1
Analysis of a passive vs. semi-acve quarter car suspension model MANOLACHE-RUSU Ioan-Cozmin 1) , SUCIU Cornel 1) , MIHAI Ioan 1) 1) Department of Mechanics and Technologies, Stefan cel Mare University of Suceava, Romania, 13 University Street, 720229, e-mail: [email protected] ABSTRACT The vast majority of suspension systems widely used in road vehicles by all major manufacturers are passive. They have a unique force - displacement or speed - force characterisc, imposed by the characteriscs of the construcve elements used. Howev- er, for the suspension system of the vehicles, to opmally perform on the widest possi- ble areas of the road unevenness, adapve suspension systems have been developed. These systems can be either semi-acve or acve. The main problem that these suspen- sion systems have to answer is the maximizaon of tracon. This involves maintaining permanent contact between re and road, while also ensuring increased passenger com- fort. Passenger comfort, on the other hand, requires smooth damping, with as lile chassis acceleraon as possible. Under these condions, it is impossible for passive sys- tems to meet these requirements, and a compromise between comfort and safety is al- ways necessary. For these reasons, adapve systems have been developed that allow the shortcomings of passive systems to be eliminated, being able to ensure opmal behavior for the enre frequency range offered by runway irregularies. Semi-acve systems usu- ally use dampers with variable parameters, dictated by various controllers such as pro- poronal, derivave, integrave or various combinaons thereof. This paper aims to sim- ulate and analyze a passive suspension by referring to the characteriscs of a semi- acve. The study evaluates the vercal movements of a vehicle with known parameters over different shapes of the cross secon of the road. The study involves the use of the Matlab-Simulink environment in which a physical study model for the quarter machine model is made, using the predefined blocks found in Simscape. According to the ob- tained results, there is a substanal change in the damping characterisc when using the semi-acve suspension, in order to reduce the oscillaons and shorten the me to reach equilibrium . Keywords: semi-active suspension, magneto-rheological damper, frequency analysis, quarter car model. INTRODUCTION The type of suspension equipping a vehicle is substanally influenced by its des- naon. The latest trends in the field of vehicle suspension mainly use one of the adap- ve suspension systems. Due to the relavely high cost of the components, adapve sus- pensions are usually found on luxury or sports models, while passive systems are com- mon to other classes of vehicles. The characteriscs of the passive suspension may differ from one manufacturer to another, from one model to another or even within the same vehicle model, depending on the equipment variant. The damping characterisc, in the case of passive systems, can only be changed by replacing the suspension components. For this reason they are not suitable for the full range of irregularies offered by a non- compliant roadway. Works such as [1], [2], [3] show a linear vibraon damping charac- terisc, when using convenonal dampers used in passive systems. However, in the case of semi-acve systems, where various variants of PI, PD or PID controllers govern the op- eraon of the shock absorber, its damping coefficient can be easily adjusted in order to adapt the suspension characteriscs to the road condions. Studies on adapve systems are undertaken in works [4], [5], in order to evaluate the damping characterisc of mag- neto-rheological dampers on road surfaces with various geometries. The acve systems are disnguished by the introducon of an independent adjust- able component, in parallel with the classic suspension system, which allows the adjust- ment of the damping characterisc based on the interpretaon of signals from various sensors, with the consumpon of an addional amount of energy. The present paper aims at an analysis of the suspension parameters of a vehicle moving over various road bumps with different shapes, using the physical model of the car quarter concept. The studied model was implemented in the Matlab-Simulink soſt- ware, by imposing the characterisc parameters of a known suspension, respecvely the values of the wheel and body masses. A PID controller governs the operaon of the sus- pended mass damper in order to improve the damping characterisc, by adjusng the damping coefficient of the telescope corresponding to the Ground-hook control strategy. Similar studies on adapve suspension using magneto-rheological dampers have been performed in Matlab-Simulink using block diagrams, such as in [6]. In the case of using block diagrams, it is first necessary to obtain