COMPARATIVE HANDLING ANALYSIS OF CONVENTIONAL AND CNG BUS IN FREQUENCY DOMAIN

transcript

X Siimppozijum - Istraživanja i projektovanja za privredu

* Dragan Sekulić, University of Belgrade, Faculty of Transport and Traffic Engineering,Kneza Višeslava 1, Belgrade, Serbia,

d.sekulic@sf.bg.ac.rs

KOMPARATIVNA ANALIZA UPRAVLJIVOSTI KONVENCIONALNOG I CNG AUTOBUSA U FREKVENTNOM

DOMENU

Dragan Sekulić, University of Belgrade, Faculty of Transport and Traffic Engineering, Vlastimir Dedović, University of Belgrade, Faculty of Transport and Traffic Engineering Ivan Ivković, University of Belgrade, Faculty of Transport and Traffic Engineering

Abstract: Within buses powered by Compressed Natural Gas (CNG) there is a gas installation which integral part is a gas tanks battery. The tanks are often placed on the bus roof front or rear. Due to the additional mass, CNG buses have different structural properties, geometric parameters and mass parameters when compared to conventional buses, and consequently, different dynamic behavior. This paper gives a comparative handling analysis of a conventional city bus IK-104 and two versions of CNG buses (batteries on the roof front/rear) in frequency domain. For preliminary dynamic handling analysis, a bus is described by a single-track model with three degrees of freedom, and simulation has been performed using a program written in the Matlab software. Simulation results indicate that transient responses to disturbance in CNG buses dampen over time. The CNG bus with gas tanks battery at the front has the largest amplitudes of yaw response. At low excitation frequencies and at higher velocities the CNG bus with the battery at the rear has the highest gain of lateral acceleration. In case of stationary motion, at low velocities, stationary responses to steering input show approximately the same value with all the buses. Moving at higher velocities, CNG buses have steering responses that are considerably different from the responses of the standard bus. Hence, properties of the CNG bus with a battery at the front or at the rear respectively indicate to a higher and lower level of understeer when compared to the conventional one.

Keywords: conventional bus, CNG bus, stability, handling, simulation, Matlab

Rezime: U sklopu autobusa sa pogonom na komprimovani prirodni gas (CNG) nalazi se gasna instalacija čiji je sastavni deo baterija rezervoara za gas. Rezervoari se često postavljaju na krov na prednjoj ili zadnjoj strani autobusa. Usled dodatne mase CNG autobusi imaju različite konstrukcijske karakteristike, geometrijske parametre i parametre mase u poređenju sa konvencionalnim, pa shodno tome i različito dinamičko ponašanje. U radu je izvršena uporedna analiza upravljivosti konvencionalnog gradskog autobusa IK-104 i dve verzije CNG autobusa (baterija na krovu napred/nazad). Za preliminarnu dinamičku analizu upravljivosti definisan je jednotražni model sa 3 stepena slobode, a simulacija je sprovedena pomoću programa napisanog u programskom paketu Matlab. Rezultati simulacije su pokazali da se prelazni odzivi na poremećaj kod CNG autobusa tokom vremena prigušuju. Najveće amplitude odziva na upravljanje pri skretanju ima autobus CNG sa baterijom napred. Na nižim frekvencijama pobude i pri većim brzinama kretanja najveće pojačanje bočnog ubrzanja ima autobus CNG sa baterijom pozadi. U uslovima stacionarnog kretanja, pri malim brzinama, stacionarni odzivi na upravljački ulaz imaju približno istu vrednost kod svih autobusa. Pri većim brzinama kretanja CNG autobusi imaju karakteristične odzive na upravljanje koji se dosta razlikuju u odnosu na odziv standardnog autobusa. Tako autobus CNG sa baterijom napred ima karakteristike koje ukazuju na viši, a CNG sa baterijom pozadi na niži nivo podupravljivosti u odnosu na standardni.

