International journal of automotive technology, tập 11, số 4, 2010

MATHEMATICAL MODEL OF AIR SPRINGFigure 3 shows the control volume of the air spring, themain variables of which are pressure, absolute temperature,air mass and volume.. The derivative of

International Journal of Automotive Technology , Vol 11, No 4, pp 447 − 453 (2010)

447

DEVELOPMENT OF ELECTROSTATIC DIESEL PARTICULATE MATTER FILTRATION SYSTEMS COMBINED WITH A METALLIC FLOW- THROUGH FILTER AND ELECTROSTATIC METHODS

H J KIM, B HAN, W S HONG, W H SHIN, G B CHO, Y K LEE and Y J KIM *

Environmental Systems Research Division, Korea Institute of Machinery and Materials (KIMM),

171 Jang-dong, Yuseong-gu, Daejeon 305-343, Korea(Received 4 May 2009; Revised 18 September 2009)

ABSTRACT− A 3000 cc diesel engine attached to an engine dynamo was used to test three newly developed electrostatic Diesel Particulate matter filtration Systems (DPS 1, 2, and 3) under four steady-state engine operating conditions: idle, 2000 rpm with no load, and 2000 rpm under 25% and 50% loads Of the two developed alternatives, DPS 1 and DPS 2, DPS 2 comprises an ionization section, electrostatic field additional section and Flow-Through Filter (FTF), which achieved almost 90% removal of particulate matter (PM) under the engine’s operating conditions, and the efficiency of the FTF was maintained between 20% and 50% Comparing the long-term performance of DPS 2 and DPS 3 (effectively a serial combination of two DPS 2s) with a commercially-available Diesel Particulate Filter (DPF), the DPS 2 and DPS 3 achieved almost the same efficiency for removing PM as the DPF but had significantly improved (75%~90% lower) differential pressure drops

KEY WORDS : Diesel particulate matters, Filtration system, Electrostatic precipitation, Flow-through filter, Removal efficiency, Differential pressure drop

1 INTRODUCTION

Diesel engines enjoy widespread use in heavy duty

vehi-cles due to their superior fuel economy and durability

com-pared with gasoline engines (Monaghan, 2000) Furthermore,

with increasing oil prices, the development of

post-treat-ment technologies, such as DPF (Diesel Particulate Filter)

and DeNOx catalysts, and the increasing world-wide

de-mand for tighter controls on CO2 emissions to address

global warming, diesel-driven cars have become a viable

alternative to gasoline-powered personal automobiles in

many European countries Nevertheless, despite their lower

fuel consumption, longer durability, and lower CO2

emi-ssions compared with gasoline-driven cars, it is well known

that diesel engines emit significant amounts of Particulate

Matter (PM) and Nitrogen Oxides (NOX) and thus

contri-bute to the overall PM and NOx pollution of the outdoor

environment (Yoon and Cho, 2009; An et al., 2006; Jacob

et al., 2006, Jacobs et al., 2006; Jeong et al., 2008) The

attendant regulation of PM emissions from diesel vehicles

is becoming increasingly stringent as the European Union

adopts new legislation in this area (e.g., Euro VI and V)

Furthermore, all diesel engines, even newly-developed

ones, produce similar amounts of ultrafine particles, and it

is the presence of these particles that largely determines the

concentration of PM in diesel exhaust The harmful effect

of diesel particles on human beings is known to be related

to particle size, and the presence of smaller particles may

be linked with more serious respiratory or cardiovasculardiseases (HEI, 2002) International environmental instituteshave therefore insisted that the regulation of PM in dieselexhaust should be based on the number of particles ratherthan their mass concentration (Kittelson et al., 1999)

To reduce both the mass and number concentrations of

PM in the exhaust gas of diesel vehicles, post-treatmentsystems using ceramic DPF have been commercialized toretrofit selected vehicles and are also on the cusp of com-mercialization in light and heavy duty diesel automobiles(Park et al., 2006) Wall-flow ceramic filters, which arecoated using metal catalysts, have been shown to have afiltration efficiency greater than 90% for diesel particulates,but diesel ceramic filters are still marred by operationalproblems, such as insufficient reliability and an excessivelyhigh pressure drop caused by solid particles that becomeclogged under low exhaust temperature conditions.Furthermore, the excessive heat released and the highthermal gradient that occurs in the filter during theirregeneration can lead to mechanical cracking and failure(Park et al., 2006; Cho et al., 2007)

The development of alternative ceramic DPF designshas generated considerable interest in the research com-munity In particular, PM control devices manufacturedusing metallic materials have shown considerable promise

in PM emission control technology because these devices

*Corresponding author. e-mail: yjkim@kimm.re.kr

448 H J KIM et al.

exhibit a relatively low pressure drop and avoid the

numer-ous problems and complex structure of DPFs As a result of

these benefits, many researchers have addressed the

development of PM removal systems using metallic filters

Yoon and Cho (2009) and An et al (2006) studied the

design of a metallic foam filter and analyzed its

aero-dynamic performance, differential pressure drop, and

filtration efficiency Their experimental results showed that

the filter removed more than 50% of the diesel PM based

on mass Other researchers applied a filtration system with

metallic Flow-Through Filters (FTFs) to heavy duty diesel

vehicles and investigated their diesel PM and gaseous

compound removal efficiency The experimental results

from these studies showed that mass concentrations of

diesel PM were decreased by 50~70% using the FTF, but

number concentrations were decreased by less than 50%

(Jeong et al., 2008; Park et al., 2006; Bruck et al., 2001;

Jacob et al., 2006) These metallic filters have open

flow-through passages that permit exhaust gases to pass when

their PM capacity is exceeded Thus, the pressure drop

does not increase dramatically, but their PM removal

effici-ency based on number concentration is low compared with

that of DPFs (Majewski, 2008)

To compensate for the weak ability of metallic filters to

remove PM, Park et al (2007) applied a corona charger

upstream of a metallic foam filter and thus increased the

PM removal efficiency of the system by 10~20% To date,

however, few studies have applied electrostatic charging

and precipitation to metallic FTF, even though these devices

have become fully commercialized in Korea and several

European countries

In this study, newly designed electrostatic filtration

systems consisting of electrostatic devices and commercial

FTFs were developed to achieve PM removal performances

as high as those of commercial DPFs by using particle

charging and an additional electrostatic force on the FTF to

enhance the removal efficiency of the standalone filter The

pressure drop and PM removal performance of the

com-bined systems were investigated and compared with those

of a commercially available ceramic DPF under a variety

of operating conditions using a diesel engine attached to a

dynamo

2 EXPERIMENTAL APPARATUS AND

PROCEDURE

2.1 Electrostatic Diesel Particulate filtration System (DPS)

Figure 1 shows the schematic representations of the

elec-trostatic Diesel Particulate filtration Systems (DPSs) used

in the study Figure 1(a) shows the two parts of DPS 1: the

electrode, which generates unipolar ions and applies an

electrostatic force to the front of the flow-through filter

simultaneously, and the filter itself

The edge electrode (an astral shape with eight legs) of

the first section was aligned parallel to the front section of

the FTF The length of the section that generated the ions

was 60 mm; the length and diameter of the FTF were 105

mm and 130 mm, respectively Figure 1(b) shows DPS 2,which is also composed of a section that generates unipolarions and imposes an additional electrostatic force and theFTF

In contrast to DPS 1, the edge electrode (the rod withedges), to which the perforated plate was attached to

Figure 1 Schematic representation of the electrostaticDPSs showing 1) the sections that generate unipolar ionsand apply an electrostatic force on the flow-through filterand 2) a flow-through filter coated with catalysts

Figure 2 Experimental setup of the performance testsusing the DPSs and the commercially available DPF

DEVELOPMENT OF ELECTROSTATIC DIESEL PARTICULATE MATTER FILTRATION SYSTEMS 449

impose the electrostatic force on the filter, was positioned

perpendicular to the face of the FTF The total length of the

electrode was 205 mm, and the length of the FTF was the

same as that of the filter in DPS 1 DPS 3, which was

designed to increase PM removal efficiency, was a

two-stage set up consisting of the same unit as the DPS 2 but

manufactured with two filters, each of which was half the

size of the FTF used in DPS 1 and DPS 2 The total length

of this system was 515 mm

2.2 Experimental Methods

The DPS devices were connected to the exhaust of a 3000

cc diesel engine with an engine dynamo The

characteri-stics of the devices were investigated by varying the engine

operating conditions and comparing their performance with

the DPF under the same experimental conditions The test

engine that we used was the 3000 cc diesel engine (Model

Frontier, Hyundai Motors, Korea) with a maximum torque

and speed of 17 kg·m and 4000 rpm, respectively The

engine speed was set at idle and 2000 rpm with no load and

2000 rpm with loads of 20% and 50% The experimental

set up is shown in Figures 2 and Figure 3, and

specifi-cations of the test diesel engine are summarized in Table 1

The high power supply (Max −30 kV/ 10 mA) was

con-nected to devices installed at the center of the exhaust line,

and the sampling probes were inserted just before and after

the DPSs to measure their PM removal efficiency

To minimize variations in the concentrations of the diesel

PM caused by gaseous compounds, all of the sampling

lines connected to the rotating dilutor (Model MD-19, Matt

Engineering, Switzerland) were electrically heated to 200

oC, and the sampled gases were mixed with air at a dilution

ratio of 1:200 A DMA (Differential Mobility Analyzer,Model 3080, TSI, USA) and a CPC (Condensation ParticleCounter, Model 3076, TSI, USA) were used to measure thenumber concentration and size distribution of the dieselparticles before and after the test filtration systems wereoperated The PM removal efficiency was calculated usingthe following formula,

Where, η is the removal efficiency (%); C out is the outletconcentration of particles per cc; and C in is the inlet con-centration of particles per cc

In addition, a device that measures pressure (Testo M/XL*testo 454, Testo, Germany) was connected to tabslocated at the inlet and outlet of the DPSs, and a thermo-couple linked to a temperature monitoring system (ModelV18, SDD, Korea) was also inserted into the line upstream

350-of the filtration systems to measure the pressure drop andthe inlet temperature

3 RESULTS AND DISCUSSION3.1 Performance Test Results of the Two Types of Electro-static DPSs

Figure 4 shows the distributions of the number ration as a function of particle diameter for the differentengine operating conditions The number concentration ofthe diesel particles increased, and the size distributionshifted to the right, as the engine speed and load increased.Most of the particles from the engine exhaust were found inthe nuclei and accumulation modes, and were less than 300

concent-nm in diameter The mean diameter of the particles was inthe range of 30~50 nm Figure 5 shows the curves of thecorona voltage against current at different engine speedsand loads, which were compared for each DPS to investi-gate the electrical characteristics of the respective systems.The curves for both DPSs moved to the left, and the coronacurrent was higher for the same applied voltage when the

η = 1 C out

C in

–

Figure 3 Photograph showing the experimental set up

Table 1 Specifications of the test diesel engine

450 H J KIM et al.

engine speed and load increased In particular, ‘sparkover’

in the DPSs, which indicates the start of the unstablecorona discharge, was observed at lower applied voltageswhen the speed and load increased This result mainlyoccurred due to the increased temperature of the exhaustgas For the negative corona discharge, as the temperature

of the gas increased, the mean free path between the gasmolecules increased, and the frequency of the collisionsbetween electrons and the gas molecules decreased signifi-cantly Consequently, those electrons that do not collidewith the gas molecules are electrically forced to the ground-

ed side Thus, high temperature leads to unstable coronadischarge (Kim et al., 2001)

In the case of DPS 2, the initial voltage was higher thanthat of DPS 1 (Figure 5) Because the distance between thesharp edges of the electrode and the grounded side in DPS

2 (see Figure 1 (b)) was wider than the distance in DPS 1(Figure 1 (a)), the corona in DPS 2 was initiated at highervoltages than in DPS 1 (Hinds, 1999)

Figures 6 and 7 show the PM removal efficiency of DPS

1 against the mean PM diameter for various applied age/current combinations at different engine speeds andloads The efficiency of DPS 1 with the FTF was 30~80%,which is higher than that of the standalone filter, whoseefficiency was 25~50% at idle, 2000 rpm without a load,and at 2000 rpm with loads of 25% and 50% Because boththe charging efficiency of the diesel particles and the

volt-Figure 5 Corona current plotted against applied voltage for

various speed/load combinations

Figure 6 PM removal efficiency plotted against PM

diameter for various applied voltage/current combinations

at different engine speeds for DPS 1

Figure 7 PM removal efficiency plotted against particlediameter for various applied voltage/current combinations

at different engine loads for DPS 1

DEVELOPMENT OF ELECTROSTATIC DIESEL PARTICULATE MATTER FILTRATION SYSTEMS 451

electrostatic force on FTF increased as the voltage applied

to DPS 1 increased, the efficiency with which the diesel

particles were removed was higher than that of the FTF

itself Furthermore, at low speed/load combinations, when

the temperature of the exhaust gas was low, the particle

removal efficiency was higher than that observed under the

higher speed/load combinations because of the higher

applied voltages and longer residence times at the low

combinations

Figures 8 and 9 show the PM removal efficiency of DPS

2 against the mean PM diameter for various applied

voltage/current combinations for each of the engine speeds

and loads In contrast with DPS 1, the efficiency with

which the diesel particles were removed in DPS 2 was

30~50% higher than that of the standalone filter, and the

removal efficiency was over 85% at temperatures over

250oC and more than 95% at temperatures less than 200oC,

which was similar to the efficiency of the commercial DPF

As shown in Figure 1, because the direction of the corona

discharge of the ionizer in DPS 1 was parallel to the

direction of the exhaust flow, the residence times of the

particles and unipolar ions in the charging region were

shorter, while the direction of the corona discharge in DPS

2 was perpendicular to the direction of flow, and the

charging region was wider than that of DPS 1 Thus, the

charging rate of the particles in DPS 2 was expected to be

higher than that in DPS 1, which explains why the ency of the DPS 2 exceeded that of DPS 1

effici-3.2 Comparison between the Electrostatic DPSs and theCommercially Available DPF

The performance of DPS 2, which showed greater PMremoval efficiency than DPS 1, was compared with that ofthe commercially-available DPF under the same experi-mental conditions: 2000 rpm under 25% and 50% loads To

Figure 8 Removal efficiency at various different engine

speeds as a function of changing particle diameter for

various applied voltage/current combinations for DPS 2

Figure 9 Removal efficiency for various different engineloads at 2000 rpm as a function of particle diameter forvarious applied voltage/current combinations for DPS 2

