sn-2012-jul simpack news full-issue spreads lr

SIMPACK NewsSIMPACK NewsSIMPACK AG, Friedrichshafener Strasse 1, 82205 Gilching, Germany

Multi-Body Simulation of a Planetary Gearing Test Bench

JUly 2012

The Chair of Mechanical Components and Power Transmission at Ruhr University of Bochum (LMGK) researches a wide range of machine components. Besides spur gears, further research focuses on worm and planetary gears as well as bearings. These fields of research are investigated on experimental and theoretical levels.Motivated by the question of how the effect of the interaction between planetary gear stages can be characterized, this article explores whether the resulting noise... See page 20

Robust and reliable gearbox designs for wind turbines require in-depth insight into gearbox dynamics. Dynamic load simulation and resonance analysis based on advanced multi-body simulation (MBS) models of gearboxes are useful methods... See page 2

The Validation of MBS Multi-Megawatt Gearbox Models on a 13.2 MW Test Rig

Simulation of Rope-Propelled Automated People Mover Systems in SIMPACKIn recent years, the use of Rope-Propelled Automated People Movers (RAPM) for public transport in airports and city centres has increased steadily. These transport systems consist of guided vehicles which are propelled by a wire rope and... See page 6

30 SIMPACK NewSSIMPACK Events in 2012

16 CuStoMer APPlICAtIoNThe Use of Active Vertical Secondary Suspension to Improve Ride Comfort in a Rail Vehicle

06 CuStoMer APPlICAtIoNSimulation of Rope-Propelled Automated People Mover Systems in SIMPACK

02 CuStoMer APPlICAtIoNThe Validation of MBS Multi-Megawatt Gearbox Models on a 13.2 MW Test Rig

20 CuStoMer APPlICAtIoNMulti-Body Simulation of a Planetary Gearing Test Bench

10 CuStoMer APPlICAtIoNUser Tire Road Model and Road Sensor for Advanced Vehicle Dynamic Applications

14 CuStoMer APPlICAtIoNResonance Analysis of Wind Turbines

31 CuStoMer APPlICAtIoNExperimental Validation of a Mass Transit Vehicle Multi-Body System with Integrated Flexible Body

26 CuStoMer APPlICAtIoNCross-Company System Simulation using the GUSMA-Standard for Co-Simulation

36 CuStoMer APPlICAtIoNA New Massless Leaf Spring Model for Full Commercial Vehicle Simulations

2MW gearbox

generator

optional speed reducer

generator optional speed reducer 3MW gearbox

2 | SIMPACK News | July 2012 SIMPACK News | July 2012 | 3

Ben Marrant, ZF Wind Power Antwerpen NV | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Ben Marrant, ZF Wind Power Antwerpen NV

The Validation of MBS Multi-Megawatt Gearbox Models on a 13.2 MW Test RigThe Validation of MBS Multi-Megawatt Gearbox Models on a 13.2 MW Test Rig

Robust and reliable gear-box designs for wind turbines require in-depth insight into gear-box dynamics. Dynamic load simulation and

resonance analysis based on advanced multi-body simulation (MBS) models of gearboxes are useful methods to predict loads and dynamic phenomena already in early phases of gearbox design. Moreover, the quasi unlimited number of simulated ‘sensors’ in virtual MBS models provide a much wider insight than a limited number of measured sen-sors in real gearboxes.

In addition, MBS based gearbox analyses can even be done before the real gearbox is available. However, insights gained from MBS models are only useful for design purposes if the simulation results prove to be representative of real world situations. In order to increase the confidence level in these results, ZF Wind Power, formerly known as Hansen Transmissions, invested considerable effort in research activities Fig. 1: 13.2 MW dynamic test rig with REpower’s 6 MW gearbox in a back-to-back configuration

see Fig. 3. Structural com-ponents with a complex geometry such as the planet carrier and gearbox housing are represented by means of flexible mod-els using modally reduced Finite Element (FE) models. The gears are represented by rigid bodies whereas spring-damper systems representing the gear mesh non-linear behavior are included in the model by means of Force Element FE225. This non-linear gear mesh stiffness causes internal excitation in the gearbox whereas clear-ances between the rigid gear bodies are also included in order to simulate events

in which gears are going through their clearance. Shafts are modeled using the SIMBEAM approach. In this way, shafts are

also represented by a flexible model in the form of a reduced one-dimensional finite element model using Timoshenko beams. Bearings are modeled at the system level as spring-damper systems with full 6x6 stiff-ness/damping matrices. Therefore, the im-portant cross-coupling terms are included in the model. The stiffness matrices are usually linearized at nominal working condi-tions where the stiffness values are usually based on Hertzian theory. All of the previ-ously described gearbox components were verified and/or validated in the course of the research project. The focus in this article is on two parts: the validation of complex structural components, such as the planet

carrier and the housing, and the validation of the complete MBS model with the two gearboxes in back-to-back configuration on the test rig in the frequency domain using dedicated measurements.

VAlIDATIon oF FleXIBle STRUCTURAl CoMPonenT MoDelSThe validation of FE models of complex structural components with measurements is important as these components contribute in a major way to the overall dynamic behav-ior of the complete gearbox. The validation of complex structural component models included the following items: the planet carrier of the first planetary stage of both gearboxes and the “empty” housing of both gearboxes. The “empty” housing model includes the parallel stage housing, covers, ring gear(s) and reaction arm but no shafts, bearings, and internal gears. Each flexible FE model was compared with its respective ex-perimental modal model. This experimental modal model was obtained from a classic

Fig. 2: MBS model of the test set-up

focusing on the experimental validation of MBS gearbox models on its 13.2 MW dynamic test rig, see Fig. 1. As a result, ZF Wind Power is able to perform resonance analyses with confidence and collabotate with customers with respect to dynamic analyses using MBS models of the complete drive train.

THe ReSeARCH PRoJeCTThis research project was unique in that the development of the gearbox MBS models for the investigation of gearbox and drive train dynamics in wind turbine applications was supported by an extensive measurement campaign at ZF Wind Power. The project took place from 2007-2011. An extensive measurement campaign was required for the validation of MBS models in order to guarantee the validity of the dynamic analy-ses with these MBS models. It was decided to validate these gearbox MBS models on a test rig rather than in a wind turbine envi-ronment because the conditions on a test rig can be controlled much better. In a wind turbine, one is at the mercy of arbitrary wind conditions, and the “test platform”

is less accessible, making a well-structured validation plan much harder to achieve. The measurements used for the validation campaign took place on the developed 13.2 MW dynamic test rig [1] where a 2 MW and a 3 MW gearbox were placed in a back-to-back set-up. This enabled the validation of two different types of MBS gearbox models varying both in size and composition. The 3 MW gearbox has two planetary stages and one parallel stage and the 2 MW gearbox has one planetary stage and two parallel stages. The validation campaign was com-prised of over 200 measurement sensors including accelerometers, strain gauges, ro-tational speed encoders, distance measuring equipment and torque sensors. The mea-surement campaign included both quasi-static measurements and measurements of dynamic events which were designed to be representative of wind turbine conditions. The set-up of the test rig is a highly accurate representa-tion of a real drive train in a wind tur-bine. This test set-up was modeled in SIMPACK and included the two gearboxes and major parts of the 13.2 MW test rig such as the generator rotors, the optional speed reducers, and the high speed and low speed couplings, see Fig. 2. The complete MBS model of the test set-up had 600 degrees of freedom, and included more than 150 bodies, 13 of which were flexible.

ZF WInD PoWeR’S GeARBoX MoDelZF Wind Power has developed a general modeling strategy for dynamic analyses with MBS gearbox models. This gearbox MBS model is a flexible 6 degrees of freedom model and is composed of several parts,

“...dynamic resonance analyses of gearboxes with MBS should always include

a flexible housing model..”

shafts

bearings

gears

structuralcomponents

planet carrier

shaker Frequency [Hz]

Sens

ors

Rotation speed [RPM]

Freq

uncy

[Hz]


Ben Marrant, ZF Wind Power Antwerpen NV | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Ben Marrant, ZF Wind Power Antwerpen NV

Experimental Modal Analysis (EMA) on each of the previously described structural com-ponents using a shaker and accelerometers, see Fig. 4. The evaluation of the correlation between the flexible FE model and the ex-perimental modal model was based on the Modal Assurance Criterion (MAC) [2]. It was found that the flexible FE model (i.e., both mode shape and eigenfrequency) correlated well with the experimental modal model. An example of this correlation exercise can be seen in Fig. 5 and Fig. 6. In Fig. 5, the FE model of the 2 MW housing is shown in blue and the experimental modal model is represented by the red wireframe for a par-ticular mode shape of the empty housing.

The MAC matrix of the 2 MW housing is shown in Fig. 6. The first 3 eigen-modes have an MAC value larger than 90% on the diagonal whereas modes 4 up to 8 have MAC values on the diagonal which are larger than 70%. The good correlation between the hous-ing model and experiments sup-ports the validity of the model. An important result from the EMA’s and the FEA’s was that the first eigen-frequency of the “empty” housing

of the 2 MW and 3 MW gearbox has been identified between 100 and 300 Hz.

VAlIDATIon oF THe TeST RIG MoDel In THe FReQUenCy DoMAInAn important part of the validation of gear-box MBS models for wind turbine applica-tions is situated in the frequency domain. Operating in variable speed wind turbines, these gearboxes will inevitably encounter resonance phenomena during operation. The purpose of the MBS gearbox model is to be able to predict the “most important” resonances (i.e., resonances with relatively high amplitudes which occur frequently in the operational range of the gearbox). For the validation of the MBS model in the fre-quency domain, the modal model obtained from simulations needs to be compared with the modal model obtained from experiments. In contrast with structural components which are supported stati-cally, classic experimental modal analysis (EMA) cannot be used for the validation of MBS models of complete drive trains or gearboxes since these need to be in “op-eration” in order to obtain reliable results for the modal analysis. Moreover, several types of measurement sensors were used in the gearboxes and on the test rig which needed to be combined in order to define the overall mode shapes and eigenfre-quencies. These issues provided an extra challenge for the validation of complete gearbox models in the frequency domain. Therefore, it was decided to come up with a composite technique for the modal analy-

sis of gearboxes. This method is both semi-quantitative and semi-qualitative yielding quantitative values for the eigenfrequencies and qualitative descriptions for the mode shapes. A brief summary of the method is presented below. Campbell diagrams for all sensors are obtained from speed run-up measurements, see Fig. 7. In these diagrams, eigenfrequencies and their “confidence level” are identified based on engineering judgement for all measurement sensors. All sensors, eigenfrequencies and confidence levels are then combined in a “flat” 3D plot which is called a “Mode Map”, see Fig. 8. A Mode Map indicates the eigenfrequencies in the drive train or gearbox. Moreover, the Mode Map shows the sensors in which the eigenfrequency is found. This allows for the possibility of obtaining a qualitative descrip-tion of a mode shape. This method has been applied to both the measurements and the simulations. Since, with this composite method, mode shapes were not available in numeric form but only as a qualitative insight, correlating the eigenmodes cannot be done based on the MAC. This provided a new challenge. The correlation of eigen-modes and eigenfrequencies identified from measurements and the simulation model is obtained from mutual comparison of Mode Maps and orders. Further means for the cor-relation of eigenmodes and eigenfrequen-cies are (Auto)-Frequency Response Funtions and eigenmode animations from the MBS model which can also be compared with measured Mode Maps and Operational De-flection Shapes (ODS) determined with the measurement set-up. From this exercise, the major part of “most important” resonances for the test set-up have been correlated. The

first type of important resonances was the well-known torsional resonance which oc-curred between 0-100 Hz. These torsional modes are usually specific for the test set-up and have a more global character. The second type of important resonance was a local gearbox mode. In this mode, the first mode of the “empty” housing which was found in the validation of structural components, was coupled with the parallel stage(s) as they are “connected” to the generator side of the housing. This coupling resulted in a significant decrease in the first “empty” housing eigenfrequency resulting in a shift of the eigenmode to a frequency range of 100-200 Hz. This research project was an eye opener as to the importance of the housing with respect to its contribution to the dynamics of multi-megawatt gearboxes. Therefore, dynamic

Fig. 6: Visualisation of the MAC matrix show-ing the mathematical correlation of numeric model (FEA) and experimental model (EMA) of the 2 MW housing shown in Fig. 4

Fig. 5: Visual correlation of the modal FE model (blue) and the experimental modal model (red) of the 2 MW housing for an eigenmode

Fig. 4: Experimental Modal Analysis of the 2 MW planet carrier

Fig. 7: Campbell diagram from speed run-up measurement for a torque sensor

Fig. 8: Mode map indicating the identified eigenfrequencies for each measurement sensor. The colorbar indicates the confidence level for the eigenfrequencies (green = high confidence, red = low confidence)

resonance analyses of gearboxes with MBS should always include a flexible housing model. The result of the validation of the test set-up model in the frequency domain is that ZF Wind Power can confidently use MBS gearbox models for the prediction of the “most important” resonances [3].