Ključne reči: konvencionali autobus, CNG autobus, stabilnost, upravljivost, simulacija, Matlab

INTRODUCTION

In order to diversify consumption of energy resources and reduce emission of the buses in public passenger transportation, the use of alternative fuels is considered. The use of any alternative energy source, in addition to the use of a modified engine, requires proper equipment which can influence, more or less, the concept of architecture and dynamic behavior of the complete vehicle [03, 04].

An appropriate autonomy of compressed natural gas (Compressed Natural Gas - CNG) driven buses require relatively large gas storage tanks, whose weight is significant. Such buses usually have multiple gas tanks outside the bus body, and mostly on the bus roof. Due to the additional weight and the position of the same, CNG buses have altered structural properties, thus setting the difference from conventional buses. Position of the gas tanks battery on the vehicle roof (front/rear) affects the bus center of gravity (by vehicle length and height), moments of inertia of the vehicle body, the static and dynamic vertical reactions on the front and rear axle, etc. Besides, aerodynamic properties of the bus body change due to the increase in frontal and lateral vehicles surfaces projections. For all that, dynamic behavior of CNG buses in longitudinal, lateral and vertical directions differs from the conventional one.

This paper presents a comparative handling analysis of the conventional city bus IK-104 and two derived types of CNG buses: with a battery mounted on the roof, front i.e. rear. Handling is analyzed using the characteristic responses to steering input during transient and stationary motion of the bus. Single-track plane model of the vehicle with three degrees of freedom (DOF) has been engaged in the analysis, while the simulation has been performed using a program written in the Matlab software.

DYNAMIC MODEL OF THE BUS

Conventional two-axle city bus IK-104 was selected as the basis for the comparative analysis of the handling properties. This bus has two tires on the front axle and two sets of double tires on the rear axle [10]. Figure 1 (a-c) shows the appearance of the basic version of the IK-104 bus and two derived CNG buses with gas tanks battery mounted on the roof, front and rear side. Usual dimensions and their values are given in Tables (1-2), as presented in the available literature [05, 10].

Figure 1. Buses a) conventional IK-104, b) CNG (battery at the front) and c) CNG (battery at the rear)

CNG bus center of gravity is calculated using equations (1-2):

gppCNG GG

20 (1)

pCNGzCNG lll (2)

Where:

l - wheelbase of the bus;

lpCNG - distance from the front axle to the center of gravity of CNG bus;

lzCNG - distance from the rear axle to the center of gravity of CNG bus;

lp - distance from the front axle to the center of gravity of IK-104 bus (lp = 0.6·l [m]);

G0 - IK-104 bus weight (partially loaded IK-104 bus M0= 14000 [kg]);

Gg - gas tanks battery weight (mass Mg = 1560 [kg], [05]).

Single-track bus model with three degrees of freedom is shown in Figure 2. The model forming assumptions are: the vehicle is moving at constant speed, vehicle motion is observed in the x-y plane (angular displacement around longitudinal x-axis and lateral y-axis as well as vertical motion of the vehicle along z-axis are neglected [02]), weight transfer from the inner to the outer wheels is also disregarded, the vehicle is symmetric against the longitudinal x-axis, ground is flat and smooth, all angles have small values and are expressed in radians, lateral forces are linearly dependent on the wheel slip angle at the front and rear bus axles, the tire cornering stiffness on the front and rear axle is identical for all buses analyzed.

Table 1. Parameters of the IK-104 bus, CNG (battery at the front) and CNG (battery at the rear)

Bus IK-104 CNG(battery at the front)

CNG(battery at the rear)

M0 - mass of the IK-104 bus (partially loaded) 14000 [kg] - -

Mg - mass of the CNG bus gas tanks - 1560 [kg] 1560 [kg]

x1 - distance from the gas tanks center of gravity to the front axle of the CNG(battery at the front)

- 0.95 [m] -

x2 - distance from the gas tanks center of gravity to the rear axle of the CNG(battery at the rear)

- - 0.45 [m]

With regard to the adopted positive steer angle (Figure 2), slip angles of the wheels on the front and rear axle show negative values, as determined by the equations (3-4):

Differential equations of motion for the single-track vehicle model (Figure 2), taking into account the above assumptions are determined by the expressions (5-6):

Figure 1. Single-track bus model

lpp (3)

lKlKmVKKmV

)()( (5)

zzppzzppZ lK

lKlKlKlKJ

)( (6)

The bus inertia moments around the vertical z-axis are calculated using the equation 7:

22 LWm

Where:

W - is the width of the bus (W=2.50 [m], (10));

L - is the length of the bus (L=12.00 [m], (10));

The values of parameters that figure in the equations (5-6) for the buses considered are given in Table 2.

