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Dynamic Response Reconstruction

Chinmay Pawaskar

Pravin Kulkarni

14 Jan 2015 Dynamic Response Reconstruction 1

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

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

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

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0

2000

4000

6000Simple Raw Data Plot

X data

Y data

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

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

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

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

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

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

Step 5. Running the Test

Testing Statistics

Durability Analysis

Performance Analysis

OptimizedDrive

Data Acquisition

u*(t)

yN(t)

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Actuators

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

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

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!

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