Design, Development and Testing of an Air Damper quarter-car suspension system subjected to the road

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  • Modern Mechanical Engineering, 2011, 1, 84-92 doi:10.4236/mme.2011.12011 Published Online November 2011 (http://www.SciRP.org/journal/mme)

    Copyright © 2011 SciRes. MME

    Design, Development and Testing of an Air Damper to Control the Resonant Response of a SDOF Quarter-Car

    Suspension System

    Ranjit G. Todkar Department of Mechanical Engineering, P.V.P. Institute of Technology, Sangli, India

    E-mail: rgtodkar@gmail.com Received October 21, 2011; revised November 3, 2011; accepted November 10, 2011

    Abstract An air damper possesses the advantages that there are no long term changes in the damping properties, there is no dependence on working temperature and additionally, it has less manufacturing and maintenance costs. As such, an air damper has been designed and developed based on the Maxwell type model concept in the approach of Nishihara and Asami and Nishihara [1]. The cylinder-piston and air-tank type damper character- istics such as air damping ratio and air spring rate have been studied by changing the length and diameter of the capillary pipe between the air cylinder and the air tank, operating air pressure and the air tank volume. A SDOF quarter-car vehicle suspension system using the developed air enclosed cylinder-piston and air-tank type damper has been analyzed for its motion transmissibility characteristics. Optimal values of the air damping ratio at various values of air spring rate have been determined for minimum motion transmissibility of the sprung mass. An experimental setup has been developed for SDOF quarter-car suspension system model using the developed air enclosed cylinder-piston and air-tank type damper to determine the motion transmissibility characteristics of the sprung mass. An attendant air pressure control system has been de- signed to vary air damping in the developed air damper. The results of the theoretical analysis have been compared with the experimental analysis. Keywords: Ride Comfort, Quarter-Car Suspension Model, Cylinder-Piston and Air-Tank Type Air Damper,

    Motion Transmissibility, Optimal Air Damping Ratio

    1. Introduction The control of response of the sprung mass of a SDOF quarter-car suspension system subjected to the road ex- citation is necessary in the neighborhood of the reso- nance for the better ride comfort, road holding and sta- bility. Various damping mechanisms such as, hydraulic, electromagnetic, ER and MR fluid and air dampers have been reported in the literature [1-3]. In this paper, an air enclosed cylinder-piston and air-tank type air damper con- figuration has been selected for design and development because in these dampers there are no long term changes in the damping properties, no dependence on working temperature. Air dampers have less manufacturing and maintenance costs. A SDOF quarter-car vehicle suspen- sion model using such a developed air damper has been analyzed for its motion transmissibility characteristics. The air damper has been designed and developed as a

    Maxwell type model in the approach of Nishihara and Asami and Nishihara [1]. The air damper characteristics such as air damping ratio and air spring rate have been studied. Optimal values of the air damping ratio at vari- ous values of air spring rate have been determined to ob- tain minimum motion transmissibility of the sprung mass. An experimental setup for SDOF quarter-car suspension system using the developed air enclosed cylinder-piston and air-tank type damper has been developed with an attendant air pressure control system. 2. Development of an Air Enclosed

    Cylinder-Piston and Air-Tank Type Damper

    A cylinder-piston and air-tank type damper, both the sides of which are connected to two surge tanks through capil- lary pipes has been developed. The arrangement is used

  • 85R. G. TODKAR

    to set the desired damping properties by allowing the changes in 1) Tank volume to cylinder volume ratio Nt, 2) Operating air pressure pi, and 3) Capillary pipe length lpipe and diameter dpipe. Figure 1(a) shows a cylinder- piston and air-tank type air damper. Figure 1(b) shows the mathematical models for the air Damper [4]. 2.1. Air Spring Rate ka [3]

    2 22 2 a

    t c

    n pi s n s pik v v

               Nt

    where (1) t cv v Nt where n is the index of expansion of air, pi is the operat- ing air pressure in the system, s is the cross sectional area of the piston, vt is the air tank volume and vc is the air cylinder volume.

    Let air spring rate ratio 1

    akk k

          

    (2)

    where k1 is the suspension spring rate. Substituting the value of ka from Equation (1) in Equa-

    tion (2), we obtain 2

    1

    2

    c

    n s pik v k Nt

              where

    Figure 1. (a) Cylinder-piston and air tank type system; (b) Mathematical models.

