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1

Analysis of the single stage cycloidal gearbox with lobe defects. Fault diagnosis attempts using coherence function and Morris minimum-bandwidth wavelets

Król Roman

Archive of Mechanical Engineering

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2023

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LXX, nr 3

409--431

EN

In this article, the frequency characteristics of the forces and torques in the various cycloidal gearbox designs were investigated. The aim of the article is the search for frequency patterns that could be used in the formulation of a fault diagnosis methodology. Numerical analysis was performed in the cycloidal gearbox without defects as well as in cycloidal gearboxes with lobe defects or with removed lobes. The results of the numerical analysis were obtained in the multibody dynamics model of the cycloidal gearbox, implemented in Fortran and using the 2nd-order Runge-Kutta method for the integration of the motion equations. The used model is planar and uses Hunt and Crossley’s nonlinear contact modelling algorithm, which was modified using the Heaviside function and backlash to fit cycloidal gearbox model convergence demands. In the analysis of fault diagnosis methods, the coherence function and Morris minimum-bandwidth wavelets were used. It is difficult to find a unique pattern in the results to use in the fault diagnosis because of the random characteristics of the torques at the input and output shafts. Based on obtained results, a promising, low-vibration cycloidal gearbox design with removed 7 lobes of the single wheel was studied using the FFT algorithm.

2

Multibody dynamics model of the cycloidal gearbox, implemented in fortran for analysis of dynamic parameters influenced by the backlash as a design tolerance

Król Roman, Król Kazimierz

Acta Mechanica et Automatica

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2023

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Vol. 17, no. 2

272--280

EN

In this study, dynamical parameters of the cycloidal gearbox working at the constant angular velocity of the input shaft were investigated in the multibody dynamics 2D model implemented in the Fortran programming language. Time courses of input and output torques and forces acting on the internal and external sleeves have been shown as a function of the contact modelling parameters and backlash. The analysis results in the model implemented in Fortran were compared with the results in the 3D model designed using MSC Adams software. The values of contact forces are similar in both models. However, in the time courses obtained in MSC Adams there are numerical singularities in the form of peaks reaching 500 N for the forces at external sleeves and 400 N for the forces acting at internal sleeves, whereas in the Fortran model, there are fewer singularities and the maximum values of contact forces at internal and external sleeves do not exceed 200 N. The contact damping and discretisation level (the number of discrete contact points on the cycloidal wheels) significantly affect the accuracy of the results. The accuracy of computations improves when contact damping and discretisation are high. The disadvantage of the high discretization is the extended analysis time. High backlash values lead to a rise in contact forces and a decrease in the force acting time. The model implemented in Fortran gives a fast solution and performs well in the gearbox optimisation process. A reduction of cycloidal wheel discretisation to 600 points, which still allows satisfactory analysis, could reduce the solution time to 4 min, corresponding to an analysis time of 0.6 s with an angular velocity of the input shaft of 52.34 rad/s (500 RPM).

3

Multi-domain approach to modeling pantograph-catenary interaction

Zdziebko Paweł, Martowicz Adam, Uhl Tadeusz

Eksploatacja i Niezawodność

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2022

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Vol. 24, no. 1

130--139

EN

When a railway pantograph interacts with a catenary during the movement of a rail vehicle, several physical phenomena, both mechanical and electrical, occur in the system. These phenomena affect the quality of power supply of a train from traction devices. The unfavourable arcing occurring when there are disturbances of contact between the pantograph’s slider and the catenary contact wire. In turn, it results in energy loss and increased wear of the components of the system. When designing new solutions, computational models are helpful to predict the quality of interaction between the components of the pantograph-contact line system already at the virtual prototyping stage. In this paper, the authors comprehensively present a multi-domain (multiphysics) model, which takes into account necessary conditions for interaction between pantograph elements and a catenary. Finally, the impact of the individual physical domains are analysed and the ones which have a significant impact on the simulation of the operation results are identified.