Figure 10 Comparison of the PM removal efficiency at themode diameter (40 nm) among the FTF, the DPS 2 and theDPF at 2000 rpm with a 25% load applied for 3 hours

452 H J KIM et al.

improve the removal efficiency of DPS 2 at 2000 rpm with

50% load, DPS 3 was designed as a serial combination of

DPS 2s, as described in Section 2.2; its performance was

also compared with that of the commercial DPF The

ceramic DPF used in this study had a diameter of 142 mm

and a length of 154 mm The PM removal efficiency was

calculated for the peak particle diameter of 40 nm

Figures 10 and 11 show the performance of the three

filtration systems, the FTF, DPS 2, and the DPF, in terms of

their PM removal and observed pressure drop, respectively

The temperature of the exhaust gas at 2000 rpm and 25%

load was 180oC The efficiency of DPS 2 when the high

voltage/current (14.3 kV/1 mA) was applied was over

90%, which was similar to that of the DPF and

signifi-cantly higher than that of the standalone FTF Furthermore,

the observed pressure drop of DPS 2 was 200 mmH2O,

which was significantly lower than the 800 mmH2O of the

DPF and did not increase during the three hours of testing

Figures 12 and 13 show the variation in the performance of

DPS 3 and the DPF over 8 hours of the test at 2000 rpm

under 50% load The temperature of the exhaust gas was

over 260oC, and the applied voltages and currents in thefirst and second stages were 13.4 kV/1 mA and 11.5 kV/2

mA, respectively As shown in Figure 12, the particleremoval efficiency was over 90% for the whole 8 hours,and the pressure drop (343 mmH2O, Figure 13) wassignificantly lower than that of the DPF Furthermore, it didnot increase over time, unlike the DPF whose initial pre-ssure drop (1700 mmH2O) increased dramatically to 3000mmH2O after 8 hours of operation

ed performance tests on each system and compared themwith those of a commercially available DPF Our majorfindings may be summarized as follows:

The DPSs were tested at constant engine speeds of idleand 2000 rpm, and loads of 25 and 50% at 2000 rpm in a3000-cc diesel engine The PM removal efficiency of theFTF improved from 20 to 60% to 40 to 95% under thevarious engine operation conditions using an electrostaticprecipitation method

The DPS 2 achieved a PM removal efficiency of over90% at an exhaust temperature of less than 170oC and anefficiency greater than 80%, even at exhaust temperaturesabove 260oC

The one-stage (DPS 2) and two-stage (DPS 3) filtrationsystems showed similar PM removal to the commercially-available DPF over 3- and 8-hour engine operation at 2000rpm at loads of 25% and 50%, while their pressure dropswere only 200 and 343 mmH2O, compared to 800 and 1700

to 3000 mmH2O of the DPF under the same operationconditions

An electrostatic technique that generates unipolar ionsand imposes a strong electrostatic force on the FTF could

Figure 11 Comparison of the differential pressure among

the FTF, DPS 2 and the DPF at 2000 rpm with a 25 % load

applied for 3 hours

Figure 12 Comparison of the PM removal efficiency at the

mode diameter (40 nm) between the DPS 3 and the DPF at

2000 rpm with a 50% load applied for 8 hours

Figure 13 Comparison of the differential pressure betweenthe DPS 3 and the DPF at 2000 rpm with a 50 % loadapplied for 8 hours

DEVELOPMENT OF ELECTROSTATIC DIESEL PARTICULATE MATTER FILTRATION SYSTEMS 453

compensate for the low PM removal performance of the

FTF while maintaining the required low pressure drop

ACKNOWLEDGEMENT−This research was supported by a

Basic Research Fund (SC0770) of the Korea Institute of

Machinery and Materials.

REFERENCES

An, S., Cho, G., Choi, H., Jeong, Y., Lee, E., Oh, K., Han,

S., Kim, K and Park, S (2006) A study on the PM

reduction of catalytic metal foam filter Fall Conf Proc.,

Korean Society of Automotive Engineers, Paper No.

06-F0055, 366−370

Bruck, R., Hirth, P., Reizig, M., Treiber, P and Breuer, J

(2001) Metal supported flow-through particulate trap; A

non-blocking solution SAE Paper No 011950

Cho, G., Choi, H., Jeong, Y., Kim, H., Ahn, S., Jeong, B.,

Choi, Y., Kim, D., Yoon, C S., Lee, E., Oh, K., Han, S.,

Kim, K., Park, S., Kim, G and Choi, S (2007) PM

reduction performance and regeneration characteristics

of catalyzed metal foam filters for a 3L diesel passenger

vehicle SAE Paper No 013456

HEI (2002) Understanding the Health Effects of

Compo-nents of the Particulate Matter Mix: Process and Next

Steps HEI Perspectives, [Online] Health Effects Institute,

Boston, MA, Available at http://www.healtheffects.org/

Pubs/Perspectives-2.pdf

Hinds, W C (1999) Aerosol Technology 2nd Edn 15,

331−341 U.S.A

Jacob, E., Lammermann, R., Pappenheimer, A and Rothe,

D (2006) Exhaust gas aftertreatment system for EURO 4

heavy-duty engines MTZ,6/2005, 1−8

Jacobs, T., Chatterjee, S., Conway, R., Walter, A., Kramer,

J and Mueller-Hass, K (2006) Development of partial

filter technology for HDD retrofit SAE Paper No.

010213

Jeong, S J., Kang, J H., Kim, T M and Lee, H S (2008)

A study on the uniform PM deposition and improvement

of regeneration performance of PDPF of heavy dutydiesel engine Spring Conf Proc., Korean Society of Automotive Engineers, Paper No. 08-S0042, 256−262.Kim, Y J., Hwang, T K and Yoo, J S (2001) A study onthe collection characteristics of submicron particles in anelectrostatic precipitator-I Electrical characteristics Korean

J Air-Conditioing and Refrigeration Engineering 7, 7,

572−578

Kittleson, D., Watts, W., Baltensperger, V., Weingartner, E.,Matter, V., Pandis, S., Clark, N and Gautum, M (1999).Diesel Aerosol Sampling Methology University ofMinessota Center for Diesel Research Report

Majewski, W A (2008) Flow-through Filters, Diesel Net Technology Guide, [Online]Ecopoint Inc Available athttp://www.dieselnet.com/tech/cat_ftf.html [Accessed

03 December 2008]

Monaghan, M L (2000) Future gasoline and diesel Review Int J Automotive Technology 1, 1, 1−8.Park, S J., Lee, D G., Kim, J., Cho, G., Kim, H and Jeong,

engines-Y (2007) Filtration characteristics of metal foam filtersfor DPF combined with electrostatic precipitation mech-anism Trans Korean Society of Automotive Engineers

15, 2, 151−158

Park, Y., Choi, Y., Jung, H., Kim, N and Lee, J (2006) Astudy on the emission reduction performance of a partialflow diesel particulate filter Fall Conf Proc., Korean Society of Automotive Engineers, Paper No. 06-F0037,

248−253

Yoon, C S and Cho, G (2009) Study of design and CFDanalysis for partial DPF utilizing metal foam Trans Korean Society of Automotive Engineers 17, 1, 24−34

International Journal of Automotive Technology , Vol 11, No 4, pp 455 − 460 (2010)

455

EXPERIMENTAL INVESTIGATION OF THE VALVETRAIN FRICTION

IN ACTUAL ENGINE OPERATION CONDITIONS

S KANG 1)* , S K KAUH 1) and K.-P HA 2)

1)School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea

2)Power Train R&D Center, Hyundai Motor Company & Kia Motor Corporation, 772-1 Jangduk-dong,

Hwaseong-si, Gyeonggi 445-706, Korea

(Received 18 August 2009; Revised 6 October 2009)

ABSTRACT− Recently, the demands for improved fuel economy have been continually rising because of environmental protection policies, legislative pressures on emissions and increases in the price of oil Reducing the friction power loss in a production engine may be regarded as one of the most effective technologies for improving fuel economy because the technology is cost effective and applicable to a great number of vehicles This paper describes attempts to measure the torque needed to drive a camshaft and to examine the sources of the torque fluctuations in order to analyze the friction in valvetrains The measurements were performed through a cam sprocket-type torquemeter, which was able to measure the torque of the valvetrain under actual engine operating conditions In the cam torque measured, the fluctuations were mainly dependent on the primary oscillations caused by cam events and the secondary oscillations caused by the valvetrain natural frequency The range of the fluctuations became greater at high speed because of the inertial mass The resulting FMEP (friction mean effective pressure) of the valvetrain decreased, and the effective peak tension increased with an increase in the engine speed.

KEY WORDS : Torque, Valvetrain, Torquemeter, Friction, FMEP

1 INTRODUCTION

For several decades, the efficient use of energy has been an

important issue in all industrial fields Fuel economy in

particular is one of the most important factors in evaluating

overall vehicle performance in the automobile industry;

therefore, fuel efficiency is considered one of the most

important issues in this industry Recently, the demands for

improved fuel economy have been continually rising

because of environmental protection policies, legislative

pressures on emissions and increases in the price of oil To

improve fuel efficiency and satisfy exhaust regulations,

several new technologies, including GDI (gasoline direct

injection), VVT (variable valve timing) and cylinder

deactivation, are being utilized Reduction of friction losses

in a production engine can be regarded as one of the most

effective technologies because the technology is cost

effective and applicable to a great number of vehicles

The valvetrain mechanism is one of the major focuses of

engine development because it has an effect on the

per-formance of spark ignition engines The friction losses

related to the cam mechanism have become important as

energy-conscious design becomes the new trend Although

the valvetrain accounts for 6~10% of the total friction

losses in an engine, attempts to reduce this number are

being made (Gangopadhyay et al., 2004) Recently, there

has been a tendency to increase engine speed and bustion pressure to improve the fuel efficiency and output.Therefore, valvetrain components move with higher speedsand accelerations As a result, vibration, friction losses andengine noise have increased (Teodorescu et al., 2002) Forthis reason, testing and verification of valvetrains havebecome more important

com-Most friction measurements on valvetrains were formed on a test rig in which the torquemeters wereconnected in-line between the driving motor and the actualcylinder head of the engine It was therefore very difficult

per-to accurately measure the dynamic characteristics of avalvetrain in a real engine environment Crane and Meyerdeveloped a comprehensive design tool that could be used

to model an engine’s valvetrain friction components andthat was validated by measuring the friction torque of thevalvetrain and removing the valvetrain parts However, thetest was made in a cylinder head, not a real engine Acamshaft was motored indirectly using a pulley and a belt

As a result, it is difficult to validate the model because ofundesirable belt oscillations and tension changes (Craneand Meyer, 1990) Teodorescu et al isolated and deter-mined the main components of the friction in a valvetrainsystem on a firing, single-cylinder diesel engine using straingauges and an accelerometer (Teodorescu et al., 2002).Baniasad and Emes measured the driving torque of avalvetrain in a real engine using strain gauges and a slipring However, each engine to be measured had to be

*Corresponding author. e-mail: pigtiger.kang@gmail.com

456 S KANG, S K KAUH and K.-P HA

modified to set up the slip ring (Baniasad and Emes, 1998)

To compensate for this weak point, a torquemeter using

telemetry was considered Recently, a cam sprocket-type

torquemeter that can measure the torque of a valvetrain in a

real engine has been developed The developed

torque-meter has wireless communication via Bluetooth and a

non-contacting power supply (Kang et al., 2007)

The objective of the research discussed in this paper was

to measure the torque of a valvetrain using a cam

sprocket-type torquemeter and to examine the complex dynamic

mechanisms of valvetrains From the measurements, an

investigation into the sources of the torque fluctuation was

performed and the FMEP (friction mean effective pressure)

of the valvetrain was determined

2 INSTRUMENTATION

2.1 Cam Sprocket-type Torquemeter

A camshaft is driven by a crankshaft; the two are connected

to each other using a timing chain and sprockets for

uniform valve timing The torque to drive the valvetrain is

transferred through a cam sprocket A cam sprocket-type

torquemeter can replace the existing cam sprocket and

measure the torque using a torque sensor and strain gauges

Figure 1 shows a schematic view of the torque sensor The

torque sensor is similar in shape to the shape of a cam

sprocket and has four spokes to connect the rim to the hub

The relationship between the strain generated in a spoke

and the torque acting on the torque sensor can be derived

from the superposition of two cantilevers through model

simplification

Considering the moments acting on the hub, at

equili-brium, we have the following if the number of spokes is n:

(1)The bending moment at the end of the spoke is

The strain on the spoke can be calculated from the

follow-ing equation of the bendfollow-ing moment:

2, and were wired to a Wheatstone full bridge for thermalstability (Kang et al., 2007)

2.2 CalibrationFigure 3 shows a comparative calibration apparatus fordetermining the relation between the output voltage of thetorque sensor and the torque value applied to the torque-meter The cam sprocket-type torquemeter and the mastertorquemeter were connected in series, and the right side ofthe cam sprocket-type torquemeter was fixed, while the leftside of the master torquemeter was connected to a canti-lever to weigh the balance weights

A bearing was installed to support the cantilever to reducethe bending moment caused by the mass The experimentrepeatedly loaded and unloaded the mass, and the appliedtorque in the calibration experiment was set using the valuefrom the master torquemeter The comparative calibrationresult is presented in Figure 4 The cam sprocket-typetorquemeter showed results with good linearity, and the

ε x x= l4= 3 Ebt 2

- R r–

R r +

- T n -

Figure 1 Schematic view of the torque sensor

Figure 2 Position of the installed strain gauge and a wiringdiagram of a full bridge

Figure 3 Comparative torque calibration apparatus

EXPERIMENTAL INVESTIGATION OF THE VALVETRAIN FRICTION IN ACTUAL ENGINE OPERATION CONDITIONS 457

hysteresis between loading and unloading was negligible

The slopes from repeated tests were almost equivalent to

each other However, the initial value varied with the

installation conditions of the torquemeter because of the

hub-loading effect The hub-loading effect usually appears

in belt-pulley or chain-sprocket systems from tension in the

belt or chain Because of the hub-loading effect, the initial

value varied with tension and angular position However,

the means of the initial values over a cycle were almost

identical, regardless of tension Therefore, if the initial value

of the torquemeter is chosen as the mean value, there is no

net effect over a cycle because of the preloading (Lee,

2007)

