Multibody Analysis Research Articles

Multibody Analysis of Sloshing Effect in a Glass Cylinder Container for Visual Inspection Activities

This paper addresses the phenomenon of sloshing and the issues that arise during liquid handling at visual inspection stations. The pharmaceutical industry, recently put under pressure by the pandemic, has long adopted modular solutions consisting mainly of robotic islands. This work focuses on a visual inspection island for glass vials and ampules called VRU. This machine uses robotic arms to optimize the inspection process and enables automated control of a wide range of products using image recognition techniques and AI algorithms. However, the handling of containers in the presence of liquids requires special precautions to avoid the occurrence of bubbles inside the fluid that can prevent the cameras from correctly capturing any defects present. The banal solution involves a drastic reduction in the speeds and accelerations to which the liquids are subjected. However, using appropriate techniques makes it possible to achieve performance values similar to those obtainable when manipulating solid materials. The developed algorithms were tested using multibody simulations in the Mathworks Simscape environment and then validated using a six-axis Fanuc robot. In this study, however, the analysis conducted aimed to determine the correlations between trajectories, laws of motion, and sloshing in containers handled at high speed in industrial applications. In this study a multibody model was developed using a CFD analysis. The container consisted of a glass vial for pharmaceutical uses containing a liquid inside. The results obtained from the CFD analysis allowed us to calibrate the multibody model for the next phase of optimization of the laws of motion to be followed by the manipulator.

Multibody Analysis of Wave Energy Converters and a Floating Platform in the Time Domain

Generally, new and renewable energy systems generate electricity by installing and operating multiple modules simultaneously. In the Republic of Korea, recent studies and developments have focused on asymmetric wave energy converters (hereafter referred to as rotors) suitable for marine environments off the western coast of Jeju. These rotors are arranged on a large floating truss-structure platform and designed to harness electricity from the rotors’ pitch motion. However, when multiple rotors operate on a platform, their behavior diverges from that of a single module due to hydrodynamic interactions between them. Moreover, because the rotors are connected to the floating platform, their motion is influenced by the platform’s dynamics. In this study, a time-domain multibody motion equation was established to analyze changes in the behavioral characteristics of the rotors, both with and without a floating platform. The hydrostatic and hydrodynamic coefficients were derived in the frequency domain using WAMIT, a commercial code based on linear potential flow theory for three-dimensional diffraction/radiation analyses. The motion equation was then applied under regular and irregular wave conditions using OrcaFlex version 11.3, a marine systems design and analysis program. The resulting behaviors were compared to elucidate the influence of the platform and hydrodynamic interactions on the rotors’ performance.

From the material behaviour to the thermo-mechanical long-term response of asphalt pavements and the alteration of surface drainage due to rutting: a sensitivity study

ABSTRACT In this contribution, a simulation chain for the thermo-mechanical and hydromechanical analysis (surface drainage) of a pavement structure during its whole service life is applied to a typical asphalt pavement (Bk100) used for motorways in Germany. Transient load signals for each tyre position of a truck-trailer combination (vehicle) are generated from a multibody analysis of the vehicle driving on a motorway with rough pavement surface. Material model parameters are derived from experimental identification tests of asphalt materials. The model parameters are used together with a continuum-mechanical description of the asphalt material representing the thermo-mechanical material behaviour at the material scale. The material response of the pavement layers is integrated on the structural scale by using the finite element method (FEM) in combination with an arbitrary Lagrangian-Eulerian (ALE) formulation and equivalent tyre loads of a representative, finite element (FE) discretised truck tyre rolling on an FE discretised pavement section. Different scenarios of rut formation are computed by varying different influence factors (climate temperature, vertical tyre force, type of asphalt material of the surface layers etc.). During the subsequent hydromechanical analysis of the pavement, the simulated deformed geometry of the pavement surface is used to numerically compute surface drainage characteristics.

