scholarly journals The Analysis and Modeling of the Synthetical Meshing Stiffness of Inner Gearing considering the Flexible Inner Ring Gear

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Shengyang Hu ◽  
Zongde Fang
Keyword(s):  
Planetary Gear ◽  
Element Model ◽  
Transmission System ◽  
Lumped Parameter Model ◽  
Ring Gear ◽  
Gear Teeth ◽  
Meshing Stiffness ◽  
Lumped Parameter ◽  
Sectional Shape ◽  
The Finite Element Model

As a key part of vibration generation and transmission of planetary gear transmissions, thin-walled inner ring gear deforms under the influence of meshing excitation and seriously affects the reliability and fatigue life of the transmission system. The effect of the flexibility of the inner ring gear on the transmission system is ignored in the calculation of making the inner ring gear as a rigid body in the lumped parameter model, while the calculation amount of the finite element model is too large. Therefore, it is very important to establish an accurate and reasonable model to solve the flexibility of the inner ring gear. In this paper, according to the supporting mode, supporting quantity, thickness, and sectional shape of the inner ring gear, the inner ring gear is reasonably separated into the form of multisection curved beam. The displacement of the gear teeth in the meshing line caused by the flexibility of the inner ring gear is obtained rapidly and accurately. It lays an important theoretical foundation for the dynamic analysis of planetary gear transmission.

A Discrete Lumped-Parameter Dynamic Model for a Planetary Gear Set with Flexible Ring Gear

2011 ◽  
Vol 86 ◽  
pp. 756-761 ◽  
Author(s):  
Jun Zhang ◽  
Yi Min Song ◽  
Jin You Xu
Keyword(s):  
Individual Component ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Vibration Modes ◽  
Ring Gear ◽  
Lumped Parameter ◽  
Planetary Gear System ◽  
Flexible Ring

A discrete lumped-parameter model for a general planetary gear set is proposed, which models the continuous flexible ring gear as discrete rigid ring gear segments connected with each other through virtual springs. The ring-planet mesh is analyzed to derive equations of motion of ring segments and planet. By assembling equations of motion of each individual component, the governing equations of planetary gear system are obtained. The solution for eigenvalue problem yields to natural frequencies and corresponding vibration modes. The simulations of example system reveal that the ring gear flexibility decreases system lower natural frequencies and the vibration modes can be classified into rotational, translational, planet and ring modes.

Nondestructive Evaluation of Parts With Degenerate Modes Using Pseudorepeated Roots

2004 ◽  
Vol 126 (3) ◽  
pp. 498-508 ◽  
Author(s):  
Brandon J. Jellison ◽  
Harold R. Kess ◽  
Douglas E. Adams ◽  
David C. Nelson
Keyword(s):  
Raw Materials ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Mass Distributions ◽  
Lumped Parameter ◽  
Fabrication Procedure ◽  
Modes Of Vibration ◽  
Systemic Problems ◽  
Vibration Tests ◽  
Degenerate Modes

The modes of vibration of manufactured parts can be good indicators of the overall quality of the manufacturing process. That is, deviations in the modal frequencies or modal vectors of mechanical parts can help to identify outlier or systemic problems in the raw materials or fabrication procedure. A novel method for characterizing nonuniformities in homogeneous symmetric parts using pseudorepeated modal frequencies is discussed in this paper. It is demonstrated that the spacing between pseudorepeated roots in dominantly symmetric manufactured parts is a direct indicator of nonuniformities (i.e., inclusions, voids) in the stiffness or mass distributions. Smaller differences between split-peaks indicate less nonuniformity, and hence, higher quality parts. A simple fourth-order lumped parameter model is used to elaborate on this technique analytically, a representative finite element model is used to further this development, root locus techniques are used to study the sensitivity to nonuniformities, and acceleration response data from impact vibration tests on deep drawn hemispherical shells are used to verify the approach experimentally.

scholarly journals The Development of a Tympanic Membrane Model and Probabilistic Dose-Response Risk Assessment of Rupture Because of Blast

2020 ◽  
Vol 185 (Supplement_1) ◽  
pp. 234-242
Author(s):  
Anthony E Iyoho ◽  
Kevin Ho ◽  
Philemon Chan
Keyword(s):  
Tympanic Membrane ◽  
Dose Response ◽  
Injury Risk ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Unintended Effects ◽  
Response Curves ◽  
Membrane Rupture ◽  
Lumped Parameter ◽  
Dose Response Curves

