an experimental investigation on performance ...nopr.niscair.res.in/bitstream/123456789/5111/1/jsir...

Journal of Scientific & Industrial Research Vol. 64, August 2005, pp.571-580

An experimental investigation on performance characteristics and natural frequency analysis of high-speed carbon – epoxy shaft in

aerostatic conical journal bearings

R B Ingle1,*and B B Ahuja2 1Department of Mechanical Engineering, 2Department of Production Engineering,

Pune Institute of Engineering and Technology, Shivajinagar, Pune 411 005

Received 10 June 2004; revised 03 February 2005; accepted 13 June 2005

Carbon-epoxy (CE) material has excellent structural properties owing to high specific modulus, high damping and low thermal expansions. In this study, CE shaft was made for the high-speed CNC grinding machines and the centrifuges. The one step composite shaft made of carbon fibers in epoxy matrix was manufactured with 16 layers having stacking angles [0°/90°/45°/-45°] 2S using filament winding process. The experimental set up was made for the static and dynamic analysis and performance characteristics of the CE shaft rotated in aerostatic conical journal bearing at high speed (10000-65000 rpm). The comparison of amplitude of vibration decides the maximum operational speed of the shaft with low vibration in aerostatic conical bearings.

Keywords: Carbon-epoxy shaft, Aerostatic conical bearing, Static and dynamic analysis, Stacking sequence, Eccentricity ratio

IPC Code: F16C15/00, C08K3/04

Introduction

Conventional aerostatic shafts, usually made of stainless steel, are not only heavy weight with little damping properties, but are also susceptible to whirling vibration at high rotational speed. Recently, high precision and high speed aerostatic bearing systems have been widely used because of low friction and low heat generation. However, the aerostatic bearing systems have low radial and axial stiffness and poor damping properties due to low viscosity of air, and consequently have a low starting value of whirl vibration if heavy metallic shafts are employed. These problems associated with metallic shafts can be overcome by incorporating the composite shafts made of carbon-epoxy (CE) shaft in aerostatic conical bearing (ACB). Ahuja1 deigned, developed and manufactured the aerostatic-aerodynamic as well as hydrostatic-hydrodynamic conical journal bearings. Bang & Lee2 studied a high-speed air spindle composed of a CE shaft and two

flanges were designed for critical speed, considering both the deflection due to bending load and the radial expansion due to centrifugal force and rise in temperature during high-speed rotation. Lee & Choi3 designed a high-speed aerostatic spindle using high modulus carbon fiber-epoxy composite material for the first time. Using the developed aerostatic spindle bearing system, its static and dynamic characteristics were compared with those of a comparable stainless steel aerostatic spindle. Cho et al4 manufactured a hybrid one piece drive shaft composed of carbon fiber epoxy composite and aluminum tube by co-curing the carbon fiber on the aluminum tube. From dynamic tests, it was found that the first natural bending frequency and minimum static torque transmission capability of the hybrid shaft were 9000 rpm and 3550 N-m. Bert & Kim5 presented a simplified theory for predicting the first-order critical speed of a shear deformable, composite-material drive shaft, modeled as a Bresse-Timoshenko beam, generalized to include bending-twisting coupling. Philippidis et al6 carried out the statistical aspects of strength and elastic properties of carbon/epoxy (C/Ep) filament wound composites through a series of static tensile and

_______________ *Author for correspondence Tel: 9120-25507210 E-mail: [email protected]; [email protected]

J SCI IND RES VOL. 64, AUGUST 2005

2

compressive tests. Singh & Gupta7 performed rotor dynamic experiments on two hollow tubular (C/Ep) filament wound composite shaft. Ingle et al8 carried out micro-macro mechanical analysis of composite laminate. The global and local stresses and strains, failure theory and strength ratios were also carried out and the author concluded that [0°/90°/45°/-45°] 2s;3s is the best suitable stacking sequence for CE shaft.

