nonlinear modelling and simulation of impact events and

DEGREE PROJECT IN AEROSPACE ENGINEERING, LIGHTWEIGHT STRUCTURES TRACK SECOND CYCLE, 30 CREDITS

STOCKHOLM, SWEDEN 2018

Nonlinear Modelling and

Simulation of Impact Events and

Validation with Experimental Test

ANDRÁS PÉTER SZÉKELY

NICOLE AL HANNA

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ENGINEERING SCIENCES

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Nonlinear Modelling and

Simulation of Impact Events

and Validation with

Experimental Test

NICOLE AL HANNA

ANDRÁS PÉTER SZÉKELY

TRITA-SCI-GRU 2019:042

Master Thesis, 2019

KTH Royal Institute of Technology

Engineering Sciences

Aeronautical and Vehicle Engineering Department

SE-100 44 Stockholm, Sweden

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Acknowledgements

A big thank you to our supervisor at Volvo Car Corporation, Mohsen Bayani

Khaknejad, our co-supervisor, Henrik Viktorsson, and everyone at the Solidity

Department who helped accomplish this thesis work.

We would also like to thank our examiner, Per Wennhage, our university, KTH Royal

Institute of Technology, and all the professors in the Aeronautical and Vehicle

Engineering Department for providing a professional and friendly environment

suitable for knowledge and self-growth.

Another big thank you to our parents whose sacrifices, love and constant support got

us here.

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Abstract

For rattle event prediction accurate models capable of estimating system response at

impact are required. In this thesis, a finite element model is built to imitate a physical

setup designed for testing rattle. First, a modal analysis is performed in

ABAQUS/Standard to validate the CAE model. Second, rattle is simulated in

ABAQUS/Explicit and a correlation between the simulated and the experimental

results is sought. Third, a sensitivity analysis is performed to investigate the effects

of selected contact parameters on rattle-sensitive criteria. The important parameters

are then identified, and preliminary guidelines are given for future CAE modelling

of rattle.

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Sammanfattning

För att motverka skramlande är nödvändigt att ha modeller kapabla till att förutspå

systemsvar från stötar. I denna uppsats presenteras en modell gjord med hjälp av

finita elementmetoden för att imitera en fysisk anordning vars syfte är att testa efter

skrammel. Först utförs en modal analys i ABAQUS/Standard för att validera CAE-

modellen. Därefter simuleras skrammel i ABAQUS/Explicit med syftet att hitta en

korrelation mellan det simulerade skramlet och experimentella resultat. Sist så

utförs en känslighetsanalys för att undersöka effekterna av utvalda

kontaktparametrar på skrammelkänsliga kriteria. De viktiga parametrarna

identifieras och preliminära riktlinjer ges för framtida CAE-modellering av

skrammel.

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Contents

Acknowledgements 3 Abstract 4 Sammanfattning 5 Contents 6 Nomenclature 7 Abbreviations 8

Introduction 8 Background 9 Objectives 9 Limitations 9

Literature study 10 Current CAE rattle predicting methods 10 Impact modelling 10 Linearity and non-linearity in FEM 11 Explicit and implicit solvers 11

Method 12 Physical tests 13

Experimental setup 13 Modal measurements 14 Time domain measurements 15

Signal processing 15 Mean removal 18 Butterworth filter 18 Moving average filter 19 Omega arithmetic 20

Setbacks and Solutions 22 FEA model 23

Mesh 24 Boundary conditions 24 Excitation 25 Material and property cards 27 Contact modelling 28 Solver Settings 29

Model validation 30 Modal correlation 30 Time domain correlation before impact event 31 Gap Size Determination 33 Time domain correlation at impact 35

Sensitivity Analysis 35 Nominated parameters and the ranges 36 Evaluating the Fundamental Rattle Criteria 38

Results of the sensitivity analysis and guidelines 41 The Effect of Contact Surface Definition 43 The Effect of Friction 44 The Effect of Contact Mechanics 47 The Effect of Material Damping 49 Guidelines 52

Conclusion 56 Findings and Lessons Learned 56 Future work 56

Distribution of labour 58 Appendix 59 References 74

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Nomenclature

α Mass-proportional Rayleigh damping coefficient [Hz] β Stiffness-proportional Rayleigh damping coefficient [s] [C] Damping matrix [N/(m/s)] [K] Stiffness matrix [N/m] [M] Mass matrix [kg] δ Logarithmic decrement [-] 𝜁 Damping ratio [-]

n Number of periods T Period [s] x(t) Displacement at time t [m] µ0 Critical damping fraction [-] ∆t Time increment [s]

ω Frequency [Rad/s] f Frequency [Hz] t0 Time at which the start curve is connected to the rest of the

excitation signal [s] a, b, c Coefficients [-]

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Abbreviations

VCC Volvo Car Corporation

NVH Noise, Vibration, Harshness

CAE Computer Aided Engineering

FEA Finite Element Analysis

FEM Finite Element Modelling

FFT Fast Fourier Transformation

S&R Squeak and Rattle

BC(s) Boundary Condition(s)

DoF Degrees of Freedom

MPC Multi-Point Constraint

St-St Steel-Steel

P-St Polypropylene-Steel

P-P Polypropylene-Polypropylene

CP Contact pair

Gen General

Kin Kinematic

Pen Penalty

Mdamp Mass proportional material damping

Sdamp Stiffness proportional material damping

El-el Surfaces of the material pair modelled as element-based

Node-el Surfaces of the material pair are modelled one as element based

and the other as node-based

Introduction

At Volvo Car Corporation (VCC), the Solidity department is concerned with Squeak

& Rattle (S&R), two types of unwanted sounds that could occur while driving, and

which the user may consider an indication of low product quality. The ideal scenario

for the engineers at VCC would be to be able to predict the location, intensity and

annoyance level of those sounds, and take the necessary measures to eliminate them,

before the manufacturing starts. That way the development process is made faster

and more efficient.

In this thesis work, rattle is the phenomenon under investigation. It is an impact

induced noise defined as “a rapid succession of short, sharp, sounds” (1) and occurs

in vehicles when two parts interact in an oscillating contact-no-contact manner.

The engineers’ primary tools are CAE softwares, such as ABAQUS, NASTRAN, and

LS-DYNA, which manifest powerful prediction abilities in the automotive world.

Rattle prediction, however, is still not fully possible due to its complicated nature,

adding to the fact that it has only recently become of bigger importance with the

boom of car electrification.

This work was done in the aim of developing a set of guidelines that the engineers at

VCC can use to simulate rattle events, and which can serve to create a method, in the

future, that is capable of predicting the certainty of this phenomenon’s occurrence.

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Background

VCC has invested a lot of effort in research to find powerful tools that are able to

predict S&R before the first prototypes are built. The E-LINE method (2), which is

currently used at VCC for rattle prediction, evaluates the clearances between parts

and, in the predicted contact areas, statistically evaluates the relative displacements

in time domain. However, without modelling the impact events, little information is

given on the variables most significant in rattle sound generation, which makes the

assessment of these predicted contact areas less reliable.

Current efforts are put into investigating the connection between sound annoyance

levels and the fundamental variables of different rattle events, and creating a

simulation-based methodology with a reliable assessment method of the predicted

rattle. This work is carried out as a doctoral thesis, split up into different parts, one

of them being this current master thesis. This part of the study is to create an

accurate method to model the rattle events in FEA, with special attention towards

the dependency of the fundamental rattle variables on the parameters and settings

of the FEA model.

The base of this work is a previous thesis project (3), where a physical test rig was

designed, built and used for rattle measurements. The main aim of these

measurements was study the impact of ambient conditions and variations in

boundary conditions on the generated rattle sounds, based on objective and

subjective rattle sound evaluation. However, these measurements also captured

acceleration and force data so the annoyance levels, rattle variables and simulation

parameters can be associated directly. Therefore, the findings of the whole study

have a higher accuracy, since the sound evaluation, and the FEA modelling are based

on the same measurement.

Objectives

The deliverables expected by July 7, 2018 were:

1. Build an FEA model of the test rig

2. Correlate the CAE rattle simulations with the experimental measurements

3. Conduct a sensitivity analysis to achieve a better understanding of the factors

affecting rattle modelling

4. Write a set of guidelines for modelling rattle with CAE

Limitations

Since the main goal is to create an accurate model of an experimental setup in CAE,

make sure it is a good representation of it, get as close to measurement results as

possible, and correlate them, many details about the experimental setup were

required. The setup, however, had already been designed and built by previous thesis

students (3). Moreover, the fact that it had been disassembled meant there was no

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way to see it in the same condition as it was used to make the measurements, so it

was not possible to check any undocumented details that could have an effect on the

behaviour of the setup. This limitation became an even bigger problem when signal

processing details contradicted the given specifications that were supposed to serve

as a foundation for the correlations. All these missing details and resulting setbacks

are documented in section 6 where approaches used to solve them are explained in

detail.

More limitations include the fact that the experiment was already conducted.

Therefore, only the captured data could be used for the correlation part, with errors

(described in the section 5) and without any means of using feedback from the

simulations. Additionally, when an attempt was made to recreate the rattle

experiment (explained in section 6), restrictions in the signal generating software

prevented the use of time domain input, and the creation of a more suitable

measurement for the correlation.

CAE software were limited by what is used at VCC. ANSA 17.1.1 was used for pre-

processing, META 17.1.1 for post-processing, and ABAQUS 6.14 and 2017 as solver.

There was a possibility to use Nastran and LS-Dyna solvers, but, due to the

limitations in time, this did not happen.

Finally, the biggest limitation was time. However, we did manage to solve most of

the problems, get a correlation, and perform the sensitivity analysis that would be of

use for future rattle simulations and validation on car parts.

Literature study

Current CAE rattle predicting methods

Two methods are used in the industry today to predict rattle. Both are linear, use

standard NVH models, and measure relative displacement between the critical parts.

One of them, the SAR-LINETM or E-line (2), operates in time domain and utilizes

user defined 3D lines to make the relative displacement calculations. The other

method operates in frequency domain and evaluates the displacement by using

connector elements (in ABAQUS terminology) referred to as “virtual sensors” (4). In

both methods, rattle is detected if the gap size and tolerance are exceeded.

The limitation of the methods is that they can only predict the possibility of rattle,

rather than its certainty. That is because contact does not necessarily mean a sound

will be produced. Therefore, a method that could detect only the impacts that will for

sure create rattle sounds is sought after in the current study.

Impact modelling

The paper referenced in (5) gives a good example of nonlinear modelling of rattle

events. Although it is not an NVH problem, it aims at an accurate modelling of the

dynamic response of suspended automotive parts impacting when subjected to

dynamic loading conditions. The model was compared to a random excitation

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experiment, and showed the significance of non-linear time domain modelling of the

vibration problem, as linear motion transmissibility could not capture the vibration

phenomenon and predict acceleration levels in the parts. The authors established a

soft constrained penalty-based contact with static and dynamic friction coefficients

and viscous damping. They also give a good way to reduce the computational costs

of long duration simulations, while maintaining accurate contact modelling, by

employing a dynamic sub-structuring strategy. This strategy is based on dividing the

structure to parts that behave linearly and nonlinearly, and then reduce the linear

substructures’ degree of freedom to speed up the computation.

In (6), a study of several parameters available in RADIOSS for contact modelling is

performed. The model consists of a table and two billiard balls, all made of linear

elastic materials. The table is fixed in all degrees of freedom at its bottom, and the

balls are made to impact each other, defining a non-linear behavior. The parameters

varied are the contact interfaces between the balls (types 7, 16 and 17 of RADIOSS),

the computation method upon node-element penetration between the table and the

balls (tied or sliding definition), and the algorithm for constraint calculation upon

contact (penalty or Lagrange multiplier method). After running the simulations and

comparing the kinetic energies obtained with analytical results, it is found that the

sliding option and type 16 interface give the smallest error.

Linearity and non-linearity in FEM

The linearity in FEA is defined by the mathematical stiffness and load matrices of

the modelled structure. In linear FEA, these matrices remain constant during the

simulation (7). There is no need for the software to update stiffness and load

components when deformation occurs. In nonlinear analyses, which may result from

geometry, material properties, contact, the stiffness or load matrices vary constantly.

A time increment is then needed, since the stiffness and force components have to

be updated at every step of the structure. This is due to the fact that the nonlinear

phenomena present in the event make the previously defined matrices unable to

describe the structure accurately.

The current study deals with nonlinearities resulting from the contact between the

parts coming together to create rattle. In finite element tools, contact modelling can

be defined by preventing (kinematic method) or eliminating (penalty method) the

penetration of the parts involved using different methods. These methods are further

described in 9.1, and the difference between them is of interest in the sensitivity

analysis.

Explicit and implicit solvers

CAE solvers use either the implicit method or the explicit method for numerical

calculations. The two methods are commonly compared in terms of computational

cost and numerical stability. Choosing one is usually dependent on the type of

analysis that needs to be done, the desired accuracy, and the type of information to

be extracted.

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The analytical difference between the two approaches lies in the number of

unknowns to be evaluated at every time increment (∆t). The implicit method, which

is an iterative technique, calculates for information about the current and the later

states of the system, so coupled equations have to be solved at every time increment.

On the other hand, the explicit method utilizes de-coupled equations since it only

calculates for the future state based on the current one.

The implicit method is unconditionally stable, meaning it converges irrespective of

∆t. The explicit method, due to the nature of its equations, is stable only if ∆t is below

a certain critical value. It is best used for short time simulations because of the ∆t

requirement and one of its main advantages is that it is less computationally

expensive than an implicit simulation with the same number of time increments.

Increasing ∆t means less computations for the implicit method, but it also hinders

the accuracy, which could be of importance depending on the behaviour under

analysis.

In ABAQUS, two solvers are available: ABAQUS/Standard which calculates using the

implicit method, and ABAQUS/Explicit.

Method

As mentioned in section 1.1, prior to this thesis, a physical setup was designed and

built by previous thesis students to test for rattle (3). The current thesis aimed to

build an FEA model of this physical setup, achieve a good correlation in time domain

simulations and use this model for a sensitivity study on the FEA parameters. The

correlation was reached in three different steps:

1. Modal measurements were performed in anticipation of the current work. That

is, for the validation of the FEA model. This experiment was performed again

during this thesis to serve as a better base for correlation work (further

explained in section 6). In the repeated experiment, the beam was excited by

imposing an initial displacement, and then letting it vibrate freely. The acquired

eigen frequency was used calibrate the mass and stiffness properties of the FEA

model, which are the most fundamental factors of the structure’s dynamic

behaviour. This intermediate step was helpful because it was also easy to

interpret any error in the results, and feedback it for a better correlation.

2. Time domain explicit analysis results were correlated to measurement data

without impact events. This step was used to validate solver settings and

calibrate model parameters like material damping and stiffness of shaker

connector rod connections.

3. Finally, time domain explicit analysis results were correlated to measurement

data with impact events. This step was used to check the validity of the model

during impact events, as a necessary step before the sensitivity study.

After reaching the desired correlation, a sensitivity study was performed to map the

connections between CAE modelling parameters and the chosen rattle criteria.

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Finally, the findings were discussed and concluded as preliminary guidelines, along

with possible future work.

Physical tests

The current thesis is based on measurements conducted on a rattle producing test

rig (3). Although this test rig was not designed or built during the current project, it

is essential to describe it in details since the FEA model is aiming to accurately

recreate it, and all the measurements used for correlations were captured with this

setup.

Experimental setup

The rattle test setup comprised of a cantilever beam with a rectangular cross section.

At one end, it was clamped with bolts to a stand. On the other end, it was drilled such

that a bolt, with a material sample glued to its head, could be inserted and fastened.

The material sample was placed in front of another material sample, similarly glued

to the head of another bolt which was fixed to an impact hammer. The material

samples could be changed by changing the bolts, carrying different samples. The gap

between the two material samples could be adjusted from 10 mm gap to a pretention

state that corresponded to -5 mm initial displacement. The beam was connected to

an electrodynamic silent shaker by means of a threaded cylindrical rod which was

fastened to both, the beam and the shaker.

Figure 1 shows a photograph of the setup, and Table 1 displays the characteristics of

the relevant parts.

Part Material Dimensions

Cantilever beam Aluminum 6061 320×20×6 mm

Material sample, beam (st) Steel ASTM-A36 15.3 mm diameter, 1.6 mm thickness

Material sample, hammer (st) Steel ASTM-A36 15.4 mm diameter, 1.5 mm thickness

Material sample, beam (p1) Daplen EE188HP 15.9 mm diameter, 2.6 mm thickness

Material sample, hammer (p1) Daplen EE188HP 15.9 mm diameter, 2.3 mm thickness

Shaker connector rod Steel grade 8.8 M6 diameter, 129 mm length

Table 1: Name, material and dimension of main parts of the experimental setup

The test rig was used in two experimental setups:

- One simplified setup for the modal analysis, which was used to measure the

eigen frequency and the damping of the structure. In this setup, the

electrodynamic shaker was disconnected, and the shaker connector and

counter sample were removed. This way the beam could vibrate freely. In this

setup, only accelerations were captured.

- The main setup for the rattle testing. The cantilever beam was connected and

excited by the electrodynamic shaker. Counter sample was fixed to an impact

hammer. Force and sound was also measured in this setup.

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The experiments were performed in a semi-anechoic chamber at room temperature.

Acceleration data was acquired from two accelerometers (Bruel & Kjaer TYPE 4524B

triaxial CCLD piezoelectric accelerometer) glued to the beam. The shaker point

accelerometer was fixed on the connection surface of the electrodynamic shaker. The

impact point accelerometer was fixed to the cantilever beam next to the sample

carrying bolt. The positions of both accelerometers are marked on Figure 1.

Figure 1: Annotated photograph of the experimental setup. Simplified model for the modal analysis (left). Main setup for the rattle testing (right).

The impact hammer, which served as a fixture for the counter sample, captured

impact forces. Sound was recorded with a binaural headset (HEAD Acoustics BHS

II) placed on an artificial head (HEAD Acoustics HMS IV). The data acquisition was

done at a sampling frequency of 48 kHz using SQuadriga II frontend from Head

Acoustics.

The electrodynamic shaker was driven by an MB Dynamics SL500VCF amplifier for

which the signal was generated by MB Win2K5 vibration control system.