ConClUSIonSZF Wind Power has chosen SIMPACK as its main tool for dynamic analyses of gearboxes in wind applications.The validation of complex structural com-ponent models such as the housing and the validation of the MBS model of the test set-up with a 2 MW and a 3 MW gearbox in a back-to-back configuration on the 13.2 MW test rig has led to new insights into the importance of gearbox housings for the dynamics of multi-megawatt gearboxes.During the project, major improvements were made to the techniques for measuring vibrations, and extensive experience has been gained in vibration analysis using the composite modal analysis technique.Due to the extensive validation of gearbox MBS models on its 13.2 MW test rig, ZF Wind Power is now able to confidently use MBS gearbox models for resonance analy-ses of wind turbine gearboxes in (1) a retro-

active phase for troubleshooting issues and (2) pro-actively in design decisions.For the investigation of specific issues regarding gearbox dynamics, a dedicated

approach is sometimes re-quired, e.g., the investigation of the influence of non-linear bearing behavior. ZF Wind Power is gaining experience

in these areas which sometimes require dedicated SIMPACK solutions.It is ZF Wind Power’s vision that MBS will become part of the virtual prototyping strategy. In this strategy, black-box models of the gearbox are incorporated into the virtual wind turbine. These combined MBS models will eventually lead to much shorter development times and gearbox dynamics which are better tuned to the wind turbine drive train right from the start.

ACKnoWleDGeMenTThis research project was done in collabora-tion with the Katholieke Universiteit Leuven and was supported by the Institute for the Promotion of Innovation by Science and Technology in Flanders.

ReFeRenCeS[1] J. Peeters, D. Leimann, R. Huijskens, F. De Coninck, First results of Hansen’s 13 MW test facility for wind turbine gearboxes, European Offshore Wind Conference & Exhibition, 2009[2] W. Heylen, S. Lammens, P. Sas, Modal Analysis Theory and Testing, PMA, Katholieke Universiteit Leuven, Belgium, 2007[3] J. Helsen, The dynamics of high power density gear units with focus on the wind turbine application, Ph.D. Dissertation, department of Mechanical Engineering, Katholieke Universiteit Leuven, Belgium, 2012

“...ZF Wind Power can confidently use MBS gearbox models...”

Fig. 3: ZF Wind Power gearbox MBS model

Front grip point Rear grip point

𝒶𝑆(0, 𝑡)𝑠 𝑢(𝑠, 𝑡)

𝑞(𝑠, 𝑡) 𝑞(𝑠, 𝑡) 𝑞(𝑠, 𝑡) 𝑞(𝑠, 𝑡)𝑃

Vehicle gripSheave

Drive bull wheel

𝑀Drive

Standard SIMPACK elements SIMPACK Force user routine

FEM rope model including sheave interaction

𝑞(𝑠, 𝑡)

Rope-bull wheel contact model

Kinematic quantities

Forces

Vehicle models

Bull wheel models

Tensioning mechanism model

Rope loop


Christian Nußbaumer, Virtual Vehicle | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Christian Nußbaumer, Virtual Vehicle

Simulation of Rope-Propelled Automated People Mover Systems in SIMPACK

In recent years, the use of Rope-Propelled Automated People Movers (RAPM) for public transport in airports and city centres has increased stead-ily. These transport systems consist of guided vehicles which are propelled by a wire rope and operate automatically on a separate guideway. With RAPM, the rope’s elasticity has a crucial influ-ence on the system dynamics. Conse-quently, an elastic rope model has been implemented in SIMPACK, which can be combined with state-of-the-art elements to enable the modeling of the complete RAPM system. This enables the predic-tion of system dynamics, in emergency stop scenarios and standard operation, which is an important input for system design.

InTRoDUCTIonAutomated People Mover (APM) systems are used to execute high-capacity passenger transportation over short distances. This task can be accomplished using either conventional on-board drive components or a rope drive which transmits the propulsion forces to the vehicles. In the latter case, the system is called an RAPM. RAPM vehicles normally contain no on-board drive or braking systems which leads to low acoustic emissions and light vehicle and guideway structures. Thus, the guideway structures used are cost-effective and desirable from an architectural viewpoint (Fig. 1).Fig. 2 shows one possible technical configu-ration of an RAPM drivetrain. The electric motors and brakes are connected to the drive bull wheel which transmits both the drive and braking forces to a closed wire

Fig. 1: Rope-propelled Automated People Mover in Las Vegas, Nevada

rope loop. The rope is guided by bull wheels in the stations and by sheaves along the guideway. Finally, the traction forces are transferred to the vehicle bogies by means of grips. Since the system lengths of modern RAPM

can reach up to 3 km, rope elasticity has a critcal influ-ence on the overall system dynamics.

In railway and automotive engineering, sys-tem dynamics prediction using multi-body systems (MBS) represents the state of the art. For RAPM, this approach can also be applied for vehicle modeling. However, in order to ensure correct drivetrain behavior in

the simulation, it is necessary to consider the rope’s mass and elasticity. There is currently no rope element available in state-of-the-art MBS software that fulfills these require-ments, and the application of a significant number of standard MBS elements (e.g., spring-mass chain) to model the complete rope loop is inefficient. Consequently, the current project has developed and imple-mented an elastic rope model designed for RAPM in SIMPACK.

one-DIMenSIonAl RoPe MoDelThe model development was based on a comprehensive determination of the deci-sive physical phenomena. The determina-tion revealed that sag oscillations of the

Fig. 2: Possible technical configuration of an RAPM drivetrain [1]

rope can be omitted due to the small sags, which result from the high pretension, and the short rope spans. Furthermore, the cen-tripetal acceleration at the bull wheels and sheaves is negligible due to the low axial rope velocities. In the substituted mechanical system, the rope is cut at the vehicle grips, and only displacements in the longitudinal direction are taken into account (Fig. 3).Consequently, a simple, one-dimensional Lagrangian approach is applied. This leads to a modified one-dimensional wave equa-tion, which describes the rope motion as a function of time and length:

In this Partial Differential Equation (PDE), the longitudinal rope displacements and the acceleration of the reference body are denoted by 𝑢(𝑠, 𝑡) and 𝒶𝑆(𝑠, 𝑡), respectively. λ is the mass per unit length, and 𝐸𝐴 rep-resents the axial stiffness of the rope. The interaction between the rope and the bull wheels is modeled by longitudinal forces 𝑞(𝑠, 𝑡). This PDE can be transformed into a set of Ordinary Differential Equations (ODEs) using Galerkin’s Method and a Finite Element approach:

This equation contains the rope’s mass ma-trix 𝑀― and the stiffness matrix 𝐶―. The vector �― includes the external loads on the rope, the boundary conditions at the grip points and the acceleration of the reference body.

IMPleMenTATIon With SIMPACK, subsystems with internal dynamics can be included by applying user-defined Force Elements. Hence, the coupled ODEs which describe the rope dynamics are implemented by means of a Force User Rou-tine. Furthermore, as shown in Fig. 4, the user routine includes a simple contact model for calculating the interaction forces 𝑞(𝑠, 𝑡)

between the rope and the bull wheels. Here, the contact force is determined by assuming that there is no slip between the bull wheel and the rope. However, with this approach, it would also be possible to apply more general contact models in cases where the interaction forces are a function of lon-gitudinal slip. Theoretically, it would be possible to model the interaction between the rope and the sheaves using a similar method. However, since RAPM usually contain several hundred sheaves, a different approach has been chosen in order to increase numerical ef-ficiency. Instead of modeling the sheaves as

Fig. 3: One-dimensional approach for the calculation of rope dynamics [1]

Fig. 4: Implementation of the rope model into SIMPACK [1]

rigid bodies with assigned rotational joints, the sheave inertias are incorporated as ad-

ditional entries in the rope’s mass matrix. The resulting mass matrix is asymmetric and time-dependent, but band-di-agonal. Hence, the unknown relative rope accelerations

can be determined efficiently at each time step using the Tridiagonal Matrix Algorithm (TDMA).In addition, the sheave’s rolling resistance is considered as an additional external force on the rope. This is important because the collective rolling resistance of all of the sheaves is the main energy dissipation factor in the overall system.

“...the current project has developed and implemented an elastic rope model

designed for RAPM in SIMPACK.”

“With SIMPACK, subsystems with internal dynamics can be included...”


Christian Nußbaumer, Virtual Vehicle | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Christian Nußbaumer, Virtual Vehicle

Finally, standard SIMPACK elements are used to model the vehicles, the bull wheels and the tensioning mechanism of the rope in the complete MBS. The kinematic quantities of these subsystems are passed to the user routine which generates the corresponding forces on the rigid bodies. Implementing the rope model in SIMPACK offers the advantage that the model depth of the vehicles and other facility compo-nents can be varied as desired. Thus, on the one hand, it is possible to generate simple models with real-time capability which only represent the longitudinal dynamics of the train. On the other hand, detailed three-

dimensional vehicle models can also be built which allow for a comprehensive dynamic analysis of the system. It is important to note that even in the three-dimensional MBS, the rope dynamics are treated as a one-dimensional problem. The spatial motion of the vehicle grips only affects the boundary conditions of the rope model.

VeRIFICATIonA physical RAPM was used to verify the modeling technique for the rope. For this purpose, a three-dimensional model of the facility was built in SIMPACK (Fig. 5). The

model contains rigid bodies for the bull wheels, the rope tensioning mechanism and the vehicles. The vehicles are guided by a three-dimensional rigid track. In order to generate data for the model verification, various experiments were conducted at the physical RAPM facility. During these tests, special attention was paid to emergency stop situations which generate the maximum values with regard to system dynamics. Fig. 6 shows a comparison of the experi-

ment and the simulation for four different physical quantities of the system. In this scenario, the emergency stop was triggered at full vehicle speed at 𝑡 = 25.5 𝑠. Clearly, the rope’s elasticity leads to low-frequency oscillations in the system during the braking phase. There is a good correlation between the values obtained from the model and the experiment for both the oscillation frequency and the peak values that arise immediately after the brake actuation.In total, ten dif-ferent emergency stop scenarios were simulated using the proposed model. The comparison demonstrates that the method is valid for different load conditions. For ex-ample, the average deviation between the simulated and measured maximum vehicle decelerations was 6.7 %. APPlICATIonAs shown in the previous section, the SIMPACK model can be used to calculate the system dynamics in the case of emergency stop scenarios. In this regard, determining the maximum vehicle deceleration during emergency braking is an important issue, since ASCE-standards limit this value to 0.25 g [2]. The model allows an efficient analysis of different brake configurations in order to meet this requirement. In a further step, both the maximum tensioning mechanism travel and the dynamic rope Fig. 6: Comparison of experiment and simulation in an emergency stop scenario

forces that occur can be determined which are important inputs for the system design. Additionally, emergency stops generally lead to the maximum vehicle loads. Applying a three-dimensional vehicle model in SIMPACK enables the analysis of worst case scenarios such as emergency braking in curves.A further field of application is enhancing standard operation. Especially in the case of long systems (2–3 km), longitudinal vehicle oscillations may reduce ride comfort. These oscillations result from rope elasticity and can be reduced by an intelligent drive control. The presented MBS can be used to design and optimize the control system.

Furthermore, the three-dimensional model also enables the analysis of the lateral vehi-

cle dynamics during standard operation. The steering behav-ior in curves, which is particularly influ-enced by the rope

drive, can be easily improved by applying detailed vehicle models in combination with the rope model presented here. SUMMARy AnD ConClUSIonIn this work, an elastic rope model with special application to RAPM has been devel-oped. The resulting PDE is transformed into a set of ODEs by applying Galerkin’s Method and the Finite Element Method, and the implementation into SIMPACK is achieved using a Force User Routine. This made it possible to generate a comprehensive MBS which was verified using data measured at a physical RAPM facility. The model can be applied to predict system dynamics during both emergency stop scenarios and stan-dard operation. Consequently, the proposed method will contribute to the enhancement of the efficiency and ride comfort of Rope-propelled Automated People Movers.

ReFeRenCeS[1] Nußbaumer, C., Schmidt L., Dietmaier P.; Three-dimensional system dynamics simulation of rope-propelled Automated People Movers, Ve-hicle System Dynamics (accepted for publication).[2] Automated People Mover Standards — Part 2, Vehicles, Propulsion and Braking (ASCE 21-98), American Society of Civil Engineers (ASCE), 1999.

ACKnoWleDGeMenTSThe author would like to acknowledge the financial support of the "COMET K2 — Competence Centres for Excellent Technolo-gies Programme" of the Austrian Federal Ministry for Transport, Innovation and Tech-nology (BMVIT), the Austrian Federal Minis-try of Economy, Family and Youth (BMWFJ), the Austrian Research Promotion Agency (FFG), the Province of Styria and the Styrian Business Promotion Agency (SFG).Furthermore, the author would like to ex-press his thanks to the supporting industrial and scientific project partners; namely, "DCC

Doppelmayr Cable Car GmbH & Co KG", "Kon-trollstelle IKSS", "Institute of Railway Engineering and Transport Economy, Graz" and to the Graz University of Technology.The author also gratefully acknowledges the permis-sion granted by the Vehicle System Dynamics journal to include copyrighted material in this article.

Fig. 5: Full-scale MBS model of an RAPM in SIMPACK [1]

“Applying a three-dimensional vehicle model in SIMPACK enables

the analysis of worst case scenarios, such as emergency braking in curves.”