This study presents experimental investigation on performance characteristics and natural frequency analysis of high-speed CE shaft in aerostatic conical journal bearings9,10 for the high-speed CNC grinding machines and the centrifuges. Design of CE Composite Shaft

Weight of CE shaft should be as light as possible to improve its natural frequency. CE shaft was designed by incorporating the conventional method.

Torque Transmission Capabilities of Adhesive Joint for CE Shaft

The torque transmission capabilities of the adhesively joined composite shaft are much dependent on the adhesive thickness between the composite shaft and the steel connectors (Fig. 1), the bonding length and the thickness of the adherent as well as the surface roughness of adherents. The stresses in the CE shaft are calculated assuming the linear properties of the carbon/epoxy composite, while nonlinear properties are used for the epoxy adhesive and the steel connector. The relationship between the nonlinear shear stress τa and the shear of

adhesives ηa is modeled by the following exponential form,

a fτ = f (ηa) = a fτ {1–exp(–Ga / a fτ * ηa}

where a fτ and Ga represent ultimate shear strength and shear modulus of adhesive, respectively. Torque transmission capability is defined as the torque value when the failure index reached one. In this study, CE shaft with a stacking sequence of [0°/90°/45°/-45°]2s;3s are selected for the torque transmission capability. The ply angle of innermost layer of composite shaft in contact with the adhesive plays vital role in its torque transmission capacity. Required torque capacity of aerostatic shaft is calculated by the following equation:

602

HTnπ

= … (1)

where T is torque capacity; H, motor power; and n, rpm. Since the maximum required torque capacity of CE shaft is quite below than the obtained value with 0° ply angle at the inner most layer at the speed of 100,000 rpm, thus the aerostatic conical journal bearing is suitable for a high-speed application.

The governing equation of the shear stress ciτ at the inner radius of the composite along the adhesive length la is expressed as follows:

2

1 22 0cia ci a

ddyτ

βη τ β η+ + = … (2)

Fig. 1⎯Single lap joint between carbon-epoxy shaft and steel connector

INGLE & AHUJA: HIGH-SPEED CARBON – EPOXY SHAFT IN AEROSTATIC CONICAL JOURNAL BEARINGS

3

Table 2⎯Specifications of the air bearing

Air density (ρo and ρs) Dynamic air viscosity (μ) Specific heat ratio (γ) Supply pressure (ρs) Atmosphere pressure (ρo) Pocket diam Bearing diam Bearing length Semi cone angle (∝), deg. Radial clearance (C) Orifice coefficient (Cd) Orifice diam No. of orifices No. of grooves & its size RL capacity Axial load capacity Concentric radial stiffness Concentric axial stiffness Flow rate for both bearings Pumping power dissipated Total power dissipated

1.220 kg/m3 1.8 E-5N s/m2 1.4 0.45 MPa 0.1013 MPa 2 mm 42 mm 42 mm 10° 30 μm 0.6 0.3 mm 32 4 Nos.; 6.0 mm x 3.5mm 157.6 N 110.7 N 9.261 MN/m 2.116 MN/m 7.427x10-4 m3/sec 0.448 HP 0.896 HP

Where 1β and 2β are expressed in Eqs 3 and 4

22 ( )1 so ci a so c

c a c ci s s

r r df r JIJ d G r J G

⎛ ⎞= − +⎜ ⎟

⎝ ⎠

π ηβ

ζλ η … (3)

22 ( )1 so ci a so

ac a c s

r r df r TI dJ d G J dy

⎛ ⎞= − +⎜ ⎟

⎝ ⎠

π η ζβ ηη λ

… (4)

where rso and rci are the outer radius of the steel sleeves and the inner radius of the composite; ζ is a non dimensional variable, which has the role of a weighting factor; λ is the adhesive thickness; and Fc, Gc, Js and Gs are the polar moments of inertia and the shear moduli of the composite and the sleeve,

Fig. 2⎯The torque transmission capabilities with respect to bonding length and ply angle (bond thickness, 0.5mm)

respectively (Tables 1 & 2). Fig. 2 shows the effect of ply angle of inner most layer on the torque transmission capabilities of adhesive joint between CE shaft and steel connector. Design of Aerostatic Conical Bearing

ACBs have two significant advantages compared to cylindrical journal and separate thrust bearings: i) By replacing two bearings with one there is an economy of flow rate, power and number of parts; and ii), Clearance is easily adjustable on assembly. ACB was designed on the basis of assumed data. Since ACBs are normally used for high-speed applications, a speed of 80,000 rpm was taken for design basis (Table 2).