Modal measurements

The modal measurements, performed during the present thesis work, were based on

free vibration of the structure, on its first eigen frequency. In order to have a free

vibration, a simplified setup was used, described in the previous subsection (Figure

1 - left). The beam was excited by imposing a load at its tip as an initial condition,

and then unloading. The measuring system also described in the previous subsection

measured the acceleration of the beam at the impact and shaker points. The beam’s

fundamental frequency is obtained by performing a Fast Fourier Transform (FFT)

on the resulting acceleration curves. In order to increase the accuracy of the

measurements, the experiment was repeated three times.

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Figure 2: Experimental eigenvalue analysis result

Time domain measurements

As explained in section 3, the time domain correlation was split into two phases, so

it required two control signals to correlate to. However, it was possible to use the

same measurement to extract both of these signals. That is because the signal with

which the beam was excited is a 10 Hz sine wave that amplifies gradually from

stationary state until the acceleration attains the pre-set target amplitude of the

measuring sequence (the used sequence had a target acceleration of 0.05 g, see the

appendix about file naming conventions). Therefore, impact between the

counterparts was not attained until the beam tip displacement was equal to the gap

size (the used sequence had a gap size of ~2 mm, see section 8.3). This made it

possible to obtain the required excitation curves from the same measuring sequence.

The acceleration data was measured near the impact point, and near the shaker

connector rod, as stated previously. Impact forces were measured with an impact

hammer, similarly explained in the previous section.

As mentioned in section 1.1 , the present work is a part of a doctoral thesis aiming to

also investigate the connection between rattle variables and sound annoyance levels.

Therefore, sound recordings were performed during these tests. These recordings

were not used in the correlation part, neither in the sensitivity analysis. However,

they helped to understand the behaviour of rattle events, and even gave some

guidelines for the frequency range that should be analysed in the results. This use of

the sound data is expounded in section 9.1.

Signal processing

In the experiment, as written earlier, accelerometers were used to capture the

dynamic behaviour of the system. The measured displacement values were used for

the validation of the model and the parameter study. The displacement data, unlike

the acceleration data, was less dependent on the numerical noise, and therefore

easier to interpret and asses the correlation in the time domain phase. The data was

obtained by integrating the acceleration. However, this introduced a drift in both the

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velocity and displacement curves as a result of accumulated errors of the numerical

integration and noises present in the measured data.

Figure 3: Unfiltered displacement-time graph of impact point. Showing the dominance of drift compared to the magnified part with real vibrations

The signals were analysed with the aim to choose filters and frequencies to filter.

Assuming that the presence of noise is constant throughout the measurement, the

pre-impact part of the signals proved to be the best to analyse, since they only

contained a clear 10 Hz excitation (for the chosen measurement, 5 and 7 Hz were

also measured) and the noise to be filtered. FFT was applied to the pre-impact part

to analyse characteristic frequencies of the noise. The possible sources of these errors

and noises were identified as:

- Ground loop of data acquisition device and signal amplifier (~50 Hz)

- Electromagnetic field of signal amplifier, electrodynamic shaker, data

acquisition device, power sources (~50 Hz)

- DC offset due to not accurate zeroing of the data acquisition device (Not visible)

- Vibrations above the accelerometers’ frequency range (~4100 Hz)

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Figure 4: Acceleration-time graph for a typical measurement (top), pre-impact part analysed with FFT (bottom)

These errors require different types of filtering depending on their nature or

frequency. The objectives of the signal processing are the following to result a good

baseline signal thus enabling further work:

- Eliminate drift

- Filter the identified noises which have an effect on the result

- Keep or improve the shape of the curves near impact events

- Eliminate or avoid phase errors during integration and filtering

The following subsections describe the applied or tested filters addressing the

identified problems. All the signal processing was done in MATLAB R2015b.

Pre-impact Impact

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Mean removal

The DC offset of the raw signal was the most straightforward to filter. The signal was

simply translated along the y-axis. The extent of the translation was calculated as the

mean value of the raw signal, which was based on the nature of the experiment. The

cantilever beam is fixed to the base of the rig, therefore the sum displacement and

the final velocity of the structure is zero during the experiment. This implies that the

mean value of the acceleration should also be zero, to keep the initial zero value of

both displacement and velocity.

Despite the fact that this error was small compared to the measured acceleration

values, it is still essential to filter, as the signals are relatively long (between 10-30

seconds) and even these small errors can accumulate due to the double integration.

Butterworth filter

Since filtering out the identified noises does not completely eliminate the drift in the

displacement-time curves due to other factors – such as the accumulating numerical

error – it was necessary to filter the integrated curves. Therefore a high-pass filter

was needed. Butterworth was chosen as a popular filter for similar applications. Both

2nd and 3rd order high-pass filters were tried, and cut-off frequency was also varied.

The results with cut-off frequency of 1 Hz showed that the frequency content of the

drift is not low enough to get good results. Increasing the cut-off frequency to 8 Hz

eliminated the drift as hoped, but its proximity to the excitation frequency (10 Hz in

this case and all presented figures) was undesirable, especially since other excitation

frequencies are below this value (5 and 7 Hz).

Figure 5: Different Butterworth high-pass filter settings applied on curve introduced in Figure 3. Zoomed on the whole length of the curves to assess drift elimination.

Since these displacement-time curves serve as a references for the correlation work

of the project, preserving their shape during the impact events is just as important if

not more as eliminating the drift. Therefore it was essential to check the form of the

impact bounces by comparing the filtered and unfiltered signals. The unfiltered

signal that was presented in the previous sections has a local minimum where the

drift does not have an effect on the shape, thus can serve as a baseline (see Figure 6).

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Figure 6: Different Butterworth high-pass filter settings applied on curve introduced in Figure 3. Zoomed on individual impact events to assess distortion of the different filters.

The figure above shows two big problem with this kind of filtering. First depending

on the proximity of the cut-off and the excitation frequency and the order, there is a

phase error in the filtered curves which has different effect on the excitation and the

impact part of the curves. This results that the impact seems to slide along the sine

curve of the excitation and impact seemingly happens after the minimum value of

displacement which is impossible in real life.

The second problem is that as the order of the filtering is increased and the cut-off

frequency is closer to the characteristic frequencies there is a distortion in the signal,

mostly visible on the upper peak of the sine wave.

Both these problems make classical RF filters unsuitable for this task, therefore they

were not used for the final signal processing codes. In the next sections other

approaches are described.

Moving average filter

The previous subsection showed that the ideal filter for this application should have

zero phase shifting and no distortion on the signal. At the same time its main purpose

is to filter the low frequency drift, while knowing relatively lot about the

characteristics of the real-life displacement-time curves, and therefore the desired

characteristics of the filtered displacement-time curves, such as:

- Due to the periodicity and the constant zero average velocity of the signal the

displacement between any time moments one period apart is zero

- The signal is perfectly symmetric to the time axis prior to the first impact, and

close to symmetric during the impacts

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These characteristics impose that the moving average of the real-life curve should be

zero, therefore the moving average of the measured signal could be used for filtering.

This was done by first calculating a moving average curve with a window size of one

period of excitation (that is 0.1 s for the 10 Hz measurement) and then subtract this

calculated curve from the unfiltered one. The theoretical result of these operations is

a curve with constant and zero moving average.

Figure 7: Removed moving average filter applied on curve introduced in Figure 3. Zoomed on individual impact events to assess distortion of the filter.

On Figure 7 it can be seen that the filter did not removed the drift perfectly, but gave

similarly good results to the 3rd order Butterworth filter with cut-off frequency of 8

Hz. However, the distortion of it is much smaller compared to all previous methods.

Omega arithmetic

As a result of further literature study (8), and with the help of the examiner, one

more non-traditional filtering method was tried. It is based on a FFT algorithm

which makes possible to integrate and filter the signal in the frequency domain, and

after an inverse FFT to obtain the filtered signal in time domain. This filtering

method is called ‘omega arithmetic’ by Prosig the publisher of the referenced paper,

where they explain this definition as:

“Why the name omega arithmetic? The answer is very simple. We are dealing with

frequency, f, which we commonly measure in Hz (formerly cycles/second).

However mathematically one uses the Greek omega character, ω , as the frequency

in radians/seconds and where of course ω = 2πf . As illustrated later the translation

between acceleration, velocity and displacement spectra just involves simple

multiplication and division operations with ω . Hence the name omega arithmetic.”

A major advantage of this method is the freedom in the filtering, as by FFT the signal

is reconstructed by a summation of its frequency components, each of these

components can be altered or eliminated. Furthermore the modification of the

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components does not have effect on the neighbouring components or causes phase

shift in the inversed signal.

These properties made a more sophisticated filtering possible than what was

presented in previous sections. Since the proximity of the filtered and unfiltered

frequency components does not cause any distortion in the final signal the drift could

be filtered by eliminating components between 0 and 8 Hz. Due to the same reasons

it was possible to filter frequencies freely on the middle of the frequency range and

therefore eliminate the noises identified in the beginning of this section. After a few

trial runs filtering out 28 to 60 Hz proved to be the most efficient while keeping the

important details of the impact events.

Figure 8: Omega arithmetic filter applied on curve introduced in Figure 3. Zoomed on individual impact events to assess distortion of the filter.

The results show that omega arithmetic is able to filter all the drift while maintaining

the shape of the curves. Moreover, it also makes it possible to filter the noises

described in the introduction of this section. Since the part of the signal presented in

Figure 8 was mainly chosen to check the drift filtering and the distortion of different

filters, it is not the best choice to examine rattle events as it consists of one single and

small impact. Therefore it worth to check and discuss other parts of the signal, which

later will be used for correlation work, to see if the filtering distorted them.

An ideal part of the signal is therefore where the samples bounce on each other, so

they have multiple local minima whose displacement should match the gap size and

so the position of the counter sample. This provides an opportunity to assess the

filtering as these local minima of bounces should be on the same line parallel to the

time axis of the graph.

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Figure 9: Omega arithmetic filtered signal showing bounces during impact event.

Figure 9 shows that the filtering fulfilled all the objectives determined in the

beginning of this section.

- Completely eliminated drift

- Filtered the identified noises which have an effect on the result

- Improved the shape of the curves near impact events, bringing local minimums

of impact moments to a straight line parallel to time axis

- Performed the whole filtering and integration process without introducing any

phase error

The final MATLAB script is attached in the appendix, including the optional use of

filters introduced in earlier subsections, and comments explaining the script and its

use. The processed signal serves as a good baseline for the following correlation work.

Table 2: Comparison of different filtering methods

Setbacks and Solutions

From this point onward, the work on the tasks assigned for this project will be

presented and explained. Up until the previous section, the discussion was

concerning the already existing results that had to be processed. Those were expected

to be ready for use, so the time it took to do all the processing was not part of the set

time-plan. Therefore this section explains all the setbacks encountered, and the way

23

they were overcome, and helps understand why the initial work-plan was distorted,

and another one, based on prioritization and limitations, had to be established.

The main issues faced are the following five.

1. Rattle was tested in the aim of getting qualitative sound results. So, although

the acceleration was recorded, they were not checked for errors because they

were not used. Upon checking those and integrating to get the required

displacement curve, a shape distortion in the shape of the curve, along with a

big drift, were found. This resulted in a 3 month period of trying out filtering

techniques to fix the shape of the signals, attempting to recreate the test to check

for possible sources of error, considering re-tests, and contacting people who

have possibly encountered this problem. Finally, a few online sources presented

the Omega Arithmetic as a solution, which was used to overcome the signal

issues. All the signal processing details are in section 5.

2. The datasheet of the accelerometer with which the measurements were

recorded specified the range of frequencies with which it gives accurate results.

The measured frequencies, however, exceeded the accelerometer specifications.

3. The signals had another problem. There was a factor of 10 difference in the units

which was assumed to be a wrong setting in the recording software during

measurement. The unit in the measurement files was m/s2 but, knowing the

distances, especially for the gap, chosen in the setup, the numbers appeared to

must have been recorded in g. This was an uncertainty which had to be assumed

and overcome. Upon trying to re-test and check Artemis, the recording software,

it appeared that the default acceleration unit setting was g, which further

enforced the assumption.

4. The signals used to excite the shaker were named with the gap size used during

each experiment. Those sizes, however, were not as precise as was needed for

the simulations. For example, a gap size of 2 mm was in the file name, but the

recordings at the impact point accelerometer showed a bigger gap size. The

determination of the actual gap size is detailed in section 8.3.

5. The first eigen frequency that was supposedly recorded during the modal

measurements was not matched when the CAE modal analysis was performed.

Trying to overcome this problem led to the recreation of a setup which did not

include the shaker and which is described in section 4.1.

FEA model

During the study, two solvers were used: Abaqus/Standard for the eigenvalue

extraction and Abaqus/Explicit was used for the time domain simulations. The

following subsections describe the model in details.

24

Mesh

The finite element model was built in ANSA software with a mixture of solid, shell

and beam elements, all of them being first order. The mesh size varied between 1 and

2 mm. The type and size of elements were chosen based on similar models from the

field of NVH. An aim was set to only change these parameters, if they were required

for the sake of correlation with physical measurements. The model totally consisted

of 2742 solid elements and either 1040 or 662 shell elements, depending on the

samples’ meshes (explained in section 9.1). The model was prepared for running the

solutions with Abaqus solver. Below is a detailed explanation of the elements used

for modelling different parts of the model.

- The beam was modelled with 2D shell elements (S4R). Using 3D elements gave

no higher accuracy, while increasing the CPU time.

- The bolt and nut pair, holding the samples and the samples themselves were

modelled with 3D brick (C3D8) and Penta (C3D6) elements. Since small details

of these parts were neglected, the density was scaled up to match the original

mass.

- The threaded rod that connected the beam to the shaker was modelled with 1D

beam elements (Abaqus B31).

- Small parts with negligible contributing geometry, like accelerometers and nuts

of the shaker connector rod were modelled as point masses. The equivalent

mass values were based on measurements and they were validated within the

first steps of the model correlation to check if they properly represented the

parts.

- The connection between the shaker connector rod and the beam was modelled

with rigid multi point constraints (MPCs). The mass point representing the

accelerometer was also connected to the beam with rigid MPCs.

Boundary conditions

The boundary conditions in the model were defined accordingly to the experimental

setup.

- The end of the beam at the support was constrained in all 6 DoF since it was

rigidly clamped in the test setup.

- The nodes of the counterpart sample on the hammer side were constrained in

all 3 DoF (3D elements were used for these parts). The effect of elasticity

coming from the hammer support was investigated and was neglected due to

its minor effect on the results.

- The shaker connector rod, at the end where it was fixed to the shaker, was

constrained in all DoF, except the Z direction, which was the excitation

25

direction in the FEA model. The Z direction had a prescribed displacement as

the input signal that will be discussed later.

Figure 10: Finite element model used for the correlation and sensitivity analysis of rattle simulations

Excitation

In order to make the simulations computationally efficient (keeping in mind that

over 100 different runs were required) only small sections of the signals were used.

Ideally, only the impact events would be simulated, starting the runs just before the

samples come into contact. Unfortunately, this was hard to achieve since the initial

conditions were unknown and calculating them was not straightforward. The

displacement, velocity and acceleration values of the beam’s nodes are dependent on

both the excitation and the free vibration of the beam. The most convenient way to

calculate these values is to run a preceding simulation, which excites the beam from

stationary state and then capture the nodal values to be used as initial conditions.

Since this project had more computational capacity than time, the simulations

simply included this preceding part in every run. The time that was spent solving the

unforeseen signal processing problem had to be deducted from this task, where

learning how to use the restart files was required. However an option was left to start

the simulations from a restart file just before the impact, in case further batch runs

are required and CPU time becomes a bottleneck.

The sections of the signals were chosen so they provide a good baseline for the

correlation work and the sensitivity analysis. Which means that the evaluated rattle

criteria should be easy to observe in the chosen signal section measured at the impact

point. The section was chosen based on the displacement data at the impact point,

but logically the shaker point displacement was used as an excitation. The

displacement was prescribed at the end of the shaker connector described in section

7.2.

26

Although the signals to be used as excitation were already processed, they could not

be applied directly to the FEA model as a boundary condition, since that would result

in a jerk. That is because the section of the signal gives either an initial velocity or

displacement depending on the starting point along the curve. A solution could be to

use initial conditions for either displacement or velocities, but the problem with this

solution was already discussed in the first paragraph. To overcome the problem of

initial conditions, a “start curve” was introduced and attached to the actual signal.

This start curve had to be generated so it starts with zero displacement, velocity and

acceleration and connects to the signal curve with C2 continuity to avoid any jerk at

the connection point (Figure 11). In order to avoid any undesired vibration of the

beam, the curve had to have a certain minimum curvature due to the inertia of the

beam. A sudden change in displacement would bring the beam into vibration even if

the curve itself is continuous.

Mathematically the simplest function that could easily fulfil all these boundary

conditions was a sine function. The fitting was ensured by solving the following

system of equations:

{

𝑎 ∗ 𝑠𝑖𝑛(𝑐 ∗ 𝑡0 + 𝑐 ∗ 𝑏) + 𝑎 = 𝑠𝑖𝑔𝑛𝑎𝑙(𝑡0)𝑑

𝑑𝑡(𝑎 ∗ 𝑠𝑖𝑛(𝑐 ∗ 𝑥 + 𝑐 ∗ 𝑏) + 𝑎) =

𝑑

𝑑𝑡𝑠𝑖𝑔𝑛𝑎𝑙(𝑡0)

𝑑2

𝑑𝑡2(𝑎 ∗ 𝑠𝑖𝑛(𝑐 ∗ 𝑥 + 𝑐 ∗ 𝑏) + 𝑎) =

𝑑2

𝑑𝑡2𝑠𝑖𝑔𝑛𝑎𝑙(𝑡0)

Where a, b and c are coefficients, which are free to change to solve the system, signal

is the signal section and 𝑡0 is the time of the connection point, which has to be chosen

as an input.

27

Figure 11: Position-time graph for test data showing the measured impact point displacement, shaker point displacement (used for excitation), initial start curve and scaled start curve. The annotated sections mark the simulation phases, not the measurement

The curvature was adjusted by scaling this start curve along the time axis (Figure 11)

so that at the connection point it is unaffected to keep the C2 continuity and

increasing the scaling factor with the square of the distance from the connection

point.

