116
Int. J Vehicle Noise ond Vibrotion, Vol. 5, Nos. 1/2,2009
A comparative ride performance and dynamic analysis of passive and semi-active suspension systems based on different vehicle models Waleed F. Faris· Faculty of Engineering, Departments of Mechanical and Mechatronics Engineering, International Islamic University Malaysia (HUM), Malaysia E-mail:
[email protected] *Corresponding author
Sanylzanlhsan Faculty of Engineering, Department of Mechanical Engineering, International Islamic University Malaysia (HUM), Malaysia E-mail:
[email protected]
Mehdi Ahmadian Department of Mechanical Engineering, Virginia Polytechnic and State University, Blacksburg, VA, USA E-mail:
[email protected] Abstract: Vehicle models used to evaluate perfonnance and dynamic behaviour are either discrete models, which includes quarter, half, and full car models, or continuous models using finite element modelling. In this work our focus will be on discrete models, which have more popularity with ground vehicle analysts owing to their shorter computational time and lower cost compared with continuous models. In this paper, ride comfort, suspension displacement and road-holding perfonnances are compared for three different models - quarter (0), half (H) and full (F) car models. In each model, semi·active system controls, namely skyhook, groundhook and hybrid controls, are used along with the conventional passive system. The analysis covers both transient and steady-state responses in the time domain and transmissibility re.'iponse in the frequency domain. Results show that while the responses give generally the same trend, the simpler model gives significantly higher responses. Keywords: hybrid; groundhook; passive suspension system; ride comfort; semi-active system; skyhook; vehicle modelling.
Copyright © 2009 Inderscience Enterprises Ltd.
A comparative ride peiformance and dynamic analysis
117
Reference to this paper should be made as follows: Faris. W.F., Dtsan. 5.1. and Ahmadian, M. (2009) 'A comparative ride perfonnance and dynamic analysis of passive and semi-active suspension systems based on diffe·rent vehicle models " Int. J. Vehicle Noise and Vibration, Vol. 5, Nos, 1/2, pp,116-140. Biographical notes: Waleed F. Faris is the Director of the Advanced Engineering and Innovation Centre (ABIC) in the International Islamic University Malaysia (HUM) and has also been an Associate Professor in the Mechanical Engineering Department and Mechatronics Depamnent of the same university, since 2004. He obtained his asc in Mechanical Engineering from Zagazig University. Egypt, in 1989. his MSc from the same university. in 1996, in Applied Mechanics and his PhD from Virginia Tech, USA. in 2003 in Nonlinear Dynamics. He has to his credit of more than 80 technical papers in reputable journals and refereed conferences. He is a Member of the Japanese Society of Automotive Engineers. He is a Technical Committee Member and a Reviewer of several international journals and conferences. He is also offering training related to the automotive industry. Sany lzan Ihsan is an Assistant Professor at the Mechanical Engineering Department, lnlernationallslamic University Malaysia (IIUM). He obtained his BSc in Mechanical Engineering at the University of Wisconsin - Madison, his MSc in Aerospace Engineering at the University of Tennessee Spaee Institute (UTSI) and his PhD in Engineering from IIUM. His research areas of interest include noise and vibration, ride quality, semi-active control systems and renewable energy. He has published several papers in international journals and conferences in the area of ride quality. semi·active systems and vibration. Mehdi Ahmadian is the Director of the Centre for Vehicle Systems and Safety
(CveSS) lIJld the Railway Technologies Laboratory (RTL). He is the Founding Director of CveSS. RTL, Virginia Institute for Performance Engineering and
Research (VIPER) lIJld the AdvlIJlccd Vehicle Dynamics Laboratory (AVDL). He has authored more than 200 teclmica1 publications. He holds seven US and international patents and has edited three teclmical volumes. CummtJy, He is an Associate Editor of AlAA Journal and the Journal ofShock Vibration and has served as an Associate Editor for ASME Journal of Vibration and Acoustics (1989--1996). He is a Fellow of the AmeriCllJl Society of Mechanical Engineers (ASME), a Senior Member of the American Institute for Aeronautics and Astronautics (AlAA) and a Member of the Society for Automotive Engineers (SAE).
