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Wear of gear of circular-arc tooth-profile: effect of helix angle and oil viscosity
Wear of gear of circular-arc tooth-profile: effect of helix angle and oil viscosity A. M. M. El Bahloul* The results are presented of an experimental investigation carried out at Mansoura University Laboratories aimed at studying the effect of change of helix angle and lubricating oil on wear of a relatively new type of gearing of circular-arc tooth-profile. Eighteen pairs of gears of 6 DP, 91.5 mm pitch diameter and different helix angles were run in power circulating gear test rig at different speeds and transmitting different loads, and the gears were lubricated with oils of different viscosities. It was found that wear increases with increasing helix angle and decreases with increase of oil viscosity. Variations of amount of wear with all the test variables are presented.
Keywords: he//ca/ gears, circular-arc tooth-profiles, lubricating oil ac motor 8/10 hp 1500/3000 r/rain Test Driven shaft 8 bolts MIO /
I /
~g
V-groove
Sec}ion at AA Fig I Layout o/the test rig
Hailing oearlngs
Helical gears of circular-arc tooth-profiles are conformal gears with point contact between teeth changing to an elliptical area under load 1-3 . Contact between these gears is along the face and no progressive contact occurs on the profile. In a previous paper 4 , the experimental results of a research programme carried out at Mansoura University Laboratories on the effect of load and speed on wear of this type of gearing arc presented. In this paper, the experimental results showing the effect of change of helix angle and viscosity of lubricating oil on wear are introduced.
Test rig The test rig is of the power circulating type where two pairs of gears are carried by two shafts running on rolling bearing as shown in Fig l. The driving shaft carries a graduated torque coupling to measure the transmitted torque. The driven shaft is composed of two parts connected together *Production Engineering Departmenl, t.'acully of Engineering, Mansoura University, Mansoura, Egypt.
TR I BOLOGY international
Loading coupling by a flange coupling. The rig is loaded by applying dead weights at the end of a lever fastened to each flange, thus twisting each part of the shaft relative to the other. The rig is driven by a 8/l 0 hp ac motor running at speeds 1500 and 3000 r/rain, respectively. Table 1 Dimensions and specifications of the test gears
Specifications
*For wheel tFor pinion
DesignA
Design B
Design C
Radii of curvature in normal plane (mm)
6 22.3 42 20 35 103.735t 90.17" 4, 231" 4, 68*
6 33.6 29 18 24 103.735T 90.17" 4.231" 4.68*
6 42.25 24 16 19.8 103.7351" 90.17" 4.231" 4.68*
Radii of curvature along helix angle (mm)
118.2t 128.6"
56.12t 61.1 *
36.2t 39.4*
Bore diameter (mm)
+0.009 30-0.000
+0.009 30-0.000
+0.009 30-0.000
Number of pairs of test gears Helix angle (degrees) Face width (mm) Number of teeth Axial pitch (mm) Blank diameter (mm)
0301-679X/87/040205-05 $03.00 @ Butterworth & Co (Publishers) Ltd
205
El B a h l o u l - wear o f gear o f circular-arc t o o t h - p r o f i l e
Table
2 Characteristics
of the
60o
lubricating oils
Characteristics
Oil A
Oil B
Oil C
54O
40°C Kinematic viscosity at { 50°C 1,100°C Specific gravity Pour point (max. °F) (°C) Flash point (min. °F) (°C) Viscosity index Timken OK load 40 Ib (18 kgf)
653 333 32.4 0.91-0.97 (-3) (260) 70 average -
462 253 30.8 0.901 5 (-15) 465 (241) 95 min. passes
200 118 17.6 0.894 -10 (-23) 405 (207) 92 rain. passes
°% 420L
Speed '500 r / m i n
,oo t
/
! /
T
!
/
.....
.oo I
/ /1
I
/ /,,'¢/,,'
'2°1::
I 1200
1600
2000
2400
2800
3200
Tooth Ioed, kgf
Fig 3 Change of weight of removed metal with tooth load at different speeds for wheel of concave teeth and pinion of convex teeth using gears of design A and oil B; test pair 3 for speed 1500 r/min and test pair 4 for speed 3000 r/min 600
Pinion
Wheel
i
ti
540
i
Design A i
480
I If
Speed 1500 r/min 420
2
E o)
300
....
240
i
180
Design B
Pinion
,.°E
l l
I
,y°.,.