Prediction of Post-Operative Clinical Parameters in Posterior Scoliosis Surgery Through An Adaptive Neuro-Fuzzy Interface System

Background and Objective: Postoperative clinical indices should be estimated accurately in scoliosis correction surgeries, which have been analyzed in various studies such as experimental (in vitro or in vivo) trials through different modeling methods (finite element or multibody analysis). These costly and time-consuming methods can only be conducted on a large number of scoliotic patients. An adaptive neuro-fuzzy interface system (ANFIS) is used in this study to estimate the postoperative cobb and thoracic kyphosis angles in adolescent idiopathic scoliosis patients undergoing posterior scoliosis correction surgeries. Methods: Four groups of 55 patients with distinct preoperative clinical indices (thoracic cobb and pelvic incidence) were considered the ANFIS inputs, whereas postoperative thoracic cobb and kyphosis angles were used as the outputs. For robustness evaluation, the predicted values of postoperative angles were compared with measurements by calculating the root mean square errors and clinical correction deviation indices (the relative deviation of postoperative predicted angles from the real angles). Results: The least root mean square errors (3.0º and 6.3° for the main thoracic cobb and thoracic kyphosis estimations, respectively) were recorded in the group with the main thoracic cobb, pelvic incidence, thoracic kyphosis, and T1 spinopelvic inclination used as inputs. The clinical correction deviation indices were calculated 0.0086 and 0.0641 for cobb angles in two cases and 0.0534 and 0.2879 for thoracic kyphosis in two other cases. Conclusion: Greater differences between preoperative and postoperative cobb angles compared with those of thoracic kyphosis decreased the root-mean-square errors and clinical deviation indices but improved accuracy

Identification of lumped stiffness parameters for a motorcycle model in investigating weave and wobble

In motorcycle dynamics, great importance is attributed to the study of the weave and wobble vibration modes and, in particular, to the effects of the flexibility of structural components on their stability. Therefore, appropriate motorcycle models for studying weave and wobble should include flexible elements for describing the flexural behavior of components such as the main frame, front assembly, and rear swingarm. Different approaches are possible for modeling flexibilities: the most common among them are the lumped stiffness and the flexible multibody approaches. While the latter certainly provides higher accuracy, the former has advantages in terms of computational load, but, above all, it makes it easier to understand in the design phase how technical parameters, such as torsional and bending stiffness of a given structural component, can influence the stability of weave and wobble. The accuracy of lumped stiffness models strongly depends on parameter identification. In this study, a general method is proposed to determine appropriate lumped stiffness parameters for any given motorcycle component. The proposed method is tested and validated by comparing the weave and wobble modal behavior with the results of flexible multibody analysis. The lumped stiffness model is then adopted to carry out a sensitivity analysis aimed at identifying the effects on the weave and wobble stability of the torsional and bending stiffness of specific structural components of the motorcycle to optimize their design.

Towards an open-source framework for Fluid–Structure Interaction using SU2, MBDyn and preCICE

Fluid–Structure Interaction (FSI) problems are a primary concern for the aerospace industry. Predicting the deformation of flexible structures due to aerodynamic forces is essential in different scenarios, e.g., for determining the performance of rotorcrafts and wind turbines. In this context, we present a new high-fidelity, open-source, modular, and user-friendly FSI simulation framework by coupling the well-established fluid solver SU2 with the multi-body structural solver MBDyn. The SU2 suite solves steady and unsteady Euler and RANS equations using a finite volume method on unstructured grids. The aerodynamic loads on the surfaces are then passed to MBDyn. Through a multi-body analysis, rotations, displacements, and the structural response of rotorcraft systems are efficiently computed and exchanged back with the fluid solver. A partitioned approach is used between the two codes, each specific for a single physical domain. Both explicit and implicit coupling were considered. The coupling is obtained through the library preCICE, which treats the two specialized solvers as “black boxes” and provides data mapping between non-matching grids. Classical FSI test cases are presented and results are compared with data from literature to validate the framework.

Comparison of Linear Flexible Aircraft Model Structures on Large Flexible Tiltrotor Aircraft

Structural modes for large aircraft occur at low frequencies and must be accounted for in the flight dynamics modeling and control system design process. An analysis is performed on various linear representations of flexible aircraft with an application to the lateral/directional flexible dynamic response of the notional Large Civil Tiltrotor (LCTR2) in hover. The goal of the work is to compare the treatment of the coupling between the rigid-body and structural states within various model structures and to develop conversions between the various model forms. The analysis shows that mean-axis and other simplified analytical representations of flexible aircraft, originally developed for fixed-wing aircraft, are also able to correctly capture the dynamic response of a tiltrotor. First, a linear model is obtained from a multibody simulation using numerical perturbation methods. This is compared with a mean-axis model, where structural dynamics are appended onto rigid-body dynamics, as would be obtained if the rigid-body aircraft response were the starting point in an analytical development of the structural coupling. Comparisons are also given with a model that would be obtained from system identification using flight-test data. Key stability and control derivatives are compared to highlight similarities and differences between the various models. The results from the analysis show the multibody model treats the structural coupling in a significantly different way than an analytical model buildup. For example, the structural coupling to roll rate response varies up to two orders of magnitude between the models, yet the overall response is identical. This work shows analysis of the structural/rigid-body coupling developed for analytical models is also valid for models developed from a multibody analysis. Lastly, structural flexibility will be shown to alter the characteristics of the lateral hovering cubic of the LCTR2 by increasing damping of an unstable oscillatory mode.

