formula of an equivalent air resistance calculation for complex sub-networks, another one of our main contributions is that we present an equivalent calculation and simplification method for arbitrarily complex sub-networks based on the principle of energy conservation. The basic idea of the method is to calculate the equivalent air resistance using the ventilation network resolution of the constructed virtual sub-networks. We realize the simplification method of arbitrarily complex mine ventilation networks, and we validate the reliability of the simplification method by comparing the air distribution results using the network solution method before and after simplification. It can be determined that, with appropriate modifications to meet specific requirements, the proposed method can also be applicable to equivalent simplification instances of other types of complex networks. Based on the results analysis of several real-world mine ventilation network examples, the effectiveness of the proposed method is further verified, which can satisfactorily meet the requirements for simplifying complex networks.

Carbon dioxide emission equivalent calculation and inter-sectoral transfer pattern of different water use terminals in China

In the context of global climate change, all industries have put forward the requirements for carbon emission reduction. The effective use of water resources is the key to achieving carbon emission reduction, so it is particularly important to review the carbon dioxide emission equivalents of water resource utilization behaviors (CEE-WRUBs) of water users. However, existing research on CEE-WRUBs across various water sectors remains inadequate. Therefore, this study integrates the enhanced CEEA method, LMDI decomposition model, and IOA method to analyze CEE-WRUBs across diverse water use terminals. Then seeks their main driving factors and their transfer pattern among different industries, which are crucial to the realization of the global carbon neutrality objective. The results showed that: (1) China's CEE-WRUBs show a significant downward trend. Industrial water use emerges as the primary source of CEE, but the CEE-WRUBs of most industrial water terminals show a fluctuating downward trend. Grains' water use behavior (WRUBs) absorbed the largest CEE, reaching 14,698 Mt in 2020. (2) the water efficiency effect emerges as the predominant driver behind the increase in CEE-WRUBs most of the time, and holding a prominent position. The carbon emission intensity effect primarily steers the reduction of CEE-WRUBs. (3) the largest net outflow sector of WRUBs embodied carbon in 2007–2020 was transformed from basic material heavy industry (−153.54 Mt in 2007) to agriculture (−128.26 Mt in 2020). Most of the WRUBs embodied carbon of agriculture flows into light industry, while most of the WRUBs embodied carbon of basic material heavy industry flows into finishing heavy industry and construction. The methods and results of this study provide a potential reference for investigating the regional water-carbon relationship and advancing the global carbon neutrality objective.

Optimized identification process of equivalent wind load calculations for offshore wind turbines under standstill conditions

In engineering, the wind excitations acting on the offshore wind turbine (OWT) structure cannot be obtained directly by the measured method. The traditional load simulation way may lead to poor accuracy because of the deviation between actual operational conditions and simulation environment parameters or load coefficients, which are always selected based on load spectrums, small scale model tests and engineering experience. To solve this project problem, an equivalent wind load optimization model and parameter identification process of OWT was established under the standstill conditions. Afterwards, two key load parameters in load model respectively called constant drag coefficient and unsteady lift coefficient can be obtained through recursive call on numerical model and feedback analysis using particle swarm optimization (PSO) algorithm based on measured vibration data. The applicability and accuracy of proposed calculation process was verified through an equivalent numerical model of OWT considering different particle position and wind speed. Further, the optimization identification on equivalent wind load and the drag and lift coefficients of one OWT was achieved based on measured data. It is illustrated that the identified drag coefficients show a drop trend from 0.629 to 0.154, consistent with the parameter range of 0.20–0.60 obtained from model experiments, before the wind speed reaches 6.0 m/s and then rise obviously with the increase of wind speed. On the contrary, the range of optimized lift coefficients form 0.133–0.480, which is as familiar as the experimental parameter range of 0.10–0.30, reflects a certain increase trend. Finally, the comparison between identified wind excitations and calculated loads based on the measured strain data explain that the proposed load optimization identification process have a good credibility on actual OWT.

