Dynamics of Hypoid Gears With Emphasis on Effect of Shaft Rotation on Vibratory Response

2007 ◽  
Author(s):  
Tao Peng ◽  
Teik C. Lim
Keyword(s):  
Rotational Motion ◽  
Degrees Of Freedom ◽  
Transmission Error ◽  
Rotor System ◽  
Large Displacement ◽  
Small Displacement ◽  
Hypoid Gears ◽  
Gear Mesh ◽  
Vibratory Motion ◽  
Multi Body

The effect of large displacement rotational motion of the shafting system on the higher frequency, small displacement vibratory motion primarily excited by gear transmission error and variation of gear mesh stiffness is examined in this paper. Traditional hypoid gear dynamic analysis based on a pure vibration model assumes that the system perturbs about its mean position without coupling to the large displacement rotational motion. To improve on this approach and understanding of the influences of the dynamic interaction, a coupled multi-body dynamic and vibration simulation of the hypoid geared rotor system is performed. In the proposed formulation, a multi-degrees-of-freedom, multi-body hypoid geared rotor system dynamic model is developed to calculate the combined motion of the large displacement rotation of the shaft and small vibratory motion of the gear pair. The formulation may be generalized to other forms of gearing because hypoid gears have more complicated geometry and time-varying mesh characteristics when compared to parallel axis gears. Numerical simulation results are compared to those derived from the classical analytical method that only considers pure vibration effect. The proposed theory also provides new approaches to investigate both steady-state and transient geared rotor system dynamics.

scholarly journals Quasi-Static Characteristics and Vibration Responses Analysis of Helical Geared Rotor System with Random Cumulative Pitch Deviations

2020 ◽  
Vol 10 (12) ◽  
pp. 4403
Author(s):  
Bing Yuan ◽  
Geng Liu ◽  
Lan Liu
Keyword(s):  
Degrees Of Freedom ◽  
Transmission Error ◽  
Rotor System ◽  
Dynamic Responses ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Long Period ◽  
Light Load ◽  
Vibration Responses ◽  
Loaded Tooth Contact Analysis

As one of the long period gear errors, the effects of random cumulative pitch deviations on mesh excitations and vibration responses of a helical geared rotor system (HGRS) are investigated. The long-period mesh stiffness (LPMS), static transmission error (STE), as well as composite mesh error (CMS), and load distributions of helical gears are calculated using an enhanced loaded tooth contact analysis (LTCA) model. A dynamic model with multi degrees of freedom (DOF) is employed to predict the vibration responses of HGRS. Mesh excitations and vibration responses analysis of unmodified HGRS are conducted in consideration of random cumulative pitch deviations. The results indicate that random cumulative pitch deviations have significant effects on mesh excitations and vibration responses of HGRS. The curve shapes of STE and CMS become irregular when the random characteristic of cumulative pitch deviations is considered, and the appearance of partial contact loss in some mesh cycles leads to decreased LPMS when load torque is relatively low. Vibration modulation phenomenon can be observed in dynamic responses of HGRS. In relatively light load conditions, the amplitudes of sideband frequencies become larger than that of mesh frequency and its harmonics (MFIHs) because of relatively high contact ratio. The influences of random cumulative pitch deviations on the vibration responses of modified HGRS are also discussed.

Optimization Design of the Geared Rotor System With Critical Speed Constraints Using the Enhanced Genetic Algorithm

2008 ◽  
Author(s):  
T. N. Shiau ◽  
C. H. Kang ◽  
D. S. Liu ◽  
E. K. Lee ◽  
W. C. Hsu
Keyword(s):  
Genetic Algorithm ◽  
Optimization Design ◽  
Critical Speed ◽  
Hybrid Genetic Algorithm ◽  
Transmission Error ◽  
Rotor System ◽  
Gear Mesh ◽  
Design Variables ◽  
Bearing Stiffness ◽  
Gear Mesh Stiffness

