Tribologytransactions

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/276880143
Design of Spur Gears Using Profile Modification
Article in Tribology Transactions · March 2015
DOI: 10.1080/10402004.2015.1010762
CITATIONS
2
READS
164
3 authors, including:
Sachidananda Hassan
Manipal University, Dubai
10 PUBLICATIONS 16 CITATIONS
Raghunandana Kurkal
Manipal University
14 PUBLICATIONS 40 CITATIONS
SEE PROFILE
SEE PROFILE
Some of the authors of this publication are also working on these related projects:
Article View project
All content following this page was uploaded by Sachidananda Hassan on 21 December 2015.
The user has requested enhancement of the downloaded file.

This article was downloaded by: [Manipal University], [sachidananda H K]
On: 26 May 2015, At: 21:24
Publisher: Taylor & Francis
Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,
37-41 Mortimer Street, London W1T 3JH, UK
Tribology Transactions
Publication details, including instructions for authors and subscription information:
http://www.tandfonline.com/loi/utrb20
Design of Spur Gears Using Profile Modification
H. K. Sachidananda a , K. Raghunandana b & J. Gonsalvis c
a School of Engineering and Information Technology, Manipal University, Dubai, 345050,
United Arab Emirates
b Department of Mechatronics Engineering, Manipal University, Manipal, 576104 India
c St. Joseph Engineering College, Mangalore, 575001, India
Accepted author version posted online: 16 Mar 2015.Published online: 26 May 2015.
Click for updates
To cite this article: H. K. Sachidananda, K. Raghunandana & J. Gonsalvis (2015) Design of Spur Gears Using Profile
Modification, Tribology Transactions, 58:4, 736-744, DOI: 10.1080/10402004.2015.1010762
To link to this article: http://dx.doi.org/10.1080/10402004.2015.1010762
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained
in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no
representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the
Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and
are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and
should be independently verified with primary sources of information. Taylor and Francis shall not be liable for
any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever
or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of
the Content.
This article may be used for research, teaching, and private study purposes. Any substantial or systematic
reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any
form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://
www.tandfonline.com/page/terms-and-conditions

Tribology Transactions, 58: 736–744, 2015
Copyright Ó Society of Tribologists and Lubrication Engineers
ISSN: 1040-2004 print / 1547-397X online
DOI: 10.1080/10402004.2015.1010762
Design of Spur Gears Using Profile Modification
H. K. SACHIDANANDA 1 , K. RAGHUNANDANA 2 , and J. GONSALVIS 3
1 School of Engineering and Information Technology, Manipal University, Dubai, 345050 United Arab Emirates
2 Department of Mechatronics Engineering, Manipal University, Manipal, 576104 India
3 St. Joseph Engineering College, Mangalore, 575001 India
Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
In this work, a profile modification technique was used in
design of a spur gear. In this technique, the tooth-sum is varied
to obtain the desired contact ratio and low contact stress for a
specified center distance. A program has been developed using
C language to compute the contact stresses by varying the
amount of profile shift for a tooth-sum of 100 teeth (§4%).
The selected tooth-sum of 96, 100, and 104 gears was subjected
to cyclic loading using a back-to-back test rig. The
morphology of the damaged gear tooth surface after cyclic
loading was examined by scanning electron microscopy. The
morphological investigation reveals that the degree of damage
observed in negative number of teeth alterations is less
compared to standard and positive alteration tooth-sum due to
lower contact stress.
KEY WORDS
Gears, Spur Gears, Scoring, Scuffing, Fatigue, Rolling-Contact
Fatigue
INTRODUCTION
The contact stress is an important factor to maintain durability
of the contact surface of external meshing gears (Nabih, et al.
(1)). Hence, stress analysis in the contact area and assessing the
most critical conditions are of particular interest to the appropriate
design of the transmission gears (Ruben, et al. (2)).