Table 2. Parameters of the buses: IK-104, CNG (battery at the front) and CNG (battery at the rear)

Bus IK-104 CNG(battery at the

front) CNG(battery at

the rear) m – bus mass; 14000 [kg] 15650 [kg] 15650 [kg]

Jz – moment of inertia around z-axis; 172670 [kgm2] 191910 [kgm2] 191910 [kgm2]

l - wheelbase; 5.65 [m] 5.65 [m] 5.65 [m]

lp - distance from the front axle to the bus center of gravity;

3.39 [m] 3.15 [m] 3.57 [m]

lz - distance from the rear axle to the bus center of gravity;

2.26 [m] 2.50 [m] 2.08 [m]

Kαp - equivalent cornering stiffness of tires on the front axle;

102500 [N/rad] 102500 [N/rad] 102500 [N/rad]

Kαz - equivalent cornering stiffness of tires on the rear axle;

205000 [N/rad] 205000 [N/rad] 205000 [N/rad]

Upon introducing the stability coefficients (expressions 8-13), differential equations of motion can be presented with expressions 14-15. Stability coefficients are used in the analytical examination of the vehicle stability and handling [01], and their physical meaning is described in [01, 08 and 09].

Upon the application of the Laplace transformation and with the initial conditions equal to zero, the system of differential equations of motion can be presented in the matrix form, through expression 16, where s is a Laplace transform operator.

Based on the matrix notation, the transfer functions of sideslip angle and yaw rate are given by the expressions 17-18:

)( azp KKY (8)

lKlKY zzpap

pKY (10)

)( zazpp lKlKN (11)

lKlKN zazpp

pplKN (13)

YYYmVmV r (14)

NNNJ rZ (15)

YmVYmVs

YmVNNYs

Transfer functions of yaw, wheel slip angles on the bus axles, both front and rear, path curvature, lateral velocity and lateral acceleration, can be presented using expressions 19-24:

ANALYSIS OF SIMULATION RESULTS

Transfer functions of the system

Figures 3, 4 and 5 show transfer functions for three usual responses of the vehicle: sideslip angle, yaw rate and lateral acceleration. Transfer functions of these responses are shown with reference to two bus speeds (low speed of 15 km/h and high-speed of 70 km/h). Transfer functions are obtained by means of a program written in the Matlab software thus using “bode” function. [12].

Figures 3 (a-d) show gain and phase angles of the sideslip angle at the speeds of 15 km/h and 70 km/h.

Figure 2. Transfer functions: a) sideslip angle gain (V=15 km/h), b) phase angles of the sideslip angle (V=15 km/h), c)

sideslip angle gain (V=70 km/h) and d) phase angles of the sideslip angle (V=70 km/h)

Based on the simulation results, sideslip angle gain of a CNG bus (battery at the front) is the most intensive, i.e. approximately 0.3 (degrees/degree), at low excitation frequencies, at low speeds. The most intensive gain in a CNG bus (battery at the rear) is at lower frequencies, at higher speeds. Its sideslip angle gain is approximately two times higher than CNG bus (battery at the front) gain. At the frequencies above 1 Hz, gains are the same for all buses and they approximately equal zero.

At lower speeds and at lower frequencies, phase angles equal zero. They raise with increasing excitation frequency. At higher speeds and at lower frequencies, there is the phase difference of 180 degrees between the sideslip angle and the excitation. Phase difference occurs due to the fact that the sideslip angle has the sign opposite to the one of the steering input at speed greater than the speed at which the sideslip angle equals zero (Table 6). At higher frequencies, phase angles equal to -90 degrees.