Moving Morphable Multi Components Introducing Intent of Designer in Topology Optimization

Topology optimization based on moving morphable components efficiently generates a topology that is expressed by a few geometrical design variables. However, conventional moving morphable components have three problems: lack of continuity between components, difficulty in describing a smooth rollup shape, and difficulty in generating a rigid joint to an optimized topology. In this study, a novel topology optimization framework was developed by introducing theories devised for multibody analysis. First, an adaptive moving morphable component based on absolute nodal coordinate formulation was proposed. Because both the position and gradient are used as design variables, continuity is ensured. Second, a position and gradient connection algorithm leveraging the linear constraint of the absolute nodal coordinate formulation was proposed to describe the smooth rollup shape. Third, a rigid joint was generated by introducing the gradient constraint equation in an optimizer. The developed framework exhibited superior convergence as compared with the conventional one in the benchmark short beam problem. It successfully generated an optimal topology with the intent of a designer (that is, designer-selected topology continuity and rigid joints), which facilitated the assembly and manufacturing of topologically optimized structural members to construct an entire aerospace structure.

Multibody analysis and soft tissue strength refute supersonic dinosaur tail.

Sauropod dinosaurs are well known for their massive sizes and long necks and tails. Among sauropods, flagellicaudatan dinosaurs are characterized by extreme tail elongation, which has led to hypotheses regarding tail function, often compared to a whip. Here, we analyse the dynamics of motion of a 3D model of an apatosaurine flagellicaudatan tail using multibody simulation and quantify the stress-bearing capabilities of the associated soft tissues. Such an elongated and slender structure would allow achieving tip velocities in the order of 30m/s, or 100km/h, far slower than the speed of sound, due to the combined effect of friction of the musculature and articulations, as well as aerodynamic drag. The material properties of the skin, tendons, and ligaments also support such evidence, proving that in life, the tail would not have withstood the stresses imposed by travelling at the speed of sound, irrespective of the conjectural 'popper', a hypothetical soft tissue structure analogue to the terminal portion of a bullwhip able to surpass the speed of sound.

Comparative study of two geometrically non-linear beam approaches for the coupled wind turbine system

In the present work, the Simo-Reissner (SR) geometrically exact beam model is integrated into the comprehensive hydro-servo-aero-elastic code hGAST for the analysis of the coupled wind turbine system. The original SR beam implementation is upgraded to account for the fully populated stiffness matrix of the arbitrary-shaped cross-section, composed of inhomogeneous and anisotropic material. Predictions of blade loads and deflections by the new beam model, for static and aero-elastic/dynamic load cases, are compared against those of the default beam model used in hGAST, i.e. a linear Timoshenko beam model in which multi-body dynamic analysis is adopted in order to account for the geometrically non-linear effects due to high deflections. The almost perfect agreement of the grid independent solutions by the two models with benchmark cases suggests that the SR beam model has been consistently incorporated within hGAST and that both modeling options can accurately predict geometrically non-linear effects due to large deflections. Their main difference is that as non-linearities become more pronounced, the number of sub-bodies used in the multi-body analysis needs to increase in order to accurately capture these effects, while the higher fidelity SR beam model provides the same level of accuracy without increasing the spatial discretization.