To determine the critical points (which have higher contact
stress) and critical conditions in a mating gear requires complex
calculations. In this context, many researchers made attempts
and found solutions. Stachowiak and Batchelor (3) estimated
contact stresses on nonconformal surfaces (spur gears) by analytical
equations based on the elasticity theory developed by Hertz.
Miryam, et al. (4) also used the Hertz equation in combination
with a model of load distribution along the line of contact to
compute contact stress in spur and helical gears. They also
reported that the load distribution is not uniform (due to the
change in rigidity of the pair of teeth) along the path of contact
and has a decisive influence on the location and magnitude of
the contact stress. Valentin (5) reported that the continuous
Manuscript received November 3, 2014
Manuscript accepted January 17, 2015
Review led by Robert Errichello
Color versions of one or more of the figures in the article can be found
online at www.tandfonline.com/utrb.
736
interaction between the profile form and contact parameters
should be considered in designing models for gear teeth (Hayrettin
(6)). Fatih and Stephen (7) showed that the wear at the beginning
and end of the tooth mesh due to instantaneous contact
loads and Hertz pressures is also a parameter that affects tooth
performance.
Further, in some of the literatures (Ali (8); Sfakiotakis, et al.
(9)), it is found that the stress distribution in gear teeth is an
elliptical pattern and the maximum stresses are in the middle
and are computed by Eq. [1]:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
Q 1 R 1
C 1 R 2
s max D t h
i: [1]
bp 1 ¡ #2 1
E 1
C 1 ¡ #2 2
E 2
An improvement over the Hertzian theory was provided by
Johnson (10), according to which the contact stress is influenced
by the adhesiveness of the surfaces in contact and the correlation
between the contact area, the elastic material properties, and
interfacial interaction strength.
As per BS ISO 6336-2 (11) standard for gears with a contact
ratio range of 1 to 2, the nominal contact stress is to be determined
at the pitch point. The contact stress at the inner limit
(single-pair tooth contact) on the pinion or wheel is to be determined
using the single-pair tooth contact factors Z B (pinion) or/
and Z D (wheel; Shuting (12)).
In meshing gears, defects like pitting, scoring, scuffing, and
wear due to fatigue effects are common defects on the tooth
surface. These defects are due to maximum Hertz surface
pressure (Anders and Soren (13)) and fluctuating load. When
gears operate at maximum load capacity, a very high contact
pressure occurs at the mesh interference. This leads to partial
breakdown of the lubricant and causes mild wear, scuffing,
scoring, spalling, and pitting (Amarnath and Sujatha (14)).
The sudden tooth load changes at lowest point of singletooth
contact (LPSTC), and the highest point of single-tooth
contact (HPSTC) causes fluctuations in contact stresses (Li
and Kahraman (15)). The fluctuation in contact stress also
causes fatigue, which leads to pitting at the contact surfaces
and generally involves combined rolling and relative sliding
actions.
It is seen that most of the literature pertains to contact
stress analysis using standard gearing. The literature on stress
analysis of altered tooth-sum gearing is limited. As the

Design of Spur Gears Using Profile Modification 737
Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
NOMENCLATURE
a D Center distance (mm)
b D Face width (mm)
E 1 D Young’s modulus (pinion) (MPa)
E 2 D Young’s modulus (gear) (MPa)
F n D Normal force (N)
GSL D Top land width (gear) (mm)
m D Module (mm)
P bn D Base pitch (mm)
PSL D Top land width (pinion) (mm)
Q D Load (N)
R 1 D Radius of curvature (pinion) (mm)
R 2 D Radius of curvature (gear) (mm)
R max1 D Maximum radius permitted (pinion) (mm)
R max2 D Maximum radius permitted (gear) (mm)
r D Radius (mm)
profile shift varies, the value of contact stress also changes,
which has not been explored in detail for altered tooth-sum
gearing. Authors in this context made attempts to investigate
contact stress analyses of altered tooth-sum gearing for 40
tooth-sums to 240 tooth-sums in steps of 20 tooth-sums
(Sachidananda, et al. (25, 26)). In that research finding, they
reported that it is possible to predict the contact stress and
tailor the design of gears for high contact ratio (lower contact
stress) by altering the tooth-sum gearing. Based on this
research output, it is also found that further investigation of
a particular tooth-sum (100 § 4%) gearing that is commonly
used in private and public transportation vehicles is needed.