60
I000 1200
I I I
Wheel Pinion
8
Whee]
I ;
I I
3000 r/min
360
'
'
1400
I"
1600 1800 2000
2200 2400 2600
Tooth load, kgf
Fig 4 Change of weight of removed metal with applied tooth load at different speeds for wheel of concave teeth and pinion of convex teeth using gears of design B and oil B; test pair 9 for speed 1500 r/min and test pair 10 for 3000 r/rain Test gears
Wheel
Pinion Design C
Fig 2 Different designs of test gears
206
The test gears were supplied by the General Electric Company Ltd, Rugby, UK. They are of the CirCarC type with the pinion made of 4155 MM steel and the wheel is made of 4164 MM steel. The test gears are of 6 DP (4.23 module), 91.5 mm pitch diameter, 25 ° normal pressure angle, 1.2 overlap ratio, 0.423 mm backlash and 1.6/am surface roughness. They are of different helix angles, number of teeth and face width. Table 1 gives dimensions
August 1987 Vol 20 No 4
E l B a h l o u l -- wear o f gear o f circular-arc t o o t h - p r o f i l e
and specifications of the test gears. Fig 2 shows the different designs of the test gears.
6OO 54O
480
....
Wear of gears of circular-arc tooth-profile was investigated for three designs of test pairs of gears of 22.3 °, 33.6 ° and 42.25 ° helix angles using lubricating oils of 200,462 and 653 C.st. at 40°C kinematic viscosity. The applied tooth loads varied from 1000 to 3000 kgf at intervals of 200 kgf corresponding to transmitting loads varying from 671 to 2516 kgf, the transmitting torques varied from 31 to 115 kgf. rot, and the test speeds were of 1500 and 3000 r/min. Thus the transmitting power ranged from 64 to 482 HP.
! I
420
Speed 1500 r/min , Test 1,5 pair ~
E 36O
o
Experimental procedure
' Wheel Pinion
3000 r/rnin
E
Test16 pair
300
-cI ,]
~
240
// I
Tests were carried out using the dip lubrication system with an initial lubricating oil temperature of 90 ° -+ 3, using heating coils, a sensor and a temperature indicator mounted on the test gear box to control the oil temperature. The characteristics of the lubricating oils used in this investigation are given in Table 2.
/
.E
180 I 120
/
/
I i
/ /
iI
6O I 0 0 0 1200 1400 1600 1800 2000 2200 2400 2600 Tooth load, kgf
Fig 5 Change of weight of removed metal with applied tooth load at different speeds for wheel of concave teeth and pinion of convex teeth using gears of design C and oil B 60t
The total number of revolutions of test pinion and wheel for each load stage was always constant, namely 22 500, and thus the running time was variable with the revolutional speed. The metal removed was measured by weighing the test gears before and after each test by a digital and analogue balance of accuracy 1 x 10 -s g and capacity 2000 g, type Chyo Jupiter C2-2000, Serial No. 30559, made in Japan. The test gears were washed before weighing using an ultrasonic cleaning tank type No. 323/201, serial No. 337226, 40 kHz frequency, 150 watts output and 220 x 130 x 150
54(
/ 320
481
~.
....
Wheel Pinion
I
280-
E 42~ 2
240
36'
/
_: o
E
/
@.
o
+/
,6o
24,
-
121
11 1800 kgf /
//
/ 40 0
P4
28
32 36 Helix angle,deg
40
44 46
Fig 6 Change of weight of removed metal with helix angle at different applied tooth loads for wheel of concave teeth and pinion of convex teeth at speed 1500 r/min and oil B using test pairs 3, 9 and 15
TR I B O L O G Y international
,;
/ 120
181
L 20
,
Tooth load. 2000 kgf "\N..{~,/"
200
"6 301 ~=
/ ,
20
600 kgf
/
O0 k g f / / kgf /
ooo
,///
~ ]~-r-24
T- / ~1 28
I I I l I 32 36 40 Helix angle, deg
I
I 44 46
Fig 7 Change of weight of removed metal with helix angle at different tooth loads for wheel of concave teeth and pinion of convex teeth at speed 3000 r/min, oil B using testpairs 4, 10 and 16
207
El Bahloul - wear o f gear of circular-arc tooth-profile
viscosity, the oil film increases which carries higher loads with continuous formation between contacting teeth, but for light viscosity, the oil film is liable to breakdown under load together with its sensitivity to surface roughness and Hertzian deformations. Thus, it could be concluded that the stability of oil film with higher viscosity decreases the amount of wear for contacting teeth under the same load and speed.
