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ME 555-10-07 Final Project Report

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OPTIMAL SEAT DESIGN FOR AN ENRICHED DRIVING EXPERIENCE

by

Raghavendra Chivukula

Balaji Ramanathan

ME 555-10-07

Winter 2010 Final Project Report

20th

April 2010

ABSTRACT

The design and subsequent optimization of the driver’s seat in a passenger car calls for a

compromise between various aspects – seat comfort, occupant safety, among others. The

complexity of the problem increases when we take into account the variance in the stature of

human occupants, who may be the potential customers of the car. To satisfy the requirements of

a wide range of human population – 5th to 95th percentile of the available population, a lot of

engineering effort is involved in packaging the interior of the car. The design practices suggested

by the Society of Automotive Engineers (SAE) through their J1100 standards and the mandatory

requirements specified by the National Highway Traffic Safety Administration (NHTSA)

through their Federal Motor Vehicle Safety Standards and Regulations (FMVSS), give us a

broad set of guidelines to initiate the design process of the driver’s operational space. However,

the variance in the New Car Assessment (NCAP) ratings obtained by the various cars gives us a

picture of how emphasizing upon one aspect of design might affect the performance with respect

to another aspect. In this study, we have aimed for an optimal design of the driver’s seat in a

passenger car based on the perspectives of seat comfort and occupant safety.


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Contents

INTRODUCTION ................................................................................................................................... 3

1. SUBSYSTEM DESIGN: SEAT COMFORT (RAGHAVENDRA CHIVUKULA) ........................... 4

1.1. Design Problem Statement ...................................................................................................... 5

1.2. Nomenclature for the seat comfort subsystem ........................................................................ 6

1.3. Model Analysis and Measurement Methods ............................................................................ 7

1.4. Mathematical Model ............................................................................................................. 10

1.5. Monotonicity Analysis............................................................................................................ 18

1.6. Optimization Method and Numerical Analysis........................................................................ 19

1.7. Optimization Study ................................................................................................................ 21

1.8. Parametric Study ................................................................................................................... 25

1.9. Discussion of Results .............................................................................................................. 27

2. SUBSYSTEM OPTIMIZATION: SEAT SAFETY (BALAJI RAMANATHAN) ........................... 29

2.1. Introduction .......................................................................................................................... 29

2.2. Problem Statement and Definitions ....................................................................................... 29

2.3. Range of Motion of the Anchorage Points .............................................................................. 30

2.4. Nomenclature ........................................................................................................................ 31

2.5. Procedure Setup .................................................................................................................... 31

2.6. Design of Experiments ........................................................................................................... 32


2.8. Model Analysis ...................................................................................................................... 34

2.9. Numerical Analysis................................................................................................................. 34

2.10. Parametric Study –Constraint Cap Study ................................................................................ 35

3. SYSTEM INTEGRATION ............................................................................................................ 37

3.1. Problem Statement................................................................................................................ 37

3.2. Nomenclature ........................................................................................................................ 38


3.4. Numerical Results .................................................................................................................. 43

3.5. Discussion of Results .............................................................................................................. 46

4. REFERENCES .............................................................................................................................. 47


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INTRODUCTION

The driver cabin design is initiated by fixing the Accelerator Heel Point (AHP) and is continued

thereupon by deciding the seat positioning, determining the reach envelopes, satisfaction of the

visibility criteria, designing the geometrical parameters of the seat and so on. In the early days,

H-point machines were used for the evaluation of various criteria in these studies. However

technological advancements in the recent past, such as the advent of advanced computer models,

have facilitated the virtual performance of the studies over the screen of a computer. Thus in

order to access these analytical tools in our study, we have simplified the driver into a

mechanical model with specified range of motion at the various joints.

The enrichment of driving experience can be obtained when the following primary criteria are

satisfied:

a) Optimal comfort for a human occupant sitting in the seat.

b) Optimal safety to the human occupant in the driver’s seat in the event of a crash/mishap.

Figure 1: Side view of the front cabin of a car


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Thus the problem of designing for an optimal driving experience can be divided into two

subsystems in the lines of the aforementioned criteria. The delineation of the subsystems is as

follows:

1. Geometric features and construction of the seat for optimum comfort to the human

occupant.

2. Optimal seat belt anchorage positions of a three point belt for providing ample safety to the

driver.

The overall objective of this study being driver’s comfort is the overall objective through the

calculation and the subsequent minimization of a driver discomfort index, which imparts weight

age to each of the subsystems towards the optimization of the overall driving experience.

Literature required for the project has been sourced from the exhaustive research done in the

field of driver safety and biomechanics at the University of Michigan Transportation Research

Institute [UMTRI].

1. SUBSYSTEM DESIGN: SEAT COMFORT (RAGHAVENDRA CHIVUKULA)

Design for comfort in the seat of a passenger car is critical in view of the economic costs (both to

the driver and the manufacturer) associated with medical conditions such as lumbar disk

herniation and cutaneous ischemia resulting from improper design.

Figure 2: A bucket seat in a car with design similar to this study

The comfort in an automobile seat is one of the most easily realized features of the driving

experience. However, in a manner of stark contrast, the objective analysis and interpretation of


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comfort is a matter of immense complexity as comfort is widely viewed as a subjective

perception varying from one individual to another. In this study we use the functional definition

of comfort as the lack of discomfort inducing stimuli. Thus we strive towards the minimization

of these stimuli for obtaining maximum comfort, even as we check the economic and ergonomic

costs associated with seat design- in terms of the volume of the seat.

1.1. Design Problem Statement

The objective of this subsystem is to design a seat of minimum volume without compromising

on the comfort of the driver. In this study the seat is subdivided into the seat cushion and the

backrest, in order to facilitate better delineation of the geometric parameters of the seat. This

would also enable an improved understanding of the role of each design variable in the

discomfort experienced by the driver and also the correlation and tradeoffs involved in the design

of different geometric features. The design of the headrest is not included in this design.

Both the cushion and the back rest are primarily designed in view of the anthropometric

measurements of the human populations.

In the design of seat the pressure acting at the Ischial Tuberosities is considered as the major

source of discomfort. Excessive pressure can lead to a host of complications such as pain in the

hip to occlusion of blood vessels - due to deformation of the skin and underlying tissues- leading

to cutaneous ischemia.

In the design of backrest apart from the necessity of ample field of vision, the support offered by

the seat to the Lumbar Spine is considered as an important feature of design. The backrest is

designed to maintain Lumbar Lordotic posture in conjunction with Thoracic Kyphotic posture,

for in this posture the stress on the spinal cord would be minimal.


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1.2. Nomenclature for the seat comfort subsystem

Table 1: Nomenclature for the seat comfort subsystem

Index Symbol Description Unit

1 αc Seat cushion angle degrees

2 αb Backrest angle degrees

3 Cs Scale factor for seating area calculation 1

4 Cit Scale factor for pressure at Ischial Tuberosities 1

5 Cl Scale factor for pressure at Lumbar spine 1

6 g Acceleration due to gravity m/s2

7 H H-point 1

8 Hl Lumbar height mm

9 Lb Length of the backrest mm

10 Lc Length of the cushion mm

11 M Mass of the human occupant kg

12 Pit Pressure at the Ischial Tuberosities N/ mm2

13 Pl Pressure at the Lumbar spine N/mm2

14 Pm Pelvis mass value 1

15 Rl Radius of curvature of the Lumbar support mm

16 Rt Radius of curvature of the Thoracic support mm

17 Sc Surface area of the cushion mm2

18 Sl Surface area of the Lumbar support section mm2

19 Ss Seating Surface area mm2

20 T Thickness of the cushion and backrest mm

21 Tm Torso mass value 1

22 θl Lumbar Lordosis angle degrees

23 θt Thoracic Kyphosis angle degrees

24 Vbc Volume of the backrest at chest or upper back mm3

25 Vbw Volume of the backrest at waist or lower back mm3


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26 Vc Volume of the cushion mm3

27 Vs Volume of the seat mm3

28 Wbc Width of the backrest at chest or upper back mm

29 Wbw Width of the backrest at waist or lower back mm

30 Wc Width of the cushion mm

1.3. Model Analysis and Measurement Methods

The seat design parameters are broadly classified into four categories based on their contribution

to the seating comfort of the human occupant:

1. Fit Parameters: The level of these parameters is determined by the anthropometry of the

occupant population and depends on the level of fit achieved by an occupant of certain

anthropometric measurements. The fit parameters employed in the seat design and their

corresponding measurement methods are as follows:

a) Length of the cushion (Lc) is the dimension measured along the thigh line from the

front of the seat cushion to the depressed surface of the seatback.

b) Width of the cushion (Wc) is the maximum dimension measured laterally across the

cushion and it is considered to be uniform from the front of the cushion to the hips.

c) Thickness of the cushion (Tc) is the distance from the seating surface of the cushion to

the underside of the cushion and is measured perpendicular to the non-deformed seating

surface.

d) Length of the backrest (Lb) is the dimension measured along the torso/manikin line

from the depressed surface of the seat cushion to the top of the seat back soft trim.

e) Width of the backrest at the waist or lower back (Wbw) is the maximum dimension

measured laterally across the backrest at the waist level and perpendicular to the

torso/manikin line.

f) Width of the backrest at the chest or upper back (Wbc) is the maximum dimension

measured laterally across the backrest at the chest level and perpendicular to the

torso/manikin line.

g) Thickness of the backrest (Tb) is the distance from the backrest surface to the underside

of the backrest and is measured perpendicular to the non-deformed backrest surface.