ABSTRACT Introduction There is no dose-response model available for the assessment of the risk of tympanic membrane rupture (TMR), commonly known as eardrum rupture, from exposures to blast from nonlethal flashbangs, which can occur concurrently with temporary threshold shift. Therefore, the objective of this work was to develop a fast-running, lumped parameter model of the tympanic membrane (TM) with probabilistic dose-dependent prediction of injury risk. Materials and Methods The lumped parameter model was first benchmarked with a finite element model of the middle ear. To develop the dose-response curves, TMR data from a historic cadaver study were utilized. From these data, the binary probability response was constructed and logistic regression was applied to generate the respective dose-response curves at moderate and severe eardrum rupture severity. Results Hosmer-Lemeshow statistical and receiver operation characteristic analyses showed that maximum stored TM energy was the overall best dose metric or injury correlate when compared with total work and peak TM pressure. Conclusions Dose-response curves are needed for probabilistic risk assessments of unintended effects like TMR. For increased functionality, the lumped parameter model was packaged as a software library that predicts eardrum rupture for a given blast loading condition.

Non-linear dynamic simulation of mechanical periodicity of end-diastolic volume of left ventricle under the influence of baroreflex

2006 ◽  
Vol 220 (3) ◽  
pp. 357-366 ◽  
Author(s):  
Q Wang ◽  
S Xu ◽  
D Chen ◽  
M Collins
Keyword(s):  
Left Ventricle ◽  
Vascular System ◽  
Element Model ◽  
Baroreceptor Reflex ◽  
Lumped Parameter Model ◽  
Linear Dynamic ◽  
End Diastolic Volume ◽  
Lumped Parameter ◽  
Non Linear ◽  
Mechanical Periodicity

Mechanical periodicity (MP) of the end-diastolic volume (EDV) of the left ventricle (LV) is closely associated with cardiovascular pathophysiology. On the basis of the Starling's law of the LV and Burattini and Gnudi's four-element model of the vascular system, and considering baroreceptor reflex, a non-linear dynamic lumped-parameter model is proposed. This simulates the MP phenomena of the EDV by solving a series of one-dimensional discrete non-linear dynamic equations. The results demonstrate that excessive deviations of some physiological parameters often induce MP - the unstable phenomena of EDV - and verify that the effects of baroreceptor reflex enhance the ability of the human physiological system to maintain stability.

Dynamic Modeling and Analysis of a Planetary Gear Involving Tooth Wedging and Bearing Clearance Nonlinearity

2009 ◽  
Author(s):  
Yi Guo ◽  
Robert G. Parker
Keyword(s):  
Gear Tooth ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Back Side ◽  
Modeling And Analysis ◽  
Bearing Clearance ◽  
Gravity Forces ◽  
Lumped Parameter ◽  
Bearing Failures ◽  
Wide Range

Tooth wedging occurs when a gear tooth comes into contact on the drive-side and back-side simultaneously. Tooth wedging risks bearing failures from elevated forces. This work studies the nonlinear tooth wedging behavior and its correlation with planet bearing forces by analyzing the dynamic response of an example planetary gear based on a real application of a wind turbine geartrain. The two-dimensional lumped-parameter model [1] is extended to include tooth separation, back-side contact, tooth wedging, and bearing clearances. The simulation results show significant impact of tooth wedging on planet bearing forces for a wide range of operating speeds. To develop a physical understanding of the tooth wedging mechanism, connections between planet bearing forces and tooth forces are studied by investigating physical forces and displacements acting throughout the planetary gear. A method to predict tooth wedging based on geometric interactions is developed and verified. The major causes of tooth wedging relate directly to translational vibrations caused by gravity forces and the presence of clearance-type nonlinearities in the form of backlash and bearing clearance.

scholarly journals Analysis of Fly Fishing Rod Casting Dynamics

2011 ◽  
Vol 18 (6) ◽  
pp. 839-855
Author(s):  
Gang Wang ◽  
Norman Wereley
Keyword(s):  
Finite Element ◽  
Initial Boundary ◽  
Element Model ◽  
Nonlinear Finite Element ◽  
Lumped Parameter Model ◽  
Parameter Method ◽  
Line System ◽  
Fly Fishing ◽  
Lumped Parameter ◽  
Rigid Rod

An analysis of fly fishing rod casting dynamics was developed comprising of a nonlinear finite element representation of the composite fly rod and a lumped parameter model for the fly line. A nonlinear finite element model was used to analyze the transient response of the fly rod, in which fly rod responses were simulated for a forward casting stroke. The lumped parameter method was used to discretize the fly line system. Fly line motions were simulated during a cast based on fly rod tip response, which was used as the initial boundary condition for the fly line. Fly line loop generation, propagation, and line turn-over were simulated numerically. Flexible rod results were compared to the rigid rod case, in which the fly tip path was prescribed by a given fly rod butt input. Our numerical results strongly suggest that nonlinear flexibility effects on the fly rod must be included in order to accurately simulate casting dynamics and associated fly line motion.