4

Analysis of the backlash in the single stage cycloidal gearbox

Król Roman

Archive of Mechanical Engineering

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2022

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LXIX, nr 4

693--711

EN

In this paper the analysis of backlash influence on the spectrum of torque at the output shaft of a cycloidal gearbox has been performed. The model of the single stage cycloidal gearbox was designed in the MSC Adams. The analysis for the excitation with the torque and the analysis with constant angular velocity of the input shaft were performed. For these analyses, the amplitude spectrums of the output torque for different backlashes was solved using FFT algorithm. The amplitude spectrums of the combined sine functions composed of the impact to impact times between the cycloidal wheel and the external sleeves were computed for verification. The performed studies show, that the backlash has significant influence on the output torque amplitude spectrum. Unfortunately the dependencies between the components of the spectrum and the backlash could not be expressed by linear equations, when vibrations of the output torque in the range of (350 Hz – 600 Hz) are considered. The gradual dependence can be found in the spectrum determined for the combined sine functions with half-periods equal impact-to-impact times. The spectrum is narrower for high values of backlash.

5

Resonance phenomenon in the single stage cycloidal gearbox. Analysis of vibrations at the output shaft as a function of the external sleeves stiffness

Król Roman

Archive of Mechanical Engineering

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2021

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LXVIII, nr 3

303--320

EN

In this paper a versatile analysis of the cycloidal gearbox vibrations and the resonance phenomenon was performed. The objective of this work was to show resonance phenomenon and vibrations study in the multibody dynamics model and in the finite element model of the cycloidal gearbox. The output torque was analyzed as a function of the external sleeves stiffness. The results from the multibody dynamics model were verified in the finite element model using natural frequency with load stiffening, direct frequency response and direct transient response analyses. It was shown that natural frequencies of the cycloidal gearbox undergo changes during motion of the mechanism. The gearbox passes through the thresholds of the increased vibration amplitudes, which lead to excessive wear of the external sleeves. The analysis in the multibody dynamics model showed, that the increase in the external sleeves stiffness increases frequency of the second-order fluctuation at the output shaft. Small stiffness of the external sleeves guarantees lower frequency of the second order vibrations and higher peak-to-peak values of the output torque. The performed research plays important role in the cycloidal gearbox design. This work shows gearbox dynamics problems which are associated with wear of the external sleeves.

6

Simulation of a deployable tensegrity column based on the finite element modeling and multibody dynamics simultions

Al Sabouni-Zawadzka A., Zawadzki A.

Archives of Civil Engineering

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2020

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Vol. 66, nr 4

543--560

EN

The present paper is dedicated to the analysis of deployable tensegrity columns. The main aim of this work is to present a technique, developed by combining the finite element (FE) analysis and the multibody dynamics (MBD) simulation, which enables precise and reliable simulations of deployable structures. While the finite element model of the column provides information on structural behavior in the deployed state, the dynamical modeling allows to analyze various deployment scenarios, choose active cables for the deployment and for the self-stress application, and to control distributions of internal forces during the assembly process. An example of a deployable column based on a popular tensegrity module - a 3-strut simplex - is presented. By analyzing the proposed column with the use of the developed method it is proven that the technique is suitable for complex simulations of deployable systems.

PL

W pracy został poruszony problem analizy rozwijalnych słupów tensegrity. Głównym celem opracowania jest zaprezentowanie techniki pozwalającej na zapewnienie niezawodnych symulacji tego typu struktur. Zaproponowana technika wykorzystuje metodę elementów skończonych (MES) oraz symulacje dynamiki układów wieloczłonowych (MBD). Metoda elementów skończonych dostarcza informacji odnośnie zachowania konstrukcji w stanie rozwiniętym, podczas gdy analiza dynamiki układu wieloczłonowego daje informacje dotyczące zachowania układu podczas realizacji różnych scenariuszy rozwijania, wyboru aktywnych cięgien, wartości samonaprężenia oraz rozkładu sił w elementach podczas rozwijania. Połączenie MES i MBD daje możliwość dokładnych i niezawodnych symulacji skomplikowanych struktur do jakich należą rozwijalne konstrukcje tensegrity.

