Performance of Automotive Air Suspension Control System

Performance of Automotive Air Suspension Control System

Mohamed Essam Shalabi, Ahmed I. Abdel-Aziz and Nabila Shawky Elnahas

Automotive Department

Faculty of Engineering, Ain Shams University Cairo, Egypt

AbstractOne type of vehicle suspension is the pneumatic suspension. This paper is an analytical investigation of the air spring stiffness variation under different operating conditions of input frequencies and amplitudes. Usually changing the stiffness of the air spring involves variations of the enclosed air pressure by pumping air into or out of air chamber or by changing its volume. Since, changing spring stiffness through controlling its pressure consumes power and is not instantaneous; hence controlling the stiffness through volume control is adapted in this investigation. This has been achieved by connecting the air spring volume to multiple auxiliary volumes through On-Off valves. By choosing two unequal additional volumes, four different stiffness setting are examined.

KeywordsPneumatic Active Suspension; Air Spring; Vehicle Ride

1. INTRODUCTION

   There are conflicting requirements between vehicle ride and handling behaviors. In order to achieve good vibration isolation for sprung mass over a wide range of frequency, a soft suspension spring is required, while to maintain good road holding capability at a frequency near natural frequency of the unsprung mass, a stiff suspension spring is required. To reduce the amplitude of the sprung mass at a frequency near its natural frequency, a high damping ratio is required, while in the high frequency range, a low damping ratio is required to provide good vibration isolation. On the other hand, a high damping ratio is required to provide good road holding capability at high frequency range. These conflicting requirements cannot be met by the conventional suspension system as its characteristics are fixed [1].

   The motivation of an automotive suspension system with variable stiffness and damping ratio comes involved for the conflicting requirements of comfort and handling. This paper will be concerned with studying the performance of air suspension and the effect of changing

   program GENSYS. The results were compared with experimental data, finding a good agreement.

   A.J. Nieto et al [3] developed an adaptive pneumatic suspension based on excitation frequency. A control strategy is proposed to avoid undesirable resonant frequencies, the control procedure is based on the pre- knowledge of incoming vibration and an efficient prediction technique is used when the incoming frequency is unknown.

   Igor Ballo [4] proposed an experimental estimation of air spring characteristics in active vibration control system, and then the results were compared with theoretical considerations estimation.

   Deo and Suh [5] have proposed an electromechanical suspension system capable of independent control of stiffness, damping and ride height to improve vehicle dynamics, but they find that the stiffness change requires power input and is not instantaneous. Then, they proposed a novel design for pneumatic air suspension system [6] capable of instantaneous change with no power input and no ride height change, this is done by changing the air spring volume through connecting auxiliary volumes to the air spring with On/Off valves. By adequately choosing N unequal volumes, they obtained 2N stiffness setting.

   III. MATHEMATICAL MODEL

   To determine the stiffness of the air spring, this is defined as the force, F acting along the centre line of the spring per unit deflection, Z in the same direction. The force F is due to the effective area, A multiplied by the gauge pressure, pg inside the air spring which is given by the equation.

   F = pgA (1)

   The spring stiffness can be calculated from the equation.

   the volume on the spring stiffness due to its advantages of

   k = dF = (pgA) = A pg + p A

   (2)

   near ideal instantaneous response and no power input.

   dZ dZ

   Z g Z

2. THEORETICAL BACKGROUND

Malin Presthus [2] proposed a new model for

Neglecting the change in the effective area, equation (2) will be:

simulation of the air spring behavior of railway train. The model is a three- dimension and consists of two parts,

k = A pg

Z

(3)

describing vertical and horizontal behavior. The air spring model is implemented in the vehicle dynamic simulation

To calculate the change of pressure inside the spring, adiabatic process is considered.

i.e. (pV = constant).

M

(p V) = p V1 V + V pg = 0 (4)

Z g g Z Z

Since the cross section area is considered constant, then the rate of change of volume per unit deflection is the effective area but with negative sign. This is due to the fact that decreasing the volume increases the deflection and vice versa.

V = A (5) k1

dZ C

Substituting equation (5) in equation (4) resulting in,

pg = pgA

(6) B2

dZ V k2

Substituting equation (6) into equation (3),

k = pgA2

V

(7)

Fig. 2. Air spring model connected to the additional volumes

In the proposed design, the air spring stiffness will be calculated using Matlab Simulink program. The stiffness value is controlled by connecting two unequal auxiliary volumes V2 and V3 to the main air volume V1 in successions through ON/OFF valves, as shown in Fig. 1. When the two valves are closed, the effective volume will be V1 (minimum volume), so the effective stiffness will be maximum as given by equation (8).

Assuming linear damping model, the behavior of air spring with additional volumes can be represented as spring k1 in series with parallel arrangement of spring and damper as shown in Fig. 2.

Where k1 is the stiffness of the air spring volume and k2 is the stiffness of the auxiliary volumes. The equations of stiffness k1 and k2 are given by

Kmax=

poA2 V1

(8)

k = poA2

1

V1

(10)

Where po

is the nominal pressure of the air spring.

k = poA2

2

V2+V3

(11)

For minimum stiffness, the two valves should be open for maximum effective volume. The effective stiffness in this case is given by.

The complex stiffness kcomp of this model is given by equation (12) [6]

Kmin

= poA2

V1+V2+V3+V4

(9)

kcomp

= k1(k2+B2s) k1+k2+B2s

(12)

Fig. 1. The proposed suspension schematic diagram with two additional volumes connected to the air spring.

Where B2 is the orifice damping coefficient

To determine B2, K2/B2 should be much greater than the system natural frequency to avoid deterioration in the performance [6].

