Shaft Model Research Articles

Feed shaft thermal expansion error modeling based on principal component regression

In order to further improve the prediction accuracy of the thermal error model of the feed shaft of the gear grinding machine, this paper proposes a feed shaft thermal expansion error modeling method based on principal component regression. The feed shaft positioning error is decoupled by linear fitting to obtain the thermal expansion slope parameter, the position correlation of the feed shaft thermal expansion error is eliminated, and a regression model of the thermal expansion slope parameter and the temperature of all measuring points is established based on the principal component regression algorithm. Different from the traditional method, the principal component regression model does not require additional screening of temperature sensitive points, and the root mean square error mean and standard deviation of the group experimental prediction results can reach 2.0 μm/m、0.9μm/m, which has higher accuracy and stability than conventional methods.

Dynamic Modeling and Vibration Characteristic Analysis of Fiber Woven Composite Shaft–Disk Rotor with Weight-Reducing Holes

In order to achieve the goal of a lightweight shaft–disk rotor, this paper applies the fiber woven composite material to the disk structure, and at the same time considers the design of the weight-reducing holes on the porous disk. It introduces the domain decomposition and coordinate mapping technology for this, and then establishes the dynamics model of the fiber woven composite material shaft–disk rotor. The model is based on the differential quadrature finite element method, which is suitable for fiber woven composite rotors with arbitrary complex hole patterns. The validity of the model is verified by comparing the results with the literature, finite element simulation, and experiments, and the mechanism of the influence of the material parameters and pore parameters on the vibration characteristics of the system is investigated, which provides the data support and theoretical basis for the analysis of the dynamics of the fiber woven composite rotor.

A new periodic shaft model for broadband ultra-low-frequency vibration reduction in spinning shafts

Vibration isolation is found in periodic structures having a special feature known as vibration band gap. A periodic shaft model is proposed and analyzed in this study. This model is composed of a spinning solid shaft carrying periodic arrays of outer cantilever hollow shafts. The generalized differential quadrature rule (GDQR) method combined with the Bloch theorem is used to calculate the vibration band gaps of this periodic shaft. Results are verified by the forced vibration responses obtained using the GDQR method. Results indicate that for each length of the hollow shafts, there is a spinning velocity range for which the first band gap starts from zero frequency. In other words, each model of this periodic shaft can be used for vibration reduction over an ultra-low-frequency band gap at different spinning velocities. Results also indicate that there is a model with specific value of the hollow shafts length for which the second band gap is very close to the first band. For this model, the width of the ultra-low-frequency band gap is much greater than other models. Finally, verification of the GDQR method shows that it can be used as a precise numerical method for free and forced vibration analysis of the spinning shafts.

Effect of AVL-based time-domain analysis on torsional vibration of engine shafting

The torsional vibration of the shaft system in hybrid car engines has a significant impact on the overall performance of the vehicle, and it is more complex in hybrid cars compared to traditional cars. Traditional methods for torsional vibration analysis of shaft systems have significant limitations and cannot handle nonlinear and transient problems. To explore the torsional vibration characteristics of hybrid vehicle shaft systems, a simplified engine shaft system torsional vibration equivalent model is innovatively constructed. In addition, a method for quickly determining the confidence level of the torsional vibration equivalent model is proposed. Additionally, the transient dynamic characteristics of a multi-body dynamics model containing a dual mass flywheel are analyzed in depth using the time-domain solver of AVL-exact PU. The results demonstrated that the simulation of 4th and 6th harmonics resonated at critical speeds of 4,195 rpm and 2,771 rpm, respectively, with angular displacement amplitudes of 0.141 deg and 0.047 deg. In fact, resonance was measured at 4,250 rpm and 3,040 rpm, with amplitudes of 0.14 deg and 0.052 deg. These two were basically consistent in key parameters. When the shaft model was started under operating conditions, the amplitudes of harmonics 1, 2, and 4 were basically consistent below 750 rpm, and there were slight differences after 750 rpm. Therefore, the AVL-based engine torsional vibration simulation model constructed has high credibility.