7

Parallel computations and co-simulation in universal mechanism software. Part 2: Examples

Pogorelov Dmitry, Rodikov Alexander, Kovalev Roman

Transport Problems

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2019

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T. 14, z. 4

31--38

EN

The second part of the paper continues a discussion on the topic of paralel computations in railway dynamics. The algorithms described in the first part of the paper are applied to parallel simulation on computers with multicore processors of six different models of rail vehicles and trains with the number of degrees of freedom from about one hundred to more than 20 thousands. A considerable simulation speedup is reported. In addition, an example of evaluation of wheel profile wear on multicore processors and comparison of different approaches to multi-variant computations are considered.

8

Parallel computations and co-simulation in universal mechanism software. Part 1: Algorithms and implementation

Pogorelov Dmitry, Rodikov Alexander, Kovalev Roman

Transport Problems

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2019

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T. 14, z. 3

163--175

EN

Parallel computations speed up simulation of multibody system dynamics, in particular, dynamics of railway vehicles and trains. It is important for reduction of required time at the stage of new railway vehicle design, for increase of complexity of studied problems and for real-time applications. We consider realization of paralel computations in Universal Mechanism software in three different areas: simulation of rail vehicle and train dynamics, evaluation of wheel profile wear and multi-variant computations. The use of clusters for parallel running of multi-variant computations is illustrated. Co-simulation based on the interface between Universal Mechanism and Matlab/Simulink and other software tools is discussed.

9

Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

Orzechowski G., Frączek J.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

977--990

EN

The analysis and solution of many modern flexible multibody dynamic problems require formulations that are able to effectively model bodies with nonlinear materials undergoing large displacements and deformations. The absolute nodal coordinate formulation (ANCF) in connection with a continuum-based approach is one way to deal with these systems. The main objective of this work is to extend an existent approach for the modelling of slender structures within the ANCF framework with nonlinear, nearly incompressible materials using the volumetric energy penalty technique. The main part of the study is devoted to the evaluation of multi-layer beam models and simplifications in the locking suppression method based on F-bar projection. The results present significantly better agreement with the reference solution for multi-layer structures built with the standard ANCF beam element as compared with the earlier implementation.

10

Experimental identification and selection of dynamic properties of a high-speed tracked vehicle suspension system

Gniłka J., Mężyk A.

Eksploatacja i Niezawodność

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2017

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Vol. 19, no. 1

108--113

EN

The material diversity of subassemblies making up the tracked vehicle suspension system and the system wear level make it difficult to determine the value of forces acting in it. This paper presents a manner in which parameters of the model of a highspeed tracked vehicle suspension system can be adjusted using the genetic algorithm optimization method. The vehicle motion is tested experimentally to find reference characteristics of kinematic quantities of the system selected points. The simulation results obtained from numerical analyses are presented in charts and compared to the results of experimental testing. Finally, damping values in the vehicle shock-absorbers are determined based on an adopted criterion.

PL

Zróżnicowanie materiałowe podzespołów wchodzących w skład gąsienicowego układu jezdnego oraz stopień jego zużycia wpływają na trudność określenia wartości sił działających w tym układzie. W artykule poprzez zastosowanie metody optymalizacji algorytmami genetycznymi, przedstawiono sposób dostosowania parametrów modelu układu zawieszenia szybkobieżnego pojazdu gąsienicowego. Przeprowadzono badania doświadczalne ruchu pojazdu, w celu wyznaczenia charakterystyk wielkości kinematycznych wybranych punktów układu, które zostały przyjęte jako referencyjne. W rezultacie przeprowadzonych analiz otrzymano wyniki symulacji numerycznych, które zestawiono na wykresach i porównano z wynikami badań doświadczalnych. W końcowym etapie na podstawie przyjętego kryterium określono wartości tłumienia w amortyzatorach pojazdu.