I
Introduction
SUSpension systems are often used to control response of various rigid and flexible
multi-body systems (Chalasani, 1986a,b) and the most commonly used suspension systems in vehicular applications, where they are used particularly to control the tyre deflection or wheelhop for handling performance and vehicle body acceleration for passenger ride comfort (Ahmadian, 1997a). Other vehicular applications of such systems include engine, cab and seat suspensions. These so-called secondary suspensions increase ride comfort by reducing vibration transmission to the operator compartment
(Ahmadian, 1997b). Since first introduced by Crosby and Kamopp (Crosby and Kamopp, 1973; Kamopp and Crosby, 1974), semi-active suspension systems continue to gain considerable
118
WF. Faris, S.l. lhsan and M Ahmadian
attention in vehicle applications. This is due to its advantageous characteristics over passive systems in overcoming the traditional conflict between vehicle safety and handling, and ride comfort, as well as its significantly less complexity and power requirement than active suspension system (Barak, 1992; Carter, 1998; Koo et aI., 2004). Semi-active dampers draw small amounts of energy to operate a valve to adjust the damping level and thus reduce the amount of energy transmitted from the source to the suspended body. Semi-active dampers can generally be classified based on their control scheme as on-off skyhook, continuous skyhook, on-off groundhook or continuous groundhook. Skyhook control is known to be able to improve the vehicle body resonance, but at the expense of the lyre resonance (wheelhop), while groundhook control provides a better control of lyre resonance, but at the expense of increasing vehicle body resonance. Hybrid control, which combine the effect of both skyhook and groundhook has been introduced and has been shown to provide a compromise between the two while still performing better than the passive system (Ahmadian, 1997; Ahmadian and Vahdati, 2006). Further studies have been conducted to extensively compare the performance of the various semi-active systems in time domain - transient and steady state, and transfer function in frequency domain, for different models - Q-car 2-DOF and F-car 7-DOF (Ihsan et aI., 2007, 2008). The results show that hybrid control performs better in mostly all of the analyses. The work presented in this paper is an extension of the above work intended to compare responses of the models. Possible correlation between the simpler models to the more complex ones is sought. The specific performance criteria of interest are the ride comfort, suspension displacement and road-holding responses. All the three different analyses used, transient state, steady state and transfer function, are presented. In the time-domain transient response analysis, peak-to-peak (PTP) value, settling time and its steady-state value are compared. PTP values of pure tone input at resonance frequencies are compared in the time-domain steady-state response analysis. Finally, in the frequency-domain transfer function analysis, the response curves are compared.
2
Modelling, derivations and analysis
All three models - Q-car 2-DOF, H-car 4-DOF and F-car 7-DOF models used in this analysis are shown in Figures 1,2 and 3, respectively. The parameters and state variables descriptions are provided in Tables I and 2, respectively, for all models. Looking at the Q·car model, one notices that all the passive and semi-active control policies can be obtained from this single model that is by letting a ~ I and a ~ 0 to obtain skyhook and groundhook control policies, respectively. The system is said to be in hybrid control when the value of a is between these values. For the purpose of this analysis, hybrid control is defined as a = 0,5. The equations of motion for passive system can be obtained by letting cofT! = Coni = C.~l • Similar deductions can be made for both H-car and F-ear models where a = t can be varied between 0 and t to obtain either groundhook, hybrid or skyhook control and equations of motion for passive system can be obtained by letting Calf! = Coni = c.~1 , coff2 = con2 = e l2 for H-ear and additionally F-car model.