Abstract Concept Visualization: Innovative Teaching Mode for Engineering Mechanics Experiments

There are persisting issues in the ineffective teaching of mechanics laboratory courses within vocational education systems. Hence, this study aimed to investigate the utility of finite element analysis (FEA) for developing instructional resources. Solid and hollow shaft models were numerically analyzed to examine their stress distributions and deformation patterns. This digitized content was incorporated into the existing curriculum. An experimental teaching activity was organized and evaluated using questionnaires and instructor-student exchanges. Results indicated that FEA-based visualization significantly improved student comprehension of stress distributions and deformation modes along the shaft. Overall satisfaction with the teaching experiment was 30 out of 33 participants, though this innovative approach enhanced interest, it lacked in fully facilitating positive discussions. In summary, FEA can effectively augment traditional torsion experiment instruction by providing clear, engaging visual representations. Further case studies merit exploration and practice by educational researchers to realize the full potential of FEA for mechanics laboratory pedagogy.

EXPERIMENTAL INVESTIGATION OF THE VIBRATION-REDUCTION CHARACTERISTICS OF THE SHAFT COATING FOR A TURBOCHARGER

A turbocharger is a system that is fitted to automotive engines to increase performance and efficiency by taking air at atmospheric pressure, compressing it to a higher pressure and passing the compressed air into the engine via the inlet valves. A turbocharger consists of a turbine and a compressor impeller interconnected with a shaft supported in most cases by journal bearings. The shaft is one of most crucial components of a turbocharger system and it operates at high speed. The shaft vibrations are an inherent phenomenon and they are travelling to the surrounding structure, effecting the stability and reliability of the turbocharger system. The selection of the appropriate shaft-material property is a critical parameter among the parameters that affect the vibration of the system. This study focuses on exploring whether it is possible to reduce the shaft vibration using different types of coating materials, including aluminum chromium nitride (AlCrN), titanium nitride (TiN) and aluminum titanium nitride (AlTiN), each having thicknesses of (2, 4, and 6) µm, for a shaft made of AISI 4140 alloy steel. The inherent natural vibration properties, such as the resonant frequencies, damping, and mode shapes of the turbocharger shaft with and without coating, were obtained by conducting an experimental modal analysis through measurements of the frequency-response function, which is about curve fitting the data using a predefined mathematical model of the turbocharger shaft. The results were validated numerically with the finite element method. From overall results, it was observed that the AlCrN, TiN, and AlTiN coating thicknesses have a small effect on the resonant frequencies, but a good damping effect. The resonant response of the turbocharger shaft at resonant frequencies was suppressed remarkably by the AlCrN and AlTiN coatings, especially those having a thickness of 6 and 4 µm.

Modeling of flexible shaft for robotics applications

Reducing moving mass and effective inertia is essential for achieving safe human–robot collaboration. This can be achieved either by employing remote actuation, which moves the mass of actuators away from the moving elements of the robot, or by elastic actuation, which decouples the inertia of the actuator from the inertia of the robot’s link. Flexible shafts, being torsionally compliant slender long shafts, offer a combination of remote and series elastic actuation over an obstacle. Modeling such transmission is complicated due to its three-dimensional deformation in torsion, bending, and helical buckling. This paper proposes an algorithm for estimating the polar moment of inertia and stiffness of the flexible shafts using their physical dimensions of length and diameter. Using an inertia-spring–damper model, the stiffness parameters are estimated experimentally for nine flexible shafts with variable diameters and lengths in straight and bent configurations. The proposed algorithm is validated with experimental stiffness values for variable diameters and lengths in straight configuration. For bent configuration, an empirical formulation is provided to incorporate the bending deformation effect till a bending angle of 45∘.