Figure 5 shows a schematic diagram of the torquemeter

installation on the engine

3 EXPERIMENTAL RESULTS

In the present study, the measurement of the valvetrain

torque was performed on an 8-cylinder (V8) engine in a

real engine environment The torquemeter was installed on

the intake valvetrain located in the bank on the #1 cylinder

side Figure 6 shows the intake valvetrain torque

wave-form, which was measured at different engine speeds in the

motored condition The positive torque in the graph

occurr-ed when a resistance was applioccurr-ed to the camshaft by the

valve spring while opening the intake valve On the otherhand, the negative torque occurred when the intake valveswere closing and the returning force from the valve springwas applied to the camshaft A V8 engine has 2 banks, andeach bank has 4-cylinders A bank of a V8 engine is similar

to an in-line 4-cylinder engine in terms of shape, but theignition order of a V8 engine is different from that of a 4-cylinder engine To determine the torque curve of a V8engine, the ignition order, which may be different for eachengine to be measured, must be considered carefully Thetorque waveform is made up of a summation of severalcylinder torques The reason why the superposition of eachcylinder torque has an effect on the shape of the torquecurve is that the time to open and close a valve is longerthan the time to drive the valve for each cylinder (Kang et

al., 2007)

At lower engine speeds, the torque waveform wascharacterized by the kinematics of the valvetrain, which aredependent on the shape of the cam profile and the valvespring It is noticeable in the graph that the fluctuationbecame larger with an increase in engine speed To ex-amine the sources of the fluctuation, a Fourier analysis wasperformed The frequency spectrum shown in Figure 7illustrates the principal frequencies of the torque wave-form A dominant frequency of the cam torque was the 1.3

EO (Engine Order) excitation caused by the cam event.This component is a primary oscillation in the cam torquewaveform The frequency of the primary oscillation varied

Figure 4 Calibration results

Figure 5 Schematic diagram of the test rig setup

Figure 6 Variation of the torque waveform with enginespeed in an 8-cylinder SI (spark ignition) engine

458 S KANG, S K KAUH and K.-P HA

with engine speed On the other hand, the constant natural

frequency of about 1 kHz occurred regardless of engine

speed This component is a secondary oscillation in the

cam torque waveform (Weber et al., 1998)

Each component of the primary and the secondary

oscillation torque was isolated from the measured torque

waveform using frequency analysis As shown in Figure 8,

the secondary oscillation torque oscillated with zero torque

as the center The amplitude of the oscillation increased

with an increase in engine speed and in particular became

higher when the valves were opened Figure 9 shows the

primary oscillation torque varying with engine speed As

the engine speed increased, the amplitude of the oscillation

increased, and the slope of the oscillation curve became

steeper This occurred because the cam torque is terized by increased inertial mass at high speed (Kim andNguyen, 2007)

charac-A timing belt or a timing chain is utilized in an internalcombustion engine for the camshaft drive The reliability

of such drive systems depends on the tension of the timingbelt or the timing chain If the tension is too tight, pre-mature failure of the bearings and the belt or the chain itselfmay occur On the other hand, if the tension is too slack,jumping of teeth in the case of timing belts or lateralvibration in the case of timing chains may occur (Fawcett,1999) The experimental engine in this study used a timingchain, not a timing belt Considering the equilibrium bet-ween tight and slack side tensions on the cam sprocket, theeffective tension is defined as following (Oh et al., 2001):

: tight side tension, : slack side tension

The maximum and the minimum values of the effectivetension occurred in the positive and negative peaks of thetorque waveform, respectively Figure 10 shows the vari-ation of the effective peak tension with engine speed Theeffective peak tension increased with an increase in enginespeed To examine the contribution of each oscillationsource to the effective peak tension, the peak values wereisolated and determined separately The peak values of theprimary oscillation tended to increase gradually On theother hand, the peak values of the secondary oscillationincreased and fluctuated seriously with engine speed As aresult, the effective peak tension had a higher value because

of the influence of the secondary oscillation The effectbecame larger on the tight side and at high speed

It is impossible to separate the individual friction ponents in the valvetrain with the current instrumentation.Nonetheless, the overall friction losses of the valvetrain can

com-be calculated from the measured cam torque If the forcesapplied to the camshaft to open and close the valves were

τ e = torquepitch radius -=τ t – τ s

Figure 7 Frequency spectrum of the measured torque

Figure 8 Variation of the torque sources isolated from the

measured torque by frequency

Figure 9 Variation of the primary oscillation torque withengine speed

EXPERIMENTAL INVESTIGATION OF THE VALVETRAIN FRICTION IN ACTUAL ENGINE OPERATION CONDITIONS 459

only applied by the valve springs, the average value of the

valvetrain torque during a cycle would be zero However,

in reality, the average torque is above zero This is because

the friction between the camshaft and the valve always

exists

Through the previously mentioned Fourier analysis, the

measured torque can be calculated from a summation of

the primary and the secondary oscillation torque The

primary oscillation torque can be regarded as a summation

of the torque caused by valve springs and by valvetrain

friction Finally the measured torque can be expressed as

follows:

T m: measured torque in a camshaft,

Tb: torque induced by primary oscillation,

T n: torque induced by secondary oscillation,

T v: torque induced by valve springs,

T f: overall friction torque

If the measured torque is integrated during a cycle, the

torque caused by valve springs and the secondary

oscilla-tion torque can be canceled out, as shown in Equaoscilla-tion (7)

Only the term representing the overall friction torque

remains If the average friction torque during a cycle is

introduced into Equation (7), Equation (8) s obtained:

, (7)

Therefore, the average friction torque during a cycle can

be calculated by taking an average of the measured torque

The FMEP of each valvetrain can be obtained by zing the friction work per cycle with the displacementvolume, as shown in Equation (9) (Heywood, 1988):

If individual sources of friction can be additive, the totalvalvetrain FMEP can be calculated by multiplying theresulting valvetrain FMEP by the number of valvetrains inthe experimental engine (Crane and Meyer, 1990) Figure

11 shows the variation of the total valvetrain FMEP withengine speed At low speeds, the total FMEP decreasedwith an increase in engine speed because boundary lubri-cation was dominant On the other hand, at high speeds, thetotal FMEP increased because of hydrodynamic lubrication

as the engine speed increased In the middle speed range,there was almost no change in the total FMEP because thevalvetrain was working under mixed-film lubrication Itcan be seen from Figure 11 that the overall trend of the totalvalvetrain FMEP agrees with a common feature of valve-train friction

4 CONCLUSIONSThis paper described a technique for measuring the drivetorque and the friction torque of a valvetrain using a camsprocket-type torquemeter The main results can be sum-marized as follows:

(1) The oscillatory cam torque was measured as a function

of engine speed in real engine operation conditions Itwas found that the measured torque could be dividedinto a primary oscillation by the cam event and asecondary oscillation by the natural frequency usingFourier analysis

(2) The primary oscillation torque was calculated from asummation of the four cylinder torques from the bank

on the #1 cylinder side The waveform did not change,and the frequency varied with engine speed The peakvalues of the oscillation became larger, and the slopes

of the torque curve became steeper as the engine speed

Figure 10 Variation of the effective peak tension with

engine speed

Figure 11 Total valvetrain FMEP

460 S KANG, S K KAUH and K.-P HA

increased

(3) The secondary oscillation torque consisted of a constant

valvetrain natural frequency of about 1 kHz At higher

speeds, the amplitude of the oscillation became higher

because of the inertial mass Nevertheless, the effect of

the oscillation from the natural frequency on the

valve-train friction was negligible, regardless of engine speed

(4) From the measured cam torque, the FMEP of a

valve-train and the effective peak tension of a timing chain

were determined The FMEP decreased, and the

effec-tive peak tension increased with an increase in engine

speed

(5) An experimental investigation into the dynamic

charac-teristics and the friction of the valvetrain was

perform-ed It is hoped that the results will be a useful tool to

validate simulations and to develop valvetrains in future

studies

ACKNOWLEDGEMENT−Authors gratefully acknowledge the

financial support by the second stage of the Brain Korea 21

Project in 2009.

REFERENCES

Baniasad, S M and Emes, M R (1998) Design and

develop-ment of method of valve-train friction measuredevelop-ment

SAE Paper No 980572

Crane, M E and Meyer, R C (1990) A process to predict

friction in an automotive valve train SAE Paper No.

901728

Fawcett, J N (1999) Improvements in belt tension setting

procedures on internal combustion engines Proc

Institu-tion of Mechanical Engineers,213, Part D, J Automobile Engineering, 119−126

Gangopadhyay, A., Soltis, E and Johnson, M D (2004).Valvetrain friction and wear: Influence of surface engi-neering and lubricants Proc Institution of Mechanical Engineers,218, Part J, J Engineering Tribology, 147−

Kim, D J and Nguyen, V T (2007) Reduction of highfrequency excitations in a cam profile by using modifiedsmoothing spline curves Int J Automotive Technology

8, 1, 59−66

Lee, J (2007) A Study on In-vehicle Torque Measurement

of an Engine and Engine Accessories Using Bluetooth.Ph.D Dissertation School of Mechanical and AerospaceEngineering Seoul Nat’l University Seoul Korea

Oh, K., Plauman, M., Romanick, J., Farmer, I., Aimone, M.and Barnaby, D (2001) performance comparison bet-ween chain and belt cam-drive systems SAE Paper No.2001-01-0365

Teodorescu, M., Taraza, D., Henein, N A and Bryzik, W.(2002) Experimental analysis of dynamics and friction

in valve train systems SAE Paper No 2002-01-0484.Weber, C., Herrmann, W and Stadtmann, J (1998) Experi-mental investigation into the dynamic engine timingchain behaviour SAE Paper No 980840

International Journal of Automotive Technology , Vol 11, No 4, pp 461 − 469 (2010)

461

MULTI-BODY ELASTIC SIMULATION OF A GO-KART: CORRELATION BETWEEN FRAME STIFFNESS AND DYNAMIC PERFORMANCE

G MIRONE *

Dipartimento di Ingegneria Industriale e Meccanica, Università di Catania, Catania 95125, Italy

(Received 30 March 2009; Revised 2 October 2009)

ABSTRACT− The elastic response of a vehicle to an applied force determines the dynamic performance, comfort, and support

of the vehicle, where the elastic response depends primarily on the stiffness of the frame/chassis Significant variations in the dynamic response of a vehicle are typically achieved with suitable shock absorbing systems, which contribute significantly to whole body flexibility The defining feature of a go-kart is the lack of devices capable of absorbing shock and dampening vibration The tires and body of a go-kart, which consist of a frame of welded beams, must also function as a shock absorption system The objective of this study was to reproduce the elastic behavior of a commercially available Italian go-kart by modeling the frame in a multibody ADAMS environment and to determine the effect of elastic features on the dynamic performance of the vehicle Frame stiffness was assessed by applying a static torsion moment, while the circular trajectory of the go-kart was evaluated at different speeds and steering wheel angles The proposed multibody, flexible model was validated

by comparing the static and dynamic response of the go-kart in simulated and experimental analyses The results of numerical simulations demonstrated that this method may be extended to the design of customized go-kart frames and to the tuning of go-karts for specific racing conditions.

KEY WORDS : Go-kart, Slip angle, Frame stiffness, Handling

1 INTRODUCTION

The go-kart was developed to provide a low-cost vehicle

for young racers Go-karts are simple vehicles with limited

components and subsystems, and are used for both training

and competition

Although research on go-karts provides interesting

information and could potentially yield new technologies,

from an engineering standpoint, go-kart related literature is

relatively scant Nevertheless, the effect of frame

charac-teristics on specific dynamic responses has been studied

over the last few years (Guglielmino et al., 2000; Mirone,

2003; Ponzo and Renzi, 2004; Muzzupappa et al., 2005;

Biancolini et al., 2007)

The main simplifications introduced into the design of a

go-kart include the removal of shock absorbing systems

and rigid rear axles that connect the driving wheels

The removal of these features may dramatically reduce

the dynamic performance because a rigid connection

bet-ween the body and wheels results in a large load transfer

and poor maneuverability (Cianetti et al., 1994; Kim and

Kim, 2007; Lee and Yoo, 2009) Moreover, the lack of any

mechanic differential between the two driving wheels leads

to uniform peripheral tire speeds, which results in poor

performance with respect to curvilinear trajectories

Neverthe-less, if the flexibility of the frame and rear axle is calibrated

with tire behavior, go-karts are very agile and capable ofundergoing large lateral accelerations

The ideal tuning of a frame depends on the currentconditions; thus, to maintain optimal frame stiffness during

an entire race, an active frame or pilot-operated tuningdevice can be utilized, where the configuration of the sus-pension is modified in real time

Complex regulation systems are not available for karts, and limited tuning may be performed by employingrear axles with different diameters and lengths Thus, theconfiguration of a go-kart is a compromise between therequirements of many conditions for a single race

go-It is clear that the simplifications in go-kart design duce substantial difficulties

intro-In this work, a commercially available go-kart was mentally tested and modeled with ADAMS software Tovalidate the model, the static-dynamic behavior of a go-kart was simulated numerically Theoretical and experi-mental results were in good agreement; thus, the proposedanalysis was suitable for predicting the performance of go-karts and for the design of frames under dynamic racingconditions

experi-2 STATIC MODELING OF THE GO-KART FRAME

As shown in Figure 1, the frame of the go-kart used in thisstudy was made of welded steel tubes with different dia-

*Corresponding author. e-mail: gmirone@diim.unict.it

462 G MIRONE

meters and thicknesses The dimensions of the go-kart are

provided in Table 1:

The steel used in the frame was 25CrMo4 and ASTM

A284, and the diameters and thickness of the tubes ranged

from 14 to 30 mm and 1.5 to 2 mm, respectively

The total weight of the vehicle and the pilot was 140 kg,

where 57% of the total weight was distributed on the rear

tires and 43% was distributed on the front tires under static

conditions

The frame was modeled with flexible links capable of

simulating the static and dynamic behavior of beam-like

elastic bodies After various preliminary analyses, each

straight beam was divided into sections with a length equal

to the diameter of the outer tube to determine the

appro-priate amount of segregation The division of the beams

provided acceptable accuracy in the evaluation of frame

elastic displacements, but significant time was required for

each analysis

The multibody model of the naked frame was statically

validated by simulating a series of experimental tests,

where torsional loads were applied to the front tube of the

frame and the rear end was fully constrained to a rigid wall

As shown in Figure 2, the center of the front bar of theframe was hinged at a fixed distance from the ground toavoid flexural displacements