     2 2 and4 p r c ps d d v s h 

       (3)

    where dp is the piston diameter and dr is the piston rod diameter and hp is the height of the cylinder volume.

    Defining the terms p1, p2 and p3 as

    1 2 3, and p pr

    c c

    d hdp p p d d

       cd

    and substituting the val-

    ues of p1, p2, p3, s and vc in Equation (3), we obtain

     2 21 2 3 12

    c n pk p p d p k Nt          

    i (4)

    Assuming the values p1 = 0.985, p2 = 0.333, p3 = 0.5 and k1 = 970 N/m, the Equation (4) becomes.

     0.00403146 c pik d Nt

         (5)

    2.1.2. Air Damping Ratio ζa [3]

    2 a t

    a r

    w v n c pi

      

        

    where 1 2

    1

    a a

    kw m  

        

    (6)

    The capillary flow coefficient cr is given as

     4π 128r

    pipe

    o pipe

    d c

    l

           

    (Refer [3]) (7)

    in which dpipe and lpipe are the capillary pipe diameter and length respectively and µo is the viscosity of air at atmospheric temperature. Taking the value of ka from Equation (1) and substituting it in Equation (6), we get

    1 22

    1 1

    2 2 a

    c c

    n pi s n piw s v Nt m v m Nt

                    (8)

    Substituting wa from Equation (8) and cr from Equa- tion (7) in Equation (6)

    we obtain

     

      1

    4

    2

    π 2

    128

    c c

    a

    pipe

    o pipe

    n pis v Nt v m Nt

    d n p

    l

     i

                 

             

    or

     1 4

    1 1

    1

    128 where

    π 2

    pipe a

    pipe

    o c

    l Q

    pid Nt

    s vQ n m

           

          

        

    (9)

    Similarly using expressions (4) and (9) respectively

    Copyright © 2011 SciRes. MME

  • R. G. TODKAR 86

    for k and ζa one can write

    2 1

    a Q k   (10)

    where    

     

    2 2 2

    1

    2 4

    1 128 4 p r p

    pipe

    w d d l Q

    d

        ipe

    2.2. Air Damper Characteristics From Equation (10), it is seen that ζa will be large for small values of k, i.e. for small values of ka for given value of k. To provide variable damping ratio, the value of k can be varied. For the application of this device as a variable damping unit smaller values of k (0.05 to 0.125) are preferred. Also k depends on the ratio (pi/Nt), (refer Equation (4)) i.e. for small values of k, ratio (pi/Nt) should be kept small. 2.2.1. Effect of the Cylinder Diameter dc on Air

    Spring Rate Ratio k (Refer Figure 2) Here dc is varied as dc = 10 mm, dc = 20.0 mm and dc = 30.0 mm. The values of dr = (0.333) (dc) = (0.333) (30.0) = 10mm and hp =(0.5) (dc )= (0.5) (30.0) = 15 mm have been obtained. Considering a sliding fit between the pis- ton and cylinder the piston diameter dp is taken as 29.95 mm for a cylinder diameter dc = 30 mm. Figure 2 shows the effect of variation of cylinder bore dc on spring rate ratio k . 2.2.2. Effect of dpipe on ζa (Refer Figure 3) Using the Equation (10), the effect of variation of ratio on air damping ratio ζa has been obtained for the values of dpipe = 2.5, 2.0 and 1.5 mm. with lpipe = 3.0 m. Figure 4 shows the effect of air spring rate ratio k on the air damping ratio ζa. for the values of dpipe = 2.5, 2.0 and 1.5 mm. with lpipe = 3.0 m .

    Figure 2. k vs (pi/Nt ) for different values of dc = a) 10 mm, b) 20 mm, c) 30 mm.

    Figure 3. ζa vs (pi/Nt) with lpipe = 3.0 m dpipe = a) 2.5 mm, b) 2.0 mm, c) 1.5mm.

    Figure 4. ζa vs k with lpipe=3.0 m and dpip = a) 2.5 mm, b) 2.0 mm, c) 1.5mm.

    From the curves of Figures 2, 3 and 4, it is seen that the developed air damper can provide appreciable increase in the damping rati

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