26C 24C
20C
2
S
16C
E
12C
7: -~
8£
4C
0 I00
200
300
400
500
600
700
Oil viscosity, cSt
Fig 8 Change of weight of removed metal with oil viscosity at different tooth loads for gears of design A, speed 1500 r/rain; pair I for oil A, pair 3 for oil B, pair 5 for oil C mm internal dimensions made in the FRG and then dried by a stream of compressed air.
Fig 10 shows the change of the weight of removed metal with the change of oil viscosity for different designs of test gears and speeds at applied tooth load of 2000 kgf. They show very clearly that wear at a speed of 3000 r/min is greater than wear at 1500 r/rain for all test pairs of gears. This difference decreases at higher rate with increasing the oil viscosity and decreasing the helix angle of the test gears, owing to the increase of the load applied on the tooth by a dynamic increment caused by the dynamic errors in transmission. In addition, with increase of speed the temperature of the oil increases due to the generated friction between the teeth. This increase of temperature decreases the viscosity of oil, which accordingly decreases the loadcarrying capacity of the oil film and increases wear. Conclusions (1) Wear of gears of circular-arc tooth-profile increases with increasing the helix angle at lower rate and nearly linear relation for light loads. The rate of increase of wear is higher for higher applied tooth loads.
Experimental results and discussion
:580
Effect of helix angle
560
Figs 3, 4 and 5 show the change of the weight of removed metal with the change of applied tooth load at different speeds for test gears of designs A, B and C, respectively and lubricated by oil B. These curves show that wear increases firstly at lower rate with nearly linear relation until the points of failure where the wear curve shoots up at higher loads reaching ultimate values. They also show that wear of wheel of the concave teeth is more than that of the pinion with its convex teeth. This may be due to the Hertzian indentations which is more in the concave from the effect of load of the convex. Figs 6 and 7 show the change of the weight of removed metal with the change of helix angle of test gears for different designs at different applied tooth loads for wheel of concave teeth and pinion of convex teeth and running at speeds of 1500 and 3000 r/min, respectively, using lubricating oil B. These curves show that the change of helix angle increases slightly the amount of wear when the gears run under light tooth loads. For higher transmitted tooth loads, the amount of wear increases at a higher rate. For decreasing the helix angle, the radii of curvature, Hertzian area of contact and sliding velocity along the face width increase, thus reducing the amount of wear. Effect of oil viscosity Figs 8 and 9 show the change of the weight of removed metal with the change of oil viscosity at different applied tooth loads for test pairs (1,2, 3, 4, 5 and 6) of design A at speeds 1500 and 3000 r/min, respectively. They show very clearly that wear decreases with increase of oil viscosity at lower rate and nearly linear relation for light loads, while wear decreases with oil viscosity at higher rate for higher applied tooth loads. With increase of
208
I
i
J
i
I
=
--
Wheel
---
Pinion
i
. . . . Tooth breakage
3201
281
240
200
~
120
80
40
o
I00
200
300
400
500
600
700
Oil viscosity, cSt
Fig 9 Change of weight of removed metal with oil viscosity at different tooth loads for design A using speed 3000 r/rain; pair 2 for oil A, pair 4 for oil B and pair 6 for oil C
August 1987 Vol 20 No 4
El B a h l o u l - wear o f gear o f circular-arc t o o t h - p r o f i l e
720
(2) Wear of test gears decreases with increasing the oil viscosity for different helix angles, t o o t h loads and speeds.
Speed 1500 r/rain ..... 640
~-
"
~,
560
480
Speed 3000 r/rain
%%%~%%%%%% %xxl
(3) The effect of change of oil viscosity in reducing wear is more applicable for higher tooth loads.
Design C
(4) Wear increases with increase o f speed arid higher t o o t h load. This increase decreases for higher oil viscosity and lower helix angle.
,
(5) Wear o f gears of concave teeth is more than wear o f gear o f convex teeth for the same working conditions and most experimental tests.
o 400
', ,,
~20
\
E
P
Acknowledgements
Design B
a~
The authors would like to thank Professor A. Y. Attia o f &in Shams University for revising the manuscript and providing constructive criticism.