the differenal equaons that characterize the dynamics of the studied model, where for analysis the Laplace transform must be applied. In this way, the workload is significant and the equaons of moon must be de- termined in advance. The equaons of moon in this case, for the quarter machine model are obtained by applying the second law of dynamics and are represented by Eq. 1 for the respecve sprung mass and Eq. 2 for the unsprung mass in [6]. , A new, easier and more convenient approach is presented in this study, through the use of the components of the Matlab-Simscape libraries, with which the physical model of the suspension of a quarter of the car was built. The advantage of using this simulaon is that the differenal equaons characterisc of the model dynamics do not necessarily have to be known or passed in the S domain by means of the Laplace trans- form. In the proposed model, the control of the damping coefficient of a semi-acve damper is reduced either by adjusng the fluid flow that can pass through the gap pro- vided by the damper piston valve during compression or expansion, or by adjusng the electrical parameters in the case of magneto-rheological dampers. The development of adapve suspension systems aims to increase the stability of the vehicle, its maneuvera- bility and comfort, which translates into increased traffic safety, possible by opmizing the value of the damping coefficient relave to road condions. SIMSCAPE SIMULATION MODEL The physical model was made in Matlab-Simulink with the help of components from the Simscape library. Fig. 1 presents the diagram of the proposed study model, which contains the component elements and the interconnecons between them, for the case of the Ground-Hook type control of the quarter-car suspension. To simplify the graphical representaon, the model developed in Simscape was in- troduced in a subsystem with the same name. The proposed model allows the study of both passive and semi-acve suspension behavior. An overview of the proposed model is shown in Fig. 2. It is observed here that a dual-output signal generator is used to simu- late the runway profile, which uses different forms of mathemacal excitaon signals. The generated mathemacal signals are introduced into the physical model aſter their conversion into physical signals, through the Simulink-PS conversion blocks, respecvely an ideal source for translaon speed. Therefore, the proposed model uses as input the evoluon of the vercal speed of the road, the study being performed for a me interval of 50 seconds. A manual switch is used to switch between the two disnct excitaon sig- nals, shown in Fig.3. In the model, the excitaon signal is introduced using a translaonal moon sensor, thus making it possible to know the track profile. To display the profile, the Road profile oscilloscope from Fig. 1. Profile display requires the conversion of the physical signal used by the model into a mathemacal signal. PS-Simulink conversion blocks are used for this purpose. The translaonal moon sensor allows displaying the speed evoluon of the sprung and unsprung masses as well as of their displacements. By deriving the speed of the signals as a funcon of me, the evoluon of the acceleraons of the two masses can be determined. Another way used in the model to determine the acceleraons of the two masses is to use force sensors. The proposed model automacally evaluates the suspension deflecon by means of an ideal translaonal moon sensor connected to the input ports R and C at the points of interest of the two masses. The sum blocks are used in the model to operate with the input signals and the system error on the PID controller, as well as to impose the Ground-hook control strate- gy of the model. For this purpose, the deflecon of the speeds of the two masses is eval- uated. As long as this difference is posive, the suspended mass must have a displace- ment in the posive direcon of the vercal axis due to the need to increase the damp- ing coefficient. The input sizes for the proposed model are summarized in Table 1. The main parameters of interest in the evaluaon of the characteriscs of passive and semi-acve suspension consist in the analysis of the displacements values, speeds and acceleraons of the sprung and unsprung masses of the studied vehicle. Fig. 1- Simscape Groundhook Quarter-Car Model Fig. 2- Simscape diagram for both passive and semi-acve suspension system models ANALYSIS OF PASSIVE AND SEMI-ACTIVE SUSPENSIONS Within the proposed model, the response of the passive and semi-acve suspen- sion system controlled with PID controller was studied. Two excitaon signals were ap- plied for a duraon of 50 seconds. The first signal, shown in Fig. 3 is a pulse type, in or- der to simulate road bump, while the second one is a random Gaussian noise. Fig. 