In addition to stress analysis, the location of maximum contact
stress points and morphological investigation at critical
points needs to be determined. In view of the above literature
gap, the authors extended earlier work and reported in
this article an investigation of the contact stress in commonly
used altered tooth-sum gearing (100) and its locations by
varying the amount of profile shift. In addition, morphological
investigation of contact surfaces of the tooth were carried
out to determine the types of damage.
METHODOLOGY
Parameters Considered for Computation
The geometrical parameters considered for computing contact
stresses are module of 2 mm, face width of 20 mm, and pressure
angles of 20 and 25 . The material for the gear considered was
steel (C40) and the Young’s modulus of the material was taken
as 200 GPa. The applied tangential tooth load of 10 N per unit
millimeter of face width was taken to compute the contact stress.
Estimation of Contact Stress
The following methodology has been used to compute the
contact stress for altered tooth-sum for various values of profile
shift.
r 11 D Pitch circle radius (pinion) (mm)
r 12 D Pitch circle radius (gear) (mm)
r a1 D Addendum circle radius (pinion) (mm)
r a2 D Addendum circle radius (gear) (mm)
r b1 D Base circle radius (pinion) (mm)
r b2 D Base circle radius (gear) (mm)
X D Profile shift coefficient (mm)
X 1 D Profile shift coefficient (pinion) (mm)
X 2 D Profile shift coefficient (gear) (mm)
e D Contact ratio
s max D Contact stress (MPa)
y 1 D Poisson’s ratio (pinion)
y 2 D Poisson’s ratio (gear)
f D Standard pressure angle ( )
f W D Working pressure angle ( )
The maximum contact stress induced was calculated based on
Eq. [2] (Fernandes and Mcduling; Moldovan, et al. (19)):
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:35Q 1 R1
s max D
C
1
R2
b 1
E1 C
1 : [2]
E2
The profile shift (X) for each tooth-sum altered has been calculated
by Eq. [3] (Gitin (20)):
½inv f
X D Z w ¡ inv fŠ
e : [3]
2 tan f
Figure 1a shows the different points along the path of contact
of meshing gears, which are identified as A, B, C, D, and E.
Figures 1b and 1c indicate the load distribution along the path of
contact as the contact ratio ranges from 1.2 to 2 and greater
than 2, respectively.
For any external gear pair, the pitch point C keeps a constant
position on the centerline of the gear, whereas points A, E and
points B, D, the single-pair gear meshing segments, change their
position along the theoretical gear segment T 1 T 2 . The influence
over the position of points A, E and points B, D is given by the
profile shift distribution between the gear pair and gear ratio in
order to maintain the normal addendum clearance between
teeth. In this analysis, the influence of profile shift on these
points AE and points BD have been considered.
The radius of curvature and maximum contact stress at different
points along the length of the path of the contact is computed
from the following set of equations (refer to Fig. 1). The steps
followed to compute the radius of curvature are as follows
(Gitin (20)):
T 1 T 2 D a sin ; w [4]
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
T 1 A D T 1 T 2 ¡ ra2 2 ¡ r2 b2
[5]
T 2 A D T 1 T 2 ¡ T 1 A [6]
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
T 1 B D ra1 2 ¡ r2 b1
¡ P bn ; [7]

738 H. K. SACHIDANANDA ET AL.
Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
Fig. 1—Path of contact from beginning to end described as A, B, C, D, and E. A, beginning of contact; B 1 , end of two-pair mesh; B 2 , beginning of singlepair
mesh; C, pitch point; D 2 , end of single-pair mesh; D 1 , beginning of two-pair mesh; E, end of contact.
where P bn D p m cos f.
