Table 3 - available via license: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Content may be subject to copyright.
Source publication
A finite-element based absolute nodal coordinate formulation (ANCF) is applied to dynamic analysis of high-speed rotating shafts. To this end, a four-node higher-order ANCF beam element with third-order derivatives in the axial and cross-section directions is studied. Using a number of eigenfrequency, static and dynamic benchmark tests, it is shown...
Context in source publication
Context 1
... eigenfrequency analysis in ANSYS was performed using SOLID186 composed of 96 × 8 × 8 elements. The selected mode shapes obtained by the higher-order ANCF beam element are depicted in Fig. 7 and those obtained by ANSYS with a solid element are illustrated in Fig. 8. Table 3 shows natural frequencies associated with the hollow circular cross-section case. Compared with the earlier eigenfrequency tests, the ANCF beam element shows stiffer behaviour with the relatively thick-walled hollow cross-section. ...
Citations
... -The use of flexible multibody dynamics through ANCF has improved the ability to simulate and execute these complex sequences with high fidelity [80][81][82]. ...
The pursuit of realism in cinema has driven significant advancements in animatronics, where the integration of mechatronics, a multidisciplinary field that combines mechanical engineering, electronics, and computer science, plays a pivotal role in enhancing the functionality and realism of animatronics. This interdisciplinary approach facilitates smoother characters movements and enhances the sophistication of behaviors in animatronic creatures, thereby increasing their realism. This article examines the most recent developments in mechatronic technology and their significant impact on the art and engineering of animatronics in the filmmaking. It explores the sophisticated integration of system components and analyzes how these enhancements foster complexity and integration, crucial for achieving unprecedented levels of realism in modern cinema. Further, the article delves into in-depth case studies of well-known movie characters, demonstrating the practical applicability of these state-of-the-art mechatronic solutions in creating compelling, lifelike cinematic experiences. This paper aims to bridge the gap between the technical aspects of mechatronics and the creative demands of the film industry, ultimately contributing to the ongoing evolution of cinematic realism.
... Yoo et al. [50] reviewed different ANCF elements and experimentally verified the large deformations of plates and 3D strips. Using different ANCF elements, the complex dynamics of various structures such as marine cables [51], cables in suspension bridges [52], rotating shafts [53], flexible pendulum [54], and planar slider-crank mechanism [55] are modeled successfully. It can represent the dynamics of the flexible beam in ANCF. ...
In this work, a semi-analytical approach called the time variational method is used to evaluate the system’s nonlinear normal modes in the time domain. A flexible cantilever beam with a cubic nonlinear spring supported at the tip is modeled using the Euler–Bernoulli beam element in the classical finite element method and the 3D gradient-deficient beam element in the Absolute Nodal Coordinate Formulation. The time variational method approach is used to extract the nonlinear normal mode for both modeling strategies, which is then compared with the nonlinear normal mode of the Euler–Bernoulli beam model computed using the harmonic balance method and is in good agreement. Furthermore, the Absolute Nodal Coordinate Formulation was able to predict additional internal resonances that were not present in the Finite Element Method’s nonlinear normal mode.
... Rotating thin plate serves as a useful model for many engineering applications, such as helicopter rotors, wind turbine blades, and flexible rotating solar sails [1][2][3][4]. Compared with non-rotating structures, rotating thin plate exhibits much more complex dynamic characteristics [4,5], among which the dynamic stability characteristics is a tough one. ...
Increasing the critical angular speed of a rotating structure can enlarge working range and enhance operating safety. To achieve this purpose, a topology optimization approach is proposed to increase the critical angular speed of a rotating thin plate in this paper. Firstly, the stability analysis of a rotating thin plate is performed by using the absolute nodal coordinate formulation modeling scheme, which can accurately account for the large deformation and large rotation of the rotating thin plate. In order to overcome the difficulty of non-differentiability of the critical angular speed with respect to the design variables, an alternative density-based topology optimization model for improving stability is then established by minimizing the real part of the eigenvalues of the rotating thin plate. A successive approximation dynamic programming method is therefore proposed to approaching the critical angular speed by repeatedly solving the aforementioned topology optimization problem. Finally, one dynamic example and two optimization examples are presented to respectively demonstrate the accuracy of the stability analysis procedure and the effectiveness of the proposed topology optimization problem.
