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Dynamic Response Reconstruction
Chinmay Pawaskar
Pravin Kulkarni
14 Jan 2015 Dynamic Response Reconstruction 1
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Agenda
• Introduction
• Modeling
• Simulation
• Design Study
• Conclusion
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About Tech Mahindra
• Tech Mahindra is a global engineering consultant and service provider to automotive, aerospace, defense & manufacturing industries; offering end-to-end Product Development Support solutions.
• We use Computer-Aided Engineering to improve product quality, shorten time-to-market and foster product innovation.
– Durability / Rigidity
– Safety & Crash
– CFD
– Optimization
– Ride & Handling
– NVH
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Computer Aided Engineering
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[CFD]External aerodynamics, under-hood flow, HVAC, Water jacket flow, cooling system design
[Durability / Rigidity]: Strength & Life Estimation of various components & systems
[Safety & Crash]Safety evaluation against regulations such as FMVSS & ECE
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Computer Aided Engineering…
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[NVH]Noise & Vibration prediction for engine and in-cab noise
[Optimization]Topology, topography, shape and size optimization
[Ride & Handling]Suspension & Steering K&C, Ride Quality, Handling - Control & Stability
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Full Vehicle Virtual TestingRide – Comfort & Durability
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Full Vehicle Virtual ModelHandling – Stability & Control
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Sub-System Virtual Testing
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MATLAB Applications…
• Automated Post-processing
• Reports
• Design Study
• Design of Experiments
• Optimization
• Control
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0 200 400 600 800 1000 1200 1400 1600 1800 2000-8000
-6000
-4000
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0
2000
4000
6000Simple Raw Data Plot
X data
Y data
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Durability Methods
• Physical Testing
• Fully-Analytical
• Semi-Analytical Method
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A Typical Durability Process
• FEA-based structural testing
• Peak acceleration from Test are applied as a body force on the component and stress & strain are reported
• Very simplistic & Intuitively inaccurate
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a
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Current Durability ProcessShort comings
• Some Field failures do not entirely match with CAE failures
• Investigated the relationship between Acceleration and strain & Loads and strain on Testing Data. Signal processing involved:
– Offset drift removal, filtering, normalization
– Metric checked for measurement time delays
– 30 highway & track events for 4 configurations checked
• Established that:
– Acceleration is not a good measure of strain (i.e. component life)
– Loads (measured in the appropriate direction) are a very good measure of strain (i.e. component life)
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Develop a method to apply inputs to the component in such a way that all loads going into the structure & all accelerations across the structure match with that of Test.
Test Test-Rig
Proposed Durability Process
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Proposed Approach – e.g. Cabin
• Measure cabin response on full vehicle
• 5 Post Shaker Test Rigs
• Use off-line FRF controllers
• Iterative procedure: No need to specially tune gains
• Automated and accurate
• Other benefits: A reduced order model
• Software based
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System Identification
• Methods to build mathematical models of dynamical systems from measured data.
– Grey Box or Black Box models
– Linear or Non-Linear models
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UnknownSystem
Knowny(t)
Knownu(t) H
HFind
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System Identification
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y(t)
u(t)
u*(t)
yd(t)
Determine u*(t) for a reduced system, such that yd(t) ≈ y(t)
1. Estimate System identification
2. Invert
3. Pass desired yd thru
4. Calculate u(t) Back Calculation
5. Iterate till convergence
Can be extended to MIMO
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Step 1. Acquire Field Data
MeasuredResponse
Data Acquisition
DisplacementsAccelerationsForcesStrains
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Step 2. System Identification
Actuators
Data Acquisition
IdentificationDrive
Identification Response
System Identification
Colored Noise u(f)ifft
fft
y(f)
H(f) = y(f)/u(f)
y(t)
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Step 3. Drive File Generation
GeneratedDrive
DesiredResponse
Data Acquisition
Generate 1st
Drive File
yd(t)
fft
yd(f)
u1(f) = H-1(f) * y(f)
u1(f)
u1(t)
y1(t)
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Actuators
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Step 4. Iteration
Error DesiredResponse
GeneratedDrive
ActualResponse
Data Acquisition
Iteration
y1(t) yd(t)
u2(t)
y2(t)
Δy1(t)
fft
Δy1(f)
Δu2(f) = H-1(f) x Δ y1(f)
Δ u2(f)
Δ u2(t)
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Actuators
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Step 5. Running the Test
Testing Statistics
Durability Analysis
Performance Analysis
OptimizedDrive
Data Acquisition
u*(t)
yN(t)
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Actuators
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Generation of Colored Noise
• Need an excitation to identify the system
– Sufficient frequency content
– Should mimic operating conditions
• MATLAB code generates colored noise
Steps:
– Specify frequency spectra
– Add random phase
– IFFT
– Normalize
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Quarter Car Model
• For development, a quarter car model was used to mimic the shaker test-rig
– This is a 2 DOF spring-mass-damper model with base excitation
• Developed in 3 flavors in MATLAB:
– State Space (ss)
– Transfer Function (tf)
– Differential Equation (ode45)
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Quarter Car Model – Typical Output
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System Identification – Estimate of System
• After exciting the system, an FRF-based estimate of the system is built using measured input and output data
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Initial Drive File
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• After exciting the system, an FRF-based estimate of the system is built using measured input and output data
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Iteration Parameters
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Stopping Criteria
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• Following are reported at the end of each iteration
– Plot of Sum of Error Squared
– Print of Maximum of Absolute value of Errors
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Design Study – Iteration Gains
The convergence speed and the stability are governed by the iteration gain parameters
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Design Study – Non Linearity
• Non-Linearity added by way of cubic spring
• Difference between and
• Iteration slows down but heads to convergence
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MATLAB – MSC.ADAMS Connect
• Interconnects are developed to read and write data seamlessly with MSC.ADAMS (a proprietary Multi-Body Dynamics software) XML based results format. MATLAB is interconnected with MSC.ADAMS. This enables running a virtual shaker in a software environment.
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Animation
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Advantages:
• The off-line frequency domain control technique
– Is able to quickly and accurately adjust the input drives and recreate the desired response.
– does not require lengthy iteration and adjustment of several parameters as in other traditional control schemes.
– is good at dealing with non-linear test structures.
• The Off-line Frequency Domain Technique shows promise for automotive durability structures
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Thank You!
Dynamic Response Reconstruction 3514 Jan 2015