Analytical and Numerical Dynamic Analysis of Gears in the Presence of Engine Acyclism

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
G. Sika ◽  
Ph. Velex
Keyword(s):  
Dynamic Analysis ◽  
Engine Speed ◽  
Degree Of Freedom ◽  
Time Varying ◽  
Numerical Techniques ◽  
Mesh Stiffness ◽  
Response Characteristics ◽  
Set Up ◽  
Speed Fluctuations

A one-degree-of-freedom model of geared transmissions is set up. It incorporates the influence of unsteady rotations due to engine speed fluctuations along with simplified time-varying mesh stiffness functions, including contact losses between the teeth and back strikes. The dynamic tooth loads are determined by several analytical and numerical techniques whose results agree well. Finally, some of the response characteristics due to speed fluctuations are presented and commented upon.

Vibration isolation with clutch disk pre-damper mechanism for the idle rattle phenomenon

2016 ◽  
Vol 24 (8) ◽  
pp. 1518-1534 ◽  
Author(s):  
Alişan Yüceşan ◽  
Semih Sezer
Keyword(s):  
Engine Speed ◽  
Vibration Isolation ◽  
Test Bench ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Speed Measurement ◽  
Proposed Model ◽  
Speed Fluctuations ◽  
Gear Mesh Stiffness

In this paper, the influence of clutch disk pre-damper mechanism constituents on the idle rattle phenomenon was investigated with an analytical model containing a new time-varying gear mesh stiffness function. Comparing experimental results to simulation results for the same excitation input was the key implementation for the validation of proposed model. The engine speed fluctuations represented in the simulation was imported from a speed measurement of a diesel engine in the test bench.

Dynamic analysis for a spur geared rotor system with tooth tip chipping based on an improved time-varying mesh stiffness model

2021 ◽  
Vol 165 ◽  
pp. 104435
Author(s):  
Yi Yang ◽  
Niaoqing Hu ◽  
Jinyuan Tang ◽  
Jiao Hu ◽  
Lun Zhang ◽  
...  
Keyword(s):  
Dynamic Analysis ◽  
Rotor System ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Stiffness Model

Nonlinear Dynamic Analysis of a Multi-Gear Train With Time-Varying Mesh Stiffness Including Modification Coefficient Effect

2011 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
K. H. Huang ◽  
C. J. Cheng ◽  
C. R. Wang
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Gear Train ◽  
Work Piece ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Harmonic Motion ◽  
Gear Profile

The nonlinear dynamic analysis of a multi-gear train with time-varying mesh stiffness on account of the modification coefficient effect is in vestigated in this paper. The proposed application of the modification coefficient will revise the center distance of the gear pair, avoid undercut and raise the mesh stiffness of the designed gear system. In this study, the gear profile is generated from the relationship between the rack cutter and the gear work piece by using the envelope theory. The rack cutter with the modification coefficient increases the mesh stiffness and thus enhances the strength of the gear tooth. Then the time-varying mesh stiffness at the contact position of the gear pair is calculated from the tooth deflection analysis using the generated gear profile. With the obtained time-varying mesh stiffness, the nonlinear dynamic behavior of multi-gear train is investigated by using Runge-Kutta integration method. The numerical results of the studied examples show the harmonic motion, sub-harmonic motion, chaotic motion and bifurcation phenomenon of the gear train.

scholarly journals An Improved Rigid Multibody Model for the Dynamic Analysis of the Planetary Gearbox in a Wind Turbine

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Wenguang Yang ◽  
Dongxiang Jiang
Keyword(s):  
Dynamic Analysis ◽  
Transient Analysis ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Vibration Signals ◽  
Planetary Gearbox ◽  
Multibody Model ◽  
Improved Model ◽  
Rigid Multibody

This paper proposes an improved rigid multibody model for the dynamic analysis of the planetary gearbox in a wind turbine. The improvements mainly include choosing the inertia frame as the reference frame of the carrier, the ring, and the sun and adding a new degree of freedom for each planet. An element assembly method is introduced to build the model, and a time-varying mesh stiffness model is presented. A planetary gear study case is employed to verify the validity of the improved model. Comparisons between the improvement model and the traditional model show that the natural characteristics are very close; the improved model can obtain the right equivalent moment of inertia of the planetary gear in the transient simulation, and all the rotation speeds satisfy the transmission relationships well; harmonic resonance and resonance modulation phenomena can be found in their vibration signals. The improved model is applied in a multistage gearbox dynamics analysis to reveal the prospects of the model. Modal analysis and transient analysis with and without time-varying mesh stiffness considered are conducted. The rotation speeds from the transient analysis are consistent with the theory, and resonance modulation can be found in the vibration signals.

Non-Linear Vibration Modeling and Simulation of a Gear Pair Based on ADAMS and Simulink

2013 ◽  
Vol 681 ◽  
pp. 219-223 ◽  
Author(s):  
Chun Jing Huo ◽  
Hui Liu ◽  
Zhong Chang Cai ◽  
Ming Zheng Wang
Keyword(s):  
Gear Train ◽  
Transmission Model ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Feedback Model ◽  
Non Linear ◽  
Speed Fluctuation ◽  
Set Up ◽  
Multi Body

To set up the virtual prototype of a gear train system in the dynamic analysis software ADAMS, the torsional vibration model of a gear pair was transformed into an equivalent transmission model in which a multi-body model was established in ADAMS and its meshing force solution model was established in Simulink. The time-varying mesh stiffness, gear clearance, meshing errors and other non-linear factors can be included in the gear meshing feedback model, more importantly, the influence of gear speed fluctuation on the time-varying mesh stiffness was taken into consideration. The simulation results contrastively prove the feasibility of co-simulation for obtaining the dynamic characteristics of gear meshing process.