Natural Frequency Analysis Analytical Approach using Kim-Bert Theory

The shaft rotates at constant speed and has a uniform, circular cross-section (either solid or hollow), i.e., no imperfection. For simplicity, the following hypotheses are selected as the basis for the analysis: (i) The shaft is perfectly balanced, i.e., the mass center coincides the geometric center; (ii) There

Table 1⎯Design variables of the carbon-epoxy shaft

Inner diam of shaft Outer diam of shaft First step diam Second step diam Composite length of shaft Overall length of shaft Shaft section shape Self weight of shaft (one step) Self weight of shaft (two step) Radial stiffness of air bearing Max operating speed

18 mm 22 mm 25 mm 28 mm 208 mm 336 mm Hollow 725 g 730 g 9.261 MN/m 80,000 rpm

For carbon-epoxy shaft (a) For one-step shaft, 16 layers max (b) For two-step shaft, 24 layers max Stacking sequence [0°/90°/45°/-45°] 2s; 3s Stacking thickness = 0.218 mm For steel connector Adherent length = 20 mm Adherent thickness = 0.5mm


4

is no axial force and no axial torque; (iii) All damping and nonlinear effects are omitted; and (iv) The analysis includes bending, twisting, and bending-twisting coupling as well as distributed lateral, torsional, and rotatory inertia and gyroscopic action.

A Cartesian coordinate system fixed in space is used; x is measured along the axis of the shaft. Let v and w represents the displacement in the y and z directions and φ be the angle of twist. Then the equations of motion for bending in the xy and xz planes and twisting about the x-axis can be written as:

4 2 2

1 1 12 2 2 2E I C T SAx x x tν φ ν∂ ∂ ∂

+ +∂ ∂ ∂ ∂

2 3

2 2 22 0Jx t x tν ωλ

⎛ ⎞∂ ∂− + Ω =⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠

4 2 2

1 2 22 2 2 2

wE I C T SAx x x t

φ ν∂ ∂ ∂+ +

∂ ∂ ∂ ∂

4 3

2 2 22 0Jx t x tν ωλ

⎛ ⎞∂ ∂− − Ω =⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠

4 2 2 2

1 22 2 2 2 2 2 0TwC T C T C J

x x t t t tν φ φ∂ ∂ ∂ ∂

+ + − =∂ ∂ ∂ ∂ ∂ ∂

l … (5)

here, A is cross-sectional area; C1T & C2T, bending twisting coupling coefficients; CT, torsional stiffness; EI, flexural stiffness; J, area polar moment of inertia; t, time; ρ, material destiny; and Ω, rotational speed.

The absence of imperfections implies that E1I1 = E1I2 = CB and C1T = C2T = CBT which yields

4 2 2

2 2 2 2B BTr rC C A

x x x tφ λ∂ ∂ ∂

+ +∂ ∂ ∂ ∂

4 3

2 2 22 0r rJ ix t x t

λ⎛ ⎞∂ ∂

− + Ω =⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ … (6)

and Eq. (3) becomes

4 2 2

2 2 2 2 0BT TrC C A

x x x tφ φλ∂ ∂ ∂

+ + =∂ ∂ ∂ ∂

… (7)

Assuming normal modes, one can write

( , ) ( ) , ( , ) ( )i t i tr x t R x e x t Q x eω ωφ= = … (8) where ω is the circular natural frequency. Thus, PDE’s are reduced to the following ODE’s

2 2'' ( 2 ) '' 0IVB BTC R C Q A R J Rρ ω ρ ω ω+ − + − Ω =

… (9)

where ( ) IV denotes d4 ( ) / dx4, etc.