Forces and moments at tire-contact-point

Tire-road kinematics:position, orientation, velocities

Integration

Parameter

Tire-force-modelRoad-model

Geometry

User

forc

e el

emen

tSI

MPA

CK

Tire's state at contact point:nominal force, longitudial slip and side slip angle


Andreas Wiesebrock, IVK, University of Stuttgart; Jens Neubeck, FKFS, University of Stuttgart | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Andreas Wiesebrock, IVK, University of Stuttgart; Jens Neubeck, FKFS, University of Stuttgart

The first derivates are used to calculate the normal vector on a surface point in a right handed system and to perform an iteration process to determine the tire road contact point as described below.

The advantages of a NURBS surface method are:

• A free definition of the interpolation or-der in both surface directions (e.g., linear interpolation in the lateral direction and second order interpolation in the longitu-dinal road direction).

• Every linear interpolated surface can be identically represented by the NURBS interpolation method (e.g., OpenCRG data).

• Increasing the interpolation order removes unwanted surface kinks and allows the user to reduce the number of interpola-tion points (e.g., a roller drum test bench or an arbitrarily sized circle can be repre-sented by a NURBS surface with only 14 interpolation points, see Fig. 3).

• By calculating the surface points derivates without a lot of additional effort, fast contact point calculation routines can be developed.

• A NURBS surface can represent all dimen-sions. For the road model, four dimen-sions are defined: the three-dimensional position x, y and z and also the friction coefficient µ.

ConTACT PoInT CAlCUlATIonThe contact point 𝑆(𝑢,  𝑣) is defined as the surface point which has the greatest intersection into a rigid wheel volume (rep-resented by a torus, defined by two param-eters: outer diameter 𝑑𝑊 and width 𝑤𝑊).The contact point is found using an advanced iteration method based on a simple concept (see also Fig. 4):During the simulation process, the contact point is continuously moving on the road surface. The contact point which was calculated at the last time step is close to the current contact point. The iteration process to find the new contact point is performed

User Tire Road Model and Road Sensor for Advanced Vehicle Dynamic Applications

The mathematical description of a road surface within multi-body simulation is a major factor in simulation error, simulation time and modeling possibilities. For advanced vehicle dynamic applications, a new road-description method has been introduced. The method uses relative kinematics to enable test rig simulations with moveable road surfaces described by an abstract nURBS surface. This allows an exceptional level of detail [1, 2]. Implementation of nURBS surface for vehicle dynamic simulation also includes an optimized algorithm for contact point determination to calculate a tire’s state. As shown in Fig. 1, the main aspect of

the new user tire road model is the road modeling part. Different existing tire force models (e.g., HSRI, Pacejka Magic Formula) are implemented by using a universal interface for single contact point tire force models.

RoAD SURFACe DeSCRIPTIonWith the new user tire road model, the road is modeled in SIMPACK as a rigid body which does not need to be equal to the inertia frame. The user has to specify a body marker as a reference system for the road surface used in the tire road force element. The road surface is described as a non-uni-form rational B-splines surface (NURBS) [3]

to enable the most efficient simulation progress. NURBS surfaces uses a re-cursive algorithm to calculate a surface point 𝑆 depending

on the surface coordinates 𝑢 and 𝑣 by con-sidering interpolation points 𝑃𝑖, 𝑗 and knot vectors 𝑈 and 𝑉 (including the interpolation order 𝑝𝑞 and 𝑞), see Fig. 2. NURBS surfaces

Fig. 1: Tire-road modeling

are only valid within the limits [𝑢min, 𝑢max) and [𝑣min, 𝑣max).

(1)

(2)

(3)

(4)

(5)

The NURBS interpolation method also enables the calculation of the surface deri-vates at 𝑢 and 𝑣: δ𝑆(𝑢,  𝑣) /δ𝑢, δ𝑆(𝑢,  𝑣) /δ𝑣.

Fig. 2: NURBS surface

Fig. 3: Reduced number of interpolation points Fig. 4: Contact point iteration

“The mathematical description of a road surface within multi-body

simulation is a major factor in simulation error, simulation time and

modeling possibilities.”

by calculating the surface point 𝑆𝑘 and the orientation matrix 𝐴𝑘 at the starting values 𝑢𝑘, 𝑣𝑘:

(6)

Using the normal vector 𝐴𝑘, 𝑧 ,  the current “deepest” point 𝐶 on the wheel (𝑊) torus volume can be calculated:

(7)

(8)

Adopting the column vectors of 𝐴𝑘 which are linearly independent, and given that the change of 𝐴𝑘 is small, the modification of 𝑢𝑘, 𝑣𝑘 results in:

(9)

(10)

Practical usage of this iteration process showed that two additional cases must be considered:

• Finding the values 𝑢0, 𝑣0 at start of simulation.

• Handling discontinuity in the surface derivates.

Both problems can be solved by considering the knot vectors 𝑈 and 𝑉. Because disconti-nuity only appears on knot vectors elements (see formula 2–5), a global search of the

front sides lip anglerear side slip angle


Andreas Wiesebrock, IVK, University of Stuttgart; Jens Neubeck, FKFS, University of Stuttgart | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Andreas Wiesebrock, IVK, University of Stuttgart; Jens Neubeck, FKFS, University of Stuttgart

“best” contact point is suggested at all knot vectors elements. Second, the iteration process (formula 10) can be limited to local intervals to avoid discontinuity.

ADDITIonAl RoAD SenSoR DATASeveral use cases (e.g., a driver model) requires the online measurement of the vehicle to road interaction. This measure-ment is performed by a second user force element as shown in Fig. 5. By defining a sensormarker 𝑀, the following measure-ments are done:

• Vertical displacement to the road in 𝑀z-axes

• Lateral distance to the road centerline• Orientation difference between the mea-

surement marker and centerline• Derivatives with respect to time by calcu-

lation of the sensor’s ground velocity• Surface coordinates 𝑢 and 𝑣

These measurements allow realization of different driver models within pure SIMPACK simulation using the “control elements” interface or by a Simulink® co-simulation. By providing the surface coordinates, it is also possible to define a reference line by 𝑣𝑟𝑒𝑓 = 𝑓(𝑢) , e.g., to perform lap time optimizations.

nURBS RoAD ToolBoXTo enable user-friendly creation of NURBS road files and also to allow simulation result visualization, a MATLAB® toolbox has been developed. This toolbox includes a NURBS- class to execute the required functions. The toolbox is integrated into a graphical user interface but can also be used by the

MATLAB command window. The following features are implemented:

• Import functions: - OpenCRG [4] - IGES data [5] - BASt Georohdaten - MATLAB data• Parameterized creation of standard road

surfaces, for example: - Roller drum test rigs - Curvature segments with specified

banking angle - Some circuit roads - Single/ double lane change maneuvers - Random z-excitation surface• Visualization• Export functions: - Wave front*.obj data for road visualiz-

tion within SIMPACK - Binary*.nrb data which can be loaded

by the user force elements - MATLAB data

The MATLAB toolbox enables the user to automate the development process over the following steps: creating the road data, setting up the inertial condi-tions, performing a parameter variation, starting a Simulink co-simulation, saving the data, and visualizing the simulation results. Sample simulation results from a double lane change maneuver are shown in Fig. 6.

SIMUlATIon enVIRonMenTCompared to the original SIMPACK tire road model, the new user ele-ment does not need a track joint

predestined for automated simulation with parameter variation. The performance of most driving maneuvers running a Simu-link co-simulated driver model is real time capable with a sampling period of 0.001 seconds.

Performing test rig Simulations:The development of vehicle dynamic test benches requires detailed information about body stresses, dominating forces, measurement er-rors or real time capability. Many of these requirements can be estimated by performing test rig simulations within the SIMPACK environ-ment. These simulations require relative calculation of the tire’s state with moveable road bodies and an own road reference sys-tem for each tire. The test rig excitation can be determined by pre-processing a specific maneuver or by online calculation of the dynamic system.

Simulating real road Measurement Data:To simulate real road measurement data for any kind of driving dynamic applications, several methods are implemented in the MATLAB toolbox to create NURBS roads from different data types. The user can specify longitudinal and lateral interpolation order and perform automated interpolation point optimization and reduction. Wave front*.obj files can also be created for visualization in SIMPACK. Simulating NURBS

roads generated from measurement data is the same process (with the same performance) as simulation with user defined road surfaces.

Vehicle energy demand assessments:Several user cases, e.g., energy demand calculation, require a more detailed rolling resistance model implemented in the tire force element. Compared to vehicle dynamic application, cumulative energy balance is of greater importance. Some simplifications

Fig. 9: Test bench

Fig. 5: Vehicle road sensor

Fig. 7: Skid pad

Fig. 6: Data visualisation of a double lane change manoeuver Fig. 8: Banked curves

to couple the vehicle. The vehicle's chassis can be connected to any other body or the inertia frame with a joint of any freedom. Furthermore, the road body need not be equal to the inertia frame.

The user tire road force element is used to calculate the tire forces between road and tire body. The force element requires the road reference marker as the “from marker”, and the tire marker as the “to marker”. A tire data file is required to define the tire’s geometry, tire force calculation type and the tire’s physical properties. If no road file is selected, the x- y-plane (z=0) is used as the road surface.

Additionally, it is possible to specify a time dependent modification of road

excitation or friction coefficient.

APPlICATIonThe new tire road model is used at the IVK/FKFS for different applications:

Validation of torque Vector Control Systems and Driver Modeling:To evaluate embedded systems, it is neces-sary to perform closed loop maneuvers, e.g., double lane change, skid pad driving, or variation of friction coefficient and bank-ing angle while driving different curvature segments. These driving maneuvers are

in existing handling tire models must be corrected by means of precise force application, point calculation and extended rolling resistance force modeling. To evaluate tire force element modifications, some tire test benches have been created. These test benches allow easy modification of road’s banking angle, curvature diameter and driving velocity.

A selection of the mentioned application samples are shown in Figs. 7–9.The introduced universal tire road model environment enables the simulation of any kind of advanced driving dynamic application.

“Compared to the original SIMPACK tire road model, the

new user element does not need a track joint to couple the vehicle.”

ReFeRenCeS[1] Wiesebrock, A.; Neubeck, J.; Wiedemann, J.; 2011: „Universal tire-road-model for advanced vehicle dynamic application”, 11th Stuttgart Inter-national Symposium — Automotive and Engine Technology, Vol. 1, S. 329–343, Tagungsband, Vieweg + Teubner Verlag / Springer Fachmedien Wiesbaden GmbH[2] Wiesebrock, A.; Neubeck, J.; Wiedemann,

J.; 2011: „New road-description

methods for advanced ve-

hicle dynamic applications”,

16th International Confer-ence Vehicle Dynamics, Mulhouse[3] Les Piegl; Wayne Tiller; “The NURBS Book”, Springer[4] OpenCRG, VIRES Simulationstechnologie GmbH, www.opencrg.org[5] US PRO Initial Graphics Exchange Specification 5.3, www.uspro.org/documents/IGES5-3_for-Download.pdf

Ampl

itude

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eEn

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z)

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RPM

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z]

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hub main shaft couplinggear box submodel

generator rotor

generator stand

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FE005

FE013 FE013FE013

FE005

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FE093


Yang Xiaolin, Liu Hua, Liao Hui, Dongfang Turbine Co. Ltd. | CUSToMeR APPlICATIon CUSToMeR APPlICATIon | Yang Xiaolin, Liu Hua, Liao Hui, Dongfang Turbine Co. Ltd.

The intensified efforts to provide alternative and renewable energy led to the quick growth of the

wind turbine industry over the past few years in China. The recent successes in increasing power output rates of wind turbines are extremely encouraging. Unfortunately, recurrent drive train failures have plagued the industry and prevented wind turbines from achieving their intended 20 year design life. The dynamic behavior of the wind turbine, es-pecially the gearbox resonance perform-ance, must be fully examined. The multi-body system (MBS) software SIMPACK is a powerful tool for resonance analysis.

InTRoDUCTIonDongfang Turbine Co. Ltd., originally Dongfang Turbine factory, a subsidiary of Dongfang Electric Corporation, founded in 1966, is one of the most important compa-nies in research, design and manufacturing of power generation equipment in China.

Resonance Analysis of Wind Turbines

It has developed into one of the big power generation equipment manufacturers in the global market and has an outstanding repu-tation in the industry after 45 years of de-velopment. The main business of Dongfang Turbine Co. Ltd. is design, manufacturing, sale and service of steam, gas, and wind turbines as well as drive devices of ship and turbo machines (including main and auxiliary machines).

MoTIVATIonIn comparison to other wind turbine design software, SIMPACK allows for a more

precise modeling of drivetrain components. The SIMPACK model of the wind turbine consists

of rotor blades, hub, main shaft, gearbox, coupling and generator (Fig. 1). It allows for determination of the natural frequencies of the complete structure, and additionally, shows the mode shapes of all drivetrain components. To detect possible ranges of resonances, the effects of the rotor, the gear meshing frequencies and rotation speed of the components can be compared to the calculated natural frequencies. Simulation in the time domain enables the determination

Fig.2: Topology graphics of a drivetrain model

of whether or not the detected resonance frequencies are real resonance points.