3- Road signal excitaon In the case of the first pulse signal, the system response for the two suspension systems studied is shown in Fig.4. From the evoluon of the graph it can be seen that the overgrowth is much more significant in the case of the passive suspension system, namely for the oscillaon of the sprung mass. Using the same values of the suspension parameters as in the case of passive suspension, with the difference that the value of the damping coefficient of the chassis damper is variable, dictated by the PID controller and the control strategy used, we note that in the case of semi-acve suspension as well as the transient me, unl which the dynamic error falls within the stabilizaon band un- dergoes an aenuaon. Fig. 4- Mass displacement for both passive and semi-acv suspension vs road profile An analysis of the system's response to an inial impulse involves linearizing the model, which is shown in Figs. 5. It is observed that the system response for both cases studied is a damped oscillang one with a subunit damping factor. The analysis shows that for the values of the control parameters chosen for the PID controller, the duraon of the transient process is halved when using the semi-acve system from 13.4 seconds to 6.77 seconds. Also the maximum amplitude of the signal shows a decrease from 0.582 to 0.149. Fig. 5- Impulse response The graph illustrated in Fig. 6 shows the response of the respecve passive sus- pension system of the studied semi-acve one to an arbitrary Gaussian signal. The evolu- on of the displacements presented in this graph, for the wheel mass, related to the lon- gitudinal secon of the roadway shows a good stability given to the vehicle by the semi- acve system, highlighng the influence of the Ground-hook control strategy. On the other hand, the movements of the suspended mass follow the road profile quite closely, the proposed semi-acve model allowing a reasonable control of the vehicle's comfort. Fig. 6- Mass displacement for an arbitrary uneven track surface CONCLUSIONS The purpose of this paper was to make an analysis of the damping capacity of a vehicle suspension through the values of the displacements of suspended and unsus- pended masses, both in the case of the passive and semi-acve system. To perform the proposed analysis, a model using the Simscape library in the Matlab Simulink simulaon environment was developed. The proposed model allows the graphical display of the evoluon of vercal displacements, speeds and acceleraons for suspended and unsuspended masses, in the case of a passive and a semi-acve system. The control of the semi-acve system is performed by interposing a PID controller be- tween the input signal, the output signal and the excitaon signal of the variable damp- er. The simulaon results, obtained aſter analyzing the response of the proposed model, illustrate that semi-acve systems bring substanal improvements on the damp- ing capacity compared to passive systems. The use of the Ground-hook control strategy, used for the proposed model is clearly reflected in the response of the semi-acve suspension system. Simulaons per- formed halving the duraon of the transient process of oscillaon of the unsuspended mass The present study shows that the transmissibility of the unsprung mass decreases with the increase of the damping coefficient, giving a good stability to the vehicle, in the case of the proposed model. REFERENCES 1.) Vinayak S.D., Sachin C.B., “Semi-acve suspension system design for quarter car model and its analysis with passive suspension model”, Internaonal Journal of Engineering Sciences & Research Technology, Vol. 6, Issue 3, 203-211 (2017). 2.) Senthil K.M., Vijayarangan, S., “Analycal and experimental studies on acve sus- pension system of light passenger vehicle to improve ride comfort”, Mechanika 1.- Kaunas: Technologija, 34-41 (2007). 3.) Guglielmino, E., Sireteanu T., Stammers W. C., Ghita, G., Giuclea M. [Semi-acve Suspension Control - Improved Vehicle Ride and Road Friendliness], London, Springer House, 1-294 (2008). 4.) Andronic, F., Manolache-Rusu, I.C., Patuleanu, L., “ Passive suspension modeling using MATLAB, quarter-car model, input signal step type”, TEHNOMUS Journal, Vol. 20, No. 1, 258-263 (2013). 5.) Andronic, F., Mihai, I., Manolache-Rusu, I.C., Patuleanu, L., Radion, I., “ Simulang passive suspension on an uneven track surface”, Journal of Engineering Studies and Research, Vol. 20, No. 1, 7-16 (2014). 6.) Andronic, F., Mihai, I., Suciu, C., Beniuga, M., “ Frequency analysis of a semi-acve suspension with magneto-rheological dampers”, Advanced Topics in Optoelectron- ics, Microelectronics, and Nanotechnologies VII Book Series: Proceedings of SPIE, Vol. 9258, (2015). s s s s u s s u mX b X X k X X u u u s s u s s u u u u u mX b X X k X X b W X k W X u