A multinode superelement in the generalized strain formulation

Design and optimization of flexure mechanisms and real time high bandwidth control of flexure based mechanisms require efficient but accurate models. The flexures can be modeled using sophisticated beam elements that are implemented in the generalized strain formulation. However, complex shaped frame parts of the flexure mechanisms could not be modeled in this formulation. The generalized strain formulation for flexible multibody analysis defines the configuration of elements using a combination of absolute nodal coordinates and deformation modes.This paper defines a multinode superelement in this formulation, i.e., an element having its properties derived from a reduced linear finite element model. This is accomplished by defining a local element frame with the coordinates depending on the absolute nodal coordinates. The linear elastic deformation is defined with respect to this frame, where rotational displacements are defined using the off-diagonal terms of local rotation matrices. The element frame can be defined in multiple ways; the most accurate results are obtained if the resulting elastic rotations are as small as possible. The inertia is defined in two different ways: the so-called “full approach” gives more accurate results than the so-called “corotational approach” but requires a special term that is not available from standard finite element models. Simulations show that (flexure based) mechanisms can be modeled accurately using smart combinations of superelements and beam elements.

Assessment of contact forces and stresses, torque ripple and efficiency of a cycloidal gear drive and its involute kinematical equivalent

In this paper, we assess and compare a conventional cycloidal drive and its involute-tooth kinematical equivalent via finite element (FE) and dynamical multi-body analysis. The analysis of the stiffer conventional cycloidal configuration reveals multiple points of contacts, although some of these have little contribution to the torque transmission. Significant non-torque loads are self-induced, with contact forces constantly changing in magnitude and orientation, consistently with the contact characteristics of the cycloid. In the involute alternative, the stress concentration was more localized to two or three points of contact, according to the involute contact ratio, leading to increased stresses. The contact forces remained constant relative to the tangential direction, as per the constant involute pressure angle, contributing to desirable torque loads. The torque ripple was found to have two components, one at the tooth engagement frequency ( f z ) and one at the high-speed shaft rotation frequency ( f n ), the former being more pronounced in the conventional cycloidal case, while the latter being larger for the cycloidal drive with involute teeth. Moreover, both analytical calculations and the multi-body dynamics simulations suggest that the involute-tooth design is more efficient compared to the conventional cycloidal-tooth design.

Joint parameters for strain-based geometrically nonlinear beam formulation: Multibody analysis and experiment

• Folding wing aircraft and offshore wind turbine are focused on. • An efficient dynamic simulation method is developed. • Experimental validation using wind tunnel was conducted. • Simulation and experiment were in good agreement. A novel singularity-free, tuning-free, and reduced-order strain-based beam formulation is developed for analyzing slender multibody systems such as folding wing aircraft and offshore wind turbines that perform large rigid body motions and geometrically nonlinear deformations. Conventional linear deformation models are not suitable for the analysis, whereas the strain-based beam formulation has a potential to describe the geometrically nonlinear deformation efficiently using a small number of strain variables and a constant stiffness matrix obtained from a recursive equation. However, it suffers from singularity, penalty-coefficient tuning, and many variables when applied to multibody systems. This study addressed these problems by proposing joint parameters. Singularity-free joint parameters introduced in the recursive equation produce a novel velocity transformation that removes coefficient tuning and achieves model reduction. We demonstrate that the proposed method can perform a more stable multibody analysis compared to that using the conventional method. Further, we measured the strain of the folding wing during deployment in a wind tunnel at the Institute of Fluid Science, Tohoku University to validate the strain-based beam formulation with the proposed joint parameters. The strain of the proposed method is in good agreement with that of the wind tunnel experiment, wherein the folding wing performed multibody dynamic motion with geometrically nonlinear deformation. .

Proximal junctional failure after surgical instrumentation in adult spinal deformity: biomechanical assessment of proximal instrumentation stiffness.