Figure 4 (a-d) shows gains and phase angles of yaw rate, at the speeds of 15 km/h and 70 km/h.

Given low speeds, yaw rate gain is approximately equal for all buses, namely less than one within the whole frequency range. At higher speeds and at lower excitation frequencies, CNG bus (battery at the rear) has the most intensive yaw rate gain (more than 2 (degree/s)/degree)). At lower frequencies, gain has the constant value. Maximum values of gain (peaks) correspond to the damped natural frequencies of the quasiperiodic motion of the buses at speed of 70 km/h (Figure 6b). Furthermore, response gains decrease as the excitation frequency increases. At higher excitation frequencies, yaw rate gains for all three buses have the same values, namely below one. The nature of change of the yaw rate gain (Figure 4c) is characteristic for understeering vehicles.

Figure 5 (a-d) shows gain and phase angles of lateral acceleration at low (15 km/h) and at high speed (70 km/h).

Figure 3. Transfer functions: a) yaw rate gain (V=15 km/h), b) phase angles of yaw rate (V=15 km/h), c) yaw rate gain

(V=70 km/h) and d) phase angles of yaw rate (V=70 km/h)

Figure 4. Transfer functions: a) lateral acceleration gain (V=15 km/h), b) phase angles of the lateral acceleration (V=15

km/h), c) lateral acceleration gain (V=70 km/h) and d) phase angles of lateral acceleration (V=70 km/h)

Given low speeds and low excitation frequencies, the acceleration gain is equal for all buses. At higher frequencies, IK-104 bus has the most intensive gain of 0.13 [(m/s2)/degree]. At high speeds and low frequencies, CNG bus (battery at the rear) has the maximum value of lateral acceleration gain (about 0.8 [(m/s2)/degree]). At high frequencies, gains are small with values which are approximately the same for all buses (0.1 [(m/s2)/degree], Figure 5c).

Given high speeds and low excitation frequencies, the phase lag between lateral acceleration and excitation for all buses is approximately -100 degrees. This can be explained by the fact that the sideslip angle response has the sign opposite to the one of the control input.

Stability of steering control

Denominator in expressions 16-17 set a characteristic equation of the system. Natural frequencies, damped natural frequencies and dimensionless damping ratio can be analyzed through the characteristic equation. Based on the above mentioned values, information regarding the nature of response in the transient mode of the vehicle motion is obtained. Zero values of the characteristic equation are poles of transfer functions which indicate the stability of the system.

Natural frequency of the system is presented through expression 25:

]/[ sradVmJ

mVNYNYNw

Upon setting in order the expression 25, natural frequency can be obtained in function of the understeer gradient K, (expression 26):

sradKmJ

Understeer gradient K is given by the expression 27:

][deg/1

3.57 ggLK

Calculated understeer gradients for buses IK-104 and CNG (battery on the front/rear) with partial load are given in Table 3:

Table 3. Understeer gradient of IK-104 bus, CNG (battery at the front) and CNG (battery at the rear)

Bus IK-104 CNG(battery at the front) CNG(battery at the rear)

Understeer gradient 0.7826 [degree/g] 1.4348 [degree/g] 0.4508 [degree/g]

All three buses considered at partial load have positive understeer gradients, thus indicating their understeering. Yet, among the mentioned ones, CNG bus with battery at the front has the highest level of understeering, namely 1.435 degree/g.

Damped natural frequency is determined by the expression 28:

sradVmJ

mVNYNYNw

Dimensionless damping ratio is given through the expression 29:

mVNYJ (29)

Damped natural frequency in the function of the natural frequency and dimensionless damping ratio is shown in the expression 30:

]/[1 2 sradww NP (30)

Figure 6 (a-b) shows the change of natural frequencies and damped natural frequencies as function of the bus speed. With the raise of speed, the natural frequency decreases and the damped natural frequency increases. CNG bus (battery at the front) has the highest value of the damped natural frequency for all speeds considered. The vehicle with a higher level of understeering has higher damped natural frequency [08, 09].