... Their studies showed that a combination of metal and composite materials in the shaft system leads to lower stresses and reduced torsional vibrations than existing metal shafts. Also, this process leads to decrease shaft deformation over a more extended time. in 2019, Babak Bozorgmehri [10] used finite element and absolute node coordinate formulation (ANCF) to analyze high-speed rotating shafts dynamically. This study first investigated the design of higher-order elements with four nodes, and static tests for a beam under distributed loads showed acceptable results. ...
This paper aims to obtain an application software using Ansys software in which a static, dynamic, and modal analysis for the power transmission of ships is presented. The objective functions of this research are maximum static stress, maximum dynamic stress, shaft mass, and modal shaft frequency analysis. A complete, comprehensive , and generalizable model for metal shaft types is presented. Then, using the kriging response surface and multi-objective genetic algorithm (NSGA II), these goals are optimized simultaneously. In this research, the optimization parameters are geometric parameters of the shaft design, including the position of the supports and the inner and outer diameters of the shaft. As a result of this optimization, the shaft's maximum static and dynamic stresses are reduced by 36% and 42%, respectively. The shaft's mass, which is one of the most critical factors during the shaft and its vibrations, is reduced by about 9%. In this regard, the first natural frequency of the optimized shaft increased by about 28.5% compared to the initial shaft.
... Likewise, Hoekman et.al (2017) developed a twin-screw extruder (having a 25 mm diameter) operating at high pressure of 25 MPa and temperature of 350 °C. It exhibited a shorter residence time (21)(22)(23)(24)(25)(26)(27)(28) sec) compared to the conventional reactor [12]. In addition, an auger-type screw reactor was used for recycling the plastic waste through pyrolysis, it is performed at temperatures between 380 °C and 600 °C with better axial dispersion and uniform flow in thermal conditions over the length with respect to time [13]. ...
... Further discretization of screw shaft was done using adaptive meshing technique for the size of 2 mm and is given in Fig. S1 c, d). Also, the high smoothing mesh was adapted to get better convergence results especially on transient conditions [28][29][30]. For pure torsion acting on the screw shaft, it was assumed that the shaft material is homogeneous and perfectly elastic. ...
Hydrothermal co-liquefaction (HTCL) is the prominent process for producing bio-products with a higher conversion rate. It is performed at high temperatures and pressure in the presence of water. Earlier, it was mostly conducted in batch reactors, but it has major limitations including operating volume, back mixing and tedious process for high productivity. With that, the present investigation is performed on designing the screw shaft for the high-pressure HTCL process. The dimensional factors including flight length, pitch, helix angle and depth were considered to design the optimal screw shaft. Likewise, principal stresses, shear stress, bending stress, bending moment and total deformation were regarded as inevitable response variables to analyze the internal strength of the shaft. In this regard, the Taguchi approach provides the L9 (34) orthogonal array as an experimental design. Then, the numerical results from the transient structural analysis were analyzed with the assistance of statistical methods such as Grey Relational Grade (GRG), Grey Fuzzy Reasoning Grade, Analysis of Variance (ANOVA) and Taguchi method to find the most influential dimensions for minimizing the response variable. Consequently, the results from both GRG and Taguchi optimization were compared and selected the most optimum parameters.
... Nonetheless, for the transverse low-order beam elements (see [29][30][31]) the cross-sectional deformation modes are very simple and will always be flat [37], which are similar to the Timoshenko beam model. But by the transverse higher-order beam elements (see [32][33][34][35]), the cross-sectional warping and distortion with more complex modes can be captured, where that proposed by the authors of [33] has been applied to some challenging nonlinear dynamics problems [38][39][40][41][42]. ...