Account of additional factors for damping torsional oscillations

Some parameters are influenced by the turbine unit's torsional oscillations. The fundamental comes from damping these oscillations, which are brought on by a departure in the turbine blades' speed from the device's prediction of the steam volume, and attenuation of fluctuations due to the distribution of energy in the turbine's productive components. The usual single-machine infinite bus system is used for the analysis. For various turbine-generator shafts and various generator operating situations, rotating mass mechanical system evaluations for small-signal stability and large disturbance are conducted. It is demonstrated that the shaft's “structural' damping (H) and “steam' damping (Kn) coefficients have a considerable impact on the damping of torsional modes. The goal of this work is to determine the effect of changing the damping factors in the mathematical model of the steam turbine shaft on the system's static stability, as well as the extent to which these variables' limits on damping rotational oscillations on the maximum torsional torques generated in the shaft masses. The mathematical model of the steam turbine shaft with a single machine and transmission line to an infinite bus system was simulated using Dymola software, and the static and dynamic effects of damping factors (H) and (Kn) on system stability were demonstrated. By evaluating the best case for parameters with the least influence on the system's stability, the results were obtained by changing the factors (Kn) from 0.005 to 0.5 and (H) from 0.005 to 0.2 and the extent of its effect on the maximum torque of the steam turbine masses and reducing it by 8.4 %, as well as by reducing the settling time of the system after disturbances occur and reaching to Steady state by about 90 %.

MECHANICAL SHAFT OPTIMIZATION: A STUDY ON STATIC STRUCTURAL ANALYSIS AND TOPOLOGICAL OPTIMIZATION IN ANSYS

Shafts are extensively used in engineering fields, serving roles in power transmission and rotational movement, thus holding significant importance. This study focuses on analyzing the structure of a selected shaft model derived from research. Subsequently, topology optimization is applied based on the obtained findings. ANSYS software is utilized for performing analysis and optimization analysis. Following the completion of these analyses, the results are thoroughly examined. The optimization process resulted in a reduction of about 2.65% in the maximum stress and approximately 2.46% decrease in the maximum strain, indicating improved mechanical performance. However, an increase of about 33.24% in maximum deformation was observed, which warrants further consideration. Most notably, the weight of the shaft decreased significantly by approximately 57.81%, resulting in the creation of a much lighter model. These outcomes highlight the potential of topology optimization, demonstrating the ability to create lighter and stronger models while utilizing resources efficiently. Consequently, it becomes imperative to explore these outcomes further by modifying selected parameters to achieve optimal results and enhance the model's performance. This study successfully showcases the potential of topology optimization, paving the way for the creation of lighter and stronger models in engineering applications.

Stochastic analysis of flexible rotor supported on hydrodynamic bearings

Rotating shaft instability leading to high amplitude vibration is a key problem with a wide range of industrial applications. The purpose of this study is to identify the response statistics for a conceptual model of a flexible shaft supported on hydrodynamic bearings (HDBs) and propose design strategies to reduce the response. A conceptual model of a flexible shaft with three discs supported on the HDBs is developed. A linearised model of the system is developed using the short bearing assumption. A Campbell diagram is developed for the conceptual model to identify the critical speeds wherein a high response is produced. These high responses occur at the rotor speeds corresponding to the synchronous forward whirl and the oil whip. The identified rotor speeds are validated by carrying out a run-up analysis on the test rig. Since the manufacturing process and operating conditions induce uncertainty by varying the eccentricity and the relative phase of the unbalance mass, the influence of the whirling modes on the response is investigated. The nominal positions of the unbalance masses are such that the predominant mode excited is the first mode. Experimentally a scatter plot on the maximum response at the bearing location is identified using six different positions of the eccentric mass. Further, a stochastic analysis using reduced order nonlinear model of the system is carried out. The probability density obtained is compared with a Monte Carlo simulation and the bounds of the experimental results. A control strategy is designed by altering the relative position of the unbalance masses to reduce the excitation of the first mode. The robustness of the strategy is verified by using a stochastic analysis, which indicates a reduction in the response magnitude.