Assessment of different proximal instrumentation stiffness features to minimize the mechanical proximal junctional failure-related risks through computer-based biomechanical models. To biomechanically assess variations of proximal instrumentation and loads acting on the spine and construct to minimize proximal junctional failure (PJF) risks. The use of less-stiff fixation such as hooks or tensioned bands, compared to pedicle screws, at the proximal instrumentation level are considered to allow for a gradual transition in stiffness with the adjacent levels, but the impact of such flexible fixation on the loads balance and complications such as PJF remain uncertain. Six patients with adult spine deformity who underwent posterior spinal instrumentation were used to numerically model and simulate the surgical steps, erected posture, and flexion functional loading in patient-specific multibody analyses. Three types of upper-level fixation (pedicle screws (PS), supralaminar hooks (SH), and sublaminar bands (SB) with tensions of 50, 250, and 350N) and rod stiffness (CoCr/6mm, CoCr/5.5mm, Ti/5.5mm) were simulated. The loads acting on the spine and implants of the 90 simulated configurations were analyzed using Kruskal-Wallis statistical tests. Simulated high-tensioned bands decreased the sagittal moment at the adjacent level proximal to the instrumentation (1.3Nm at 250N; 2.5Nm at 350N) compared to screws alone (PS) (15.6Nm). At one level above, the high-tensioned SB increased the sagittal moment (17.7Nm-SB vs. 15.5Nm-PS) and bending moment on the rods (5.4Nm and 5.7Nm vs. 0.6Nm) (p < 0.05). SB with 50N tension yielded smaller changes in load transition compared to higher tension, with moments of 8.1Nm and 16.8Nm one and two levels above the instrumentation. The sagittal moment at the upper implant-vertebra connection decreased with the rod stiffness (1.0Nm for CoCr/6mm vs. 0.7Nm for Ti/5.5mm; p < 0.05). Simulated sublaminar bands with lower tension produced smaller changes in the load transition across proximal junctional levels. Decreasing the rod stiffness further modified these changes, with a decrease in loads associated with bone failure, however, lower stiffness did increase the rod breakage risk. N/A.

Analysis of fall kinematics and injury risks in ground impact in car-pedestrian collisions using impulse

In vehicle-to-pedestrian collisions, pedestrian injuries occur due to contact with the car and the ground. Previous studies investigated pedestrian kinematic behavior using a parameter study or through statistical analysis although the force interaction between the pedestrian and the vehicle has not been considered.In this study, multibody analyses were conducted for vehicle–pedestrian collisions for adult and child pedestrian with various vehicle shapes. The impulse and impulse moment acting on the pedestrian from the vehicle were introduced, and the kinematic behavior, rotation and ground impact of the pedestrian model were examined. It was found that if an impulse moment acts on the pedestrian when the pedestrian re-contacts with the hood of the car, the angular velocity of the pedestrian’s torso changes in the opposite direction (away from the car), and the torso angle prior to the ground contact decreases to less than 90°. This re-contact between the pedestrian and the vehicle was more likely to occur for cases where the collision involves an adult pedestrian, lower hood leading edge (HLE), longer hood length, and lower collision velocity. When the pedestrian torso angle in contact with the ground was less than 90°, the head vertical impact velocity with respect to the ground became less than 2.9 m/s which corresponds to the injury threshold of the head.This study demonstrated that pedestrian-vehicle re-contact is crucial for reducing ground injury. The vehicle shape, pedestrian size, and collision velocity can determine whether re-contact of the pedestrian with the vehicle occurs. This can then explain the factors affecting pedestrian ground impact injury (e.g., higher HLE, higher risk of ground head injury for children) that were shown in previous studies. A strategy to mitigate ground injury is to apply enough impulse moment onto the pedestrian’s upper body from the hood in order to change the torso angular velocity during re-contact, thus making the torso angle less than 90°prior to the ground contact.

Bioinspired flapping wing UAV and its kinematic analysis—a novel approach

A rich development in the domain of flapping wing Unmanned Aerial Vehicle (FWUAV) is not yet entirely sufficient to implement the findings of real-life situations. Using the limited knowledge of this domain, this work enlightens the scientific community by introducing a homegrown, patented flapping mechanism of foldable wing aerial vehicle. The synchronized dual wing flapping mechanism consists of a crank slotted lever, a gear train and a special type of 4 bar kinematic chain. The entire sets are powered by a DC motor through crank connected motor shaft. Flapping cycle works on quick return principle generated by crank slotted lever mechanism and foldable wing structure by the special type 4 bar chain with gear train ensure the controlled flapping frequency, twist angle, altitude gain and attitude parameters (Pitch, roll, yaw). This work majorly focuses on the kinematics of the developed bio mimic mechanism by observing the variation of flapping wing orientation, angular velocity and angular acceleration with respect to the crank rotation as well as different crank speeds. These analytically obtained kinematic parameters are further validated after developing a three-dimensional model of the said mechanism as well as multibody analysis by MSC ADAMS. The patterns of the kinematic parameters such that angular displacement, angular velocity and angular acceleration between output and input links are similar and its validation guarantees the correctness of developed mechanism. The kinematic analyzes of linkages are also essential for dynamic study as well as fabrication of prototype.

