scholarly journals Estimation of a Planetary Gear Mesh Stiffness: An Approach Based on Minimising Error Function

2021 ◽  
Vol 6 (3) ◽  
pp. 164-169
Author(s):  
K. A. Olanipekun
Keyword(s):  
Natural Frequencies ◽  
Sliding Friction ◽  
Gear Tooth ◽  
Contact Stiffness ◽  
Error Function ◽  
Planetary Gear ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Planetary Gear System ◽  
Parallel Axis

The mesh stiffness of gear teeth is one of the major sources of excitation in gear systems. Many analytical and finite element methods have been proposed in order to determine the mesh stiffness of gears especially parallel axis spur gears. Most of these methods are not trivial because they involve complicated analyses which incorporate parameters like gear tooth error, gear spalling sizes and shapes, nonlinear contact stiffness and sliding friction before mesh stiffness can be determined. In this work, a method is proposed to determine the sun-planet and ring-planet mesh stiffnesses of a planetary gear system. This approach involves fitting a relationship between the measured natural frequencies from an experimental modal test and natural frequencies predicted using an analytical model of a planetary gear. This method is relatively easier compared to the existing methods which involve complicated analyses. For this study, the average mesh stiffness estimated is 12.5 MN/m.

Dynamic Characteristics of Double Helical Planetary Gear Train With Tooth Friction

2015 ◽  
Author(s):  
Fengxia Lu ◽  
Rupeng Zhu ◽  
Haofei Wang ◽  
Heyun Bao ◽  
Miaomiao Li
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Step Size ◽  
Planetary Gear Train ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Nonlinear Dynamics Model

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.

Coupled Bending-Torsion Vibration of Geared Rotors

1995 ◽  
Author(s):  
J. S. Rao ◽  
J. R. Chang ◽  
T. N. Shiau
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Mesh Stiffness ◽  
Present Program ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Torsion Vibration ◽  
Gear Mesh Stiffness

Abstract A general finite element model is presented for determining the coupled bending-torsion natural frequencies and mode shapes of geared rotors. Uncoupled bending and torsion frequencies are obtained for examples available in literature and the present program is verified against these. The effect of the gear box is considered to determine the coupled frequencies. Parameters studied include the pressure angle, gear mesh stiffness, and bearing properties. The gear pressure angle is shown to have no effect on the natural frequencies of rotors supported on isotropic bearing supports. Several case studies with bending-torsion coupling are considered and the results obtained are compared with those available in literature. The results of a general rotor system with 8lodes are also presented.

Effect of the bearing clearance on vibrations of a double-row planetary gear system

2019 ◽  
Vol 234 (2) ◽  
pp. 347-357
Author(s):  
Jing Liu ◽  
Shizhao Ding ◽  
Linfeng Wang ◽  
Hongwu Li ◽  
Jin Xu
Keyword(s):  
Contact Stiffness ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Gear System ◽  
Double Row ◽  
External Torque ◽  
Bearing Clearance ◽  
Gear Systems ◽  
Planetary Gear System ◽  
Stiffness And Damping

The bearing clearance, external torque, and input speed can greatly affect vibrations of the planetary gear system. The double-row planetary gear systems are commonly used in the gearbox of special vehicles, which are the key parts to obtain a larger gear ratio. Although many works have been presented to study those factors on vibrations of the single-row planetary gear system, a few works were focused on vibrations of the double-row planetary gear system with the bearing clearance. To overcome this problem, a multi-body dynamic model of a double-row planetary gear system with six planet bearings and one supported bearing of the sun gear is presented. This model is the main part of a gear box transmission system. The new model is developed for studying the effect of the bearing clearance on the planetary system. The meshing stiffness and damping between the gears are obtained by current methods in the listed references, as well as the contact stiffness and damping in bearings. The liner stiffness and damping model is used. The effects of the bearing clearance, external torque, and input speed on vibrations of the system are analyzed. The results show that vibrations of the ring gear and sun gear decrease with the increment of the external torque and increase with the increment of the input speed. Moreover, a reasonable bearing clearance can be helpful for reducing system vibrations for some mating external torque and input speed conditions. The results can provide some guidance to find new method to reduce vibrations and increase the service life of planetary gear systems.

