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Experimental investigation of conical bearings lubricated with non-newtonian fluids
157
Wear, 67 (1981) 157 - 165 0 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
EXPERIMENTAL INVESTIGATION OF CONICAL LUBRICATED WITH NON-NEWTONIAN FLUIDS
A. EL-KAYAR,
BEARINGS
E. A. SALEM and M. F. KHALIL
Mechanical Engineering Alexandria (Egypt)
Department,
Faculty of Engineering,
Alexandria
University,
Department,
Faculty of Engineering,
Minia University, Minia
M. BEDEWI Mechanical Engineering (Egypt) (Received August 8,1979;
in revised form December 10, 1979)
Summary
The performance characteristics of externally pressurized conical bearings lubricated with non-newtonian fluids including the effects of film thickness, rotational speed and polymer concentration in tap water were investigated experimentally. The results are presented and compared with earlier theoretical results.
1. Introduction
A theoretical analysis of the effect of different parameters including fluid film thickness, rotational speed, recess radius ratio, flow behaviour index, cone angle and supply pressure has been presented by El-Kayar et al. [ 11. The results of an experimental programme designed to investigate these predictions are presented in this paper.
2. Experimental
work
The effects of rotational speed, film thickness and polymer concentration in tap water on the pressure distribution along the flow between conical bearing elements, the volume flow rate, the load-carrying capacity and the stiffness were investigated experimentally to verify earlier theoretical predictions [l]. The bearing was mounted in the test apparatus shown in Fig. 1. The fluid measuring system is shown in Fig. 2. The conical pad and bed were truncated steel cones of the following dimensions: cone apex angle 201,60”; maximum diameter, 118.23 mm;
Fig. 1. Test apparatus: 1, calibrated ring; 2, load transmission shaft; 3, pad; 4, bed; 5, pulley; 6, bed carrier,
Prass”
re gouge
reciiculoling to”k
Multitube
man~m~tPr
Fig. 2. Hydrklic
measuring system.
159
minimum diameter, 38.24 mm; recess depth, 10 mm; supply hole diameter, 7 mm. Solutions of sodium carboxymethyl starch (C,MS) in water, which are pseudoplastic non-newtonian fluids, were used as lubricants. The rheological properties of these solutions at room temperature are given in Table 1. TABLE 1 Rheological parameters of the non-newtonian fluids Fluid composition (wt.% C,MS in H20)
q0 at 2jz”C (Nsm )
Behaviour index n
Fluid density p (g cmh3)
1.0 2.0
0.024 0.040
0.985 0.975
1.01 1.02
The following experiments were carried out. (1) The rheological properties of the non-newtonian fluids were determined. (2) The pressure distribution along the fluid flow was measured for various values of film thickness, rotational speed and polymer concentration in tap water. (3) The load-carrying capacity L was measured at different values of film thickness and polymer concentration. (4) The relation between flow rate and film thickness at different polymer concentrations was determined. The following measuring instruments were used. The rheological properties of the non-newtonian fluids were determined with a rotary viscometer (Rheo-test type), and the pressure distribution in the fluid film was measured with a mercury-in-glass manometer. Two different calibrated orifice plates were used to measure the volume flow rates for the three polymer concentrations. The load was measured with a calibrated proof ring, and a dial gauge with 0.001 mm graduations was used to measure the film thickness.
3. Discussion 3.1. Pressure distribution The results of a series of measurements of the pressure distribution along the fluid flow for an externally pressurized conical bearing are shown in Figs. 3 - 9. These results show that increasing the rotational speed and the polymer concentration and decreasing the film thickness improves the pressure distribution. A comparison between the theoretical isothermal and experimental dimensionless pressure distribution P/PI for a polymer concentration of
160
0.0 o,o
0.2
0.4
O-6
08
1.0
R/R3
00
02
04
O-6
OS
R/R)
1 ‘0
fb)
@I
Fig. 3. Effect of film thickness on pressure distribution (P, = 150 kN rnm2;polymer concentration, 5000 ppm; Rz/R3 = 0.47; (Y= 30” ; al r=10 mm): (a) N = 1000 rev min-‘; (b) N = 2800 rev min-l.
fz
J?
