A multibody dynamic model for predicting operational load spectra of dual clutch transmissions

2021 ◽  
Vol 263 (2) ◽  
pp. 4132-4143
Author(s):  
Murat Inalpolat ◽  
Enes Timur Ozdemir ◽  
Bahadir Sarikaya ◽  
Hyun Ku Lee
Keyword(s):  
Steady State ◽  
Dynamic Model ◽  
Forced Vibration ◽  
Linear Time ◽  
Vibration Response ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Time Step ◽  
Gear Mesh ◽  
Multibody Dynamic

In this paper, a generalized nonlinear time-varying multibody dynamic model of dual clutch transmissions (DCT) is presented. The model consists of clutches, shafts, gears and synchronizers, and can be used to model any DCT architecture. A nonlinear clutch model is used to determine the transmitted power to the transmission at any speed and clutch temperature. The clutch can be a single- or multi-plate clutch and can operate in a wet or dry-clutch configuration. A combined kinematic and powerflow simulation enables calculation of gear, shaft, bearing and clutch quasi-static loads as well as gear mesh frequencies following a duty cycle as the input. For the corresponding Linear-Time-Invariant (LTI) system model, natural frequencies and mode shapes are obtained by solving the eigenvalue problem. The modal summation technique is used to determine the steady state forced vibration response of the system. For the corresponding NTV system, Newmark's time-step marching based integration is used to determine both the steady state and transient forced vibration response of the system. The DCT model is exercised using a common transmission architecture operating at several different operating conditions. The resulting impact of changing operational conditions on gear and bearing loads as well as dynamic transmission error spectra are demonstrated.

A Dynamic Model for Double-Planet Planetary Gearsets

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Dylan C. Fyler ◽  
Murat Inalpolat
Keyword(s):  
Dynamic Model ◽  
Forced Vibration ◽  
Transmission Error ◽  
Vibration Response ◽  
Operating Conditions ◽  
Distribution Model ◽  
Design Parameters ◽  
Gear Mesh ◽  
Load Spectra ◽  
Modal Summation

In this study, a two-dimensional (2D), steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of N number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

A Dynamic Model for Double-Planet Planetary Gearsets

2015 ◽  
Author(s):  
Dylan C. Fyler ◽  
Murat Inalpolat
Keyword(s):  
Dynamic Model ◽  
Forced Vibration ◽  
Transmission Error ◽  
Vibration Response ◽  
Operating Conditions ◽  
Distribution Model ◽  
Design Parameters ◽  
Gear Mesh ◽  
Load Spectra ◽  
Modal Summation

In this study, a two-dimensional, steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

scholarly journals The Determination of Steady-State Movements Using Blade Tip Timing Data

2018 ◽  
Author(s):  
Mohamed Mohamed ◽  
Philip Bonello ◽  
Peter Russhard
Keyword(s):  
Steady State ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Fe Model ◽  
Measurement Point ◽  
Fe Modelling ◽  
Timing Data ◽  
Blade Tip ◽  
Dc Component ◽  
Change In Mean

One of the main challenges of the Blade Tip Timing (BTT) measurement method is to be able to determine the sensing position of the probe relative to the blade tip. It is highly important to identify the measurement point of BTT since each point of the blade tip may have a different vibration response. This means that a change in measurement position will affect the amplitude, phase and DC component of the results obtained from BTT data. This increases the uncertainty in the correlation between BTT measurements and Finite Element (FE) modelling. Also, the measurement point should ideally be located to measure as many modes as possible. This means that the probe’s position should not coincide with a node, or a position at which the sensor misses the blade tip. Changes in the sensing position usually arise from the steady state movements of the blades (change in mean displacement). Such movements are caused by changes to the static (thermal and pressure) loading conditions that result from changes in the rotational speed. Such movements usually have a constant direction at normal operating conditions, but the direction may fluctuate if the machine develops a fault. There are three main types of movements of the sensing position that are considered in this paper: (1) axial movement; (2) blade lean; (3) blade untwist. Ideally, the sensing position is known based on the geometries of both the blade and the probe, but due to different types of movements of the blade this position is lost. Very few works have researched the extraction of the sensing position. Such preliminary works have required a pre-knowledge of mode shapes and additional instrumentation. The aim of this paper is to present a novel method for the identification of the BTT sensing position of the probes relative to a blade tip, which can be used to quantify the above movements. The developed method works by extracting the steady state offset from measurements of blade tip displacements over a number of revolutions as the speed changes from zero to a certain value. Hence, that part of the offset that is due to the angular positioning error of the probes (outside the scope of this work) is cancelled out (since it is independent of speed). The change in steady state offset is then processed to identify the three possible movements. The new method is validated using a novel BTT simulator that is based on the modal model of the FE model of a bladed disk (“blisk”). The simulator generates BTT data for prescribed changes to the sensing position. The validation tests show that the novel algorithm can identify such movements within a 2% margin of error.