THe MoDel oF THe WInD TURBIne DRIVeTRAInThe purpose of the model is focused on investigating the dynamic behavior of the drivetrain in the wind turbine. Therefore, the main frame can be considered as rigid and the tower is not included in this model. The topology graphics of the drivetrain model are shown in Fig. 2. The gearbox and rotor blades are built with SIMPACK substructures. Some of the components in the gearbox are considered as flexible bodies which come from their FE models. If there are two bearings mounted on one flexible part, one is constrained with a “revolute joint” and the other is set as a high stiffness spring in the radial directions. The whole gearbox model in SIMPACK is shown in Fig. 3.There are two torques acting on the drive-train: one is the aerodynamic torque from the rotorblades and the other is the feed-back torque from the generator.The aerodynamic torque from the rotorblades is simplified as a torque on the hub center. In real working conditions, this torques changes with the wind speed

and pitch angle. In these simulations, the torque are added on the hub as excitations (SIMPACK FE 093). There are two sets of torque applied to the model for different calculation conditions. One is a dynamic equilibrium calculation; another is a velocity sweep analysis. In the first condition, the torque on the hub is set to a constant value until a constant rotational speed, under loaded conditions, is reached. The eigenfrequency can then be calculated from the equilibrium state.The feedback torque is set between the generator rotor and the shell (SIMPACK FE 050). When the generator is working, it changes with the speed of the generator rotor.

AnAlySIS In THe FReQUenCy DoMAInA Campbell diagram with frequency data is plotted to investigate the potential reso-nances in the drivetrain. The horizontal lines in the diagram are natural frequencies, and the diagonal lines are excitation frequencies. The cross points in the diagram can be used to determine if there are possible resonance concerns with the model. In order to make the diagram easy to interpret, the excitation frequencies are separated into several parts by the range of frequency. Fig. 4 is one of the Campbell diagrams. All the natural frequency lines have cross points with exci-tation lines. But to decide if the cross point is a potential resonance point or not, it is necessary to plot the energy distribution of the components over the eigenfrequencies (Fig. 5).

AnAlySIS In TIMe DoMAInIn order to investigate the influ-

ence of danger frequencies in Campbell diagrams, it

is necessary to check the model with time

domain simulation. The time domain calculation is set as a “run up” procedure covering the entire

working speed range. The 3D Campbell dia-

gram is shown in Fig. 6.

ConClUSIonSIMPACK is a powerful tool that

can be used to investigate the resonance Fig. 3: SIMPACK gearbox model

“SIMPACK is exceptionally fast, robust and accurate.”

Fig. 1: Drivetrain model

Fig. 4: Campbell diagram

Fig. 5: Amplitude, phase and energy distribution

Fig. 6: 3D Campbell diagram

of wind turbine drivetrains. SIMPACK is exceptionally fast, robust and accurate. With SIMPACK, the dynamic behavior of wind turbines can be further understood.


Anneli Orvnäs, KTH Royal Institute of Technology | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Anneli Orvnäs, KTH Royal Institute of Technology

Active vertical secondary sus-pension (AVS) in a rail vehicle enables signifi-cant ride comfort improvement as compared to

a passive system. In addition to verti-cal dynamic control, the actuators can generate quasi-static roll control of the car body. This allows for higher speed in curves without negative effects on ride comfort.

InTRoDUCTIonIn rail operation today, the general trend is aiming towards increased vehicle speeds. However, higher speeds usually generate increased forces and accelerations on the vehicle which have a negative effect on ride comfort. The suspension of the vehicle has to be modified in order to compensate for

amplified vibrations in the car body. The possibilities of improvement by means of conventional passive damping are reaching their limit. Active suspension technology is considered a viable alternative to passive solutions because it offers more options for improving a vehicle’s dynamic performance.The study of active vertical secondary suspension (AVS) is part of the Swedish research and develop-ment program Gröna Tåget (Green Train), which aims at de-veloping a concept for the next generation of high-speed trains for Nordic conditions. The overall focus is to increase vehicle speed from today’s 200 km/h to 250 km/h on existing conventional lines and up to around 300 km/h on new dedicated high-speed lines. With the AVS system, ride comfort can be improved, or at least maintained,

at increased vehicle speeds or when track conditions are unfavorable.

SIMUlATIon MoDelThe vehicle model in SIMPACK was originally developed by Bombardier Transportation and models a one-car "Regina" vehicle with

a flexible car body connected to two motor bogies through the secondary suspen-sion (Fig. 1). The two conventional vertical dampers in each bogie are replaced by

two vertical actuators (Fig. 2).The idea is to reduce the car body vibrations by using the vertical car body accelerations as reference signals. The signals are pro-cessed in the controller to create the appro-priate force demands on the actuators. The generated actuator forces then counteract and reduce the car body vibrations.

The control strategy is modeled in the MATLAB® tool Simulink® (Fig. 3). In addtion to passive systems, dynamic vertical control is applied to further reduce vibrations of the car body and hence improve ride comfort.

The Use of Active Vertical Secondary Suspension to Improve Ride Comfort in a Rail Vehicle

“With the active vertical suspension system, ride comfort

can be improved, or at least maintained, at increased

vehicle speeds or when track conditions are unfavorable.”

© image courtesy of Bombardier Transportation

Fig. 1: The SIMPACK simulation model

Further, quasi-static roll control is applied to reduce the relative roll angle between the car body and bogies thus enabling higher speed in curves without negatively impacting ride comfort.

The actuator used in this study is an electro-hydraulic actuator modeled with its actual characteristics in Simulink. It is able to generate a force response up to 30 kN for a relative speed of 50 mm/s.

Co-SIMUlATIonBy means of the co-simulation interface SIMAT, SIMPACK and Simulink are able to communicate and exchange data (Fig. 3).The simulation is initiated in SIMPACK by starting a server to which MATLAB is con-nected. The simulation time and other in-tegration parameters are given in MATLAB which acts as master. SIMPACK acts as slave and reacts to these parameters. As the sim-ulation is started in MATLAB, the two pro-grams are independently solving their part of the equation system during one sample time period. At the end of each period, data is exchanged between the two programs and the process continues until the end of the simulation time. Measurements have to

Passively suspended carbody

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CUSToMeR APPlICATIon | Anneli Orvnäs, KTH Royal Institute of Technology Anneli Orvnäs, KTH Royal Institute of Technology | CUSToMeR APPlICATIon

Fig. 4: Vertical ride comfort (ISO 2631) is significantly improved with the active system

Fig. 5: The active vertical suspension reduces the relative roll angle between the car body and the bogie

Fig. 6: The AVS system allows for a lower bending mode frequency of the carbody without negative effects on ride comfort

be performed after the termination of the simulation for post-processing of the simu-lation results.

DynAMIC AnD QUASI-STATIC ConTRolDynamic control reduces car body vibrations, particularly on straight and large-radius tracks at high speeds. In the present study, this is achieved by means of so-called sky-hook damping which is a straightforward and commonly used active control strategy in rail vehicles. The reference signals are fil-

tered, integrated and multiplied by damping coefficients to create the appropriate force demands on the actuators.The quasi-static roll control enables a reduc-tion of the car body roll outwards in curves. Depending on the tuning of the system, it is even possible to achieve inwards tilt-ing. This reduces the lateral acceleration felt by passengers, and higher speeds in curves can be achieved without the need to increase the track cant.

SIMUlATIon ReSUlTSSimulations were performed on a straight track section, as well as on a large-radius curve section, at a vehicle speed of 250 km/h. The curve section consisted of a circular curve with radius R = 3.200 m and track

cant D = 0.080 m, corresponding to a track plane accel-eration of 1.0 m/s2. Measured track

irregularities were applied as excitations in the simulation model.Fig. 4 shows the vertical ride comfort on the straight track section, evaluated ac-cording to ISO 2631, above the bogies and in the middle of the car body for the pas-sive and active system, respectively. Ride comfort is significantly improved with the active suspension system compared to the conventional passive system. The car body vibrations above the front bogie are reduced by 20 %, in the middle of the car body by 28 %, and above the rear bogie by 33 %.Fig. 5 illustrates the effect of the quasi-static roll control, showing the relative roll angles between the car body and the front bogie for the passive and the active system, respec-tively. These simulations are performed in the curved section. The passively suspended car body is inclined outwards in the curve section relative to the bogie plane (negative roll angle), increasing the lateral acceleration felt by passengers. In the active system, the quasi-static roll control reduces the relative roll angle between the car body and bogie — an average of zero relative roll angle is achieved — hence reducing lateral accelera-tion. In this case, reduction of the relative roll angle with one degree (~0.017 rad) enables a speed increase of approximately 5 % with maintained ride comfort.

FURTHeR BeneFITS oF AVSThe AVS system compensates for negative ride comfort effects if the frequency of the

“...a lower structural stiffness of the car body can be allowed without negative effects on ride comfort.”

Fig. 3: The SIMAT interface enables co-simulation between SIMPACK and MATLAB

first vertical bending mode of the car body is reduced. Generally, a higher frequency of the first vertical bending mode has a positive effect on ride comfort. However, this normally means that the mass of the car body is increased, leading to increased vehicle costs. Fig. 6 shows that ride comfort is negatively affected with decreasing frequency in the passively suspended car body, while remaining generally unchanged in the actively suspended car body. Hence, a lower structural stiffness of the car body can be allowed without negative effects on ride comfort. This means that added elements

“...it is even possible to achieve inwards tilting. This reduces the lateral

acceleration felt by passengers...”

Fig. 2: Vertical actuators in the vehicle model

sensors

actuators

actuators

to stiffen up the car body can be reduced which, in turn, reduces the total car body

mass. The mass reduction is less in relation to the stiffness reduction which implies reduced

bending mode frequency.

ConClUSIonSA simulation model of a one-car Regina vehicle has been used to evaluate the impact on ride comfort by means of active vertical secondary suspension. The conventional vertical dampers in the secondary suspen-sion are replaced by actuators. The control strategy consists of dynamic vertical control

as well as quasi-static roll control of the car body.Simulation results show that vertical ride comfort is significantly improved by means of dynamic control compared to a passive system. Further, quasi-static roll control reduces the relative roll angle between the car body and bogies. The vertical actuators are able to generate car body tilting up to around one degree in curves to reduce the lateral acceleration perceived by the pas-sengers, and hence, allow for higher speeds without negative effects on ride comfort.


Wolfgang Predki, Dietmar Vill, Jennifer Papies, Chair of Mechanical Components and | CUSToMeR APPlICATIon Power Transmission, Ruhr University Bochum

CUSToMeR APPlICATIon | Wolfgang Predki, Dietmar Vill, Jennifer Papies, Chair of Mechanical Components and Power Transmission, Ruhr University Bochum

Multi-Body Simulation of a Planetary Gearing Test Bench

The Chair of Mechanical Components and Power Transmission at Ruhr Uni-versity of Bochum (lMGK) researches a wide range of machine components. Besides spur gears, further research focuses on worm and planetary gears as well as bearings. These fields of re-search are investigated on experimental and theoretical levels.Motivated by the question of how the effect of the interaction between plan-etary gear stages can be characterized, this article explores whether the result-ing noise level can be influenced by the choice of meshing sequence. Theo-retical conclusions are compared with experimental results in order to prove whether the level of noise emanating from gear interaction can be predicted and reduced with the help of simula-tions. In addition, this article deals with the analysis of the dynamic behavior of bearings, describing the simulation of cylindrical roller bearings and introduces a pilot study on the implementation of ball bearings.

InTRoDUCTIonDue to the increasing demands on power trains in the wind power and automotive industries, planetary gears are used more frequently. This is partly due to their coaxial, and thus, space saving design. Secondly, because of their torque division, they have an especially high power density and, in general, good efficiencies. To single out these advantageous properties and their be-havior within the entire drive train, effective simulation programs have become avail-able. Especially in the investigation of multi-body dynamics of planetary gears, LMGK looks back on many years of experi-ence from theoretical and experimental points of view. To analyze the dynamic be-

Fig 1: Digital test bench

havior of planetary gears, the Chair has built a number of test benches which were used

in various research projects. One of these existing back-to-back planetary gearing test benches (center dis-tance of 100 mm) is

represented and simulated within SIMPACK. In this investigation, the influence of differ-ent contact mesh sequences on the dynam-

ics of the total system has been analyzed. In order to evaluate the simulation results they were compared with test bench data and results, from the Chair´s own simulation program from a previous project [5]. In planetary gears, the chronology of the meshing of the teeth involved depends

used to connect the sun shafts and planet carriers respectively, which also allows for compensation of any possible axial, radial and angular shaft misalignment. The transmission gear box is located on the motor facing side. By interlocking the central elements, a circulating mechanical power is achieved. By turning the ring gear of the transmission gear box, the load level of the test gear box can be adjusted. This design offers the advantage that the engine only has to compensate for the power dissipation in the system, which represents only a fractional amount of the whole circular power. The coupling shaft between the two sun gears also functions as a gauge bar providing an electrical signal in proportional relation to the torque setting. In both the test gear box and the transmission gear box, sun shafts are embedded by tapered roller bearings to absorb any arising axial forces by using helical test gears. The outer rings of the transmission gear sun shafts are attached to the housing. A schematic representation is shown in Fig. 2.