Figure 5. Frequency a) of undamped oscillation motion and b) of damped oscillation motion

Figure 7 shows the change of dimensionless damping ratio versus the bus speed. Damping ratio decreases while the speed increases.

The CNG bus with battery at the front has the lowest values of the dimensionless damping ratio; therefore responses to disturbance of this bus will have a more evident oscillatory character (Figure 8). A vehicle with more understeering has smaller damping value [08, 09].

Table 4 shows transitional speeds for which the damped natural frequencies equal zero (Figure 6b), i.e. dimensionless damping ratio equals one (Fig. 7). Above this speed, vehicle response to disturbance has an oscillatory character. At speeds below transitional ones, disturbed motion is dampened without oscillations, i.e. vehicle responses are aperiodic.

Figure 6. Dimensionless damping ratio in function of the bus speed

Table 4: Transitional speeds of IK-104 bus, CNG (battery at the front) and CNG (battery at the rear)

Bus IK-104 CNG(battery at the front) CNG(battery at the rear)

Transitional speed 22.48 [km/h] 18.87 [km/h] 27.74 [km/h]

Figure 8 shows comparative changes of the yaw in function of time for 1-degree disturbance at speeds of 15 km/h, 70 km/h and 100 km/h, for both IK-104 and CNG buses. Response is aperiodic at lower speeds, and at higher speeds the response has an oscillatory character. As the speed increases, amplitudes of oscillation for all buses increase as well, with the largest amplitude of oscillation with the CNG bus (battery at the front). Change of the yaw for this bus has more distinct oscillatory character.

Figure 7. Yaw for the bus a) IK-104, b) CNG (battery at the front) and c) CNG (battery at the rear)

Poles of the transfer function are represented by the roots of the characteristic equation. They are given by the expression 31:

mVNYNYNVmJmVNYJmVNYJ

rrZrZrZ

)(4)()( 2

Table 5 shows the calculation of the value of the roots of the characteristic equation for the IK-104 bus and CNG buses (battery at the front/rear) in the range of speeds from 10 km/h to 100 km/h, with step of 10 km/h.

Table 5. The roots of the characteristic equation for the IK-104 bus, CNG (battery at the front) and CNG (battery at the rear)

Speed [km/h]

10 20 30 40 50

IK-104 -4.5553/-7.9214 -2.6581/-3.5802 -

2.0794±0.52211i-

1.5596±0.66515i -

1.2477±0.72182iCNG (battery at the front)

-4.0603/-7.3042 -

2.8411±0.27885i-

1.8941±0.76115i -

1.4206±0.86885i -

1.1365±0.91442i

CNG (battery at the rear)

-4.1036/-7.0632 -2.2292/-3.3542 -

1.8611±0.17478i-

1.3959±0.38984i -

1.1167±0.45627i

Speed [km/h]

60 70 80 90 100

IK-104 -1.0397±0.75081i -0.89119±0.76776i -0.77979±0.77857i -0.69315±0.78589i -0.62383±0.79109iCNG (battery at the front)

-0.94704±0.93824ii

-0.81175±0.95232i -0.71028±0.96135i -0.63136±0.96749i -0.56823±0.97186i

CNG (battery at the rear)

-0.93057±0.48858i -0.79763±0.50707i -0.69793±0.51871i -0.62038±0.52655i -0.55834±0.53209i

The roots of the characteristic equation at low speed of the bus (below 20 km/h) are negative real numbers. At higher speed (above 20 km/h) the roots of the characteristic equation are conjugate complex numbers with negative real parts. Based on the calculated values of the roots of the characteristic equation one can draw a conclusion that the system is stable for a given speed range. This gives an opportunity to apply the Final Value Theorem, the expression 32, [11], when determining response of the vehicles in the conditions of stationary motion.