Numerical Study on Explosion Risk and Building Structure Dynamics of Long-Distance Oil and Gas Tunnels

To comprehensively understand the explosion risk in underground energy transportation tunnels, this study employed computational fluid dynamics technology and finite element simulation to numerically analyze the potential impact of an accidental explosion for a specific oil and gas pipeline in China and the potential damage risk to nearby buildings. Furthermore, the study investigated the effects of tunnel inner diameter (d = 4.25 m, 6.5 m), tunnel length (L = 4 km, 8 km, 16 km), and soil depth (primarily Lsoil = 20 m, 30 m, 40 m) on explosion dynamics and on structural response characteristics. The findings indicated that as the tunnel length and inner diameter increased, the maximum explosion overpressure gradually rose and the peak arrival time was delayed, especially when d = 4.25 m; with the increase in L, the maximum explosion overpressure rapidly increased from 1.03 MPa to 2.12 MPa. However, when d = 6.5 m, the maximum explosion overpressure increased significantly by 72.8% from 1.25 MPa. Evidently, compared to the change in tunnel inner diameter, tunnel length has a more significant effect on the increase in explosion risk. According to the principle of maximum explosion risk, based on the peak explosion overpressure of 2.16 MPa under various conditions and the TNT equivalent calculation formula, the TNT explosion equivalent of a single section of the tunnel was determined to be 1.52 kg. This theoretical result is further supported by the AUTODYN 15.0 software simulation result of 2.39 MPa (error < 10%). As the soil depth increased, the distance between the building and the explosion source also increased. Consequently, the vibration peak acceleration and velocity gradually decreased, and the peak arrival time was delayed. In comparison to a soil depth of 10 m, the vibration acceleration at soil depths of 20 m and 30 m decreased by 81.3% and 91.7%, respectively. When the soil depth was 10 m, the building was at critical risk of vibration damage.

Stability of cold-formed steel stud walls subjected to vertical compression

Cold-formed steel (CFS) stud walls are the primary vertical load-bearing units in CFS residential systems. These walls need to meet both strength requirements and good stability. In this study, a CFS stud wall was simplified into a mechanical model of an orthotropic plate rib system using the orthotropic plate (OP) method. A formula for calculating the equivalent stiffness of the stud wall was obtained, and the correctness of the simplified calculation model and equivalent stiffness calculation formula was verified by finite element analysis. Various factors that affected the equivalent stiffness of the wall were investigated. Additionally, the stability of the stud walls under a vertical load was derived by considering the stability theory of the plate. The results indicated that the stability of the stud walls was mainly related to the height-thickness ratio of the walls. Finally, the correction factor of the allowable height-thickness ratio of the walls was obtained by analyzing the parameters of the wall thickness, stud spacing, sheathing materials, and wall opening, and a case study was used to illustrate the procedure of this simplified method.

Calculation Method of New Assembled Corrugated Steel Initial Support Structure of Highway Tunnel

The assembled corrugated steel initial support structure is a new prefabricated structure in highway tunnel engineering, achieving a balance between economy and safety. This study proposes a simplified calculation method and elucidates the mechanical mechanisms of assembled corrugated steel initial support structures. Firstly, the stiffness characteristics of corrugated steel plates were studied based on full-scale tests. A general equivalent stiffness coefficient table was established. Numerical simulations of corrugated steel flange joints were conducted to explore their bending mechanical properties. A two-stage rotational stiffness model for corrugated steel flange joints was proposed. Finally, a plane strain-spring simplified calculation method for the assembled corrugated steel initial support structure was developed, and the monitoring data from the Qipanshan Tunnel validated the correctness and reliability of the proposed method. The results demonstrate that (1) the plane strain-spring simplified model consists of the planar strain equivalent calculation method for corrugated steel plates and the two-line stiffness equivalent spring of the corrugated steel flange joint. The simplified model was validated as effective by monitoring data. (2) Corrugated steel plates exhibit two stages under loading, namely gap elimination and elastic stages. The elastic stage stiffness of corrugated steel plates decreases with increasing ratio of depth to pitch (RDP), positively correlating with plate thickness when the RDP exceeds 0.333 and otherwise negatively correlated. (3) Corrugated steel lining flange joints exhibit distinct elastic and plastic stages in their linear moment–rotation curves under loading.