Design A
24o
References
160
1. Davies W.J. Novikov gearing. Machinery, January 13, 1960 80
2. Chironis N. Design of Novikov gears. Product Engineering, September 17, 1962
0 L
I00
~
200
300
400
500
600
700
Oil viscosity, cSt
Fig 10 Change o f weight o f removed metal with oil viscosity for different designs and speeds at applied tooth load o f 2000 kgf using all test pairs
TR I B O L O G Y
international
3. French M.J. Conformity of circular-arc gears. J. Mechanical Engineering Science, Vol 7, No 2, 1965 4. El Bahloui A.M.M. Wear of gears of circular-arc tooth-profileeffect of tooth load and speed of rotation, on Proc. 3rd Int. Conf. on Production EngineeringDesign and Control Alexandria University, l-gypt, 12-14 December, 1986
209
Keywords: he//ca/ gears, circular-arc tooth-profiles, lubricating oil ac motor 8/10 hp 1500/3000 r/rain Test Driven shaft 8 bolts MIO /
I /
~g
V-groove
Sec}ion at AA Fig I Layout o/the test rig
Hailing oearlngs
Helical gears of circular-arc tooth-profiles are conformal gears with point contact between teeth changing to an elliptical area under load 1-3 . Contact between these gears is along the face and no progressive contact occurs on the profile. In a previous paper 4 , the experimental results of a research programme carried out at Mansoura University Laboratories on the effect of load and speed on wear of this type of gearing arc presented. In this paper, the experimental results showing the effect of change of helix angle and viscosity of lubricating oil on wear are introduced.
Test rig The test rig is of the power circulating type where two pairs of gears are carried by two shafts running on rolling bearing as shown in Fig l. The driving shaft carries a graduated torque coupling to measure the transmitted torque. The driven shaft is composed of two parts connected together *Production Engineering Departmenl, t.'acully of Engineering, Mansoura University, Mansoura, Egypt.
TR I BOLOGY international
Loading coupling by a flange coupling. The rig is loaded by applying dead weights at the end of a lever fastened to each flange, thus twisting each part of the shaft relative to the other. The rig is driven by a 8/l 0 hp ac motor running at speeds 1500 and 3000 r/rain, respectively. Table 1 Dimensions and specifications of the test gears
Specifications
*For wheel tFor pinion
DesignA
Design B
Design C
Radii of curvature in normal plane (mm)
6 22.3 42 20 35 103.735t 90.17" 4, 231" 4, 68*
6 33.6 29 18 24 103.735T 90.17" 4.231" 4.68*
6 42.25 24 16 19.8 103.7351" 90.17" 4.231" 4.68*
Radii of curvature along helix angle (mm)
118.2t 128.6"
56.12t 61.1 *
36.2t 39.4*
Bore diameter (mm)
+0.009 30-0.000
+0.009 30-0.000
+0.009 30-0.000
Number of pairs of test gears Helix angle (degrees) Face width (mm) Number of teeth Axial pitch (mm) Blank diameter (mm)
0301-679X/87/040205-05 $03.00 @ Butterworth & Co (Publishers) Ltd
205
El B a h l o u l - wear o f gear o f circular-arc t o o t h - p r o f i l e
Table
2 Characteristics
of the
60o
lubricating oils
Characteristics
Oil A
Oil B
Oil C
54O
40°C Kinematic viscosity at { 50°C 1,100°C Specific gravity Pour point (max. °F) (°C) Flash point (min. °F) (°C) Viscosity index Timken OK load 40 Ib (18 kgf)
653 333 32.4 0.91-0.97 (-3) (260) 70 average -
462 253 30.8 0.901 5 (-15) 465 (241) 95 min. passes
200 118 17.6 0.894 -10 (-23) 405 (207) 92 rain. passes
°% 420L
Speed '500 r / m i n
,oo t
/
! /
T
!
/
.....
.oo I
/ /1
I
/ /,,'¢/,,'
'2°1::
I 1200
1600
2000
2400
2800
3200
Tooth Ioed, kgf
Fig 3 Change of weight of removed metal with tooth load at different speeds for wheel of concave teeth and pinion of convex teeth using gears of design A and oil B; test pair 3 for speed 1500 r/min and test pair 4 for speed 3000 r/min 600
Pinion
Wheel
i
ti
540
i
Design A i
480
I If
Speed 1500 r/min 420
2
E o)
300
....
240
i
180
Design B
Pinion
,.°E
l l
I
,y°.,.