Material and property cards

The finite element model consisted of three types of property cards. One shell

property for the cantilever beam, describing its thickness of 6 [mm], solid properties

with the corresponding material cards, and the beam property (B31) for the shaker

connector rod. For the beam elements of the rod, the material and cross sectional

properties were also included in the property as: 7.85e-9 [t/mm3] density, 2.5 [mm]

radius of circular cross section, 210 000 [MPa] elasticity modulus and 80 796 [MPa]

shear modulus.

Since the modelled part of the setup consisted of only steel and aluminium parts, two

groups of materials were used. The steel with 210 000 [MPa] elasticity modulus and

0.3 [-] Poisson’s ratio, and varying density, as it was required to scale the mass of

parts because of geometric simplifications. The baseline density was 7.85e-9 [t/mm3].

The aluminium parts had only one material property with 68 900 [MPa] elasticity

modulus, 0.33 [-] Poisson’s ratio and 2.609e-9 [t/mm3] density. These values were

based on 6061 aluminium alloy, and were validated by the eigenvalue analysis.

28

For the sensitivity analysis, the sample material was changed to polypropylene from

“Borealis Daplen™ EE188HP” which has a modulus of 1850 [MPa], 0.42 [-]

Poisson’s ratio, and 1.02e-9 [t/mm3] density.

Contact modelling

To model contact, four settings are important to define: the contact type, the contact

surfaces, the mechanical constraint, and the interaction.

Two types of contact exist in ABAQUS. They can be used individually or together.

Selecting “contact pair” requires the user to manually select the surfaces that are

expected to come in contact. On the other hand, the “general contact” formulation

allows the definition of an area of, or the whole, model and locates any contact within

that region as the simulation runs. In this thesis’s FEA model, the two surfaces that

come in contact are known and clear, so the contact pair type was picked for the

baseline simulations which had St-St, Shell, Pen, CP, el-el, no material damping,

0.03 contact damping, 0.2 friction settings (see Abbreviations for the meaning and

the following sections for the values).

Next, the two surfaces that come in contact, denoted as “master” and “slave” in CAE,

have to be defined. The master can only be chosen to be element-based, but the slave

can be either element or node-based. Using either of the two is dependent on the

problem under investigation (9). Both surfaces were chosen to be element-based for

the baseline simulations as it is the default setting in ABAQUS.

The way ABAQUS/Explicit calculates and measures the contact is chosen in the

“mechanical constraints” field. One of the two methods can be selected. The hard

kinematic contact does not allow any penetrations by using a kinematic

predictor/corrector contact algorithm. The penalty contact method searches for

penetrations and applies forces, calculated as a function of penetrations, to the slave

nodes to eliminate penetration. ABAQUS/Explicit allows the definition of either of

the two constraints with the contact pair type, but with general contact, only the

penalty enforcement is possible. For the first simulations, the kinematic method,

which is the default with contact pair definition, was used.

Finally, a predefined “interaction” must be specified for the contact, where

properties such as friction (using the Coulomb model) and contact damping can be

edited. For the first simulations, the default ABAQUS/Explicit values were kept.

Therefore, there was no friction between the surfaces, and the contact damping

coefficient, which is given as a fraction of the critical damping coefficient, was 0.03.

A relevant note is that contact damping is not available for hard kinematic contact

in ABAQUS/Explicit.

Several other options are available in the contact module of ABAQUS/Explicit for

more detailed modelling. In this study, the above mentioned friction, contact

damping, contact type, surface definition, and mechanical constraint are the

investigated parameters that are later varied for the sensitivity analysis (section 9.1).

29

Solver Settings

As written in the introduction of the section, two solvers were used during the thesis.

Abaqus/Standard was used for the validation step with modal analysis, using the

Lanczos method and extracting the first 10 modes. Similarly to the physical tests the

BCs at the shaker and the shaker connector rod itself were disabled for modal

analysis. Modal and nodal outputs were requested to obtain eigen frequency values

and also the shapes of different modes.

The dynamic simulations were run in Abaqus/Explicit solver. The decision of using

explicit solver over implicit was based on preliminary assumptions about the impact

velocity, that was higher than the suggested limit for implicit solvers (10). The stable

time increments were chosen automatically based on the critical element in each

increment. No mass scaling was used since the high velocities would result in poor

accuracy. All other settings were left default in the solver.

The explicit runs were split into two time steps in order to help eliminate any

undesired vibration in the beam due to the excitation. The problem was already

explained in 7.3. That part focused on the excitation signal, while this subsection

aims to help the problem with introducing material damping in the first time step:

that is the start curve and excitation sections marked on Figure 11. A mass

proportional damping was applied to the beam material with a coefficient value of

43.35, which corresponds to 0.5 times the critical damping coefficient at the first

eigen frequency of the beam (31.27 Hz). The calculations for damping coefficients

are explained in 9.1.2. The contact interfaces were disabled for the first time step to

reduce the CPU time of the runs.

The second time step contained the impact section marked on Figure 11 (starting at

0.2035 s in simulation time and ending at 0.26 s). In this step, the material damping

of the beam material was adjusted to the value studied in the given run. At the same

time, contact interfaces were enabled.

The material damping in the first time step eliminated the vibrations in the beam.

The variation of material damping is not available through any pre-processors, only

through input files as a keyword only option. It required the definition of a tabular

damping coefficient input that was dependent on a field variable, changed at the

beginning of the second time step. Since the use of this function is not

straightforward, the simplified input file of the runs is attached in the Appendix.

During the explicit runs different outputs were requested described in Table 3. The

outputs were written in either history or field outputs depending on their nature.

Energy and contact outputs were requested but not used in this paper. Energy

outputs aimed to investigate the dissipated energy during the impacts but proved to

be insignificant as a rattle criteria. The contact outputs aimed to analyse the contact

outputs, but the reaction force measured on the boundary conditions proved to be a

more similar solution to the experimental setup.

30

Table 3: Output requirements by categories for both time steps

Model validation

The method of the model validation used is summarized here and explained in depth

in the following subsections.

1. Perform a modal analysis of the beam to ensure the CAE model is a good

representation of the experimental setup.

2. Perform a dynamic analysis of the beam without impact, to study its response

to the shaker excitation.

3. Perform a dynamic analysis of the beam with a single impact to minimize the

amount of variables while still having a well correlated contact model.

Modal correlation

As a first step of ensuring the validity of the model before the planned impact

correlations, the mass and dimensions of each part were matched with the FEA

model, and material properties were set according to the material datasheets. Then

the Young’s modulus and Poisson's ratio of the beam were modified in reasonable

range to improve the correlation with the empirical data. A modal analysis was

finally run in ABAQUS/Standard and gave a first eigen frequency of 31.334 Hz, as

shown in Figure 12. Compared with the measurement result (Figure 2), the error is

0.2%, which meant a valid model was obtained, and the second part of the

correlation could start.

Nodal output Time step #1 Time step #2

Acceleration (A) Yes Yes

Velocity (V) Yes Yes

Displacement (U) Yes Yes

Reaction force (RF) Yes Yes

Element output Time step #1 Time step #2

Strain for non-linear analysis (LE) Yes Yes

All stress components (S) Yes Yes

Energy output Time step #1 Time step #2

"Artificial" strain energy (ALLAE) Yes Yes

Total strain energy (ALLIE) Yes Yes

Kinetic energy (ALLKE) Yes Yes

Total energy balance (ETOTAL) Yes Yes

Contact output Time step #1 Time step #2

Contact normal force (CFORCE) No Yes

Contact pressure (CSTRESS) No Yes

Force components from contact pressure(CFN) No Yes

Force magnitude from contact pressure (CFNM) No Yes

Force components from contact pressure and friction (CFT) No Yes

Force magnitude from contact pressure and friction (CFTM) No Yes

31

Figure 12: Eigenfrequency vs. time curve showing the first eigenfrequency of the CAE model

Time domain correlation before impact event

As mentioned, the nut holding the shaker rod tightly to the beam was modelled as

an MPC. MPCs are constraints that allow the restriction of a region’s nodes to the

motion of a single control point (9). In the beginning, the control point was placed

at the middle of the nut, at a distance of 5.5 mm from the beam surface. The resulting

displacement vs. time curve measured at the impact point accelerometer before

impact did not have an amplitude that - as a fraction of the shaker displacement

amplitude - corresponded to the expected value. That was found as a result of the nut

not being tight enough, or the offset between the diameter of the beam hole and rod,

or both. In addition, the displacement vs. time curve at the accelerometer impact

point had breakpoints preventing it from being a smooth sine wave (can be seen in

Figure 13 and Figure 14). Therefore, as a first step, the location of the control point

of the MPC was varied to fix the mentioned ratio. The variation first involved

increasing the distance to 8 mm, before noticing that the distance must actually be

decreased. The best fit was at 2.28 mm. Only 3 variations are shown in Figure 13 for

clarity.

32

Figure 13: Curves showing the variation of the distance between the beam and the MPC control node, in comparison with the measurement curve

Then, the end point of the start curve (explained in 7.3) was iterated to smoothen the

observed breakpoints. The best iteration found was when the end point was chosen

towards the first peak of the input signal (Figure 14).

Figure 14: Curves showing the effect of the variation of the end point of the start curve (used on the input signal)

Finally, as a third step, further smoothing was needed and was done by applying a

material damping of value 43.35 Hz. After that, the curves had to be scaled to obtain

33

the right gap size, a process that is explained in section 8.3. The final correlation

before impact is in Figure 15. As visible there is a time shift between the

measurement and simulation results. This shift was not investigated further since

the displacement curves showed a good correlation near the impact events presented

in the following sections. Moreover the difference is decreasing towards the second

local minimum thanks to the mass proportional damping described in section 7.6.

As visible in Figure 17 the time shift during the impact event decreased to ~0,001 s.

Figure 15: Displacement vs. time curve showing the correlation between the measurement and CAE simulation results before impact

Gap Size Determination

One requirement for the correlation is to know all the parameters of the physical test

setup, since the aim of the correlation work is to simulate the same setup and obtain

the results of the experiments. As written in section 6, although the gap size was

documented during the measurements, it did not have the desired precision. Since

knowing the accurate gap size was crucial for the next section, since it has a

significant effect on the results, a method was needed to obtain it from the existing

data.

The final solution used both the simulations from previous steps and the filtered

measurement data. The bases of the method is, since the measurements had a

continuously increasing amplitude with a constant gap size, that before the first

impact the local maximum of the displacement-time curve is very close to the gap

size. The problem with this that the displacement, which is calculated from the

34

measured accelerations, was not measured at the impact point, therefore the

displacement of this measured point (accelerometer displacement) is less than the

gap size (or impact point displacement) when the sample is touching the counter

sample. The problem is illustrated on Figure 16.

Figure 16: Illustrating the displacement difference between accelerometer and impact point displacements. Green model represents initial position of the beam, red represents the bended position of the beam. Shells are displayed with their thickness, and displacements are scaled up 10 times to better illustrate the problem.

The problem was solved using the simulations without impacts already introduced

in the previous subsection. Since in the simulation results any node’s displacement

can be measured it is perfect to convert the accelerometer displacements to impact

point displacements. Therefore, the local maximum of measured accelerometer

displacement just before the first impact could be converted to impact point

displacement that should be equal to the gap size. Keeping in mind that the

amplitude is increased by ~0.01 mm per wavelength and the local maximum can be

measured just half wavelength before the first impact, due to the symmetric signal,

this method theoretically gives a 0.005 mm accuracy. Although this accuracy is

probably reduced by undiscovered errors and errors from signal processing, it is still

assumed to be more accurate than the documented gap size precision.

The determined gap size were 2.48 mm for steel-steel, 2.22 mm for plastic-steel (the

name plastic was used for Daplen EE188HP polypropylene as the only plastic

material during the project) and 1.93 mm for plastic-plastic material pairs.

35

Time domain correlation at impact

Figure 17: Displacement vs. time curve showing the correlation between the measurement and the chosen baseline CAE simulation results at impact

The time domain correlation at impact did not involve any editing more than what

was explained in sections 8.1 and 8.2. The shapes of the measurement and the CAE

simulation result curves displayed a good correlation that completed the third

objective of the project, and allowed the start of the parameter variation and

sensitivity analysis.

Sensitivity Analysis

After the first part of the project was done by establishing the desired correlations, a

sensitivity analysis was performed. The use of the word “parameter” in what follows

is restricted to the independent specifications that were varied in ABAQUS. The word

“criteria” will refer to the dependent variables whose responses to parameter

changes were analysed. The aim was to understand the effect of material and model

parameters on the criteria that characterize rattle sounds.

The parameters investigated in the sensitivity analysis can be categorized as either

'structural and material properties' or 'CAE-specific options'. The CAE-specific

options are explained below using ABAQUS terminology (9), but equivalent terms

can be found in similar solvers. The parameters and their explanations are given in

section 9.1.

The criteria studied play an influential role in the generation of sound according to

(11). They are presented and explained in section 9.2.

Measurements for Steel and Polypropylene, which are two common materials found

in car interiors, were carried out in the test-rig. Consequently, rattle between two

36

steel material samples (St-St), two polypropylene plastic material samples (P-P) and

a polypropylene and a steel material sample (P-St) was simulated in ABAQUS.

Further details of the material properties are available in Table 1 and section 7.4. The

material appears in the comparison tables and discussions although it is not a

parameter.

Nominated parameters and the ranges

Element type for material samples

The difference between the use of solid and shell elements in contact interactions

was of interest. That is why either the whole of both material samples was meshed

with 3D brick and penta elements (C3D8, C3D6), referred to as "solid" in the

following sections, or the surface was meshed with 2D shell elements (S4) while the

rest was in solids. Figure 18 shows the two different meshes. In the result tables

(Table 6 onward), this parameter is referred to as “Sample Mesh” for convenience.

Figure 18: Meshing the material samples with (left) solid elements, and (right) shell elements only on the surface of the samples

Material Damping

Rayleigh damping was defined for the material card of the beam. It is a superposition

of a mass and a stiffness damping as shown in the equation:

[C] = α[M] + β[K] (1)

where the stiffness proportional coefficient damps out systems with high frequencies,

and the mass proportional coefficient damps out systems with low frequencies, as

can be seen in the equation below.

ζ =α

2ω+β

2ω (2)

In this study, three different options were investigated for the material damping

parameter: one with no damping; one with the stiffness-proportional coefficient of

Rayleigh damping set to zero; and one with the mass-proportional coefficient of

Rayleigh damping set to zero.

37

The mass-proportional damping coefficient (α) was calculated from the damping

ratio recorded during the eigenvalue test described in section 4.2. Using the

logarithmic decrement δ to get the damping ratio 𝜁, α is calculated from equation 2

to a value of 0.8418 with β set to zero.

𝛿 =1

𝑛ln (

𝑥(𝑡)

𝑥(𝑡 + 𝑛𝑇)) =

1

8ln (

0.0007954

0.0007142) = 0.01346

𝜁 =𝛿

2𝜋= 0.0021423

The stiffness proportional damping (β) was calculated as 5% of the target time step,

based on a suggestion in the literature (12), giving a value of 6.627e-9.

The remaining parameters, “Contact type definition”, “Contact mechanical

constraint”, “Contact damping”, “Contact surfaces” and “Friction”, are explained in

more detail in section 7.5, and briefly stated below with their abbreviations.

Contact type definition

Simulation with both contact type definitions, “contact pair” and “general contact”,

were run to study their effects. In the result tables (Table 6 onward), this parameter

is referred to as “Contact Definition” for convenience.

Contact mechanical constraint

The two contact methods are the kinematic and the penalty. In the result tables

(Table 6 onward), this parameter is referred to as “Contact Mechanics” for

convenience.

Contact Damping

Contact damping was given as a fraction of the critical damping coefficient and was

varied from the default value of 0.03 to the values 0.05, 0.1, and 0.2.

Contact Surfaces

The two variations of contact surfaces investigated in this study are denoted “el-el”

and “node-el”. El-el refers to the case where both sample surfaces are defined as

element-based, and node-el refers to when the slave surface is defined as node-based.

Friction

Friction was either zero or had a coefficient of 0.2 to study its effect.

38

Evaluating the Fundamental Rattle Criteria

The criteria studied in the sensitivity analysis are: impact velocity, height of the

biggest bounce upon impact, duration of the bounce (and frequency), peak impact

force, and the duration of impact.

After running the simulations with different parameter combinations, the results

were post-processed in META. The criteria of interest were extracted from the

relevant plots at the relevant nodes, shown in Figure 19.

Figure 19: Figure showing the two nodes at which the CAE results were plotted and analyzed Note: The model colors have been changed for better visibility)

39

The impact velocity, height of biggest bounce, and the duration (and frequency) of

the biggest bounce were extracted from the plots displaying the displacement at

point B vs. time. The reason for choosing this point is that the accelerometer was

placed at this point in the experiment, therefore this point of the FEA model has to

be investigated to make the findings comparable to the experiment. The impact force

and duration of impact were extracted from the plots displaying the force at point A

vs. time. This point was also chosen based on the experiment since the acoustic

hammer was measuring forces at this point, and the force data was used to determine

duration of impact for the experimental data.

Figure 20: Extracted points marked on plotted displacement in Z direction at point B (blue) and hammer force in Z direction at point A (orange). The curves belong to v64_stst_1struct_p248_expl026_nodrift14693_scaled12539_shell_pen_gen_elel_nomatdamp_contdampoc999_nofric_nosslide.odb

The points are extracted and moved to an excel sheet where the values for the criteria

are calculated, and the all data is organized and coded such that every parameter and

rattle criterion can be filtered and rearranged according to alphabetical order and/or

increasing/decreasing order. This kind of arrangement helps analyse the results and

deduce the desired conclusions which are presented in section 10.

The general idea of the sensitivity analysis, which is to analyse the effect of selected

parameters (materials, element type…) on the chosen rattle criteria (impact velocity,

height of bounce…), is displayed in Figure 21 as a summary and for clarity.

40

Figure 21: A schematic of the sensitivity analysis: Nominated simulation parameters and evaluated rattle criteria.