scholarly journals Improvement on Meshing Stiffness Algorithms of Gear with Peeling

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 609
Author(s):  
Lingli Cui ◽  
Tongtong Liu ◽  
Jinfeng Huang ◽  
Huaqing Wang
Keyword(s):  
Simulation Analysis ◽  
Gear Tooth ◽  
Gear Wheel ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Involute Gears ◽  
Gear Mesh Stiffness ◽  
Meshing Process

This paper investigates the effect of a gear tooth peeling on meshing stiffness of involute gears. The tooth of the gear wheel is symmetric about the axis, and its symmetry will change after the gear spalling, and its meshing stiffness will also change during the meshing process. On this basis, an analytical model was developed, and based on the energy method a meshing stiffness algorithm for the complete meshing process of single gear teeth with peeling gears was proposed. According to the influence of the change of meshing point relative to the peeling position on the meshing stiffness, this algorithm calculates its stiffness separately. The influence of the peeling sizes on mesh stiffness is studied by simulation analysis. As a very important parameter, the study of gear mesh stiffness is of great significance to the monitoring of working conditions and the prevention of sudden failure of the gear box system.

Torsional Vibrations and Dynamic Loads in a Basic Planetary Gear System

1986 ◽  
Vol 108 (3) ◽  
pp. 348-353 ◽  
Author(s):  
R. August ◽  
R. Kasuba
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear System ◽  
Dynamic Loads ◽  
Ring Gear ◽  
Gear Mesh ◽  
Input And Output ◽  
Planetary Gear System ◽  
Three Degrees Of Freedom

An interative method has been developed for analyzing dynamic loads in a light weight basic planetary gear system. The effects of fixed, semi-floating, and fully-floating sun gear conditions have been emphasized. The load dependent variable gear mesh stiffnesses were incorporated into a practical torsional dynamic model of a planetary gear system. The dynamic model consists of input and output units, shafts, and a planetary train. In this model, the sun gear has three degrees of freedom; two transverse and one rotational. The planets, ring gear, and the input and output units have one degree of freedom, (rotation) thus giving a total of nine degrees of freedoms for the basic system. The ring gear has a continuous radial support. The results indicate that the fixed sun gear arrangement with accurate or errorless gearing offers in general better performance than the floating sun gear system.

Design and Test of Differential Planetary Gear System for Open Rotor Power Gearbox

2013 ◽  
Author(s):  
Hideyuki Imai ◽  
Tatsuhiko Goi ◽  
Kenichi Kijima ◽  
Tooru Nishida ◽  
Hidenori Arisawa ◽  
...  
Keyword(s):  
Performance Test ◽  
High Efficiency ◽  
High Reliability ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Design Concept ◽  
Gear System ◽  
Open Rotor ◽  
Planetary Gear System ◽  
Validation Tests

The open rotor engine is a next generation aero-engine that satisfies the demand for high fuel efficiency and low CO2 emission. A differential planetary gear system is incorporated in the open rotor engine to connect the turbine output shaft and fan rotors in order to counter-rotate the fan rotors as well as allow the turbine and fan rotors to operate at more efficient speeds. The open rotor gear system is required to have not only 20,000 hp high power transmission, but also an increasingly high efficiency, high reliability and light weight. To achieve these requirements, the following design works were conducted; (1) a low misalignment and lightweight carrier, (2) a flexible structure to absorb the displacement caused by the flight load, (3) an optimum gear tooth modification and (4) reduction of oil churning and windage losses. Also, extensive analyses and simulations such as lube oil flow CFD, FEA and tooth contact analysis were conducted. A full scale prototype gear system was manufactured and validation tests were conducted using a newly constructed test rig to validate the design concept. A slow roll test, rated performance test and efficiency test were conducted. And the design concept was found to be valid. This paper describes details of the prototype design and the results of the validation tests.