Micrometers were placed at eight specific locationsalong the frame to measure the vertical displacement due tothe applied loads, as shown in Figure 2 Points 1, 2, 7 and 8corresponded to the front steering hubs and the rear axle,respectively Two different magnitudes of torsion were ap-plied to assess the behavior of load-displacement in theframe

Figure 3 confirmed that the behavior of the frame waslinear under all applied loads Linearity was indicated bythe complete coincidence of displacement data (normalizedwith respect to the applied torque) at 35 and 70 Nm oftorque Furthermore, the results indicated that stiffness wassignificantly lower in the front end tube In this zone, theframe was reduced to two parallel tubes, which were closer

to the longitudinal axis of the frame than other areas

In other words, the region of the frame near points 3 and

4 is primarily responsible for the torsional compliance ofthe entire frame

The application of 70 Nm of torque was simulated withthe ADAMS numerical model by applying two fixed con-straints at the rear of the kart, a rotational constraint (ahinge with a rotational axis parallel to the frame’s longitu-dinal axis) in the midsection of the front transverse tube,and a torque of 70 Nm to the midsection of the tube

Figure 1 Go-kart frame

Table 1 Principal dimensions of the go-kart frame

Pitch

(mm) Front (mm)track (mm)trackRear Caster angle(deg) Kingpin angle(deg) Front tire radius(mm) Rear tire radius(mm)

1068 960 1160 12.8 6.5 130 140

Figure 2 Experimental static tests to determine the torsional stiffness of the frame

Figure 3 Vertical displacement at frame control pointsunder torsional stress

MULTI-BODY ELASTIC SIMULATION OF A GO-KART: CORRELATION BETWEEN FRAME STIFFNESS 463

The theoretical displacement at the control points was

compared to the experimental results in Table 2

An acceptable agreement was obtained, confirming that

the static model of the frame was appropriate

By inducing relative rotation between the rear axle and

the imaginary line between the axes of the front tires at a

null steering angle, a meaningful quantification of frame

stiffness was obtained from the applied torsion The

experi-mental and theoretical stiffness of the frame, obtained from

the aforementioned analysis, was 166 and 161 Nm/deg,

respectively

The multibody model of the go-kart frame was validated

with respect to static elastic response and was completed

by modeling the steering system, rear axle, tires, driving

torque on the rear axle, and motion law for the steering

wheel, as well as the mass of the pilot, fuel tank and engine

3 DYNAMIC MODELING OF THE COMPLETE

VEHICLE

In the model of the steering system, the front tires were

considered hinges, the spherical joints were considered

rigid bodies, and the steering rods and steering wheel shaft

were considered elastic beams Verification of the

cine-matic response of the model was performed by comparing

tire movement at five steering angles and the movement of

the experimental go-kart A maximum discrepancy of 7%

was observed at high angles (40~50 degs)

The rear axle was connected to the frame by two hinges

placed at the ball-bearings, while the pilot, fuel tank and

engine were simulated as rigid bodies with a given weight,gravity center and inertia The pilot’s weight was subdivid-

ed into two parts including the legs, which were placed in anearly horizontal position (15 Kg, where the center ofgravity was halfway between the base of the pelvis andknees), and the torso and head (50 kg, where the center ofgravity was placed under the sternum bone) Each of theserigid parts was linked to locations in the frame, includingthe point of attachment for the seat, steering wheel andseat-belt

To validate the dynamic behavior of the go-kart, fullycircular turns at constant speeds and steering angles weresimulated in the multibody model The same maneuverswere conducted experimentally and were compared to thesimulated turns

To ensure that the desired speed was maintained, aspecific amount of torque was required to compensate forthe friction between the joints and tire-rod In the actualmaneuver, torque is provided by the pilot, who acts on thethrottle and brakes In the simulation, torque acted on therear axle, where the magnitude of torque was proportional

to the difference between the effective current axle speedand the target axle speed (V eff -V targ)

A proportionality constant between the applied torqueand delta-speed was implemented As a result, the maxi-mum torque, which corresponded to a delta-speed of 15m/s, did not exceed that of an average two-stroke engine at

35 BHP and 12000 RPM

In each simulation, the go-kart traveled along a straightpath for the first 0.2 or 0.4 seconds Next, a progressiverotation at a rate of 25 degrees per second was imposed onthe steering wheel until the desired angle was achieved.The selected angle was maintained for two or three circulartrajectories, and the results were evaluated In the experi-mental study, an actual go-kart was subjected to the samesequence of events

The tire model utilized in the theoretical study was the

handling/compre-hensive slip analyses The main assumptions of this model

Table 2 Experimental and theoretical elastic displacement

R1 Outer radius of the unloaded (undeformed) tire

R2 Inner radius of the tire (outer radius of the tire hub)

CN Tire radial stiffness

Cs Tangent of the curve “longitudinal load-vs.-slip ratio”, evaluated at null slip ratio

Cα Tangent of the curve “lateral load-vs.-slip angle”, evaluated at null slip angle

Cγ Tangent of the curve “lateral load-vs.-incl angle”, evaluated at null incl angle

CRR Eccentricity of the vertical force on the contact patch (rolling resist moment arm)

RDR Relative damping ratio

U0 Friction coefficient at null comprehensive slip

U1 Friction coefficient at full comprehensive slip

464 G MIRONE

include a rectangular contact patch and a parabolic

distri-bution of pressure across the contact patch, where tire

response is modeled as a beam on an elastic foundation

The input parameters required to characterize each tire

according to the UATire model are described schematically

in Table 3

The majority of these constants can be obtained from

experimental tests with specific equipment However, the

machinery necessary to conduct these tests was not

avai-lable, and the appropriate data was not found in the

liter-ature Thus, characterization of go-kart tires was

accom-plished indirectly

In circular trajectories at a constant speed and steering

angle, the effect of Cs is negligible because the longitudinal

slip and corresponding contact forces are low

Under the aforementioned conditions, C γdoes not have

a significant effect because the lateral force due to the

inclination angle is many times lower than the lateral force

due to the lateral slip angle Thus, Cs and C γwere based on

the C α of sport automotive tires

CRR was estimated by measuring the distance covered

by the vehicle before coming to a complete stop without

the assistance of traction or braking at different initial speeds

The estimation of CRR was approximate because the effects

of friction in the transmission chain were included

RDR was determined on the basis of a qualitative

esti-mation at different vertical loads RDR varies substantially

with tire pressure and does not have a significant effect on

the dynamic equilibrium of a vehicle traveling at a constant

speed in circular trajectories

The friction coefficients U0 and U1 were estimated

according to the hypothesis of negligible load transfers

Specifically, U0 and U1 were obtained by measuring the

distance covered during braking at the sliding limit or

under full slip conditions at various speeds

C α was the most influential coefficient in the simulated

conditions and was evaluated for rear and front tires

By approximating a linear function, the relationship

bet-ween moderate slip angle and lateral forces (1) was

obtain-ed As shown in Figure 4, the rotational equilibrium equation

(2) provided a relationship between the C α of the front and

rear tires, which reduced the number of unknowns to one

Y 1=C α_rear·α rear; =C α_ front · α front; (1)

By substituting Equation (1) into Equation (2), the ratio

between C α of the rear and front tires was obtained

C α_rear·α rear·a −2·C α_ front · α front ·b=0;

In Equation (2), the load Y2 was assumed to be nullbecause the rear tire on the internal side of the curve wasnot in contact with the surface of the ground To com-pensate for the lack of differential, go-karts are designed tominimize contact between the rear tire and the ground The above assumptions reduced the number of unknowntire parameters to one, and the remaining parameter wasobtained by trial and error Specifically, each cycle con-sisted of simulations at a given speed and steering angle,where the experimental results of the analysis were known(radius of the circular trajectory) Iterations were repeated

by varying the initially random value of C α until the lysis agreed with the experimental data After an appro-priate value of C α and an accurate simulation was obtain-

ana-ed, other experimental tests (different combinations ofspeed-steering angle) were conducted Overall, the resultssuggested that the properties of tires were successfullycharacterized

The set of coefficients determined by this procedure areshown in Table 4, while the corresponding tire behaviorexpressed as the UATire subroutine in terms of lateral force

vs slip angle is shown in Figures 5 and 6, as a function ofvertical load (Fz)

Tire characterization was the final step in the dynamicmodeling of the go-kart The complete model of the go-kartwas used to perform seven analyses simulating severalexperimental tests

≅

⋅

Figure 4 Lateral forces in circular paths at a constantspeed.

Table 4 Estimated tire parameters

Parameter widthmm mmR1 mmR2 N/mmCN CsN N/radCα N/radCγ CRRmm RDR− U0− U1−

MULTI-BODY ELASTIC SIMULATION OF A GO-KART: CORRELATION BETWEEN FRAME STIFFNESS 465

4 EXPERIMENTAL−NUMERICAL

COMPARISON FOR CIRCULAR

TRAJECTORIES AT CONSTANT SPEED

As shown in Figure 7, the go-kart was equipped with a

digital odometer on the right front wheel and a protractor

on the steering wheel to assist the pilot in controlling the

speed and steering wheel angle A bottle containing white

liquid was placed behind the pilot’s seat, and the liquid was

allowed to drip from the bottle as the go-kart progressed

As a result, the liquid marked the trajectory of the go-kart

on the surface of the road

The test consisted of a short acceleration ramp and sevencircular trajectories at a constant speed and steering angle.The speed and steering wheel angles investigated in thisstudy were 16 km/h at 15 deg, 21.5 km/h at 20 deg, 33.5km/h at 20 deg, 15 km/h at 30 deg, 22 km/h at 30 deg, 19km/h at 40 deg, and 15 km/h at 50 deg

Simulations were conducted at initial speeds and ing angles identical to those used in actual experiments Tocompensate for rolling resistance and to maintain a con-stant speed, the theoretical analysis included torque on therear axle Moreover, after an initial steering transitionperiod, sufficient time was allotted to complete at least onecircular trajectory

steer-The time interval of the theoretical analysis was mately 10−3 seconds, resulting in 7000 to 21000 intervalswithin the seven simulated conditions

approxi-Figure 8 shows a typical output of a simulated circulartrajectory (at 22 km/h and 30 deg) The trajectory displayssuccessive positions assumed by the center of gravity of thepilot’s torso

The most intuitive comparison of experimental andtheoretical results was made by examining the radii of go-kart trajectories, as reported in Table 5 and Figure 9

Figure 5 Transverse forces vs slip angle at four vertical

loads for front tires.

Figure 6 Transverse forces vs slip angle at four vertical

loads for the rear tires

Figure 7 Instrumented go-kart

Figure 8 ADAMS simulation of the circular trajectories

466 G MIRONE

The torque applied to the rear axle adequately balanced

the rolling resistance of the tires, producing very small

differences (<0.5 km/h) between the effective and target

speed

The radii of predicted trajectories were in agreement

with those determined experimentally (maximum error less

than 9%) A significant portion of error could be due to

slight differences between the steering cinematic chain in

the model and the actual chain For instance, further

ana-lyses performed with steering angles modified by 2~3degrees led to the accurate prediction of trajectory radii

As shown in Figure 9, the proposed theoretical modelreproduced the speed-steering angle and radius of curva- ture in triplicate Even with different combinations of vari-ables, the results were in agreement with the experimentaldata

5 ANALYSIS OF RESULTS The response of the multibody model under differentsimulated conditions provided useful information on thedynamic behavior of go-karts, including the load transferand frame torsion in circular trajectories

As shown in Figures 10~12, in six of the seven lations, the vertical load acting on the tires was transferredfrom the internal side of the curve to the outer side due tocentripetal acceleration (expressed for each plot as a frac-tion of the acceleration of gravity) and the steering angle

simu-In the figure, tires 1, 2, 3 and 4indicate the rear external,rear internal, front internal and front external tires, respec-tively

Longitudinal acceleration of the go-kart was negligiblebecause the torque required to maintain a constant speedwas low Thus, the static distribution of vertical forcesvaried horizontally, without any front-rear load transfer.Alternatively, the lateral load transfer on tires was affect-

ed by the steering angle and centripetal acceleration.The contribution of the steering motion to the verticalload transfer was due to the caster angle, which is typical ingo-karts The effect of the caster angle was clearly visiblewhen the steering wheel was rotated under static conditions(null speed, no pilot on board, frame not deformed elasti-cally) Under these conditions, one of the four tires tended

to rise off the surface of the road This behavior is tional and is included in the kart design because it faci-litates the unloading of the rear tire on the internal side ofthe curve, creating an effect similar to that of a differential.Lateral acceleration transfers vertical loads toward theexternal side of the trajectory in the front and rear tiresalmost equally In theory, if the center of gravity wasplaced halfway between the front and rear axles, a differ-ence in the load transfer of the front and rear tires wouldnot be observed

inten-Table 5 Comparison of theoretical and experimental

results (circular trajectories at various speeds and steering

accelera-[g]

Radius of the experi-mental tra-ject [m]

Radius of the numeri-cal traject

Figure 9 Graphical representation of theoretical and

experimental results (radii of circular trajectories at various

speeds and steering angles)

Figure 10 Vertical load transfer at acceleration values of 0.16 and 0.3 g

MULTI-BODY ELASTIC SIMULATION OF A GO-KART: CORRELATION BETWEEN FRAME STIFFNESS 467

On the contrary, the motion of the steering system causes

different load transfers in the front and rear tires In the

front tires, the vertical load was shifted towards the internal

side of the trajectory, opposing the effect of lateral

accele-ration Alternatively, in the rear tires, the load was shifted

towards the external side, increasing the effect of lateral

acceleration

As shown in Figures 10~12, the effect of steering angle

exceeded that of centrifugal force in the front tires at low

and medium lateral accelerations (from 0.16 g up to 0.65

g), which caused the internal front tire (n 3) to carry a

higher load than the external tire (n 4) A comparison of

the simulated front tire load at a steering angle of 30

de-grees and an acceleration of 0.3 g and 0.56 g revealed that

centrifugal force tended to increase the load on the external

side of the trajectory, reducing the unbalance in the front

tires caused by the steering angle In the last simulation, the

external front tire (n 4) carried a larger load than the

internal tire (n 3) because the effect of centrifugal force at

a lateral acceleration of 0.94 g exceeded the effect of

steering wheel rotation at 20 degrees

In simulations conducted at 0.3 and 0.39 g, the

centri-fugal force and the steering wheel angle increased the load

on the external side of the trajectory Moreover, the rear

tires carried a nearly identical load, indicating that an

additional rotation of 10 degrees (first case) had almost the

same effect as 0.09 g of centripetal acceleration (second

case) on the vertical load of the rear tires

Saturation behavior with respect to load transfer on the

rear tires did not allow the maximum load to exceed 700 N

on the external rear tire

Finally, Figure 13 displays the torsion angle of theframe, evaluated by the vertical displacement of the tireattachment points