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Figure 3: Illustration of Fit Parameters

2. Support parameters: These parameters affect the posture of the human occupant. They

are determined by the anatomy of the human body and the stress induced in different

segments of human when subjected to various postures. The support parameters employed

in the seat design are as follows:

a) Radius of curvature of the Lumbar support (Rl) is the longitudinal radius of curvature in

the lower back region along with a prominence.

b) Radius of curvature of the Thoracic support (Rt) is the longitudinal radius of curvature

in the chest region along with a depression.

c) Lumbar Lordosis angle (θl) is the curvature of the lordotic curve in the lumbar region of

the spine.

d) Thoracic Kyphosis angle (θt) is the curvature of the thoracic vertebrae which composes

the middle segment of the vertebral column.

Lb

Lc

T

Ws

Wbw

Wbc


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Figure 4: Illustration of Support Parameters and Seat Adjustment angles

3. Seat adjustment angles: These angles are adjustment features provided to the seat cushion

and backrest to facilitate the comfort of the human occupant in seating and during ingress

and egress. The seat adjustment angles are as follows:

a) Seat cushion angle (αc) is the angle measured between the thigh centerline and the

horizontal.

b) Backrest angle (αb) is the angle measured between torso/manikin centerline and the

horizontal.

4. Feel Parameters: These parameters are related to the physical contact between the

occupant and the seat and are directly related to the sensory perceptions of the human

occupant. The feel parameters employed in the seat design are as follows:

a) Pressure at the Ischial Tuberosities (Pit), which is the peak pressure in the seat cushion

experienced at the ischii due to flexion of the hip joint in the seating posture.

Height of the backrest

Seat Cushion angle

Backrest angle

Radius of Curvature of Lumbar Support

Radius of Curvature of Thoracic Support

Min. Lumbar Height


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b) Pressure in the region of Lumbar spine (Pl) from L2-L5 assists in maintaining Lumbar

Lordosis, thereby reducing the incidence and intensity of back ache.

Scale factors employed:

The following scale factors have been employed to facilitate the ease of calculation:

a) The scale factor of seating area calculation (Cs) ) [ Expresses the seating surface area with

respect to the surface area of the cushion(Sc)]

b) The scale factor for pressure at Ischial Tuberosities (5)

(Cit) ) [ Expresses the pressure on the

Ischial Tuberosities region(Pit) with respect to the mean pressure over the cushion]

c) The scale factor for pressure at Lumbar Spine (7)

(Cl) [Expresses the pressure on the

Lumbar spine region (Pl) with respect to the mean pressure over the backrest].

d) The Pelvis mass value(6)

(Pm) [ Expresses the mass of the pelvis relative to the body mass]

e) The Torso mass value(6)

(Tm) ) [Expresses the mass of the torso relative to the body mass]

1.4. Mathematical Model

Objective Function:

The objective of the seat comfort subsystem optimization design is to minimize the volume of

the seat, while maintaining satisfactory comfort levels to the human occupant in terms of fit,

support and feel parameters.

The choice of minimization of the volume of the seat is a consequence of the primary objective

of minimizing the weight of the seat. However upon assuming the seat to be uniform in

construction (for the simplicity of the design model), passing the density of the seat as a

parameter would not be of any particular interest in the design of seat for comfort. Hence the

additional redundant parameter of density is avoided and the objective function is structured to

minimize the volume.

The Objective function is modeled as follows:

Minimize

Volume of seat (Vs) = Volume of the cushion (Vc) + Volume of the backrest (Vb)

𝑓 = 𝑉𝑠 = 𝐿𝑐𝑊𝑐𝑇𝑐 + 𝑊𝑏𝑤. 𝜋. 𝜃𝑙

360 𝑅𝑙 +

𝑇

2

2

− 𝑅𝑙 −𝑇

2

2

+ 𝑊𝑏𝑐. 𝜋. 𝜃𝑡

360 𝑅𝑡 +

𝑇

2

2

− 𝑅𝑡 −𝑇

2

2


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Constraints:

The constraint functions are obtained on the basis of functional definition of comfort as it is

applied to seating. Comfort in seating can be expressed as a state of reduced discomfort. Thus the

aim of the seat design would be to reduce or eliminate the factors causing discomfort such as a

cushion that is too long or a backrest that lacks lumbar support, among others.

Thus for this project the following constraints have been employed to decrease the discomfort

inducing factors. The choice of the constraints is based on the level of detail and scope of the

project, with many other constraints being excluded because of the difficulty in their

mathematical formulation and/or the complexity added to the optimization problem.

The constraints are structured along the four parameters of seat design as explained in the

previous section. The constraint set is sourced from the literature listed in the References and is a

product of exhaustive study on human test subjects and human anatomy.

Note: The constraints were originally structured in reference to the H-Point which is the pivot

center of the torso and thigh on the two-or three- dimensional devices used in defining and

measuring vehicle seat accommodation(1)

. For the convenience of interpretation the

measurements along the H-Point manikin backrest line where scaled up by assuming a 95-mm

distance from the point of maximum deflection of the seat surface to the H-point (1)

. Similarly the

measurements on the H-Point thigh line where scaled up by assuming a 135 mm distance from

H-Point to the depressed backrest surface.

Fit Constraints

a) The length of the seat cushion (Lc) is a critical parameter for comfort since a cushion which

is too long can put pressure on the back of the sitter's legs near the knee, an area that has

many superficial nerves and blood vessels. Pressure in this area will lead to local

discomfort and restricted blood flow to the legs. Second, a cushion that is too long will pull

sitters forward, away from the backrest, eliminating the possibility of providing appropriate

lumbar support(2)

. While a shorter cushion would deprieve the occupant from ample

support beneath the thighs.

According to Grandjean (1980) recommendations the seat cushion length (Lc) is bounded

below at 440 mm and above at 550 mm.


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𝑔1 = 440 − 𝐿𝑐 ≤ 0

𝑔2 = 𝐿𝑐 − 550 ≤ 0

b) The hip dimensions of 95th

percentile female population is considered for determining the

width of the seat cushion. Thus the seat cushion should be 500 mm wide at the hips. The

front of the cushion should also have a minimum of 500 mm width to allow for

comfortable leg splay. Thus we employ a lower bound of 500 mm for the seat cushion

width(Wc)

𝑔3 = 500 − 𝑊𝑐 ≤ 0

c) Minimum backrest width at the waist level is constrained by the back width of the large

male segment of the population (2)

.

The backrest should be a minimum of 360 mm wide at the waist or lower back region

(Wbw) and a minimum of 456 mm wide at the chest or upper back region(2)

(Wbc). The

division of the backrest between these widths is affected by Rl , Rt, θl and θt.

𝑔4 = 360 − 𝑊𝑏𝑤 ≤ 0

𝑔5 = 456 − 𝑊𝑏𝑐 ≤ 0

d) The bounds for the thickness of the seat (T) have been determined from empirical data. The

thickness of the seat is bounded below at 100 mm and above at 120 mm.

𝑔6 = 100 − 𝑇 ≤ 0

𝑔7 = 𝑇 − 120 ≤ 0

e) Backrest length (Lb) requirements are affected by geometric constraints imposed by

FMVSS 202 (U.S. Office of the Federal Register 1992) dealing with head restraints for

protection in rear impacts (2)

.

We employ Gordon et al. recommendations (3)

for the backrest height (Lb), according to

which Lb is bounded below at 509 mm and above at 646 mm.

𝐿𝑏 = 2𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360+ 2𝑅𝑡. 𝑠𝑖𝑛

𝜋. 𝜃𝑡

360

𝑔8 = 509 − 2𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360− 2𝑅𝑡. 𝑠𝑖𝑛

𝜋. 𝜃𝑡

360≤ 0

𝑔9 = 2𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360+ 2𝑅𝑡. 𝑠𝑖𝑛

𝜋. 𝜃𝑡

360− 646 ≤ 0


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Support Constraints

a) The Lumbar support should be sufficiently padded to avoid discomfort due to high

pressure. Ideally the support should be adjustable. However for this project the support is

assumed to be fixed and the support is defined on the basis of its longitudinal curvature.

According to the recommendations of Floyd and Roberts (2)

(1958) the Lumbar support

curvature (Rl) is bounded below at 400 mm and above at 460 mm.

𝑔10 = 400 − 𝑅𝑙 ≤ 0

𝑔11 = 𝑅𝑙 − 460 ≤ 0

b) The Thoracic support curvature (Rt) is not extensively researched in the seat design and is

generally assumed to be flat. However for the purpose of this project we bound (3)

Rt below

at the upper bound of Rl and above at 500 mm.

𝑔12 = 460 − 𝑅𝑡 ≤ 0

𝑔13 = 𝑅𝑡 − 500 ≤ 0

c) On the basis of anatomical studies (4)

, the Lumbar Lordosis angle (θl) angle is bounded

below at 40 deg and above at 60 deg.

𝑔14 = 40 − 𝜃1 ≤ 0

𝑔15 = 𝜃1 − 60 ≤ 0

d) On the basis of anatomical studies (4)

, the Thoracic Kyphosis angle (θt) angle is bounded

below at 20 deg and above at 40 deg.

𝑔16 = 20 − 𝜃𝑡 ≤ 0

𝑔17 = 𝜃𝑡 − 40 ≤ 0

e) The height of the apex of the Lumbar support (Hl) is very critical for the comfort of the

human occupant. Ample support can be offered to the Lumbar spine if the apex of the

Lumbar support curvature falls in the region of L5-L2 vertebrae of the Lumbar spine. Thus

we employ modified Reed et al.(2)

recommendations for the Lumbar Height(Hl) which

constraint the Hl below at 200 mm and above at 250 mm.