These equations are simulated in Matlab and Fig. 3 was obtained

Fig. 3. Variations of the air spring stiffness at the four different volume settings with the input frequency

M

Fig. 3 shows the results for the four stiffness settings Z1

k

comp1, kcomp2, kcomp3 and kcomp4 calculated in dB with reference to 4956 N/m (minimum stiffness). The four stiffness are calculated when the volumes V1, V1+V2, V1+V3 and V1+V2+V3 are selected, respectively. These options are selected through the ON/OFF valves shown in Fig. 1.

From Fig. 3, it can be found that the system has low stiffness at low frequencies and high stiffness at high frequencies.

Further, it is obvious that the stiffness decreases as volume increases at low frequency. But at high frequencies, the change in stiffness is negligible as the air doesnt have time to go o the additional volume.

Comfort provided by the suspension system is characterized by its road induced vibration isolation. To get the transfer function to determine road vibration isolation, the model in Fig. 2 will be simplified into Fig. 4.

From Fig. 4, the equation of motion is obtained as.

kcoil C

Z2

Mz1 + C(z1 z2 ) + kcomp(z1 z2) = 0

Assume general solution:

z1 = Z1ejt, z2 = Z2ejt

(M2 + kcomp + jC)Z1 = (kcomp + jC)Z2

Z1 = kcomp+jC Z2 M2+kcomp+jC

(13)

Fig. 5. Conventional coil spring suspension model

To know the enhancement in comfort behavior in the pneumatic suspension system, the road induced vibration isolation for the conventional suspension should be determined.

Similarly, the transfer function that describes the road vibration isolation for conventional coil spring suspension as shown in Fig. 5 is

Equation (13) is the transfer function which describes

Z1 = kcoil+jC

(14)

road vibration isolation, where

Z1: Vertical amplitude of the sprung mass Z2: Vertical amplitude of the road excitation M: Sprung mass

C: Suspension damping coefficient

: Angular frequency

M

Z1

Z2 M2+kcoil+jC

Where: kcoil is the coil spring stiffness

To determine the suspension damping coefficient C, the damping ratio has to be in the range 0.2 0.4 to avoid excessive magnification at resonance.

From equations (13, 14 and 15), Fig. 6 and Fig. 7. have been plotted.

kcomp C

Z2

Fig. 4. Simplified air spring model

Fig.6. Comparison of road vibration isolation between a single volume air spring and conventional coil spring with sinusoidal input frequency

Fig. 7. Variations of road vibration isolation at four different volume settings with sinusoidal input frequency

Fig. 6 shows the road vibration isolation for the air spring without any additional volumes compared with the road vibration isolation for conventional coil spring suspension for the same damping coefficient. It was found that the natural frequency reduces by 0.52 Hz and the amplitude ratio reduces by 0.467.

The four settings in Fig. 7 are calculated when the volumes V1, V1+V2, V1+V3 and V1+V2+V3 are selected, respectively. It was found that the natural frequency for the condition 1 of air spring vibration isolation is 0.81 Hz and its amplitude ratio is about 1.527, when connecting the air spring to the auxiliary volume V3. The natural frequency of condition 3 becomes 0.57 Hz and its amplitude ratio reduces to about 1.339. When V1 and V2 are selected, the natural frequency for condition 2 is 0.49 Hz and its amplitude ratio becomes 1.289. Finally, when V1, V2 and V3 are selected, the natural frequency for condition 4 is

0.41 Hz and its amplitude ratio becomes 1.232.

IV. CONCLUSIONS

• Replacing the coil spring in the conventional suspension by air spring reduces the system natural frequency by 0.92 and its amplitude ratio by 0.762.

• Adding auxiliary volumes to the main air spring reduces the system natural frequency and its amplitude ratio.

• Adjusting the air suspension spring stiffness can be achieved practically almost instantaneously by utilizing solenoid ON/OFF valves through intelligent logic microprocessor to provide good ride and handling behavior.

REFERENCES

1. Wong, J.Y., Theory of Ground Vehicles, Third edition, ISBN 0- 471-35461-9.

2. Presthus, M., Derivation of Air Spring Model Parameters for Train Simulation, Lulea University of Technology, Sweden, January 2002.

3. Nieto, A.J., Morales A.L., Trapero J.R., Chicharro J.M. and Pintado P., An Adaptive Pneumatic Suspension Based on The

4. Ballo, I., Properties of Air Spring as a Force generator in Active Vibration Control Systems, Vehicle System Dynamics, Vol. 35, No. 1, pp. 67 – 72, 2001.

5. Deo, H. V. and Suh, N. P., Axiomatic Design of a Customizable Automotive Suspension, Proceedings of the Third International Conference on Axiomatic Design, Seoul, Korea, June 21 – 24, 2004.

6. Deo, H. V. and Suh, N. P., Pneumatic Suspension System with Independent Control of Damping, Stiffness and Ride Height, Proceeding of the Fourth International Conference on Axiomatic Design, Firenze, June 13 16, 2006.

   APPENDIX

   Vehicle parameters used in Matlab model

   1. Adiabatic index, = 1.4

   2. Quarter car mass, M = 500 kg

   3. Effective area, A = 0.01227 m2

   4. Air spring volume, V1 = 5 liters

   5. First air reservoir volume,

      V2 = 5 liters

   6. Second air reservoir volume,

      V3 = 7 liters

   7. Nominal air spring pressure,

      p = M 9.81 N

      o A m2

   8. Damping ratio, = 0.3

   9. Coil spring stiffness, kcoil = 40000 N/m