In the expression 32, the function F(s) is the system response to the unit step function, and H(s) is the transfer function of the system. The expressions 33-39, respectively, present stationary vehicle responses to steering input - sideslip angle, yaw rate, wheel slip angle on the front axle, wheel slip angle on the rear axle, path curvature, lateral velocity and lateral acceleration:

lim)(lim)(lim 00 sHs

sssFtf sst (32)

)(1lim 0 radrad

YmVNNY

]/)/[()()(

)(1lim 0 radsrad

YmVNNY

]/[))((

)())(()(

)(1lim 0 radrad

YmVNNYV

YYVNNNYmVVYNNYl

]/[))((

)(1lim 0 radrad

YmVNNYV

YVNYNYNlYmVVN

]/)/1[())(()(

0 radmYmVNNYV

]/)/[()(

)(1lim 0 radsm

YmVNNY

YmVNNYVV

]/)/[()(

)(1lim 2

0 radsmYmVNNY

YNNYVrV

Vehicle responses within bus stationary motion conditions

This section of the paper discuss typical vehicle responses (sideslip angle, wheel slip angles on the front and rear axle, yaw rate, path curvature, lateral velocity and lateral acceleration) within conditions of stationary motion of the vehicle, i.e. the conditions dβ/dt=0 and dω/dt=0 are met.

Responses were analyzed for the bus speed within the range from 10 km/h to 100 km/h, in steps of 10 km/h.

Figure 9 shows the change of the sideslip angle steering response. Sideslip angle is positive at low speeds and negative at high speeds. Sideslip angles for speeds up to 30 km/h are approximately the same for all buses. For speeds above 30 km/h CNG bus (battery at the rear) has the smallest response values. For example, at the speed of 70 km/h sideslip angles of CNG buses (battery at the rear), IK-104 and CNG (battery at the front) are -2 degrees, -1.4 degrees and -0.8 degrees, respectively. Speeds at which the sideslip angle is zero are given in Table 6.

Table 6. The speeds at which the sideslip angle is zero for buses IK-104, CNG (battery at the front) and CNG (battery at the rear)

Bus IK-104 CNG (battery at the front) CNG (battery at the rear)

Speed (for β=0) 26.74 [km/h] 27.72 [km/h] 23.69 [km/h]

Figure 8. Sideslip angle as a function of the bus speed

Figure 10 (a-b) shows wheel slip angles on the front and rear axle of the bus in function of the bus speed. As vehicle speed increases, wheel slip angles of both axles decrease, i.e. their absolute value increase. CNG bus (battery at the rear) has minimum values of the slip angle for both front and rear wheels. The absolute values of slip angles of the front axle are higher than values of slip angles of the rear axle for all buses and at all speeds considered. Based on the values of slip angles, one can draw a conclusion that buses have understeering behavior. At low speeds (up to 25 km/h), slip angles of the front axle wheels and the rear axle wheels are approximately the same for all buses.

Figure 9. Slip angles for the bus a) front axle wheels and b) rear axle wheels

Figure 11 shows the change of the bus yaw rate versus speed function. CNG bus (battery at the rear) yaw rate increases as the speed increases for the whole speed range. In IK-104 bus and CNG(battery at the front) yaw rate increases along with the speed to about 70 km/h i.e. 50 km/h, and thereafter it slightly decreases. CNG bus (battery at the rear) has the highest values of the stationary yaw rate response. For example, for the speed of 70 km/h, yaw rate for CNG bus (battery at the rear) equals 2.3 [(degree/s)/degree], for IK-104 bus it equals 1.8 [(degree/s)/degree], and for the CNG bus (battery at the front) it approximately equals 1.3 [(degree/s)/degree].

Figure 12 shows the path curvature responses for one degree steer angle as a function of the bus speed. With all buses considered, with the increase in speed, path curvature decreases (i.e. the cornering radius increases). CNG bus (battery at the rear) has the highest values of this response.