Epicyclic Gear Vibrations

1976 ◽  
Vol 98 (3) ◽  
pp. 811-815 ◽  
Author(s):  
M. Botman
Keyword(s):  
Natural Frequencies ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Periodic Coefficients ◽  
Plane Vibration ◽  
Epicyclic Gear ◽  
Floquet’S Theory ◽  
Floquet's Theory

The natural frequenices of in-plane vibration of a single planetary gear stage are analyzed. The gear tooth stiffnesses are approximated as linear springs. The effect of planet pin stiffness on the natural frequencies is evaluated. Rotation of the carrier gives rise to a system with periodic coefficients which is solved by means of Floquet’s theory. The rotation of the carrier appears to suppress the nonaxisymmetric modes which are present in the system with nonrotating carrier.

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

2018 ◽  
Vol 32 (8) ◽  
pp. 3537-3545 ◽  
Author(s):  
Mohsen Rezaei ◽  
Mehrdad Poursina ◽  
Shahram Hadian Jazi ◽  
Farhad Haji Aboutalebi
Keyword(s):  
Analytical Approach ◽  
Planetary Gear ◽  
Gear System ◽  
Time Dependent ◽  
Mesh Stiffness ◽  
Planetary Gear System

Effect of Rim Thickness on Tooth Root Stress and Mesh Stiffness of Internal Gears

2014 ◽  
Author(s):  
F. Karpat ◽  
B. Engin ◽  
O. Dogan ◽  
C. Yuce ◽  
T. G. Yilmaz
Keyword(s):  
Weight Ratio ◽  
Planetary Gear ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Aerospace Applications ◽  
Bending Stresses ◽  
Gear Mechanism ◽  
Internal Gear ◽  
Gear Mesh Stiffness ◽  
Root Stress

In recent years, internal gears are used commonly in a number of automotive and aerospace applications especially in planetary gear drives. Planetary gears have many advantages such as compactness, large torque-to-weight ratio, large transmission ratios, reduced noise and vibrations. Although internal gears have many advantages, there are not enough studies on it. Designing an internal gear mechanism includes two important parameters. The gear mesh stiffness which is the main excitation source of the system. In this paper, 2D gear models are developed in order to compute gear mesh stiffness for various rim thicknesses and different rim shapes of the internal gear design. Effects of root stress with varying rim thickness and some tooth parameters are investigated by using 2D gear models. The stress calculated according to ISO 6336 and the stresses calculated against FEM are compared. These results are well-matched. It is observed that when the rim thicknesses are increased, both the maximum bending stresses and gear mesh stiffness are decreased considerably.

Dynamic Response Analysis of Wind Turbine Planetary Gear System With Interval Stiffness Parameters

2014 ◽  
Author(s):  
Sha Wei ◽  
Qinkai Han ◽  
Zhipeng Feng ◽  
Yanhua Shen ◽  
Fulei Chu
Keyword(s):  
Wind Turbine ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear System ◽  
Dynamic Responses ◽  
Lumped Parameter Model ◽  
Response Analysis ◽  
Mesh Stiffness ◽  
Gear Trains ◽  
Planetary Gear System

Planetary gear transmission system is one of the primary parts of the wind turbine drive train. Due to the assembly state, lubrication conditions and wear, the mesh stiffness of the planetary gear system is an uncertain parameter. In this paper, taking the uncertainty of mesh stiffness into account, the dynamic responses of a wind turbine gear system subjected to wind loads and transmission error excitations are studied. Firstly, a lumped-parameter model is extended to include both the planetary and parallel gears. Then the fluctuation ranges of dynamic mesh forces are predicted quantitatively and intuitively based on the combined Chebyshev interval inclusion function and numerical integration method. Finally, examples of gear trains with different interval mesh stiffnesses are simulated and the results show that tooth separations are becoming more obvious at the resonant speed by considering the fluctuating mesh stiffness of the second parallel gear stage. The nonlinear tooth separations are degenerated obviously as the fluctuation error of the mesh stiffness of the second parallel gear set is increased.

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