ATILA Tutorial – Nov. 2009

Micromechatronics, Inc.Micromechatronics, Inc.“User Defined Waveform Generation

using ATILA Transient Module with Wilson-θ Methods”

Seung Ho Park and Alfredo Vazquez Carazo

200 Innovations Blvd., Suite 155 State College, PA 16803Micromechatronics, Inc.

www mmech comwww.mmech.com

Three Transient Analysis in ATILAThere are three methods that ATILA can use to solve transient analysis: Central Difference, Newmark and Wilson-θ. In this tutorial, we will concentrate on the Wilson-θ method and

C t l Diff M th d

specifically the use of user-defined excitations (like triangular, square, polynomial, etc excitations).

Central Difference Method

Second order (parabolic) interpolation along the time axisand deriving the first and second order derivative from it.

Newmark Method

Truncated Taylor series expansion and its first derivative.

Wilson-θ Method

Similar to Newmark Method, except the time step ∆t isreplaced with θ ∆treplaced with θ·∆t.

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How to apply a user-defined waveformATILA has several types of electrical and mechanical excitations pre-defined for the transient simulation. If you check the GiD menu to can find: Sine, rise cosine, step, pulse, external.

Sine: Rise Cosine

SStep Pulse

However, how can you apply a waveform not pre-defined to f t i t l i ? (lik t i l th

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perform a transient analysis? (like triangular, square, or any other shape). We call these excitations, USER-DEFINED excitations.

Steps for User-defined Excitation We will guide you through the following steps to create user-defined excitations.

1. Preparation of Simulation Structure

2 Assignment of Temporary Electric Potential2. Assignment of Temporary Electric Potential

3. Deciding Transient Parameters

4. Desired Waveform Preparation through Generating ‘project.exc’

5. ‘project.ati’ File Generation

6. Modification of ‘project.ati’

7 M l Si l i R d R l G i

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7. Manual Simulation Run and Results Generation

Points that will help understanding...

Initially assigned electric potential will be later replaced by a user defined waveform.

Integration of user-defined waveform requires manual modification of ATILA code.

‘project.exc’ is a file that contains user-defined waveform and it needs to be manually generated and placed in the simulation file folder.

‘project.ati’ is a file that contains condition and dimensional information in ATILA codes and it should be modified to declare there is a user-defined file.

Manual run of simulation is required since ‘Calculate’ function of GiD will reset a modification made to ‘project.ati’.

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Preparation of SimulationProblem to be solvedLet’s assume that a transient simulation is required for a piezoelectric actuator under a square wave excitation.

Square Piezo-Actuator

qexcitation

We try to determine the Transient displacement at Transient displacement at top face

Electrical Excitation

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Preparation of Simulation

E l 5 X 5 X 2 A (PZT5HA)

The first step is to prepare the model to be simulated.

Example: 5mm X 5mm X 2mm Actuator (PZT5HA)

Temporarily, excite the actuator with 1V with a conventional with 1V with a conventional forced potential .It will be later modified into a waveform we define.

Polarization

7Ground

Transient ParametersThe next step is to select the Transient simulation and set certain parameters

Integration MethodIntegration Method

Increment of Time Gap

Skipped Step

Time Gap (∆T)

Frequency for Loss Calculation

θ P t

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θ Parameter

Ignored Parameter

Transient Parameters - Details

Integration Method: Central, Newmark, Wilson

NS: Number of Steps between each Calculated Step

NSKIP: Skipped Step before the First Calculation PointNSKIP: Skipped Step before the First Calculation Point

DELTA T: Time Gap (∆T)

FL: Frequency for Loss Calculation

PAR1: Ignored in Central γ in Newmark θ in Wilson (should be >1 366)PAR1: Ignored in Central, γ in Newmark, θ in Wilson (should be >1.366)

PAR2: Ignored in Central, β in Newmark, Ignored in Wilson

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External Excitation Waveform Now is time to create the user-defined excitation. You will need to do some calculation work and generate the file “project.exc” manually.This file is NOT automatically generated by ATILA.

User-defined Waveform can be integrated through ATILA Transient Module.

‘project.exc’ is the file that contains waveform information.

It should be a text document format and placed in a simulation file folder.

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Format of ‘project.exc’ FileThe project.exc file contains 4 columns. (1st column: Time steps, 2nd

column: Amplitude of the excitation, 3rd column: 1st derivative, 4th column: 2nd derivative.) For electrical excitations, the 2nd column will be typically the voltage and then the third and fourth columns will be the first and second derivative of the voltage. For a mechanical excitation, the second column will correspond with the displacement or mechanical stress, and then the corresponding 1st and 2nd derivatives.

Zero values for the first raw as default.