T 2 B D T 1 T 2 ¡ T 1 B [8]
T 1 C D ða sin f W Þ=2 [9]
T 2 C D T 1 T 2 ¡ T 1 C [10]
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
T 1 D D T 1 T 2 ¡ ra2 2 ¡ r2 b2
C P bn [11]
T 2 D D T 1 T 2 ¡ T 1 D [12]
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
T 1 E D ra1 2 ¡ r2 b1
[13]
T 2 E D T 1 T 2 ¡ T 1 E: [14]
The steps followed to compute the contact ratio ( 2 ) are as follow
(Gitin (20)):
2D T 1E ¡ T 1 A
P bn
: [15]
The maximum radius permitted without any interference for the
pinion and gear is given by (Gitin (20))
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R max1 D R 2 b1 C ð a sin f wÞ 2
[16]
(Gitin (90)):
f w D cos ¡ 1 Z e cosf
; [18]
Z
where Z e is the altered tooth-sum and Z is the standard toothsum.
The addendum radius of the pinion and gear was calculated
using the following set of equations (Gitin (20)):
R a1 D ða C m ¡ x 2 mÞ¡ r 12 [19]
R a2 D ða C m ¡ x 1 mÞ¡ r 11 : [20]
where r 11 and r 12 are the pitch circle radii of the pinion and gear.
The restricting conditions are maximum radius permitted as follows
(Li and Kahraman (15)):
R max1 R a1 and R max2 R a2 : [21]
In addition to the above condition, the top land width of the
pinion and gear should satisfy the following condition (Gitin
(20)):
PSL 0:25 m and GSL 0:25 m: [22]
The individual radius of curvature at different points along the
length of path of contact is calculated using Eq. [23] (Fernandes
and Mcduling (19)):
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R max2 D R 2 b2 C ð a sin f wÞ ; [17]
ðRTR
Þ X
D T 1XðT 1 T 2 ¡ T 1 XÞ
; [23]
T 1 T 2
where f w is the change in pressure angle and is called the working
pressure angle and calculated using the following equation
where X stands for different points along the length of the path
of contact (A, B 1 ,B 2 ,C,D 1 ,D 2 , and E).

Design of Spur Gears Using Profile Modification 739
Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
The normal force along the different points along the length of
path of contact was calculated using Eq. [24]:
F t
FNX D ; [24]
cos tan ¡ 1
where F t is the tangential force (N).
The individual load along the different points on the length of
the path of contact was calculated using Eq. [25]:
T 1 X
R b1
QX D FNX
b ; [25]
where b is the face width (mm).
The maximum contact stress along different points on the
length of the path of contact was calculated using Eq. [26]:
where
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
QX
.s max / X D con ; [26]
ðRTR
rffiffiffiffiffiffiffiffiffiffiffiffi
0:35E
con D
2
Þ X
[27]
if the pinion and gear are of the same material.
A computer program was developed based on the above
methodology using C language to compute the contact stresses.
Experimental Investigation
Figure 2 shows the digital photograph of back-to-back cyclic
loading experimental test rig. It is one of the standard test rigs
used to test gears for finite life fatigue (Nabih, et al. (1)). In the
present research work, a selected tooth-sum of 96, 100, and 104
gears was tested for a total of 10 6 cycles.
Fig. 2—FZG testing machine used for experimentation. 1, Gear train
under test (heat treated); 2, shaft; 3, torque meter; 4, vernier
coupling; 5, support plate; 6, transmission gear (untreated).
