Dynamic Analysis of a Multi-Shaft Helical Gear Transmission by Finite Elements: Model and Experiment

2004 ◽  
Vol 126 (3) ◽  
pp. 398-406 ◽  
Author(s):  
M. Kubur ◽  
A. Kahraman ◽  
D. M. Zini ◽  
K. Kienzle
Keyword(s):  
Three Dimensional ◽  
Element Model ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Vibrations ◽  
Forced Response ◽  
System Parameters ◽  
Free And Forced Vibrations ◽  
Modal Summation ◽  
Finite Elements Model

A dynamic model of a multi-shaft helical gear reduction unit formed by N flexible shafts is proposed in this study. The model consists of a finite element model of shaft structures combined with a three-dimensional discrete model of helical gear pairs. Bearing and housing flexibilities are included in the model as well. Eigenvalue solution and the Modal Summation Technique are used to predict the free and forced vibrations of the system. Results of experimental study on a helical gear-shaft-bearing system are also presented for validation of the model. It is demonstrated that the predictions match well with the experimental data in terms of excited modes and the forced response given in the form of the dynamic transmission error. Forced vibrations of an example system formed by three shafts are also studied to demonstrate the influence of some of the key system parameters.

Dynamic Analysis of Multi-Mesh Helical Gear Sets by Finite Elements

2003 ◽  
Author(s):  
M. Kubur ◽  
A. Kahraman ◽  
D. M. Zini ◽  
K. Kienzle
Keyword(s):  
Finite Element ◽  
Discrete Model ◽  
Three Dimensional ◽  
Element Model ◽  
Helical Gear ◽  
Forced Vibrations ◽  
System Parameters ◽  
Gear Mesh ◽  
Free And Forced Vibrations ◽  
Mesh Phasing

A dynamic model of a multi-shaft helical gear reduction unit is proposed in this study. The model consists of a finite element model of shaft structures combined with a three-dimensional discrete model of helical gear pairs. Both counter-shaft reduction and idler configurations are included in the model. Bearing and housing flexibilities are included in the model as well. Free and forced vibrations were studied to quantify the influence of a number of system parameters including, shaft position angles, shaft dimensions, bearing types and locations, and gear mesh phasing relationships. A limited parametric study is performed to demonstrate the sensitivity of the model to certain system parameters.

Dynamic Analysis of a Multi-Mesh Helical Gear Train

1994 ◽  
Vol 116 (3) ◽  
pp. 706-712 ◽  
Author(s):  
A. Kahraman
Keyword(s):  
Three Dimensional ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Gear Train ◽  
Loading Conditions ◽  
Natural Modes ◽  
Static Transmission Error ◽  
Gear Meshes

In this paper, the dynamic behavior of a multi-mesh helical gear train has been studied. The gear train consists of three helical gears, with one of the gears in mesh with the other two. A three dimensional dynamic model which includes transverse, torsional, axial and rotational (rocking) motions of the flexibility mounted gears has been developed. Two different loading conditions have been identified. In case-I, the system is driven by the gear in the middle, and in case-II, the system is driven by one of the gears at either end of the gear train. The phase difference between the two gear meshes has been determined under each loading condition. The natural modes have been predicted, and their sensitivity to the helix angle and different loading conditions has been quantified. The forced response, which includes dynamic mesh and bearing forces, due to the static transmission error excitation has been obtained. Effects of loading conditions and asymmetric positioning on the response have also been explored.

Dynamic Analysis of a Multi-Mesh Helical Gear Train

1992 ◽  
Author(s):  
Ahmet Kahraman
Keyword(s):  
Loading Condition ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Gear Train ◽  
Loading Conditions ◽  
Gear Mesh ◽  
Natural Modes ◽  
Static Transmission Error

Abstract In this paper, the dynamic behavior of a multi-mesh helical gear train is studied. The gear train consists of three helical gears, with one of the gears in mesh with the other two. An 18-degree-of-freedom dynamic model which includes transverse, torsional, axial and rotational (rocking) motions of the flexibly mounted gears is developed. Two different loading conditions are identified. For case I, the system is driven by the gear in the middle, and for case II, the system is driven by one of the gears at either end of the gear train. Gear mesh phases under each loading condition are determined. The natural modes are predicted, and effects of the helix angle and the loading condition on the natural modes are explained. The forced response, which includes dynamic mesh and bearing forces, due to the static transmission error excitation is found. Effects of loading conditions and asymmetric positioning on the response are also explored. The results suggest that the dynamic forces are lower if the number of teeth of the gear in the middle is (i) an odd number for case I type loading, and (ii) an even number for case II type loading.

