printing machine simulation
TRANSCRIPT
Presentation29.08.2011
Printing Machine Simulation
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Presentation29.08.2011
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
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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
-150
-100
Mag
nitu
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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
-350
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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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Step2: Combination flexible+rigid Bodies
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• Interpolation between Nodes• Runtime-Interpolation between two closest
nodes
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Step2: Combination flexible+rigid Bodies
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O4
O5
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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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Step2: Combination flexible+rigid Bodies
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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
-10
-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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Step2: Combination flexible+rigid Bodies
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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
orm
atio
n X
[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
-160
-140
-120
-100
Mag
nitu
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dB)
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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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Step2: Combination flexible+rigid Bodies
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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!
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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
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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
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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
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Acknowledgements
Florian Fässler, Polytype SA, Switzerland ⇒ Printing machine Simulation
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Johannes Renner, Institute of Print Technology, Switzerland
⇒ Printout Simulation
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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]