Frictional dynamic model predictions of FZG-A10 spur gear pairs considering profile errors

2020 ◽  
pp. 135065012096297
Author(s):  
Nabih Feki ◽  
Maroua Hammami ◽  
Olfa Ksentini ◽  
Mohamed Slim Abbes ◽  
Mohamed Haddar
Keyword(s):  
Dynamic Model ◽  
Coefficient Of Friction ◽  
Power Loss ◽  
Spur Gear ◽  
Operating Conditions ◽  
Time Dependent ◽  
Nonlinear Dynamic Model ◽  
Gear Mesh ◽  
Proposed Model ◽  
Profile Errors

In this work, a nonlinear dynamic model of an FZG-A10 spur gear was investigated by taking into account for the actual time-varying gear mesh stiffness and the frictional effects between meshing gear teeth to evaluate the influence of the dynamic effects on frictional gear power loss predictions. The equations of motion of the generalized translational-torsional coupled dynamic system derived from Lagrange principle was extended compared to authors’ previous work in order to account for time dependent coefficient of friction and profile errors. The dynamic response of spur gears, computed by an iterative implicit scheme of Newmark, is changed due to the presence of coefficient of friction and profile errors. A dynamic analysis was performed and the influence of frictional effect including tooth shape deviations, in particular, was scrutinized since a time-dependent coefficient of friction is deeply related to the gear surface roughness and all parameters dependent on gears error profiles are introduced in the proposed model. The predicted meshing gear power losses with constant and local friction coefficient were compared. The influence of constant and variable profile errors considered in the local coefficient of friction formulation was also studied and their corresponding root mean square (RMS) power loss was compared to the experimental results. The results using FZG A10 spur gear pairs running under several operating conditions (different loads and speeds) validate the superiority of the proposed model against previous similar models.

An Adaptive Perturbation Scheme for the Analysis of Mistuned Bladed Disks

1995 ◽  
Author(s):  
Chung-Chih Lin ◽  
Marc P. Mignolet
Keyword(s):  
Steady State ◽  
Forced Vibration ◽  
Perturbation Technique ◽  
Computational Effort ◽  
Vibration Response ◽  
Perturbation Scheme ◽  
Bladed Disks ◽  
Steady State Analysis ◽  
At Will

In this paper, a novel perturbation technique is introduced for the determination of the forced vibration response of mistimed bladed disks. The proposed technique is adaptive in the sense that the level of approximation can be varied at will to accommodate any specificities of the tuned system and/or of the existing mistuning. This versatility of the proposed approach not only guarantees the reliability of the computed response but also leads to an excellent compromise between accuracy and computational effort. Numerical results are presented that demonstrate both the reliability of the computed response and the computational saving obtained by relying on the suggested perturbation technique as opposed to a straightforward steady state analysis.

scholarly journals Identification of Solar Collector Dynamics Using Physical Model-Based Approach

1994 ◽  
Vol 116 (4) ◽  
pp. 755-763 ◽  
Author(s):  
B. J. Huang ◽  
S. B. Wang
Keyword(s):  
Steady State ◽  
System Dynamics ◽  
Physical Model ◽  
Transfer Functions ◽  
Linear Time ◽  
Operating Conditions ◽  
Distributed Model ◽  
Response Analysis ◽  
Linear Perturbation ◽  
Model Parameters

A system dynamics model of flat-plate solar collectors was derived and identified here. A nonlinear physical model was first derived from a two-node concept and energy conservation principle. The model was then approximated by the linear perturbation equations which were Laplace transformed and solved to lead to a distributed model in terms of the transfer functions. A model reduction was further employed to yield a linear time-invariant model with parameters as functions of steady-state operating conditions. The model parameters were identified by a dynamic test with step inputs at various operating conditions using frequency response analysis and model fitting in frequency domain. The identified parameters were then fitted to a function of steady-state mass flowrate mw. Thus, the model can describe the system dynamics behavior under various operating conditions through the identified parameters. The simulations using the model were shown to agree very well with the test results.

Performance Evaluation of Dynamic Model of Compact Heat Exchange Reformer for High-Temperature Fuel Cell Systems

2013 ◽  
Vol 11 (1) ◽  
Author(s):  
Jeongpill Ki ◽  
Daejong Kim
Keyword(s):  
Steady State ◽  
Heat Exchanger ◽  
Fuel Cell ◽  
Heat Exchange ◽  
Dynamic Model ◽  
Operating Conditions ◽  
Transfer Model ◽  
Thermal Dynamics ◽  
Internal Reforming ◽  
Experimental Apparatus