The data in Figure 13 revealed that the elastic deformation

of the frame depended exclusively on the steering angle.For instance, the torsion angle of the frame increased with

an increase in steering angle, and the centrifugal force didnot affect frame torsion In fact, the fourth and the fifthsimulations confirmed that equal lateral accelerations (56%and 59% of g) and different steering angles (30 and 50degs) induced very different torsion angles (0.57 deg and0.87 deg) On the contrary, the second and fourth curves ofFigure 13 confirmed that different accelerations (30% and56% of g) at an identical steering angle (30 degrees)induced the same amount of frame torsion (0.57 degrees).Identical trends were observed in simulations conducted at

a steering angle of 20 degrees For instance, despite

vari-Figure 11 Vertical load transfer at acceleration values of 0.39 and 0.56 g

Figure 12 Vertical load transfer at acceleration values of 0.65 and 0.94 g

Figure 13 Torsion angle of the frame in all sevensimulations

468 G MIRONE

ations in lateral acceleration (from 0.39 to 0.94 g), frame

torsion remained constant at approximately 0.4 degrees

To further simply the tuning procedure, a new basic

model of the kart was assembled by substituting the elastic

frame with two rigid parts connected by a torsion spring,

which concentrates the compliance of the entire frame on

its longitudinal axis (points 3 and 4 of Figure 2)

To determine the effect of frame stiffness on the

per-formance of the go-kart, the spring stiffness was set to

165000 Nmm/deg, which corresponded to a frame stiffness

of 16500

Speeds and steering wheel angles used in the original

experiments were also used to simulate the response of

simplified frames

The resulting trajectories are displayed in Figure 14

The theoretical response of the simplified frame and the

stiffness of the actual frame were similar to the

experi-mental response, indicating that the total stiffness between

the rear and front tires was more important than the

distri-bution of stiffness along the longitudinal axis of the frame

Variations in the trajectory due to increased or decreased

frame stiffness were clearly visible, confirming that

multi-body analyses are able to estimate the interaction between

the elasticity of the frame and the dynamic behavior of the

go-kart

The validation of the model indicated that numericalanalyses can quantify the effect of frame stiffness on loadtransfer and the dynamic performance of the vehicle.Many different motion sequences can be modeled, allow-ing the prediction of corresponding go-kart responses andframe optimization for specific conditions

6 CONCLUSIONSExperimental tests were conducted on a go-kart to deter-mine frame stiffness and the radius of circular trajectories

at selected speeds and steering angles

Multibody modeling of the go-kart was achieved bytaking into account the elastic properties of the frame Theresults indicated that elastic components were primarilyresponsible for the dynamic performance of go-karts.The tires were characterized by adopting a set of hypo-theses based on the dynamic conditions in experimentaltests Theoretical and experimental data were compared tovalidate the model’s response and the proposed tireparameters The results indicated that a maximum error of9% was observed in the radii of circular trajectories

An analysis of the theoretical results provided interestingFigure 14 Effect of frame stiffness on the trajectory

MULTI-BODY ELASTIC SIMULATION OF A GO-KART: CORRELATION BETWEEN FRAME STIFFNESS 469

aspects of go-kart behavior with respect to tire load transfer

and frame torsion, suggesting that a simplified frame

repre-sentation may be useful for a first evaluation of frame

response under a set of dynamic conditions The effect of

frame stiffness on the trajectories at a fixed speed and

steering angle was evaluated, confirming that simplified

models are able to predict the effect of frame configuration

on the dynamic performance of the vehicle

Further developments of the model should include a

rigorous characterization of the tires; however, the results

indicated that the model can be used successfully in the

design and tuning of go-kart frames and tires Thus, the

model can be applied to optimize the go-kart for specific

conditions

REFERENCES

Biancolini, M E., Cerullo, A and Reccia, L (2007)

Design of a tuned sandwich chassis for competition

go-kart Int J Vehicle Design, 44, 360−378

Cianetti, F., Di Pietro, G., Guglielmino, E and La Rosa, G

(1994) Structural optimization of a composite material

racing-car body 4th Int Conf New Design Frontiers for

More Efficent, Reliable and Ecological Vehicles, Firenze

Guglielmino, E., Guglielmino, I D and Mirone, G (2000).Caratterizzazione numerico-sperimentale di un go-kart

da competizione Atti del XXIX° Convegno AIAS,Lucca, 57−68

Kim, K C and Kim, C M (2007) Analysis processapplied to a high stiffness body for improved vehiclehandling properties Int J Automotive Technology 8, 5,

629−636

Lee, J H and Yoo, W S (2009) Predictive control of avehicle trajectory using a coupled vector with vehiclevelocity and sideslip angle. Int J Automotive Technology

10, 2, 211−217

Mirone, G (2003) Mulibody modelisation of a go-Kartwith flexible frame: simulation of the dynamic behavi-our and experimental validation Proc JSAE Int Body Engineering Conf 2003

Muzzupappa, M., Matrangolo, G and Vena, G (2005).Experimental and numerical analysis of the go-kartframe torsional behaviour XVII Ingegraf – XV ADM Seville.

Ponzo, C and Renzi, F (2004) Parametric multi-bodyanalysis of kart dynamics The 30th FISITA World Cong.

2004, Barcelona, Spain

International Journal of Automotive Technology , Vol 11, No 4, pp 471 − 479 (2010)

471

DEVELOPMENT AND ANALYSIS OF AN AIR SPRING MODEL

S J LEE *

Department of Mechanical Engineering, Myongji University, Gyeonggi 449-728, Korea

(Received 18 June 2009; Revised 23 October 2009)

ABSTRACT− The analytical model of an air spring can be effectively used for the design of air spring equipped vehicles to provide better ride and handling characteristics along with various functions for passenger convenience However, establishing

a general model of an air spring poses particular difficulties due to the severe nonlinearities in the stiffness and the hysteresis effects, which are hardly observed in conventional coil springs The purpose of this study is to develop a general analytic model of an air spring − one which represents the main characteristics of stiffness and hysteresis and which can be connected

to a model of pneumatic systems desigined to control air spring height To this end, the mathematical model was established

on the basis of thermodynamics with the assumptions that the thermodynamic parameters do not vary with the position inside the air spring, that the air has the ideal gas property, and that the kinetic and potential energies of the air are negligible The analysis of the model has revealed that the stiffness is affected by the volume variation, the heat transfer, and the variation of the air mass and the effective area However, the hysteresis is mainly affected by the heat transfer and the variation of the effective area In particular, it was revealed that the increase of the volume due to the cross-sectional area increases the stiffness, while the increase of the volume due to the other reason decreases it In addition, the model was used to develop the sufficient stability condition, and the stability of the model was analyzed The paper also presents the comparison between the simulation and experimental results to validate the established model and demonstrates the potential of the model to be usefully employed for the development of the air spring and its algorithm for use in a pneumatic system.

KEY WORDS : Air spring, Analytic model, Stiffness, Hysteresis, Thermodynamic model, Stability

NOMENCLATURE

: air mass flow rate flowing into air spring

: air mass flow rate flowing out of air spring

: air mass inside air spring

V cv : control volume of air spring

: heat transfer rate

A heat : area of heat transfer

h c : heat transfer coefficient

W : work performed on air spring

h in : enthalpy flowing into air spring

h out : enthalpy flowing out of air spring

U cv : internal energy inside air spring

Pcv : pressure inside air spring

P atm : pressure of environment

T cv : temperature inside air spring

T in : temperature of air flowing into the air spring

T env : temperature of environment around air spring

c v : specific heat at constant volume

c p : specific heat at constant pressure

k : specific heat ratio

R : ideal gas constant

F as : force applied to vehicle body by air spring

A eff : effective area of air spring

z : vertical displacement

z 0 : magnitude of displacement sinusoid

f : frequency of displacement sinusoid

t : time

V cv 0 : fixed volume of air spring

A cs : cross-sectional area of the air spring

z max : maximum displacement of bottom of air spring

z curr : current displacement of bottom of air spring

1 INTRODUCTIONAir springs have been primarily applied to commercialvehicles and luxury passenger cars because they are costly.They have many advantages, however, compared withconventional coil springs Air springs provide better com-fort and improvement in the handling performance becausethey can have relatively low stiffness and enable a vehicle

to maintain optimum wheel alignment In addition, airsprings can protect the body of a vehicle on rough roadsand make the task of loading baggage into the trunk of avehicle more convenient (Figure 1) because the heights ofthe air springs can be adjusted through supplying and ex-hausting the air via the pneumatic circuit connected to theair spring (Jang et al., 2007; Hyundai Motor Company,2009; Kia Motor Company, 2009) Figure 2 shows an airspring and its relevant pneumatic system

472 S J LEE

The analytic model can be usefully employed for the

design of an air spring, the related pneumatic system, and

the algorithm for the operation of the pneumatic system

(Jang et al., 2007; Kim et al., 2001) However, it is very

difficult to develop an accurate air spring model due to its

severe nonlinearities, which are not found in conventional

coil springs More specifically, the stiffness of an air spring,

which has a significant effect on the ride and handling

characteristics of a vehicle, varies nonlinearly with the

frequency of the road excitation The hysteresis

characteri-stics of an air spring, which provides a vehicle with the

additional damping force, cannot be neglected compared

with the force of the damper, and it also varies with the

frequency of the road excitation (Nieto et al., 2008; Chang

and Lu, 2008)

Some research works (Kim et al., 2001; Nieto et al.,

2008; Chang and Lu, 2008; Kim and Kim, 2005; Quaglia

and Sorli, 2001; Seong et al., 2008; Cha et al., 2006) have

been carried out to develop an analytic model for an air

spring involving these nonlinear characteristics Kim et al

(2001) have developed a model of an air spring and a

vehicle with a flexible body using ADAMS, which has

been used to estimate the performance of a vehicle with a

control algorithm for the pneumatic system The stiffness

of the air spring model is expressed as a function of

pre-ssure, volume, area, and the polytropic index, but the

process that determines the pressure of the air spring is not

described Nieto et al. (2008) derived a nonlinear model of

an air spring on the basis of thermodynamics, assuming

adiabatic or isothermal conditions, and analyzed the

stiff-ness, the damping factor, and the transmissibility using the

derived model Chang and Lu (2008) also developed a

model of an air spring on the basis of thermodynamics,which consisted of two steps First, the air spring pressure

is obtained using the adiabatic condition, and then it iscorrected by considering the temperature obtained by theheat transfer equation Because the model does not consi-der the air supply or the air exhaust to/from the air spring, itcannot be employed in the design of the pneumatic system

or its control algorithm In addition, it is difficult to employthe model for the stability analysis because the model isexpressed by algebraic equations

The objective of this study is to develop the general airspring model on the basis of the thermodynamic equationwithout the assumption of adiabatic or isothermal condi-tions and with the variation of air mass The analysis of thedeveloped model will reveal the important factors that have

a significant effect on the stiffness and hysteresis of an airspring The author of this paper performed the study on theair spring model and its analysis in previous research (Cha

model of an air spring The further analysis is performed onthe basis of the enhanced model Moreover, the stability ofthe air spring model is analyzed in this paper

The rest of this paper is organized in the following order

In Section 2, the generalized model of the air spring isderived on the basis of the thermodynamic equation InSection 3, the derived model is validated by experimentalresults, and the stability and important characteristics of theair spring such as the stiffness and hysteresis are analyzed.Finally, Section 4 presents a summary of the results anddraws the conclusions

2 MATHEMATICAL MODEL OF AIR SPRINGFigure 3 shows the control volume of the air spring, themain variables of which are pressure, absolute temperature,air mass and volume The mathematical model of the airspring can be derived using the energy conservation law.The flow of the air mass into or out of the controlvolume, shown in Figure 3, is controlled by the operation

of the control valve in the pneumatic circuit, as shown inFigure 2 The flow of the air accompanies the enthalpy Inaddition, work is performed on the control volume by thevehicle body and the wheel, and the difference of temper-Figure 1 Adjustment of the height of a vehicle

Figure 2 Air spring and its pneumatic supply system

(Folchert, 2006; Jang et al., 2007) Figure 3 Control volume of the air spring

DEVELOPMENT AND ANALYSIS OF AN AIR SPRING MODEL 473

atures between the inner and the outer sides of the control

volume generates some heat transfer between them These

power flows can be modeled by the following energy

conservation equation (Fernandez and Woods, 1999; Cha

et al., 2006)

(1)where the time derivative of work that is performed on the

control volume, , is defined using the pressure inside the

control volume, P cv, and the time derivative of the control

volume, V cv, by

(2)The enthalpies flowing into and out of the control volume,

h in and h out, are expressed using the specific heat at constant

pressure, c p, and the temperatures of the air mass flowing

into and inside the control volume, T in and T cv, respectively,

by

(3)The enthalpies multiplied by the air mass flow rate flowing

into and out of the air spring, and , represent

power flows The internal energy of the control volume,

U cv, is defined using the specific heat at constant volume,

c v, the air mass, m cv, and the temperature inside the control

volume by

(4)The heat transfer rate between the inner and the outer sides

of the control volume, , is expressed using the heat

transfer coefficient, h c, the area of the heat transfer, A heat,

and temperatures of the outer and the inner sides of the

control volume, T env and T cv, in the following form

(5)

To derive the pressure dynamic equation from the equation

(1), the temperature inside the control volume is replaced

with the pressure inside the control volume using the

following ideal gas equation

(6)where R is the ideal gas constant The derivative of the

temperature inside the control volume with respect to time

can be derived by differentiating equation (6) with respect

to time, as follows:

(7)where the air mass inside the control volume varies with

the air mass flowing into and out of the control volume on

the basis of the mass conservation law, as follows:

(8)

Finally, the first order differential equation for the pressure

of the air in the control volume can be obtained fromequations (1), (6), (7), the specific heat ratio k=c p/c v, and

R/c v=k −1 as follows:

(9)

