Printing Machine Simulation

Presentation29.08.2011

Printing Machine Simulation

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Printing Machine SimulationMotivation• Perfect dots, printed

at the wrong place• For a good printout

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• For a good printoutyou need to handle the whole printing machine as well => e.g. vibrations

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Motivation – Design of a MachineA printing machine should be …• Light weight (material costs, transport) • high dynamic• Heavy and stiff construction to prevent vibrations• Cost efficient

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⇒It‘s always a compromise

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Benefits of using Simulations• Reduce mass, increase performance, with acceptable

stiffness• No time/money to build more than one prototype• influence of the controllers and drives can be

estimated and optimized during the design process• Enables interdisciplinary and parallel workingP

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⇒It‘s always a compromise


Classical Design ProcessStandard in industry: sequential workflow

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•Inefficient link between departments•Result: “Pandoras Box

Classical Design ProcessP

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Classical Design ProcessP

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Simulation of the print machine• Mechanical Simulation with FEM• Control Design&Simulation with

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Classical Design Process

Common simulations • Structural Mechanics Simulation with FEM • Multi Body Simulation (e.g. SimMechanics)• Control Design&Simulation with e.g.

Matlab/Simulink

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Matlab/Simulink

New approach• Link the Simulations, the knowledge and the

people behind

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Sample MachineP

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Finite Element Analysis• Static stress and displacement analysis• Modal Analysis: Resonant Frequencies and

Eigenmodes => Which frequencies will be excited and how the oscillation mode will look like

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Finite Element Analysis• Modal Analysis: Resonant Frequencies and

Eigenmodes

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Mode 3: 132 Hz Mode 5: 209 Hz Mode 6: 356 Hz

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Structrual Mechanics FE - Analysis

Advantages• Simulation of static behaviour• Modalanalysis

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Drawbacks• No possibility to simulate real controllers and drive

systems• Simulations in time domain very expensive

⇒Only useful for mechanical engineers!!!

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Multi Body Simulation• Model of the machine consisting of• Undeformable masses• Joints• Springs�Tool Matlab Simulink / SimMechanics

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�Tool Matlab Simulink / SimMechanics

• Basic Model

B F

Y-Axis

B

F

X-Axis

Step

CS1 CS2

Spindel

Scope

CS1 CS2

Maschinenbett

Joint Actuator

Base

CS1 CS2

Balken

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Multi Body Simulation

CS1

CS2

B

F

B

F CS1 CS7

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1

Out1

CS2

CS3

CS4

CS5

Spindel

Scope

CS1

CS3

CS4

CS5

Maschinenbett

B

F

B

F

B

F

B

F

B

F

B

F

Base

CS2

CS3

CS4

CS9

CS16

CS17

Balken

1

In1

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Multi Body Simulation

Advantages• Simulation of kinematic behaviour• Fast simulation in time domain• Export of linearized models to Control Systems

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SimulationDrawbacks• No deformable bodies• The structural behavior considering vibrations is not

respected� Useful as a basic model, but not can not consider

vibrations, which are often crucial for the control design

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Combination of methodsP

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Step1: Export from FEM to MatlabP

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• Masses and spring constants can be representedby Eigenvalues (Resonant Frequencies) andEigenvectors (shape of the vibration modes)

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Step1: Export from FEM to Matlab�Row in Modal Matrix = 1-Mass-Oscillator

Resonant Frequency determined by eigenvalue

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-100

Mag

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dB)

Bode Diagram

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�Order Reduction= Elimination of modal DOF�Precision = Depends on the chosen modes�Result: StateSpace-Model

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-300

-250

-200

Mag

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dB)

0

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WorkflowP

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Result 1: Bode Plot

Mode 3

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Compliance of the print head

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Mode 5

Mode 6

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Result 2: Control Design

• Controller Design e.g. using SISO TOOL

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Step 2: CombinationFEM�SimMechanics (MBS)

• The StateSpace-Model from FEM represents the machine at one specific position only

• The MBS Simulation does only represent the

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• The MBS Simulation does only represent the rigid bodies

�Solution: Combination of the StateSpace-Model from FEM with the MBS- Simulation

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Step2: Combination flexible+rigid Bodies

• Integration of flexible Models intoSimMechanics

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•

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• Integration of flexible Models intoSimMechanics