41

Results of the sensitivity analysis and guidelines

MaterialsSample

mesh

Contact

definition

Contact

mechanicsDamping

Contact

damping

Contact

SurfacesFriction

Impact

velocity

[mm/s]

Height

of

biggest

bounce

[mm]

Duration

of

biggest

bounce

[s]

Frequency

of biggest

bounce

[Hz]

Ratio of

height of

bounce to

impact

velocity

[mm/s]

Peak

impact

force

[N]

Duration

of

impact

[s]

p-p Shell CP Kin Mdamp 0.03 el-el Friction -75.59 0.0395 0.00529 189.0 0.000523 22.66 0.00171

p-p Shell CP Kin Mdamp 0.03 el-el No friction -75.59 0.0452 0.00539 185.5 0.000598 20.82 0.00169

p-p Shell CP Kin No 0.03 el-el Friction -75.40 0.0395 0.00526 190.1 0.000524 22.02 0.00171

p-p Shell CP Kin No 0.03 el-el No friction -75.40 0.0450 0.00540 185.2 0.000597 20.63 0.00169

p-p Shell CP Kin No 0.03 node-el No friction -75.40 0.0498 0.00553 180.8 0.000660 26.53 0.00167

p-p Shell CP Kin Sdamp 0.03 el-el No friction -75.42 0.0450 0.00539 185.5 0.000597 20.08 0.00169

p-p Shell CP Pen Mdamp 0.03 el-el Friction -75.59 0.0318 0.00519 192.7 0.000421 21.50 0.00175

p-p Shell CP Pen Mdamp 0.03 el-el No friction -75.59 0.0332 0.00516 193.8 0.000439 20.53 0.00181

p-p Shell CP Pen No 0.03 el-el Friction -75.40 0.0317 0.00517 193.4 0.000420 21.36 0.00175

p-p Shell CP Pen No 0.03 el-el No friction -75.40 0.0329 0.00515 194.2 0.000436 20.43 0.00180




p-p Shell CP Pen Sdamp 0.03 el-el No friction -75.42 0.0332 0.00516 193.8 0.000440 20.38 0.00181

p-p Shell CP Pen Sdamp 0.2 el-el Friction -75.42 0.0316 0.00518 193.1 0.000419 21.29 0.00175

p-p Shell Gen Pen Mdamp 0.03 el-el No friction -75.59 0.0451 0.00538 185.9 0.000597 20.49 0.00169

p-p Shell Gen Pen Mdamp 0.2 el-el No friction -75.59 0.0451 0.00539 185.5 0.000597 20.49 0.00169

p-p Shell Gen Pen No 0.03 el-el Friction -75.40 0.0387 0.00525 190.5 0.000513 21.74 0.00172

p-p Shell Gen Pen No 999 el-el No friction -75.40 0.0416 0.00532 188.0 0.000552 22.07 0.00178

p-p Shell Gen Pen Sdamp 0.03 el-el No friction -75.42 0.0448 0.00537 186.2 0.000594 20.11 0.00169

p-p Shell Gen Pen Sdamp 0.2 el-el No friction -75.42 0.0450 0.00540 185.2 0.000597 20.10 0.00170

p-p Solid CP Kin Mdamp 0.03 el-el No friction -75.59 0.0559 0.00563 177.6 0.000739 27.91 0.00162

p-p Solid CP Kin No 0.03 el-el Friction -75.41 0.0441 0.00540 185.2 0.000585 31.42 0.00163

p-p Solid CP Kin No 0.03 el-el No friction -75.41 0.0557 0.00562 177.9 0.000739 28.39 0.00163

p-p Solid CP Kin No 0.03 node-el No friction -75.41 0.0557 0.00562 177.9 0.000739 28.00 0.00163

p-p Solid CP Kin Sdamp 0.03 el-el No friction -75.43 0.0557 0.00561 178.3 0.000738 28.26 0.00163

p-p Solid CP Pen Mdamp 0.03 el-el Friction -75.59 0.0322 0.00518 193.1 0.000426 25.53 0.00168

p-p Solid CP Pen Mdamp 0.03 el-el No friction -75.59 0.0461 0.00545 183.5 0.000610 24.04 0.00167

p-p Solid CP Pen No 0.03 el-el Friction -75.41 0.0319 0.00517 193.4 0.000423 25.53 0.00169

p-p Solid CP Pen No 0.03 el-el No friction -75.41 0.0459 0.00545 183.5 0.000609 23.98 0.00167




p-p Solid CP Pen Sdamp 0.03 el-el Friction -75.43 0.0320 0.00518 193.1 0.000424 25.51 0.00168

p-p Solid CP Pen Sdamp 0.03 el-el No friction -75.43 0.0459 0.00545 183.5 0.000609 23.95 0.00167

p-p Solid CP Pen Sdamp 0.2 el-el Friction -75.43 0.0320 0.00517 193.4 0.000424 25.24 0.00170

p-p Solid Gen Pen Mdamp 0.03 el-el No friction -75.59 0.0568 0.00564 177.3 0.000751 27.60 0.00161

p-p Solid Gen Pen No 0.03 el-el Friction -75.41 0.0444 0.00542 184.5 0.000589 30.59 0.00162

p-p Solid Gen Pen No 0.03 el-el No friction -75.41 0.0567 0.00563 177.6 0.000752 27.41 0.00161

p-p Solid Gen Pen Sdamp 0.03 el-el No friction -75.43 0.0566 0.00563 177.6 0.000750 27.31 0.00161

p-st Shell CP Kin Mdamp 0.03 el-el Friction -114.25 0.0514 0.00523 191.2 0.000450 58.56 0.00166

p-st Shell CP Kin Mdamp 0.03 el-el No friction -114.25 0.0833 0.00554 180.5 0.000729 53.05 0.00149

p-st Shell CP Kin No 0.03 el-el Friction -114.06 0.0524 0.00522 191.6 0.000459 54.96 0.00163

p-st Shell CP Kin No 0.03 el-el No friction -114.06 0.0815 0.00551 181.5 0.000715 50.38 0.00151

p-st Shell CP Kin No 0.03 node-el No friction -114.06 0.0942 0.00572 174.8 0.000826 62.54 0.00138

p-st Shell CP Kin Sdamp 0.03 el-el No friction -114.08 0.0820 0.00552 181.2 0.000719 50.20 0.00149

p-st Shell CP Pen Mdamp 0.03 el-el Friction -114.25 0.0647 0.00529 189.0 0.000566 47.64 0.00171

p-st Shell CP Pen Mdamp 0.03 el-el No friction -114.25 0.0780 0.00547 182.8 0.000683 46.52 0.00167

p-st Shell CP Pen No 0.03 el-el Friction -114.06 0.0630 0.00528 189.4 0.000552 47.42 0.00170

p-st Shell CP Pen No 0.03 el-el No friction -114.06 0.0773 0.00547 182.8 0.000678 45.98 0.00167




p-st Shell CP Pen Sdamp 0.03 el-el No friction -114.08 0.0773 0.00547 182.8 0.000678 45.79 0.00167

p-st Shell CP Pen Sdamp 0.2 el-el Friction -114.08 0.0628 0.00529 189.0 0.000551 47.21 0.00170

p-st Shell Gen Pen Mdamp 0.03 el-el No friction -114.25 0.0830 0.00558 179.2 0.000726 53.00 0.00148

p-st Shell Gen Pen Mdamp 0.2 el-el No friction -114.25 0.0833 0.00554 180.5 0.000729 52.98 0.00148

p-st Shell Gen Pen No 0.03 el-el Friction -114.06 0.0523 0.00525 190.5 0.000459 54.66 0.00164

p-st Shell Gen Pen No 999 el-el No friction -114.06 0.0821 0.00554 180.5 0.000720 48.75 0.00153

p-st Shell Gen Pen Sdamp 0.03 el-el No friction -114.08 0.0819 0.00551 181.5 0.000718 50.20 0.00150

p-st Shell Gen Pen Sdamp 0.2 el-el No friction -114.08 0.0819 0.00552 181.2 0.000718 50.22 0.00150

p-st Solid CP Kin Mdamp 0.03 el-el No friction -114.25 0.0603 0.00531 188.3 0.000528 60.80 0.00156

p-st Solid CP Kin No 0.03 el-el Friction -114.06 0.0725 0.00552 181.2 0.000636 70.27 0.00139

p-st Solid CP Kin No 0.03 el-el No friction -114.06 0.0587 0.00534 187.3 0.000515 62.14 0.00155

p-st Solid CP Kin No 0.03 node-el No friction -114.06 0.0590 0.00532 188.0 0.000517 61.97 0.00156

42

Table 4: CAE simulations run for the sensitivity analysis

Table 4 displays all the simulation runs in ABAQUS/Explicit for the sensitivity

analysis. Those results are analysed and grouped separately in this section to explain

the effect of different parameters on the criteria.

Although different material pairs were simulated, conclusions should not be deduced

from the differences between these results as the input signals for the shaker point

were also different. The inputs signals were based on the measurements and

unfortunately the gap size between these measurements varied. Since the signal

applied on the electrodynamic shaker was an amplitude sweep, different gap sizes

resulted in a different input amplitude at the moment of impact events.

p-st Solid CP Kin Sdamp 0.03 el-el No friction -114.08 0.0596 0.00530 188.7 0.000522 61.95 0.00156

p-st Solid CP Pen Mdamp 0.03 el-el Friction -114.25 0.0696 0.00544 183.8 0.000609 53.51 0.00157

p-st Solid CP Pen Mdamp 0.03 el-el No friction -114.25 0.0719 0.00551 181.5 0.000629 51.04 0.00158

p-st Solid CP Pen No 0.03 el-el Friction -114.06 0.0696 0.00543 184.2 0.000610 54.01 0.00157

p-st Solid CP Pen No 0.03 el-el No friction -114.06 0.0721 0.00549 182.1 0.000632 52.03 0.00158




p-st Solid CP Pen Sdamp 0.03 el-el Friction -114.08 0.0698 0.00544 183.8 0.000612 53.92 0.00158

p-st Solid CP Pen Sdamp 0.03 el-el No friction -114.08 0.0722 0.00547 182.8 0.000633 51.85 0.00158

p-st Solid CP Pen Sdamp 0.2 el-el Friction -114.08 0.0697 0.00543 184.2 0.000611 53.93 0.00157

p-st Solid Gen Pen Mdamp 0.03 el-el No friction -114.25 0.0537 0.00527 189.8 0.000470 60.55 0.00157

p-st Solid Gen Pen No 0.03 el-el Friction -114.06 0.0736 0.00550 181.8 0.000645 69.38 0.00135

p-st Solid Gen Pen No 0.03 el-el No friction -114.06 0.0533 0.00522 191.6 0.000467 62.65 0.00156

p-st Solid Gen Pen Sdamp 0.03 el-el No friction -114.08 0.0532 0.00522 191.6 0.000466 62.40 0.00156

st-st Shell CP Kin Mdamp 0.03 el-el Friction -91.07 0.0593 0.00477 209.6 0.000651 104.42 0.00111

st-st Shell CP Kin Mdamp 0.03 el-el No friction -91.07 0.0734 0.00499 200.4 0.000806 92.30 0.00113

st-st Shell CP Kin No 0.03 el-el Friction -90.83 0.0593 0.00476 210.1 0.000653 107.67 0.00113

st-st Shell CP Kin No 0.03 el-el No friction -90.83 0.0717 0.00495 202.0 0.000789 94.51 0.00112

st-st Shell CP Kin No 0.03 node-el No friction -90.83 0.0517 0.00470 212.8 0.000569 80.53 0.00133

st-st Shell CP Kin Sdamp 0.03 el-el No friction -90.84 0.0720 0.00497 201.2 0.000793 94.43 0.00112

st-st Shell CP Pen Mdamp 0.03 el-el Friction -91.07 0.0529 0.00469 213.2 0.000581 63.37 0.00120

st-st Shell CP Pen Mdamp 0.03 el-el No friction -91.07 0.0564 0.00478 209.2 0.000619 59.21 0.00142

st-st Shell CP Pen No 0.03 el-el Friction -90.83 0.0533 0.00472 211.9 0.000587 65.95 0.00118

st-st Shell CP Pen No 0.03 el-el No friction -90.83 0.0575 0.00479 208.8 0.000633 61.50 0.00142




st-st Shell CP Pen Sdamp 0.03 el-el No friction -90.84 0.0571 0.00479 208.8 0.000629 61.48 0.00142

st-st Shell CP Pen Sdamp 0.2 el-el Friction -90.84 0.0527 0.00469 213.2 0.000580 65.71 0.00120

st-st Shell Gen Pen Mdamp 0.03 el-el No friction -91.07 0.0563 0.00476 210.1 0.000618 82.86 0.00119

st-st Shell Gen Pen Mdamp 0.2 el-el No friction -91.07 0.0563 0.00478 209.2 0.000618 82.85 0.00118

st-st Shell Gen Pen No 0.03 el-el Friction -90.83 0.0583 0.00475 210.5 0.000642 99.21 0.00113

st-st Shell Gen Pen No 999 el-el No friction -90.83 0.0825 0.00517 193.4 0.000908 26.65 0.00145

st-st Shell Gen Pen Sdamp 0.03 el-el No friction -90.84 0.0666 0.00494 202.4 0.000733 88.04 0.00116

st-st Shell Gen Pen Sdamp 0.2 el-el No friction -90.84 0.0664 0.00493 202.8 0.000731 88.01 0.00116

st-st Solid CP Kin No 0.03 el-el Friction -90.89 0.0308 0.00490 204.1 0.000339 97.83 0.00126

st-st Solid CP Kin No 0.03 node-el No friction -90.89 0.0358 0.00491 203.7 0.000394 84.75 0.00149

st-st Solid CP Kin Sdamp 0.03 el-el No friction -90.89 0.0333 0.00493 202.8 0.000366 84.66 0.00150

st-st Solid CP Pen Mdamp 0.03 el-el Friction -91.13 0.0525 0.00506 197.6 0.000576 91.21 0.00123

st-st Solid CP Pen Mdamp 0.03 el-el No friction -91.13 0.0357 0.00492 203.3 0.000392 78.88 0.00152

st-st Solid CP Pen No 0.03 el-el Friction -90.89 0.0463 0.00493 202.8 0.000509 87.15 0.00125

st-st Solid CP Pen No 0.03 el-el No friction -90.89 0.0376 0.00490 204.1 0.000414 78.51 0.00151




st-st Solid CP Pen Sdamp 0.03 el-el Friction -90.89 0.0462 0.00494 202.4 0.000508 87.11 0.00125

st-st Solid CP Pen Sdamp 0.03 el-el No friction -90.89 0.0381 0.00492 203.3 0.000419 78.44 0.00151

st-st Solid CP Pen Sdamp 0.2 el-el Friction -90.89 0.0455 0.00491 203.7 0.000501 86.97 0.00125

st-st Solid Gen Pen Mdamp 0.03 el-el No friction -91.13 0.0293 0.00492 203.3 0.000322 93.52 0.00152

st-st Solid Gen Pen No 0.03 el-el Friction -90.89 0.0630 0.00524 190.8 0.000693 106.07 0.00120

st-st Solid Gen Pen No 0.03 el-el No friction -90.89 0.0336 0.00494 202.4 0.000370 91.32 0.00153

st-st Solid Gen Pen Sdamp 0.03 el-el No friction -90.89 0.0343 0.00495 202.0 0.000377 91.22 0.00151

43

The Effect of Contact Surface Definition

Table 5: Results showing the effect of the el-el and node-el contact surface definition on the studied criteria

All models in Table 5, have a CP, Kin, no material damping, default (0.03) contact

damping, no friction configuration. The aim is to study the difference between using

the node-el and the el-el contact surface parameter. It is visible from the results that

there is a significant difference when comparing the values for the models where the

sample surfaces are meshed as shell, but barely any difference for samples meshed

as solids. The height of the biggest bounce, duration of the biggest bounce, ratio of

the height of bounce to impact velocity and peak impact force are higher for the P-

P and P-St pairs where the node-el surfaces are used. The duration of impact for

those pairs is lower with node-el. On the other hand, for the St-St material pair, the

opposite is true: the height of the biggest bounce, duration of the biggest bounce,

ratio of height of bounce to impact velocity and peak impact force are lower where

the node-el surfaces are used, and the duration of impact is higher.

MaterialsSample

mesh

Contact

Surfaces

Height of

biggest

bounce [mm]

Duration of

biggest

bounce [s]

Ratio of height of

bounce to impact

velocity [mm/s]

Peak impact

force [N]

Duration of

impact [s]

p-p Shell el-el 0.0450 0.00540 0.000597 20.63 0.00169

p-p Shell node-el 0.0498 0.00553 0.000660 26.53 0.00167

p-p Solid el-el 0.0557 0.00562 0.000739 28.39 0.00163

p-p Solid node-el 0.0557 0.00562 0.000739 28.00 0.00163

p-st Shell el-el 0.0815 0.00551 0.000715 50.38 0.00151

p-st Shell node-el 0.0942 0.00572 0.000826 62.54 0.00138

p-st Solid el-el 0.0587 0.00534 0.000515 62.14 0.00155

p-st Solid node-el 0.0590 0.00532 0.000517 61.97 0.00156

st-st Shell el-el 0.0717 0.00495 0.000789 94.51 0.00112

st-st Shell node-el 0.0517 0.00470 0.000569 80.53 0.00133

44

The Effect of Friction

In this subsection, the value for contact damping is the default ABAQUS value which

is 0.03.

St-St material pair

Table 6: Results showing the effect of friction on the criteria for the St-St material pair

The use of shell or solid elements to model the St-St samples makes a significant

difference on how friction affects the height of the biggest bounce, the duration of

the bounce, and the ratio of the height of bounce to the impact velocity. As the results

for the material pair St-St in Table 6 show, the use of friction:

- Decreases the height of the biggest bounce and the ratio of the height of

bounce to the impact velocity when the samples are modelled as shell

elements and increases them when the samples are modelled as solid

elements. Looking at the numbers and comparing Shell-CP-Pen with Solid-CP-

Pen models, friction has a bigger effect when the elements are solid.

- Decreases the duration of the bounce when the samples are modelled as shell

elements and increases it when the samples are modelled as solid elements.

However, the effect on CP-Pen models is barely visible.

- Increases the peak impact force irrespective of the element type

- Decreases the duration of impact, irrespective of the element type. However,

when the Kinematic (Kin) method is in action, friction has a negligible effect on

the duration compared with no-friction models.

One more find that can be extracted from this table is that general contact definition

has a bigger effect than the contact pair definition. The numbers show that the

percent difference between models with and without friction is the biggest for the

Solid-Gen models compared with the remaining comparable models.

