RANDOM RESPONSE & FATIGUE

OPTIMIZATION IN THE FREQUENCY DOMAIN

Fatma Kocer, Keshav Sundaresh, Sridhar Ravikoti, Valdir Cardoso Altair Engineering Inc. Neil Bishop CAEfatigue

Abstract

Frequency based methods for random response and fatigue are becoming more widely

used in the automotive industry. The use of PSD’s (Power Spectral Densities) coupled with

system properties in the frequency domain (transfer functions) offers significant benefits

over time based approaches in terms of analysis time, model size that can be handled,

and most importantly, such methods facilitate the incorporation of optimization

techniques to find the optimal values for parameters such as shell thicknesses, material

properties, weight.

In this paper, application of frequency based methods for random response and fatigue

optimization is demonstrated on an automotive full body system. The process followed

uses MotionSolve generated body loads and OptiStruct stress results as input to a

CAEfatigue VIBRATION analysis. This process is executed from HyperStudy for

optimization and the results produced are then post processed in HyperView. Using the

process outlined, it is feasible to achieve considerable weight reduction while maintaining

desired fatigue life.

Introduction Structural analysis (and fatigue calculations) in the aerospace community are often done

using loads specified originally in the frequency domain. In this case the CAEfatigue

VIBRATION (CFV) code is directly applicable. In other situations the loads begin in the time

domain. This is typical, for example, in the automotive industry. In this situation it is useful

to know the advantages of switching loading environment from time to frequency

domain. There are two main areas where benefits occur - related to performance and

information generated.

In terms of performance there can be a huge benefit because in the time domain it is

necessary (for dynamic systems) to perform a full transient dynamic analysis for every

event applied to the structure in order to obtain the loading Modal Participation Factors

(MPF’s). Typically up to 100 such events might be specified - meaning 100 full transient

dynamic analyses have to be done. In the frequency domain the system properties

(transfer functions) are independent of the loads applied. Therefore, only one structural

analysis is necessary.

In terms of information generated the results from a transient dynamic analysis can be

processed to obtain fatigue damage at every point on the structure. This provides fringe

plots of damage and absolute values. So we will know if the structure survives. In the

frequency domain we get the same fringe data (as well as numerous other statistics like

the irregularity factor). We can also easily see, for each event individually, the damage

done, the response statistics like RMS, the irregularity factor and the linear peak stress

and non-linear elastic-plastic strain. And crucially, at any point, we can obtain the

response PSD. This will indicate the frequencies where resonances occurred. So, not only

do we see what the fatigue life and damage that occurred were, but we also see why that

damage occurred. Then, if we combine that with the event by event histogram for

damage we see what the damage was, what caused it, and what to do about it (which

event to focus on).

Overview of the Entire Process

A virtual durability process has been set up to generate body loads using the multi-body

system solver MotionSolve and frequency response function stresses in OptiStruct that

are combined in CAEfatigue Vibration to do the fatigue assessment in the frequency

domain. The multi-disciplinary optimization tool HyperStudy was used to perform gauge

optimization on the body in white (BIW) model maintaining the fatigue damage life under

specified failure limits.

Figure 1. Multi-disciplinary durability analysis in the frequency domain using Altair HyperWorks and CAEfatigue

Loads Cascading Using Multi-Body Simulation (MBS)

In conventional vehicle development, the fatigue strength of the chassis, and its

components, are evaluated through physical testing. Since a complete set of component

load and stress measurements is hard to obtain, field-testing is commonly augmented

with laboratory measurement. Through coupled Multi-body Simulation (MBS), Finite

Element Analysis (FEA), and fatigue simulations, the need for physical testing can be

minimized. The purpose of running a Multi-body simulation is to extract accurate dynamic

loads coming onto the structure. The first step is to define a duty cycle for the test

product. The vehicle is instrumented with wheel force transducers to capture the time

history of the loads on each of the spindles. The vehicle is driven over different road

conditions on the test track. A duty cycle representative of real-life usage is then

synthesized. Figure 2 shows one such test signal that was applied as an input to attenuate

the full vehicle model. In general these inputs will be multiple channel inputs with

correlation.