ColD
= Con3 = Cl3 and c off4 = c on4 = cs4 for
119
A comparative ride performance and dynamic analysis Figure 1
Q-car 2-DOF model
Coff
===-
k
Figure 2
,
1 '"
n
H-ear 4·DOF model
k" e·ffI
of
k"
.t
=='==
(/- a)(eMI- e.JPJ
Figure 3
x,
L-[:m~,~, :J
F-car 7·DOF model
ka
"'"
(/ - a)(eM, - eoJPJ
"",
c:::::::!:::=--------f
120 Table 1
WF. Faris, S.f. fhsan and M Ahmadian
Model parameters for the various models
Symbol Description m,
Sprung mass Pitch moment of inertia
Q-car
H-car
F-car
365
730 2,460
ai,
Front-left unsprung mass (muJ Rear-left unsprung mass (m us ) Rear-right unsprung mass (m us ) Front-right unsprung mass (row) Front-left suspension stiflhess coefficient Rear-left suspension stiffuess coefficient Rear-right suspension stiffness coefficient Front-right suspension stifthess coefficient Front-left suspension damping coefficient Rear·left suspension damping coefficient Rear-right suspension damping coefficient Front·right sllspension damping coefficient Front-left. lyre stiffitess coefficient Rear-left tyre stiffness coefficient ReaHight tyre stiffuess coefficient Front-right tyre stiffness coefficient Side distance from ms e.G. to the front axle Side distance from ms e.G. to the rear axle Frontal distance from ms e.G. to the front-left axle Frontal distance from ms e.G. to the rear-left axle
a"
Frontal distance from ills e.G. to the rear-right axle
1,460 2,460 460 40 35.5 35.5 40 19,960 17,500 17,500 19,960 1,290 1,620 1,620 1,290 175,500 175,500 175,500 175,500 1.011 1.803 0.761 0.755 0.755
a'f
Frontal distance from m, e.G. to the front-right axle
0.761
Iyy I" mJm,d
m", m.] m", kik" k.~
k,] k,. cieri
c" c,] c,. klk" k"
k" k.. If I,
alf
Table 2
Roll moment of inertia
40
40 35.5
19,960
19,960 17,500
1,290
1,290 1,620
175,500 175,500 175,500
1.011 1.803
State variables and inputs description for the various models
Symbol
Q-car
H-car
F-car
x, x, x] x, x, x, x,
ms heave (m) mw displacement (m)
ms heave(m) m, pitcb (rad) rant mw (m) ear mIlS (m)
ms heave (m) m, pitch (rad) m, roll (rad) Front-left m", (m) ear-left mus (m) ear-right mus (m) rant-right roLlS (m) Front-left input (m) Rear-left input (m) ar-rigbt input (m) rant-right input (m)
X;,/XIIlI Xl1l2 Xill3 Xl1l4
Inpul (m)
Units kg kgm
2
kgm
2
kg
kg kg kg
Nfm Nfm Nfm N/m Nslm Nslm Nslm Nslm N/m N/m N/m Nlm m m m m m m
121
A comparative ride performance and dynamic analysis Toble3
Q-ear
H-car
F-ear
Natural frequencies ofeach system and control policy for the various models System
f.l
f.,
Passive
1.126
11.022
Skybook
1.115
11.127
Groundhook
1.115
11.132
Hybrid
1.115
11.131
f.,
f.,
f.,
f ••
f.,
..~
n~
;;;:.;\:0 Wlm
;F'i"
Passive
0.811
1.132
11.060
11.550
Skyhook
0.814
1.017
11.126
11.731
Groundhook
0.803
1.Il7
11.130
11.740
Hybrid
0.807
1.112
11.129
11.737
Passive
1.005
1.304
1.499
11.038
11.043
11.454
11.545
Skyhook
0.998
1.274
1.464
11.126
11.127
11.730
11.728
Groundhook
1.002
1.273
1.462
11.131
11.131
11.739
11.742
Hyhrid
0.998
1.273
1.463
11.130
11.130
11.737
11.738
Typical semi-active damping coefficients are chosen using the relationships of Coni = coo2 = con) = C0ll4 = 2.2c1 and Coffl = coff2 = corr) = coff4 = O.2c1 (Blancard, 2003).