𝐻𝑙 = 𝑅𝑙. 𝑠𝑖𝑛 𝜋𝜃𝑙

360


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(The factor π/180 is employed for conversion of the angle from degrees to radians to be

compatible for use in MATLAB.)

𝑔18 = 200 − 𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360≤ 0

𝑔19 = 𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360− 250 ≤ 0

Feel Constraints

The feel constraints employed in the seat design are the peak pressures acting in the critical

regions of the seat cushion and backrest.

As described in the previous section the critical region in the seat cushion is the region near the

Ischial Tuberosities. In order to provide ample comfort, the pressure at the Ischial Tuberosities

(Pit) is bounded above at 3 kN/m2.

Pit=𝑔20 = 𝐶𝑖𝑡. 𝑀. 𝑔. 𝑃𝑚. 𝑐𝑜𝑠 𝜋.𝛼𝑐

180 / 𝐶𝑠. 𝐿𝑐. 𝑊𝑐 – (3𝑒 − 3) ≤ 0

where

The seating surface area (Ss) = Cs.Lc.Wc

The scale factor of seating area calculation (Cs) = (432/500)

The scale factor for pressure at Ischial Tuberosities(5)

(Cit) = 3.624

The Pelvis mass value (6)

(Pm) =

The acceleration due to gravity (g) = 9.8 m/s2

Pressure in the region of Lumbar spine plays a critical role in maintaining the prescribed posture

of Lumbar Lordosis, which subjects the Lumbar vertebrae to lesser stress levels when compared

to other postures. Thus adequate Lumbar support of the backrest is necessary for maintaining this

posture and the pressure at the Lumbar spine is consequently bounded below at 2.5 kPa for the

comfort of the human occupant.

Pl = 𝑔21 = 2.5𝑒 − 3 − 𝐶𝑙. 𝑀. 𝑔. 𝑇𝑚. 𝑐𝑜𝑠(𝜋.180−𝛼𝑏

180)/ 2𝜋. 𝜃𝑙. 𝑊𝑏𝑤. (𝑅𝑙 +

𝑇

2)/360 ≤ 0

0.2997 (for men); 0.3157 (for women)


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where

The surface area of the lumbar section (Sl) = 2𝜋. θl. Wbw. (Rl +T

2)/360

The scale factor for pressure at Lumbar Spine (7)

(Cl) = 0.719

The Torso mass value (6)

(Tm) = 0.3213 (for men); 0.3092 (for women)


Design Variables, Parameters and Constants:

Table 2: Design variables, parameters and constants

Symbol Description Type

Lc Length of the cushion Variable

Wc Width of the cushion Variable

Wbw Width of the backrest at waist or lower back Variable

Wbc Width of the backrest at chest or upper back Variable

T Thickness of the cushion and backrest Variable

Rl Radius of curvature of the Lumbar support Variable

Rt Radius of curvature of the Thoracic support Variable

θl Lumbar Lordosis angle Variable

θt Thoracic Kyphosis angle Variable

αc Seat cushion angle Parameter

αb Backrest angle Parameter

Pm Pelvis mass value Parameter

Tm Torso mass value Parameter

M Mass of the human occupant Parameter

Cs Scale factor for seating area calculation Parameter

Cit Scale factor for pressure at Ischial Tuberosities Parameter

Cl Scale factor for pressure at Lumbar spine Parameter

g Acceleration due to gravity Constant


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The values of the parameters and constants employed in this study are as follows:

Parameters:

Seat Cushion angle (αc) = (10,15,20,25) deg.

Backrest angle (αb) = (105,110,115,120) deg.

The Pelvis mass value(6)

(Pm) = 0.2997 (for men)

0.3157 (for women)

The Torso mass value(6)

(Tm) = 0.3213 (for men)

0.3092 (for women)

Constants:

Mass of the Human Occupant (M) = 70 kg



(Cit) = 3.624

The scale factor for pressure at Lumbar Spine(7)

(Cl) = 0.719


Summary Model:

Objective function

Minimize

𝑉𝑠 = 𝐿𝑐𝑊𝑐𝑇𝑐 + 𝑊𝑏𝑤 .𝜋 .𝜃𝑙

360 𝑅𝑙 +

𝑇

2

2


2

2

+ 𝑊𝑏𝑐 .𝜋 .𝜃𝑡

360 𝑅𝑡 +

𝑇

2

2


2

2

subject to:

𝑔1 = 440 − 𝐿𝑐 ≤ 0

𝑔2 = 𝐿𝑐 − 550 ≤ 0

𝑔3 = 500 − 𝑊𝑐 ≤ 0

𝑔4 = 360 − 𝑊𝑏𝑤 ≤ 0

𝑔5 = 456 − 𝑊𝑏𝑐 ≤ 0

𝑔6 = 100 − 𝑇 ≤ 0

𝑔7 = 𝑇 − 120 ≤ 0


17

𝑔8 = 509 − 2𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360− 2𝑅𝑡. 𝑠𝑖𝑛

𝜋. 𝜃𝑡

360≤ 0


360+ 2𝑅𝑡. 𝑠𝑖𝑛

𝜋. 𝜃𝑡

360− 646 ≤ 0

𝑔10 = 400 − 𝑅𝑙 ≤ 0

𝑔11 = 𝑅𝑙 − 460 ≤ 0

𝑔12 = 460 − 𝑅𝑡 ≤ 0

𝑔13 = 𝑅𝑡 − 500 ≤ 0

𝑔14 = 40 − 𝜃𝑙 ≤ 0

𝑔15 = 𝜃𝑙 − 60 ≤ 0

𝑔16 = 20 − 𝜃𝑡 ≤ 0

𝑔17 = 𝜃𝑡 − 40 ≤ 0

𝑔18 = 200 − 𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360≤ 0


360− 250 ≤ 0

𝑔20 = 𝐶𝑖𝑡. 𝑀. 𝑔. 𝑃𝑚. 𝑐𝑜𝑠 𝜋.𝛼𝑐

180 / 𝐶𝑠. 𝐿𝑐. 𝑊𝑐 – (3𝑒 − 3) ≤ 0

𝑔21 = 2.5𝑒 − 3 − 𝐶𝑙. 𝑀. 𝑔. 𝑇𝑚. 𝑐𝑜𝑠(𝜋.180 − 𝛼𝑏

180)/ 2𝜋. 𝜃𝑙. 𝑊𝑏𝑤. (𝑅𝑙 +

𝑇

2)/360 ≤ 0

Set Constraints:

Lc, Wc, Wbw,Wbc, T, Rl, Rt ≥ 0

θl, θt ≥ 0 deg; θl, θt≤ 90 deg


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1.5. Monotonicity Analysis

Table 3:Monotonicity Analysis

Lc Wc Wbw Wbc T Rl Rt θl θt

f + + + + + + + + +

g1 -

g2 +

g3 -

g4 -

g5 -

g6 -

g7 +

g8 - - - -

g9 + + + +

g10 -

g11 +

g12 -

g13 +

g14 -

g15 +

g16 -

g17 +

g18 - -

g19 + +

g20 - -

g21 + + + +

Discussion of Monotonicity Analysis and activity of constraints:

From the Monotonicity Analysis in Table-3, we can realize the following features with regard to

the behavior of the objective function and the constraints:


19

1. The objective function deals with the volume of the seat and hence is heavily monotonic

with respect to the design variables. The volume of the seat depends on the geometric

parameters involved in the construction of the seat and upon observing the objective

function it would be evident to us that increase in any of the design variables- which are the

geometric parameters in seat design- would consequently increase the volume of the seat.

This observation explains the monotonically increasing behavior of the objective function

with respect to all the design variables.

2. Both the constraints g1 and g20 have opposite monotonicity to that of f with respect to Lc.

Hence activity of either of the constraints cannot be deduced from monotonicity analysis.

Since neither of them is uniquely critical, they form a conditional critical set in which either

of them can be active.

3. Similarly

a) g3 and g20 form a conditionally critical set in which either of them can be active with

respect to Wc.

b) g8, g10 and g18 form a conditionally critical set in which either of them can be active

with respect to Rl.

c) g8 and g12 form a conditionally critical set in which either of them can be active with

respect to Rt.

d) g8, g14 and g18 form a conditionally critical set in which either of them can be active

with respect to θl.

e) g8 and g16 form a conditionally critical set in which either of them can be active with

respect to θt.

4. By Monotonicity Principle 1 we can realize that:

a) g4 is active and critical with respect to Wbw.

b) g5 is active and critical with respect to Wbc.

c) g6 is active and critical with respect to T.

1.6. Optimization Method and Numerical Analysis

The optimization study is carried out by employing fmincon solver from the optimization

toolbox of MATLAB. The optimum solution is evaluated through an iterative procedure based

on Sequential Quadratic Programming.


20

In this routine Active set algorithm was employed which searches for the solution by checking

for the validity of Karush-Kuhn Tucker ( KKT ) conditions. The KKT conditions are the

necessary conditions for the optimality of the constrained optimization problem. In this process

the activity of the constraints is also evaluated through the computation of values of Langrange

multipliers of the KKT equations; with any multiplier having a value equal to zero being

associated with an inactive constraint.

Line search is employed in the iterations and the use of Quasi Newton Hessian approximation

ensures super linear convergence.