... (28) and using these vectors in Eqs. (40) and (41), one obtains ...
A sufficiently accurate prediction of mechanics behavior for thin-walled structures has always received much attention in the development of beam theory. This paper proposes a novel modeling approach for thin-walled beams in the framework of the absolute nodal coordinate formulation, in which cross-sectional warping and distortion effects can be explicitly captured by using the Taylor-like polynomials as the description of the kinematics of beam cross-section. Meanwhile, the linear Lagrange interpolation and the cubic Hermite interpolation are respectively adopted for the off-axis vectors of the position coordinates, where it is found that the thin-walled beam elements constructed from the latter have a faster convergence rate. Elastic forces and the Jacobian of the thin-walled composite beams are derived on the basis of nonlinear continuum mechanics, which will therefore contain a strong coupling between various deformations. Furthermore, their efficient calculation scheme is presented by separating the axial and transverse variables of shape functions and by expressing the vector and matrix quantities in terms of their components. By comparison to finite shell element, the accuracy and characteristic features of the new elements are illustrated.
... Lots of scholars use 3D ANCF beam to analyze the dynamics of rotating shaft. 22,23 However, 3D ANCF beam elements yielded too large torsional and flexural rigidities so that shear locking effectively suppressed the asymmetric bending mode for a slender flexible spatial beam. Schwab et al. 24 proposed new absolute nodal coordinate formulation with the elastic line approach to calculate a slender flexible spatial beam. ...
... Dynamic model of round balance with BRSR. If the round balance rope is connected to the conveyance through BRSR, the constraint equation Φ N Φ N ¼ ½ g 1 g 2 g 3 g 4 g 5 g 6 (23) when both BRSRs are stuck, constraint equation Φ N can be written as equation (22). Φ T denotes the relative tangential displacement of torsion constraint joint ...
Torsion deformable spatial beam and Costello theory are used to establish longitudinal-torsional-lateral coupled model of round balance rope. Based on Coulomb’s friction law and longitudinal-torsional-lateral coupled model, the nonlinear coupled dynamic model with friction constraint of round balance rope is established. Meanwhile, time-varying multi-segments non–equal-length element transformation method (TMN-ETM) is proposed to save computation time. Then, natural frequencies, lateral responses are calculated when the coupled stiffness coefficient is zero. And the calculations are compared with traditional solution method. The results show that only about few areas in the round balance rope loop have large stress norm value, while the rest parts have small stress values. Besides, dynamic responses of the balance rope with balance rope suspension rotor releasing are conducted. When the static friction is converted to dynamic friction, the friction torque and angle acceleration will be mutated at the switching instants, and slip-stick transition in angle acceleration occurs.
... Usually mechanical oscillations (vibrations) that occur in technological units and in electromechanical complexes (EMCs) are undesirable phenomena. Therefore, there is a need for continuous monitoring of motion and vibration parameters, as well as a comprehensive assessment of the state of machines with rotating shafts [1][2][3][4][5]. ...
... Experience in the construction and operation of technological units, energy-intensive machines, metal cutting machines, instruments and electromechanical complexes indicates the need to obtain information about the motion and vibration parameters of dynamic objects. Nowadays, an urgent task is to obtain information about the radial deformation of rotating shafts in the electromechanical complexes under operation [1][2][3][4][5][6][7]. In machines with rotating shafts elastic couplings are used, which absorb axial, radial and angular displacements due to their elastic, damping and dissipative properties [8]. ...
The task of measuring of rotating shafts angular deformation by means of ultrasonic vibration meter is considered in the article. Measurement of vibration parameters of rotating objects is an urgent task in the technical diagnostics of electromechanical units, turbines, drilling rigs and metal-cutting machines subject to vibration disturbances. The measured vibration parameters of rotating shafts include their angular deformation and torques arising from torsional vibrations of shafting of machines in the stationary and mobile objects. Timely monitoring of the torsional vibrations of the shafting and other factors of vibration disturbances by the frequency of shaft beats makes it possible to identify defects at an early stage and eliminate breakdowns that threaten the life and safety of personnel. It was found out that the reflected acoustic signal phase measurement relative to the reference one incident onto the investigated shaft surface can be carried out with error at 0.6 % at velocities not more than 0.5 m/s. This article is intended for mechanical engineers involved in the development and operation of rotating machines of stationary and mobile objects.