Equation (9), which represents the mathematical modelfor the air spring, consists of two kinds of variables, inwhich the specific heat ratio, heat transfer coefficient, andthe area of heat transfer are the parameters, and the volumeand the rate of change of the volume in the air spring, theair mass flow rates, and the temperature of the environmentare the variables determined by the components connected

to the air spring Each parameter was obtained through thefollowing methods The ideal gas constant was selectedfrom the property of the air, and the air mass inside the airspring was calculated from the ideal gas equation Thespecific heat ratio was estimated from the comparison bet-ween the experimental and simulation results The area ofheat transfer and the volume of the air spring werecalculated from the measured geometric data and adjustedthrough the comparison between the experimental andsimulation results The heat transfer coefficient was select-

ed from the well-known heat transfer coefficients andadjusted through the comparison between the experimentaland simulation results

Equation (9) can be transformed into the following statespace form

(10)where t stands for time, and a(t) and u(t) representfunctions of time defined by

(11) (12)This representation is used for the stability analysis of thedynamic equation Although this equation is a first order

Q·heat + W · + (hin m·in – h out m·out )= U·cv

474 S J LEE

linear system, its stability cannot be determined by only the

sign of the time constant, a(t), because the dynamic

equa-tion (10) is not a time invariant system The stability for the

dynamic system will be analyzed in the next section

The pressure inside the air spring, which is determined

by equation (10), is transformed into the force acting on the

vehicle body

(13)where F as is the force, A eff is the effective area of the air

spring, through which pressure is transformed into the

force, and P atm is the pressure of the environment

3 ANALYSIS AND VALIDATION OF AIR

SPRING MODEL

The air spring model of equation (9) was developed to

describe the important characteristics such as the hysteresis

and nonlinear spring stiffness The experimental results for

the air spring validate the mathematical model, and the

factors that affect the stiffness and the hysteresis of the air

spring are analyzed in this section

3.1 Experiments of the Air Spring

Figure 4 briefly shows the experimental setup where a

sinusoidal displacement is vertically applied to the air

spring by a linear actuator, which is positioned in the lower

part of the air spring instead of the road excitation The

force, which is applied to the vehicle body by the air

spring, is measured by the sensor which is positioned in the

upper part of the air spring The pressure of the air spring is

measured by the sensor, which is positioned in the air

passage between the air spring and the control valve

Experiments in which the air spring is excited at various

frequencies are performed Through the experiments, the

signals such as vertical displacement which represents the

vertical movement of the wheel with respect to the vehicle

body, the pressure inside the air spring and the force aremeasured to validate the established model

3.2 Analysis and Validation for HysteresisThe experimental data on the forces generated by the airspring are plotted versus the vertical displacement in Figure

5, which clearly shows the hysteresis Because the force is

F as =A eff ( P cv – P atm )

Figure 4 Schematic representation of the experimental

setup

Table 2 Experimental conditions

Initial pressure 7.7 bar (absolute pressure)Environment

temperature Room temperatureDisplacement

input (sinusoid) 10 mm (amplitude)0.05 Hz, 0.5 Hz, 5 Hz (frequency)

Figure 5 Experimental results of force versus verticaldisplacement for sinusoidal motion excitation at 0.05 Hz,0.5 Hz and 5 Hz (the 0.05 Hz and 5 Hz data are represented

200 N lower and higher than the actual values for ease indistinction between the different data plots, respectively)

Figure 6 Simulation results for pressure response due toonly variation of the volume for sinusoidal motionexcitation at 0.05 Hz, 0.5 Hz and 5 Hz (the 0.05 Hz and 5

Hz data are represented 200 mbar lower and higher thanthe actual values, respectively)

DEVELOPMENT AND ANALYSIS OF AN AIR SPRING MODEL 475

the effective area times the pressure, the cause of the

hysteresis can be found in the pressure dynamic equation

(9) The inspection of equation (9) reveals that the hysteresis

can be caused by three terms

The first term, , occurs due to the volume

change in an air spring according to the vertical

displace-ment The hysteresis on the pressure response can occur

when the volume is a function of other variables as well as

the vertical displacement However, for the fixed air mass

and the given temperature, the volume of the air spring is

assumed to be a function of only the vertical displacement

on the basis of test results on some air springs Hence, the

pressure responses due to only the variation of the volume,

which is a function of only the vertical displacement, do

not show the hysteresis as in Figure 6

The second term, , which occurs

due to the heat transfer between the air spring and the

environment, is a function of the pressure as well as the

vertical displacement The hysteresis due to this second term

can be analyzed through the pressure dynamic equation,

which consists of the first term and the second term as follows:

(14)

This equation has the form of a first-order low-pass filter in

which a(t) is the cut-off frequency, u(t) is the input signal,

and P cv is the filtered output signal The low-pass filter

causes the phase shift of the output signal with respect to

the input signal, which in turn generates the hysteresis of

the output signal with respect to the input signal Because

a(t) is time-varying, equation (14) represents the

charac-teristics that are significantly different from the low-pass

filter with a time-invariant cut-off frequency However, the

first order dynamics of equation (14) generate the phase

shift between the input and the output, which causes the

hysteresis in the pressure output More specifically, the phase

shift of the pressure output with respect to the displacement

input decreases as the frequency of the input increases from

0.05 Hz to 5 Hz, which decreases the magnitude of the

hysteresis in the pressure, as shown in Figure 7 (Pressures

of all the figures in this paper represent the relative

pressure.) In addition, the variation of the magnitude of the

hysteresis can also be shown in the following equation,

which is derived by considering only the first term and the

second term of equation (9) when the sinusoidal vertical

displacement, z=z 0 sin(2π f t), is applied to the air spring

where z 0 and f represent the magnitude and the frequency ofthe vertical displacement sinusoid, respectively This equa-tion indicates that the increase of the frequency reduces theeffect of the hysteresis due to the second term

The simulated pressure responses shown in Figure 7 arecompared with the experimental results shown in Figure 8,which are obtained without the air mass flowing into or out

of the air spring The similarity between the simulation andexperimental results validates the air spring model develop-

ed and its analysis

The third term, , in equation (9)occurs when air is supplied to or exhausted from the airspring, which means that the vehicle body is lifted orlowered for some specific purpose, as shown in Figure 1

200 mbar lower and higher than the actual values, tively)

respec-Figure 8 Experimental results of pressure versus verticaldisplacement for sinusoidal motion excitation at 0.05 Hz,0.5 Hz and 5 Hz (the 0.05 Hz and 5 Hz data are represented

200 mbar lower and higher than the actual values, tively)

respec-476 S J LEE

This term is also a function of the pressure as well as the

vertical displacement and is expressed including the first

term by the first order filter form as follows:

(16)Unlike the second term, the third term does not show the

typical form of a hysteresis but shows the pressure

re-sponses presented in Figure 9 This figure represents the

pressure responses due to the first term and the third term

when the upper part of the air spring is lowered by 10 mm,

which means that the vehicle height is lowered when the

lower part of the air spring is excited at 0.5 Hz In Figure 9,

the thin lines represent the pressure responses before and

after the variation of the air mass inside the air spring, and

the thick line stands for the pressure response while the air

mass varies This figure indicates that the variation of the

air mass inside the air spring has an effect on the pressureresponse, but no hysteresis occurs due to the variation ofthe air mass

Because the force is defined by the effective area timesthe pressure such as expressed in equation (13), the effec-tive area in addition to the pressure has an effect on thehysteresis of the force response The effective area varieswith the vertical displacement because it varies with thevertical shape of the contour of the piston in the lower part

of the air spring, which changes the ride comfort of thevehicle In addition, the effective area varies with the pre-ssure at the same displacement, which yields the hysteresis

of the effective area In Figures 10 and 11, the effect of thishysteresis is represented Simulation results in Figure 10 donot include the hysteresis of the effective area, while those

in Figure 11 include it These figures show that the hysteresis

of the effective area enlarges the hysteresis of the forceresponse Finally, the comparison between the simulatedand the experimental results in Figure 11 confirms thevalidity of the air spring model

3.3 Analysis and Validation of StiffnessThe stiffness of the air spring can be obtained by differenti-ating equation (13) with respect to the vertical displace-ment, as follows:

(17)where kas represents the stiffness of the air spring, and z thevertical displacement This equation indicates that the stiff-ness of the air spring varies with the derivatives of thepressure and the effective area with respect to the verticaldisplacement

In equation (9), the first term, which represents the effect

of the volume variation, is one of the factors that change

-Figure 9 Simulation results for pressure responses due to

the variations of the volume and the air mass inside the air

spring

Figure 10 Force responses for sinusoidal motion excitation

at 0.05 Hz, 0.5 Hz and 5 Hz (the 0.05 Hz and 5 Hz data are

represented 200 N lower and higher than the actual values,

respectively) Simulation results do not include the hysteresis

of the effective area while experimental results include it

Figure 11 Force response for sinusoidal motion excitation

at 0.05 Hz, 0.5 Hz and 5 Hz (the 0.05 Hz and 5 Hz data arerepresented 200 N lower and higher than the actual values,respectively) Simulation results include all effects exceptthe air mass variation

DEVELOPMENT AND ANALYSIS OF AN AIR SPRING MODEL 477

the stiffness of the air spring expressed in equation (17)

The variation of the pressure due to the first term is

rewritten in the following equation

(18)

where V cv0 stands for the fixed volume like the additional

volume attached to some air spring in order to improve the

comfort, A cs represents the cross-sectional area of the air

spring, and zmax and z curr are the maximum displacement and

the current displacement of the bottom of the air spring,

respectively It is well known that an increase of the volume

of the air spring reduces the stiffness of the air spring

However, a close inspection of equation (18) reveals that

the absolute value of the derivative of the pressure with

respect to the vertical displacement, which represents a part

of the stiffness expressed in equation (17), decreases as the

entire volume of the air spring increases but increases as

the derivative of the volume with respect to the vertical

displacement increases Hence, the derivative of the pressure

increases, which increases the stiffness, if the increment of

the derivative of the volume is larger than the increment of

the volume even though the entire volume increases The

term, , in the denominator of equation (19)

represents the entire volume, and the cross-sectional area,

A cs, in the numerator stands for the derivative of the entire

volume with respect to the vertical displacement When the

cross-sectional area increases, the increment of the

deriva-tive of the volume is larger than the increment of the entire

volume For example, when the cross-sectional area increases

by 50 percent, the entire volume cannot increase by up to

50 percent because the fixed volume does not increase

Hence, the increase of the volume due to the

cross-sectional area increases the stiffness of the air spring, while

the increase of the volume without the variation of the

cross-sectional area decreases the stiffness

The heat transfer, which is included in the second term

of equation (9), also has an effect on the variation of the

stiffness Equation (15) clearly shows the variation of the

stiffness due to the heat transfer In equation (15), the

derivative of the pressure with respect to the displacement

due to the heat transfer is added to that due to the variation

of the volume, which changes the stiffness due to the

vari-ation of the volume In addition, because the term due to

the heat transfer is divided by the frequency of the

dis-placement in equation (15), the stiffness due to the heat

transfer is reduced as the frequency increases The stiffness

variation with frequency is shown in Figure 12, which

re-presents the pressure responses due to only the heat

trans-fer The entire pressure response in equation (15) is

deter-mined by the sum of Figure 6 and Figure 12 Hence, the

heat transfer at the low frequency has a significant effect on

the entire stiffness, unlike that at the high frequency More

specifically, the heat transfer at the low frequency cantly reduces the stiffness due to the variation of thevolume, while at the high frequency it slightly reduces thestiffness The negative pressure in Figure 12 occurs for thefollowing reason When the air spring is compressed, thepressure increases due to the compressed volume Theresulting increment of the pressure increases the temper-ature of the air spring in equation (6) and decreases the rate

signifi-of change signifi-of pressure due to the second term in equation(15) Consequently, when the temperature of the air springbecomes larger than that of the environment, the pressuredue to heat transfer decreases, which can yield a negativepressure However, the entire pressure increases becausethe increase of the pressure due to the volume variation islarger than the decrease of the pressure due to the heattransfer even when the temperature of the air spring islarger than the environment

The pressure response due to the variation of the airmass, which is included in the third term of equation (9), isalso added to that due to the other two terms, which in turnchanges the stiffness which is determined by the otherterms The equation (9) shows that the mass flow rateflowing into the air spring, , increases the stiffness, whilethe mass flow rate flowing out of the air spring, ,decreases it Figure 9 represents the pressure response due

to variations of the volume and the air mass when the airmass is flowing out of the air spring

In addition to the pressure variation, the variation of theeffective area has an effect on the stiffness As mentionedearlier, the contour of the piston of the air spring is manu-factured in order to obtain the optimum ride comfort,which yields the variation of the effective area Hence, thelarge variation of the effective area can have a significanteffect on the variation of the stiffness This study on the airspring which was employed in this experiment shows thatmost of values of the stiffness due to the second term inequation (17), which represents the effect of the effectivearea variation, vary within 40% of the entire stiffness

478 S J LEE

The slopes of the force curves in Figure 11 represent the

entire stiffness, which includes the rate of change of the

effective area as well as the pressure Figure 11 indicates

that the stiffness varies with the displacement and

fre-quency In addition, it is observed that the stiffness of the

simulation curves is similar to that of experimental curves

in the full range of the displacement

3.4 Stability Analysis of the Air Spring System

The stability of the air spring is very important for the

vehicle stability However, the stability of the pressure

dynamics of the air spring is not simply determined like a

time-invariant system because a(t) in the air spring model

equation (10) is time-varying

For the stability analysis of the dynamic equation (10),

linear time-invariant dynamic systems are introduced as

follows:

(20)where Pmax and Pmin are the pressure variables, and amax and

a min are the constant maximum and minimum values of a(t)

Because a(t) is bounded by a max and a min, P cv is also

bounded by Pmax and Pmin as follows:

(21)Because equation (20) is a linear time-invariant system,

Pmax and Pmin are bounded if amax and amin are negative values

and the input, u(t), is bounded (Khalil, 1996). u(t) in the

equation (12) is bounded when the air mass flow rate

flowing into the air spring, , is bounded Consequently,

the pressure of the air spring, P cv, is bounded, when is

bounded and the following condition is satisfied

(22)This stability criterion is a sufficient condition because it

has not been proven that the air spring model is unstable ifthe derived stability condition is not satisfied

Equation (22) indicates that the increase of the fixedvolume of the air spring, the heat transfer coefficient andarea, and the air mass flow rate flowing out of the air springare helpful in satisfying the stability condition (22), whilethe increase of the negative rate of change of the volumeand the air mass prevent the stability condition (22) frombeing satisfied Figure 13 shows that a(t) has the negativevalues for sinusoidal motion excitation at 0.5 Hz For othersinusoidal motion excitation of 0.05 Hz and 5 Hz, a(t) alsohas the negative value