Sample

mesh

Contact

definition

Contact

mechanicsDamping Friction

Impact

velocity

[mm/s]

Percent

Difference

[%]

Height of

biggest

bounce

[mm]

Percent

Difference

[%]

Duration

of biggest

bounce [s]

Percent

Difference

[%]

Ratio of

height of

bounce to

impact

velocity

Percent

Difference

[%]

Peak

impact

force [N]

Percent

Difference

[%]

Duration

of impact

[s]

Percent

Difference

[%]

Shell CP Kin Mdamp Friction -91.07 0.0593 0.00477 0.000651 104.42 0.00111

Shell CP Kin Mdamp No friction -91.07 0.0734 0.00499 0.000806 92.30 0.00113

Shell CP Kin No Friction -90.83 0.0593 0.00476 0.000653 107.67 0.00113

Shell CP Kin No No friction -90.83 0.0717 0.00495 0.000789 94.51 0.00112

Shell CP Pen Mdamp Friction -91.07 0.0529 0.00469 0.000581 63.37 0.00120

Shell CP Pen Mdamp No friction -91.07 0.0564 0.00478 0.000619 59.21 0.00142

Shell CP Pen No Friction -90.83 0.0533 0.00472 0.000587 65.95 0.00118

Shell CP Pen No No friction -90.83 0.0575 0.00479 0.000633 61.50 0.00142

Solid CP Pen No Friction -90.89 0.0463 0.00493 0.000509 87.15 0.00125

Solid CP Pen No No friction -90.89 0.0376 0.00490 0.000414 78.51 0.00151

Solid CP Pen Sdamp Friction -90.89 0.0462 0.00494 0.000508 87.11 0.00125

Solid CP Pen Sdamp No friction -90.89 0.0381 0.00492 0.000419 78.44 0.00151

Solid CP Pen Mdamp Friction -91.13 0.0525 0.00506 0.000576 91.21 0.00123

Solid CP Pen Mdamp No friction -91.13 0.0357 0.00492 0.000392 78.88 0.00152

Solid Gen Pen No Friction -90.89 0.0630 0.00524 0.000693 106.07 0.00120

Solid Gen Pen No No friction -90.89 0.0336 0.00494 0.000370 91.32 0.00153

0%

0%

0%

0%

0%

0%

0%

0%

1.8%

18.3%

-0.9%

20.3%

20.8%

27.5%

20.8%

23.6%-31.9%

-11.6%

-6.6%

-12.2%

-6.7%

-9.9%

-13.9%

-10.0%

-13.5%

-0.4%

-2.8%

23.8%

6.5%

20.8%

7.8%

-18.7%

-46.6%

-17.5%

4.6%

1.9%

4.0%

1.5%

-0.6%

-5.7%

23.8%

6.6%

20.9%

7.9%

-18.8%

-46.7%

-17.5%

-32.0%

45

P-P material pair

Table 7: Results showing the effect of friction on the criteria for the P-P material pair

As the P-P results in Table 7 show, the use of friction:

- Decreases the height of the biggest bounce and the ratio of the height of

bounce to the impact velocity. Looking at the numbers, friction has a bigger

effect when the elements are solid.

- Decreases the duration of the biggest bounce, much more significantly for

solid samples. Friction has a negligible effect on the duration of the biggest

bounce for the Shell-CP-Pen combination.

- Increases the peak impact force.

- Has an insignificant effect on the duration of impact for all models except for

the Shell-CP-Pen combination where friction causes a decrease in value.

The effect of the general contact definition is not noticeable for P-P as in St-St

results. For P-P samples, the more noticeable results are those for the Solid-CP-Pen,

which show the highest percent difference (between models with and without

friction) for the height of the biggest bounce, the duration of the bounce, and the

ratio of the height of bounce to the impact velocity.

Sample

mesh

Contact

definition

Contact


Impact

velocity

[mm/s]

Percent

Difference

[%]

Height of

biggest

bounce

[mm]

Percent

Difference

[%]

Duration

of biggest

bounce [s]

Percent

Difference

[%]

Ratio of

height of

bounce to

impact

velocity

Percent

Difference

[%]

Peak

impact

force [N]

Percent

Difference

[%]

Duration

of impact

[s]

Percent

Difference

[%]









Solid CP Kin No Friction -75.41 0.0441 0.00540 0.000585 31.42 0.00163

Solid CP Kin No No friction -75.41 0.0557 0.00562 0.000739 28.39 0.00163









2.9%

-1.2%

-0.6%

-0.6%

-1.2%

3.4%

-0.6%

-1.2%

0.0%

44.0%

27.7%

43.6%

-8.1%

-4.5%

-5.8%

-6.3%

-9.6%

-4.4%

-6.1%

-10.4%

-6.1%

3.8%

43.9%

27.7%

43.4%

1.9%

-0.6%

5.2%

2.7%

4.1%

-0.4%

5.4%

3.9%

5.2%

14.4%

4.4%

43.2%

13.9%

26.3%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

14.3%

4.3%

43.2%

13.9%

26.3%

3.8%

46

P-St material pair

Table 8: Results showing the effect of friction on the criteria for the P-St material pair

As the P-St results in Table 8 show, the use of friction:

- Decreases the height of the biggest bounce, the duration of the biggest

bounce, and the ratio of the height of bounce to the impact velocity for all

models except the Solid-CP-Kin and Solid-Gen-Pen configurations. For those,

friction significantly increases the 3 above mentioned criteria. Comparing

with the remaining models, it seems that the combination of solid with CP-Kin

is what makes this difference. The only uncertainty is whether running Shell-

Gen would give the same result, or if also for that, the solid meshing is what

makes the difference.

- Increases the peak impact force.

- Increases the duration of impact for shell samples, and decreases it for

solid samples. For Solid-CP-Pen, however, the change is insignificant.

The effect of the general contact definition, and the kinematic contact mechanics is

visible in this case and discussed for more visible results in section 10.3.

Sample

mesh

Contact

definition

Contact


Impact

velocity

[mm/s]

Percent

Difference

[%]

Height of

biggest

bounce

[mm]

Percent

Difference

[%]

Duration

of biggest

bounce [s]

Percent

Difference

[%]

Ratio of

height of

bounce to

impact

velocity

Percent

Difference

[%]

Peak

impact

force [N]

Percent

Difference

[%]

Duration

of impact

[s]

Percent

Difference

[%]









Solid CP Kin No Friction -114.06 0.0725 0.00552 0.000636 70.27 0.00139

Solid CP Kin No No friction -114.06 0.0587 0.00534 0.000515 62.14 0.00155









0.0%

15.6%

-3.7%

-3.8%

-9.7%

-10.2%

-7.4%

11.5%

-2.3%

-1.8%

0.6%

0.6%

-9.4%

-8.3%

-11.6%

-2.4%

-3.0%

-4.6%

-5.1%

62.0%

55.8%

-19.0%

20.7%

22.8%

3.3%

3.6%

3.4%

-27.6%

3.4%

-27.6%

5.9%

5.6%

-3.3%

3.4%

3.6%

1.3%

1.1%

0.6%

0.0%

0.0%

0.0%

62.1%

55.5%

-19.0%

20.6%

22.7%

3.3%

3.6%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

47

The Effect of Contact Mechanics

In Table 9, Table 10, and Table 11 all the models have a shell, contact pair, el-el

configuration. The main parameter to be compared is the contact mechanics.

St-St material pair

Table 9: Results showing the effect of the penalty and kinematic methods on the criteria for the St-St material pair

The rows in Table 9 are ordered from lowest to highest peak impact force. Clearly,

the penalty method gives a lower impact force than the kinematic, and, to further

validate the results of subsection 10.2, the increase in the force due to friction, is also

visible. The mass proportional damping coefficient is also noticed to be producing

the lowest force in every differently-colored set.

Furthermore, the kinematic method gives a bigger height of biggest bounce,

duration of biggest bounce, and ratio of height of bounce to impact velocity than

the penalty, and when combined with friction, the values are reduced for both

methods.

The duration of impact and the peak impact force are indirectly proportional in the

table, the higher values appearing when the penalty method is used. As previously

mentioned, the effect of friction becomes less visible when that the kinematic method

is in action.

Sample

mesh

Contact

mechanicsDamping

Contact

dampingFriction

Height of

biggest

bounce

[mm]

Duration of

biggest

bounce [s]

Ratio of

height of

bounce to

impact

velocity

[mm/s]

Peak

impact

force [N]

Duration of

impact [s]

Shell Pen Mdamp 0.03 No friction 0.0564 0.00478 0.000619 59.21 0.00142

Shell Pen No 0.2 No friction 0.0569 0.00479 0.000626 61.24 0.00142



Shell Pen Sdamp 0.03 No friction 0.0571 0.00479 0.000629 61.48 0.00142


Shell Pen Mdamp 0.03 Friction 0.0529 0.00469 0.000581 63.37 0.00120

Shell Pen Sdamp 0.2 Friction 0.0527 0.00469 0.000580 65.71 0.00120

Shell Pen No 0.03 Friction 0.0533 0.00472 0.000587 65.95 0.00118

Shell Kin Mdamp 0.03 No friction 0.0734 0.00499 0.000806 92.30 0.00113

Shell Kin Sdamp 0.03 No friction 0.0720 0.00497 0.000793 94.43 0.00112

Shell Kin No 0.03 No friction 0.0717 0.00495 0.000789 94.51 0.00112

Shell Kin Mdamp 0.03 Friction 0.0593 0.00477 0.000651 104.42 0.00111

Shell Kin No 0.03 Friction 0.0593 0.00476 0.000653 107.67 0.00113

48

P-P material pair

Table 10: Results showing the effect of the penalty and kinematic methods on the criteria for the P-P material pair

The variation in peak impact force due to the contact mechanics method used is not

as big as for the St-St models. It is insignificant in this case. (Table 10)

The results found for the height of biggest bounce, duration of biggest bounce, and

ratio of height of bounce to impact velocity are the same as for the St-St models.

The duration of impact is higher when the penalty method is used.

P-St material pair

Table 11: Results showing the effect of the penalty and kinematic methods on the criteria for the P-St material pair

Sample

mesh

Contact

mechanic

s

DampingContact

dampingFriction

Height of

biggest

bounce

[mm]

Duration of

biggest

bounce [s]

Ratio of

height of

bounce to

impact

velocity

Peak

impact

force [N]

Duration of

impact [s]















Sample

mesh

Contact

mechanicsDamping

Contact

dampingFriction

Height of

biggest

bounce

[mm]

Duration of

biggest

bounce [s]

Ratio of height

of bounce to

impact velocity

[mm/s]

Peak

impact

force [N]

Duration of

impact [s]















49

The rows in Table 11 are ordered from lowest to highest peak impact force. The

penalty method gives a lower impact force than the kinematic, and the increase in

the force due to friction is visible. The mass proportional damping coefficient is

noticed to be producing the highest force in every differently coloured set, just

opposite to the St-St results.

For P-St, the kinematic method gives a bigger height of biggest bounce, duration of

biggest bounce, and ratio of height of bounce to impact velocity than the penalty

only when the friction is not included. Upon adding friction, the penalty method

gives higher values for the 3 above mentioned criteria.

The duration of impact has a higher value when the penalty method is used. The

effect of friction is more visible for the kinematic method here, and less for the

penalty.

The Effect of Material Damping

All models in Table 12, Table 13, and Table 14 have an el-el, default (0.03) contact

damping, no-friction configuration. The main comparison is between the three

material damping options used. A first look reveals what was found in the literature:

the effect of the stiffness proportional damping coefficient is negligible in such

problems where the high frequencies of the structure are dominant over the lower

ones.

The effect of using the mass proportional damping is more significant, and is

compared with its respective no material damping model in each of the paragraphs

below.

St-St material pair

Table 12: Results showing the effect of material damping on the criteria for the St-St material pair

Table 12 shows the models with the two steel samples (St-St) and varying material

damping.

The effect of using the mass proportional damping, compared with its respective no-

material-damping model can be described as follows:

- An increase in the impact velocity, although small, is relatively noticeable.

Sample

mesh

Contact

definition

Contact

mechanicsDamping

Impact

velocity

[mm/s]

Percent

Difference

[%]

Height of

biggest

bounce

[mm]

Percent

Difference

[%]

Duration of

biggest

bounce [s]

Percent

Difference

[%]

Ratio of

height of

bounce to

impact

velocity

Percent

Difference

[%]

Peak

impact

force [N]

Percent

Difference

[%]

Duration of

impact [s]

Percent

Difference

[%]

Shell CP Kin Mdamp -91.07 0.27% 0.0734 2.37% 0.00499 0.81% 0.000806 2.15% 92.30 -2.34% 0.00113 0.89%

Shell CP Kin No -90.83 0.0717 0.00495 0.000789 94.51 0.00112

Shell CP Kin Sdamp -90.84 0.01% 0.0720 0.42% 0.00497 0.40% 0.000793 0.51% 94.43 -0.08% 0.00112 0.00%

Shell CP Pen Mdamp -91.07 0.27% 0.0564 -1.91% 0.00478 -0.21% 0.000619 -2.21% 59.21 -3.72% 0.00142 0.00%

Shell CP Pen No -90.83 0.0575 0.00479 0.000633 61.50 0.00142

Shell CP Pen Sdamp -90.84 0.01% 0.0571 -0.70% 0.00479 0.00% 0.000629 -0.63% 61.48 -0.03% 0.00142 0.00%

Solid CP Pen Mdamp -91.13 0.27% 0.0357 -5.05% 0.00492 0.41% 0.000392 -5.31% 78.88 0.47% 0.00152 0.66%

Solid CP Pen No -90.89 0.0376 0.00490 0.000414 78.51 0.00151

Solid CP Pen Sdamp -90.89 0.01% 0.0381 1.33% 0.00492 0.41% 0.000419 1.21% 78.44 -0.09% 0.00151 0.00%

Solid Gen Pen Mdamp -91.13 0.27% 0.0293 -12.80% 0.00492 -0.40% 0.000322 -12.97% 93.52 2.41% 0.00152 -0.65%

Solid Gen Pen No -90.89 0.0336 0.00494 0.000370 91.32 0.00153

Solid Gen Pen Sdamp -90.89 0.01% 0.0343 2.08% 0.00495 0.20% 0.000377 1.89% 91.22 -0.11% 0.00151 -1.31%

50

- The height of the biggest bounce and the ratio of the height to the impact

velocity decrease or increase depending on the use of the penalty or kinematic

method respectively. Comparing Solid-Pen-CP and Solid-Pen-Gen, the general

definition causes a bigger lowering of the values.

- The duration of the biggest bounce, and the duration of impact are

insignificantly affected

- The peak impact force is lower or higher, irrespective of the contact mechanics,

but depending on the samples’ element modelling. For solid samples, it is higher,

and for shells, it is lower.

P-P material pair

Table 13: Results showing the effect of material damping on the criteria for the P-P material pair

Table 13 shows the models with the two polypropylene samples and varying material

dampings.

No big effect of using the mass proportional damping is detected:


- The height of the biggest bounce, the duration of the biggest bounce, the ratio

of the height to the impact velocity, and the duration of impact are

insignificantly affected.

Sample

mesh

Contact

definition

Contact

mechanicsDamping

Impact

velocity

[mm/s]

Percent

Difference

[%]

Height of

biggest

bounce

[mm]

Percent

Difference

[%]

Duration

of biggest

bounce [s]

Percent

Difference

[%]

Ratio of

height of

bounce to

impact

velocity

Percent

Difference

[%]

Peak

impact

force [N]

Percent

Difference

[%]

Duration

of impact

[s]

Percent

Difference

[%]

Shell CP Kin Mdamp -75.59 0.24% 0.0452 0.44% 0.00539 -0.19% 0.000598 0.17% 20.82 0.92% 0.00169 0.00%

Shell CP Kin No -75.40 0.0450 0.00540 0.000597 20.63 0.00169

Shell CP Kin Sdamp -75.42 0.02% 0.0450 0.00% 0.00539 -0.19% 0.000597 0.00% 20.08 -2.67% 0.00169 0.00%

Shell CP Pen Mdamp -75.59 0.24% 0.0332 0.91% 0.00516 0.19% 0.000439 0.69% 20.53 0.49% 0.00181 0.56%

Shell CP Pen No -75.40 0.0329 0.00515 0.000436 20.43 0.00180

Shell CP Pen Sdamp -75.42 0.02% 0.0332 0.91% 0.00516 0.19% 0.000440 0.92% 20.38 -0.24% 0.00181 0.56%

Solid CP Kin Mdamp -75.59 0.24% 0.0559 0.36% 0.00563 0.18% 0.000739 0.00% 27.91 -1.69% 0.00162 -0.61%

Solid CP Kin No -75.41 0.0557 0.00562 0.000739 28.39 0.00163

Solid CP Kin Sdamp -75.43 0.02% 0.0557 0.00% 0.00561 -0.18% 0.000738 -0.14% 28.26 -0.46% 0.00163 0.00%

Solid CP Pen Mdamp -75.59 0.24% 0.0461 0.44% 0.00545 0.00% 0.000610 0.16% 24.04 0.25% 0.00167 0.00%

Solid CP Pen No -75.41 0.0459 0.00545 0.000609 23.98 0.00167

Solid CP Pen Sdamp -75.43 0.02% 0.0459 0.00% 0.00545 0.00% 0.000609 0.00% 23.95 -0.13% 0.00167 0.00%

Solid Gen Pen Mdamp -75.59 0.24% 0.0568 0.18% 0.00564 0.18% 0.000751 -0.13% 27.60 0.69% 0.00161 0.00%

Solid Gen Pen No -75.41 0.0567 0.00563 0.000752 27.41 0.00161

Solid Gen Pen Sdamp -75.43 0.02% 0.0566 -0.18% 0.00563 0.00% 0.000750 -0.27% 27.31 -0.36% 0.00161 0.00%

51

P-St material pair

Table 14: Results showing the effect of material damping on the criteria for the P-St material pair

Table 14 shows the models with the polypropylene and steel samples and varying

material dampings.

The effect of using the mass proportional damping, compared with its respective no

material damping model can be described as follows:


- The height of the biggest bounce, and the ratio of the height to the impact

velocity are affected, and increase, by the kinematic contact mechanics, but not

by the penalty.

- The duration of the biggest bounce and the duration of the impact are

insignificantly affected.

- The peak impact force increase for samples modelled with shell elements, and

decreases for samples modelled with solid elements.