DIFFeRenT TeST BenCH ConFIGURATIonSTwelve different test bench configurations are analyzed with respect to their excitation behavior. Due to the requirement of the kinematic equality of both gear boxes, it is also necessary to vary the transmission gear box configuration. The design parameters of the test gears have been chosen to allow a combination of several test gear boxes with one transmission gear unit.

MoDel DeSCRIPTIonThe SIMPACK model of the test bench [1] consists of several subsystems which are representative of the real test bench components and allow the analysis of the different configurations. The model provides a true representation of sun shafts broken down into their various sections for which the respective stiffnesses and mass properties are estimated by means of established calculation methods. The individual results are added together using bushing elements to arrive at a realistic model of the real deflection of the sun shaft in reaction to torsional and bending loads. The necessary grade of discretization is verified by FEM. For modeling of involute gear contacts, SIMPACK dedicated Force Element FE225 is used within the model. This element enables the fluctuating tooth stiffness which is indis-pensable in analyzing the different contact mesh sequences. To improve the calculated stiffness, the parameterization of FE225

different contact meshing sequences can be divided into the following: sequential, symmetric and unbalanced.

TeST BenCHThe test bench mentioned above has a back-to-back design, two planetary gear boxes that are directly connected to each other. For this purpose, tooth couplings are

only on the macro-geometry of the gears, namely the number of teeth and the angular pitch of the planet carrier. The interaction between these meshing teeth provides an additional parameter for excitation because of their phase delayed stiffnesses. Here, the

“...FE225 enables the fluctuating tooth stiffness, which is indispensable

in analyzing the different contact mesh sequences.”

test gear box transmission gear box

coupling coupling

gauge bar sensor telementry speed sensing

electric motorgauge bar

faulty gripping




can be changed until it corresponds to a solution derived from an approximate equation from previous projects. All gears are regarded as free of deviation within this model. The electric motor is represented by its torque-drive characteristic which is included by Expressions in the program. All couplings are only represented by their stiffness characteristics. To take account of the stiffness behavior of bearings, which is

Fig 2: Schematic diagram of the test bench

Fig 3: Start-up procedure

Fig 4: RPM profile

Fig 5: Sun and planet carrier displacement

“...bearings including a non-linear characteristic and

clearance are used...”

dependent on the loading condition, bear-ings including a non-linear characteristic and clear-ance are used within the model. Subsequently, the stiffness is then considered

with the help of Input Functions.

SeTTInGS FoR THe SIMUlATIon RUnSFor the calculation of the different levels of the several variants these were, with few exceptions, always averaged over a speed

range of 0 rpm to 2.500 rpm. Due to the high computing time and the resulting amount of data, a continuous determina-tion of the level values of certain variables is not possible. An average determination is made over five stationary operating points at different speeds for comparism to experi-mental results. Since the start-up procedure to a steady state system status makes up a substantial part of the computing time, the system is first accelerated to 2.500 rpm. The system is then decelerated as shown in Fig. 4. The rotational position of the planet carrier is also plotted in this diagram. The length of time in which an operating point must be considered is determined by the rotational speed of the planet carrier. The figure shows that, in each case, one planet carrier rotation is captured. The specified measurement rates are based on the Nyquist-Shannon sampling theorem.

SIMUlATIon ReSUlTSThe comparison between the measurements gained and the simulation show qualitatively similar results. Given symmetric contact mesh sequences, the central elements hardly ever misalign. In sequential variants, the behavior is rather periodic, and in unbalanced mesh sequences, the characteristic proves to be chaotic (Fig. 5). The behavior of unbalanced variants can be attributed to a predominant power imbalance which moves the central elements out of their central points. Therefore, symmetric variants show a significantly lower level of displacement to unbalanced ones. This is shown in Figures 6 and 7.

By contrast, the speed level presents an inverse attitude (Fig. 8). The meshing itself can be identified as a decisive parameter for the excitation of the system.Compared to sequential types, variants with a symmetric mesh sequence show, a significantly less favorable behavior in regard to their displacement excitation. This is justified by the permanent change of stiffness levels which occur in distinctive steps caused by symmetric variants. Here, sequential variants with four planets turned out to be particularly balanced. The absolute tooth force level LFz characterizes the vibration excitation of gearings [2]. This parameter unites all essential constituents of the vibration excitation and can be correlated with the emitted airborne noise. Fig. 9 shows the absolute tooth force level as well as the measured sum acceleration level on the ring gear of the test gear box.

FUTURe WoRKTo improve the quality of these current models, and to take other important influ-ences into account, these models are being further developed. The consideration of gearing deviations and tolerances play an especially important role on the system dynamics and is treated in current projects. However, gearing deviations only cause an appreciable inhomogeneity on the load dis-tribution of the different tooth engagements in planetary gears if all central elements

are firmly embedded, i.e., no compensa-tory adjustment movements are possible.

To capture this within the simulations, two different approaches are pursued. On one hand, representa-tive normalized functions for the acting excitation

of the gearing deviations are imported into SIMPACK Expressions and are used in the

model from then on. However, this solution is quite complex. Therefore, on the other hand, SIMPACK User elements are used in which these functions are calculated. Both solutions work in test models (Fig. 10), but must be included and tested in the overall model of the test bench. Simultaneously, calculations of load distribu-tions are performed, and the influence of the planet carrier deformation should be considered within this model.

FURTHeR APPlICATIonSIn addition to the overall dynamic of drive train systems, the department is dealing with the dynamic behavior of their subcomponents, for example, bearings. A typical application of cylindrical roller bearings is, due to their high load carrying capacity and their compact design, on the output stage of spur or planetary gear boxes. At this point, because of the permanently increasing power density, very high loads occur at low speeds so that the requirement rises in accordance with these components.The simulation of the slow-speed abrasive wear of cylindrical roller bearings is based on a research project [3] within the department. The lubrication oil film is not considered in this model; only boundary friction exists. This assumption is legitimate because the lubrication oil film does not form at low speed. The inner ring is loaded by a constant dead weight with large mass; the outer ring is fixed.

“...the influence of the planet carrier deformation

should be considered...”

Sum level of sun displacementspur gears 6-DOF models

T1=200 Nm

Sum level of planet carrier displacementspur gears 6-DOF models

T1=200 Nm

Sum level of sun speedspur gear 6-DOF models

T1=200 Nm

Absolute tooth force level Lfzspur gear 6-DOF models

T1=200 Nm

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Fig 13: Ball bearing

Fig 12: Cylindrical roller bearing SL 18 3010

Fig 10: Individual pitch variation Fig 11: Roll angular velocity [4]

Fig 9: Absolute tooth force level

Fig 7: Sum level of planet carrier displacement

Fig 8: Sum level of sun speed

Fig 6: Sum level of sun displacement

PIlot StuDY: Cylindrical roller Bearing under loads within A Planetary Gear StageThe model parameters differ from those of [4]. This allows only a qualitative comparison of the results. It can be concluded that the friction of planetary gear bearings is much higher than in non-portable bearings.The increase of the angular velocity before entering the load zone can clearly be explained by the fact that the roller element installed before the one under observation, which can rotate freely, is already gripped by the load zone. The following roller element, which is attached to the one before, is turned with increasing speed in the opposite direction until it enters the load zone itself.

PIlot StuDY: Ball BearingIn general, ball bearings can absorb radial and axial forces in both directions. However, they can absorb much greater forces in the radial direction. This property can be attributed to their raceway geometry and

their ball-shaped rolling elements. However, the osculation of the rolling elements and the raceways gives it the ability to carry loads. Similar to the roller bearing, the outer ring is considered to be fixed. In contrast, the inner ring is provided with six degrees of freedom. Finally, it should be able to reduce and rotate in direct reaction to the load. In addition, the modeling of the raceways forms another challenge. This was solved by the approximation of the contact ellipse through several point-to-point contacts. To guarantee a correct bearing deflection, the e-modulus within the Force Element was adjusted. The deflection characteristic was given by the manufacturer. The bearing is designed with clearance. The contact between the rolling elements and their housing is described by the Hertzian contact. For this purpose, within the model, the cage pockets themselves are represented as spheres and are positioned inside the rolling elements. The rolling elements are designed

as spheres as well. All contacts are modeled with the help of the Hertzian contact Force Element FE222. Some simulation results are shown in Fig. 13.The angular velocity of the roller elements shows an expected pattern. The rotational velocity changes during the passage through the load zone. Even the circular course of the increase and the decrease of speed is recognizable. This effect is based on the deformation of the rolling element within the load zone. The radius minimizes continuously from the time of the arrival at the load zone to the crown of the ball position. From this point it decreases until the roller element resurges in the load zone. A more detailed view of the angular velocity of the housing shows fluctuation from the calculated value. The reason for this is the movement of the roller elements since, they both push and slow down the cage pocket. Additionally, the slip velocity of one roller element is shown in Fig. 13. Due to the

geometry and the driven inner ring, the roller element has a higher slip velocity on the inner ring. The roller element has no angular velocity once it has reached the load zone. The slip velocity then reaches its maximum due to the high speed difference.

ReFeRenCeS[1] Feller, H.: Systemdynamik eines Planetenge-triebeverspannungsprüfstands, Ruhr-Universität Bochum, Unveröffentlichte Bachelorarbeit, 2011[2] Müller, R: Schwingungs- und Geräuschan-regung bei Stirnradgetrieben, Dissertation, TU München, 1991[3] Elfert, G.: Langsamlaufverschleiß von vollrol-ligen Radialzylinderrollenlagern, Dissertation, Ruhr-Universität Bochum, 2005[4] Potthoff, H.: Anwendungsgrenzen vollrolli-ger Planetenrad-Wälzlager, Dissertation, Ruhr-Universität Bochum, 1986[5] Sfar, M.: Bestimmung von Verzahnungs-korrekturen und Lagerkräften in Planetenge-trieben für Lastkollektive, FVA 328 IV Plankorr, Bochum, 2011

numbers of modeling tools closed

simulationdistributed simulation

distributed modeling

closed modeling

combination of equations of seperately modeled

subsystemsco-simulation

"classic" simulation

seperation of model for simulation

numbers of integrators

=1

=1 >1

>1

I II

III IV

output

Input

GuSMA – platform


Andreas Rüdenauer, Karlsruhe Institute of Technology | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Andreas Rüdenauer, Karlsruhe Institute of Technology

InCReASInG PRoDUCT CoMPleXITy AS A CHAllenGe FoR PRoDUCT DeVeloPMenTThe demand for efficient products and processes can be seen in every area of our industry. On-going system automation, and the establishment of mechatronic systems, which are defined by a harmonic interaction of different subsystems such as mechanics,

hydraulics, electronics, control and so on, underline this fact. In the future, enabling technologies such as cyber-physical-systems will have a high relevance in the market, and they will contribute to the growing complexity of technical systems [1]. Companies have to face these challenges and come up with new and innovative solutions.

VIRTUAl PRoToTyPeS AS A Key SolUTIonIn order to deal with increasing complexity in product development, the application of simulation tools has turned out to be a key factor for reducing development time and costs. Especially in the field of complex mechatronic systems, the approach of using virtual products seems to be promising. In

The industry of mobile machines is well known for the development of highly innovative and complex products. They are affected by all mechatronic disciplines, all of which can be found in one system. Along with the trend to intelligent and adaptive systems, automation is becoming more important on all system levels. This leads to an even higher interdependence between the specific mechatronic disciplines. Co-operation between in-house engineers and suppliers puts further emphasis on a highly efficient product development process. one promising approach is to establish close oeM-supplier-networks by using cross-company virtual prototypes. For this reason, a coupled simulation in a cross-company development process was created in the joint project GUSMA.

Cross-Company System Simulation using the GUSMA-Standard for Co-SimulationCross-Company System Simulation using the GUSMA-Standard for Co-Simulation

Fig. 1: Definition of co-simulation in context of using different modeling tools [1]

Fig. 2: Concept of the GUSMA-Platform

an early stage of the product development process, a virtual prototype can help to gain valuable information, to identify potential risks, and to initiate according optimization measures. To build up a virtual prototype, it is essential to gather all existing expert knowledge about the product which is to be developed, including its subsystems. De-pending on the manufacturing capabilities of a company, not only in-house depart-ments but also external suppliers need to be included in the initial stages. As an example, the industry of mobile machines is mainly characterized by small and medium-sized enterprises (SME) which are strongly interconnected in networks of suppliers and vehicle manufacturers. The products integrate the latest powertrain technologies with reliable and robust work-ing functions. A large variety in product volume, which in some cases is as low as one, imposes high demands on the devel-opment of these machines. In order to face the challenges of increasing complexity as mentioned above, the usage of virtual pro-totypes including the vehicle manufacturer and its suppliers in a cross-company network seems to be a promising approach. As for the predominantly middle-sized companies of the mobile machine industry, this approach has yet to be established. The joint project GUSMA pursued this aim.