Figure 2. 4-post shaker road load history signal applied to the full vehicle Multi-body

model

MotionView – Altair’s Multi-body Dynamics preprocessor was used to assemble a full

vehicle model. MotionView provides users with a built-in, fully parameterized, interactive

suspension and vehicle dynamics model library which can be used as a starting point to

rapidly assemble a half- or a full-vehicle model. In this case, a full vehicle model with a

front MacPherson suspension, a rack pin steering system and a rear twist beam

suspension was assembled using the vehicle library. These templates come with a pre-

defined vehicle topology and data such as hard points, body mass and inertia, joints,

bushings, spring dampers and sensors.

Figure 3. Full Vehicle Model Assembled in MotionView

In order to account for the structural flexibility of the Body-In-White (BIW) structure in

the Multi-body simulation, a Finite Element model of the structure was used as an input

in OptiStruct – Altair’s structural solver and a Component Mode Synthesis (CMS) analysis

was run. The output of the OptiStruct CMS analysis was further used to model the

flexbody in MotionView. With the inclusion of the BIW structure as a flexbody, we now

have a hybrid (i.e., a model with both rigid and flexible bodies/parts) in MotionView as

shown in Figure 4.

Figure 4. Component Mode Synthesis (CMS) flexbody of the Body-In-White Structure in

MotionView

MotionView also provides users with a set of pre-defined industry standard events for

half- and full-vehicle analysis. In this instance, we used a pre-defined 4-post shaker test

rig event to define the semi-analytical durabilty analysis. The experimental signals from

test are applied as prescribed motion to the shaker bench as highlighted in Figure 5.

Figure 5. Multi-body model with road load histories applied as input to attenuate the 4-

post Front Left, Front Right, Rear Left and Rear Right jacks

Then a transient Multi-body dynamics analysis of the virtual high-fidelity vehicle model

(that’s attenuated by a virtual 4-post shaker) was run using MotionSolve – Altair’s Multi-

body solver. A set of 15 interface node locations were selected to output the reaction

force histories as highlighted in Figures 6 and 7.

Figure 6. Schematic list of interface nodes to extract forces from MotionSolve

Figure 7. Interface node list to measure output forces from MotionSolve

Once the Multi-body analysis was run in MotionSolve, the corresponding reaction force

histories/cascaded loads were post-processed using HyperGraph – Altair’s plotting client.

The force histories were further exported as RPC files directly from HyperGraph. Figure 8

and 9 show the reaction force/torque output from MotionSolve plotted in HyperGraph.

Figure 8. Force histories measured from MotionSolve

Figure 9. Torque histories measured from MotionSolve

OptiStruct Setup

The loading channels from the MotionSolve model are mapped on the car flexbodies in

OptiStruct to perform a frequency response analysis (FRA) and also the static mean stress

loadcases. A total of 90 FRA loadcases and 90 mean static loadcase results are generated

in OptiStruct and the results are then fed into CAEfatigue Vibration.

CAEfatigue Process

The CAEfatigue VIBRATION software produces a variety of fringe type data for quantities

like fatigue damage, fatigue life etc. Figure 10 shows the fringe plot of fatigue damage

plotted using HyperView.

Figure 10. Fringe plot of damage obtained using the CAEfatigue VIBRATION software

This fringe plot of damage is made up from the sum of damage for all the contributing

events (10 in this case). At each output (grid) point the result can be further broken down

into its constituent parts (per event) in order to better understand the structures

behavior. Figure 11 shows the response plot obtained at a critical element grid point for

one event. Each event will have its own response.

Figure 11. Stress response PSD obtained using the CAEfatigue VIBRATION software

The best way to indicate the response per event is with the event plotter. Figure 12 shows

the RMS stress per event at the same critical location.

Figure 12. RMS stress per event obtained using the CAEfatigue VIBRATION software

Figure 13 shows the RMS strain per event at the critical location. Note that this is the

elastic-plastic strain obtained using a Neubers Rule approach.

Figure 13. RMS strain per event obtained using the CAEfatigue VIBRATION software

Figure 14 shows the Irregularity Factor per event at the critical location. Note that values

approaching 1.0 indicate that the response is approximately narrow band and as the value

drops below 1.0 multi-mode (wide band) response is indicated.

Figure 14. Irregularity Factor per event using the CAEfatigue VIBRATION software

Figure 15 shows the maximum stress per event at the critical location, obtained by using

3 times the RMS stress as a peak estimator. This can be a useful way to obtain non-fatigue

related response data. The P factor (3 in this case) is user definable. If a higher confidence

that the value will not be exceeded is required then P could be set to 4.0, or even 5.0.