Figure 10. Yaw rate as a function of the bus speed

Figure 11. Path curvature per degree of steer angle of the bus as function of the bus speed

Figure 12. Lateral velocity per degree of steer angle of the bus as function of the bus speed

Figure 13 shows the change of lateral velocity per degree of steer angle as a function of the bus speed. The absolute value of the lateral velocity increases along with the increase in the vehicle speed. CNG bus (battery at the rear) has the lowest value of the response. For example, for the speed of 70 km/h stationary lateral velocity response for a CNG bus (battery at the rear) is approximately -0.65 [(m/s)/degree], and for a CNG bus (battery at the front) it equals -0.3 [(m/s)/degree], while the same, at the speed of 100 km/h, have the value of -1.4 [(m/s)/degree], and -0.6 [(m/s)/ degree], respectively. At low speeds (up to 30 km/h) lateral velocities for all the buses are approximately equal to 0 [(m/s)/degree].

Figure 14 shows the change of the lateral acceleration per degree of steer angle as a function of speed. One can note that as speed increases, lateral acceleration increases as well. CNG bus (battery at the rear) has the highest, while CNG bus (battery at the front) has the lowest value of response. For example, at the speed of 70 km/h lateral acceleration in CNG bus (battery at the rear) approximately equals 0.75 [(m/s2)/degree], for the IK-104 bus this response has the value of 0.6 [(m/s2)/degree], while a CNG bus (battery at the front) has the response value approximately equal to 0.43 [(m/s2)/degree]. At low speeds (up to 30 km/h) values of lateral acceleration are small and almost the same for all buses.

Figure 13. Lateral acceleration per degree of steer angle of the bus as function of bus speed

CONCLUSION

The use of compressed natural gas (CNG) as a bus power source, in addition to an appropriate engine, requires also the installation of suitable gas equipment. As a part of this installation there are multiple compressed natural gas tanks organized in a battery. Gas tanks battery is often mounted on the bus roof, at the front or at the rear. Due to additional weight, CNG buses have structure and dynamic properties different from the ones of conventional buses.

This paper makes comparative analysis of handling of conventional city bus IK-104 and two derived CNG buses in frequency domain. CNG buses with the battery on the roof, positioned either at the front or the rear side, are analyzed. Handling analysis has been performed on the basis of characteristic responses to the steering input for a transitional and stationary bus motion.

Simulation results indicate that the added mass does not affect stability of the system, i.e. transient responses of CNG bus on the disturbance are damped over time. Responses of the buses at low speeds are aperiodic. At high speeds, responses to the disturbance have an oscillatory character. CNG bus (battery at the front) has the largest amplitude of the yaw response, as well as it has also the most prominent oscillatory character. With the increase in speed, oscillation amplitudes of yaw response increase with all buses.

At lower frequencies and at higher speeds the CNG bus (battery at the rear) has the highest gain of the lateral acceleration - about 0.75 [(m/s2)/degree], while the gain for the CNG bus (battery at the front) is approximately 0.42 [(m/s2)/degree].

During stationary motion, responses to steering input at lower speeds have almost the same values for all buses analyzed. At higher speeds there is a considerable discrepancy between the responses of sideslip angle, slip angle of the front and of the rear axle wheels of the bus, yaw rate, lateral velocity and lateral acceleration. For example, at the bus speed of 70 km/h lateral acceleration per degree of steer angle for CNG bus (battery at the rear) is about 0.75 [(m/s2)/degree], and for the CNG bus (battery at the front) the response value is almost twice less and is approximately 0.42 [(m/s2)/degree]. Lower value of lateral acceleration is more convenient for cornering at a reduced lateral adhesion coefficient.

Due to the added mass on the roof, the center of gravity of the CNG bus is higher compared to the CG position of the conventional bus. Therefore, during cornering, the transfer of weight from the inner to the outer wheels of the CNG bus is higher compared to the conventional one. The analysis

of the impact of this weight transfer to the handling characteristics requires a more complex model, and such an analysis will be discussed in subsequent papers.

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COMPARATIVE HANDLING ANALYSIS OF CONVENTIONAL AND CNG BUS IN FREQUENCY DOMAIN

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