This paper presents an efficient enhanced genetic algorithm to minimize the shaft weight, the unbalance response and the response due to the transmission error simultaneously. The minimization plays an important role in designing the geared rotor system under critical speed constraints. In the process of optimization, the design variables consist of shaft inner radii, bearing stiffness and the gear mesh stiffness. The enhanced genetic algorithm of optimization comprises the Hybrid Genetic Algorithm (HGA) and the Interval Genetic Algorithm (IGA). The HGA deals with this optimal design problem and the IGA accomplishes the interval optimization design. The results show that the presented enhanced genetic algorithm can not only effectively reduce the shaft weight and the transmission error response, but also precisely determine the interval ranges of design variables with feasible corresponding objective error.

scholarly journals Human Joint Simulation Using LifeMOD Co-Simulation

2008 ◽  
Vol 2 (2) ◽  
Author(s):  
Eric Fahlgren ◽  
Mark Carlson ◽  
Andrew S. Elliott
Keyword(s):  
Chromium Steel ◽  
Large Displacement ◽  
Small Displacement ◽  
Cobalt Chromium ◽  
Artificial Joints ◽  
Walking Gait ◽  
Body Dynamics ◽  
Elastic Responses ◽  
Multi Body ◽  
Ultra High Molecular Weight

Advanced design of human artificial joints requires an in-depth understanding of the dynamic interaction between the very stiff bone replacement material and the softer viscoelastic cartilage replacement material. It must take into account both the large displacement gross motions as well as the small displacement elastic responses. A co-simulation methodology has been developed in BRG LifeMOD, connecting Adams∕Solver, a large displacement multi-body dynamics code, to Marc, a nonlinear finite element code. This efficient co-simulation approach allows for each code to handle that portion of the system for which it is most capable, while adding the potential to work across multiple CPUs and operating systems as desired. The method was applied using LifeMOD∕KneeSIM to simulate an artificial knee joint, containing cobalt chromium steel and ultra-high molecular weight polyethylene contact elements, undergoing a normal walking gait to predict kinematics, forces and the resulting wear patterns.

Multi-body Dynamics Based Gear Mesh Models for Prediction of Gear Dynamics and Transmission Error

2010 ◽  
Author(s):  
Zdenek Neusser ◽  
Martin Sopouch ◽  
Thomas Schaffner ◽  
Hans-Herwig Priebsch
Keyword(s):  
Transmission Error ◽  
Gear Dynamics ◽  
Gear Mesh ◽  
Body Dynamics ◽  
Multi Body ◽  
Mesh Models

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.

Simulation and Experimental Measurement of the Transmission Error of Real Hypoid Gears Under Load

2000 ◽  
Vol 122 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Claude Gosselin ◽  
Thierry Guertin ◽  
Didier Remond ◽  
Yves Jean
Keyword(s):  
Measurement Data ◽  
Simulation Models ◽  
Transmission Error ◽  
Contact Analysis ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Loaded Tooth Contact Analysis ◽  
Analysis Models

The Transmission Error and Bearing Pattern of a gear set are fundamental aspects of its meshing behavior. To assess the validity of gear simulation models, the Transmission Error and Bearing Pattern of a Formate Hypoid gear set are measured under a variety of operating positions and applied loads. Measurement data are compared to simulation results of Tooth Contact Analysis and Loaded Tooth Contact Analysis models, and show excellent agreement for the considered test gear set. [S1050-0472(00)00901-6]

Dynamic Analysis of Geared Rotor-Bearing Systems by the Transfer Matrix Method

1995 ◽  
Author(s):  
Siu-Tong Choi ◽  
Sheng-Yang Mau
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Transmission Error ◽  
Mode Shapes ◽  
Rotor Systems ◽  
Gear Mesh ◽  
Mass Unbalance ◽  
Rotor Bearing

Abstract In this paper, an analytical study of the dynamic characteristics of geared rotor-bearing systems by the transfer matrix method is presented. Rotating shafts are modeled as Timoshenko beam with shear deformation and gyroscopic effects taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set and a transmission-error exciter. The transfer matrix of a gear mesh is developed. The coupling motions of the lateral and torsional vibration are studied. In free vibration analysis of geared rotor systems, natural frequencies and corresponding mode shapes, and the whirl frequencies under different spin speeds are determined. Effects of bearing stiffness, isotropic and orthotropic bearings, pressure angle of the gear mesh are studied. In steady-state vibration analysis, responses due to the excitation of mass unbalance and the transmission error are studied. Parametric characteristics of geared rotor systems are discussed.