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• Interpolation between Nodes• Runtime-Interpolation between two closest

nodes

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O4

O5

1

TCP_Disp

CS1

CS2

CS5

CS6

xIn f Out

Base Mov er

RO

CS1

CS2

CS3

xIn f Out

Base Mov er

LO

B

F

B

F

B

F

B

F

Base

CS1

CS2

CS7

CS9

1

TCP_Force

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xDRIVE

3

yEncoder

2

xEncoder

CS3

CS4

CS8

CS7

CS9

Spindel

Scope1

xIn f Out

Base Mov er

RU

CS4

CS5

Maschinenbett

xIn f Out

Base Mov er

LU

RO_F

LO_F

RU_F

LU_F

y Axis_R

y Axis_L

RO_Disp

LO_Disp

RU_Disp

LU_Disp

Dynamik Balken1

B

F

B

F

B

F

B

F

00

CS3

CS4

CS21

CS16

CS17

CS22

Balken

3

yDrive

2

xDrive

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.5

0

0.5

1

t / s

Y Position / m

Motion in Y Direction

0.2

0.4

0.6

X Velocity / m/s

Velocity in Y Direction

a)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-15

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-5

0

5x 10

-6

t / s

Displacement X / m

Displacement in X Direction

x 10-6 Displacement in Y Direction

b)

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.2

0

t / s

X Velocity / m/s

c)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-6

-5

-4

-3

-2

-1x 10

t / s

Displacement Y / m

Displacement in Y Direction

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.5

0

0.5

1x 10

-5

t / s

φ / rad

Displacement in φ Direction

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Result 3: Time -domain simulation• Print head - Movement

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

0

2x 10

-4

Def

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[m]

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Def

orm

atio

n X

[m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.5

0

0.5

1

Def

orm

atio

n Y

[m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2x 10

-5

Def

orm

atio

n Z

[m]

Time [sec]

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Result 4: 3D-Simulation

• Visualization of „Beam-Twister“

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Result 4: 3D-Simulation

• Visualization of „Beam-Twister“

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Result 5: Moving DynamicsP

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Model Verification• Different Ways to create the same model

A: FEM � Full Model � BodeB: FEM � Beam Model � SimMechanics � Bodeallows comparison and verification

-80From: TCP X To: TCP X

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-200

-180

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-100

Mag

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de (

dB)

101

102

103

104

-180

-135

-90

-45

0

Pha

se (

deg)

Frequency (rad/sec)

FEMRBSFMBS

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Benefits• Deformable Bodies in MBS ( e.g. SimMechanics)• Advantages from FEM and Rigid Body Simulation• Model linerisation in different axis configurations

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• Model linerisation in different axis configurations• Realistic Time-Domain simulation• Simulation of nonlinear effects (e.g. Actuators)• A model which includes the knowledge of the

mechanical structure and the control algorithms

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Conclusion

• Automatic Import FEM�Matlab• Links Control Design – FEM Simulation• Links electrical and mechanical engineering

• Combination FEM / Matlab / SimMechanics

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• Combination FEM / Matlab / SimMechanics• Time-Domain simulation of flexible bodies• Fully integrated in Simulink

• Control Engineering• Automatic Plant Modeling• Influence of Controllers on Machine Dynamics

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Conclusion

• With linking the tools, you also link thepeople behind them!

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Intermezzo 2 Cooking recipe for simulations

• Define the goal of the simulation!

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• Idealisation• Mathematical modelling: Equation type?

Simulation tool?• Build up your model stepwise!


Intermezzo 2 Cooking recipe for simulations

• Model verification : Are the equations solved correctly? Is the model behaviour reasonably

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correctly? Is the model behaviour reasonably concerning the idealisations?

• Model validation : Are the right equations being solved? Are the idealisations appropriate concerning the goals of the simulation? => Can only be fully answered by experiments


Simulation of the PrintoutMotivation: What effect will this vibrations have on the final print result?

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Measured vibrations of a printing machine

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A‘ = R(φ)*A+r(x,y)

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Ideal printout Simulated printout with vibrations

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Ideal printout Simulated printout with vibrations

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Good vibrations?

Approach for critical mode detection:�isolate the impact of a single

vibration mode on the printout

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Benefits and limits of Simulations

• Complex mechatronic systems have to be regarded as a whole and not only as

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regarded as a whole and not only as configurations of different isolated components

• A common simulation model of the different disciplines and physics is a helpful tool to bring the knowledge of the different people together


Limits

• You can never create a model, which fits the reality absolute exactly!

• The simulation tool, which is able to solve all simulation problems, does not exist!

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all simulation problems, does not exist!• Never start a simulation without knowing

your goal!• Simulations are not cost free as well• You have to build up and cultivate the

simulation know how


Acknowledgements

Florian Fässler, Polytype SA, Switzerland ⇒ Printing machine Simulation

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Johannes Renner, Institute of Print Technology, Switzerland

⇒ Printout Simulation


Bern University of Applied SciencesInstitute of Print Technology

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Philip Marmet

+41 (0)34 426 43 44 (direct)+41 (0)34 426 41 83 (secretariat)[email protected]

Printing Machine Simulation

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