4

2 2BT x

T x

C dQC d Jρ ω

−=

+ … (10)

where dx denotes d/dx.

2 24 2 2

2 2 ( 2 ) ( ) 0BT XB X X

T X

C dC d A d RC d J

ρ ω ωρ ω

⎡ ⎤− − − Ω =⎢ ⎥+⎣ ⎦

… (11)

Considering the boundary conditions to be pinned at each end, one can take the mode shape to be

R(x) = R0 sin λ x ; λ = π / L … (12)

where L is the length of the shaft. Reduction to Special Cases Case 1: No coupling and no gyroscopic action. Thus

CBT = 0 and J = 0 (13)

This is the frequency of a Bernoulli-Euler beam. Case 2: No coupling. Now

CBT = 0 (14)

For forward precession, ω = Ω

42

2

( / )1 ( / )

Bcrfwd

C AJ Aρ λω

λ=

− … (15)

For backward precession, ω = –Ω

42

2

( / )1 3( / )

Bcrbwd

C AJ Aρ λω

λ=

+ … (16)

The critical speeds with various couplings of CE shafts are as follows: Bending-twisting, 33929.7; No coupling, 27894.9; and No gyroscopic and bending-twisting, 27441.9. It is observed that the effect of coupling mechanisms in the shaft tends to increase the first critical speed. The increase is about 1.2 times the speed without these mechanisms. Also the forward and the backward precessional speeds remains the same without the coupling mechanisms included. The natural frequency of shaft is calculated by incorporating the coupling effect includes bending, twisting, and bending-twisting coupling as well as distributed lateral, torsional, and rotatory inertia and gyroscopic action.


5

FEM Approach Using Ansys 5.4 In this approach, shaft is analyzed using ANSYS

5.4 with Shell 99, Solid 45 and 8 noded elements. Fig. 3 depicts meshing of two-step CE shaft with stacking sequence [0°/90°/45°/-45°] 3s conical bearing bushes and connectors. The modal analysis with reduced matrix method was done by selecting 20 elements along circumference and 40 elements along length. The maximum operating rotational speed of the shaft in aerostatic bearing is limited by the natural frequency of the shaft. Therefore, main design objective of CE shaft is to increase natural frequency of the shaft in aerostatic bearings. Here static and dynamic characteristics of the one step and two step CE shaft having stacking sequence [0°/90°/45°/ -45°]2s;3s with 0° at the outer most layer as well as inner most layer are investigated through finite element analysis and the results are compared with steel shaft of same dimensions.

For 3.5 mm wall thickness, if the number of layers are increased from 8 to 10 layers for set 1, natural frequency of the one step shaft without conical bearing bushes, connectors and disc decrease by 9.3, 8.2 and 3.9 percent respectively (Figs 4 & 5). It is further decreased by 15.4, 28.2 and 16.0 percent for set 2, whereas for set 3 all the three frequencies increased by 5.0, 3.0 and 2.3 percent respectively. All the three frequencies are decreased by 19.6, 7.0 and 9.3 percent for set 4. It is observed that the set 1 stacking sequence for 8 layers has high natural frequency than staking sequence of set 1 for 10 layers. Thus, for the same wall thickness, with increase in number of layers, the natural frequency decreases as the layer thickness decreases. Hence, considering the

manufacturing simplicity as well as to include the shear moduli effect, the most suitable stacking sequence [0°/90°/45°/-45°]2s;3s is selected for the shaft. All the three natural frequencies are slightly more for the step 1(one step) shaft than step 2 (two steps) shaft due to increase in the weight of the shaft (Fig. 6). By providing the more number of steps to the shaft, the wall thickness as well as number of layers are increased, therefore as discussed earlier, by increasing the wall thickness with increase in number

Fig. 3⎯Meshing of two-step carbon- epoxy shaft with stacking sequence [0°/90°/45°/-45°] 3s conical bearing bushes and connectors

Fig. 4⎯Effect of different sets of stacking sequence on natural frequency of carbon-epoxy shaft with 8 layers without bushes, connectors and disc