4 CONCLUSION This research developed a general model of an air springbased on thermodynamics This model was derived fromthe energy conservation law The thermodynamic para-meters inside the air spring are assumed to be uniform,which means that the parameters do not vary with theposition inside the air spring The air inside an air spring isalso assumed to have an ideal gas property, and the kineticand potential energies of the air are neglected However,the resulting model can represent all processes rangingfrom isothermal to adiabatic conditions because the assump-tion that the process is adiabatic or isothermal has not beenemployed In addition, the model can be used to simulatethe system with the pneumatic circuit able to adjust thevehicle height because it includes the air mass flowing intoand out of the air spring

The analysis of the established model revealed that thevolume variation, the heat transfer, the variation of the airmass and the effective area have an effect on the stiffnessand hysteresis The heat transfer yields the larger hysteresisunder the input with the low frequency than that with thehigh frequency, and the effective area enlarges the hy-steresis In addition, the heat transfer significantly reducesthe stiffness at the low frequency, and the air mass flow rateflowing into the air spring increases the stiffness, while theair mass flow rate flowing out of the air spring decreases it

In particular, the increase of the volume due to the sectional area increases the stiffness, while the increase ofthe volume due to the other reason decreases it Addition-ally, most of the stiffness due to the effective area variedwithin about 40% of the entire stiffness for the air springused in this study

cross-The stability condition for the air spring was also derivedfrom the study regarding the established time-varyingmodel The inspection of the stability condition revealedthat the increases of the fixed volume, the heat transfercoefficient and area as well as the air mass flow rate flow-ing out of the air spring have a positive effect on thestability, while the increases of the negative rate of change

of the volume and the air mass have a negative effect on it.However, the analysis for the parameters has some limitationbecause the derived stability criterion is a sufficient condi-

P·max = a max P max + u t ( )

P·min = a min P min + u t ( )

Figure 13 Values of the variable, a(t), of equation (22) for

sinusoidal motion excitation at 0.5 Hz when there is no air

mass flowing into or out of the air spring

DEVELOPMENT AND ANALYSIS OF AN AIR SPRING MODEL 479

tion

Simulation results of the model were presented, and these

were in substantial agreement with experimental

measure-ments of force and pressure with respect to displacement

excitations of 0.05 Hz, 0.5 Hz, and 5 Hz, which validates

the modeling approach presented here for the air spring

The resulting validated model will be especially useful for

the study of air spring systems including the pneumatic

circuit and its control algorithm

REFERENCES

Cha, C J., Kim, P G and Lee, S J (2006) Development

of an analytical air spring model with hysteresis

charac-teristics Fall Conf Proc., Korean Society of

Auto-motive Engineers, 1964−1969

Chang, F and Lu, Z.-H (2008) Dynamic model of an air

spring and integration into a vehicle dynamics model

Proc Institution of Mechanical Engineers, Part D, J.

Automobile Engineering 222, 10, 1813−1826

Fernandez, R and Woods, R L (1999) Thermal

conside-rations in fluid power systems modeling Proc Fluid

Power Systems and Technology, 47−54

Folchert, U (2006) Air Supply System for a Motor Vehicle

Continental Aktiengesellschaft US Patent No 7097166

Hyundai Motor Company (2009) Instruction Manual for

GENESIS 5−35

Jang, I., Kim, H., Lee, H and Han, S (2007) Height

con-trol and failsafe algorithm for closed loop air suspensioncontrol system Proc Int Conf Control, Automation and Systems, 373−378

Khalil, H K (1996) Nonlinear Systems 2nd Edn PrenticeHall New Jersey

Kia Motor Company (2009) Instruction Manual for MOHAVE, 5, 37−38

Kim, W., Lee, J W., Kim, H K., Doo, M S., Kim, H S.and Doh, W J (2001) Handling analysis of active heightcontrol system for SUV using ADASMS Fall Conf Proc., Korean Society of Automotive Engineers, 908−

914

Kim, W Y and Kim, D K (2005) Improvement of rideand handling characteristics using multi-objective optimi-zation techniques Int J Automotive Technology 6, 2,

141−148

Nieto, A J., Morales, A L., Gonzalez, A., Chicharro, J M.and Pintado, P (2008) An analytical model of pneu-matic suspensions based on an experimental characteri-zation J Sound and Vibration 313, 1/2, 290−307.Quaglia, G and Sorli, M (2001) Air suspension dimen-sionless analysis and design procedure Vehicle System Dynamics 35, 6, 443−475

Seong, J H., Lee, K W., Park, G B and Yang, H J.(2008) Study on air spring modeling method for railwayvehicle dynamics Proc Spring Conf., Korean Society for Railway, 2216−2221

International Journal of Automotive Technology , Vol 11, No 4, pp 481 − 488 (2010)

481

STOCHASTIC ANALYSIS OF THE VARIATION IN INJURY NUMBERS

OF AUTOMOBILE FRONTAL CRASH TESTS

T.-W KIM and H.-Y JEONG *

Department of Mechanical Engineering, Sogang University, Seoul 121-742, Korea

(Received 17 February 2009; Revised 16 September 2009)

ABSTRACT− Although automobile crash test data have a comparatively large variation because of the complexity of the tests, only a limited number of crash tests are usually conducted due to monetary and time limitations Thus, it is necessary

to control input variables that cause the variation in test data to obtain consistent crash test results and to correctly assess the safety performance of an automobile under development In this study, a MADYMO model was validated deterministically

to yield the head, chest, pelvis deceleration pulses of anthropomorphic test devices and the belt load pulses similar to those from actual tests, and it was also validated stochastically to yield means and standard deviations of the head and chest injury numbers, i.e., HIC 15 and 3 msec clip similar to those from actual tests A stochastic analysis was conducted using the validated MADYMO model to calculate the sensitivity of the standard deviations of the injury numbers to the standard deviations of influential input variables to determine the most influential input variable that makes the largest contribution to the variation

in the injury numbers Moreover, the Taguchi approach was used to determine the optimal values of the influential input variables to improve safety performance.

KEY WORDS : Stochastic analysis, Frontal crash test, HIC 15 , 3 msec clip, Taguchi approach

1 INTRODUCTION

Air bag deployment has saved about 5,300 people but

killed about 160 people in the United States from 1986 to

March, 2003 (NHTSA, 2000) To reduce the risk of air bag

deployment, advanced air bag technologies have been

developed and are now widely used The development of

sophisticated safety systems that satisfy relevant safety

standard requirements and result in better star ratings in

relevant crash tests requires more crash tests than before

because these safety systems are supposed to modulate the

air bag power according to crash severity, occupant weight

and position, and belt usage Unfortunately, crash tests

result in a comparatively large variation in test data because

of their complexity In other words, crash tests involve

many input variables with comparatively large standard

deviations such as crash speed, crash angle, the

anthropo-morphic test device (so called dummy) setup, inflator

out-put, gas leakage through the air bag module and cushion,

the critical load of the load limiter, and the collapsing load

of the steering column However, only a limited number of

crash tests are usually conducted during the development

of an automobile safety system due to monetary and time

limitations Thus, to achieve consistent safety performance,

it is necessary to find influential input variables that cause

significant variations in the test data and to control those

variables within a desired limit

Deterministic analyses have been conducted with fixedinput values resulting in fixed output values in manydisciplines In frontal crash tests, however, variations ininput variables cause variations in output variables Thisstudy conducted a stochastic analysis to determine theinput variable that caused most of the variation in the injurynumbers during frontal crash tests In a stochastic analysis,

a set of input values are randomly selected from normaldistributions with specified means and standard deviations,and they are put into a validated simulation model as inputs(Reuter et al., 2001; Shah et al., 2003; Riha et al., 2003).Then, a comparatively large number of simulations usingthe model generate a set of outputs with variations Thestandard deviation of an input variable can be intentionallydecreased to determine the effect on the standard deviation

of an output variable as the ratio of the standard deviation

of an output variable to that of an input variable If the ratio

is high, the standard deviation of the output variable can bereduced mainly by reducing the standard deviation of theinput variable, i.e., the standard deviation of the inputvariable needs to be controlled within a narrower range toreduce the standard deviation of the output variable

In this study, test data such as the crash pulse, the head,chest, and pelvis deceleration pulses, and the seat belt loadswere first analyzed Then, the restraint energies of the seatbelt, the air bag and the steering column were calculated tounderstand the crash phenomenon and injury mechanisms.Second, a MADYMO (MAthematical DYnamic MOdel-ing; an engineering software tool developed by TNO that

*Corresponding author. e-mail: jeonghy@sogang.ac.kr

482 T.-W KIM and H.-Y JEONG

helps users analyze, design and optimize automobile safety

systems) model for frontal crash tests was deterministically

validated against test data Third, the influential input

variables that caused variations in the injury numbers were

found, and their standard deviations were determined

Fourth, the MADYMO model was stochastically validated

against the test data Fifth, a stochastic analysis was

con-ducted again for the influential input variables with

inten-tionally reduced standard deviations, and the subsequent

standard deviations of the injury numbers were determined

By comparing the ratios of the standard deviations of the

injury numbers to those of the influential input variables,

the most influential input variable on the variation in the

injury numbers could be determined These results suggest

that the variation in air bag permeability and in the critical

load of the load limiter in the seat belt should be controlled

to reduce the variation in HIC 15 and 3 msec clip,

respec-tively

Moreover, the optimal values of the input variables were

determined using the Taguchi approach The

signal-to-noise (SN) ratios for HIC 15, 3 msec clip and P comb, a

com-bined expression incorporating both HIC 15 and 3 msec clip,

were defined as the objective function to maximize Then,

27 deterministic simulations were conducted to determine

optimal values of the input variables In addition, another

stochastic analysis was conducted to evaluate the optimal

values, showing that the optimal values could result in a

9.5% reduction in the mean and a 1.0% reduction in the

standard deviation of P comb

2 TEST DATA ANALYSIS

2.1 Crash Pulse Analysis

During an automobile crash, there are usually two phases

of collision; the primary collision and the secondary

collision The primary collision is the collision between the

automobile and the obstacle, and the secondary collision is

the collision between the occupant and the automobile

interior In cases of ejection, however, there is also a deadly

tertiary collision between the occupant and the ground or

the obstacle In an accident with no ejection, the occupant

is injured due to the secondary collision To assess the

safety performance of an automobile during a frontal crash,

the NCAP (New Car Assessment Program) test is mostly

conducted with belted dummies at a crash speed of 35 mph

against a rigid wall, and P comb is determined from Equation

(1) (Morgan et al., 1998) Based on the value of P comb, a star

rating is assigned to the automobile

(1)Thus, to understand the injury mechanisms and to find

influential input variables that affect the injury numbers

HIC 15 and 3 msec clip, it is important to analyze the relative

motion of the occupant (or the dummy) with respect to theautomobile

Since the dummy and the automobile mainly move alongthe longitudinal direction during a frontal crash test, onlythe longitudinal components of deceleration pulses wereanalyzed The relative deceleration of the head, chest andpelvis were defined as follows

(2)Here, A h, A c, A p and A v are the deceleration of the head,chest, pelvis and vehicle, respectively The vehicle decele-ration was integrated once or twice to obtain the speedchange from the crash speed or the crush amount, and therelative deceleration was integrated once or twice to obtainthe relative speed or relative displacement of the head,chest and pelvis with respect to the automobile interior.Analyzing the speed change, the relative speeds and therelative displacements together allowed for an understand-ing of the crash phenomenon and the injury mechanisms,and the influential input variables that significantly affectedthe injury numbers could be determined As an example,Figure 1(a) shows the speed change of the automobile, therelative speed of the chest, the deceleration of the chest andthe shoulder belt load over time as measured from two tests

of the same automobile The speed change in test A washigher than that of test B, resulting in a higher 3 msec clipeven though the critical load of the load limiter was almost

P comb =P head + P chest – ( P head × P chest )

STOCHASTIC ANALYSIS OF THE VARIATION IN INJURY NUMBERS OF AUTOMOBILE FRONTAL CRASH TESTS 483

the same Figure 1(b) shows the same test data with respect

to the relative displacement of the chest except that the

speed change of the automobile is shown with respect to

the crush amount Figure 1(b) clearly shows that the

maximum relative displacement of the chest was longer in

test A due to a greater speed change even though the

critical load of the load limiter was almost the same In

other words, the chest moved forward by about 220 mm in

test A, but it moved forward by about 200 mm in test B

Figure 2 shows the data from tests A and C Figure 2(a)

shows that the chest deceleration of test C was lower,

resulting in a lower 3 msec clip due to a lower critical load

of the load limiter, even though the speed change was

almost the same as that of test A Figure 2(b) also shows

that the deceleration of the chest was lower in test C due to

a lower critical load of the load limiter, resulting in a lower

3 msec clip and a longer maximum relative displacement of

the chest

2.2 Restraint Energy Analysis

The restraint energies of the seat belt, the air bag and the

steering column were estimated to evaluate their

contribu-tion to the overall restraint performance During a crash,

restraint components such as the shoulder belt, the lap belt,

the air bag, the steering column and the knee bolster apply

a restraint force against the dummy (or the occupant) The

initial kinetic energy of the dummy is consumed by two

energies; the ride-down energy that the dummy consumes

while riding down with the automobile and the restraintenergy that the dummy consumes by its relative motionwith respect to the restraint component The ride-downenergy and the restraint energy can be calculated fromEquation (3) and (4), respectively (Huang, 2002)

(3) (4)Here, m and are the mass and deceleration of adummy part, x v is the crush amount, F rc is the force of arestraint component, and dx rc / v is the relative displacement

of the restraint component with respect to the automobile

The dummy was divided into three parts, i.e., the head,chest and pelvis The relative displacement of the shoulderbelt was assumed to be the same as that of the chest, andthe relative displacements of the lap belt and knee bolsterwere assumed to be the same as that of the pelvis Therestraint force of the knee bolster was also assumed to bethe same as the sum of the right femur load and the leftfemur load Note that the change in the kinetic energy ofthe dummy from the moment when a crash starts to themoment that the dummy’s chest has the greatest forwardmotion is the sum of the ride-down energy and the restraintenergy because the dummy usually bounces backward afterthe chest moves the most forward Thus, subtracting theride-down energy of the dummy as well as the restraintenergy of the belt and knee bolster from the kinetic energychange of the dummy, the restraint energy of both the airbag and the steering column could be determined as inEquation (5) Of course, there must have been some loss offrictional energy between the dummy and the seat cushion,but this frictional energy was negligible (less than 100 Jeven with a coefficient of friction of 0.3)