60
I000 1200
I I I
Wheel Pinion
8
Whee]
I ;
I I
3000 r/min
360
'
'
1400
I"
1600 1800 2000
2200 2400 2600
Tooth load, kgf
Fig 4 Change of weight of removed metal with applied tooth load at different speeds for wheel of concave teeth and pinion of convex teeth using gears of design B and oil B; test pair 9 for speed 1500 r/min and test pair 10 for 3000 r/rain Test gears
Wheel
Pinion Design C
Fig 2 Different designs of test gears
206
The test gears were supplied by the General Electric Company Ltd, Rugby, UK. They are of the CirCarC type with the pinion made of 4155 MM steel and the wheel is made of 4164 MM steel. The test gears are of 6 DP (4.23 module), 91.5 mm pitch diameter, 25 ° normal pressure angle, 1.2 overlap ratio, 0.423 mm backlash and 1.6/am surface roughness. They are of different helix angles, number of teeth and face width. Table 1 gives dimensions
August 1987 Vol 20 No 4
E l B a h l o u l -- wear o f gear o f circular-arc t o o t h - p r o f i l e
and specifications of the test gears. Fig 2 shows the different designs of the test gears.
6OO 54O
480
....
Wear of gears of circular-arc tooth-profile was investigated for three designs of test pairs of gears of 22.3 °, 33.6 ° and 42.25 ° helix angles using lubricating oils of 200,462 and 653 C.st. at 40°C kinematic viscosity. The applied tooth loads varied from 1000 to 3000 kgf at intervals of 200 kgf corresponding to transmitting loads varying from 671 to 2516 kgf, the transmitting torques varied from 31 to 115 kgf. rot, and the test speeds were of 1500 and 3000 r/min. Thus the transmitting power ranged from 64 to 482 HP.
! I
420
Speed 1500 r/min , Test 1,5 pair ~
E 36O
o
Experimental procedure
' Wheel Pinion
3000 r/rnin
E
Test16 pair
300
-cI ,]
~
240
// I
Tests were carried out using the dip lubrication system with an initial lubricating oil temperature of 90 ° -+ 3, using heating coils, a sensor and a temperature indicator mounted on the test gear box to control the oil temperature. The characteristics of the lubricating oils used in this investigation are given in Table 2.
/
.E
180 I 120
/
/
I i
/ /
iI
6O I 0 0 0 1200 1400 1600 1800 2000 2200 2400 2600 Tooth load, kgf
Fig 5 Change of weight of removed metal with applied tooth load at different speeds for wheel of concave teeth and pinion of convex teeth using gears of design C and oil B 60t
The total number of revolutions of test pinion and wheel for each load stage was always constant, namely 22 500, and thus the running time was variable with the revolutional speed. The metal removed was measured by weighing the test gears before and after each test by a digital and analogue balance of accuracy 1 x 10 -s g and capacity 2000 g, type Chyo Jupiter C2-2000, Serial No. 30559, made in Japan. The test gears were washed before weighing using an ultrasonic cleaning tank type No. 323/201, serial No. 337226, 40 kHz frequency, 150 watts output and 220 x 130 x 150
54(
/ 320
481
~.
....
Wheel Pinion
I
280-
E 42~ 2
240
36'
/
_: o
E
/
@.
o
+/
,6o
24,
-
121
11 1800 kgf /
//
/ 40 0
P4
28
32 36 Helix angle,deg
40
44 46
Fig 6 Change of weight of removed metal with helix angle at different applied tooth loads for wheel of concave teeth and pinion of convex teeth at speed 1500 r/min and oil B using test pairs 3, 9 and 15
TR I B O L O G Y international
,;
/ 120
181
L 20
,
Tooth load. 2000 kgf "\N..{~,/"
200
"6 301 ~=
/ ,
20
600 kgf
/
O0 k g f / / kgf /
ooo
,///
~ ]~-r-24
T- / ~1 28
I I I l I 32 36 40 Helix angle, deg
I
I 44 46
Fig 7 Change of weight of removed metal with helix angle at different tooth loads for wheel of concave teeth and pinion of convex teeth at speed 3000 r/min, oil B using testpairs 4, 10 and 16
207
El Bahloul - wear o f gear of circular-arc tooth-profile
viscosity, the oil film increases which carries higher loads with continuous formation between contacting teeth, but for light viscosity, the oil film is liable to breakdown under load together with its sensitivity to surface roughness and Hertzian deformations. Thus, it could be concluded that the stability of oil film with higher viscosity decreases the amount of wear for contacting teeth under the same load and speed.
26C 24C
20C
2
S
16C
E
12C
7: -~
8£
4C
0 I00
200
300
400
500
600
700
Oil viscosity, cSt
Fig 8 Change of weight of removed metal with oil viscosity at different tooth loads for gears of design A, speed 1500 r/rain; pair I for oil A, pair 3 for oil B, pair 5 for oil C mm internal dimensions made in the FRG and then dried by a stream of compressed air.
