# Active Vibration Control using Air Spring

• Surbhi Razdan
• P. J. Awasare
• Suresh Y. Bhave
Original Contribution

## Abstract

In the present study, a novel method of active vibration control of machines subject to base excitation using air spring is proposed. The study also includes proposes of a feedback control system, for active vibration control with mass flow rate as a function of the velocity of the mass, and/or base of air spring. Earlier study shows application of air spring as a force actuator. The mass flow introduces additional input excitation into the system by means of which the stiffness or resultant excitation force on the mass can be changed. A mathematical model is developed and response to steady state and transient base input are obtained. The use of appropriate value of gain in the system can ensure that the amplitude of response to excitation from the base is lower than the amplitude of base excitation. Some suitable values of gain depending on the special cases considered are suggested. An active control system with mass flow rate as a function of base velocity and gain equal to − 1 is most effective in controlling the vibration. This is highly desirable in case of high precision equipment. The interesting observation is that the spring rate can be changed and even made negative.

## Keywords

Air spring Active vibration control Controlled mass flow Spring rate Pneumatic vibration control

## Notations

A

Area of cross section of air spring, m2

c

Damping coefficient of air spring, Ns/m

M

Mass of the machine, kg

P

Pressure in the air spring, Pa

R

Universal gas constant, kJ/kgK−1

T

Temperature of air, °K

v

Volume of air spring, m3

x

Mass displacement (machine displacement), m

y

Base displacement (ground displacement), m

$$\dot{\text{m}}$$

Mass flow rate, kg/s

$$\dot{\text{p}}$$

Rate of change of pressure, Pa/s

$$\dot{\text{x}}$$

Mass velocity, m/s

$$\dot{\text{y}}$$

Base velocity, m/s

$$\upeta_{1}$$

Gain for mass flow rate as a function of base velocity

$$\upeta_{2}$$

Gain for mass flow rate as a function of mass velocity

$$\upomega_{\text{n}}$$

$$\upgamma$$

$$\upeta$$

Gain for mass flow rate as a function of difference between mass velocity and base velocity

$$\upxi$$

Damping ratio of air spring

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© The Institution of Engineers (India) 2018

## Authors and Affiliations

• Surbhi Razdan
• 1
• P. J. Awasare
• 1
• Suresh Y. Bhave
• 2