Figure 16 shows the maximum per event obtained using a Neubers Rule approach.

Figure 15. Maximum stress per event using the CAEfatigue VIBRATION software

Figure 16. Maximum strain per event using the CAEfatigue VIBRATION software

Figure 17 shows the damage per event. This indicates that events 7 and 10 are

dominating the damage.

Figure 17. Damage per event obtained using the CAEfatigue VIBRATION software

Figure 18 shows the Plasticity Index per event. This is the ratio of the elastic-plastic peak

strain divided by the elastic strain. Values much larger than 1.0 indicate significant plastic

behavior.

Figure 18. Plasticity Index per event obtained using the CAEfatigue VIBRATION software

Optimization Problem with HyperStudy

First step in formulating the design problem as an optimization problem is identifying the

design variables and their properties. Next, responses that are measures of the

performance need to be defined. Finally, objective and constraint functions need to be

created using the defined responses.

For this problem, shell thicknesses of the 40 parts are selected as design variables (Figure

19). These parts are identified as contributing parts based on experience. Objective

function is to minimize the mass, and the constraints are imposed on damage to be less

than 1.0 at the 3 locations in each iteration where highest damage occurs. The Global

response surface method (GRSM) was used as the optimization methodology. This allows

users to explore as much as time and computer resources are available, with the ability

to perform a manual stop if needed.

Some of the important functionalities in HyperStudy for this process involved a quick

study setup through HyperMesh parametrization by automatic transfer of the model

parameters from HyperMesh to HyperStudy, utilization of HyperWorks result readers for

response extraction, execution of a number of concurrent jobs utilizing multiple cores,

multi-model optimization with OptiStruct for structural analysis and CAEfatigue for

damage calculations, and a real-time study monitoring through HyperStudy’s dynamic

post-processing.

Figure 19: BIW gauges optimized for fatigue life

Observations and Conclusions

The baseline model was infeasible because some of the damage values were > 1, but the

1st iteration result was feasible with maximum damage < 1. Some panel thickness of the

1st iteration result are increased from the initial model and the total mass is increased

(151 kg in the infeasible initial model and about 320 kg in the feasible 1st iteration). It is

a useful finding to know which panels must have increased thickness in order to survive

the loading (damage < 1). Starting from the feasible 1st iteration HyperStudy proceeded

to minimize mass while maintaining constraints (damage < 1). HyperStudy reduced mass

from the feasible 1st iteration 320 kg to 196 kg (38.75%) in the final iteration, still an

increase from the baseline (an increase of about 30% from the initial infeasible design).

The 1st pass iteration history curves of panel thickness in HyperStudy highlighted 2 panels

which appear to limit the progress of the optimization. We decided to investigate the

effect of removing those 2 panel thicknesses for the 2nd pass. We removed those 2 panel

thicknesses as independent variables and the weight of those 2 panels as part of the mass

minimization objective function. HyperStudy reduced mass from the 1st iteration 151 kg

to 89 kg (41%) in the final iteration. The history curves in HyperStudy show that one

important load-bearing component cannot be reduced further in thickness.

Figure 20 shows the optimization history, with mass reduced by 41% in the final iteration

and all the constraints representing damages at the top 3 locations less than 1.0.

Figure 20: Optimization history plotted from HyperStudy

Figure 21 shows the history of gauges of 40 parts as HyperStudy tries to find an optimal

solution

Figure 21: Gauge iteration history

It is important to note that fatigue damage was the only design constraint in this study.

In general, other criteria would need to be included and this might change the amount by

which mass could be reduced.

Future Work

Initial scope of the project produced interesting results considering only fatigue life as the

driving constraint. The scope of the problem can be expanded to a multi-disciplinary

optimization scenario by considering noise, vibration, and harshness responses due to the

change of gauges along with fatigue life. Also the gauge changes can be propagated

upstream to the MBD analysis along with the FRF stresses to regenerate the loads PSD

matrix. Finally, the failure locations were predetermined from the baseline run, and the

damage values at these locations were monitored through the optimization history.

However, a plausible future work can consider neighboring regions and locations that

originate due to changing loads and thicknesses.

Acknowledgements

The authors would like to thank Felipe Leila, Paulo Tonett, and Ravi Kodwani at Altair for

for their contributions in this project.