Set 1 [0°/90°/45°/-45°]s Set 2 [45°/-45°/90°/0°]s Set 3 [0°/0°/90°/90°]s Set 4 [0°/0°/45°/-45°]s

Fig. 5⎯Effect of different sets of stacking sequence on natural frequency of carbon-epoxy shaft with 10 layers without bushes, connectors and disc

Set 1 [0°/0°/90°/45°/-45°]s Set 2 [45°/45°/-45°/90°/0°]s Set 3 [0°/0°/0°/90°/90°]s Set 4 [0°/0°/0°/45°/-45°]s


6

of layers, the natural frequency decreases. For one step shaft (wall thickness, 2 mm) the first three natural frequencies of CE shaft are 4019.4, 5351.1 and 1378.4 Hz, respectively and for steel shaft are 696.13, 754.53 and 1239.1Hz, respectively (Fig. 7). All the three natural frequencies in steel shaft are decreased by 82.68, 85.89 and 91.00 percent, respectively, for the same wall thickness. For two-step shaft (wall thickness, 2 mm), the first three natural frequencies of CE shaft are 3670.3, 5083.2 and 12564Hz, respectively and for steel shaft are 619.26, 690.69 and 1173.6Hz, respectively. It is further observed that all the three natural frequencies in steel shaft are decreased by 83.12, 86.41 and 90.65 percent, respectively, for the same wall thickness. The comparison of first natural frequency of various composite shafts, when ply angles are 0°, 30°, 45°, 60°, 90°, showed that the natural frequency in Graphite–epoxy shaft is quite high whereas it has a moderate value for CE shaft (Fig. 8). The Glass- Epoxy shaft has low natural frequency. Since carbon fibers are available with ease in manufacturing by filament winding method, hence these fibers are selected for analysis purpose.

Fig. 8⎯Comparison of natural frequency of various composite shafts when ply angles are 0°, 30°, 45°, 60°, 90°

Fig. 9⎯Block diagram of experimental set up Experimental Study

The block diagram (Fig. 9) consists of ACB assembly unit, pneumatic motor, rotameter, oil filter-air filter regulator unit, air dryer and two compressors etc. The medium duty compressor is incorporated for supply of air through air dryer and rotameter to conical bearing assembly. The heavy-duty compressor is incorporated for supply of air through filter unit to pneumatic motor. The housing of ACB assembly consists of CE shaft, conical bushes and spacers. The bearing end caps are fitted from both ends with rubber seal. The assembly provides two separate inlet manifold and air is allowed to enter through the two-plane admission zone to the system and escapes through the exhaust port. All the components were given precision work to ensure closer tolerances, were subsequently heat treated, ground lapped and balanced before assembly. The radial clearance

Fig. 6⎯Effect of steps on carbon-epoxy shaft with stacking sequence [0°/90°/45°/-45°]2s ; 3s on its natural frequency

Fig. 7⎯Comparison of first three natural frequencies of carbon-epoxy shafts and steel shafts


7

obtained on assembly is 30 microns. The air supplied to the system is passed through an air dryer and a 5-micron filter. The airflow is controlled through a pressure regulator. The flow of air to the bearing is permitted through air dryer so that moisture effect can be neglected. The air motor of 0.75 hp with 18000 rpm is used to rotate the composite shaft with about 4.33 times greater speed in ACB through belt drive. At other end of the shaft, a rotor is mounted and for application of load on shaft, the small leather belt is passed over the shaft with the pan at its end.

The main objective of the experimental work conducted is to study the static and dynamic deflection analysis, performance characteristics and vibration spectrum analysis of CE shaft in ACB at various speeds. Fig. 10 depicts the photograph of actual experimental setup with necessary instrumen-tations. For the experimental purpose, two CE shafts (one step and two steps) with stacking sequence [0°/90°/45°/-45°]2S;3S having 16 and 24 layers respec-tively are manufactured using filament winding process. The effect of flow rate as well as radial load (RL) on static and dynamic deflection of shaft at various speeds was carried out. The laser type deflection-measuring instrument is used to measure

horizontal and vertical deflection of shaft at various load and speed. For the measurement of vibration spectrum, a dynamic structural analyzer is used. The two accelerometers were mounted on the top of each bearing and vibration spectrum was noted at various load and shaft speeds. For vibration spectrum analysis, all parameters were kept same as used for the measurement of deflections.