An Investigation of the Structural Dynamics of a Racing Yacht

1999 ◽  
Author(s):  
Frederic Louarn ◽  
Pandeli Temarel
Keyword(s):  
Dynamic Properties ◽  
Three Dimensional ◽  
Element Model ◽  
Point Of View ◽  
Mode Shapes ◽  
Function Technique ◽  
Operational Conditions ◽  
Principal Coordinates ◽  
Modal Summation ◽  
Structural Responses

The dynamic behaviour of a WOR 60 is investigated using three dimensional hydroelasticity theory. Global structural responses (e.g. stresses) in waves are obtained corresponding to the upright as well as to the more realistic heeled sailing configurations, revealing the connection between the ballast keel and the hull as being a critical area of the structure. For the "dry hull" analysis, a global finite element model has been developed, incorporating the hull and deck shell, the internal structure, the ballast keel and the rig together with rigging loads. The modular nature of the model has been used to assess the relative influence of each of the aforementioned components upon the required characteristic dynamic properties (e.g. natural frequencies and principal mode shapes). Regarding the "wet hull" analysis, a three dimensional Green's function technique, using pulsating sources distributed over the wetted surface, provides a numerical solution to the case of the yacht sailing in regular waves at arbitrary heading. Principal coordinates for the rigid body motions and flexible distortions of interest are evaluated and the latter are used to obtain the dynamic stresses in waves using modal summation. This paper will describe the modelling techniques used and discuss the applicability / limitations of hydroelasticity theory regarding this type of structures in the light of the results obtained for the upright and heeled operational conditions, as well as from the point of view of design aspects such as "L" and "T" keel configurations. The ABS design criteria will provide a practical reference for comparing the results from the dynamic analysis.

The Design and Finite Element Analysis for Crane Turntable Gear Based on Pro/E and ANSYS

2013 ◽  
Vol 710 ◽  
pp. 243-246
Author(s):  
Xian Hong Yang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Product Design ◽  
Optimization Design ◽  
Three Dimensional ◽  
Reference Value ◽  
Element Model ◽  
Helical Gear ◽  
Engineering Analysis ◽  
Element Analysis

The use of Pro/E and their respective advantages ANSYS software product design and engineering analysis to solve the case, first of all in the Pro/E, the completion of three-dimensional helical gear design, and then in the Pro/MECHANICA completed finite element model of helical gear, and then into ANSYS for finite element analysis of bevel gear calculation and simulation, finite element analysis of the final results of optimization design model is presented recommendations for improvement. The product design and engineering analysis method has some reference value in engineering design.

scholarly journals Calculation and Correlation of the Unsteady Flowfield in a High Pressure Turbine

2002 ◽  
Author(s):  
Milind A. Bakhle ◽  
Jong S. Liu ◽  
Josef Panovsky ◽  
Theo G. Keith ◽  
Oral Mehmed
Keyword(s):  
High Pressure ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Forced Vibrations ◽  
Forced Response ◽  
Operating Conditions ◽  
Test Facility ◽  
Navier Stokes ◽  
Turbine Stage ◽  
High Pressure Turbine

Forced vibrations in turbomachinery components can cause blades to crack or fail due to high-cycle fatigue. Such forced response problems will become more pronounced in newer engines with higher pressure ratios and smaller axial gap between blade rows. An accurate numerical prediction of the unsteady aerodynamics phenomena that cause resonant forced vibrations is increasingly important to designers. Validation of the computational fluid dynamics (CFD) codes used to model the unsteady aerodynamic excitations is necessary before these codes can be used with confidence. Recently published benchmark data, including unsteady pressures and vibratory strains, for a high-pressure turbine stage makes such code validation possible. In the present work, a three dimensional, unsteady, multi blade-row, Reynolds-Averaged Navier Stokes code is applied to a turbine stage that was recently tested in a short duration test facility. Two configurations with three operating conditions corresponding to modes 2, 3, and 4 crossings on the Campbell diagram are analyzed. Unsteady pressures on the rotor surface are compared with data.