The exploration of the solution through the sole use of fmincon solver has been influenced by the

following factors:

a) The optimization problem being a non-linear constrained problem.

b) The robustness of the optimization algorithm of fmincon.

c) The heavy monotonicity of the objective function with respect to the design variables and

the presence of both upper and lower bounds on a majority of variables gives a preliminary

suggestion of convergence to a global optimum, thus imposing faith in the solution of a

single optimization tool (However this intuition needs to be verified as done in the

subsequent section).

The results from the fmincon solver are as follows:

Table 4: Results from fmincon solver


Starting

Point 540 1000 1000 1000 90 410 450 59 25

Value at

the

solution

521.21 500.20 360 456 100 460 460 51.40 20

The volume of the seat at this set of design variables = 4.8251 * 107 mm

3.

This solution was computed by setting the parameters at:


21

Pm = 0.2997; Tm = 0.3213; αc = 25 deg; αb=105 deg.

The level of the design variables is shown in Figure 4.

Figure 5: Level of Design Variables

1.7. Optimization Study

Upon reviewing the results of the optimization process we can observe that the iterative search

ends at a possible value of local minimum that satisfies the constraints as indicated by the output

of ‘exitflag = 4’. The solution is referred to as possible local minimum as the search stopped due

to size of the search direction being less than twice the default value of step size tolerance. The

attainment of local minimum can be verified by checking the value of the first order optimality

measure, the value of the violation of the constraints at the obtained solution and by employing

different starting points; as done in the following analysis.

The significant results of the optimization process are discussed below:

a) The first order optimality measure (= 3.3204*10-6

) is close to the default value (= 1*10-6

).

This indicates that the solution is sufficiently close to the optimal. This behavior is shown in

Figure 5.

1 2 3 4 5 6 7 8 90

100

200

300

400

500

600

Number of variables: 9

Cur

rent

poi

nt

Current Point


22

b) The violation of constraints at the optimal solution (= 3.8207*10-16

) is also less than the

default value (= 1*10-6

) indicating the validity of the solution. This behavior is shown in

Figure 6.

Figure 6: Function value

Figure 7: First order optimality measure

0 2 4 6 8 10 12 144

5

6

7

8

9

10

11

12x 10

7

Iteration

Fun

ctio

n va

lue

Current Function Value

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14x 10

6

Iteration

Firs

t-or

der op

timal

ity

First-order Optimality


23

c) The activity of constraints from the ‘Active inequalities’ output of MATLAB can be

analyzed as follows:

1. The variables that touch the lower bound are Wbw, Wbc, T, Rt and θt. This verifies the

activity and criticality of constraints g4 with respect to Wbw; g5 with respect to Wbc and

g6 with respect to T. It also identifies the activity of constraints g12 with respect to Rt

and g16 with respect to θt.

2. The variable that touches the upper bound is Rl; this verifies the inactivity of the

constraint g10 with respect to Rl. Upon further analysis by plugging in the values of Rl

and θl obtained from the optimization process, we realize that the constraint g8 is active

with respect to both Rl and θl, while g18 constraint is inactive for these variables.

Note: In this regard it is observed that although the volume decreases with decrease in

both Rl and θl , the search for the minimum volume is carried by decreasing the value

of θl while correspondingly increasing Rl to maintain the equality of g8 (with inequality

constraint now being active). Thus the value of is Rl increased until it is bounded above

by g11, making the upper bound active

3. MATLAB further confirms the activity of the non-linear inequality constraint g8. The

non linear inequality constraint g20 is also classified to be an active constraint. By

plugging the values of Lc and Wc we can realize that g20 is active with respect to these

variables.

It can be realized the values of the Lagrangian multipliers are greater than or equal to zero (with

the equality arising for the case of inactive constraints and inequality for the active constraints-

g4, g5, g6, g8, g11, g12, g16 and g20). This is consistent with the KKT conditions, which are to

be satisfied to attain a feasible solution for a constrained optimization problem. Thus the flag that

local minimum is obtained indicates the satisfaction of KKT conditions.

Now the robustness of the solution can be checked by starting from different values of the design

variables. For this study we employ 3 starting points each for the variables Lc ,Wc and θl. The

other design variables meet their bounds and hence changing the starting point of any such

variable would not affect the solution, when the starting points of other variables are held

constant.


24

The strategy adopted for this study involves each variable being swept across its feasible space,

by sampling four points from the feasible space while the starting points of other variables are

held constant. The sampling points chosen are – the lower bound, upper bound and two

intermediate values in the feasible space of these variables. This apart the solution is also verified

for the two cases of Lc ,Wc and θl , simultaneously starting at their lower bounds and upper

bounds. The results of this study are recorded in the Table-5 shown below:

Table 5: Study of robustness by choosing different starting points for Lc, Wc and θ1

Starting Points Lc(mm) Wc(mm) θl(mm) Vs

(Volume) (mm3)

(440,500,40) 483.4615 539.2669 51.4504 4.8251 * 107

(440,1000,59) 519.4653 501.8907 51.4054 4.8251 * 107

(480,1000,59) 521.2252 500.1941 51.4054 4.8251 * 107

(520,1000,59) 521.2179 500.2030 51.4054 4.8251 * 107

(550,1000,59) 521.2112 500.2095 51.4054 4.8251 * 107

(540,500,59)*

440.0192 592.5078 51.4054 4.8251 * 107

(540,700,59)*

521.3998 500.0286 51.4054 4.8251 * 107

(540,1000,59)*

521.2110 500.2097 51.4054 4.8251 * 107

(540,1800,59)*

519.0817 502.2616 51.4054 4.8251 * 107

(540,1000,40) 440.0147 592.5138 51.4054 4.8251 * 107

(540,1000,47) 440.5046 591.8549 51.4054 4.8251 * 107

(540,1000,53) 442.2441 589.5269 51.4054 4.8251 * 107

(540,1000,60) 521.4296 500 51.4054 4.8251 * 107

(550,1800,60)*

474.7604 549.1503 51.4054 4.8251 * 107

* The upper bound for Wc being infinity, intermediate values above 500 are chosen for analysis.

By this study we can be observe that:

a) The value of the objective function [4.8251*107mm

3] remains the same irrespective of the

starting point. Hence it can be assumed we obtain a local minimum which is independent of

the choice of the starting points.


25

b) The value of Lumbar Lordosis angle (θl) remains the same irrespective of the starting point

because of the active upper bound on the radius of curvature of the Lumbar Support (Rl).

c) The design variables always lie within their respective feasible space irrespective of the

starting point.

d) The product of the width of the seat (Wc) and the length of the seat (Lc) remains the same.

Thus for a given value of seat cushion angle(αc) and backrest angle(αb) the surface area of

the seat cushion remains the same as the pressure acting on the Ischial Tuberosities is

unchanged.

The study of change in design affected by change in αc and αb is carried out in the following

section.

1.8. Parametric Study

Analysis of the behavior of the objective function [Volume of the seat (Vs)] with change in the

four parameters employed in this optimization study would be of particular interest to obtain a

better understanding of the correlation between the design model and the optimum value of Vs.

The parametric study is done separately with respect to the Seat Cushion angle (αc), Backrest

angle (αb) and Pelvis mass value(6)

(Pm) - Torso mass value(6)

(Tm) and the behavior of the width

of the seat (Wc) and the length of the seat (Lc) are also analyzed along with the volume of the

seat (Vs).

Note: The behavior of Lumbar Lordosis angle (θl) is not analyzed for we realized that its value

always remains the same due to active upper bound on the radius of curvature of the Lumbar

Support (Rl)

Parametric Study with respect to the Seat Cushion angle (αc):

Table 6: Parametric Study with respect to the Seat Cushion angle (αc )

αc (deg)*

Wc (mm) Lc (mm) Vs (mm3)

10 549.9741 515.3475 5.022*107

15 549.9541 505.4317 4.9976*107

20 540.5336 500.1982 4.9217*107

25 521.2110 500.2097 4.8251*107


26

* For each selection of αc, the value of αb =105 deg and the values of Pm ,Tm are 0.2997, 0.3092

respectively and the starting points of the design variables are same as in the Numerical Analysis

section.

From the parametric study with respect to the seat cushion angle (αc), it can be realized that with

the increase in the seat cushion angle, there is a decrease in the values of the width of the seat

(Wc), length of the seat (Lc) and the volume of the seat (Vs). This behavior is along the expected

lines as Wc and Lc are related to αc by the cosine of the angle, as expressed in the constraint g20,

which is an active constraint. Thus with the increase in the value of αc , its cosine component

decreases (as αc ≤ 90 deg) and subsequently the values of Wc and Lc decrease to maintain the

equality at the active constraint. Consequently the volume of the seat (Vs) increases.

With the decrease in the seat cushion angle, the pressure in the region of Ischial

Tuberosities (Pit) increases. Hence the practical application of this parametric study would

involve modification in the structural construction of the seat cushion (with decreasing αc) such

that there is a better distribution of the pressure over the surface of the cushion, thus decreasing

the peak pressure at Ischial Tuberosities (and consequently decreasing the discomfort).

Parametric Study with respect to the Backrest angle (αb):

Table 7: Parametric Study with respect to the backrest angle (αb )

αb (deg)*


105 521.2110 500.2097 4.8251*107

110 521.2110 500.2097 4.8251*107

115 521.2110 500.2097 4.8251*107

120 521.2110 500.2097 4.8251*107

* For each selection of αb, the value of αc =10 deg and the values of Pm ,Tm are 0.2997, 0.3092

respectively and the starting points of the design variables are same as in the Numerical Analysis

section.