Results & Discussion Static, Dynamic and Vibration Spectrum Analysis

All the deflection curves of shaft (rpm, 65,000; RL, 3.0312 N) are steady except the substantial change in the static deflection curve (Fig. 11). The vertical and horizontal curves are slightly shifted towards the dynamic deflection curve. The static and dynamic deflection curves are closer with increase in flow rate. With further increase in RLs [(4.0122 N, Fig. 12), (5.483 N, Fig. 13) and (5.9742 N, Fig. 14)], airflow rates changes sharply. With increase in speed (40,000 - 65,000 rpm), there is a further decrease in static and dynamic deflection at 31 NLPM. The increase in flow rate (31-35 NLPM) increases the static and dynamic deflections. For the shaft speed of 65,000 rpm, the shaft deflection continuously changes with increase in

Fig. 10⎯Photograph depicting aerostatic conical bearing unit with instrumentations


8

Fig. 11⎯Effect of air flow rate on shaft defection at RL = 3.0312 N when shaft speed is 65,000 rpm

Fig. 12⎯Effect of air flow rate on shaft defection at RL = 4.0122N when shaft speed is 65,000 rpm



Fig. 15⎯Effect of RL on eccentricity ratio at various shaft speeds [air flow rate 35 NLPM, supply pressure 4.00E+05 N /m2)]

Fig. 16⎯Effect of RL on static deflection with the variation in flow rate when shaft speed is 10,000 rpm

speed (10,000-65,000 rpm). The increase in speed increases the magnitude of vertical deflection, which leads to the vibration in shaft.

With increase in RL at various shaft speeds (10,000 - 65,000 rpm), eccentricity ratio (ER) increased from 5.5E-1 to 7.8E-1 (Fig. 15). For a speed range of 10,000 to 40,000 rpm, ER decreases with increase in air flow rate and supply pressure. ER decreases with increase in RL for a speed range above 50,000 rpm.

With increase in the flow rate (20-40 NLPM) and RL (3.0312-5.9742 N) at constant shaft speed of 10,000 rpm, static deflection first increases and then subsequently decreases (Fig. 16). At same parameters, dynamic deflection decreases with increase in the flow rate and then decreases as the flow rate is further increased (Fig. 17). As the RL is increased, dynamic deflection increases with increase in flow rate, and then with further increase in RL, the dynamic deflection decreases as the flow rate is increased.

At shaft speed of 40,000 rpm, static deflection of shaft (Fig. 18) is maximum (RL, 4.0122N) and minimum (RL, 5.9742N), whereas the dynamic


9

deflection of shaft (Fig. 19) is maximum (RL, 3.0312N) and minimum (RL, 5.9742N). With increase in RL, dynamic deflection of shaft increases with increase in flow rate and then with further increase in RL, dynamic deflection decreases as flow rate is increased.

When CE shaft rotates at 10,000 rpm (RL, 5.9742 N), the amplitude of vibration is large at right hand side bearing which is away from belt drive and motor (Fig. 20). The maximum amplitude of vibration was observed at 139.534 m/sec2. Similarly, when CE shaft rotates at 40,000 rpm (RL, 5.9742 N), the amplitude of vibration is large at right hand side

bearing which is away from belt drive and motor (Fig. 21). The maximum amplitude was observed at 151.127 m/sec2.