... Some other applications include components spinning or rotating at very high speeds. Examples of application problems that have been solved using ANCF elements are belt drives [12,13,76]; rotating structures, shafts, beams, strings, and plates [4,15,24,31,38,172,175,211]; vehicle components [74]; wind-turbine blades [2,3], nuclear-reactor applications [8]; catenary and power-transmission lines [30,46,47,50,88,141,149,171]; cables, tethers, ropes, and cable/pulley systems [10,32,33,56,61,62,71,75,200]; and space applications and deployable structures [52,66,91,135,180,196,197,210]. ...
This paper presents an overview of the finite-element (FE) absolute nodal coordinate formulation (ANCF), provides justifications for its use, and discusses issues relevant to its proper computer implementation and interpretation of its numerical results. The paper discusses future research directions for using ANCF finite elements in new areas such as soft tissues and materials relevant to broader areas of computational engineering and science. Selection of coordinates, definitions of forces and moments, geometric interpretation of the position gradients, and noncommutativity of finite rotations are among the topics discussed. To address concerns associated with finite-rotation noncommutativity and definition of moments in flexible-body dynamics, the paper demonstrates that the interpolation order is not preserved when the finite-rotation sequence is changed. Position gradients, on the other hand, are unique and preserve the highest interpolation order. It is shown that, while the spin tensor used to define the ANCF generalized forces due to moment application is associated with a rigid frame defined by the polar decomposition theorem, explicit polar decomposition of the matrix of position-gradient vectors is not required. ANCF elements have features that distinguish them from conventional finite elements and make them suited for large-displacement analysis of multibody systems (MBS). Their displacement fields, which allow increasing interpolation order without increasing number of nodes or using noncommutative finite rotations, are the basis for developing lower-dimension consistent rotation-based formulations (CRBF) without lowering the interpolation order. Nonetheless, the continuum-kinematic description of fully parameterized ANCF elements cannot be ignored when interpreting the ANCF numerical results. This issue is particularly important when comparing ANCF results with solutions obtained using semi-continuum conventional beam and plate models and simplified analytical approaches.
... Recently, a new ANCF element with an additional gradient vector with respect to a warping function was introduced in Tang et al. (2022) where the element delivered acceptable displacement-based results for the Princeton experiment. However, the challenging bi-moment beam problem was missing in the work and moreover, the superiority of the proposed element over the existing higher-order elements in terms of the stress measures over cross-section (Bozorgmehri et al., 2019) was not discussed. ...
... The element 3363 has also showed its performance and accuracy with Princeton benchmark in Nachbagauer et al. (2013a). The four-node element 34X3 exhibited the excellent capability of capturing complex cross-section deformation modes and accurate stress distribution over its cross-section thanks to the cubic interpolation along the crosssectional directions (Bozorgmehri et al., 2019). Element 3463 that is also a four-node beam element, but with a quadratic interpolation bases along the cross-sectional directions, aims to be a counterpart for the element 34X3. ...
This paper explores the usability of several beam elements based on the Absolute Nodal Coordinate Formulation (ANCF) subjected to torsional and bi-moment loading scenarios. ANCF beam element solutions are compared against an analytical solution and beam and solid finite element solutions. When subjected to bi-moment loading, most of studied higher-order ANCF beam elements suffer from strong “non-smooth” displacement continuity between elements, and therefore they should be used with caution. The distribution of warping displacement was shown to be unacceptable for four-node higher-order ANCF beam elements. Numerical results revealed that the higher-order elements failed to characterize local loading scenarios such as a bi-moment. This problem can be alleviated using very fine beam discretization, which would be more computationally intensive.