Sample meshContact

definition

Contact

mechanicsDamping

Impact

velocity

[mm/s]

Percent

Difference

[%]

Height of

biggest

bounce

[mm]

Percent

Difference

[%]

Duration

of biggest

bounce [s]

Percent

Difference

[%]

Ratio of

height of

bounce to

impact

velocity

Percent

Difference

[%]

Peak

impact

force [N]

Percent

Difference

[%]

Duration

of impact

[s]

Percent

Difference

[%]

Shell CP Kin Mdamp -114.25 0.17% 0.0833 2.21% 0.00554 0.54% 0.000729 1.96% 53.05 5.30% 0.00149 -1.32%

Shell CP Kin No -114.06 0.0815 0.00551 0.000715 50.38 0.00151

Shell CP Kin Sdamp -114.08 0.02% 0.0820 0.61% 0.00552 0.18% 0.000719 0.56% 50.20 -0.36% 0.00149 -1.32%

Solid CP Kin Mdamp -114.25 0.17% 0.0603 2.73% 0.00531 -0.56% 0.000528 2.52% 60.80 -2.16% 0.00156 0.65%

Solid CP Kin No -114.06 0.0587 0.00534 0.000515 62.14 0.00155

Solid CP Kin Sdamp -114.08 0.02% 0.0596 1.53% 0.00530 -0.75% 0.000522 1.36% 61.95 -0.31% 0.00156 0.65%

Shell CP Pen Mdamp -114.25 0.17% 0.0780 0.91% 0.00547 0.00% 0.000683 0.74% 46.52 1.17% 0.00167 0.00%

Shell CP Pen No -114.06 0.0773 0.00547 0.000678 45.98 0.00167

Shell CP Pen Sdamp -114.08 0.02% 0.0773 0.00% 0.00547 0.00% 0.000678 0.00% 45.79 -0.41% 0.00167 0.00%

Solid CP Pen Mdamp -114.25 0.17% 0.0719 -0.28% 0.00551 0.36% 0.000629 -0.47% 51.04 -1.90% 0.00158 0.00%

Solid CP Pen No -114.06 0.0721 0.00549 0.000632 52.03 0.00158

Solid CP Pen Sdamp -114.08 0.02% 0.0722 0.14% 0.00547 -0.36% 0.000633 0.16% 51.85 -0.35% 0.00158 0.00%

Solid Gen Pen Mdamp -114.25 0.17% 0.0537 0.75% 0.00527 0.96% 0.000470 0.64% 60.55 -3.35% 0.00157 0.64%

Solid Gen Pen No -114.06 0.0533 0.00522 0.000467 62.65 0.00156

Solid Gen Pen Sdamp -114.08 0.02% 0.0532 -0.19% 0.00522 0.00% 0.000466 -0.21% 62.40 -0.40% 0.00156 0.00%

52

Guidelines

For clarity, the results are compiled in a set of guidelines presented in this section.

The following guidelines are for modelling rattle between two surfaces coming in

contact.

Contact Surface Definition

Use the node-el, instead of the el-el, surface definition for P-P and P-St

shell-meshed structures to:

- Increase the height of the biggest bounce

- Increase the duration of the biggest bounce

- Increase the ratio of the height of bounce to impact velocity

- Increase the peak impact force

- Decrease the duration of impact

Use the node-el, instead of the el-el, surface definition for St-St shell-

meshed structures to:

- Decrease the height of the biggest bounce

- Decrease the duration of the biggest bounce

- Decrease the ratio of the height of bounce to impact velocity

- Decrease the peak impact force

- Increase the duration of impact

For solid-meshed structures, no difference in rattle criteria is to be expected

when node-el is used instead of el-el.

Friction

Add friction between two St-St shell-meshed structures to:



- Decrease the ratio of the height of bounce to the impact velocity



53

Add friction between two St-St solid-meshed structures to:

- Increase the height of the biggest bounce

- Increase the duration of the biggest bounce

- Increase the ratio of the height of bounce to the impact velocity



For shell and solid St-St structures, the duration of the biggest bounce is not

affected when the model is CP-Pen.

For shell and solid St-St structures, when the kinematic method is used, no

difference in duration of impact is to be expected.

For shell and solid St-St structures, the general contact type has a bigger effect

on the rattle criteria than the contact pair type.

Add friction between two P-P structures to:





- Decrease the duration of impact only for Shell-CP-PEN

For solid P-P structures, friction is expected to have a bigger effect than on shell

structures.

For shell P-P structures, the duration of the biggest bounce is not affected when

the model is CP-Pen.

Add friction between two P-St shell-meshed structures to






54

Add friction between two P-St solid-meshed structures to

- Increase the height of the biggest bounce only for CP-Kin and Gen-Pen models

- Decrease the height of the biggest bounce only for CP-Pen models

- Increase the duration of the biggest bounce only for CP-Kin and Gen-Pen

models

- Decrease the duration of the biggest bounce only for CP-Pen models

- Increase the ratio of the height of bounce to the impact velocity only for CP-Kin

and Gen-Pen models

- Decrease the duration of the biggest bounce only for CP-Pen models



For solid P-St structures, the duration of impact is not affected when the model

is CP-Pen.

Contact Mechanics

This part only applies to contact type “contact pair”

Use the penalty method, instead of the kinematic, with St-St structures

to:




- Decrease the impact force


Use the penalty method, instead of the kinematic, with P-P structures to:





55

Use the penalty method, instead of the kinematic, with P-St structures to:

- Decrease the height of the biggest bounce only when there is no friction

- Increase the height of the biggest bounce only when there is friction

- Decrease the duration of the biggest bounce only when there is no friction

- Increase the duration of the biggest bounce only when there is friction

- Decrease the ratio of height of bounce to impact velocity only when there is no

friction

- Increase the ratio of height of bounce to impact velocity only when there is

friction

- Decrease the peak impact force


Material Damping

The effect of the stiffness proportional damping coefficient is negligible in such

problems where the high frequencies of the structure are dominant over the lower

ones.

Add a mass proportional damping to St-St structures to:

- Increase the height of the biggest bounce only when the kinematic method is

used

- Decrease the height of the biggest bounce only when the penalty method is used

- Increase the ratio of the height of bounce to the impact velocity only when the

kinematic method is used

- Decrease the ratio of the height of bounce to the impact velocity only when the

penalty method is used

- Increase the peak impact force only when the structures are solid-meshed

- Decrease the peak impact force only when the structures are shell-meshed

For shell and solid St-St structures, the general contact type has a bigger effect

on the height of the biggest bounce and the ratio of the height of bounce to the impact

velocity than the contact pair type.

For shell and solid St-St structures, adding mass damping does not affect the

duration of the biggest bounce and the duration of impact.

56

For shell and solid P-P structures, adding a mass proportional damping

structures does not show any significant effect on the rattle criteria.

Add a mass proportional damping to P-St structures to:

- Increase the height of the biggest bounce only when the kinematic method is

used

- Increase the ratio of the height of bounce to the impact velocity only when the

kinematic method is used

- Increase the peak impact force only with shell structures

- Decrease the peak impact force only with solid structures

For shell and solid P-St structures, adding mass damping does not affect the

duration of the biggest bounce and the duration of impact.

Conclusion

Findings and Lessons Learned

The first conclusion of the project was found while achieving the first and second

objectives of building an FEA model of the test rig and correlating the simulation

results to experimental measurements. It proved to be possible to model the test rig

despite the limitations described in 1.3 and get satisfactory results regarding rattle

criteria explained in section 9. This suggested that the imperfections do not have to

be modelled at all cost to predict these criteria. This is a necessary condition to apply

the method on real life applications where these imperfections could vary from part

to part.

The third objective promised the most findings, however not all of the results could

be generalized. The contact surface definition has little to no effect on the results for

samples with solid elements. Friction clearly increased the peak impact force and

decreased the duration of impact in all cases. Penalty based contact mechanics

resulted in a lower peak impact force compared to kinematic contact mechanics,

while the duration of the impact was lower for the kinematic contacts. For cases

unmentioned in this paragraph, the effect of investigated parameters could not be

generalized as it is changing with other parameters.

The findings of the thesis work were concluded in a guideline for rattle modelling

described in section 10.

Future work

Over the course of the project many ideas were considered for possible future work.

By the time of writing the final report it became clearer which ideas are worth to put

in extra effort. Below these ideas can be read.

57

Validation of guidelines on car components

Validation of the guidelines on real car components. This was always an optional goal

of the project. Unfortunately, mainly due to the problems described in section 6

Setbacks and Solutions, there was no sufficient time to run these simulations.

However, the control measurements for this steps were conducted during the project.

The front right door of an XC60 was measured on a shaker pad. Two different

excitations were applied, one recreating a rough road surface, and another with pure

roll around the vehicle’s X axis.

Since this test was conducted on a car in production, by default, there was no audible

rattle in the door. To still catch rattle sound 2 bolts were removed from the speaker

holder component, so it could vibrate due to lateral acceleration.

Modification of test rig

During the thesis it was a huge obstacle that there was no fully reliable control

measurement for the displacement of rattling parts. This was a problem in the signal

processing, correlation and also the sensitivity analysis parts.

A possible solution to this problem is to measure the displacements directly as this

could serve as a control signal for the signal processing, and be a direct input for

further simulations or correlations. As an example in other applications inductive or

Eddy-current sensors are employed with great results. For example stick-slip test

bench (13) uses Eddy-current sensor to register displacement of the sample carrier.

Another limitation coming from the test rig was the solid like material samples.

Although the thesis tried to analyse rattle simulation with shell elements, the

measurements were conducted with solid like material samples. To improve the

accuracy of the findings of the project shell like material samples should also be

measured.

Further simulations

Despite the efforts to include all useful simulation parameters in the sensitivity

analysis there is still room to improve. A big potential could be in using implicit

solvers, based on their efficient use in other solidity and NVH applications. During

the current thesis explicit solver was selected based on the impact velocity, further

explained in section 7.6 Solver Settings.

58

Distribution of labour

In the beginning we organized multiple brainstorming meetings to understand the

problem and to come out with a way to approach it. For the literature work Nicole

was in charge for linearity and non-linearity in FEM, explicit and implicit solvers.

András was in charge for current CAE rattle predicting methods and impact

modelling. Each significant literature was shared between to give a basic knowledge

about the topic. The later stages were performed in close collaboration, however each

step had its own responsible to finish the tasks on time and have it reviewed. András

was in charge for physical tests, signal processing and pre-processing of the FEA

model, while Nicole was responsible for the correlation work, the sensitivity analysis,

the analysis of the results and writing guidelines based on our findings.

59

Appendix

Matlab codes

%% Header % Experimental test data process - Rattle test % Created on 2018-02-22 - Nicole al Hanna; András Péter Székely % Thesis work: Nonlinear modelling and simulation of impact events and validation with

experimental test clear all close all %% Input input_type=1; % 1 - Default *.asc output from Artemis eg.: Measurements; 2 - *.csv without

header; 3 - Test data from FSAE measurements

selective_data=0; % only takes into consideration the data between the start and stop times

given in the next row. Main use of this is to avoid drift coming from numerical integration,

that is present for long data. start_time=15; stop_time=16.5; %% Settings for output - by default only applies to the filtered shaker signal sampling_reducing=7; % takes every x-th data point to reduce sampling size of data with

sampling frequency

start_curve=1; % fits a G1 continous cubic curve to the begining of the signal. It is used

to avoid initial velocity, acceleration at the excitation point. The start curve is attached

to the point given in the next row. The data between stat_time and match_time is deleted. match_time=15.19; start_curve_scaling=1; % scales the start curve non linearly with the origin at the match

point start_curve_scale=100; % the ration between the length of original and new starting curve

shift_data=1; % shifts data, so it starts at time 0 and value 0

generate_sine_signal=1; % generates a sine signal trying to recreate the shaker input sine_signal_length=1; % gives the sine signal output length %% Settings for filtering filter_acc_bw_lowpass=0; % never worked as we hoped, we also needed a highpass more than a

lowpass, we don't use it filter_acc_mean_removal=0; % decreases the drift a bit, but not significantly. We left it at

0, because many simulations had input with 0 filter_vel_moving_avg=1; filter_vel_mean_removal=1; filter_pos_moving_avg=1; filter_pos_mean_removal=1; filter_pos_omega_arithmetics=1; %% Reading input if input_type==1 filename='Experimental_data/sine_NVH2_st-st_10hz_0.05g_p2gap.asc'; A = importdata(filename,'\t',15); data=getfield(A, 'data'); acc_imp=-data(:,2); acc_shk=-data(:,4); freq=10; %Excitation frequency used for moving average filtering

elseif input_type==2 filename='beam_v04_acc_vel_disp_spatial.csv'; A =importdata(filename,',',1); data=getfield(A, 'data'); acc_imp=data(:,4)/1000; acc_shk=data(:,4)/1000; vel_check=data(:,2)/1000; pos_check=data(:,3)/1000;

elseif input_type==3 filename='Experimental_data/adatok_2_check_out_code.csv'; A = importdata(filename,';'); data=getfield(A, 'data'); acc_imp=data(:,2); acc_shk=data(:,2);

60

end

time=data(:,1); time_step_length=zeros(length(time),1); for i=2:length(time) time_step_length(i)=time(i)-time(i-1); end time_step_length(1)=time_step_length(2); sampling_freq=1/max(time_step_length);

if selective_data==1 [temp start_index]=min(abs(time-start_time)); [temp stop_index]=min(abs(time-stop_time)); temp=time(start_index:stop_index); clear time time=temp; temp=acc_imp(start_index:stop_index); clear acc_imp acc_imp=temp; temp=acc_shk(start_index:stop_index); clear acc_shk acc_shk=temp; if input_type==2 temp=vel_check(start_index:stop_index); clear vel_check vel_check=temp; temp=pos_check(start_index:stop_index); clear pos_check pos_check=temp; end clear temp end %% Filtering - acceleration if filter_acc_bw_lowpass==1 fc=10000; %cutoff frequency [b,a] =

butter(6,fc/(sampling_freq/2)); %https://stackoverflow.com/questions/1783633/matlab-apply-a-

low-pass-or-high-pass-filter-to-an-array acc_imp=filter(b,a,acc_imp); end

if filter_acc_mean_removal==1 acc_imp=acc_imp-mean(acc_imp); acc_shk=acc_shk-mean(acc_shk); end %% Process - cumtrapz - to be continued... vel_imp=cumtrapz(time,acc_imp); vel_shk=cumtrapz(time,acc_shk); %% Filtering - velocity if filter_vel_moving_avg==1 windowSize_length=1; %windowSize in number of waves windowSize=round(windowSize_length*(sampling_freq/freq)); b = (1/windowSize)*ones(1,windowSize); a = 1;

vel_imp_moving_avg=filter(b,a,vel_imp); vel_imp_filtered=vel_imp-vel_imp_moving_avg; vel_shk_moving_avg=filter(b,a,vel_shk); vel_shk_filtered=vel_shk-vel_shk_moving_avg; end

if filter_vel_mean_removal==1 vel_imp=vel_imp-mean(vel_imp); %cancels the 'DC offset' from the integration vel_shk=vel_shk-mean(vel_shk); %cancels the 'DC offset' from the integration end %% Process - cumtrapz - ...continued pos_imp=cumtrapz(time,vel_imp_filtered); pos_shk=cumtrapz(time,vel_shk_filtered); %% Filtering - position if filter_pos_moving_avg==1 sampling_freq=1/time_step_length(1);

61

windowSize_length=1; %windowSize in number of waves windowSize=round(windowSize_length*(sampling_freq/freq)); b = (1/windowSize)*ones(1,windowSize); a = 1;

pos_imp_moving_avg=filter(b,a,pos_imp); pos_imp_filtered=pos_imp-pos_imp_moving_avg; pos_shk_moving_avg=filter(b,a,pos_shk); pos_shk_filtered=pos_shk-pos_shk_moving_avg; end

if filter_pos_mean_removal==1 pos_imp=pos_imp-mean(pos_imp); %cancels the 'DC offset' from the integration pos_shk=pos_shk-mean(pos_shk); %cancels the 'DC offset' from the integration end %% FFT % T = 1/sampling_freq; % Sampling period % L = length(acc_imp); % Length of signal % t = (0:L-1)*T; % Time vector % % Y=fft(acc_imp); % P2 = abs(Y/L); % P1 = P2(1:L/2+1); % P1(2:end-1) = 2*P1(2:end-1); % % figure(7) % hold on % f = sampling_freq*(0:(L/2))/L; % semilogx(f,P1) % title('Single-Sided Amplitude Spectrum of X(t)') % xlabel('f (Hz)') % ylabel('|P1(f)|') % title({['FFT of acceleration']}, 'Interpreter', 'none'); % hold off %% Omega arithmetics if filter_pos_omega_arithmetics==1 Y_shk = (fft(acc_shk)); % Fast fourier Transform Y_imp = (fft(acc_imp)); % Fast fourier Transform

L = length(acc_shk); %% signal length f = sampling_freq*(0:L-1)/L; %% frequency vector

for i = 1 : L if f(i) ~= 0 && f(i) > 8 && f(i) < 28 Yf_shk(i) = Y_shk(i)/(2*pi*f(i))^2 *2; %% doubling signal to preserve energy Yf_imp(i) = Y_imp(i)/(2*pi*f(i))^2 *2; %% doubling signal to preserve energy else Yf_shk(i) = 0; Yf_imp(i) = 0; end end

for i = 1 : L if f(i) ~= 0 && f(i) > 60 && f(i) < sampling_freq/2; Yf_shk(i) = Y_shk(i)/(2*pi*f(i))^2 *2; %% doubling signal to preserve energy Yf_imp(i) = Y_imp(i)/(2*pi*f(i))^2 *2; %% doubling signal to preserve energy end end

pos_shk_oa = -transpose(real(ifft(Yf_shk))); pos_imp_oa = -transpose(real(ifft(Yf_imp))); end %% Reducing sampling time_less_increm=time(1:sampling_reducing:end); pos_shk_filtered_less_increm= pos_shk_filtered (1:sampling_reducing:end); pos_imp_filtered_less_increm= pos_imp_filtered (1:sampling_reducing:end); %% Start curve if start_curve==1 [temp match_index]=min(abs(time_less_increm-match_time)); match_time=time_less_increm(match_index); match_time_plus_1=time_less_increm(match_index+1);