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Page 1: Analysis of a passive vs. semi active quarter car suspension model · er, for the suspension system of the vehicles, to optimally perform on the widest possi-ble areas of the road

Analysis of a passive vs. semi-active quarter car suspension model MANOLACHE-RUSU Ioan-Cozmin1), SUCIU Cornel1), MIHAI Ioan1)

1) Department of Mechanics and Technologies, Stefan cel Mare University of Suceava, Romania, 13 University Street, 720229, e-mail: [email protected]

ABSTRACT

The vast majority of suspension systems widely used in road vehicles by all major

manufacturers are passive. They have a unique force - displacement or speed - force

characteristic, imposed by the characteristics of the constructive elements used. Howev-

er, for the suspension system of the vehicles, to optimally perform on the widest possi-

ble areas of the road unevenness, adaptive suspension systems have been developed.

These systems can be either semi-active or active. The main problem that these suspen-

sion systems have to answer is the maximization of traction. This involves maintaining

permanent contact between tire and road, while also ensuring increased passenger com-

fort. Passenger comfort, on the other hand, requires smooth damping, with as little

chassis acceleration as possible. Under these conditions, it is impossible for passive sys-

tems to meet these requirements, and a compromise between comfort and safety is al-

ways necessary. For these reasons, adaptive systems have been developed that allow the

shortcomings of passive systems to be eliminated, being able to ensure optimal behavior

for the entire frequency range offered by runway irregularities. Semi-active systems usu-

ally use dampers with variable parameters, dictated by various controllers such as pro-

portional, derivative, integrative or various combinations thereof. This paper aims to sim-

ulate and analyze a passive suspension by referring to the characteristics of a semi-

active. The study evaluates the vertical movements of a vehicle with known parameters

over different shapes of the cross section of the road. The study involves the use of the

Matlab-Simulink environment in which a physical study model for the quarter machine

model is made, using the predefined blocks found in Simscape. According to the ob-

tained results, there is a substantial change in the damping characteristic when using the

semi-active suspension, in order to reduce the oscillations and shorten the time to reach

equilibrium .

Keywords:

semi-active suspension, magneto-rheological damper, frequency analysis, quarter car model.

INTRODUCTION

The type of suspension equipping a vehicle is substantially influenced by its desti-

nation. The latest trends in the field of vehicle suspension mainly use one of the adap-

tive suspension systems. Due to the relatively high cost of the components, adaptive sus-

pensions are usually found on luxury or sports models, while passive systems are com-

mon to other classes of vehicles. The characteristics of the passive suspension may differ

from one manufacturer to another, from one model to another or even within the same

vehicle model, depending on the equipment variant. The damping characteristic, in the

case of passive systems, can only be changed by replacing the suspension components.

For this reason they are not suitable for the full range of irregularities offered by a non-

compliant roadway. Works such as [1], [2], [3] show a linear vibration damping charac-

teristic, when using conventional dampers used in passive systems. However, in the case

of semi-active systems, where various variants of PI, PD or PID controllers govern the op-

eration of the shock absorber, its damping coefficient can be easily adjusted in order to

adapt the suspension characteristics to the road conditions. Studies on adaptive systems

are undertaken in works [4], [5], in order to evaluate the damping characteristic of mag-

neto-rheological dampers on road surfaces with various geometries.

The active systems are distinguished by the introduction of an independent adjust-

able component, in parallel with the classic suspension system, which allows the adjust-

ment of the damping characteristic based on the interpretation of signals from various

sensors, with the consumption of an additional amount of energy.

The present paper aims at an analysis of the suspension parameters of a vehicle

moving over various road bumps with different shapes, using the physical model of the

car quarter concept. The studied model was implemented in the Matlab-Simulink soft-

ware, by imposing the characteristic parameters of a known suspension, respectively the

values of the wheel and body masses. A PID controller governs the operation of the sus-

pended mass damper in order to improve the damping characteristic, by adjusting the

damping coefficient of the telescope corresponding to the Ground-hook control strategy.

Similar studies on adaptive suspension using magneto-rheological dampers have been

performed in Matlab-Simulink using block diagrams, such as in [6]. In the case of using

block diagrams, it is first necessary to obtain the differential equations that characterize

the dynamics of the studied model, where for analysis the Laplace transform must be

applied. In this way, the workload is significant and the equations of motion must be de-

termined in advance. The equations of motion in this case, for the quarter machine

model are obtained by applying the second law of dynamics and are represented by Eq.