Infrared radiation characteristics simulation of exhaust suppression type ships

An equivalent calculation method for the infrared-suppressed ship’s infrared radiation is carried out, which couples thermal characteristics of the ship surface and the exhaust system. Firstly, a refined physical model for the infrared suppressed exhaust system is proposed, which considers the processes of convective heat transfer and radiative heat transfer. The model generates the equivalent heat flow boundary conditions of the internal heat source through the numerical calculation of Computational Fluid Dynamics (CFD), and combines with the energy balance physical model. The energy balance model on the ship surface is developed, which considers external thermal environment conditions including itself radiation, solar radiation, atmospheric radiation, and reflective radiation among surface elements. The temperature calculation model for the ship with a jet exhaust system is formed. Subsequently, an exhaust-suppressed ship infrared radiation calculation model is formed based on the infrared radiation rendering of solid targets and the narrow spectral principle of exhaust plumes, which considers the spontaneous radiation and environmental radiation of ships. Finally, the infrared simulation results are compared and verified based on experimental data. The results indicate that the infrared radiation error on the ship’s typical parts is less than 30 %. Additionally, 90.1 % of the cabin walls using exhaust suppression systems have a temperature difference of less than 3 K under different operating conditions. It suggests that the exhaust suppression system is effective in reducing the temperature of the cabin wall. The calculation method for ship infrared characteristics constructed in this paper has reasonable results, and it can be used for infrared characteristic analysis of exhaust suppression ships.

Experimental validation study of equivalent bare charge calculation model for two shelled warheads

After the explosion of the warhead shell fragments will consume a portion of the charge release energy, a method of calculating the shockwave overpressure value of the explosion of the warhead is to calculate the shockwave overpressure value by firstly converting the actual charge C of the warhead into the charge CEB of the bare charge, and then converting CEB into TNT equivalent. Experimental results were used to compare the calculation error size of the two models for calculating the equivalent bare charge of the warhead, and the results show that the calculation results of Chi Jiachun's modified model are in better conformity with the experimental results; by analyzing the influence of the empirical constant in Chi Jiachun's modified model on the calculation results, the value of the empirical constant is given as a suggestion.

A Quantitative Adverse Outcome Pathway for Embryonic Activation of the Aryl Hydrocarbon Receptor of Fishes by Polycyclic Aromatic Hydrocarbons Leading to Decreased Fecundity at Adulthood.

Quantitative adverse outcome pathways (qAOPs) describe the response-response relationships that link the magnitude and/or duration of chemical interaction with a specific molecular target to the probability and/or severity of the resulting apical-level toxicity of regulatory relevance. The present study developed the first qAOP for latent toxicities showing that early life exposure adversely affects health at adulthood. Specifically, a qAOP for embryonic activation of the aryl hydrocarbon receptor 2 (AHR2) of fishes by polycyclic aromatic hydrocarbons (PAHs) leading to decreased fecundity of females at adulthood was developed by building on existing qAOPs for (1) activation of the AHR leading to early life mortality in birds and fishes, and (2) inhibition of cytochrome P450 aromatase activity leading to decreased fecundity in fishes. Using zebrafish (Danio rerio) as a model species and benzo[a]pyrene as a model PAH, three linked quantitative relationships were developed: (1) plasma estrogen in adult females as a function of embryonic exposure, (2) plasma vitellogenin in adult females as a function of plasma estrogen, and (3) fecundity of adult females as a function of plasma vitellogenin. A fourth quantitative relationship was developed for early life mortality as a function of sensitivity to activation of the AHR2 in a standardized in vitro AHR transactivation assay to integrate toxic equivalence calculations that would allow prediction of effects of exposure to untested PAHs. The accuracy of the predictions from the resulting qAOP were evaluated using experimental data from zebrafish exposed as embryos to another PAH, benzo[k]fluoranthene. The qAOP developed in the present study demonstrates the potential of the AOP framework in enabling consideration of latent toxicities in quantitative ecological risk assessments and regulatory decision-making. Environ Toxicol Chem 2024;43:2145-2156. © 2024 SETAC.

A shape-independent analytical method for gear mesh stiffness with asymmetric spalling defects

Spalling, a common failure mechanism of gear systems, greatly affects the dynamics of gears operation, which is reflected in the time-varying mesh stiffness (TVMS). Current TVMS models often overestimate the asymmetric spalling phenomenon and may lead to inaccuracy in identifying and predicting the spalling failure. To address this problem, in this paper, a new stiffness, namely torsional stiffness, is introduced to quantify the effect of asymmetric spalling defects, and an equivalent stiffness calculation method for different asymmetric shapes is proposed. Based on this, a shape-independent TVMS model is constructed, which can realize the fast calculation of TVMS for spalling defects with different shapes at arbitrary asymmetric locations. Furthermore, a FEM-based validation method is developed by considering diverse loading states and improving the current result extraction method. Case studies are presented to illustrate the proposed model and to analyze the effects of different types of asymmetric spalling defects on gear dynamics. The FEM validation has shown that the proposed model has a good effectiveness.