The Mechanism on Prediction of Transient Maximum Amplitude for Tuned and Mistuned Blisks

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Luohui Ouyang ◽  
Hai Shang ◽  
Hua Chen ◽  
Qingzhen Bi ◽  
Li-Min Zhu
Keyword(s):  
Damping Ratio ◽  
Maximum Amplitude ◽  
Element Model ◽  
Forced Response ◽  
Lumped Parameter Model ◽  
Fundamental Parameter ◽  
Reduced Order ◽  
Lumped Parameter ◽  
Engine Order ◽  
Acceleration And Deceleration

Abstract Blisks are subjected to frequent acceleration and deceleration, which leads to a transient forced response; however, there is limited understanding of this response. In this work, the mechanism on prediction of transient maximum amplitude is found. An analytical link is proposed between the transient maximum amplitude and a fundamental dimensionless parameter which combines the damping ratio, natural frequency, acceleration, and engine order of the system to reveal the mechanism of the transient maximum amplitude. Therefore, the transient maximum amplitudes of tuned and mistuned blisks are predicted analytically. First, a lumped parameter model is used to study the mechanism of the transient maximum amplitude for a tuned blisk, and an approximated analytical expression is derived between the fundamental parameter and the transient amplification factor of a 1DOF (degree-of-freedom) model. The relationship is also applicable to a reduced order, tuned finite element model (FEM). Second, the mechanism of the transient response for a mistuned blisk is studied in the decoupled modal space of the blisk, based on the 1DOF transient relationship. The transient maximum amplitude in a reduced order, mistuned FEM is predicted. Two lumped parameter models and a FEM are employed to validate the prediction.

Dynamical Analysis of Planetary Gear Transmission System Under Support Stiffness Effects

2020 ◽  
Vol 30 (06) ◽  
pp. 2050080
Author(s):  
Ling Xiang ◽  
Zeqi Deng ◽  
Aijun Hu
Keyword(s):  
Excitation Frequency ◽  
Global Bifurcation ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Dynamical Analysis ◽  
Largest Lyapunov Exponent ◽  
Meshing Stiffness ◽  
Gear Transmission System

The transverse-torsional nonlinear model of multistage gear transmission system which is comprised of a planetary gear set and two parallel gear stages is proposed with time-varying meshing stiffness, comprehensive gear errors and gear backlash. The nonlinear dynamic responses are analyzed by applying excitation frequency and support stiffness as the bifurcation parameters. The motions of the system are identified through global bifurcation diagram, largest Lyapunov exponent (LLE) and Poincaré map. The numerical results demonstrate that the support stiffness affects the system, especially on planetary gear set. The motions of the system with the changes of the support stiffness are diverse including some different multiperiodic motions. Also, the state of the system undergoes 2T-periodic motion, chaos, quasi-periodic behavior and multiperiodic motion. For the support stiffness or other nonlinear factors of the gear system, the suitable range of working frequencies could make the system stable. Correspondingly, parameters of the system should be designed properly and controlled for the better operation and enhancing the life of the system.

Planetary Gear Modal Properties and Dynamic Response: Experiments and Analytical Simulation

2011 ◽  
Author(s):  
Tristan M. Ericson ◽  
Robert G. Parker
Keyword(s):  
Natural Frequencies ◽  
Planetary Gear ◽  
Forced Response ◽  
Operating Conditions ◽  
Modal Testing ◽  
Lumped Parameter Model ◽  
Lumped Parameter ◽  
Analytical Simulation ◽  
Analytical Research ◽  
Independent Motion

Planetary gear vibration is a major source of noise and may lead to fatigue-induced failures in bearings or other drivetrain components. Gear designers use mathematical models to analyze potential designs, but these models remain unverified by experimental data. This paper presents experiments that completely characterize the dynamic behavior of a spur planetary gear by modal testing and spinning tests under representative operating conditions, focusing on the independent motion of planetary components. Accelerometers are mounted directly to individual gear bodies. Rotational and translational accelerations obtained from the experiments are compared to the predictions of a lumped parameter model. Natural frequencies, modes, and forced response agree well between experiments and the model. Rotational, translational, and planet mode types presented in published analytical research are observed experimentally.

Sign in / Sign up

Export Citation Format

Share Document