Here, m h, m c, and m p are the mass of the head, chest andpelvis, respectively, v h and v p are the head speed and thepelvis speed at the moment when the chest moves mostforward, respectively, and v cs is the crash speed

Figure 3 shows the initial kinetic energy of the dummy

as well as the restraint energies of the belt, the air bag, thesteering column and the knee bolster calculated from fivesets of test data Note that the restraint energy of both theair bag and the steering column was slightly more than that

of the seat belt in three out of the five tests, and the average

of the restraint energy of both the air bag and the steeringcolumn was 21.8% of the initial kinetic energy of thedummy while that of the seat belt was 19.5% and that ofthe knee bolster was only 3.0% Thus, the air bag andsteering column restrain the driver as much as or slightly

Figure 2 Differences due to different critical loads of the

load limiter

484 T.-W KIM and H.-Y JEONG

more than the seat belt in a frontal crash

3 STOCHASTIC ANALYSIS

3.1 Deterministic Validation

Like other computational analyses, reliable stochastic

ana-lysis requires a validated simulation model In particular, a

stochastic analysis requires not only the mean but also the

standard deviation of the simulation results to be accurate

Thus, a MADYMO model was validated through two

steps, deterministic validation and stochastic validation In

deterministic validation, the model parameters are tuned toresult in output values compatible with test data using fixedinput values However, in stochastic validation, the modelparameters are tuned to result in compatible means andstandard deviations of output values with those from testsusing input values selected from their correspondingnormal distributions

Because the safety performance of an automobile in theNCAP test is the major concern in the assessment of safetyperformance in frontal crashes, a MADYMO model wasvalidated against several sets of test data obtained fromNCAP tests in terms of the head, chest and pelvis decele-ration pulses, the shoulder and lap belt loads as well as theinjury numbers (TNO Automotive, 2001) The simulationresults and test data are shown in in Figures 4 through 7 Inthese deterministic validation simulations, the input valueswere fixed except for the crash pulse because the crashpulse varied mainly due to the crash speed which was notoften constant Note that even though the simulation resultswere in good agreement with the test data, there were stillnoticeable differences not only between the simulationresults and the test results but also between the results oftests A and B This indicates that frontal crash tests musthave significant variations in input values that result invariable output values

3.2 Stochastic ValidationThe crash pulse analysis mentioned in 2.1 and the deter-Figure 3 Kinetic energy and restraint energies

Figure 4 Longitudinal deceleration of the head Figure 5 Longitudinal deceleration of the chest

STOCHASTIC ANALYSIS OF THE VARIATION IN INJURY NUMBERS OF AUTOMOBILE FRONTAL CRASH TESTS 485

ministic validation mentioned in the previous section mined the influential input variables that significantlyaffected the injury numbers The influential input variableswere determined to be the crash pulse magnitude andduration, the critical load of the load limiter, the seat beltstiffness, the mass flow rate of the inflator, the air bagpermeability and the collapsing load of the steering column.The parameters of the deterministically validated MADYMOmodel had to be tuned slightly until the mean and standarddeviation of HIC 15 and 3 msec clip from the simulationsbecame compatible with those from the test data However,stochastic validation simulations require prior knowledge

deter-of the mean and standard deviation deter-of the influential inputvariables The crash deceleration pulse was filtered by aBessel filter with a cut-off frequency of 100 Hz, and therebounding time when the crash deceleration pulse crossedzero was determined Then, the crash pulse was integrated

to obtain the speed change, and the mean and standarddeviation of the speed change at the average reboundingtime were determined In addition, the mean and standarddeviation of the critical load of the load limiter and themass flow rate of the inflator were determined from testdata However, the mean and standard deviation of thesteering column collapsing load, the belt stiffness and theair bag permeability were tuned to make the means andstandard deviations of HIC 15 and 3 msec clip from thesimulations compatible with those from the test data because

no test data were available for those input variables Table

1 presents the ratios of the standard deviations to the means

of the influential input variables

Figure 6 Longitudinal deceleration of the pelvis

Figure 7 Belt loads from test A and simulation

Table 1 Ratio of standard deviation to the mean value ofinput variables

Input variables Standard dev./MeanSpeed at the average rebounding time 0.030Duration of the crash pulse 0.037Critical load of the load limiter 0.138Mass flow rate of the inflator 0.024Collapsing load of the steering column 0.070

Table 2 Ratio of the mean and standard deviation ofstochastic validation results to those of test data

(Stochastic Validation)/(Test)

[%]

HIC 15 standard dev 95.44

3 msec clip standard dev 98.86

486 T.-W KIM and H.-Y JEONG

Simulations were conducted with input values selected

from normal distributions specified by the mean and

standard deviation, and the injury numbers of HIC 15 and 3

msec clip were obtained The injury numbers are shown

with the test data in Figure 8, and the ratios of the means

and standard deviations of the injury numbers determined

from the simulations to those determined from the test data

are shown in Table 2 Note that the mean and standard

deviation of the injury numbers determined from the

simu-lations were slightly smaller but in good agreement with

those determined from the test data

3.3 Stochastic Analysis

To find the most influential input variable that accounts for

the greatest portion of variation in the injury numbers, the

standard deviation of each influential input variable was

cut in half and a stochastic analysis was conducted again

As an example, the magnitude of the crash pulse was

changed by multiplying the crash pulse by a constant in

such a way that the speed at the average rebounding time

had a standard deviation half of that shown in Table 1 In

addition, the duration of the crash pulse was changed by

multiplying the crash time by a constant in such a way that

the rebounding time had a standard deviation half of that

shown in Table 1 Reducing the standard deviation of an

influential input variable resulted in a reduction in the

variation of the injury numbers The standard deviations of

the influential input variables and those of the injury

numbers were used to determine the ratio of the standard

deviation of each injury number to that of each influential

input variable This ratio indicates the sensitivity of the

standard deviation of the injury number to that of an

influential input variable A high sensitivity indicates that

the variation in the influential input variable should be

reduced to reduce the variation in the injury number

signifi-cantly

Tables 3 and 4 show the sensitivity of HIC 15 and 3 msec

clip, respectively, of each influential input variable Notethat the variation in the permeability of the air bag cushionhad the greatest effect on the variability of HIC 15, and thevariation in the critical load of the load limiter had thegreatest effect on 3 msec clip Note also that the durationand magnitude of the crash pulse had the second greatesteffect on the variation of both injury numbers In otherwords, the gas leakage through vents, modules and cushionsshould be controlled to reduce the variation in HIC 15, andthe critical load of the load limiter should be controlled toreduce the variation in 3 msec clip The variation in the beltstiffness, the mass flow rate of the inflator and the collap-sing load of the steering column had a comparatively smalleffect on the variation in the injury numbers, especially for

3 msec clip.3.4 Optimal Input ValuesThe previous section analyzed the effect of the variation ofeach influential input variable on the variation of HIC 15 and

3 msec clip However, it was also important to determinethe optimal values of the input variables that would result

in the lowest value of P comb and consequently the best starrating Thus, the Taguchi approach was used to determineoptimal input values that were insensitive to uncontrollablevariables (Taguchi, 1987)

Since it is not easy to control a crash pulse in designingthe restraint components, a crash pulse should be consider-

ed as a noise factor However, all other variables can beconsidered as control factors That is, the magnitude andduration of the crash signal were considered as noisefactors, and the critical load of the load limiter, the belt

Figure 8 Distribution of HIC 15 and 3 msec clip obtained

from tests and stochastic validation simulations

Table 3 Sensitivity of HIC 15

Input variable Sensitivity [%]Magnitude of the crash pulse 11.18Duration of the crash pulse 18.64Critical load of the load limiter 8.88

Mass flow rate of the inflator 8.13

Collapsing load of the steering column 8.25

Table 4 Sensitivity of 3 msec clip.

Input variable Sensitivity [%]Magnitude of the crash pulse 10.06Duration of the crash pulse 13.43Critical load of the load limiter 19.80

Mass flow rate of the inflator 0.47

Collapsing load of the steering column 0.58

STOCHASTIC ANALYSIS OF THE VARIATION IN INJURY NUMBERS OF AUTOMOBILE FRONTAL CRASH TESTS 487

stiffness, the inflator mass flow rate, the air bag

perme-ability and the collapsing load of the steering column were

considered as control factors In addition, the values of the

input variables were set at three different levels to take the

nonlinear coupling effects of all the input variables into

account Because there were five control factors and two

noise factors in three levels, an L 27(313) orthogonal array

was used in the inner array and an L 9(32) orthogonal array

was used in the outer array (Taguchi, 1987) Tables 5 and 6

show the levels of control and noise factors, respectively

Since lower HIC 15, 3 msec clip and P comb were desirable, the

SN ratio in Equation (6) was defined as the objective

function to maximize

(6)Here, y i is either HIC 15, 3 msec clip or P comb obtained at

the ith simulation, and n is the total number of simulations

The variable levels that resulted in the highest SN ratio in

27 deterministic simulations were determined and are

shown in Table 7 A1B1C3D3F3 resulted in the highest SN

ratio for HIC 15 and P comb, but A1B2C2D3F3 resulted in the

highest SN ratio for 3 msec clip by a slim margin Thus,

A1B1C3D3F3 was the optimal combination of variable levels

in this study because the objective was to have the lowest

value of P comb to obtain the best star rating That is, the

optimal values turned out to be a 0.5 kgf reduction in the

critical load of the load limiter compared with the normal

value, a 10% reduction in the inflator mass flow rate, a

20% increase in the steering column collapsing load, a 0.5

GPa increase in the belt stiffness and a 20% increase in the

air bag permeability

Another stochastic analysis was conducted to evaluate

the effects of the optimal input values on the mean and

standard deviation of P comb HIC 15, 3 msec clip and the mean

and standard deviation of P comb were obtained from the

stochastic analysis with the optimal input values as shown

in Figure 9 and Table 8, respectively The mean value of

P comb was reduced by 9.5% and the standard deviation of

P comb was reduced by only 1.0% compared with thestochastic validation analysis with normal input values.This result was expected because maximization of the SNratio given in Equation (6) mainly minimized the magni-tude or the mean value of the injury numbers or P comb

4 CONCLUSION

A MADYMO model was validated deterministically andstochastically against test data That is, the model para-meters were tuned to yield the head, chest and pelvisdeceleration pulses and the belt load pulses similar to thosefrom test data as well as to yield the means and standarddeviations of HIC 15 and 3 msec clip similar to those fromthe test data To understand the frontal crash phenomenon

SN= 10 – log 1n -

i = 1

n

∑y i2

Figure 9 Distribution of HIC 15 and 3 msec clip obtained

from tests and stochastic simulations with normal input

values and optimal input values

Table 5 Level of control factors

Control Factor Level 1 Level 2 Level 3

A Critical load of the load limiter 3.5 kgf 4 kgf 4.5 kgf

B Mass flow rate of the inflator −10% mean +10%

C Collapsing load ofthe steering column −20% mean +20%

D Belt stiffness 3.5 GPa 4 GPa 4.5 GPa

F Air bag permeability −20% mean +20%

Table 6 Level of noise factors

Noise Factor Level 1 Level 2 Level 3

U Magnitude of the crash pulse −mean 0.5 σ mean mean

+0.5 σ

V Duration of the crash pulse −mean 0.5 σ mean mean

+0.5 σ

Table 7. SN ratio of HIC 15, 3 msec clip and P comb at optimalconditions

Optimalconditions HIC15 3 msec clip P comb

A1B2C2D3F3 −50.25 −32.52 21.21Table 8 Comparison of P comb at optimal conditions with that

488 T.-W KIM and H.-Y JEONG

and injury mechanisms and to find influential input

vari-ables that significantly affected the injury numbers, the

relative motions of the head, chest and pelvis were

analy-zed along with other crash pulses In addition, the

ride-down and restraint energies were estimated, and the restraint

energy of the air bag and steering column was found to be

slightly higher than that of the seat belt

To determine the variation in the influential input

vari-ables, the mean and standard deviation of the crash pulse,

the critical load of the load limiter and the mass flow rate of

the inflator were calculated from test data However, the

mean and standard deviation of the belt stiffness, the air

bag permeability and the collapsing load of the steering

column were tuned in such a way that the mean and standard

deviation of the injury numbers from the stochastic

valida-tion simulavalida-tions became close to those from test data By

reducing the standard deviation of each influential input

variable, the reduced standard deviations of HIC 15 and 3

msec clip were obtained from the stochastic simulations

From the standard deviations of the influential input

vari-ables and the injury numbers, the sensitivity of the standard

deviation of the injury numbers to that of each influential

input variable was easily determined The sensitivity

im-plied that the variation in the air bag permeability and the

critical load of the load limiter should be controlled to

reduce the variation in HIC 15 and 3 msec clip, respectively

However, reducing the variation in the belt stiffness, the

mass flow rate of the inflator and the collapsing load of the

steering column would not result in a noticeable reduction

of the variation in the injury numbers

Moreover, the optimal values of the input variables were

determined by applying the Taguchi approach In addition,

another stochastic analysis was conducted with the optimal

input values, demonstrating that the optimal values couldreduce the mean of P comb by 9.5% and the standard devia-tion of P comb by 1.0% Therefore, the variation of HIC 15 and

3 msec clip could be reduced by controlling the variation ofthe air bag permeability and the critical load of the loadlimiter, respectively, and the mean of the injury numberscould be reduced by designing safety components based onthe optimal values determined from the Taguchi approach.REFERENCES

Huang, M (2002) Vehicle Crash Mechanics CRC Press.Dearborn Michigan USA

Morgan, R M., Hackney, J R., Versailles, M L., Molino,

L and Lowrie, J C (1998) NHTSA crash testing andsafety information for consumers CRASHTECH Conf Munich Germany

NHTSA (2000) Final Rule on FMVSS208 Docket No.NHTSA 00-7013

Reuter, R., Hoffmann, R and Kamarajan, J (2001) cation of Stochastic Simulation in the Automotive Industry.EASi Engineering GmbH Alzenau Germany

Appli-Riha, D S., Hassan, J., Forrest, M and Ding, K (2003).Stochastic Approach for Vehicle Crash Models SAE.USA

Shah, P (2003) Stochastic Analysis of Frontal Crash Model.NAFEMS Seminar Wiesbaden Germany

Taguchi, G (1987) Introduction to Quality Engineering.American Supplier Institute, Inc Michigan USA.TNO Automotive (2001) MADYMO Database Manual.Version 6 0 1

TNO Automotive (2001) MADYMO Theory Manual.Version 6 0 1