CAE Driven Parameter Studies Using the DoE

CAE Driven Parameter Studies Using the DoE Method and Tailored Objective Functions Karl M. Siebertz and Djamal E. Midoun Ford Motor Company

Abstract Madymo simulations have been used to screen numerous design parameters with respect to their potential effects on dummy loads. A specific objective function has been derived to combine the two load parameters to one single scalar. The DoE technique has been applied using the objective function to quantify the system performance.

Introduction Modern restraint systems have to fulfill a rapidly increasing number of requirements. Apart from that robust designs have become one of the major goals in product development. There is no doubt that this cannot be achieved without a massive usage of occupant simulations due to the vast number of parameters that need to be handled simultaneously. Having a well correlated Madymo model however does not solve the whole problem. Two issues remain: 1. The system performance is currently described by dozens of load parameters which need to be reduced to one scalar as a pre-condition for any kind of optimization. 2. A strategy needs to be developed to handle a huge number of design variables without numerical problems and without wasting computer power. Optimization techniques used in Madymizer for example are very effective in optimizing a limited number of parameters, but it cannot be

recommended to extend the number of variables to more than 10. For robustness studies it is not only important to reach the optimum combination of variables, but also to detect and quantify the interactions between the parameters. The FMVSS208 unbelted vehicle crash test is known to be a difficult requirement. The significant test to test variability as well as the extraordinary interaction of subsystems such as airbag, steering system or knee bolster are challenging. Reducing the chest loads under these crash conditions is a practical application of CAE driven parameter studies.

Method A standard occupant model for front impact has been used in this study. The model represented a straight front unbelted vehicle test with 31mph impact speed. Objective Function Two load parameter, the chest deflection and the chest accelerations have been combined in one objective function. In general an objective function needs to fulfill several requirements: • Weight factors for all load parameters need to be defined. In this study all parameters were weighted equal. • Exceeding the reference value of one parameter is critical. Therefore the function needs to be flat in the range of acceptable results and steep gradients are necessary to prevent single load parameters from clipping above the particular reference value. • Singularities should be avoided within the range of calculated results.

Results The objective function is shown in Figure 1. It results in a nice flat plateau within the area of both reference values. The reference values for chest deflection and chest deceleration were set to 58mm and 50g respectively. The gradients are quite steep around the reference values and there is no singularity until one of the load parameters exceeds the particular reference value by 20%. DoE Setup Typically a huge number of design parameters leads to numerical instabilities, nonconvergence and often to a large consumption of CPU time. The “Design of Experiment”approach has proven to be very effective to overcome these issues. Figure 2 shows the parameters, their settings as well as the configuration of the DoE matrices. For simplicity and rapid model generation, L8 matrices with four parameters have been used to screen 20 parameters. Alternatively to the usage of five L8 matrices, the 20 factors could have been screened with one big L32 matrix, but this would require automated model generation, which is currently not available within the software package. Five parameters have been selected later on and were investigated in a second loop using a L16 matrix. The L16 matrix with five factors is less saturated and therefore allows the separation of all first order interactions. To better represent the latest design level the baseline configuration for this matrix and some of the settings were modified slightly. A Madymizer run would have been possible as an alternative to the second DoE loop, but in this case the interactions were of particular interest.

Figure 3 illustrates effects and interactions of the five parameters that were selected for matrix 6. The effects on chest deflection are very different compared to the effects on the chest deceleration. The reduced airbag tether length for instance is very effective in reducing the chest deflection, but it also leads to higher chest decelerations. Some of the first order interactions are of the same magnitude as the main effects. A different inflator with delayed mass flow for instance interacts with vent size and tether length, such that the overall effect strongly depends on the setting of those parameters. This highlights that it is important to explore the system responses in detail as opposed to just accepting the computed optimum.

Conclusion Even a large number of design variables can be effectively investigated with Madymo occupant models using the Design of Experiment method. Objective functions can be successfully used to feed the DoE, since they are describing the system performance and reduce the number of descriptors to one single scalar.

Acknowledgments The authors thank Ed Abramoski and Martin Funke for supporting the whole CAE investigation.