Optimization and design analysis of 2-kW induction motor shaft by using Finite Element Analysis

The shaft is a very critical part of a 2-kW induction motor due to its function to support other vital components, such as the rotor, bearing, and casing. Finite Element Analysis (FEA) is used to analyze the shaft model. A meshing convergence test was conducted prior to the optimization. In which a mesh size of 0.5 mm and a tetrahedron shape are selected for the whole simulation to determine critical areas on the electric motor shaft (EMS). In this study, shaft optimization was conducted by using three manners in a sequential process, namely reducing the shaft seat for the rear bearing, modifying the step in front of the rear bearing, and then making the taper from the step in the previous process. This design modification was made to reduce the shaft mass and the maximum equivalent stress. At first optimization, namely replacing the rear bearing and its mount on the shaft, it succeeded in reducing the axle weight by 2,81%. However, the max equivalent stress increased from 30.347 MPa to 54.756 MPa which is located at the intersection of the stepped area, as well as deformation also increased from 0.002434 mm to 0.0026894 mm at the middle shaft. This drawback is overcome by changing the depth of the stepped area and creating a taper. In which the shaft mass can be reduced from 431.07 g to 408.20 g, as well as max equivalent stress is reduced from 54.756 MPa to 28.637 MPa.

Body Force Modeling of the Fan Stage of a Windmilling Turbofan

Abstract The determination of the rotational speed and massflow of the fan of a turbofan at windmill is critical in the design of the engine-supporting structure and the sizing of the vertical stabilizer. Given the very high bypass ratio obtained at windmill, the flow in the fan stage and bypass duct is of prime interest. Classical computational fluid dynamics simulations have been shown to predict such flows accurately, but extensive parametric studies can be needed, stressing the need for reduced-cost modeling of the flow in the engine. A body force modeling (BFM) approach for windmilling simulations is examined in the present contribution. The BFM approach replaces turbomachinery rows by source terms, reducing the computational cost (here by a factor 6). A shaft model is coupled to the BFM source terms, to drive the simulation to a power balance of the low-pressure shaft. The overall approach is thus self-contained and can predict both the massflow and the rotational speed in the windmilling regime. Comparisons with engine experimental results show the proposed model can predict the rotational speed within 7%, and the massflow within 5%. Local analysis and comparisons with experimental data and reference blade calculations show that the work exchange, in term of total temperature variation, is predicted within 0.5 K, and the overall total pressure ratio within 1%. However, the losses in the stator are largely underestimated, which explains the discrepancy for the massflow predictions.

Study on temperature distribution and smoke diffusion characteristics of cable shafts in high-rise buildings

The smoke and poisonous gas produced during combustion is one of the direct hazards of cable fire. For power cables laid vertically in the cable shaft of high-rise buildings, the chimney effect will speed up the spread and expand the harm of cable fire. The paper proposes a simulation method based on fire dynamics theory to analyze the diffusion and spread characteristics of cable fire. First, a three-dimensional model of the double-floor cable shaft with multiple cables laid vertically inside was built in the paper. Second, with the abnormal heating caused by overload or insulation breakdown as the excitation condition, the development process of cable fire is simulated. The diffusion of smoke and gas during the whole combustion process is studied and discussed. Then, the paper compares the simulation results of the model with different fire blocking materials. The simulation results show that the application of blocking materials will cause differences between the spread of fire and flue gases, and the difference can be used to evaluate the quality and performance of the fire blocking material. Finally, A test platform is constructed to verify the validity of the simulation analysis.

Investigation of wt.% Si and Heat Treatment on the Mechanical Properties of Al6063 Aluminum Alloy by the Casting Product Propeller Shaft Model