1 for the respective sprung mass and Eq. 2 for the unsprung mass in [6].

,

A new, easier and more convenient approach is presented in this study, through

the use of the components of the Matlab-Simscape libraries, with which the physical

model of the suspension of a quarter of the car was built. The advantage of using this

simulation is that the differential equations characteristic of the model dynamics do not

necessarily have to be known or passed in the S domain by means of the Laplace trans-

form. In the proposed model, the control of the damping coefficient of a semi-active

damper is reduced either by adjusting the fluid flow that can pass through the gap pro-

vided by the damper piston valve during compression or expansion, or by adjusting the

electrical parameters in the case of magneto-rheological dampers. The development of

adaptive suspension systems aims to increase the stability of the vehicle, its maneuvera-

bility and comfort, which translates into increased traffic safety, possible by optimizing

the value of the damping coefficient relative to road conditions.

SIMSCAPE SIMULATION MODEL

The physical model was made in Matlab-Simulink with the help of components

from the Simscape library. Fig. 1 presents the diagram of the proposed study model,

which contains the component elements and the interconnections between them, for

the case of the Ground-Hook type control of the quarter-car suspension.

To simplify the graphical representation, the model developed in Simscape was in-

troduced in a subsystem with the same name. The proposed model allows the study of

both passive and semi-active suspension behavior. An overview of the proposed model is

shown in Fig. 2. It is observed here that a dual-output signal generator is used to simu-

late the runway profile, which uses different forms of mathematical excitation signals.

The generated mathematical signals are introduced into the physical model after their

conversion into physical signals, through the Simulink-PS conversion blocks, respectively

an ideal source for translation speed. Therefore, the proposed model uses as input the

evolution of the vertical speed of the road, the study being performed for a time interval

of 50 seconds. A manual switch is used to switch between the two distinct excitation sig-

nals, shown in Fig.3. In the model, the excitation signal is introduced using a translational

motion sensor, thus making it possible to know the track profile. To display the profile,

the Road profile oscilloscope from Fig. 1. Profile display requires the conversion of the

physical signal used by the model into a mathematical signal. PS-Simulink conversion

blocks are used for this purpose.

The translational motion sensor allows displaying the speed evolution of the

sprung and unsprung masses as well as of their displacements. By deriving the speed of

the signals as a function of time, the evolution of the accelerations of the two masses

can be determined. Another way used in the model to determine the accelerations of

the two masses is to use force sensors.

The proposed model automatically evaluates the suspension deflection by means

of an ideal translational motion sensor connected to the input ports R and C at the

points of interest of the two masses.

The sum blocks are used in the model to operate with the input signals and the

system error on the PID controller, as well as to impose the Ground-hook control strate-

gy of the model. For this purpose, the deflection of the speeds of the two masses is eval-

uated. As long as this difference is positive, the suspended mass must have a displace-

ment in the positive direction of the vertical axis due to the need to increase the damp-

ing coefficient.

The input sizes for the proposed model are summarized in Table 1.

The main parameters of interest in the evaluation of the characteristics of passive

and semi-active suspension consist in the analysis of the displacements values, speeds

and accelerations of the sprung and unsprung masses of the studied vehicle.

Fig. 1- Simscape Groundhook Quarter-Car Model

Fig. 2- Simscape diagram for both passive and semi-active suspension system models

ANALYSIS OF PASSIVE AND SEMI-ACTIVE SUSPENSIONS

Within the proposed model, the response of the passive and semi-active suspen-

sion system controlled with PID controller was studied. Two excitation signals were ap-

plied for a duration of 50 seconds. The first signal, shown in Fig. 3 is a pulse type, in or-

der to simulate road bump, while the second one is a random Gaussian noise.

Fig. 3- Road signal excitation

In the case of the first pulse signal, the system response for the two suspension

systems studied is shown in Fig.4. From the evolution of the graph it can be seen that

the overgrowth is much more significant in the case of the passive suspension system,

namely for the oscillation of the sprung mass. Using the same values of the suspension

parameters as in the case of passive suspension, with the difference that the value of the

damping coefficient of the chassis damper is variable, dictated by the PID controller and

the control strategy used, we note that in the case of semi-active suspension as well as

the transient time, until which the dynamic error falls within the stabilization band un-

dergoes an attenuation.