Using the built-in MATLAB command, the natural frequencies of the systems for various models and conlrollcrs are obtained as shown in Tabie 3.
2.1
Input types
Only one type of input is possible in the Q-car model, which is vertical input. Two types
of input are used in the H-car modeL The first type is called heave input signal, where VUlI = vin2 = vin' and the second type is pitch input signal, where Vinl = Vir!' Vin2 =-Vin • These are illustrated in Figure 4. Three types of inputs are used in this work for F-car. The first type is called heave
input signal, where Xinl =X'in2 = Xin] = Xin4 =Xin' the second type is pitch input signal, where X'inl = Xin4 = X'1Jl ,xin2 = xtn3 = -xin' and the third type is roll input signal, where Xin] = xin2 = X'in' Xin) = Xin4 = -Xm . These inputs are illustrated in Figure s. Figure 4 Types of input signals for H-car analysis
f-f
f-J
(a) Heave Input
(b) Pitch Input
Vin2
= Vin
WF. Faris, s.1. Ihsan and M Ahmadian
122 Figure 5
Types ofinput signal for F-car analysis: (a) heave input; (b) pitch input and (c) roll input
(a)
2.2
(b)
(c)
Performance criteria
Three different analyses were conducted to compare the passive to the semi-active control techniques (skyhook, ground hook and hybrid) that are transient and steady-state responses in time-domain and transfer function response in frequency domain.
2.2.1 Transienl slale analysis In the transient response analysis, the system is excited at time, t = 0 with a step input signal of amplitude 0.05 m. PTP value and settling time, Is values are noted for each control technique and compared. PTP values are calculated as
PTP = max (X(I))- min(x(t))
where xCI) is either displacement or acceleration, depending on the response of interest. The minimums and maximums are defined as the maximums and minimums of the overshoot. Settling time, I, is defined as the time required for the system in order for the response to reach and stay within 2% range of steady-state value.
2.2.2 Sleady-slate analysis In the steady-state response analysis, the system is excited with a sinusoidal input which amplitude is 0.05 m and frequency set to be equal to the natural frequencies of the system. This is to simulate the worst-case scenario at which resonances occur. PTP value is used as performance criteria for comparison. Similar definition of PTP in transient state is used, except that the maximums and minimums values are taken as the system reaches steady-state condition.
2.2.3 Frequency domain analysis In frequency-domain analysis, transfer functions ofthe states of interest are plotted over a frequency span. Using this analysis, general response of each model and control policies throughout the frequency span can be obtained. Usually one is interested in peak responses or resonances, which occur at the natural frequencies of the system. Response trend at low frequencies - below the natural frequencies, and high frequencies beyond the natural frequencies are also noted and compared.
A comparative ride performance and dynamic analysis
123
The results of the analyses for two models, quarter and fuJI car model have been discussed and published (Ihsan et ai" 2007, 2008). In this paper, we added the half car model and it is intended to compare responses between the three models and to see for any correlation, Special interest is taken in looking at the possibility of reasonably estimate the responses in the more complex model by using simpler ones.
3 3.1
Results and discussion Q-car, H-car and F-car comparison
3.1.1 m, vertical acceleration Sprung mass vertical acceleration responses of all models in frequency-domain transfer fuoetions are shown in Figure 6. The time-domain transient and steady-states responses are summarised in Tables 4 and 5, respectively. Figure 6
m 5 vertical response of all models - frequency domain: (a) Q-car response; (b) H-car
with heave input response; (c) H-car with pitch input response; (d) F-car with heave input response and (e) F-car with pitch input response (see online version for colours)
00'
(.) lr1
H _ 4-OOF l,tquency."*PO"Q - m. vtorU".~,~--.~~".:.\.
--I'~"~
·~·-'Gfo .. ndI'1-6ol