THe PRoJeCT GUSMAThis project was a joint research project initiated by the Chair of Mobile Machines (Mobima) at the Karlsruhe Institute of Technology (KIT) in 2008. It ended in 2011. GUSMA is an acronym in German which stands for "Coupled Simulation of Mobile Machines between different business partners for the virtualization of product design". The project was realized in a consortium consisting of a research institution (Mobima), a vehicle manufacturer (AGCO GmbH/Fendt), an application company (Hydac System GmbH) and three companies in the area of simulation software: Fluidon GmbH, LMS Deutschland GmbH, and SIMPACK AG. As every company uses different simulation tools depending on its specialization, the technology of the coupled simulation was chosen as a basis in the project. Coupled simulation or co-simulation is the connection of at least two modeling tools by using at least two numerical integrators (solvers) at the same time, see Fig. 1. In this way, it is possible to model each sub-system in simulation software which is suitable for the specific tasks in a company and which is familiar to the in-house engineer as well.

Additionally, a model can be solved with its optimized integrator, and an adequate integration step size — depending on which phenomenon and which frequencies are important. Last but not least, co-simulation pro-vides the possibil-ity of accelerating the engineering process by modeling the corresponding sub-models simultaneously — both in different departments or even different companies. The main objective of project GUSMA is to make co-simulation accessible as a tool for cross-company collaboration in the product

development process. To ensure an easy application and build-up of a complete system using co-simulation, a key element in the project was the standardization of co-

simulation. The standardization considers three aspects — the approach of using a central platform

for the build-up of a complete system, a standard data interface and a standardized procedure for building up the system. Also, a focus was put on the protection of know-how for the exchange of simulation models.

“The main objective of the project GUSMA is to make co-simulation accessible as a

tool for cross-company collaboration in the product development process.”

modeling

mechanics control system hydraulicsuspension system

hydraulicpressure supply

modeling modeling modeling

model exportGuSMA-standard




GUSMA-platform

SIMPACK DSHPlusAMeSimSimulink

import of fully functional, parameterized submodels per drag & drop

force_left

force_right

displace_ri

verlocity_ri

velocity_le

displace_le

current_PositionSensor

SIMAT 8905/R2010a(Co-Simulation Interface via IPC)

Sampling period: 0.001 [s] Server remote: off Server address: 172.0.0.1 Server port: 20222 Auto start: off

SIMPACKCo-Simulation Interface

>

>

>

>

>

>

>


CUSToMeR APPlICATIon | Andreas Rüdenauer, Karlsruhe Institute of Technology Andreas Rüdenauer, Karlsruhe Institute of Technology | CUSToMeR APPlICATIon

Fig. 3: Process of cross-company collaboration in project GUSMA

THe IDeA oF A CenTRAl PlATFoRMA central element of the project incorporated the idea of a platform on which a coupled simulation can be executed. The system to be simulated can be divided up into sub-systems of different domains and different manufacturers/suppliers, respectively. Every submodel can be created in its own domain-specific simulation program. Afterwards, it can be exported in a platform-compatible format. By exporting the submodel and its involved conversion, the protection of pro-prietary information is realized. Therefore, in the simulation program, where a submodel is created, the possibility to secure or hide data — such as parameters — has to be integrated. Ideally, apart from the protected submodels, the right solver can be export-ed on the platform so that every submodel can be executed independently. Fig. 2 shows this interrelation.The platform provides the possibility for each user to build up a complete model via a graphical user interface by linking the respective submodels. Additionally, adminis-tration of parameters and determination of initial values for the simulation is enabled. Finally, the feature of saving data is given on the platform.As a basis for the platform, Mathwork’s MATLAB® and Simulink® were chosen. On the one hand, MATLAB and Simulink are widely used in industry and, on the other hand, many commercial software tools already provide a co-simulation interface to Simulink. This way, the GUSMA Standard

with the GUSMA platform. Fig. 3 shows the process of this project.After analyzing the system and defining the exchange variables in the project team, the In-house development of the simulation models began. Also, individual validation of the models was part of the project. The hydro-pneumatic front-axle suspension was split up into four submodels. A mechanical model, which was created in SIMPACK, and a control model of the level-control, mod-eled in Simulink, was created by AGCO/Fendt. In the project, two hydraulic models were used — one for the hydraulic suspen-sion system and one for hydraulic pressure supply. This way, the real situation of two different suppliers for hydraulic systems is re-flected. The company HYDAC modeled the hydraulic suspension system using AMESim, and the company FLUIDON created the hydraulic pressure supply in DSHPlus. During project GUSMA, all participating software partners implemented the requirements for the GUSMA-Standard in their software. In this way, all created submodels could be integrated on the platform proving its func-tionality. After each submodel had been modeled, the models were exported accord-ing to the GUSMA-Standard. In the project, a uniform layout of the exported model block (S-Function Block in Simulink) was added to the standard. Fig. 4 shows the lay-out of the adapted SIMPACK-Co-simulation interface block for MATLAB “SIMAT”. As all the input and output variables are shown on the block automatically, the build-up of the complete system is facilitated.The role of the OEM in the project was taken over by the research institution, Mobima, where the complete system was built up. The GUSMA-platform provides a standardized procedure for building up a fully functional co-simulation within six steps. A graphical user interface guides the user along these steps.In the first modeling step, all submodels have to be drawn on the platform. The parameters of the submodels are imported automatically in the background. In GUSMA, parameters are distinguished between three groups — protected, modifiable and joint parameters. Protected parameters are only accessible for the actual creator of a submodel and they are not visible on the platform. This way, proprietary information of a company can be protected. Modifiable parameters can be viewed and changed on the platform (e.g., bezel size). Optimization of the entire system is enabled. Joint parameters are the parameters which are used by different submodels (e.g., cylinder length) and should be set and modified

Fig. 4: Layout of the adapted SIMAT-Block according to GUSMA-requirements

can be applied easily on the side of the soft-ware company as well as on the side of the customer. Also, it represents an opportunity, especially for small and medium-sized com-panies, to use co-simulation in the product development process beyond corporate borders.

STAnDARDIZeD DATA InTeRFACeIn order to enable easy handling of all ac-cessible simulation data — parameters and initialization variables — the workspace of MATLAB was chosen. As a central ele-ment of MATLAB, the workspace provides version independency as well as minimum maintenance.While importing a submodel, all data is au-

tomatically written in the workspace. Dur-ing a co-simulation, the GUSMA platform and all participating simulation programs

exchange date via the workspace. The exchange data is written in a MATLAB structure array. Besides the name of the parameter or the initialization variable, the value, the unit, the factor to the correspond-ing SI-unit and a marker is transferred. The latter determines if the exchanged data is a parameter or an initialization variable.

ReFeRenCe APPlICATIon AnD CRoSS-CoMPAny CollABoRATIon USInG THe GUSMA-PlATFoRMA tractor’s hydro-pneumatic front axle-suspension with level-control was used as a reference application to demonstrate the functionality of cross-company development

“A central element of the project incorporated the idea of a platform

on which a coupled simulation can be executed.”

intertia frame

translation

𝑢 𝑐

body fixed reference frame

undeformed position

𝑑


Massimiliano Bianchini, Mario Romani, Guido Saporito, AnsaldoBreda S.p.A. | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Andreas Rüdenauer, Karlsruhe Institute of Technology

SIMPACK neWS | SIMPACK AG𝑢(𝑐,  𝑡) = � 𝜓𝑗 (𝑐) x 𝑞𝑗 (𝑡)

𝑛

𝑗=𝑙

unitarily. The same definitions apply to the so called initialization variables. These determine the start values of state variables, e.g., an initial pressure or position. In the second step, the submodels have to be connected with each other according to their in- and outputs. Items from the Simulink library, such as visualization or storage options, can be added as well.In the third step, the user has to enter a filename. The data which is generated during the build-up of the complete model is saved under that filename. Here, the user is also able to load a data set which was saved earlier. In the fourth step, the user is able to manage the parameters, which are visible for him, by identifying and setting the joint parameters — or joint initialization variables, respectively. In the fifth step, the possibility is given to change the value of all accessible data.The sixth step allows setting the commu-nication interval for the co-simulation. This interval defines the temporal step size when submodels exchange data among each other.

A hydro-pneumatic front axle suspension of a tractor was used for validating the platform. This was executed not only with the virtual model upon the developed platform but also with practical tests on a test bench.The software partners who participated in the project here already integrated the requirements for the co-simulation standard in their modeling tools. The GUSMA-Standard will be published as a guideline of the German Engineering Federation (VDMA). Interested parties are welcome to contact the Chair of Mobile Machines (Mobima) or visit the homepage (www.gusma.de).

ReFeRenCeS[1] Geisberger, E; Cengarle, M.V.; Keil, P.; Niehaus, J.; Thiel, C.; Thönnißen-Fries, H.J.: Cyber-Physical Systems — Innovationsmotor für Mobilität, Gesundheit, Energie und Produktion, acatech (Hrsg.), Munich 2011[2] Geimer M., Krüger T., Linsel P.: Co-Simulation, gekoppelte Simulation oder Simu-lations-kopplung? Ein Versuch der Begriffsver-einheitlichung, O+P Zeitschrift für Fluidtechnik — Aktorik, Steuerelektronik und Sensorik 50 (2006) Nr. 11-12, S. 572-576.

After completing the above-mentioned steps, the simulation can be executed using the start button on the Simulink platform.The complete system model of the front-axle suspension was validated afterwards with experiments on a test-bench.

ConClUSIonThe application of virtual prototypes offers great potential for time and cost reduction in product development processes. Especially in the industry of small and medium-sized

enterprises, such as the mobile machine industry, the approach of using a coupled simulation for the

representation and validation of complete systems in cross-company collaboration is very promising. In order to make the co-simulation available as a modeling variant between different business partners, the joint project GUSMA was initiated. A simulation platform was developed which integrates a standard for co-simulation and ensures intuitive handling. In this way, the platform can facilitate the application of a co-simulation and support the engineering process between different business partners.

“...all created sub-models could be integrated on the platform

proving its functionality.” In recent years, greater emphasis has been placed on the design of high-speed, lightweight precision systems. The design and performance analysis of such systems can be greatly enhanced through transient dynamic simulations, provided that all significant effects are incorporated into the mathematical model. The need for better design, in addition to the fact that many mechani-cal and structural systems operate in adverse environments, demand the in-clusion of many factors that have been ignored in the past.

When these system sare analyzed, ne-glecting deformation effects can lead to a mathematical model that poorly represents the real system. The interaction of software tools for MBS dynamics, such as SIMPACK, and software tools for finite elements analy-sis can allow for the optimization of vehicle design. The integration of body flexibility into these models allows for realistic simula-tion of structures, components and safety systems.

This work is concerned with a mass transit vehicle’s multi-body dynamics and

the reliability of such analysis is proved by experimental validation, i.e., a comparison between vehicle accelerations recorded during running

tests and corresponding data computed by simulations.

FleXIBle BoDy InTeGRATIon InTo MBSIn MBS theory, a flexible body motion can be obtained as the superposition of a large reference motion and small displacements with respect to the body reference frame.

This gives rise to deformations, as shown in Fig. 1. In order to reduce the system order, this relative displacement field u is described by a linear combination of assumed shape functions 𝜓𝑗, with corresponding time de-pendent weighting factors 𝑞𝑗, similar to an FE approach:

(1)

This approach, called modal [1], requires the calculation of the shape functions before performing the multi-body analysis, but it is advantageous because it leads to results very close to those obtained by an FE approach, despite using few modes. The mode shapes

Fig. 1: Deformation description in MBA

Fig. 2: Master DOFs selection for dynamic reduction of carbody (FE Mesh -> nodes of super element)

“The interaction of software tools for MBS dynamics, such as SIMPACK, ... can allow for the

optimization of vehicle design.”

SIMPACK Academy: Basics on Dynamics of Multi-Body Systems

30–31 October 2012, Hotel Seitner Hof, Pullach/Munich, Germany

Speaker: Prof. Dr. Oskar Wallrapp

Multi-Body Dynamics is one of the most prominent subjects of mechanical, mechatronics and biomechanical engineering. A brief knowledge of kinematics and dynamics is essential for efficient usage of multi-body programs like SIMPACK. This course gives a detailed overview of the kinematics and dynamics of rigid bodies in multi-body systems (MBS).

SIMPACK Conference: Wind Turbine and Drivetrain

26 September 2012, Radisson Blue Hotel, Hamburg, Germany

Guest Speaker Presentations by SIMPACK Users, including Repower, SkyWind, Vestas and ZF

The main focus of the conference is to demonstrate new SIMPACK functionalities such as automatic load calculations and database management. Guest speakers will also be presenting their work with SIMPACK.