Fig 10 shows the change of the weight of removed metal with the change of oil viscosity for different designs of test gears and speeds at applied tooth load of 2000 kgf. They show very clearly that wear at a speed of 3000 r/min is greater than wear at 1500 r/rain for all test pairs of gears. This difference decreases at higher rate with increasing the oil viscosity and decreasing the helix angle of the test gears, owing to the increase of the load applied on the tooth by a dynamic increment caused by the dynamic errors in transmission. In addition, with increase of speed the temperature of the oil increases due to the generated friction between the teeth. This increase of temperature decreases the viscosity of oil, which accordingly decreases the loadcarrying capacity of the oil film and increases wear. Conclusions (1) Wear of gears of circular-arc tooth-profile increases with increasing the helix angle at lower rate and nearly linear relation for light loads. The rate of increase of wear is higher for higher applied tooth loads.
Experimental results and discussion
:580
Effect of helix angle
560
Figs 3, 4 and 5 show the change of the weight of removed metal with the change of applied tooth load at different speeds for test gears of designs A, B and C, respectively and lubricated by oil B. These curves show that wear increases firstly at lower rate with nearly linear relation until the points of failure where the wear curve shoots up at higher loads reaching ultimate values. They also show that wear of wheel of the concave teeth is more than that of the pinion with its convex teeth. This may be due to the Hertzian indentations which is more in the concave from the effect of load of the convex. Figs 6 and 7 show the change of the weight of removed metal with the change of helix angle of test gears for different designs at different applied tooth loads for wheel of concave teeth and pinion of convex teeth and running at speeds of 1500 and 3000 r/min, respectively, using lubricating oil B. These curves show that the change of helix angle increases slightly the amount of wear when the gears run under light tooth loads. For higher transmitted tooth loads, the amount of wear increases at a higher rate. For decreasing the helix angle, the radii of curvature, Hertzian area of contact and sliding velocity along the face width increase, thus reducing the amount of wear. Effect of oil viscosity Figs 8 and 9 show the change of the weight of removed metal with the change of oil viscosity at different applied tooth loads for test pairs (1,2, 3, 4, 5 and 6) of design A at speeds 1500 and 3000 r/min, respectively. They show very clearly that wear decreases with increase of oil viscosity at lower rate and nearly linear relation for light loads, while wear decreases with oil viscosity at higher rate for higher applied tooth loads. With increase of
208
I
i
J
i
I
=
--
Wheel
---
Pinion
i
. . . . Tooth breakage
3201
281
240
200
~
120
80
40
o
I00
200
300
400
500
600
700
Oil viscosity, cSt
Fig 9 Change of weight of removed metal with oil viscosity at different tooth loads for design A using speed 3000 r/rain; pair 2 for oil A, pair 4 for oil B and pair 6 for oil C
August 1987 Vol 20 No 4
El B a h l o u l - wear o f gear o f circular-arc t o o t h - p r o f i l e
720
(2) Wear of test gears decreases with increasing the oil viscosity for different helix angles, t o o t h loads and speeds.
Speed 1500 r/rain ..... 640
~-
"
~,
560
480
Speed 3000 r/rain
%%%~%%%%%% %xxl
(3) The effect of change of oil viscosity in reducing wear is more applicable for higher tooth loads.
Design C
(4) Wear increases with increase o f speed arid higher t o o t h load. This increase decreases for higher oil viscosity and lower helix angle.
,
(5) Wear o f gears of concave teeth is more than wear o f gear o f convex teeth for the same working conditions and most experimental tests.
o 400
', ,,
~20
\
E
P
Acknowledgements
Design B
a~
The authors would like to thank Professor A. Y. Attia o f &in Shams University for revising the manuscript and providing constructive criticism.
Design A
24o
References
160
1. Davies W.J. Novikov gearing. Machinery, January 13, 1960 80
2. Chironis N. Design of Novikov gears. Product Engineering, September 17, 1962
0 L
I00
~
200
300
400
500
600
700
Oil viscosity, cSt
Fig 10 Change o f weight o f removed metal with oil viscosity for different designs and speeds at applied tooth load o f 2000 kgf using all test pairs
TR I B O L O G Y
international
3. French M.J. Conformity of circular-arc gears. J. Mechanical Engineering Science, Vol 7, No 2, 1965 4. El Bahloui A.M.M. Wear of gears of circular-arc tooth-profileeffect of tooth load and speed of rotation, on Proc. 3rd Int. Conf. on Production EngineeringDesign and Control Alexandria University, l-gypt, 12-14 December, 1986
209