Solid oxide fuel cell (SOFC) systems are the most advanced power generation system with the highest thermal efficiency. The current trend of research on the SOFC systems is focused on multikilowatt scale systems, which require either internal reforming within the stack or a compact external reformer. Even if the internal reforming within the SOFC stack allows compact system configuration, it causes significant and complicated temperature gradients within the stack, due to endothermic reforming reactions and exothermic electrochemical reactions. As an alternative solution to the internal reforming, an external compact heat exchange reformer (CHER) is investigated in this work. The CHER is based on a typical plate-fin counterflow or coflow heat exchanger platform, and it can save space without causing large thermal stress and degradation to the SOFC stack (i.e., eventually reducing the overall system cost). In this work, a previously developed transient dynamic model of the CHER is validated by experiments. An experimental apparatus, which comprises the CHER, air heater, gas heater, steam generator, several mass flow controllers, and controller cabinet, was designed to investigate steady state reforming performance of the CHER for various hot air inlet temperatures (thermal energy source) and steam to carbon ratios (SCRs). The transient thermal dynamics of the CHER was also measured and compared with simulations when the CHER is used as a heat exchanger with inert gas. The measured transient dynamics of CHER matches very well with simulations, validating the heat transfer model within the CHER. The measured molar fractions of reformate gases at steady state also agree well with the simulations validating the used reaction kinetics. The transient CHER model can be easily integrated into a total integrated SOFC system, and the model can be also used for optimal design of similar CHERs and provides a guideline to select optimal operating conditions of the CHERs and the integrated SOFC system.

scholarly journals On the Large Amplitude Forced Vibration Analysis of Composite Sectorial Plates

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Ahmad Saood ◽  
Zain A. Khan ◽  
Mohd T. Parvez ◽  
Arshad H. Khan
Keyword(s):  
Steady State ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Laminated Composite ◽  
Vibration Response ◽  
Arc Length ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate ◽  
State Stress

The nonlinear steady state large amplitude forced vibration response of a laminated composite annular sector plate is presented. The nonlinear governing equation of motion of the laminated composite annular sector plate has been obtained using kinematics of first-order shear deformation theory (FSDT) and employing Hamilton’s principle. The governing equations of motion have been solved in a time domain using a modified shooting method and arc-length/pseudo-arc length continuation technique. The influence of the boundary condition, sector angle, and annularity ratio on the linear as well as nonlinear steady state forced vibration response has been investigated. The strain/stress variation across the thickness of the annular sector plate is presented to explain the reason for a decrease/increase in hardening nonlinear behaviour. The periodic variation of the non-linear steady state stress has also been obtained to throw light into the factors influencing the unequal stress half cycles and multiple cyclic stress reversals, which is detrimental to the fatigue design of laminated composite annular sectorial plates. The frequency spectra of the steady state stress reveals large even and odd higher harmonic contributions for different cases due to changes in the restoring force dynamics. The modal interaction/exchange during a cycle is demonstrated using a deformed configuration of the laminated annular sector plate.

Multibody Dynamic Model of a Double Nut Preloaded Ball Screw Mechanism With Lubrication

2020 ◽  
Author(s):  
Antonio Carlo Bertolino ◽  
Stefano Mauro ◽  
Giovanni Jacazio ◽  
Massimo Sorli
Keyword(s):  
Dynamic Model ◽  
Operating Conditions ◽  
Ball Screw ◽  
Time Variability ◽  
Theoretical Point ◽  
Grease Lubrication ◽  
Normal Contact ◽  
Model Based ◽  
Multibody Dynamic ◽  
Static Conditions

Abstract Ball screws have been investigated by several researchers from a theoretical point of view because the intrinsic complexity of experimental investigation of these mechanisms. Most of the models developed so far have been developed in quasi-static conditions ignoring inertia terms and time variability of operating conditions. A detailed multibody dynamic model of a double nut preloaded ball screw is presented in this paper, taking into account the full dynamic of each subcomponent as well as the mutual interactions. A 3D contact model is introduced, considering Hertzian normal contact and a simplified friction model based on grease lubrication. This model takes into account the time variability of the operating conditions and it is suitable to be used for prognostic and model-based design approaches. The results of dynamic simulations in presence of backlash are presented to highlight the model’s capabilities.

scholarly journals Linear parameter-varying model for a refuellable zinc–air battery

2020 ◽  
Vol 7 (12) ◽  
pp. 201107
Author(s):  
Woranunt Lao-atiman ◽  
Sorin Olaru ◽  
Sette Diop ◽  
Sigurd Skogestad ◽  
Amornchai Arpornwichanop ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Linear Time ◽  
Storage System ◽  
High Capacity ◽  
Operating Conditions ◽  
Nonlinear Behaviour ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Air Battery ◽  
Parameter Varying

Due to the increasing trend of using renewable energy, the development of an energy storage system (ESS) attracts great research interest. A zinc–air battery (ZAB) is a promising ESS due to its high capacity, low cost and high potential to support circular economy principles. However, despite ZABs' technological advancements, a generic dynamic model for a ZAB, which is a key component for effective battery management and monitoring, is still lacking. ZABs show nonlinear behaviour where the steady-state gain is strongly dependent on operating conditions. The present study aims to develop a dynamic model, being capable of predicting the nonlinear dynamic behaviour of a refuellable ZAB, using a linear parameter-varying (LPV) technique. The LPV model is constructed from a family of linear time-invariant models, where the discharge current level is used as a scheduling parameter. The developed LPV model is benchmarked against linear and nonlinear model counterparts. Herein, the LPV model performs remarkably well in capturing the nonlinear behaviour of a ZAB. It significantly outperforms the linear model. Overall, the LPV approach provides a systematic way to construct a robust dynamic model which well represents the nonlinear behaviour of a ZAB.

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