Subsurface cracks, multiple cracks on the surface, scuffing,
and pitting are the surface defects that are commonly developed
during fatigue loading of gear teeth. In this work, in order to
obtain a clear picture of surface damage, a morphological study
of the tested gear tooth was conducted using scanning electron
microscopy (SEM; JEOL-JSM-6380LA, Japan). The samples
were prepared by wire electrodischarge machining at appropriate
points on the gear tooth and the sample surface was coated
with gold using a sputtering unit. SEM microphotographs were
taken at appropriate voltage.
RESULTS AND DISCUSSION
Contact Stress
The s max point shifts along the path of contact and it depends
on profile shift and position of pitch point C. It is shown in
Fig. 1a that T 1 C > T 1 B; hence, the ratio T1C
T >1 and s 1B max for the
pinion appears at point B. Otherwise, if T 1 C T 1 B, the ratio T1C
T 1B
1 and s max for the pinion appears at point C. Similarly, if T 2 C
> T 2 D, and if T 2 C T 2 D, the s max for the gear appears at points
D and C, respectively (Moldovan, et al. (24)).
The length of T 1 T 2 for 100 tooth-sum gears altered by §4%
for 20 and 25 pressure angles was computed using Eq. [4] and
tabulated as shown in Table 1.
Based on the these tabulated values, the ratio of contact
lengths versus profile shift for 20 and 25 pressure angles was
computed using the developed C program and the plots were
drawn as shown in Fig. 3. The ratio of T1C T2C
T 1B
and
T at s 2D max point
for 20 and 25 pressure angles was identified by the output and
tabulated as shown in Table 2. The computed values of contact
ratio, addendum, dedendum, and whole depth using C program
were compared with the appendix F and appendix D in Gitin
(20) and it was found that the values are in line.
From the ratio of contact lengths versus profile shift plots
(refer to Fig. 3), the following analysis was made. The ratio T1C
T 1B
decreases and the ratio T2C
T 2D
increases with an increase in profile
shift on the pinion. The range of profile shift (X 1 ) for a 20 pressure
angle varies between ¡0.6 to 1 and ¡1.6 to 0.6 for negative
and positive alteration tooth-sum, respectively. Similarly, the
range of profile shift for 25 pressure angle varies between ¡0.6
to 1.8 and ¡1.8 to 0.7 for negative alteration and positive alteration
tooth-sum, respectively. From Table 2, it is seen that for a
tooth-sum of 96 teeth the ratio T1C
T 1B
is 1.014 for the profile shift
X 1 D 1.6 and the ratio T1C
T is 0.996 for profile shift X 1B 1 D 1.7 for a
20 pressure angle. This indicates that s max shifts from point B to
point C. Similarly, for the same tooth-sum the ratio of T2C
T 2D
is 0.984
for the profile shift X 1 D 0.3 and 1.001 for the profile shift X 1 D
0.4, where the s max shifts from point C to point D. These are the
critical points where s max shifts from the inner contact point (B)
of a single-pair mesh to the pitch point (C) and vice versa.
In general, from Table 2, for negative alteration (96, 97, 98,
and 99) tooth-sum and for standard tooth-sum (100), it is seen
that the ratio of T1C T2C
T 1B
and
T 2D
changes from point B to point C and
from point C to point D for positive values of profile shift. Similarly,
for positive alteration (101, 102, 103, and 104) in tooth-sum

740 H. K. SACHIDANANDA ET AL.
TABLE 1—LENGTH OF PATH OF CONTACT (MM) FOR TOOTH-SUM OF 100 ALTERED BY §4TEETH
Altered tooth-sum 96 97 98 99 100 101 102 103 104
Length of T 1 T 2 (’ D 20 ) 43.15 41.13 38.98 36.68 34.2 31.5 28.51 25.14 21.2
Length of T 1 T 2 (’ D 25 ) 49.22 47.66 45.95 44.15 42.26 40.26 38.14 35.86 33.41
Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
the ratio of T1C
T 1B
T2C
and
T 2D
changes from point B to point C and point
C to point D for negative values of profile shift.
The magnitude and point of s max for altered tooth-sum gearing
has been computed by C program and tabulated in Table 3.