62

match_time_plus_2=time_less_increm(match_index+2);

match_signal=pos_shk_filtered_less_increm(match_index); match_signal_plus_1=pos_shk_filtered_less_increm(match_index+1); match_signal_plus_2=pos_shk_filtered_less_increm(match_index+2);

match_diff1_1=(match_signal_plus_1-match_signal)/(match_time_plus_1-match_time); match_diff1_2=(match_signal_plus_2-match_signal_plus_1)/(match_time_plus_2-

match_time_plus_1); match_diff2=(match_diff1_2-match_diff1_1)/(match_time_plus_2-match_time_plus_1);

syms a b c x signal fun_start=symfun(a*sin(c*x+c*b)+a,[a b c x]); fun_diff1_start=diff(fun_start,x,1); fun_diff2_start=diff(fun_start,x,2);

eqn_1=fun_start==match_signal; eqn_2=fun_diff1_start==match_diff1_1; eqn_3=fun_diff2_start==match_diff2; eqns=[eqn_1,eqn_2,eqn_3]; eqns=subs(eqns,x,match_time); solutions=vpasolve(eqns,[a b c]);

a_res=double(solutions.a(1)); b_res=double(solutions.b(1)); c_res=double(solutions.c(1));

abs_b_res=-b_res; if abs_b_res>0 start_origin=1*(abs_b_res-ceil((abs_b_res-

match_time)/((2*pi)/c_res))*((2*pi)/c_res))-((.5*pi)/c_res) elseif abs_b_res<0 start_origin=1*(abs_b_res+floor((match_time-

abs_b_res)/((2*pi)/c_res))*((2*pi)/c_res))-((.5*pi)/c_res) end

fun_start_subs=subs(fun_start,a,a_res); fun_start_subs=subs(fun_start_subs,b,b_res); fun_start_subs=subs(fun_start_subs,c,c_res);

start_function=symfun(a_res*sin(c_res*x+c_res*b_res)+a_res,x);

time_start=start_origin:(match_time_plus_1-match_time):match_time;

pos_shk_output=transpose([time_start

transpose(time_less_increm(match_index:end));double(start_function(time_start))

transpose(pos_shk_filtered_less_increm(match_index:end))]); end

%% Data shifting if shift_data==1 k=pos_shk_output(1,1); l=pos_shk_output(1,2); if start_curve==1 pos_shk_output(:,1)=pos_shk_output(:,1)-k; pos_shk_output(:,2)=pos_shk_output(:,2)-l; else pos_shk_output(:,1)=time_less_increm(:,1)-time_less_increm(1,1); pos_shk_output(:,2)=pos_shk_filtered_less_increm(:,1)-

pos_shk_filtered_less_increm(1,1); pos_shk_output(:,3)=time_less_increm(:,1)-time_less_increm(1,1); pos_shk_output(:,4)=pos_imp_filtered_less_increm(:,1)-

pos_imp_filtered_less_increm(1,1); end end %% Generate sine signal if start_curve==1 & generate_sine_signal==1 clear temp

63

temp=pos_shk_output(length(time_start):length(time_start)+ceil(1/(sampling_reducing*freq*tim

e_step_length(1))),2); sine_amplitude=abs(max(temp)-min(temp))/2; [temp_1 max_index]=max(temp) [temp_1 min_index]=min(temp) sine_x_transl=-(pos_shk_output(length(time_start)+max_index,1)-0.25/freq) sine_x_scale=freq*(2*pi); fun_sine=symfun(sine_amplitude*sin(sine_x_scale*x+sine_x_scale*sine_x_transl),x); clear temp_1

temp_1=0:abs(time_less_increm(2)-time_less_increm(1)):sine_signal_length; temp_2=linspace(0,1,length(temp_1)); sine_output=transpose([temp_1;temp_2.*double(fun_sine(temp_1))]); clear temp_1 temp_2 end %% Scale start curve if start_curve_scaling==1 clear temp temp=pos_shk_output(1:length(time_start),:); fun_scaling=symfun(3*start_curve_scale*x^2,x);

fun_scaling_vector=double(fun_scaling(linspace(0,1,length(time_start)))); i=length(temp); while i>0 temp(i,1)=temp(i,1)-abs(time_less_increm(2)-

time_less_increm(1))*fun_scaling_vector(length(fun_scaling_vector)-i+1) i=i-1 end

pos_shk_output_scaled_start=pos_shk_output; pos_shk_output_scaled_start(1:length(time_start),:)=temp; end %% Plotting figure('name','Imp:Acc') plot(time,acc_imp) grid on xlabel({'Time [s]'}); ylabel({'Acceleration [m/s^2]'}); title({['Acceleration - Time graph for test data //',filename,' at Impact point']},

'Interpreter', 'none');

figure('name','Imp:Vel') hold on grid on plot(time,vel_imp) xlabel({'Time [s]'}); ylabel({'Velocity [m/s]'}); if filter_vel_moving_avg==1 plot(time,vel_imp_moving_avg) plot(time,vel_imp_filtered) legend('raw data','moving average','filtered data - removed moving average'); elseif input_type==2 plot(time,vel_check) legend('integrated velocity','measured velocity'); end title({['Velocity - Time graph for test data //',filename,' at Impact point']},

'Interpreter', 'none'); hold off

figure('name','Imp:Disp') hold on grid on xlabel({'Time [s]'}); ylabel({'Displacement [m]'}); plot(time,pos_imp) if filter_pos_moving_avg==1 plot(time,pos_imp_moving_avg) plot(time,pos_imp_filtered) legend('raw data','moving average','filtered data - removed moving average'); elseif input_type==2

64

plot(time,pos_check) legend('integrated displacement','measured displacement'); end if filter_pos_omega_arithmetics==1 plot(time,pos_imp_oa) legend('raw data','moving average','filtered data - removed moving average','filtered

data - omega arithmetics'); end title({['Displacement - Time graph for test data //',filename,' at Impact point']},


if input_type==1 figure('name','Shk:Acc') plot(time,acc_shk) grid on xlabel({'Time [s]'}); ylabel({'Acceleration [m/s^2]'}); title({['Acceleration - Time graph for test data //',filename,' at Shaker point']},

'Interpreter', 'none');

figure('name','Shk:Vel') hold on plot(time,vel_shk) if filter_vel_moving_avg==1 plot(time,vel_shk_moving_avg) plot(time,vel_shk_filtered) legend('raw data','moving average','filtered data - removed moving average'); end grid on xlabel({'Time [s]'}); ylabel({'Velocity [m/s]'}); title({['Velocity - Time graph for test data //',filename,' at Shaker point']},


figure('name','Shk:Disp') hold on plot(time,pos_shk) if filter_pos_moving_avg==1 plot(time,pos_shk_moving_avg) plot(time,pos_shk_filtered) legend('raw data','moving average','filtered data - removed moving average'); end if filter_pos_omega_arithmetics==1 plot(time,pos_shk_oa) legend('raw data','moving average','filtered data - removed moving

average','filtered data - omega arithmetics'); end grid on xlabel({'Time [s]'}); ylabel({'Displacement [m]'}); title({['Displacement - Time graph for test data //',filename,' at Shaker point']},

'Interpreter', 'none'); hold off end

figure('name','Positions of Impact and Shaker Points') hold on plot(pos_shk_output(:,1),pos_shk_output(:,2)) legend('shaker position') if length(pos_shk_output(1,:))==4 plot(pos_shk_output(:,3),pos_shk_output(:,4)) legend('shaker position','impact point position'); end if start_curve_scaling==1 plot(pos_shk_output_scaled_start(:,1),pos_shk_output_scaled_start(:,2)) legend('shaker position with scaled start curve') end grid on xlabel({'Time [s]'}); ylabel({'Position [m]'});

65

title({['Position - Time graph for test data //',filename,' at shaker point to be written to

output']}, 'Interpreter', 'none');

66

Simplified Input file

** **ANSA_VERSION;17.1.1; ** ** file created by A N S A Fri Jul 6 05:12:45 2018 ** *NODE 1, 90.000228914545, 18.742879951587625, -55.37764823358 2, 89.99974568769542, 12.499858961940573, -2.4999997999034727 ** ...nodes of the geometry... 78258, 310.51992042901, 2.0615519098987, -8.189999999675 87769, 89.99974564492165, 9.999859197190592, 5.28 87770, 89.99974568769542, 9.999859161940574, 0.72 ** ** MEMBRANE and STRUCTURAL ELEMENTS ** *ELEMENT, TYPE=S4R, ELSET=P100;beam_shell 43707, 71271, 71272, 71277, 71270 43708, 71270, 71277, 71278, 71269 ** ...4 node shell elements of beam 44398, 72083, 72087, 72088, 72082 44399, 72082, 72088, 71774, 71775 *ELEMENT, TYPE=S4, ELSET=P107;sample_beam_shell 194, 78252, 78253, 78233, 78230 195, 78237, 78185, 78253, 78252 ** ...4 node shell elements of beam side sample 381, 78256, 78247, 78087, 78170 382, 78254, 78213, 78214, 78255 *ELEMENT, TYPE=S3R, ELSET=P107;sample_beam_shell 200, 78136, 78138, 78137 211, 78114, 78186, 78113 ** ...3 node shell elements of beam side sample 344, 78139, 78109, 78090 351, 78216, 78108, 78215 *ELEMENT, TYPE=S4, ELSET=P108;sample_hammer_shell 5, 77204, 77138, 77255, 77256 6, 77205, 77132, 77138, 77204 ** ...4 node shell elements of hammer side sample 192, 77182, 77181, 77195, 77219 193, 77095, 77094, 77220, 77240 *ELEMENT, TYPE=S3R, ELSET=P108;sample_hammer_shell 9, 77205, 77133, 77132 20, 77157, 77155, 77156 ** ...3 node shell elements of hammer side sample 161, 77183, 77262, 77184 167, 77096, 77177, 77097 ** ** SOLID ELEMENTS ** *ELEMENT, TYPE=C3D8, ELSET=P101;bolt_beam_side 45522, 72810, 72815, 72807, 72804, 72819, 72820, 72821, 72822 45523, 72811, 72792, 72791, 72806, 72823, 72824, 72825, 72826 ** ...8 node solid elements of beam side bolt 48940, 75816, 75888, 76883, 76880, 75812, 75884, 75940, 75939 48941, 76885, 76882, 76877, 76880, 75938, 75937, 75945, 75939 *ELEMENT, TYPE=C3D6, ELSET=P101;bolt_beam_side 45859, 71348, 71326, 72921, 73159, 73163, 73162 45861, 71265, 71347, 72924, 73168, 73160, 73161 ** ...6 node solid elements of beam side bolt 48400, 75855, 75798, 67440, 75927, 75870, 67441 48402, 75803, 75856, 67416, 75875, 75928, 67417 *ELEMENT, TYPE=C3D8, ELSET=P102;nut_beam_side 46606, 73732, 73728, 73967, 73966, 73733, 73729, 73973, 73972 46607, 73728, 73724, 73968, 73967, 73729, 73725, 73975, 73973 ** ...8 node solid elements of beam side nut 46700, 73793, 73792, 74197, 74195, 73724, 73720, 73969, 73968 46701, 73792, 73663, 74199, 74197, 73720, 73674, 73970, 73969 *ELEMENT, TYPE=C3D8, ELSET=P103;fixture_hammer_side 50922, 77546, 77548, 77483, 77481, 77671, 77674, 77673, 77672 50923, 77529, 77607, 77627, 77525, 77675, 77678, 77677, 77676 ** ...8 node solid elements of hammer side fixture 51298, 77731, 77801, 77852, 77739, 77927, 77997, 78048, 77935

67

51299, 77827, 77822, 77797, 77671, 78023, 78018, 77993, 77867 *ELEMENT, TYPE=C3D6, ELSET=P103;fixture_hammer_side 50924, 77511, 77510, 77477, 77679, 77681, 77680 50926, 77557, 77556, 77540, 77686, 77688, 77687 ** ...6 node solid elements of hammer side fixture 51295, 77816, 77687, 77765, 78012, 77883, 77961 51296, 77795, 77842, 77680, 77991, 78038, 77876 *ELEMENT, TYPE=C3D8, ELSET=P105;sample_beam 49551, 73538, 73539, 73541, 73540, 76886, 76889, 76888, 76887 49552, 73531, 73532, 73562, 73563, 76890, 76893, 76892, 76891 ** ...8 node elements of beam side sample base 49927, 76983, 76970, 77071, 77081, 78160, 78147, 78248, 78258 49928, 76958, 76963, 76909, 77027, 78135, 78140, 78086, 78204 *ELEMENT, TYPE=C3D6, ELSET=P105;sample_beam 49559, 67831, 75308, 75302, 76918, 76920, 76919 49567, 67495, 75340, 75334, 76943, 76945, 76944 ** ...6 node elements of beam side sample base 49922, 77062, 77063, 76955, 78239, 78240, 78132 49924, 76897, 77069, 76997, 78074, 78246, 78174 *ELEMENT, TYPE=C3D8, ELSET=P106;sample_hammer 50391, 77083, 77082, 77085, 77084, 77363, 77364, 77345, 77359 50392, 77251, 77252, 77157, 77248, 77365, 77366, 77289, 77321 ** ...8 node elements of hammer side sample base 50731, 77322, 77300, 77281, 77279, 77518, 77496, 77477, 77475 50732, 77431, 77405, 77328, 77329, 77627, 77601, 77524, 77525 *ELEMENT, TYPE=C3D6, ELSET=P106;sample_hammer 50355, 77115, 77114, 77116, 77279, 77281, 77280 50356, 77140, 77139, 77141, 77282, 77284, 77283 ** ...6 node elements of hammer side sample base 50578, 77360, 77344, 77361, 77556, 77540, 77557 50579, 77332, 77330, 77362, 77528, 77526, 77558 ** ** BEAM ELEMENTS - used to connect shaker to beam ** *ELEMENT, TYPE=B31, ELSET=P104;shaker_connector 7531, 2875, 2876, 1 7532, 87770, 2887, 2 7533, 87769, 2893, 3 7534, 2876, 2878, 4 7535, 2878, 2880, 5 7536, 2880, 2882, 6 7537, 2882, 2884, 7 7538, 2884, 87770, 8 7539, 2887, 2889, 9 7540, 2889, 2891, 10 7541, 2891, 87769, 11 7542, 2893, 2895, 12 7543, 2895, 2899, 13 7544, 2899, 2902, 14 7545, 2902, 7042, 15 7546, 7042, 7064, 16 7547, 7064, 7082, 17 7548, 7082, 1496, 18 ** ** MPC - used to connect shaker connector to beam and accelerometer adhesions ** **ANSA_ID;1; *MPC BEAM, shaker_connector_1, 87769 **ANSA_ID;12; *NSET, NSET=shaker_connector_1 71448, 71454, 71455, 71459, 71463, 71464, 71465, 71466, 71467,

71468, 71469, 71470, 71471, 71472, 71473, 72061, 72062, 72075, 72076,

72077, 72078, 72079, 72080, 72081 **ANSA_ID;2; *MPC BEAM, shaker_connector_2, 87770 **ANSA_ID;17; *NSET, NSET=shaker_connector_2 71448, 71454, 71455, 71459, 71463, 71464, 71465, 71466, 71467,

71468,

68

71469, 71470, 71471, 71472, 71473, 72061, 72062, 72075, 72076,

72077, 72078, 72079, 72080, 72081 **ANSA_ID;3; *MPC BEAM, 77991, 19 ** ...beam elements BEAM, 77938, 19 **ANSA_ID;80762; *MPC BEAM, acceleration_adhesion, 9510 **ANSA_ID;11; *NSET, NSET=acceleration_adhesion 71361, 71362, 71363, 71364, 71377, 71378, 71379, 71380, 71389,

71390, 71391, 71392, 71393, 71394, 71395, 71396 ** ** MASS and ROTARY ** *MASS, ELSET=MS60697;M6_nut_at_beam_1 3.33E-6, *ELEMENT, TYPE=MASS, ELSET=MS60697;M6_nut_at_beam_1 60697, 87770 *MASS, ELSET=MS60698;M6_nut_at_beam_2 3.33E-6, *ELEMENT, TYPE=MASS, ELSET=MS60698;M6_nut_at_beam_2 60698, 87769 *MASS, ELSET=MS58829;M6_nut_at_shaker 3.33E-6, *ELEMENT, TYPE=MASS, ELSET=MS58829;M6_nut_at_shaker 58829, 1496 *MASS, ELSET=MS60694;accelerometer_and_connector 9.5E-6, *ELEMENT, TYPE=MASS, ELSET=MS60694;accelerometer_and_connector 60694, 9510 ** ** ** SURFACE INTERACTIONS ** *SURFACE INTERACTION, NAME=I1;ANONYMOUS_SURF_INTERACTION **ANSA_ID;1; *FRICTION 0.2, ** ** SECTION DATA ** **ANSA_ID;100; *SHELL SECTION, ELSET=P100;beam_shell, MATERIAL=M2;aluminum 6., **ANSA_ID;101; *SOLID SECTION, ELSET=P101;bolt_beam_side, MATERIAL=M4;steel_M10_bolt_beam_side **ANSA_ID;102; *SOLID SECTION, ELSET=P102;nut_beam_side, MATERIAL=M3;steel_M10_nut_beam_side **ANSA_ID;103; *SOLID SECTION, ELSET=P103;fixture_hammer_side, MATERIAL=M2;aluminum *BEAM GENERAL SECTION, ELSET=P104;shaker_connector, SECTION=CIRC, DENSITY=7.85E-9, ROTARY

INERTIA=ISOTROPIC, ZERO=0. 2.48,

210000., 80769. *SOLID SECTION, ELSET=P105;sample_beam, MATERIAL=M5;sample_beam *SOLID SECTION, ELSET=P106;sample_hammer, MATERIAL=M6;sample_hammer *SHELL SECTION, ELSET=P107;sample_beam_shell, MATERIAL=M5;sample_beam 0.01, *SHELL SECTION, ELSET=P108;sample_hammer_shell, MATERIAL=M6;sample_hammer 0.01, ** ** MATERIALS ** *MATERIAL, NAME=M1;steel *DENSITY 7.85E-9, *ELASTIC, TYPE=ISOTROPIC