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 Analytical and Numerical Investigation of Modulation Sidebands of a Planetary Gear Under Fluctuated External Torque

2018 ◽  
Author(s):  
Yunbo Yuan ◽  
Wei Liu ◽  
Yahui Chen ◽  
Donghua Wang
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Operating Conditions ◽  
Radial Acceleration ◽  
External Torque ◽  
Gear Mesh ◽  
Planetary Gear Sets ◽  
Static Transmission Error ◽  
Frequency Modulations ◽  
Mesh Phasing

Certain operating conditions such as fluctuation of the external torque to planetary gear sets can cause additional sidebands. In this paper, a mathematical model is proposed to investigate the modulation mechanisms due to a fluctuated external torque (FET), and the combined influence of such an external torque and manufacturing errors (ME) on modulation sidebands. Gear mesh interface excitations, namely gear static transmission error excitations and time-varying gear mesh stiffness, are defined in Fourier series forms. Amplitude and frequency modulations are demonstrated separately. The predicted dynamic gear mesh force spectra and radial acceleration spectra at a fixed position on ring gear are both shown to exhibit well-defined modulation sidebands. Comparing with sidebands caused by ME, more complex sidebands appear when taking both FET and ME into account. An obvious intermodulation is found around the fundamental gear mesh frequency between the FET and ME in the form of frequency modulations, however, no intermodulation in the form of amplitude modulations. Additionally, the results indicate that some of the sidebands are cancelled out in radial acceleration spectra mainly due to the effect of planet mesh phasing, especially when only amplitude modulations are present.

Effect of a Planetary Gearbox on the Dynamics of a Rotor System

2018 ◽  
Author(s):  
Ali Tatar ◽  
Christoph W. Schwingshackl
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Rotor System ◽  
Mode Shapes ◽  
Rotating System ◽  
Planetary Gearbox ◽  
Finite Element Software ◽  
Gyroscopic Effects ◽  
The Masses ◽  
Parameter Values

The dynamic analysis of rotors with bladed disks has been investigated in detail over many decades and is reasonably well understood today. In contrast, the dynamic behaviour of two rotors that are coupled via a planetary gearbox is much less well understood. The planetary gearbox adds inertia, mass, stiffness, damping and gyroscopic moments to the system and can strongly affect the modal properties and the dynamic behaviour of the global rotating system. The main objective of this paper is to create a six degrees of freedom numerical model of a rotor system with a planetary gearbox and to investigate its effect on the coupled rotor system. The analysis is based on the newly developed finite element software “GEAROT” which provides axial, torsional and lateral deflections of the two shafts at different speeds via Timoshenko beam elements and also takes gyroscopic effects into account. The disks are currently considered as rigid and the bearings are modelled with isotropic stiffness elements in the translational and rotational directions. A novel planetary gearbox model has been developed, which takes the translational and rotational stiffness and the damping of the gearbox, as well as the masses and inertias of the sun gear, ring gear, planet gears and carrier into account. A rotating system with a planetary gearbox has been investigated with GEAROT. The gearbox mass and stiffness parameters are identified as having a significant effect on the modal behaviour of the rotor system, affecting its natural frequencies and mode shapes. The higher frequency modes are found to be more sensitive to the parameter changes as well as the modes which have a higher deflection at the location of the gearbox on the rotor system. Compared with a single shaft system, the presence of a gearbox introduces new global modes to the rotor system and decouples the mode shapes of the two shafts. The introduction of a planetary gearbox may also lead to an increase or a reduction of the frequency response of the rotor system based on gear parameter values.

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