Amplitude of 1st Derivative 2nd Derivative

11Time stepsNSKIP*∆T, (NSKIP+NS+θ)*∆T, (NSKIP+2NS+θ)*∆T, .... etc.

pthe excitation

Format of ‘project.exc’ FileExample: How to generate the project.exc file for a square voltage excitation

Define the excitation waveform in segments: 1 b

Am

plit

ude 1

0 f(t)

ti

a c

b: f(t)=1 f`(t)=0 f"(t)=0

a: f(t)=0, f`(t)=0, f"(t)=0

time

c: f(t)=0, f`(t)=0, f"(t)=0

b: f(t)=1, f (t)=0, f (t)=0

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Example: Square Wave

0

Amplitude changes

1st and 2nd derivatives are 0,i th i l i thi 1

changes between 0 and 1

since there is no slope in this case.1

0

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How to Decide Time Step?

The first column (time) of the ‘project.exc’ combines Transient Time Step and Calculation Time Step.

Transient Time Step: Internal Steps for ATILA0, θ* ∆T, (1+ θ)* ∆T, (2+ θ)* ∆T, (3+ θ)* ∆T .... (First step is 0 as default value)

Calculation Time Step: Actually Calculated and Shown as ResultsNS*∆T, 2*NS*∆T, 3*NS*∆T, 4*NS* ∆T.... etc.

(First step is 0 as default value)

( But initial # of steps designated in NSKIP will be skipped. )

When NS=1, NSKIP=1, and θ=2, two steps become the same thus the first column can be easily prepared (Suggested method for beginner)

Wilson-θ method is stable when θ is larger than 1.366. Therefore suggested θ=2 will be stable and easy to prepare the

column can be easily prepared (Suggested method for beginner).

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‘project.exc’. However there will be some amount of numerical damping which increases as θ is getting larger than 1.366.

Time Step ExamplesEx. 1) NS=2, NSKIP=1, ∆T=0.001, θ=2,

Transient Time Step: 0, 0.002, 0.003, 0.004, 0.006, 0.008 ....

0 0.002 0.003 0.004 0.005 0.006 0.007 0.008 ...

Calculation Time Step: 0.004, 0.006, 0.008, 0.010, ....

Therefore, the numbers in the first column should be:

0, 0.002, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, ...

Ex. 2) NS=3, NSKIP=2, ∆T=0.001, θ=1.4,Transient Time Step: 0, 0.0014, 0.0024, 0.0034, 0.0044, 0.0054, 0.0064, 0.0074, 0.0084, 0.0094, ....

Calculation Time Step: 0.009, 0.012, 0.015, 0.018, ....

0, 0.0014, 0.0024, 0.0034, 0.0044, 0.0054, 0.0064, 0.0074, 0 0084 0 009 0 0094

Calculation Time Step: 0.009, 0.012, 0.015, 0.018, ....

Therefore, the numbers in the first column should be:

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0.0084, 0.009, 0.0094, ....

(Note: θ=1.4 can avoid damping but time step becomes complex.)

Generation of ‘Project.exc’Example for Excel Step 2: Save as Web Page (i.e.,

HTML format).

Step 1: Build a waveform function using the Excel

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Generation of ‘Project.exc’ (cont.)

Step 3: Open the HTML file and copy the numbers

Step 4: Paste the numbers to Notepad and save as py p‘project.exc’ in the simulation file folder.

Note: If Excel data are directly copied into

It is opened by Explorer.Use Ctrl+A and Ctrl+C

Note: If Excel data are directly copied into Notepad, columns are not properly recognized by ATILA. ‘project.exc’ can be generated also by program languages, such as C, in a much i l b di tl ti t t

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Use Ctrl+A and Ctrl+C. simpler way by directly generating a text document.

Calculation Process 1Generation of ATI File

This is a step converting geometric information and conditions prepared in GiD interface into ATILA code.Y h ld b bl t fi d ‘ j t ti’ i th i l ti fil f ld

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You should be able to find ‘project.ati’ in the simulation file folder, after execution of this function.

Calculation Process 2Modification of ‘project.ati’ File

‘project.ati’ can be opened by Notepad or WordPad.project.ati can be opened by Notepad or WordPad.

Currently, excitation amplitude is 1 because it was temporarily set as 1 in the slide 7.

It should be changed to ZERO whichis declaring that there is a ‘project.exc’.

After changing to 0, ATILA will use ‘project.exc’ for excitation.

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Calculation Process 3Simulation Running and Results Generation

Run ATILA Solver forRun ATILA Solver forCalculation

Convert ATILA simulation resultsinto GiD format and move toGiD post process

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GiD post-process

Generated Square WaveformSquare Waveform can be confirmedby using Point by using Point Analysis Function.

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Overshoot and RingingDisplacement data show transient response of the structure.

22Overshoot

Ringing

Th k f i i ATILAThank you for your interest in ATILA.

Micromechatronics Inc

For further information please contact us.

Micromechatronics, Inc.200 Innovation Blvd. Suite 155State College, PA 16803, U.S.A.

1-814-861-5688contact@mmech.com

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