Dynamic Analysis of a Geared Rotor-Bearing System with Time-Varying Gear Mesh Stiffness and Pressure Angle

2013 ◽  
Vol 284-287 ◽  
pp. 461-467
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Responses ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Proposed Model ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The dynamic analysis of a geared rotor-bearing system with time-varying gear mesh stiffness and pressure angle is presented in this paper. Although there are analyses for both of the gear and rotor-bearing system dynamics, the coupling effect of the time-varying mesh and geared rotor-bearing system is deficient. Therefore, the pressure angle and contact ratio of the geared rotor-bearing system are treated as time-varying variables in the proposed model while they were considered as constant in previous models. The gear mesh stiffness is varied with different contact ratios of the gear pair in the meshing process. The nonlinear equations of motion for the geared rotor-bearing system are obtained by applying Lagrange’s equation and the dynamic responses are computed by using the Runge-Kutta numerical method. Numerical results of this study indicated that the proposed model provides realistic dynamic response of a geared rotor-bearing system.

Parametric Instability in Planetary Gears With Frequency-Modulated Time-Varying Mesh Stiffness

2014 ◽  
Author(s):  
Xinghui Qiu ◽  
Qinkai Han ◽  
Fulei Chu
Keyword(s):  
Parametric Instability ◽  
Operating Conditions ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Rotational Model ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Speed Fluctuations ◽  
Gear Mesh Stiffness

A rotational model of planetary gears is developed which incorporates mesh stiffness variation and input speed fluctuations. Gear mesh stiffness is approximated by rectangle wave and different harmonic orders are considered. Because of speed fluctuations, the mesh stiffness is frequency modulated. The parametric instability associated with frequency-modulated time-varying stiffness is numerically investigated. The operating conditions leading to parametric instability are identified using Floquet theory and numerical integration. Whether the general laws derived for steady speed to suppress particular instabilities are applicable for fluctuating speed is verified. The effects of speed fluctuations on parametric instability are examined.

scholarly journals Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Xinghui Qiu ◽  
Qinkai Han ◽  
Fulei Chu
Keyword(s):  
Parametric Instability ◽  
Phase Speed ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Time Varying ◽  
Mesh Stiffness ◽  
New Thought ◽  
Lumped Parameter ◽  
Speed Fluctuation ◽  
Speed Fluctuations

Planetary gear is widely used in engineering and usually has symmetrical structure. As the number of teeth in contact changes during rotation, the time-varying mesh stiffness parametrically excites the planetary gear and may cause severe vibrations and instabilities. Taking speed fluctuations into account, the time-varying mesh stiffness is frequency modulated, and therefore sideband instabilities may arise and original instabilities are significantly affected. Considering two different speed fluctuations, original and sideband instabilities are numerically and analytically investigated. A rotational lumped-parameter model of the planetary gear is developed, in which the time-varying mesh stiffness, input speed fluctuations, and damping are considered. Closed-form approximations of instability boundaries for primary and combination instabilities are obtained by perturbation analysis and verified by numerical analysis. The effects of speed fluctuations and damping on parametric instability are systematically examined. Because of the frequency modulation, whether a parametric instability occurs cannot be simply predicted by the planet meshing phase which is applicable to constant speed. Besides adjusting the planet meshing phase, speed fluctuation supplies a new thought to minimize certain instability by adjusting the amplitude or frequency of the speed fluctuation. Both original and sideband instabilities are shrunken by damping, and speed fluctuation further shrinks the original instability.

Analysis of the Interactions Between Indicated and Reciprocating Torques for the Development of a Torsional Behavior Model of the Powertrain

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Fabrizio Ponti ◽  
Luca Solieri
Keyword(s):  
Engine Speed ◽  
Wave Form ◽  
Behavior Model ◽  
Identification Process ◽  
Speed Measurement ◽  
Torque Estimation ◽  
Torsional Behavior ◽  
Set Up ◽  
Correct Estimation ◽  
Speed Fluctuations

Torque-based engine control systems usually employ a produced torque estimation feedback in order to verify that the strategy target torque has been met. Torque estimation can be performed using static maps describing the engine behavior or using models describing the existing relationships between signals measured on the engine and the indicated torque produced. Signals containing information on the combustion development, suitable for this purpose, are, among others, the ion-current signal, the vibration signals obtained from accelerometers mounted on the engine block, or the instantaneous engine speed fluctuations. This paper presents the development and the identification process of an engine-driveline torsional behavior model that enables indicated torque estimation from instantaneous engine speed measurement. Particular attention has been devoted to the interactions between indicated and reciprocating torques, and their effects over instantaneous engine speed fluctuations. Indicated and reciprocating torques produce, in fact, opposite excitations on the driveline that show opposite effects on the engine speed wave form: For low engine speed, usually indicated torque prevails, while the opposite applies for higher engine speed. In order to correctly estimate indicated torque from engine speed measurement, it is therefore necessary to correctly evaluate the reciprocating torque contribution. Reciprocating torque is usually described using a wave form as a function of crank angle, while its amplitude depends on the value of the reciprocating masses. As mentioned before, knowledge of the reciprocating masses is fundamental in order to obtain correct estimation of the indicated torque. The identification process that has been set up for the engine-driveline torsional model enables to evaluate the relationship between torques applied to the engine and the corresponding engine speed wave form even without knowing the value of the reciprocating masses. In addition, once this model has been set up, it is possible to estimate with high precision the value of the reciprocating masses. Particular attention has also been devoted to the feasibility of the application of the identified model onboard for torque estimation; for this reason, the model has been developed in a very simple form. The approach proved to be effective both on gasoline and diesel engines, both for engine mounted on a test cell and onboard, with different engine configurations. Examples of application are given for some of the configurations investigated.

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