Static and Dynamic Transmission Error Measurements of Helical Gear Pairs With Various Tooth Modifications

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
M. Benatar ◽  
M. Handschuh ◽  
A. Kahraman ◽  
D. Talbot
Keyword(s):  
Dynamic Models ◽  
Nonlinear Behavior ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Test Machine ◽  
Response Curves ◽  
Gear Mesh ◽  
Dynamic Transmission Error ◽  
Static Transmission Error

This paper presents a set of motion transmission error data for a family of helical gears having different profile and lead modifications operated under both low-speed (quasi-static) and dynamic conditions. A power circulatory test machine is used along with encoder and accelerometer-based transmission error measurement systems to quantify motion transmission behavior within wide ranges of torque and speed. Results of these experiments indicate that the tooth modifications impact the resultant static and dynamic transmission error amplitudes significantly. A design load is shown to exist for each gear pair of different modifications where static transmission error amplitude is minimum. Forced response curves and waterfall plots are presented to demonstrate that the helical gear pairs tested act linearly with no signs of nonlinear behavior such as tooth contact separations. Furthermore, static and dynamic transmission error amplitudes are observed to be nearly proportional, suggesting that static transmission error can be employed in helical gear dynamic models as the main gear mesh excitation. The data presented here is intended to fill a void in the literature by providing means for validation of load distribution and dynamic models of helical gear pairs.

On the Equations Governing the Free and Forced Vibrations of a General Non-Conservative System

1976 ◽  
Vol 18 (1) ◽  
pp. 6-10 ◽  
Author(s):  
I. F. A. Wahed ◽  
R. E. D. Bishop
Keyword(s):  
Conservative System ◽  
Forced Vibrations ◽  
Forced Response ◽  
Hamiltonian Form ◽  
Free And Forced Vibrations ◽  
Lagrange Approach

An expression is derived for the steady forced response of a system governed by the equation in which A, B and C are real but not symmetric. The theory is effectively an adaptation and exploration of previous work by Woodcock (1)‡. His studies were published in the ‘Hamiltonian’ form, while in the present paper the Lagrange approach is used.

Effect of Axial Vibrations on the Dynamics of a Helical Gear Pair

1993 ◽  
Vol 115 (1) ◽  
pp. 33-39 ◽  
Author(s):  
A. Kahraman
Keyword(s):  
Natural Frequencies ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Helical Gear Pair

In this paper, a linear dynamic model of a helical gear pair has been developed. The model accounts for the shaft and bearing flexibilities, and the dynamic coupling among the transverse, torsional, axial and rotational (rocking) motions due to the gear mesh. The natural frequencies and the mode shapes have been predicted, and the modes which are excited by the static transmission error have been identified. The forced response due to the static transmission error has also been predicted, including the dynamic mesh and bearing forces. A parametric study has been performed to investigate the effect of the helix angle on the free and forced vibrational characteristics of the gear pair. It has been shown that the helix angle can be neglected in predicting the natural frequencies and the dynamic mesh forces. An accurate prediction of dynamic bearing forces and moments requires inclusion of the helix angle in the analysis.

scholarly journals Application of the finite difference method for modeling cantilever bar vibrations

2020 ◽  
Vol 224 ◽  
pp. 02002
Author(s):  
M I Volnikov
Keyword(s):  
Mathematical Modeling ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Structural Mechanics ◽  
Forced Vibrations ◽  
Cantilever Beams ◽  
System Parameters ◽  
Free And Forced Vibrations ◽  
The Finite Difference Method

The paper is devoted to mathematical modeling of cantilever bars using the finite difference method. This method is widely used in structural mechanics for solving static problems. The novelty lies in the application of the finite difference method to simulate the dynamics of free and forced vibrations of the cantilever. Models have been developed that allow calculating the static and dynamic deflections of the cantilevers during free and forced vibrations, as well as simulating the vibrations of cantilever beams with attached vibration dampers. The resulting models of cantilever structures make it easy to modify system parameters, external influences and damping elements. All calculations were performed using the finite difference approach when moving along geometric and temporal coordinates.

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