Generalized Gibbs–Appell’s equations and two-dimensional finite elements model used in flexible multibody analysis

Generalized Gibbs–Appell’s equations and two-dimensional finite elements model used in flexible multibody analysis

Efficient Computation of Large Deformation of Spatial Flexure-Based Mechanisms in Design Optimizations

Abstract Design optimizations of flexure-based mechanisms take a lot of computation time, in particular when large deformations are involved. In an optimization procedure, statically deformed configurations of many designs have to be obtained, while finding the statically deformed configuration itself requires tens to hundreds of load step iterations. The kinematically started deformation method (KSD-method) (Dwarshuis, K. S., Aarts, R. G. K. M., Ellenbroek, M. H. M., and Brouwer, D. M., 2020, “Kinematically Started Efficient Position Analysis of Deformed Compliant Mechanisms Utilizing Data of Standard Joints,” Mech. Mach. Theory, 152, p. 103911) computes deformed configurations fast by starting the computation from an approximation. This approximation is obtained by allowing the mechanism only to move in the compliant motion-direction, based on kinematic equations, using data of the flexure joints in the mechanism. This is possible as flexure-based mechanisms are typically designed to be kinematically determined in the motion directions. In this paper, the KSD-method is extended such that it can also be applied without joint-data, such that it is not necessary to maintain a database with joint-data. This paper also shows that the method can be used for mechanisms containing joints that allow full spatial motion. Several variants of the KSD-method are presented and evaluated for accuracy and required computation time. One variant, which uses joint-data, is 21 times faster and shows errors in stress and stiffness below 1% compared to a conventional multibody analysis on the same model. Another variant, which does not use joint-data, reduces the computation time by a factor of 14, keeping errors below 1%. The KSD-method is shown to be helpful in design optimizations of complex flexure mechanisms for large range of motion.

Structural design of multi-body heave wave energy conversion system and analysis of energy efficiency of floating body on water surface

Abstract. Due to the defects of the internal structure and energy supply carrier, conventional deep sea unoccupied marine equipment cannot meet the requirements of low power consumption. In this paper, the whole structure of a multi-body heave wave energy conversion system was designed to capture and convert wave energy. The conversion system consists of a floating body, an underwater absorber and a power takeoff system (PTO). The dynamic model of the energy conversion system and the mathematical model of energy efficiency evaluation were established according to the dynamic analysis. Based on the real service environment in the South China Sea, the energy efficiency characteristics of floating bodies with different shapes were simulated, and the amplitude response operator (RAO), radiation damping, added mass and Froude–Krylov force of floating bodies with different shapes were compared. Then, the optimal energy efficiency parameters of surface floating body were explored. Finally, the correctness of the conclusion was verified by the energy efficiency test. The results show that, under the limitation of low power consumption and space scale, the energy conversion system of an axisymmetric rotary body with the same sea conditions, same material and the largest scale can significantly improve the conversion efficiency, and the spherical rotary body performs the best, which makes the unoccupied marine equipment have a broad prospect for development.

Effect of Web Flexibility in Gear Engagement: A Proposal of Analysis Strategy

Increasing torque and power density in geared transmissions is a constant trend, especially due to the electrification and the research of higher efficiency. Thinner web of the gears has led to potentially higher vibration amplitudes and noise levels, which need to be accounted for in the design stage to avoid fatigue or NVH problems. In the present paper a novel model to represent the dynamic interaction in geared transmissions is presented. The compliances of the shafts are taken into account in two different ways: in a simple strategy, by means of three-dimensional beam elements; in a more detailed methodology, by reduction in a FE model of the gear and shaft assembly. The different gears are connected using kinematic relationships exploited by means of rigid joints and rigid body elements. The flexibility of the teeth and of the gear body is introduced based on an established nonlinear calculation model and is employed as the only dynamic excitation source as a time varying mesh stiffness. Thanks to the reduced size of the matrices a direct integration scheme is used for the time domain analysis of the transmission. Such methodology enables the possibility of modeling dynamic contact loss and torque variations at different rotational velocities with reduced computational times in comparison to other approaches. The technique is then applied to two different geometries of driven gear: one with solid web and one with flexible web. The dynamic behavior of the two different solutions is studied and the differences are highlighted. The proposed approach proves to be more efficient than traditional multibody analyses and quicker than finite element approaches, while maintaining a similar accuracy. It proves to be effective also for studying the transmission with flexible web.