69

210000., 0.3 *MATERIAL, NAME=M2;aluminum *DENSITY 2.609E-9, *ELASTIC, TYPE=ISOTROPIC 68900., 0.33 *DAMPING, ALPHA=TABULAR, BETA=0., COMPOSITE=0., STRUCTURAL=0., DEPENDENCIES=1 43.35, 0., 0. 0., 0., 1. *MATERIAL, NAME=M3;steel_M10_nut_beam_side *DENSITY 1.148E-8, *ELASTIC, TYPE=ISOTROPIC 210000., 0.3 *MATERIAL, NAME=M4;steel_M10_bolt_beam_side *DENSITY 7.85E-9, *ELASTIC, TYPE=ISOTROPIC 210000., 0.3 *MATERIAL, NAME=M5;sample_beam *DENSITY 7.85E-9, *ELASTIC, TYPE=ISOTROPIC 210000., 0.3 *MATERIAL, NAME=M6;sample_hammer *DENSITY 7.85E-9, *ELASTIC, TYPE=ISOTROPIC 210000., 0.3 ** ** AMPLITUDES ** *AMPLITUDE, NAME=FIELDSTEP 0.0, 1.0, 1, 1.0 *AMPLITUDE, NAME=A2;sine_NVH2_st-st_10hz_0X05g_p2gap_omega_arithmetics_BEFORE_IMPACT_14693,

DEFINITION=TABULAR, SMOOTH=0., VALUE=RELATIVE, TIME=TOTAL TIME, SCALEY=12539., SHIFTX=-

14.6145 14.6145, 1.29772E-30, 14.615,

2.68738E-9, 14.6155, 1.07491E-8, 14.616,

2.41837E-8, 14.6165, 4.29888E-8, 14.617,

6.71614E-8, 14.6175, 9.66971E-8, 14.618,

1.31591E-7, ** ...data points of shaker input 23.7991, -8.36237E-6, 23.7993, -

8.81197E-6, 23.7994, -9.25156E-6, 23.7996,

-9.68087E-6, 23.7997, -1.00997E-5, 23.7999,

-1.0508E-5 ** ** ** ***INITIAL CONDITIONS ** *INITIAL CONDITIONS, VARIABLE=1, TYPE=FIELD 1496, 0. ** ** ** SURFACE DEFINITIONS ** *SURFACE, NAME=S18;solid_contact_general, TYPE=ELEMENT **ANSA_SURFACE_NAME;S18\;solid_contact_general; solid_contact_general, *SURFACE, NAME=S3;shell_contact_beam, TYPE=ELEMENT **ANSA_SURFACE_NAME;S3\;shell_contact_beam; shell_contact_beam, *SURFACE, NAME=S4;shell_contact_hammer, TYPE=ELEMENT **ANSA_SURFACE_NAME;S4\;shell_contact_hammer; shell_contact_hammer, *SURFACE, NAME=S5;solid_contact_beam, TYPE=ELEMENT **ANSA_SURFACE_NAME;S5\;solid_contact_beam; solid_contact_beam, *SURFACE, NAME=S6;solid_contact_hammer, TYPE=ELEMENT **ANSA_SURFACE_NAME;S6\;solid_contact_hammer;

70

solid_contact_hammer, ** ** SETS ** **ANSA_ID;3; *ELSET, ELSET=shell_contact_beam 194, 195, 196, 197, 198, 199, 200, 201, 202,

203, 204, 205, 206, 207, 208, 209, 210, 211, 212,

213, ** ...list of elements 364, 365, 366, 367, 368, 369, 370, 371, 372,

373, 374, 375, 376, 377, 378, 379, 380, 381, 382 **ANSA_ID;4; *ELSET, ELSET=shell_contact_hammer 5, 6, 7, 8, 9, 10, 11, 12, 13,

14, 15, 16, 17, 18, 19, 20, 21, 22, 23,

24, ** ...list of elements 175, 176, 177, 178, 179, 180, 181, 182, 183,

184, 185, 186, 187, 188, 189, 190, 191, 192, 193 **ANSA_ID;5; *ELSET, ELSET=solid_contact_beam 49740, 49741, 49742, 49743, 49744, 49745, 49746, 49747, 49748,

49749, 49750, 49751, 49752, 49753, 49754, 49755, 49756, 49757, 49758,

49759, ** ...list of elements 49910, 49911, 49912, 49913, 49914, 49915, 49916, 49917, 49918,

49919, 49920, 49921, 49922, 49923, 49924, 49925, 49926, 49927, 49928 **ANSA_ID;6; *ELSET, ELSET=solid_contact_hammer 50355, 50356, 50357, 50358, 50359, 50360, 50361, 50362, 50363,

50364, 50365, 50366, 50367, 50368, 50369, 50370, 50371, 50372, 50373,

50374, ** ...list of elements 50525, 50526, 50527, 50528, 50529, 50530, 50531, 50532, 50533,

50534, 50535, 50536, 50537, 50538, 50539, 50540, 50541, 50542, 50543 **ANSA_ID;7; *NSET, NSET=output_nodes 19, 1496, 9510, 37756, 78249 **ANSA_ID;8; *NSET, NSET=BCs_beam 71694, 71695, 71696, 71697, 71796, 71797, 71798 **ANSA_ID;9; *NSET, NSET=BCs_shaker 1496, **ANSA_ID;10; *NSET, NSET=BCs_hammer 19, **ANSA_ID;13; *NSET, NSET=shell_contact_beam_nodal 37756, 78063, 78064, 78065, 78066, 78067, 78068, 78069, 78071,

78072, 78073, 78074, 78075, 78076, 78077, 78078, 78079, 78080, 78081,

78082, ** ...list of elements 78243, 78244, 78245, 78246, 78247, 78248, 78249, 78250, 78251,

78252, 78253, 78254, 78255, 78256, 78257, 78258 **ANSA_ID;14; *NSET, NSET=shell_contact_hammer_nodal 77082, 77083, 77084, 77085, 77086, 77087, 77088, 77089, 77090,

77091, 77092, 77093, 77094, 77095, 77096, 77097, 77098, 77099, 77100,

77101, ** ...list of elements

71

77262, 77263, 77264, 77265, 77266, 77267, 77268, 77269, 77270,

77271, 77272, 77273, 77274, 77275, 77276, 77277 **ANSA_ID;15; *NSET, NSET=solid_contact_beam_nodal 37756, 78063, 78064, 78065, 78066, 78067, 78068, 78069, 78071,

78072, 78073, 78074, 78075, 78076, 78077, 78078, 78079, 78080, 78081,

78082, ** ...list of elements 78243, 78244, 78245, 78246, 78247, 78248, 78249, 78250, 78251,

78252, 78253, 78254, 78255, 78256, 78257, 78258 **ANSA_ID;16; *NSET, NSET=solid_contact_hammer_nodal 77082, 77083, 77084, 77085, 77086, 77087, 77088, 77089, 77090,

77091, 77092, 77093, 77094, 77095, 77096, 77097, 77098, 77099, 77100,

77101, ** ...list of elements 77262, 77263, 77264, 77265, 77266, 77267, 77268, 77269, 77270,

77271, 77272, 77273, 77274, 77275, 77276, 77277 **ANSA_ID;18; *ELSET, ELSET=solid_contact_general 49740, 49741, 49742, 49743, 49744, 49745, 49746, 49747, 49748,

49749, 49750, 49751, 49752, 49753, 49754, 49755, 49756, 49757, 49758,

49759, ** ...list of elements 50526, 50527, 50528, 50529, 50530, 50531, 50532, 50533, 50534,

50535, 50536, 50537, 50538, 50539, 50540, 50541, 50542, 50543 **ANSA_ID;19; *NSET, NSET=shell_contact_general 37756, 77082, 77083, 77084, 77085, 77086, 77087, 77088, 77089,

77090, 77091, 77092, 77093, 77094, 77095, 77096, 77097, 77098, 77099,

77100, ** ...list of elements 78247, 78248, 78249, 78250, 78251, 78252, 78253, 78254, 78255,

78256, 78257, 78258 ** ** STEPS ** **ANSA_ID;1; ** ** STEP 1 ** *STEP, NAME=DYN_EXP *DYNAMIC, EXPLICIT , 0.2035 *RESTART, WRITE, OVERLAY ** ** BOUNDARY ** *BOUNDARY, TYPE=DISPLACEMENT **ANSA_ID;43; BCs_beam, 1, 6, 0. **ANSA_ID;1; BCs_shaker, 1, 2, 0. **ANSA_ID;44; BCs_shaker, 4, 6, 0. **ANSA_ID;40; BCs_hammer, 1, 6, 0. *BOUNDARY, TYPE=DISPLACEMENT, AMPLITUDE=A2;sine_NVH2_st-

st_10hz_0X05g_p2gap_omega_arithmetics_BEFORE_IMPACT_14693 **ANSA_ID;42; 1496, 3, , 1. *OUTPUT, FIELD, TIME INTERVAL=0.001 *NODE OUTPUT A, RF,

72

U, V, *ELEMENT OUTPUT LE, S, *OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=output_nodes, VARIABLE=ALL *ENERGY OUTPUT ALLAE, ALLIE, ALLKE, ETOTAL, *END STEP **ANSA_ID;2; ** ** STEP 2 ** *STEP, NAME=DYN_EXP@_1 *DYNAMIC, EXPLICIT , 0.0565 *RESTART, WRITE, OVERLAY *FIELD, VARIABLE=1, AMPLITUDE=FIELDSTEP 1496, 1 ** ** CONTACT DEFINITIONS ** *CONTACT, OP=NEW **ANSA_ID;1; *CONTACT PAIR, CPSET=T1;CONTACT_PAIR_001, INTERACTION=I1;ANONYMOUS_SURF_INTERACTION,

MECHANICAL CONSTRAINT=PENALTY S3;shell_contact_beam, S4;shell_contact_hammer *OUTPUT, FIELD, TIME INTERVAL=0.001 *NODE OUTPUT A, RF, U, V, *ELEMENT OUTPUT LE, S, *CONTACT OUTPUT CFORCE, CSTRESS, *OUTPUT, HISTORY, TIME INTERVAL=1.E-5 *NODE OUTPUT, NSET=output_nodes, VARIABLE=ALL *ENERGY OUTPUT ALLAE, ALLIE, ALLKE, ETOTAL, *CONTACT OUTPUT, CPSET=T1;CONTACT_PAIR_001 CFN, CFNM, CFT, CFTM, *END STEP **ANSA_COLOR;100;SHELL_SECTION;.815686285495758;.705882370471954;.086274512112141 **;1.; **ANSA_COLOR;101;SOLID_SECTION;0.82745099067688;.572549045085907;.007843137718737 **;1.; **ANSA_COLOR;102;SOLID_SECTION;.835294127464294;.439215689897537;.925490200519562 **;1.; **ANSA_COLOR;103;SOLID_SECTION;.843137264251709;0.30588236451149;.843137264251709 **;1.; **ANSA_COLOR;104;BEAM_SECTION;.772549033164978;.054901961237192;.882352948188782; **1.; **ANSA_COLOR;105;SOLID_SECTION;.780392169952393;.921568632125854;.803921580314636 **;1.; **ANSA_COLOR;106;SOLID_SECTION;.933333337306976;.360784322023392;.258823543787003 **;1.; **ANSA_COLOR;107;SHELL_SECTION;.498039215803146;0.34901961684227;0.39215686917305 **;1.; **ANSA_COLOR;108;SHELL_SECTION;.509803950786591;0.;.384313732385635;1.; **ANSA_COLOR;1;MATERIAL;0.;1.;0.;1.;

73

**ANSA_COLOR;2;MATERIAL;.545098066329956;.243137255311012;.184313729405403;1.; **ANSA_COLOR;3;MATERIAL;.886274516582489;.341176480054855;.415686279535294;1.; **ANSA_COLOR;4;MATERIAL;.701960802078247;.498039215803146;.321568638086319;1.; **ANSA_COLOR;5;MATERIAL;.600000023841858;.690196096897125;.388235300779343;1.; **ANSA_COLOR;6;MATERIAL;.796078443527222;.721568644046783;.949019610881805;1.; **ANSA_COLOR;1;STEP;.949019610881805;.670588254928589;.470588237047195;1.; **ANSA_COLOR;2;STEP;.733333349227905;.129411771893501;.149019613862038;1.; **ANSA_NAME_COMMENT;1;BOUNDARY;BCs_shaker_guiding;;NO;NO;NO; **ANSA_NAME_COMMENT;40;BOUNDARY;BCs_hammer;;NO;NO;NO; **ANSA_NAME_COMMENT;42;BOUNDARY;Imp_displ_shaker_input;;NO;NO;NO; **ANSA_NAME_COMMENT;43;BOUNDARY;BCs_beam;;NO;NO;NO; **ANSA_NAME_COMMENT;1;CONTACT_PAIR;CONTACT_PAIR_001;;NO;NO;NO; **ANSA_NAME_COMMENT;1;MPC;shaker_connector_1;;NO;NO;NO; **ANSA_NAME_COMMENT;2;MPC;shaker_connector_2;;NO;NO;NO; **ANSA_NAME_COMMENT;80762;MPC;acceleration_adhesive;;NO;NO;NO; **ANSA_NAME_COMMENT;100;SHELL_SECTION;beam_shell;;YES;NO;NO; **ANSA_NAME_COMMENT;101;SOLID_SECTION;bolt_beam_side;;YES;NO;NO; **ANSA_NAME_COMMENT;102;SOLID_SECTION;nut_beam_side;;YES;NO;NO; **ANSA_NAME_COMMENT;103;SOLID_SECTION;fixture_hammer_side;;YES;NO;NO; **ANSA_NAME_COMMENT;1;WPLANE;X-Y default plane;;NO;YES;NO; **ANSA_NAME_COMMENT;2;WPLANE;Y-Z default plane;;NO;YES;NO; **ANSA_NAME_COMMENT;3;WPLANE;Z-X default plane;;NO;YES;NO; **ANSA_USER_ATTRIBUTES;SHELL_SECTION;User/cad_material;TEXT;RW;YES;;; **ANSA_USER_ATTRIBUTES;SHELL_SECTION;User/cad_thickness;TEXT;RW;YES;;; **ANSA_USER_ATTRIBUTES;SOLID_SECTION;User/cad_material;TEXT;RW;YES;;; **ANSA_PART;GROUP;ID;18;NAME;1mm_solid.inp;BELONGS_HERE;YES;PID_OFFSET;0;COLOR;20 **1;236;118;0;IS_COLOR_ACTIVE;1;ATTRIBUTES;2;DM/File Type;ANSA;DM/Status;WIP;CONT **AINS;ANSAPART;12-17; **ANSA_PART;PART;ID;12;MID;103;NAME;P103\;fixture_hammer_side;BELONGS_HERE;YES;ST **UDY_VERSION;0;PID_OFFSET;0;COLOR;217;253;228;0;IS_COLOR_ACTIVE;1;ATTRIBUTES;2;D **M/File Type;ANSA;DM/Status;WIP;CONTAINS;MPC;3;SOLID_SECTION;103; **ANSA_PART;PART;ID;13;MID;98;NAME;samples;BELONGS_HERE;YES;STUDY_VERSION;0;PID_O **FFSET;0;COLOR;215;32;249;0;IS_COLOR_ACTIVE;1;ATTRIBUTES;2;DM/File Type;ANSA;DM/ **Status;WIP;CONTAINS;SHELL_SECTION;107-108;SOLID_SECTION;105-106; **ANSA_PART;PART;ID;14;MID;102;NAME;P102\;nut_beam_side;BELONGS_HERE;YES;STUDY_VE **RSION;0;PID_OFFSET;0;COLOR;212;66;15;0;IS_COLOR_ACTIVE;1;ATTRIBUTES;2;DM/File T **ype;ANSA;DM/Status;WIP;CONTAINS;SOLID_SECTION;102; **ANSA_PART;PART;ID;15;MID;101;NAME;P101\;bolt_beam_side;BELONGS_HERE;YES;STUDY_V **ERSION;0;PID_OFFSET;0;COLOR;210;100;35;0;IS_COLOR_ACTIVE;1;ATTRIBUTES;2;DM/File ** Type;ANSA;DM/Status;WIP;CONTAINS;SOLID_SECTION;101; **ANSA_PART;PART;ID;16;NAME;BARs;BELONGS_HERE;YES;STUDY_VERSION;0;PID_OFFSET;0;CO **LOR;208;134;56;0;IS_COLOR_ACTIVE;1;ATTRIBUTES;2;DM/File Type;ANSA;DM/Status;WIP **;CONTAINS;BEAM_SECTION;104;MPC;1-2; **ANSA_PART;PART;ID;17;MID;100;NAME;P100\;beam_shell;BELONGS_HERE;YES;STUDY_VERSI **ON;0;PID_OFFSET;0;COLOR;206;168;77;0;IS_COLOR_ACTIVE;1;ATTRIBUTES;2;DM/File Typ **e;ANSA;DM/Status;WIP;CONTAINS;SHELL_SECTION;100; **ANSA_PART;PART;ID;27;NAME;rigids;BELONGS_HERE;YES;STUDY_VERSION;0;PID_OFFSET;0; **COLOR;215;99;152;0;IS_COLOR_ACTIVE;1;ATTRIBUTES;2;DM/File Type;ANSA;DM/Status;W **IP;CONTAINS;MASS;58829,60694,60697-60698;MPC;80762;

74

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4. Eduard Caamano, Inés Lama, Andreas Rousounelos, Jordi Vinas, 2011 “Improved methodology for squeak & rattle analysis with abaqus and correlation with test results”, IDIADA Automotive Technology.

5. A.Ramanathan, S. Noll, E. Dehoff, R. Rittenhouse, 2017 “An Investigation into Modeling Approaches for the Dynamic Response of a Shipping Contaiter Cart and Suspended Automotive Parts Under Random Base Excitation using LS-DYNA”, 11th European LS-DYNA Conference.

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G_FINAL.pdf, Solidworks. [Cited on 2018-08-30]

8. Dr. Colin Mercer, 2006 “Acceleration, velocity and displacement spectra – Omega Arithmetic” Prosig.

9. Dassault Systemes, 2013 “Abaqus Analysis User's Guide” http://dsk.ippt.pan.pl/docs/abaqus/v

6.13/books/usb/default.htm [Cited on 2018-08-30]

10. Tony Abbey, 2013 “Impact, Drop and Crash Testing and Analysis” http://www.digitaleng.news/de/impact-drop-and-crash-testing-and-analysis/, Digital Engineering. [Cited on 2018-08-30]

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