From the parametric study with respect to the backrest angle (αb), it can be realized that with the

increase in the seat cushion angle, there is no change in the values of the width of the seat (Wc),

length of the seat (Lc) and the volume of the seat (Vs). This can be attributed to the generous

nature of the constraint applied to the backrest angle (αb), as expressed by the inactivity of the


27

constraint g21. Hence the pressure in the region of Lumbar spine (Pl) would always be in excess

of the constraint value and the level of comfort would not be affected by the change in the value

of the backrest angle (αb).

Parametric Study with respect to Gender [Pelvis mass value(6)

(Pm) - Torso mass value(6)

(Tm)]:

Table 8: Parametric Study with respect to the gender

Gender Pm

Tm


Male 0.2997

0.3213

521.2110 500.2097 4.8251*107

Female 0.3157

0.3092

549.0516 500.1962 4.9643*107

* For each selection of gender value of αc =10 deg and the value of αb =105 deg and the starting

points of the design variables are same as in the Numerical Analysis section.

From the parametric study with respect to the gender it can be realized that, when the gender

being accommodated in the seat is changed from male to female, there is an increase in the

values of the length of the seat (Lc) and the volume of the seat (Vs), while the width of the seat

(Wc) remains almost unchanged. This can be attributed to different distribution of body mass

between the pelvis and torso, in men and woman. However as we have realized from the

previous parametric studies that level of discomfort in our construction of optimization problem

is influenced by the pressure in the region of Ischial Tuberosities (Pit) but remains unchanged

with the pressure in the region of Lumbar spine (Pl).

Hence due to greater Pelvis mass value(6)

(Pm) in females than in males, greater pressure

would act in the region of Ischial Tuberosities. This calls for a construction of a seat such that

there is a better distribution of the pressure over the surface of the cushion. This need is

expressed as increase in the cushion surface area (Sc), while in practice the structure of the seat

should be changed to facilitate better pressure distribution, thus reducing discomfort.

1.9. Discussion of Results

Thus the optimization study and the subsequent analysis would recommend the following design

practices to minimize the volume of the seat (Vs):


28

1. The decrease in the volume of seat can be affected by the decreasing the values of width of

the backrest at waist (Wbw), width of the backrest at chest (Wbc), Thickness of the cushion

and backrest (T), Radius of curvature of the Thoracic support (Rt) and Thoracic kyphosis

angle (θt), subject to the values of their lower bounds as specified by anthropometric

measurements.

2. The decrease in the volume of seat can be affected by the increasing the value Radius of

curvature of the Lumbar support (Rl), subject to the value of its upper bound as specified by

anthropometric measurements.

3. The decrease in the volume of seat can be achieved by the decreasing the values of the width

of the seat (Wc) and length of the seat (Lc)), subject to the lower constraint on the support

parameter – the height of the apex of the Lumbar Support.

4. The decrease in the volume of seat also results from the decrease in the values of the

Lumbar Lordosis angle (θt), subjected to the upper constraint applied on the pressure at the

Ischial Tuberosities (Pit).

These recommendations are not restricted to any particular anthropmetric percentile of human

population, as they have been constructed by providing implicit weight age to the design variable

causing most discomfort to a human occupant classified under any segment of anthropometric

data. Thus in the design for the width of the seat the hip dimensions of 95th percentile female

population is considered while for the radius of curvature of the Lumbar support, the Lumbar

vertebral measurement of the 95th

percentile male population is considered. Hence the

recommendations yield a seat design that imparts generic comfort to the human population.

Simultaneous implementation of the above mentioned design recommendations would minimize

the volume of the seat (Vs), which attains a value of 4.8251*107

mm3 at the following values of

the design variables (in respective units).

Table 9: Values of the design variables at the solution


Value at

the

solution

521.2110 500.2097 360 456 100 460 460 51.4054 20


29

2. SUBSYSTEM OPTIMIZATION: SEAT SAFETY (BALAJI RAMANATHAN)

2.1. Introduction

Occupant Safety is one of the factors which cannot be compromised during the process of

development of a new vehicle platform. One of the critical tests performed over the vehicle is the

frontal crash test. Typically, this test involves a fully occupational vehicle with a Hybrid III

dummy placed in the driver position. The main parameters noted from the test are Head Injury

Criterion (HIC), Head and Knee excursions, Chest deflection and pelvis acceleration. Ideally,

minimization of these parameters is a multi-objective problem. However in this work, the chest

deflection and pelvis acceleration values are neglected. The head and knee excursion values are

placed as constraints and the single objective remains the Head Injury Criterion.

2.2. Problem Statement and Definitions

The objective of the optimization problem is to minimize the head injury criterion within

allowable limits of head and knee excursion values. The variables of the minimization problem

are the positions of the anchorage points of a three-point seat belt system which is a passive

safety device used to minimize injury levels of the occupants in case of an accident. The three

anchorage points of the three-point seat belt are anchor point, buckle point and D-ring point. The

graphical representation of these three points is shown in the figure below.

Figure 8: Three-point seatbelt


30

The head injury criterion is a measure of the likelihood of head injury arising from an impact.

The variable is derived from the acceleration/time history of an accelerometer mounted at the

center of gravity of a dummy’s head, when the dummy is exposed to crash forces.

𝐻𝐼𝐶 = 1

𝑡2 − 𝑡1. 𝑎𝑑𝑡

𝑡2

𝑡1

2.5

. (𝑡2 − 𝑡1)

𝑚𝑎𝑥

where 𝑡1 and 𝑡2 are the initial and final times (in seconds) of the interval during which HIC

attains a maximum value, and acceleration is measured in g’s. It should also be noted that the

maximum time duration, 𝑡2 − 𝑡1, is limited to a specific value, usually and in this work to 15 ms.

Head excursion is a measure of the maximum distance travelled by the center of gravity of the

head from its initial position. Similarly, knee excursion is a measure of the maximum distance

travelled by the knee joint from its initial position. In this work, the head and knee excursions are

measured in the longitudinal direction of the vehicle co-ordinate system (i.e.) forward

movement.

2.3. Range of Motion of the Anchorage Points

The allowable limits for the positioning of the anchorage points of the seat belt are taken as

prescribed in Reed et al.1 with the H-point of the Anthropomorphic Test Dummy (ATD) taken as

the origin, X-axis is positive forward, Y-axis is positive to the right when viewed from front and

Z-axis is positive upward. The prescribed values are transformed by moving the origin of co-

ordinate system of measurement to the seat reference point (SgRP) of the seat. The bounds of the

three points with respect to the seat reference point (SgRP) are mentioned in the table below. All

the dimensions mentioned are in meters.

Table 10: Upper and Lower bounds of variables

Point Component Lower Bound Upper Bound

Anchor

X -0.194 -0.007

Y -0.2

Z -0.01

Buckle

X -0.125 0.007

Y 0.25

Z 0.04


31

D-ring

X -0.5 -0.198

Y -0.292 -0.194

Z 0.524 0.668

2.4. Nomenclature

It can be seen from the above table that the number of variables in the system is five. There are

some parameters in the system which interact with the other subsystems – seat back angle and

seat cushion angle to name a few. The detailed list of variables, parameters and their notation are

listed in the table below.

Table 11: Nomenclature of Seat Belt Anchorage Point Positions

S. No. Notation Unit Type Description

1 f NA Objective Head Injury Criterion

2 g1 m Constraint Head Excursion

3 g2 m Constraint Knee Excursion

4 x1 m Variable Anchor point X position w.r.t. SgRP

5 x2 m Variable Buckle point X position w.r.t. SgRP

6 x3 m Variable D-ring point X position w.r.t. SgRP

7 x4 m Variable D-ring point Y position w.r.t. SgRP

8 x5 m Variable D-ring point Z position w.r.t. SgRP

9 a1 deg Parameter Seat Back Angle w.r.t. vertical

10 a2 deg Parameter Seat Cushion Angle w.r.t. horizontal

11 L1 m Parameter Seat Back Length

12 L2 m Parameter Seat Cushion Length

13 W1 m Parameter Width of Seat Cushion

14 W2 m Parameter Width of Seat Back

2.5. Procedure Setup

The crash test is simulated in MADYMO software environment. A standard FMVSS pulse is

used to evaluate the occupant kinematics as seen in figure 2. Even though the pulse is defined for

200 ms, the test is conducted only for 120 ms as the dominant part of the pulse ends at 100 ms


32

and rebound starts thereafter. The seat back and cushion angles are set to 20 degrees and 15

degrees from the vertical and horizontal respectively. The buckle point is set to be to the left of

the occupant when viewed from front which corresponds to a driver in countries like UK or India

or to a front seat passenger in the USA. However, the dummy is perfectly symmetric about the

sagittal plane and hence it the simulation also corresponds to a driver in the USA.

A Hybrid III 50th percentile male dummy as available in the MADYMO database is used across

the simulations. For every set of values of the anchorage points’ positions, belt-fitting has to be

performed to adapt the natural path of the seat belt. Hence, a pre-simulation is performed every

time before the main simulation is performed. A Python code was written and is used to read the

seat belt data and the end of the pre-simulation run and use that seat belt data for the actual crash

simulation. This linking is possible as most of MADYMO’s inputs and outputs are ASCII

readable.

There are some known limitations in the design of this particular procedure setup. In reality, the

airbag deploys within the first few milliseconds of crash. In this particular setup, the airbag has

been neglected. The MADYMO dummy is modeled out of ellipsoids which may not represent

the actual geometry of a 50th

percentile male American. However, given the scope of this

particular work is anchorage points positioning, the comparative results should be valid enough

to select the optimal position of the anchorage points.