F:
F: 7.0
3 0
08
0.8
H=O,,mm-----
I
~~1 i __i_ -+._.
0.20
-
0,6
“___
L__._i-__
h-_-L_
06
1
I
-3
I
j
I
0.15
--e--w”
04
02
no
Fig. 4. Effect of the film thickness on the pressure distribution (PS = 150 kN mw2; polymer concentration, 10 000 ppm; Rz/Ra = 0.47;CY= 30";'11= 10 mm): (a) N = 2800 rev min-l; (b) N = 1000 rev min-1.
10 000 ppm (n = 0.985) is shown in Figs. 10 - 12. Agreement between the results is reasonable. However, as the rotational speed N increases, some deviation between the results occurs. This deviation can be attributed to the assumption of a linear tangent&d velocity and the negkt of the inert& due to the fluid ffow.
161
0.8 H=O.l
m m
H = 0.1 mm
-*--*
__f_ 0.6
0.2
0 .4
0%
0.8
w
1.0
R/R3
0.20
0.0
0.2
0.4
0.6
0.8
-A-
1.0
--A--
R/R3
@I
Fig. 5. Effect of the film thickness on the pressure distribution (Ps = 150 kN me2; polymer concentration, 20 000 ppm;R2/Ra = 0.47; ar= 30”;~~ = 10 mm): (a) N = 1000 rev min-’ ; (b) N = 2800 rev min-‘.
0.8 -y0.6
2000
-
-x-
-x---y-
-
2000
-
0.4
0.0 (a)
0.2
0.4
0.6
0.8
1 .o
R/R3
0.0
0.2
04
0.6
0.8
10
R/R3
(b)
Fig. 6. Effect of the rotational speed on the pressure distribution (P, = 150 kN mP2; polymer concentration, 5000 ppm; R2/R3 = 0.47;CY= 30";a1 = 10 mm): (a) H = 0.05mm; (b) H = 0.15 mm.
3.2. Volume flow rate Q The experimental interrelation between the volume flow rate of the polymer solution and the film thickness for various polymer concentrations is shown in Fig. 13. The rate of decrease of Q with decreasing film thickness increases as the film thickness decreases. The volume flow rate at the same film thickness increases as the concentration decreases.
00
02
04
06
og
I.0
R/R3
(a1
0.0
O-2
0.40
06
08
IO
FUR3
@I
Fig. 7, Effect of the rotational speed on the pressure distribution (P, = 150 kN me2; polymer concentration, 10 000 ppm; R2/R3 = 0.47;(Y= 30";al = 10 mm): (a) H = 0.05mm;(b) H = 0.15 mm. +5 t 0
N- 500 rpm
08
-+--
+-
N
=500rpm
--x---J(-
-+---A-x----x-
06
2000
v
08
1.0
04
00 00
(a)
02
04
06
08
10
R/R,
00
02
04
06
R/R3
@I
Fig. 8. Effect of the rotational speed on the pressure distribution (Ps = 150 kN m-‘; polymer ~on~entrat~on* 20 000 ppm; R&s = 0.47; ty = 30” ; ~1 = 10 mm): (a) H = 0.05 mm;(b) H = 0.15mm.
3.3. Load factor Lf Figure 14 shows that the load factor increases with decreasing film thickness and polymer conce~tmtion. 3.4. Bearing stiffness X The stiffness can be determined from the slope of the curve of loadcarrying capacity uersus film thickness at constant supply pressure (Fig. 15)
163
0.8
0.6
10000
---
20000
-
0.4
0.2
I
A
00 02
O-4
0.6
08
10
0.0 0.0
R/R3
02
0.4
0 6
0 8
1.0
(b)
Fig. 9. Effect of the polymer concentration on the pressure distribution (PS = 150 kN mm2; N = 1000 rev min-l; Rz/Ra = 0.47;(Y= 30";a1 = 10 mm): (a) H = 0.05mm; (b) H = 0.15 mm.
Fig. 10. Comparison between the theoretical and experimental pressure distributions. Fig. 11. Comparison between the theoretical and experimental pressure distributions.