11

Design and Analysis of an Interconnected Suspension for a Small Off-Road Vehicle

Minaker B. P., Yao Z

Archive of Mechanical Engineering

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2017

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Vol. LXIV, nr 1

5--21

EN

The paper describes the design and multibody dynamic analysis of a mechanically interconnected suspension, as applied to a small off-road vehicle. Interconnected suspensions use some sort of connection between the axles of a vehicle in order improve ride quality or vehicle handling. In principle, the connection may be hydraulic, pneumatic, or mechanical, but for installation in a typical passenger car, a mechanical connection would likely be impractical due to weight and complexity. In this paper, the vehicle in question is the University of Windsor SAE Baja off-road competition vehicle, and novel mechanical design is proposed. A multibody dynamic analysis is performed on the proposed design using the EoM open source multibody software developed by the University of Windsor Vehicle Dynamics and Control research group in order to assess any potential performance improvements.

12

Rigid-Body Motion of Planar Mechanisms by Finite Element Method With Comparison to the Multibody Approach

Hać M., Łazęcki J.

Machine Dynamics Research

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2016

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Vol. 40, No. 3

15--24

EN

In this paper the rigid-body motion of planar mechanisms (e.g. rigid rod, robotic arm, slider-crank mechanism) is considered by using two different approaches: FEM with modified truss elements named here as a stick model and the multibody method used in the engineering software (e.g. Adams, Modelica, etc.). The analysis shows that the stick model of mechanisms consisting of modified truss-type elements gives reliable results when compared to the solid model of multibody approach by using the Adams software. The presented method of description of motion of rigid mechanism can be successfully used as a preliminary calculation of mechanism motion. The method is illustrated with planar examples of mechanisms, however with the use of proper elements the method can be extended to the 3D case.

13

Comparison of natural complement formulations for multibody dynamics

Pękal M., Frączek J.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1391--1404

EN

The main aim of this paper is to compare the effectiveness of numerical techniques used for spatial multibody dynamics simulation by applying the natural complement method. In the paper, seven numerical schemes are considered: zero eigenvalue formulation, Pseudo Upper Triangular Decomposition, Schur decomposition, Singular Value Decomposition, QR decomposition, coordinate partitioning and Wang-Huston formulation. In order to illustrate the effectiveness of these schemes, two McPherson struts are considered. Simulations are performed with four error tolerance values and for three stabilization cases. Some suggestions on possible applications of the selected methods are formulated.

14

Constraint embedding for vehicle suspension dynamics

Jain A., Kuo C., Jayakumar P., Cameron J.

Archive of Mechanical Engineering

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2016

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Vol. LXIII, nr 2

193--213

EN

The goal of this research is to achieve close to real-time dynamics performance for allowing auto-pilot in-the-loop testing of unmanned ground vehicles (UGV) for urban as well as off-road scenarios. The overall vehicle dynamics performance is governed by the multibody dynamics model for the vehicle, the wheel/terrain interaction dynamics and the onboard control system. The topic of this paper is the development of computationally efficient and accurate dynamics model for ground vehicles with complex suspension dynamics. A challenge is that typical vehicle suspensions involve closed-chain loops which require expensive DAE integration techniques. In this paper, we illustrate the use the alternative constraint embedding technique to reduce the cost and improve the accuracy of the dynamics model for the vehicle.

PL

Celem badań było uzyskanie osiągów bliskich dynamice czasu rzeczywistego, by umożliwić testowanie bezzałogowych pojazdów naziemnych (UGV) z autopilotem w zamkniętej pętli w warunkach ruchu miejskiego i jazdy terenowej. O ogólnych osiągach dynamicznych pojazdu decyduje model dynamiczny układu wielu ciał dla tego pojazdu, dynamika oddziaływań wzajemnych kół i podłoża i pokładowy system sterowania. Tematem artykułu jest opracowanie wydajnego obliczeniowo i dokładnego modelu dynamiki pojazdu naziemnego ze złożoną dynamiką zawieszenia. Wyzwanie polega na tym, że typowe zawieszenia pojazdów zawierają pętle łańcuchów zamkniętych, które wymagają kosztownych technik całkowania równań różniczkowo-algebraicznych (DAE). W artykule autorzy zilustrowali zastosowanie podejścia alternatywnego, metody więzów wbudowanych (Constraint Embedding, CE), co pozwala zredukować koszty obliczeniowe i poprawić dokładność modelu dynamiki pojazdu.