2.6. Design of Experiments

The relation between the given variables, the objective and constraints in this given problem is

quite complicated when computed analytically and at times, practically impossible. Hence, a

meta-model relationship between the variables, objective and the constraint has to be developed.

For this purpose, DOE points were extracted and a second-order curve fitting was used.

modeFrontier, a commercial multi-objective optimization and design software was used for these

processes.

A total of 500 data points were generated using Uniform Latin Hypercube method. These data

points were fed into the MADYMO environment through integration with modeFrontier. The

workflow is shown in figure 3. Each iteration took close to a minute and up to three parallel

iterations were allowed. In total, it took 3 hours to generate the entire test matrix. The R-square


33

values of the data fitting processes are 0.9771, 0.9695 and 0.9693 respectively for HIC, head

excursion and knee excursion respectively and are acceptable.


The mathematical expression for HIC, head excursion and knee excursion in terms of the given

variables as a second order polynomial can be given as follows.

𝑓 = −377.557 + 299.884𝑥1 + 1507.444𝑥2 + 805.908𝑥3 − 3882.742𝑥4

+ 858.493𝑥5 − 128.598𝑥12 − 1347.607𝑥1𝑥2 + 264.933𝑥2

2 − 138.8𝑥1𝑥3

− 74.633𝑥2𝑥3 + 2305.629𝑥32 + 178.824𝑥1𝑥4 + 387.882𝑥2𝑥4 − 3610.233𝑥3𝑥4

+ 1623.466𝑥42 − 851.659𝑥1𝑥5 − 4041.634𝑥2𝑥5 + 483.056𝑥2𝑥5

+ 5205.753𝑥4𝑥5 + 642.869𝑥52

𝑔1 = 0.237 + 0.022𝑥1 + 0.122𝑥2 + 0.176𝑥3 − 1.106𝑥4 − 0.364𝑥5 + 0.071𝑥12

+ 0.378𝑥1𝑥2 + 1.082𝑥22 + 0.054𝑥1𝑥3 + 0.329𝑥2𝑥3 + 0.688𝑥3

2 − 0.052𝑥1𝑥4

− 0.378𝑥2𝑥4 − 1.269𝑥3𝑥4 + 0.414𝑥42 + 0.093𝑥1𝑥5 − 0.032𝑥2𝑥5 + 0.222𝑥2𝑥5

+ 0.697𝑥4𝑥5 + 0.504𝑥52

𝑔2 = 0.218 + 0.029𝑥1 + 0.166𝑥2 + 0.172𝑥3 − 1.109𝑥4 − 0.418𝑥5 + 0.085𝑥12

+ 0.404𝑥1𝑥2 + 1.101𝑥22 + 0.060𝑥1𝑥3 + 0.320𝑥2𝑥3 + 0.690𝑥3

2 − 0.087𝑥1𝑥4

− 0.426𝑥2𝑥4 − 1.280𝑥3𝑥4 + 0.477𝑥42 + 0.072𝑥1𝑥5 − 0.133𝑥2𝑥5 + 0.226𝑥2𝑥5

+ 0.741𝑥4𝑥5 + 0.557𝑥52

Let us assume that the safe excursion limits before the occupant hits any part of the car in front

of him/her is 25 cm. Then, the head excursion and knee excursion values can be capped at 0.25m

and 0.25m respectively. However, it is evident that if both the values of excursion are set to the

same upper cap value, the knee excursion constraint is going to be dominated by head excursion

constraint as the head has more options for movement because of the rotation about the hip. So,

the knee excursion constraint can be capped at a more stringent value, say 20 cm, considering

safety factor of 5 cm. Hence, the constraints can be written in negative form as follows.

𝑔1 − 0.250 ≤ 0

𝑔2 − 0.200 ≤ 0


34

2.8. Model Analysis

The table below shows a monotonicity analysis of the objective and the constraint functions in

the given bound of the variables.

Table 12: Monotonicity Analysis

𝑥1 𝑥2 𝑥3 𝑥4 𝑥5

𝑓 - - * - +

𝑔1 + * * - *

𝑔2 + * * - *

* varying monotonicity (descent and then uphill with increase in variable)

It can be seen from the monotonicity analysis table that the optimal value of 𝑥4 is set at its upper

bound. However, the behaviors of the other variables are not evident from the analysis. It can

also be observed that the two constraints have the same behavior with respect to the variables. It

can be possible that one of the constraints is dominant over the other over the entire domain of

operation of the variables. However, the data points of the DOE study do not indicate any such

dominance.

2.9. Numerical Analysis

The above defined mathematical model of the objective function and constraints were input to

MATLAB for optimization. Sequential Quadratic Programming (SQP) method was used for

optimization by the use of ‘fmincon’ function. The code is given in appendix and the output

given by MATLAB is as follows.

𝑥∗ = −0.0893 0.007 − 0.3858 − 0.194 0.524 → (𝐾𝐾𝑇 𝑝𝑜𝑖𝑛𝑡)

𝑓∗ = 204.9787

𝑔1∗ − 0.25 = −0.016 & 𝑔2∗ − 0.20 = 0.0

𝑒𝑥𝑖𝑡 𝑓𝑙𝑎𝑔 = 5 (∆𝑓 < 𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒)

It can be seen from the above result that 𝑔2 i.e. the knee excursion is an active constraint and

hence an equality constraint at the solution. The corresponding output as delivered by

MADYMO for 𝑥∗ is as follows.

𝑓∗ = 208.98


35

𝑔1∗ − 0.25 = −0.0010 & 𝑔2∗ − 0.20 = 0.0002

HIC value of 208.98 is very much acceptable. In fact, most of the HIC values obtained in the

DOE were below 560 (a suggested limit)2 and are acceptable. This is because the bounds to these

variables are selected as prescribed by Reed et al. based on statistical data and some laboratory

measurements.

2.10. Parametric Study –Constraint Cap Study

A parametric study was conducted to evaluate the variation in the objective function with respect

to variations in the constraints. The results are as follows.

First, the knee excursion cap was relaxed to 0.25m. The results obtained were as follows.

𝑥∗ = −0.007 0.007 − 0.3816 − 0.194 0.524 → (𝐾𝐾𝑇 𝑝𝑜𝑖𝑛𝑡)

𝑓∗ = 194.6857

𝑔1∗ − 0.25 = −0.0614 & 𝑔2∗ − 0.25 = −0.0454


It can be observed that both the constraints are inactive at the solution and four of five variables

are controlled by bounds. The variable 𝑥3 is determined by the unconstrained minimum of the

objective function after fixing the values of the other variables at its optimal values (bounds),

provided it satisfies the constraints also. It can also be noted that if the knee excursion cap is

placed anywhere above 0.2046m, it turns inactive. The corresponding MADYMO output is as

follows.

𝑓∗ = 196.11

𝑔1∗ − 0.25 = −0.0647 & 𝑔2∗ − 0.25 = −0.0408

Second, the knee excursion cap was restricted to 0.15m. The solution did not converge as there

was no feasible solution. The knee excursion cap was relaxed slightly from its new cap value of

0.15m until a value of 0.193cm when a feasible solution was found as follows.

𝑥∗ = −0.194 0.007 − 0.3941 − 0.194 0.5883 → (𝐾𝐾𝑇 𝑝𝑜𝑖𝑛𝑡)

𝑓∗ = 248.3958

𝑔1∗ − 0.25 = −0.0233 & 𝑔2∗ − 0.193 = 0.0


36


The corresponding MADYMO output is as follows.

𝑓∗ = 252.18

𝑔1∗ − 0.25 = −0.0201 & 𝑔2∗ − 0.193 = −0.0001

From the above result, it can be seen that by changing the knee constraint cap between 19.3cm

and 20.46cm, the HIC value reduces from 252.18 to 196.11 drastically. As mentioned before, the

actual problem is a multi-objective problem and the trade-off to slightly increase the knee

excursion cap to achieve a considerable reduction in HIC value is arguable. In all these cases, the

head excursion was within limits and can be maintained the same.


37

3. SYSTEM INTEGRATION

3.1. Problem Statement

The task of system integration poses a unique challenge primarily on two accounts:

a. The sub system level objectives deal with quantities that cannot be coalesced into a single

objective function because of dealing with disparate entities like the volume of the seat and

the Head Injury Criterion.

b. The tedium involved in computing the Head Injury Criterion at each value of the Seat

Cushion Angle (αc).

Thus we seek to adopt an integration scheme that incorporates the subsystem level objectives of

the ‘Seat Comfort’ and ‘Seat Safety’, with minimal level of tradeoffs. The subsystems interact

through the seat cushion angle (αc) and the backrest angle (αb), with these angles serving as

parameters for both the subsystems. With regard to the ‘Seat Comfort” subsystem the increase in

the seat cushion angle (αc) affects a decrease in the volume of seat (Vs) while the backrest angle

(αb) does not affect the volume of the seat with its increase of decrease within the feasible space.

However such a study of the Head Injury Criterion with the change in the seat adjustment angles

does not figure in the ‘Seat Safety’ subsystem. Further, the coefficients associated with the

mathematical representation of the Head Injury Criterion differ from one value of the seat

adjustment angles to other. Hence the prediction of the change in Head Injury Criterion with the

change in seat adjustment angles at any set value of seat adjustment angles would be infeasible.