Figure1: Objective Function

α

0 . 04

=

 Chest Deflection  1. 2 −   58 mm 

2

+

0 . 04  Chest g  1. 2 −   50 g 

2

Chest Deflection [mm] Chest G

38 0,25 0,26 0,28 0,31 0,34 0,38 0,44 0,53 0,64 0,83 1,13 1,70 2,91

30 32 34 36 38 40 42 44 46 48 50 52 54

40 0,26 0,28 0,30 0,33 0,36 0,40 0,46 0,54 0,66 0,85 1,15 1,72 2,93

42 0,29 0,30 0,32 0,35 0,38 0,43 0,49 0,57 0,69 0,87 1,18 1,74 2,95

44 0,32 0,33 0,35 0,38 0,41 0,46 0,51 0,60 0,72 0,90 1,21 1,77 2,98

46 0,35 0,37 0,39 0,42 0,45 0,49 0,55 0,63 0,75 0,94 1,24 1,80 3,02

48 0,40 0,42 0,44 0,46 0,50 0,54 0,60 0,68 0,80 0,98 1,29 1,85 3,07

50 0,46 0,48 0,50 0,52 0,56 0,60 0,66 0,74 0,86 1,04 1,35 1,91 3,13

52 0,55 0,56 0,58 0,61 0,64 0,68 0,74 0,83 0,94 1,13 1,43 2,00 3,21

54 0,66 0,68 0,70 0,73 0,76 0,80 0,86 0,94 1,06 1,25 1,55 2,12 3,33

56 0,84 0,86 0,88 0,90 0,93 0,98 1,04 1,12 1,24 1,42 1,73 2,29 3,51

58 1,11 1,13 1,15 1,17 1,21 1,25 1,31 1,39 1,51 1,69 2,00 2,56 3,78

60 1,57 1,59 1,61 1,63 1,67 1,71 1,77 1,85 1,97 2,15 2,46 3,02 4,24

62 2,44 2,46 2,48 2,50 2,54 2,58 2,64 2,72 2,84 3,02 3,33 3,89 5,11

64 4,40 4,42 4,44 4,46 4,50 4,54 4,60 4,68 4,80 4,99 5,29 5,85 7,07

Target Function 6,00

5,00-6,00 5,00 4,00-5,00

4,00

3,00-4,00 2,00-3,00

3,00

1,00-2,00 0,00-1,00

2,00 54 50 46

1,00 42 38 Chest G

0,00

34 30 38

42

46

50

54

58

62

Chest Deflection

Figure 2: DoE Settings

Parameter

-

+

base base base base

both plateau forces approx. 6kN -30% 8 inches delayed mass flow

base base base base

plateau force approx. 6kN -30% +50% lower bag position

base base base base

80mm -30% -30% 20mm closer

base base base base

20mm upward 20mm closer 20mm lower 20mm closer

base base base base

pulse from test 2100 -25% 15 Deg -25%

Matrix 1 A B C D

Knee Bolster Stiffness, left + right Steering Wheel, Lower Rim Stiffness Tether Length Inflator

Matrix 2 A B C D

Knee Bolster Stiffness, left Vent Coefficients Steering Wheel, Upper Rim Stiffness Airbag Position

Matrix 3 A B C D

Steering Column, Ride Down Steering Column, Stroke Stiffness Steering Column, Rot. Stiffness Steering Column Position, axial

Matrix 4 A B C D

Steering Column Position, vertical Seating Position, horizontal Seating Position, vertical Knee Bolster Position

Matrix 5 A B C D

Crash Pulse Toeboard Intrusion Toeboard Rotation Seat Cushion Stiffness

Matrix 6 A B C D E

New Baseline: Optimized Knee Bolster + Reduced Lower Rim Stiffness Inflator base delayed mass flow Tether Length base 8 inches Seat Back Ankle / Seating Position, hor.base 17 Deg. / 25mm closer Steering Column Position, axial base 15mm closer Vent size base 25

Figure 3: Results of Matrix 6, Potential Improvements of Objective Function , Chest Deflection (mm)

and Chest Deceleration (g)


 




 

 

 

    
 

Inflator Tether Length Seat Back Angle Steering Column Vent Size I x Tether Length I x Seat Back Ang. I x Steering Col. Pos. I x Vent Size T x Inflator T x Seat Back Angle T x Steering Col. Pos. T x Vent Size SBA x

Improvement Inflator Chest Deflection [mm] SBA x Tether SBA x Steering SBA x Vent Size SCP x Inflator SCP x Tether SCP x Seat Back Angle SCP x Vent Size V x Inflator V x Tether Length V x Seat Back Angle V x Steering Col. Pos