15

Comparison of selected formulations for multibody system dynamics with redundant constraints

Pękal M., Frączek J.

Archive of Mechanical Engineering

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2016

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Vol. LXIII, nr 1

93--112

EN

This paper compares selected optimization-based methods for the analysis of multibody systems with redundant constraints. The following numerical schemes are examined: direct integration method, Udwadia-Kalaba formulation, two types of least-squares block solution method and Udwadia-Phohomsiri formulation. In order to compare efficiency of the algorithms, a series of simulations is performed on two exemplary McPherson struts. In the first variant, the mechanism has no redundant constraints whereas the other is overconstrained. Three constraint stabilization schemes are also compared in terms of integration errors.

PL

W pracy porównano wybrane metody analizy układów wieloczłonowych z więzami nadmiarowymi z zastosowaniem metod optymalizacji. Porównano następujące metody całkowania równań ruchu: metodę bezpośredniego całkowania, dwa rodzaje metody najmniejszych kwadratów oraz trzy różne sformułowania przedstawione w piśmiennictwie. Przeanalizowano trzy przypadki stabilizacji rozwiązania, przeprowadzono serie symulacji na dwóch przykładach mechanizmów kolumny McPhersona. Sformułowano wnioski co do efektywności rozwiązania układów równań ruchu mechanizmów, które mogą być przydatne dla doboru odpowiedniej metody całkowania.

16

Dynamical analysis of a constrained flexible extensible link with rigid support and clearance

Dupac M

Journal of Theoretical and Applied Mechanics

|

2014

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Vol. 52 nr 3

665--676

EN

Dynamic response of robotic systems is affected by deformation of their flexible components, velocity and mass of the systems, as well as by the presence of clearance or impact between the components. Since accurate simulations of such robotic systems are increasingly important, the modelling and dynamical behaviour of an extensible mechanism with a rigid crank and a flexible link is investigated in this paper. The equations of motion of the extensible flexible link, constrained to a circular, Cartesian, elliptical, Cassinian, Lame or pear-shaped quartic path, are presented. A dynamical analysis is carried out in order to compare the dynamical response of the flexible link vs. a rigid link under the combined effect of different parameters such as flexibility and clearance. The simulation result shows clear trajectories divergence due to the impact effect of the flexible link on the rigid crank.

17

Simulation of contact forces and contact characteristics during meshing of elastic beveloid gears

Do T. P., Ziegler P., Eberhard P.

Computer Assisted Methods in Engineering and Science

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2014

|

Vol. 21, no. 2

91--111

EN

Beveloid gears, also known as conical involute gears with very complex tooth shapes, gain more and more importance in industrial practice due to their ability to realize gear stages with crossed axes. This is why they are frequently found in power transmissions. The most familiar application of beveloid gears is the reduction gear used in marine transmissions, but in the last few years they have also been used increasingly often in the automotive industry. In the last decade many studies on beveloid gears were published, however, the meshing between teeth and the contact characteristics during meshing of beveloid gears still have not been studied in detail using fully elastic models. In this work, the fully elastic multibody approach will be applied to study contact forces and contact characteristics including contact patterns during meshing of straight beveloid gears. To validate the fully elastic approach, simulation results of a beveloid gear pair by finite element method and by the fully elastic multibody system are compared. The comparison shows very good agreement.