Thus, the search for an optimal solution is formulated as a multi objective problem involving

minimization of the volume of the seat (Vs) and the Head Injury Criterion. The investigation of

the optimal solution for this multi objective problem is conducted at discrete points in the

feasible design space of the seat cushion angle (αc). The choice of this optimization scheme is

consequence of the following observations:

a. The tedium associated with the computation of the Head Injury Criterion and its input as a

parameter would render the study of the entire feasible design space of the seat adjustment

angles practically infeasible.

b. The change in the backrest angle (αb) affects the Head Injury Criterion but does not affect

the volume of the seat (Vs). Thus in order to facilitate a study over a considerable number of

reference points of significance, the backrest angle (αb) is held fixed, while the seat cushion

angle (αc) is varied through discrete points in its feasible design space.

Note: In this regard, a reference point of significance is one which affects change in both

the volume of the seat (Vs) and the Head Injury Criterion.

Thus in this design scheme the optimum value of the Head Injury Criterion may be compromised

owing to the backrest angle (αb) being held fixed. But this trade off is essential for a

comprehensive analysis of the entire system (within a reasonable allotment of time).


38

Further the design space of the seat cushion angle (αc), for the purpose of study is restricted to

the integer values of αc from 15 deg to 25 deg. This decision on the domain of αc is arrived upon

by establishing a maximum permissible limit of 4 % on the change in the volume of seat from its

subsystem level minimum volume of 4.8251*107

mm3

and its necessity is again dictated by the

desire to limit the tediousness of the Head Injury Criterion calculation without losing data points

of significance. Although this design preference can be satisfactorily be applied with regard to

change in Vs, the robustness of the design preference needs to verified by the observed change in

the value of Head Injury Criterion. The robustness of the design preference is validated if the

value of Head Injury Criterion at the system level optimum is also within reasonably small

deviation from its subsystem level optimal value, as realized in the subsequent section.

3.2. Nomenclature Table 13: Nomenclature used in the system model

Index Symbol Description Unit

1 αc Seat cushion angle degrees

2 αb Backrest angle degrees

3 Cs Scale factor for seating area calculation 1

4 Cit Scale factor for pressure at Ischial Tuberosities 1

5 Cl Scale factor for pressure at Lumbar spine 1

6 g Acceleration due to gravity m/s2

7 H H-point 1

8 Hl Lumbar height mm

9 Lb Length of the backrest mm

10 Lc Length of the cushion mm

11 M Mass of the human occupant kg

12 Pit Pressure at the Ischial Tuberosities N/ mm2

13 Pl Pressure at the Lumbar spine N/mm2

14 Pm Pelvis mass value 1

15 Rl Radius of curvature of the Lumbar support mm

16 Rt Radius of curvature of the Thoracic support mm

17 Sc Surface area of the cushion mm2

18 Sl Surface area of the Lumbar support section mm2

19 Ss Seating Surface area mm2


39

20 T Thickness of the cushion and backrest mm

21 Tm Torso mass value 1

22 θl Lumbar Lordosis angle degrees

23 θt Thoracic Kyphosis angle degrees

24 Vbc Volume of the backrest at chest or upper back mm3

25 Vbw Volume of the backrest at waist or lower back mm3

26 Vc Volume of the cushion mm3

27 Vs Volume of the seat mm3

28 Wbc Width of the backrest at chest or upper back mm

29 Wbw Width of the backrest at waist or lower back mm

30 Wc Width of the cushion mm

31 x1 Anchor point X position w.r.t. SgRP m

32 x2 Buckle point X position w.r.t. SgRP m

33 x3 D-ring point X position w.r.t. SgRP m

34 x4 D-ring point Y position w.r.t. SgRP m

35 x5 D-ring point Z position w.r.t. SgRP m


Objective function

The objective of the integrated system is to minimize the volume of the seat (Vs) and the Head

Injury Criterion, under the requirements of fit, feel, support constraints as well as head and knee

excursion criteria. Thus the system objective is modeled as a multi objective problem and these

objectives may be competing with decreasing Head Injury Criterion increasing the volume of the

seat or vice versa (as subsequently realized).

Objective Function

Minimize 𝑓 = 𝑓1

𝑓2

𝑓1 = 𝑉𝑠 = 𝐿𝑐𝑊𝑐𝑇𝑐 + 𝑊𝑏𝑤. 𝜋. 𝜃𝑙

360 𝑅𝑙 +

𝑇

2

2


2

2


360 𝑅𝑡 +

𝑇

2

2


2

2

and


40

𝑓2 = 𝐻𝐼𝐶 = 𝐶0 + 𝐶1𝑥1 + 𝐶2𝑥2 + 𝐶3𝑥3 + 𝐶4𝑥4 + 𝐶5𝑥5 + 𝐶11𝑥12 + 𝐶12𝑥1𝑥2 + 𝐶22𝑥2

2 + 𝐶13𝑥1𝑥3 + 𝐶23𝑥2𝑥3

+ 𝐶33𝑥32 + 𝐶14𝑥1𝑥4 + 𝐶24𝑥2𝑥4 + 𝐶34𝑥3𝑥4 + 𝐶44𝑥4

2 + 𝐶15𝑥1𝑥5 + 𝐶25𝑥2𝑥5 + 𝐶35𝑥2𝑥5

+ 𝐶45𝑥4𝑥5 + 𝐶55𝑥52

where C0, C1…C55 are the second order polynomial curve fitting coefficients of HIC.

Constraints

The system level constraint set is the unified set of constraint sets of the sub system level

constraints as briefly described below:

1. The constraints for the ‘Seat Comfort’ subsystem are mainly categorized as the fit,

support and feel constraints.

2. The constraints for the ‘Seat Safety’ subsystem are the Head Excursion and Knee

Excursion criteria apart from bounds on selected coordinates of anchor point, buckle

point and D-ring point.

Design Variables, Parameters and Constants:

Table 14: Design variables, parameters and constants

Symbol Description Type

Lc Length of the cushion Variable

Wc Width of the cushion Variable

Wbw Width of the backrest at waist or lower back Variable

Wbc Width of the backrest at chest or upper back Variable

T Thickness of the cushion and backrest Variable

Rl Radius of curvature of the Lumbar support Variable

Rt Radius of curvature of the Thoracic support Variable

θl Lumbar Lordosis angle Variable

θt Thoracic Kyphosis angle Variable

x1 Anchor point X position w.r.t. SgRP Variable

x2 Buckle point X position w.r.t. SgRP Variable

x3 D-ring point X position w.r.t. SgRP Variable

x4 D-ring point Y position w.r.t. SgRP Variable


41

x5 D-ring point Z position w.r.t. SgRP Variable

αc Seat cushion angle Parameter

αb Backrest angle Parameter

Pm Pelvis mass value Parameter

Tm Torso mass value Parameter

M Mass of the human occupant Parameter

Cs Scale factor for seating area calculation Parameter

Cit Scale factor for pressure at Ischial Tuberosities Parameter

Cl Scale factor for pressure at Lumbar spine Parameter

g Acceleration due to gravity Constant

The values of the parameters and constants employed in this study are as follows:

Parameters:

Seat Cushion angle (αc) = [15,16,17,18,19,20,21,22,23,24,25] deg.

Backrest angle (αb) = 110 deg.

The Pelvis mass value(6)

(Pm) = 0.2997 (for men)

0.3157 (for women)

The Torso mass value(6)

(Tm) = 0.3213 (for men)

0.3092 (for women)

Constants:

Mass of the Human Occupant (M) = 70 kg



(Cit) = 3.624

The scale factor for pressure at Lumbar Spine(7)

(Cl) = 0.719



42

Summary Model:

Objective Function

Minimize 𝑓 = 𝑓1

𝑓2

𝑓1 = 𝑉𝑠 = 𝐿𝑐𝑊𝑐𝑇𝑐 + 𝑊𝑏𝑤. 𝜋. 𝜃𝑙

360 𝑅𝑙 +

𝑇

2

2


2

2


360 𝑅𝑡 +

𝑇

2

2


2

2

and

𝑓2 = 𝐻𝐼𝐶 = 𝐶0 + 𝐶1𝑥1 + 𝐶2𝑥2 + 𝐶3𝑥3 + 𝐶4𝑥4 + 𝐶5𝑥5 + 𝐶11𝑥12 + 𝐶12𝑥1𝑥2 + 𝐶22𝑥2

2 + 𝐶13𝑥1𝑥3 + 𝐶23𝑥2𝑥3

+ 𝐶33𝑥32 + 𝐶14𝑥1𝑥4 + 𝐶24𝑥2𝑥4 + 𝐶34𝑥3𝑥4 + 𝐶44𝑥4

2 + 𝐶15𝑥1𝑥5 + 𝐶25𝑥2𝑥5 + 𝐶35𝑥2𝑥5

+ 𝐶45𝑥4𝑥5 + 𝐶55𝑥52

where C0, C1…C55 are the second order polynomial curve fitting coefficients of HIC.

subject to:

𝑔1 = 440 − 𝐿𝑐 ≤ 0

𝑔2 = 𝐿𝑐 − 550 ≤ 0

𝑔3 = 500 − 𝑊𝑐 ≤ 0

𝑔4 = 360 − 𝑊𝑏𝑤 ≤ 0

𝑔5 = 456 − 𝑊𝑏𝑐 ≤ 0

𝑔6 = 100 − 𝑇 ≤ 0

𝑔7 = 𝑇 − 120 ≤ 0

𝑔8 = 509 − 2𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360− 2𝑅𝑡. 𝑠𝑖𝑛

𝜋. 𝜃𝑡

360≤ 0


360+ 2𝑅𝑡. 𝑠𝑖𝑛

𝜋. 𝜃𝑡

360− 646 ≤ 0

𝑔10 = 400 − 𝑅𝑙 ≤ 0

𝑔11 = 𝑅𝑙 − 460 ≤ 0

𝑔12 = 460 − 𝑅𝑡 ≤ 0

𝑔13 = 𝑅𝑡 − 500 ≤ 0

𝑔14 = 40 − 𝜃𝑙 ≤ 0

𝑔15 = 𝜃𝑙 − 60 ≤ 0


43

𝑔16 = 20 − 𝜃𝑡 ≤ 0

𝑔17 = 𝜃𝑡 − 40 ≤ 0

𝑔18 = 200 − 𝑅𝑙. 𝑠𝑖𝑛𝜋. 𝜃𝑙

360≤ 0


360− 250 ≤ 0

𝑔20 = 𝐶𝑖𝑡. 𝑀. 𝑔. 𝑃𝑚. 𝑐𝑜𝑠 𝜋.𝛼𝑐

180 / 𝐶𝑠. 𝐿𝑐. 𝑊𝑐 – (3𝑒 − 3) ≤ 0

𝑔21 = 2.5𝑒 − 3 − 𝐶𝑙. 𝑀. 𝑔. 𝑇𝑚. 𝑐𝑜𝑠(𝜋.180 − 𝛼𝑏

180)/ 2𝜋. 𝜃𝑙. 𝑊𝑏𝑤. (𝑅𝑙 +

𝑇

2)/360 ≤ 0

𝑔22 = 𝐶0 + 𝐶1𝑥1 + 𝐶2𝑥2 + 𝐶3𝑥3 + 𝐶4𝑥4 + 𝐶5𝑥5 + 𝐶11𝑥12 + 𝐶12𝑥1𝑥2 + 𝐶22𝑥2

2 + 𝐶13𝑥1𝑥3

+ 𝐶23𝑥2𝑥3 + 𝐶33𝑥32 + 𝐶14𝑥1𝑥4 + 𝐶24𝑥2𝑥4 + 𝐶34𝑥3𝑥4 + 𝐶44𝑥4

2 + 𝐶15𝑥1𝑥5 + 𝐶25𝑥2𝑥5

+ 𝐶35𝑥2𝑥5 + 𝐶45𝑥4𝑥5 + 𝐶55𝑥52 − 0.25 ≤ 0

where C0, C1…C55 the second order polynomial curve fitting coefficients of Head Excursion.

𝑔23 = 𝐶0 + 𝐶1𝑥1 + 𝐶2𝑥2 + 𝐶3𝑥3 + 𝐶4𝑥4 + 𝐶5𝑥5 + 𝐶11𝑥12 + 𝐶12𝑥1𝑥2 + 𝐶22𝑥2

2 + 𝐶13𝑥1𝑥3

+ 𝐶23𝑥2𝑥3 + 𝐶33𝑥32 + 𝐶14𝑥1𝑥4 + 𝐶24𝑥2𝑥4 + 𝐶34𝑥3𝑥4 + 𝐶44𝑥4

2 + 𝐶15𝑥1𝑥5 + 𝐶25𝑥2𝑥5

+ 𝐶35𝑥2𝑥5 + 𝐶45𝑥4𝑥5 + 𝐶55𝑥52 − 0.20 ≤ 0

where C0, C1…C55 the second order polynomial curve fitting coefficients of Knee Excursion

Set Constraints:

Lc, Wc, Wbw,Wbc, T, Rl, Rt ≥ 0

θl, θt ≥ 0 deg; θl, θt≤ 90 deg

3.4. Numerical Results

The system level optimization (for calculation of Pareto optimal points) is carried out through an

iterative procedure by Sequential Quadratic Programming (with Quasi Newton Hessian update)

as supported by the ‘fmincon’ solver of the optimization toolbox of MATLAB and HIC

verification from MADYMO.

The Pareto set of optimal points for the selected values of the seat cushion angles (αc) are plotted

to realize the interaction between the seemingly contesting objectives of the volume of the seat


44

(Vs) and the Head Injury Criterion (from MADYMO). The behaviour of the individual objectives

is plotted in Figure 9 and Figure 10

Figure 9: Variation of Seat Volume with Seat Cushion Angle

Figure 10: Variation of HIC with Seat Cushion Angle

From these plots it can be realized that the volume of the seat (Vs) decreases with the increase in

the seat cushion angle (αc) over the set of selected values. However the Head Injury Criterion is

observed to decrease with the increase in the seat cushion angle (αc) from 15 deg to 19 deg and

4.80E+07

4.82E+07

4.84E+07

4.86E+07

4.88E+07

4.90E+07

4.92E+07

4.94E+07

4.96E+07

4.98E+07

5.00E+07

15 17 19 21 23 25

Seat

Vo

lum

e, m

m3

Seat Cushion Angle (from horizontal), deg

195

200

205

210

215

220

225

230

235

240

15 17 19 21 23 25

Min

imal

He

ad In

jury

Cri

teri

on

, no

un

it

Seat Cushion Angle (from horizontal), deg


45

subsequently increases with increasing value of αc. Thus on the basis of this observed behaviour

we evaluate the volume of seat (Vs) at the seat cushion angle (αc) of 19 deg and realize that the

value obtained (Vs = 4.9385*107 mm3) is within 2.5% of the subsystem level optimum value of Vs (Vs =

4.8251 *107 mm3). This deviation of the volume of seat (Vs) is thus acceptable to predefined design

preferences and the Pareto Optimal point – Vs = 4.9385*107 mm3 and Head Injury Criterion =

197.64 (no unit) – is chosen as the optimum value of the multi objective problem.

Figure 11: Pareto Curve for the bi-criterion problem (HIC vs. Seat Volume)

The coefficients of the Head Injury Criterion and the head and knee excursions at the optimal

point (seat back angle = 19 degrees) are as follows.

Table 15: Coefficients of the second order curve fitted for HIC, Head and Knee Excursions (αc = 19 deg)

Coefficient f2 g22 g23

C0 -347.387 0.698 0.639

C1 613.625 -0.200 -0.211

C2 1142.132 0.109 0.128

C3 764.298 0.214 0.204

C4 -3387.370 -0.713 -0.717

C5 916.005 -1.825 -1.747

C11 1271.920 0.680 0.738

C12 69.774 1.529 1.567

C22 -1130.387 1.249 1.260

195

200

205

210

215

220

225

230

235

240

4.80E+07 4.85E+07 4.90E+07 4.95E+07 5.00E+07

Min

imal

He

ad In

jury

Cri

teri

on

, no

un

it

Seat Volume, mm3


46

C13 -255.064 0.056 0.116

C23 -892.002 0.071 0.102

C33 2364.759 0.737 0.726

C14 21.402 0.763 0.655

C24 1066.676 0.866 0.799

C34 -2882.054 -1.505 -1.517

C44 -347.098 1.633 1.633

C15 -855.779 1.011 1.025

C25 -3210.646 0.604 0.531

C35 895.712 0.116 0.120

C45 3138.135 1.132 1.134

C55 326.822 1.861 1.799

The values of the design variables at the local optimum are

Table 16: Values of the design variables at the solution


𝑥∗ 543.90 500.20 360 456 100 460 460 51.41 20

x1 x2 x3 x4 x5

𝑥∗ -0.102 0.007 -0.383 -0.194 0.524

3.5. Discussion of Results

Hence at the system level optimum the Head Injury Criterion (197.64, no unit) attains its

minimum value over the selected set of values of the seat cushion angles (αc),while the volume

of the seat (Vs = 4.9385*107 mm

3) deviates from its minimum value over the selected set of

values of the seat cushion angles (αc) by 2.5%. This satisfies the previously established design

preferences of the volume of the seat (Vs) to lie within 4% from its subsystem level minimum

volume of 4.8251*107

mm3. Hence, these values of volume of the seat (Vs) and Head Injury

Criterion can be considered as optimum values for the integrated system (without further

revising the design preferences).


47

4. REFERENCES

1. Passenger Car Dimension Definitions – SAE J1100 (UMTRI-29721 A01).

2. Matthew P. Reed, Lawrence W. Schneider, Leda L. Ricci, Survey of Auto Seat Design

Recommendations for Improved Comfort (UMTRI 94-6).

3. Automotive Ergonomics edited by Brian Peacock and Waldemar Karwowski,( Taylor

and Francis).

4. http://www.spineuniverse.com/anatomy/spinal-curves

5. Human Factors in 2000: Driving, Lighting, Seating Comfort, and Harmony in Vehicle

Systems (SP – 1539).

6. Don B. Chaffin, Gunnar B.J. Andersson, Bernard J. Martin, Occupational

Biomechanics, 4th Edition.

7. Human Factors in Driving, Vehicle Seating and Rear Vision (SP-1358)

8. Assessing Child Belt Fit, Volume 1: Effects of Vehicle Seat and Belt Geometry on

Belt Fit for Children with and without Belt positioning Booster seats, Matthew P.

Reed, Sheila M. Ebert-Hamilton, Kathleen D. Klinich, Miriam A. Manary, Jonathan

D. Rupp, UMTRI Sep 08

9. http://www.iihs.org/ratings/protocols/pdf/measures_frontal.pdf

http://www.spineuniverse.com/anatomy/spinal-curves

http://www.iihs.org/ratings/protocols/pdf/measures_frontal.pdf

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