Analytical solution of spur gear mesh using linear model

Zajíček, Martin; Dupal, J.

doi:10.1016/j.mechmachtheory.2017.08.008

Cited by 19 publications

(6 citation statements)

References 20 publications

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“…By contrast, the rotating parts of the turbo-machine (turbine shaft, generator non-symmetrical shaft, blade rings and bandages) will be time-invariable in the rotating coordinate system fixed to the turbo-machine. For response determination and stability assessment, it is possible to use the approach and methodology described by the authors of this paper in [2,3,10].…”

Section: Discussionmentioning

confidence: 99%

1D finite element for modelling of turbine blade vibration in the field of centrifugal forces

Dupal

Zajíček

Lukeš

2019

ACM

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The paper deals with the modelling of turbine blade vibrations by means of a novel 1D finite element that has only 16 degrees of freedom. Assuming linear elastic behaviour of the blade material and considering small displacements and strains, the derived blade finite element takes into account the effects of tension, torsion and bending in accordance with the Bernoulli's hypothesis. Additionally, the finite element interlinks bending and torsion, and respects membrane forces acting on the blade. The derivation of matrices and vectors describing the blade finite element is provided in detail by using the Lagrange's equations while the effect of membrane forces is included via the virtual work principle. For modelling purposes, the mathematical model of a turbine blade requires only the knowledge of cross-section contour points at several selected sections along the turbine blade axis. On the basis of these points, cross-section characteristics including the warping function are approximated along the blade axis by means of cubic splines. The advantage of this approach lies in the fact that all the blade cross-section parameters are identified before running numerical simulations. The warping function introduced in this paper and derived by variational principle describes cross-section warping caused just by torsion of a prismatic rod. For the verification of the proposed 1D finite element, an analysis of modal properties of the turbine blade M6 L-1 manufactured by Doosan Š koda Power is performed. This is achieved by comparing the lowest natural frequencies and corresponding mode shapes computed by the 1D and 3D models for a standing blade. The results revealed good agreement between both models despite the significant difference in their degrees of freedom. The applicability of the 1D finite element is further demonstrated by analyzing the dependence of natural frequencies on rotor speed.

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Section: Discussionmentioning

confidence: 99%

1D finite element for modelling of turbine blade vibration in the field of centrifugal forces

Dupal

Zajíček

Lukeš

2019

ACM

Self Cite

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“…The linear model can well approximate the real system dynamics behavior in normal conditions, but overall, it is a simplified model, wherein, it is difficult to obtain a stable and reliable linear approximation (Atanasovska, 2017;Zajicek and Dupal, 2017). Especially, in the analysis of long time-history, the extremely weak nonlinear factors that simplify or even ignore often lead to some unpredictable errors.…”

Section: Analysis Of Nonlinear Dynamic Characteristics Of Face Gearmentioning

confidence: 99%

Numerical modeling and dynamic characteristics study of coupling vibration of multistage face gearsplanetary transmission

Chen

et al. 2019

Mech. Sci.

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Abstract. A novel transmission with multistage face gears as the core component achieves variable speeds via differential gear shifting. Single/multistage coupled vibration models have been established in this study to derive the coupled vibration equation in order to accurately solve the load distribution between the meshing teeth and the vibration shock between the shifting stages in the transmission process, improve the transmission smoothness of the face gears during the shifting processing, suppress the resonance of face gears meshing, reduce the noise, and optimize the power transmission performance. The characterization relationships of the key parameters such as equivalent mass, rotational inertia, equivalent mesh stiffness, support stiffness, and meshing damping coefficient to dynamic characteristics were investigated. The linear and nonlinear dynamic characteristics of coupled vibration differential equations were solved. The influence rules of factors such as integrated transmission error, dynamic load, tooth surface friction, loading speed, and load on the transmission system were analyzed. The results of the study provide a theoretical basis for the expansion of field of application of transmission devices.

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“…Three types of meshing impacts-mesh-in, mesh-out, and node-have been observed in gear transmission systems [7][8][9]. Node impact has the lowest effect, followed by mesh-out impact and then by mesh-in impact.…”

Section: Introductionmentioning

confidence: 99%

Optimal analysis of gear modification fitting in alternating time domain aiming at minimizing meshing-in impact of teeth-pair contact interface

Wang¹,

An²,

Wang³

et al. 2021

J. vibroeng.

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In a pair of actual gears alternating meshing process, the transmission system errors and thermal elastic deformation of the gear teeth can cause gears in the meshing zone to form high contact pairs inconsistently mesh-in and mesh-out points to deviate from the theoretical line, which will lead to sudden changes in meshing velocity and an instantaneous meshing effect. Offline meshing impact generates large additional loads, and it increases the vibration and noise of gear transmission system. Further, the gear teeth mesh-in impact is significantly greater than that of gear teeth mesh out. Therefore, to analyze the impact with the minimum value of gear teeth mesh in, the initial mesh-in points need to be determined, and the meshing impact velocity and impact force of teeth meshing-out need to be calculated. The optimized meshing tooth-pair contact interface (CI) anti-impact numerical calculation mode is validated using the loaded teeth contact analysis method.

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Analytical solution of spur gear mesh using linear model

Cited by 19 publications

References 20 publications

1D finite element for modelling of turbine blade vibration in the field of centrifugal forces

1D finite element for modelling of turbine blade vibration in the field of centrifugal forces

Numerical modeling and dynamic characteristics study of coupling vibration of multistage face gearsplanetary transmission

Optimal analysis of gear modification fitting in alternating time domain aiming at minimizing meshing-in impact of teeth-pair contact interface

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