When RL decreases, the magnitude of vibration increases (Fig. 22) more (7.28 %) at 10,000 rpm than (6.78 %) at 65,000 rpm. It means that the maximum amplitude of vibration at high speed is comparatively less in magnitude provided the speed of shaft should be above critical speed and below natural frequency. As the CE shaft supported in aerostatic bearing has

Fig. 17⎯Effect of RL on dynamic deflection with the variation in flow rate when shaft speed is 10,000 rpm

Fig. 18⎯Effect of RL on static deflection with the variation in flow rate when shaft speed is 40,000 rpm

Fig. 19⎯Effect of RL on dynamic deflection with the variation in flow rate when shaft speed is 40,000 rpm

Fig. 20⎯Vibration spectrum of carbon-epoxy shaft in aerostatic conical bearing at 10,000 rpm, when RL = 5.9742 N

Fig. 21⎯Vibration spectrum of carbon-epoxy shaft in aerostatic conical bearing at 40,000 rpm, when RL = 5.9742 N

Fig. 22⎯Effect of RL and shaft speed on amplitude of vibration


10

high damping therefore, it is concluded that with RL 6N, the shaft runs at 65,000 rpm in more stable manner.

Conclusions

Torque transmission capabilities of adhesive joint between CE shaft and steel connector is dependent on ply angle of the inner most layer. Torque transmitted with 0° ply angle is 354.68 N-m, which is quite higher than the required torque for CNC grinding machine. Using Kim-Bert theory, critical speed is determined with and without coupling effect and using ANSYS 5.4, the natural frequency was checked for the selected stacking sequence. Among all the stacking sequences, [0°/90°/45°/-45°] 2s;3s was found the best suitable for CE shaft. Static and dynamic deflection of shaft plays vital role in selection of ER as it changes with RL. ER is dependent on supply pressure and RL, connected by generalized equation showing expo-nential relationship, with high degree of regression coefficient. The stiffness in aerostatic bearing rises with increase in dynamic deflection for constant supply pressure. Maximum RL carrying capacity was found at: Bearing clearance, 30 x 10-6 m; and, Supply pressure, 4.5E+5 N/ mm2. CE shaft rotates smoothly in ACB up to 70,000 rpm.

Acknowledgements

Authors are grateful to AICTE, New Delhi for financial grant. They are also thankful to Dr K Gupta,

IIT, New Delhi for valuable suggestions. Thanks are also due to Dr Rajeev Vaghmare, of EMQD, ISRO, Ahmedabad for the test report for carbon fibers.

References 1 Ahuja, B B, Computer aided study and analysis of dynamic

characteristics of a CNC machining system, Ph D Thesis, University of Pune, India, 1996.

2 Bang Kyung Geun & Lee Dai Gil, Design of carbon fiber composite shafts for high-speed air spindles, J Comp Struct, 55 (2002) 247-259.

3 Lee Dai Gil & Choi Jin Kyung, Design and manufacture of an aerostatic spindle bearing system with carbon fiber- epoxy composites, J Comp Mater, 34 (2000) 1150-1175.

4 Cho Durk Hyun, Lee Dai Gill & Choi Jin Ho, Manufacture of one-piece automotive drive shafts with aluminum and composite materials, J Comp Struct, 38 (1997) 309-319.

5 Bert C W & Kim C D, Whirling of composite material drive shafts including bending and twisting, J Vib Acoust, 117 (1995) 17-21.

6 Philippidis T P, Lekou D J & Aggelis D G, Mechanical property distribution of CFRP filament wound composites, J Comp Struct, 45 (1999) 41-50.

7 Singh S P & Gupta K, Rotor dynamic experiments on composite shafts, J Comp Tech Res, 18 (1996) 256-264.

8 Ingle R B, Ahuja B B & Joshi S M, Analysis of carbon-epoxy shaft in aerostatic conical journal bearings- no rotational case, J Inst Engr (India), 85 (2004) 69-77.

9 Powell J W, Design of Aerostatic Bearings (The Machinery Publications Co. Ltd., Brighton) 1970.

10 Jones Robert M, Mechanics of Composite Materials (McGraw- Hill Kogakusha, Ltd., Tokyo) 1975.

Sehgal/JSIR-648…formatted S DHARAN

an experimental investigation on performance ...nopr.niscair.res.in/bitstream/123456789/5111/1/jsir...

Documents