R/R3
164
00
3 35
c 13
015
0 20
0 25
H(m)
Fig. 12. Comparison between the theoretical and experimental pressure distributions. Fig. 13. Effect of the concentration on the volume flow rate (Ps= 150 kN me2; N = 1000 rev min-l; Rg/Ra = 0.47; 01 = 30” ; al = 10 mm).
lOOC __c_ t-
00
I-
005
5000
ppm
10000
/
0 10
0 15
p --,
3 20
--x--
c 25
Yh4
Fig. 14. Effect of the concentration on the load factor (P, = 150 kN rne2; N = 1000 rev min-l; R2/R3 = 0.47;~~=30~;al = 10mm). Fig. 15. Effect of the concentration on the stiffness (P, = 150 kN me2; N = 1000 rev mm * -1;R2/R3=0.47;0i=300;al = 10mm).
and is found to increase with decreasing film thkkness and increasing concentration.
165
4. Conclusions The following conclusions can be drawn. (1) Increasing the speed and concentration and decreasing the film thickness improves the pressure distribution. (2) The one-dimensional viscous inertia flow treatment in which a linear tangential velocity was assumed and the inertia due to the flow was neglected gives a reasonable prediction of the pressure distribution. (3) Increasing the polymer concentration results in a decrease in the volume flow rate and load factor and makes the bearing stiffer.
Nomenclature =1
H L Lf
k
P Pl
ps Q
R2 R3
2a 7)O x
recess depth (mm) vertical film thickness (mm) load-carrying capacity (N) L/nR32P1, load factor hehaviour index rotational speed (rev min -1 ) pressure (N mP2) inlet pressure (N mW2) supply pressure (N mh2) discharge (m3 s-l) recess radius (m) outlet bed radius (m) cone apex angle (rad) viscosit_y20f the non-newtonian fluid at the reference shear rate (D, = 1 s-l) (Nsm ) -dL/dH, stiffness (N mm-l)
Reference 1 A. El-Kayar, E. A. Salem, M. F. Khalil and M. Bedewi, Wear, 67 (1981)
133.
Wear, 67 (1981) 157 - 165 0 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
EXPERIMENTAL INVESTIGATION OF CONICAL LUBRICATED WITH NON-NEWTONIAN FLUIDS
A. EL-KAYAR,
BEARINGS
E. A. SALEM and M. F. KHALIL
Mechanical Engineering Alexandria (Egypt)
Department,
Faculty of Engineering,
Alexandria
University,
Department,
Faculty of Engineering,
Minia University, Minia
M. BEDEWI Mechanical Engineering (Egypt) (Received August 8,1979;
in revised form December 10, 1979)
Summary
The performance characteristics of externally pressurized conical bearings lubricated with non-newtonian fluids including the effects of film thickness, rotational speed and polymer concentration in tap water were investigated experimentally. The results are presented and compared with earlier theoretical results.
1. Introduction
A theoretical analysis of the effect of different parameters including fluid film thickness, rotational speed, recess radius ratio, flow behaviour index, cone angle and supply pressure has been presented by El-Kayar et al. [ 11. The results of an experimental programme designed to investigate these predictions are presented in this paper.
2. Experimental
work
The effects of rotational speed, film thickness and polymer concentration in tap water on the pressure distribution along the flow between conical bearing elements, the volume flow rate, the load-carrying capacity and the stiffness were investigated experimentally to verify earlier theoretical predictions [l]. The bearing was mounted in the test apparatus shown in Fig. 1. The fluid measuring system is shown in Fig. 2. The conical pad and bed were truncated steel cones of the following dimensions: cone apex angle 201,60”; maximum diameter, 118.23 mm;
Fig. 1. Test apparatus: 1, calibrated ring; 2, load transmission shaft; 3, pad; 4, bed; 5, pulley; 6, bed carrier,
Prass”
re gouge
reciiculoling to”k
Multitube
man~m~tPr
Fig. 2. Hydrklic
measuring system.