Shaft propeller is one of the most important parts of ship propulsion installations. To produce a good quality shaft propeller, the ship propeller designer must consider various parameters, in order to produce the type and size of the propeller that has the value of effectiveness and high propulsion efficiency. Shaft propellers are usually made of steel but, in this study the propeller shaft model is made of Aluminum Alloy base material. So the material must have good mechanical properties. The purpose of this study is to see the mechanical properties of the sheller propeller with aluminum alloy base material with the addition of silicon elements and magnesium by going through the heat treatment process. The main base material used is 6063 aluminum alloy, with variations in the addition of Si (1, 2, 4 wt%). The addition of Mg can improve the mechanical properties of the casting. Alloy Al6063 is heated to a temperature of 790°C to reach a complete liquid state. Then the temperature is lowered to 645°C, then the Si element is inserted into the heating furnace and stirred. Then the temperature is lowered to 615°C, then the Mg element is added, then stirred thoroughly by a mechanical stirrer. The rotational speed of the stirrer is 70 rpm and the stirring time is 240 seconds. Then heated to a pouring temperature of 670°C. The mold is heated to a temperature of 265°C. Then poured into the mold and pressed 7 MPa. After that, it was allowed to stand for 600 seconds, and then removed from the mould. The cast propeller shaft is cooled at room temperature. Then the propeller shaft was heat treated with a solution treatment temperature of 485°C for 3600 seconds and then quenched using a fluid. After that, the casting products were treated with artificial aging. The results of the study are, Porosity will decrease along with the addition of Silicon elements. The lowest porosity level is in addition of 3% wt Silicon that is equal to 1.15%. Tensile test with the addition of 1% wt Silicon ie, 106.882 MPa, in addition of 2% wt Silicon that is, 128.713 MPa, and in addition of 3% wt Silicon ie 132.668 MPa. So the highest tensile stress value is at 3% wt. Hardness values will increase with the addition of Silicon elements. The highest hardness value found in the variation of 3% wt Silicon ie, 69.9 HB. While in the variation (0, 1, 2% wt) that is, 43.75 HB, 51.24 HB and 56.45 HB. So this study, proving that the addition of silicon elements can improve the mechanical properties of the shaft propeller.

Construction Method for a Three-Dimensional Tunnel General Monomer Model Based on Parallel Pathfinding

Existing approaches for the 3D modeling of tunnels suffer from several problems, such as highly difficult data acquisition, redundancy of model data, large computational burden, and the inability of the resulting models to be monolithic. Therefore, solutions to the tunnel network modeling problem for complex structures need to be proposed and elaborated in detail. In this paper, a construction method for a three-dimensional tunnel general monomer model based on parallel pathfinding is proposed. Widely used tunnel CAD drawings are analyzed and read, a disordered arc ensemble intersection trend decision method is developed, and an automatic path extraction solution algorithm for unidirectional modeling of tunnel centerlines is constructed. By constructing and splicing the surface elements of the 3D model, a monomeric 3D tunnel model representing the complex network structure is finally obtained. Moreover, the modeling of shafts is realized based on the monomer model, allowing for the three-dimensional topological relationships between different sub-levels of the tunnel and the ground to be established. The automatic modeling method proposed in this paper is applied to the digital twin platform of a filling project in a mining area in Gansu province, China. The experimental results demonstrate that the 3D tunnel models constructed in this way have a smaller data volume, higher modeling accuracy, and more stable growth of modeling speed.

Dynamics Analysis of a Rolling Rotor Compressor Considering the Electromagnetic Force

Rolling rotor compressor is a commonly used compressor in air conditioning systems, and studying its internal dynamic characteristics plays an important role in the vibration and noise of air conditioning systems. Due to the integration of the motor rotor and shaft inside the compressor, the influence of electromagnetic force needs to be considered when analyzing the dynamics of the compressor. This paper studies the rotor dynamics characteristics of a rolling rotor compressor, considering not only the bearing force and gas force inside the cylinder, but also the electromagnetic force of the motor rotor. Firstly, the gas force, electromagnetic force, and bearing force on the compressor shaft are analyzed; Secondly, a two degree of freedom rotor bearing dynamic model of the compressor shaft is established, and the dynamic characteristics of the shaft are obtained by solving the model though the Runge-Kutta method; Finally, the vibration characteristics of the compressor shaft are analyzed in both the time and frequency domains. The results indicate that the influence of electromagnetic force cannot be ignored, and the coupling effect between electromagnetic force and bearing force can be seen.