Fig. 4- Mass displacement for both passive and semi-activ suspension vs road profile

An analysis of the system's response to an initial impulse involves linearizing the

model, which is shown in Figs. 5. It is observed that the system response for both cases

studied is a damped oscillating one with a subunit damping factor. The analysis shows

that for the values of the control parameters chosen for the PID controller, the duration

of the transient process is halved when using the semi-active system from 13.4 seconds

to 6.77 seconds. Also the maximum amplitude of the signal shows a decrease from 0.582

to 0.149.

Fig. 5- Impulse response

The graph illustrated in Fig. 6 shows the response of the respective passive sus-

pension system of the studied semi-active one to an arbitrary Gaussian signal. The evolu-

tion of the displacements presented in this graph, for the wheel mass, related to the lon-

gitudinal section of the roadway shows a good stability given to the vehicle by the semi-

active system, highlighting the influence of the Ground-hook control strategy. On the

other hand, the movements of the suspended mass follow the road profile quite closely,

the proposed semi-active model allowing a reasonable control of the vehicle's comfort.

Fig. 6- Mass displacement for an arbitrary uneven track surface

CONCLUSIONS

The purpose of this paper was to make an analysis of the damping capacity of a

vehicle suspension through the values of the displacements of suspended and unsus-

pended masses, both in the case of the passive and semi-active system.

To perform the proposed analysis, a model using the Simscape library in the

Matlab Simulink simulation environment was developed. The proposed model allows the

graphical display of the evolution of vertical displacements, speeds and accelerations for

suspended and unsuspended masses, in the case of a passive and a semi-active system.

The control of the semi-active system is performed by interposing a PID controller be-

tween the input signal, the output signal and the excitation signal of the variable damp-

er.

The simulation results, obtained after analyzing the response of the proposed

model, illustrate that semi-active systems bring substantial improvements on the damp-

ing capacity compared to passive systems.

The use of the Ground-hook control strategy, used for the proposed model is

clearly reflected in the response of the semi-active suspension system. Simulations per-

formed halving the duration of the transient process of oscillation of the unsuspended

mass

The present study shows that the transmissibility of the unsprung mass decreases

with the increase of the damping coefficient, giving a good stability to the vehicle, in the

case of the proposed model.

REFERENCES

1.) Vinayak S.D., Sachin C.B., “Semi-active suspension system design for quarter car

model and its analysis with passive suspension model”, International Journal of

Engineering Sciences & Research Technology, Vol. 6, Issue 3, 203-211 (2017).

2.) Senthil K.M., Vijayarangan, S., “Analytical and experimental studies on active sus-

pension system of light passenger vehicle to improve ride comfort”, Mechanika 1.-

Kaunas: Technologija, 34-41 (2007).

3.) Guglielmino, E., Sireteanu T., Stammers W. C., Ghita, G., Giuclea M. [Semi-active

Suspension Control - Improved Vehicle Ride and Road Friendliness], London,

Springer House, 1-294 (2008).

4.) Andronic, F., Manolache-Rusu, I.C., Patuleanu, L., “ Passive suspension modeling

using MATLAB, quarter-car model, input signal step type”, TEHNOMUS Journal,

Vol. 20, No. 1, 258-263 (2013).

5.) Andronic, F., Mihai, I., Manolache-Rusu, I.C., Patuleanu, L., Radion, I., “ Simulating

passive suspension on an uneven track surface”, Journal of Engineering Studies

and Research, Vol. 20, No. 1, 7-16 (2014).

6.) Andronic, F., Mihai, I., Suciu, C., Beniuga, M., “ Frequency analysis of a semi-active

suspension with magneto-rheological dampers”, Advanced Topics in Optoelectron-

ics, Microelectronics, and Nanotechnologies VII Book Series: Proceedings of SPIE,

Vol. 9258, (2015).

s s s s u s s um X b X X k X X u

u u s s u s s u u u u um X b X X k X X b W X k W X u