159
minimum diameter, 38.24 mm; recess depth, 10 mm; supply hole diameter, 7 mm. Solutions of sodium carboxymethyl starch (C,MS) in water, which are pseudoplastic non-newtonian fluids, were used as lubricants. The rheological properties of these solutions at room temperature are given in Table 1. TABLE 1 Rheological parameters of the non-newtonian fluids Fluid composition (wt.% C,MS in H20)
q0 at 2jz”C (Nsm )
Behaviour index n
Fluid density p (g cmh3)
1.0 2.0
0.024 0.040
0.985 0.975
1.01 1.02
The following experiments were carried out. (1) The rheological properties of the non-newtonian fluids were determined. (2) The pressure distribution along the fluid flow was measured for various values of film thickness, rotational speed and polymer concentration in tap water. (3) The load-carrying capacity L was measured at different values of film thickness and polymer concentration. (4) The relation between flow rate and film thickness at different polymer concentrations was determined. The following measuring instruments were used. The rheological properties of the non-newtonian fluids were determined with a rotary viscometer (Rheo-test type), and the pressure distribution in the fluid film was measured with a mercury-in-glass manometer. Two different calibrated orifice plates were used to measure the volume flow rates for the three polymer concentrations. The load was measured with a calibrated proof ring, and a dial gauge with 0.001 mm graduations was used to measure the film thickness.
3. Discussion 3.1. Pressure distribution The results of a series of measurements of the pressure distribution along the fluid flow for an externally pressurized conical bearing are shown in Figs. 3 - 9. These results show that increasing the rotational speed and the polymer concentration and decreasing the film thickness improves the pressure distribution. A comparison between the theoretical isothermal and experimental dimensionless pressure distribution P/PI for a polymer concentration of
160
0.0 o,o
0.2
0.4
O-6
08
1.0
R/R3
00
02
04
O-6
OS
R/R)
1 ‘0
fb)
@I
Fig. 3. Effect of film thickness on pressure distribution (P, = 150 kN rnm2;polymer concentration, 5000 ppm; Rz/R3 = 0.47; (Y= 30” ; al r=10 mm): (a) N = 1000 rev min-‘; (b) N = 2800 rev min-l.
fz
J?
F:
F: 7.0
3 0
08
0.8
H=O,,mm-----
I
~~1 i __i_ -+._.
0.20
-
0,6
“___
L__._i-__
h-_-L_
06
1
I
-3
I
j
I
0.15
--e--w”
04
02
no
Fig. 4. Effect of the film thickness on the pressure distribution (PS = 150 kN mw2; polymer concentration, 10 000 ppm; Rz/Ra = 0.47;CY= 30";'11= 10 mm): (a) N = 2800 rev min-l; (b) N = 1000 rev min-1.
10 000 ppm (n = 0.985) is shown in Figs. 10 - 12. Agreement between the results is reasonable. However, as the rotational speed N increases, some deviation between the results occurs. This deviation can be attributed to the assumption of a linear tangent&d velocity and the negkt of the inert& due to the fluid ffow.
161
0.8 H=O.l
m m
H = 0.1 mm
-*--*
__f_ 0.6
0.2
0 .4
0%
0.8
w
1.0
R/R3
0.20
0.0
0.2
0.4
0.6
0.8
-A-
1.0
--A--
R/R3
@I
Fig. 5. Effect of the film thickness on the pressure distribution (Ps = 150 kN me2; polymer concentration, 20 000 ppm;R2/Ra = 0.47; ar= 30”;~~ = 10 mm): (a) N = 1000 rev min-’ ; (b) N = 2800 rev min-‘.
0.8 -y0.6
2000
-
-x-
-x---y-
-
2000
-
0.4
0.0 (a)
0.2
0.4
0.6
0.8
1 .o
R/R3
0.0
0.2
04
0.6
0.8
10
R/R3
(b)
Fig. 6. Effect of the rotational speed on the pressure distribution (P, = 150 kN mP2; polymer concentration, 5000 ppm; R2/R3 = 0.47;CY= 30";a1 = 10 mm): (a) H = 0.05mm; (b) H = 0.15 mm.