18

Helicopter rotor sailing by non-smooth dynamics co-simulation

Fancello M, Morandini M, Masarati P

Archive of Mechanical Engineering

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2014

|

Vol. LXI, nr 2

253--268

EN

This paper presents the application of a co-simulation approach for the simulation of frictional contact in general-purpose multibody dynamics to a rotorcraft dynamics problem. The proposed approach is based on the co-simulation of a main problem, which is described and solved as a set of differential algebraic equations, with a subproblem that is characterized by nonsmooth dynamics events and solved using a timestepping technique. The implementation and validation of the formulation is presented. The method is applied to the analysis of the droop and anti-flap contacts of helicopter rotor blades. Simulations focusing on the problem of blade sailing are conducted to understand the behavior and assess the validity of the method. For this purpose, the results obtained using a contact model based on Hertzian reaction forces at the interface are compared with those of the proposed approach.

PL

W artykule przedstawiono problem dynamiki wiropłatu rozwiĄzany przy zastosowaniu ogólnej metody kosymulacji używanej do symulacji kontaktu ciernego w dynamice układu wieloczłonowego. Proponowane podejście jest oparte na kosymulacji głównego problemu, opisanego i rozwiĄzanego jako układ algebraicznych równań różniczkowych wspólnie z podproblemem, który jest scharakteryzowany przez zdarzenia niegładkiej dynamiki i rozwiĄzany technikĄ kroków czasowych. Zaprezentowano implementację i walidację takiego sformułowania. Metodę zastosowano do analizy zwisu i łopotania łopatek wirnika helikoptera. By zrozumieć działanie metody i ocenić jej przydatność przeprowadzono symulacje dotyczĄce zachowania wirnika helikoptera w warunkach żeglugi. Dla oceny metody porównano wyniki uzyskane przy użyciu modelu kontaktowego wykorzystujĄcego siły reakcji Hertza z wynikami uzyskanymi w proponowanym podejściu.

19

Simulation of elastic gears with non-standard flank profiles

Do T. P., Siegler P., Eberhard P.

Archive of Mechanical Engineering

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2013

|

Vol. LX, nr 1

55--73

EN

There exist cases where precise simulations of contact forces do not allow modeling the gears as rigid bodies but a fully elastic description is needed. In this paper, a modally reduced elastic multibody system including gear contact based on a floating frame of reference formulation is proposed that allows very precise simulations of fully elastic gears with appropriately meshed gears in reasonable time even for many rotations. One advantage of this approach is that there is no assumption about the geometry of the gears and, therefore, it allows precise investigations of contacts between gears with almost arbitrary non-standard tooth geometries including flank profile corrections. This study presents simulation results that show how this modal approach can be used to efficiently investigate the interaction between elastic deformations and flank profile corrections as well as their influence on the contact forces. It is shown that the elastic approach is able to describe important phenomena like early addendum contact for insufficiently corrected profiles in dependence of the transmitted load. Furthermore, it is shown how this approach can be used for precise and efficient simulations of beveloid gears.

PL

Istnieją przypadki, gdy dla dokładnej symulacji sił kontaktowych nie można modelować kół zębatych jako ciał sztywnych, lecz jest potrzebny opis w pełni sprężysty. W artykule zaproponowano model systemu wielu ciał uwzględniajacy styki między zębami, modalnie zredukowany i z zastosowaniem układu odniesienia o płynnych ramach, umożliwiający bardzo dokładną symulację w pełni sprężystych kół zębatych o różnych rodzajach zazębienia. Symulacja jest możliwa dla znacznej liczby obrotów, przy czym wymagany czas obliczeń jest stosunkowo krótki. Zaletą tego podejścia jest, że nie wymaga ono założeń co to geometrii zębów, dzięki czemu można dokładnie badać zjawiska na stykach między zębami dla dowolnych, niestandardowych geometrii zębów, w tym również o skorygowanym profilu powierzchni bocznej. W artykule przedstawiono wyniki symulacji, które pokazują, że takie modalne podejście może być użyteczne przy badaniu zależności między odkształceniami sprężystymi a korekcją profili zębów, a także ich wpływu na siły kontaktowe. Pokazano, ze stosując model sprężysty można opisywać ważne zjawiska, takie jak wczesny kontakt głowy zęba w przypadku niedostatecznej korekcji profilu w zależności od przenoszonego obciążenia. Co więcej, pokazano że opisany sposób podejścia może być wykorzystany przy precyzyjnej i wydajnej symulacji przekładni stożkowych.