CFD‐DEM Modeling of Shaft Furnaces Using the Volume Fraction Smoother Approach

AbstractShaft furnaces are widely used in high‐temperature processes for granular materials due to their high energy efficiency. The modeling of these furnaces is challenging because of large domains and long process times. Small geometric details like the natural gas burner nozzles demand a fine grid on the computational fluid dynamics (CFD) side, resulting in a grid size smaller than the particle size. Resolving a discrete element particle over several cells is computationally expensive. Interpolation methods on non‐structured grids are complex. In order to provide a fast and simple solution, the volume fraction smoother was developed, and to shorten the calculation time, the time scale splitting method, which separates the time steps for CFD and the discrete‐element method (DEM), was introduced.

Effect of CNTs on Dynamic Performance of Carbon Fiber Composite Boring Bar

In this paper, through the secondary development of the finite element software ABAQUS, we try to add different contents of CNT to the CFRP composite boring bar, and establish the finite element models with different CNT contents. Firstly, on the basis of the classical laminated plate theory, combined with the composite damping loss factor model and finite element analysis method, an improved numerical model of CFRP hollow shaft damping based on inverse deviatoric transformation is adopted. Secondly, the Lanczos method was used for modal analysis, and the natural frequencies, vibration modes, stress and strain components under different fiber orientation angles (0°, 30°, 45°, 60°, 90°) and different CNT content structure constraint modes were extracted. Combined with the finite element method, the damping numerical model based on modal strain energy is established, and the damping loss factor calculation program based on strain energy is compiled by using the powerful calculation ability of MATLAB. The extracted strain component data are brought into the compiled damping loss factor calculation program, and the damping loss factors under different modes can be calculated.

Campbell diagrams, dynamics and instability zones of graphene-based spinning shafts

Carbon-based nanocomposite drive shafts have received considerable attention because of their excellent material and mechanical properties, with applications in modern aerospace, automotive industries and others. Therefore, for the first time, new Campbell diagrams, vibration and bifurcation points for multilayer shafts reinforced with three technologically justified distribution patterns of graphene nanoplatelets (GPLs) in the polymer matrix are presented and examined. A new formulation in the framework of a modified Timoshenko beam theory making use of the rotation angles of the cross sections of the shaft with five degrees of freedom is utilized. The modulus of elasticity of the nanocomposite material is estimated using the Halpin-Tsai micromechanical model, whereas the mass density and Poisson's ratio are computed by means of the law of mixtures. Hamilton's variational principle is used to derive weak and strong forms of motion equations of the shaft with classical and mixed boundary conditions. Assumptions for the derived model of the nanocomposite shaft are presented to clearly describe the mechanical state of the system. The Ritz-Chebyshev method is applied to discretize the governing equations and obtain the generalized nonlinear characteristic equations in matrix form including the gyroscopic effect and elastic stiffness caused by the rotation of the shaft. Verification of obtained results and convergence study were performed to show the correctness and advantages of the proposed solution method. The effect of different key parameters such as GPLs distribution and weight percentage, axial speed of the shaft, and boundary conditions, on its global damping, dynamics and instability zones are shown. For the first time, it is clearly shown how studied factors affect the shape of Campbell diagrams as well as the shift of natural frequency and bifurcation point of the graphene-based nanocomposite shafts.

Dynamic modeling and analysis of planetary gear train system considering structural flexibility and dynamic multi-teeth mesh process

The structural flexibility of planetary gear trains (PGTs) is a significant factor that affects tooth loads and system vibrations, especially in heavy-duty wind turbine gearboxes. Therefore, it is crucial to investigate the influence mechanisms of complex structural deformations on tooth loads and system vibrations. In this work, a dynamic modeling approach is proposed for the complex carrier and ring gear based on the condensation theory of finite elements. The dynamic model of the sun shaft is modeled using the Euler-Bernoulli beam element, and the planetary gear set is modeled using the lumped parameter method. Then, the dynamic multi-teeth mesh process is developed using variable-speed characterization variables and virtual vibration line displacements. Lastly, the rigid-flexible coupling dynamic model of PGT is established and validated. The results indicate that treating components as rigid solids may lead to an underestimation of the impact of input torque variation on system vibrations. When the input torque remains stable, the tooth stiffness can be used to assess the overall change trend of tooth loads. However, when the input torque varies significantly, it is necessary to take into account the comprehensive structural deformations.