The conference will be free of charge. Limited space available. Prior registration is necessary.

experimental Validation of a Mass Transit Vehicle Multi-Body System

with Integrated Flexible Body

SIMPACK events in 2012

For more information and registration please visit: www.SIMPACK.com

Procedure2 runs

RUN 2analysis of

complete model

Sol 103

AltIer('alter_check_ab')

RUN 1analysis of

reduced model

Sol 103

Expandend eigenvectors and eigenfrequencies

File 1-pch

NCo CroSS-NCoFile 3-pch

output

input

output

Mode reduced model Mode complete model

Check orthogonality eigen-vectors complete-reduced

NCO

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Accelerometer D: lateral acceleration

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Accelerometer D: DFT of lateral accelerations

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2 ]32 | SIMPACK News | July 2012 SIMPACK News | July 2012 | 33

Massimiliano Bianchini, Mario Romani, Guido Saporito, AnsaldoBreda S.p.A | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Massimiliano Bianchini, Mario Romani, Guido Saporito, AnsaldoBreda S.p.A

could be calculated by a structural modal analysis of the single flexible body or static problems. In SIMPACK, all the features of a flexible body, like mass and stiffness matrices and modal content, are defined in a Standard Input Data file (SID), which can be generated by FEMBS, an interface software between SIMPACK and most of the commercial FEA tools.Often, if FE models have many degrees of freedom (DOF), modal approach is not sufficient to reduce computational burden, and a reduction of dimensions of mass, stiffness and modal matrices is needed. This reduction can be performed by means of techniques like Guyan Reduction (or Static) or Craigh-Bampton Reduction (or Dynamic), each one defining a condensation matrix 𝐺𝑛𝑚 to transform the matrices of the model, as described below:

(2)

where:• 𝑢𝑛: vector of displacements of complete

FE-model DOF• 𝑢𝑚: vector of displacements of reduced

FE-model DOF, named “Master Degrees”• 𝑀𝑅𝐸𝐷: mass matrix of the reduced

FE-model• 𝐾𝑅𝐸𝐷: stiffness matrix of the reduced

FE-model• 𝑀𝐹𝐸: mass matrix of the complete

FE-model• 𝐾𝐹𝐸: stiffness matrix of the complete

FE-model

The aim of these techniques is to use as small a number of DOF as possible, translat-ing to a minimum error in the description of the dynamic behavior of the model in the frequency range of interest (see Fig. 2).

To ensure a proper representation of the full FE-model into the MBS, an analytical verification of reduction process has been conceived, developed and implemented. The procedure developed can be used to optimize the condensation of the full FE-model and consists of three steps:

1. Evaluation of the mode shape correlation between complete and reduced models using a vector criterion, the “Normalized Check Orthogonality”, which defines a NCO index as follows:

(3) 𝑁𝐶𝑂𝑖𝑗 = �𝛷𝑖 x 𝑀𝐹𝐸 x 𝛷𝑗

𝑟𝑒𝑑 �

Where 𝑀𝐹𝐸 is the complete mass matrix, 𝜙𝑖 are the eigenvectors of the complete FE-model and 𝜙𝑖

𝑟𝑒𝑑, the expanded eigen-vectors of the reduced one. This index is defined to be in the numerical range between 0 and 1.

2. Evaluation of the dynamic behavior of the mode shapes that are similar, in terms of eigenfrequency difference;

3. Synthesis of a global index of correlation between reduced FE-model and complete FE-model as the ratio between the number of eigenmodes of the reduced FE-model characterized by a low error of NCO and eigenfrequency values, 𝑛𝑟𝑒𝑑, and the total number of eigenmodes of the complete FE-model in the frequency range of interest, 𝑛𝑒𝑔.

A further check concerning the mode shape is the evaluation of the mutual cross-corre-lation of the expanded eigenvectors of the reduced FE-model (CROSS-NCO index), in order to assess the validity and consistency of the applied reduction technique. Due to matrix and vector sizes, common software for programming, like MATLAB®, cannot allow one to directly manage the modal analysis results for NCO evaluation due to hardware memory constraints. Therefore, an algorithm was developed directly by means of DMAP, “Direct Matrix Abstraction Pro-

Fig. 3: Procedure for performing and validating FE model reduction

Fig. 4: MBS of Metro Rome Line C

gram” of NASTRAN, which can be included in the Input File Deck for the modal analysis. Hence, a procedure has been implemented that reduces the FE-model and evaluates NCO indices in two runs of NASTRAN (see Fig. 3).

MUlTI-BoDy SySTeM oF VeHICleThe subject of this work is the mass-transit vehicle “Metro Roma linea C”, manufac-tured by Ansaldobreda, which will be in service in 2012. This is a bidirectional vehicle

Fig. 5: NCO matrix of carbody reduced FE model

composed of six carriages with two run-ning gears for each one; the general layout is symmetric. Hence, a simplified MBS of Metro Roma line C has been created. The

Fig. 7: Frequency content comparison of bogie lateral acceleration

model is composed of the head motor carriage only, as shown in Fig. 4, because it is known that each car body can be con-sidered independent of the others in lateral and vertical dynamics, and both are more important than the longitudinal dynamics [4]. The modeled flexible body was the car body. This model was chosen in order to compare comfort indexes calculated with multi-body analysis with those coming from running test results. For the flexible body de-scription, only 250 DOF have been retained using the dynamic reduction, obtaining a correlation global index of 92 % accord-ing to the validation procedure mentioned above. The NCO matrix is shown in Fig. 5.

eXPeRIMenTAl VAlIDATIon oF MBS oF MeTRo RoMA-lIne CThe reliability of multi-body analysis results, in terms of flexible body implementation, has been proved by an experimental valida-tion, i.e., a comparison between vehicle accelerations recorded during running tests and corresponding data computed by simulations.In order to do this, test conditions were recreated. First of all, inertial properties of vehicle multi-body system were set accord-ing to a weighing test. Further, the test track was modeled in terms of geometry and measured irregularities. Accuracy of track description was demonstrated by com-paring lateral and vertical accelerations of

Fig. 6: Quasi-static signal comparison of bogie lateral acceleration in an emergency stop scenario

𝑢𝑛 = 𝐺𝑛𝑚 x 𝑢𝑚

𝑀𝑅𝐸𝐷 = 𝐺𝑇𝑛𝑚 x 𝑀𝐹𝐸 x 𝐺𝑛𝑚

𝐾𝑅𝐸𝐷 = 𝐺𝑇𝑛𝑚 x 𝑀𝐹𝐸 x 𝐺𝑛𝑚

�

Standard

MBS modelvehicletrackwheel-rail contact

MBA irregularitiesvelocitiescant deficiency

definition

load cases

running dynamics requirements

Vehicletechnical system

MBS software

identification

Flexible BodiesFRMflexible bodies equations

Intermediatesoftware

FE modelsnormal modes analysisreduction (optimization)stess analyses

FEM software

implemenation

text file

integration

SID-file (text file)

Structual requirements

AccelerometerDirection

longitudinal

lateral

vertical pivot 1

centre

pivot 2

Signal Comparison Indexes (SCI) of carbody accelerations

SCI NMVsimulationNMVtest

Diff%

Pivot 1

X 0.74

2.47 2.22 +11%Y 0.95

Z 0.97

Mid

X 0.74

2.85 2.75 +4%Y 0.94

Z 0.99

Pivot 2

X 0.74

2.10 2.30 -6%Y 0.94

Z 0.85

s [m]


Accelerometer D: RMS of lateral accelerations

RMS

acce

lera

tion

[m/s

2 ]

cross-correlation

g

f

delay


Massimiliano Bianchini, Mario Romani, Guido Saporito, AnsaldoBreda S.p.A | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Massimiliano Bianchini, Mario Romani, Guido Saporito, AnsaldoBreda S.p.A

𝑆𝐶𝐼 = 1 - � 𝐶0

- 𝐴0 � 𝐴0

- �𝐶(𝑡) = �𝑓* (𝜏) x 𝑔(𝑡+𝜏) 𝑑𝜏

+�

first filtered as prescribed in UNI ENV 12299 comfort norm [3], then frequency content and 5-second RMS values were computed in order to obtain 𝑁𝑀𝑉 mean comfort in-dexes [3]. A sensitivity study about flexible car body description was done, analyzing SCIs and comparing test/simulation mean comfort indexes. In Fig. 10, car body accel-eration SCIs for all motion directions were plotted.The result is that an accurate modeling process, i.e., consistent car body deformation behavior and correct description of system-environment interaction leads to very good results for computed accelerations, as shown in Table 1.

THe neW IMPRoVeD SInGle PRoCeSS FoR VeHICle DeSIGnIncorporating multi-body analysis capability and reliability, an improved single process for vehicle design is proposed which integrates both structural and dynamic requirements (see Fig. 11):

1. Firstly, a simplified multi-body simulation (MBS) model of vehicle has to be defined by means of vehicle typology and appli-cable standards.

2. Then, flexible bodies obtained from re-duced FE-models of the components are implemented in the MBS model after the reduction procedure is validated by the analytical method.

3. Such an MBS model is used for perform-ing running simulations in several opera-tive conditions.

conditions for the bogie-frame are used for stress analyses.

ReFeRenCeS[1] A. Shabana, “Dynamics of Multi-body Sys-tems”, University of Illinois at Chicago, Cambridge University Press, 2005.[2] M. Bianchini, “Experimental validation of a mass transit vehicle multi-body system with inte-grated flexible bodies”, University of Pisa, Thesis 2010.[3] A. Baroni, “Multi-Purpose Flexible Bodies Inte-gration into a Metro-Vehicle Multi-Body System”, University of Pisa, Thesis 2009.[4] UNI EN 12299 norm, “Railway applications — Ride comfort for passengers — Measurement and evaluation”, CEN, 2006.[5] S. Iwnicki, “Handbook of Railway Vehicle Dy-namics”, Taylor & Francis, Boca-Raton (FL), USA, 2006.[6] “Railway vehicle system dynamics”, SIMPACK Academy, 2008.[7] SIMPACK Documentation, version 8.903.[8] S. Dietz, O. Wallrapp, Ch. Wiedemann, “Nodal vs. modal representation in flexible multi-body system dynamics”, INTEC GmbH, Munich Univer-sity of Applied Sciences, 2003.[9] Harris, Piersol, “Harris shock and vibration handbook” — 5th ed., McGraw-Hill.

Fig. 10: SCI histogram for carbody accelerations

Fig. 11: Integrated vehicle design process

4. Results obtained from the multi-body analysis are directly used for verifying run-ning dynamics requirements. Concerning structural requirements, computed load bogies computed by a running simulation to

the corresponding ones recorded during the tests. More in depth, quasi-static signals, frequency content and root mean square values above 5-seconds period (RMS) of bo-gie accelerations were analyzed. The quasi-static signal of bogie lateral acceleration depends on track geometry features, i.e., curve radius and rail superelevation, and ve-

Fig. 8: RMS value comparison of bogie lateral acceleration

Table 1: Comfort index comparison for Metro Rome line C

hicle run speed; whereas, signal frequency content analysis underlines track irregular-ity effect. Finally, root mean square values synthesize both aspects and provide global information about track features. During this activity, the need for an objective criterion for setting out signals similitude has risen; hence, a signal comparison index (SCI) was defined, which was cross correlated

and concept-based. The cross-correlation function 𝐶(𝑡) can be computed for a pair of functions 𝑓(𝑡) and 𝑔(𝑡) in the following way:

(4)

and usually has a peak for 𝑡 = 0 whether functions are similar or correlated (see Fig. 9). The idea was to compare the cross-correlation peak computed simulation accel-eration signals 𝐶0 with the auto-correlation peak of test signal 𝐴0; SCI has been defined in a way to result in a range between 0 and 1:

(5)

This comparison has led to positive results and demonstrated that interaction between vehicle and environment was correctly described in MBS. Figs. 6, 7 and 8 show quasi-static signal, frequency content, and RMS values comparison of bogie lateral ac-celeration, respectively.Lastly, comfort tests were simulated and car body acceleration signals compared. During running tests, three accelerometers were placed above the car body floor, at the two bogie pivot locations, and the middle car body. Thus, correspondent signals were cal-culated by multi-body analysis. These were

Fig. 9: Cross-correlation function for two signals.

secant method to adjust σB

u = 0

u bearing eye x, y, z, β, γ

T��𝑟�u beam end


Gabor Müller, Virtual Vehicle Research and Test Center | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Gabor Müller, Virtual Vehicle Research and Test Center

“The mechanical model of the leaf spring

is a cantilever beam.”

mials, the terms of the stiffness matrix and the effective length change of the spring have been determined [3]. The stiffness matrix is constant. It must be determined before the calculation. The internal node positions and the forces at the end nodes are calculated using a static reduction method (Guyan). To consider contact with the S-Bump, a non-equidistant node distribution is also easy to realize.Two different parameterization methods are offered. The first one is suitable to model a leaf spring with known geometry; in this case, the width and height characteristics are given. Alternatively, a requested vertical

step is to determine the heights and widths. There are two parameterization strategies: the first one based on a given geometry, a

given width and height char-acteristic; the second one goes out from a required vertical stiffness. In the case of the geometry based

parameterization, the characteristic of the height and width are given as input func-tions. These must be interpolated according to the coordinates along the longitudinal beam axle. If the leaf spring geometry is not given, which is usually the case in the concept phase, the process to determine the element geometry is more complex. In this case the only known parameters are the required vertical stiffness (Cz0) and the width characteristic (bi). The assumption is that the bending stress is constant along the cantilever beam which corresponds to a parabolic leaf spring. With the help of the maximal bending stress (σB) and vertical load (Fn), the height for each element (hi) can be determined (Fig. 2). To avoid the zero height at the leaf spring eye, the user defines the ratio of the maximal to minimal height which is usually a constant value in the commercial vehicle industry. The mechanical model of the leaf spring is a cantilever beam. The generalized coordinates lay at the end of the beam, by the axle, and by the leaf spring eye. Considering half of a leaf spring, the end by the axle is modeled

as a clamped end while the end by the leaf spring eye has five degrees of freedom (Fig. 3): three translational and the rotation about the lateral (y) and the vertical (z) axis (β and γ respectively). Because the clamped end means zero displacements and rotations the system has only five generalized coordinates. Considering the two rotations, moment free, the only given coordinates are the displacements and the torsional rotation at the leaf spring eye — which come from the From Marker in SIMPACK. To determine the other two rotations, the displacements and rotations of the inner nodes, a Guyan reduction has been applied. The stiffness matrix must be partitioned according to the master nodes (x, y, z, α → um), and the displacements of the inner nodes plus the two rotation angles can be determined as slaves (us):

In the case of the geometry based param-eterization, the model is ready for the simu-lation. The stiffness matrix is determined. If the model is parameterized on the basis of the vertical stiffness, a further investigation is needed because the determined structure does not have the same stiffness as the input value. If it is within the given toler-ance range, it will be accepted. If not, the bending stress will be adjusted according to the second method (Fig. 2), and the whole process will be carried out to determine a new height characteristic until the vertical stiffness meets the tolerance conditions. If the positions are known, the forces and mo-

Fig. 3: Mechanical model of one half of a leaf spring

Fig. 4: Modeling approach to describe the static beam deformations

Fig. 2: Determination of the vertical stiffness (Cz) in case of a stiffness based parameterization

stiffness and a width characteristic are given by the user and a parabolic thickness profile is determined at the initialization process.