3.2. Volume flow rate Q The experimental interrelation between the volume flow rate of the polymer solution and the film thickness for various polymer concentrations is shown in Fig. 13. The rate of decrease of Q with decreasing film thickness increases as the film thickness decreases. The volume flow rate at the same film thickness increases as the concentration decreases.
00
02
04
06
og
I.0
R/R3
(a1
0.0
O-2
0.40
06
08
IO
FUR3
@I
Fig. 7, Effect of the rotational speed on the pressure distribution (P, = 150 kN me2; polymer concentration, 10 000 ppm; R2/R3 = 0.47;(Y= 30";al = 10 mm): (a) H = 0.05mm;(b) H = 0.15 mm. +5 t 0
N- 500 rpm
08
-+--
+-
N
=500rpm
--x---J(-
-+---A-x----x-
06
2000
v
08
1.0
04
00 00
(a)
02
04
06
08
10
R/R,
00
02
04
06
R/R3
@I
Fig. 8. Effect of the rotational speed on the pressure distribution (Ps = 150 kN m-‘; polymer ~on~entrat~on* 20 000 ppm; R&s = 0.47; ty = 30” ; ~1 = 10 mm): (a) H = 0.05 mm;(b) H = 0.15mm.
3.3. Load factor Lf Figure 14 shows that the load factor increases with decreasing film thickness and polymer conce~tmtion. 3.4. Bearing stiffness X The stiffness can be determined from the slope of the curve of loadcarrying capacity uersus film thickness at constant supply pressure (Fig. 15)
163
0.8
0.6
10000
---
20000
-
0.4
0.2
I
A
00 02
O-4
0.6
08
10
0.0 0.0
R/R3
02
0.4
0 6
0 8
1.0
(b)
Fig. 9. Effect of the polymer concentration on the pressure distribution (PS = 150 kN mm2; N = 1000 rev min-l; Rz/Ra = 0.47;(Y= 30";a1 = 10 mm): (a) H = 0.05mm; (b) H = 0.15 mm.
Fig. 10. Comparison between the theoretical and experimental pressure distributions. Fig. 11. Comparison between the theoretical and experimental pressure distributions.
R/R3
164
00
3 35
c 13
015
0 20
0 25
H(m)
Fig. 12. Comparison between the theoretical and experimental pressure distributions. Fig. 13. Effect of the concentration on the volume flow rate (Ps= 150 kN me2; N = 1000 rev min-l; Rg/Ra = 0.47; 01 = 30” ; al = 10 mm).
lOOC __c_ t-
00
I-
005
5000
ppm
10000
/
0 10
0 15
p --,
3 20
--x--
c 25
Yh4
Fig. 14. Effect of the concentration on the load factor (P, = 150 kN rne2; N = 1000 rev min-l; R2/R3 = 0.47;~~=30~;al = 10mm). Fig. 15. Effect of the concentration on the stiffness (P, = 150 kN me2; N = 1000 rev mm * -1;R2/R3=0.47;0i=300;al = 10mm).
and is found to increase with decreasing film thkkness and increasing concentration.
165
4. Conclusions The following conclusions can be drawn. (1) Increasing the speed and concentration and decreasing the film thickness improves the pressure distribution. (2) The one-dimensional viscous inertia flow treatment in which a linear tangential velocity was assumed and the inertia due to the flow was neglected gives a reasonable prediction of the pressure distribution. (3) Increasing the polymer concentration results in a decrease in the volume flow rate and load factor and makes the bearing stiffer.
Nomenclature =1
H L Lf
k
P Pl
ps Q
R2 R3
2a 7)O x
recess depth (mm) vertical film thickness (mm) load-carrying capacity (N) L/nR32P1, load factor hehaviour index rotational speed (rev min -1 ) pressure (N mP2) inlet pressure (N mW2) supply pressure (N mh2) discharge (m3 s-l) recess radius (m) outlet bed radius (m) cone apex angle (rad) viscosit_y20f the non-newtonian fluid at the reference shear rate (D, = 1 s-l) (Nsm ) -dL/dH, stiffness (N mm-l)
Reference 1 A. El-Kayar, E. A. Salem, M. F. Khalil and M. Bedewi, Wear, 67 (1981)
133.