20

Reduction of a vehicle multibody dynamic model using homotopy optimization

Hall A., Uchida T., Loch F., Schmitke C., McPhee J.

Archive of Mechanical Engineering

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2013

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Vol. LX, nr 1

23--35

EN

Despite the ever-increasing computational power of modern processors, the reduction of complex multibody dynamic models remains an important topic of investigation, particularly for design optimization, sensitivity analysis, parameter identification, and controller tuning tasks, which can require hundreds or thousands of simulations. In this work, we first develop a high-fidelity model of a production sports utility vehicle in Adams/Car. Single-link equivalent kinematic quarter-car (SLEKQ, pronounced “sleek”) models for the front and rear suspensions are then developed in MapleSim. To avoid the computational complexity associated with introducing bushings or kinematic loops, all suspension linkages are lumped into a single unsprung mass at each corner of the vehicle. The SLEKQ models are designed to replicate the kinematic behaviour of a full suspension model using lookup tables or polynomial functions, which are obtained from the high-fidelity Adams model in this work. The predictive capability of each SLEKQ model relies on the use of appropriate parameters for the nonlinear spring and damper, which include the stiffness and damping contributions of the bushings, and the unsprung mass. Homotopy optimization is used to identify the parameters that minimize the difference between the responses of the Adams and MapleSim models. Finally, the SLEKQ models are assembled to construct a reduced 10-degree-of-freedom model of the full vehicle, the dynamic performance of which is validated against that of the high-fidelity Adams model using four-post heave and pitch tests.

PL

Pomimo stale rosnącej mocy obliczeniowej współczesnych procesorów, redukcja złożonych, wieloczłonowych modeli dynamicznych pozostaje ważnym tematem badań, zwłaszcza dla optymalizacji projektowania, analizy wrażliwości, identyfikacji parametrów i optymalizacji sterowników, które mogą wymagać setek lub tysięcy symulacji. W pierwszej części pracy autorzy przedstawiają model o wysokiej wierności opracowany dla seryjnie produkowanego samochodu sportowo-użytkowego (SUV) przy pomocy oprogramowania Adams/Car (MSC.Software Corporation). Następnie w środowisku MapleSim (Waterloo Maple Inc.) zostały opracowane równoważne ćwiartkowe (quarter-car) modele kinematyczne o jednym połączeniu, typu SLEKQ, dla zawieszenia przedniego i tylnego. By uniknąć komplikacji obliczeniowych związanych z wprowadzeniem tulejowania lub pętli kinematycznych, wszystkie układy przenoszące zawieszenia zostały zastąpione pojedynczymi skupionymi nieresorowanymi masami w każdym rogu pojazdu. Zaprojektowane modele typu SLEKQ odtwarzają właściwości kinematyczne modelu kompletnego zawieszenia wykorzystując przy tym tablice przeglądowe lub funkcje wielomianowe, które zostały wcześniej wyznaczone za pomocą wysokiej wierności modelu typu Adams. Zdolność predykcyjna każdego modelu SLEKQ zależy od użycia właściwych parametrów opisujących nieliniowe sprężyny i amortyzatory, które uwzględniają sztywność i wpływ na tłumienie drgań wnoszony przez tulejowanie i nieresorowane masy. Optymalizację homotopową zastosowano w celu identyfikacji tych parametrów, które minimalizują różnice między odpowiedziami uzyskanymi w modelach typu Adams i SLEKQ. Ostatecznie, z modeli SLEKQ zostaje złożony zredukowany model o dziesięciu stopniach swobody reprezentujący cały pojazd. Właściwości dynamiczne tego modelu są poddane walidacji przez porównanie z właściwościami wysokiej wierności modelu typu Adams w czterokolumnowych testach kołysania i pochylania.