FUnCTIonAlITy oF THe MASSleSS-MoDelThe first step is to determine the stiffness matrix. The user defines the number of beam elements (up to 10) and the segmentation process begins. If the leaf spring has an S-Bump, a node must be placed coincident with the marker of the S-Bump. The solver finds the segment in which the S-Bump lies and divides the beam accordingly. When the lengths of the elements are fixed, the next

FuS =

=

0m

s

m

sssm

msmm Fuu

SSSS

0=+ sssmsmuSuS

msmsss uSSu 1−−=⇒

A new Massless leaf Spring Model for Full Commercial Vehicle Simulations

STATe oF THe ARTIn the commercial vehicle industry, there is no documented standard for modeling leaf springs. This means that the modeling pro-cess is fault-prone as well as uncertain and the simulations produce hard-to-compare results. The quality of the model depends mainly on the experience of the user, on the applied methodology and, in some cases, on the availability of measurement data. Because of the large influence on axle kinematics [1], it is important to consider

the main deformations of a leaf spring in an early development phase. During operation, the vertical deflection will be excited due to track irregularities and, in the case of a braking process, the so-called S-Shape occurs.In the analysis of the modal behavior of an FE-model, the first two eigenmodes are equivalent to these two deformations (Fig. 1).

These functionalities can be described with a very detailed leaf spring model. The main problem is that this detailed modeling is not required in all of the modeling stages. This means that in the concept phase, the geometrical data are not available to build up an elastic body model. The only avail-able value is the required vertical stiffness. To use this vertical stiffness, a simple spring secures high computational efficiency, but cannot describe the geometrical effects from the real leaf spring deformation which can be critical for the dynamic behavior of the vehicle. On the standard model level, the model can be expected to describe the important physical effects (contact with the S-Bump and geometric coupling vertical-longitudinal). One stage higher — the com-plex model — the dynamic effects, twisting

and the description of other parts (e.g., bearing eye) must also be considered. The higher the model

complexity, the more time is required for both the modeling and the simulation. Another disadvantage is that these different stages require different models. Switching between them is not possible, and a com-pletely new model is necessary. In this paper, a new standard modeling approach will be described — the so-called "massless-model". After the theoretical background, the description of the imple-mentation of the massless-model as a SIM-PACK User Routine will be presented. The massless-model has been validated with test-rig measurements at MAN Truck & Bus AG in Munich, and some comparison simu-lations have been carried out using a modal description of the leaf spring as a reference in SIMPACK.

MoDelInG ConCePTThe proposed model approach represents one half of a leaf spring with a limited num-ber of three-dimensional massless beam elements. As the name indicates, it neglects the mass and therefore the dynamic ef-fects. The following two important effects are considered within the model: linear beam static deformation and nonlinear geometrical coupling between rotation and displacement — the so-called shortening effect. With the help of the Hermite polyno-

Fig. 1: First (above) and second (bottom) bending mode of a leaf spring Finite Element (FE) model

“In the commercial vehicle industry there is no documented standard for

modeling leaf springs.”

leaf springs are widely used suspension compo-nents for heavy commercial vehicles because of their robustness and low cost. A leaf spring has two functions: suspension of the vehicle and support of the axle. The deformation of the leaf spring has an influence on the axle kinematics, and therefore, it affects the dynamic behavior of the vehicle.

Model building in an early development phase is complicated because of the lack of parameters for a multi-body system (MBS) model. Most commercial MBS software packages prefer a model approach with elastic beams whose data sets are usually not known in the early phase of vehicle development. In this article, a new leaf spring model is described which offers a capable leaf spring description in both the concept and fine tuning phase.

K1 K2 K3

time [s]

time [s] time [s]time [s]

time [s] time [s]

x Br

ake

cyl [

mm

]

F z [kN

]x

Brak

e cy

l [m

m]

F z [kN

]x

Brak

e cy

l [m

m]

F z [kN

]

MeasurementsSim-Massless


Gabor Müller, Virtual Vehicle Research and Test Center | CUSToMeR APPlICATIonCUSToMeR APPlICATIon | Gabor Müller, Virtual Vehicle Research and Test Center

Fig 6: Test rig measurements at MAN Truck Truck & Bus AG vs. simulation with massless-model, test phase K1-K3, vertical force (above) and displacement of the hydraulic brake cylinder (bottom)

The load is mainly applied in the vertical direction, but a leaf spring must also guide the axle along the direction of motion. The longitudinal displacement due to the shortening effect has a big influence on the steering behavior of the vehicle. Twisting can occur in cornering or by asymmetrical deflections. During the braking process, a moment is developed about the lateral axis and excites the second bending eigenmode (S-shape) of the leaf spring. If the S-bump makes contact with the leaf spring, then there is an influence on the deformed shape of the spring.On the basis of the MAN leaf spring test rig, a virtual test rig has been built up in SIMPACK (Fig. 5) to carry out the virtual testing of the behav-ior of the massless leaf spring model. There is good correlation between measurements and simulation by test rig scenarios. In Fig. 6, one can see the first three tests from Table 1 (K1 – K3) which are a combination of vertical load and brak-ing moment. The pictures above show the measured (blue) and the SIMPACK produced (red) vertical forces while on the bottom pic-

tures, the longitudinal displacement of the brake cylinder can be seen. The computing performance of the massless-model allows the user to carry out real time simulation with full vehicle models. SUMMARyDuring this project a new massless leaf spring model has been developed at Virtual Vehicle for SIMPACK applications. The as-sumption is linear beam statics, i.e., the model neglects the dynamic effects. The deformed shape has been determined with the help of the Guyan-reduction which se-cures an effective time integration process.

Although the model is linear, a nonlinear cou-pling exists between displacement and ro-tation to consider the shortening effect. The

S-Bump and the bearing eye are considered internally, parameterized with their spring characteristic and radius, respectively. The model has been implemented in SIMPACK as a user force element. There are two possible parameterizations. The first one is based on vertical stiffness. It needs only a stiffness value and the main dimensions to

create a leaf spring model. For fine tuning of a given leaf spring, the second one is dedicated. It needs a geometry — thickness and width — to build up the stiffness ma-trix, which is a constant matrix and its terms are calculated only once before the time simulation. To reduce modeling time, and to simplify the transition between the different parameterization strategies, a leaf spring generator has been developed. It is steered with an ASCII-file with the input data sets.The massless-model has been validated due to test-rig measurements. The results show very good correlations with the measure-ments. The comparison simulations with the elastic beam model show good agreement. The competitive CPU-time allows the appli-cation in real time full vehicle simulations.

ACKnoWleDGeMenTThe authors would like to acknowledge the financial support of the “COMET K2 — Competence Centres for Excellent Technologies Programme” of the Austrian Federal Ministry of Transport, Innovation and Technology (BMVIT), the Austrian Federal Ministry of economy, Family and Youth (BMWFJ), the Austrian Research Promotion Agency (FFG), the Province of Styria and the Styrian Business Promotion Agency (SFG).We would furthermore like to express our thanks to our supporting industrial and scientific project partners, namely MAN Truck & Bus AG, SIMPACK AG, Bundeswehr University of Munich, and to the Graz University of Technology.

ReFeRenCeS[1] W. Matschinsky, Radführung der Straßen-fahrzeuge, 3. Auflage[2] G. Rill et al, Leaf Spring Modelling for Real Time Applications, In the 18th IAVSD-Symposium, Atsugi, Japan, 2003[3] P. Steinke, Finite-Elemente-Methode, Springer-Verlag Berlin, Heidelberg, 2. Auflage, 2007[4] SIMPACK AG, Software documentation SIM-PACK, 2009[5] G. Müller, N. Geiger, S. Waser, W. Hirschberg, T. Ille, R. Zander, A New Massless Leaf Spring Model and Its Application in the Simulation of Heavy Commercial Vehicles, 22nd IAVSD-Sympo-sium, Manchester, UK, 2011

“The applied mechanical model has been validated via test-rig

measurements at the MAN Truck & Bus AG in Munich.”

ments can be determined with help of the linear beam statics. The radius of the leaf spring eye is also handled internally in the massless-model (Fig. 3). The displace-ments by the leaf spring eye must be transformed to the end of the beam. Not only the geometric coupling-radius, but the radial stiffness of the leaf spring eye is considered. After the modification of the stiffness matrix (T��𝑟�) a Guyan reduction is car-ried out to determine the deformed shape of the leaf spring. It is possible to calculate the shortening from these displacements and rotations but, this step affects the master positions. With the help of a second Guyan reduc-tion, the end state of the deformed leaf spring is determined (Fig. 4). If an S-bump also exists, a contact must be moni-tored. In the case of a contact with an S-Bump, the contact force will be calculated with the help of the given S-Bump stiffness — which can be in a form of a constant value or of a stiffness chart — and of the calculated penetration. The stiffness will be interpo-

Fig. 5: Virtual test rig in SIMPACK (MAN Truck & Bus AG, Virtual Vehicle)

Table 1: Description of the preset forces and displacements during the test rig measurements (MAN Truck & Bus AG)

(Task = 2). The stiffness matrix, the inverse of the slave part of the stiffness matrix, the mass, and vertical stiffness are determined. These are saved in the memory, and are imported in every integration step. From the displacements and rotations, a force is determined.The massless-model needs different input data sets for the different parameterization strategies (geometry- and stiffness-based). To define and to simplify the modeling process, a leaf spring generator has been developed. This is an ASCII-file steered tool which creates the required models in much less time. With the help of this tool, the changes of the model and the transition between the parameterization strategies are more effective and simplified. The leaf spring generator is also able to build an elas-tic beam model as well as the two massless variants from a quite similar data set. VAlIDATIon oF THe MASSleSS-MoDelThe applied mechanical model has been validated via test-rig measurements at the MAN Truck & Bus AG in Munich. During the tests, different load cases (Table 1) have been defined to map of all the possible load cases during operation of the heavy vehicle.

No. oftest

phase

Pre-set for vertical displacement

(z)

Pre-set for brake force

Pre-set for lateral force

K1 deflection (+/-) no no

K2 deflection (+) yes no

K3 0 yes no

K4 deflection (-) yes no

K5 deflection (+/-) yes (const.) no

K6 deflection (+) yes no

K7 deflection (+/-) no yes

K8 0 no yes

lated according to the penetration, and this value affects the corresponding terms of the stiffness matrix. The deformed shape is iteratively determined with the Newton-Raphson algorithm within a given required

tolerance.If the deformed shape is known (u), the mo-ments and forces (F) can be calculated from the well-known static equation system. Be-cause the deformed shape has been de-termined from a static equation, the model cannot describe dy-namic effects.

IMPleMenTATIon In SIMPACKThe massless-model is implemented in SIMPACK as a User Routine, a force ele-ment. The buildup of the leaf spring model is carried out before the simulation process

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EDITORIAL, DESIGN & LAYOUT:

Steven Mulski, Nicole Blum

© SIMPACK AG

SIMPACK AG

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Fax: +49 (0)8105 77266-11

[email protected]

www.SIMPACK.com

CIRCULATION: 5.300

PUBLICATION YEARS: 1996–2012

1. The Validation of MBS Multi-Megawatt Gearbox Models on a 13 MW Test Rig

2. Simulation of Rope-Propelled Automated People Mover Systems in SIMPACK

3. User Tire Road Model and Road Sensor for Advanced Vehicle Dynamic Applications

4. Resonance Analysis of Wind Turbines

5. The Use of Active Vertical Secondary Suspension to Improve Ride Comfort in a Rail Vehicle

6. Multi-Body Simulation of a Planetary Gearing Test Bench

7. Cross-Company System Simulation using the GUSMA-Standard for Co-Simulation

8. SIMPACK Events in 2012

9. Experimental Validation of a Mass Transit Vehicle Multi-Body System with Integrated Flexible Body

10. A New Massless Leaf Spring Model for Full Commercial Vehicle Simulations

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