The following salient features were observed from Table 3. It is
seen from the results at a profile shift of 1.6 the s max is in a single-pair
mesh (point B). For f D 20 and X 1 D 1.6 it is seen that
value of s max for a tooth-sum of 96 at point C is 189.48 MPa. In
this case, the length of T 1 C is greater than T 1 B (21.57 mm >
21.27 mm) and T 1 C is less than T 1 E (27.17 mm). Hence, the
s max is at pitch point C, which lies in a single-pair mesh between
point B and point D. For the same tooth-sum, the value of s max
for the profile shift X 1 D 1.7 at point C is 133.98 MPa, which is
less compared to previous value of profile shift and is due to
smaller length of T 1 C (21.57 mm), which is less than T 1 B
(21.65 mm). Therefore, the magnitude of s max is reduced as the
pitch point C lies in between point A and point B (two-pair
mesh). In addition, for f D 25 and X 1 D 1.6, a similar trend was
observed.
It is observed that the magnitude of s max at points B and C is
lower at a 25 pressure angle compared to a 20 pressure angle
for profile shifts of 1.6 and 1.7. The length of the path of contact
T 1 T 2 is 49.22 mm in the case of a 25 pressure angle is higher
compared to the length of the path of contact at a 20 pressure
angle (43.15 mm). This leads to an increased radius of curvature
and results in reduced contact stress.
In the case of f D 20 , X 1 D 0.1, and tooth-sum of 100, the s max
at pitch point C is 208.53 MPa, and the length of T 1 C is greater
than T 1 B (17.10 mm >16.84 mm) and less than T 1 D (18.29 mm).
The pitch point C lies in between point B and point D; hence, C
lies in a single-pair mesh. In this case, the contact ratio is 1.75.
Similarly, for f D 25 for the same tooth-sum, the s max at point
Fig. 3—Plots of ratio of contact lengths versus profile shift: (a) (T 1 C)/(T 1 B) versus X 1 and (b) (T 2 C)/(T 2 D) versus X 1 for a 20 pressure angle; (c) (T 1 C)/(T 1 B)
versus X 1 and (d) (T 2 C)/(T 2 D) versus X 1 for a 25 pressure angle.

Design of Spur Gears Using Profile Modification 741
TABLE 2—RATIO T1C
T 1B AND T 2C
T 2 D AT s MAX POINT FOR 20 AND 25 PRESSURE ANGLES
For f D 20
For f D 25
Altered tooth-sum X 1 T 1 C/T 1 B X 1 T 2 C/T 2 D X 1 T 1 C/T 1 B X 1 T 2 C/T 2 D
Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
96 1.6 1.014 0.3 0.984 1.6 1.012 0.4 0.988
1.7 0.996 0.4 1.001 1.7 0.998 0.5 1.002
97 1.2 1.019 0.2 0.991 1.3 1.011 0.3 0.994
1.3 0.999 0.3 1.01 1.4 0.996 0.4 1.01
98 0.8 1.013 0.1 0.998 0.9 1.011 0 0.998
0.9 0.992 0.2 1.02 1 0.995 0.1 1.004
99 0.5 1.006 0 0.984 0.7 1 ¡0.1 0.995
0.6 0.985 0 1.008 0.8 0.983 0 1.012
100 0.1 1.015 ¡0.2 0.989 0.3 1.005 ¡0.4 0.987
0.2 0.989 ¡0.1 1.015 0.4 0.987 ¡0.3 1.005
101 ¡0.2 1.027 ¡0.3 0.998 0 1.018 ¡0.5 0.994
¡0.1 0.996 ¡0.2 1.03 0.1 0.998 ¡0.4 1.015
102 ¡0.4 1.028 ¡0.5 0.998 ¡0.3 1.015 ¡0.8 0.982
¡0.3 0.999 ¡0.4 1.036 ¡0.2 0.993 ¡0.7 1.004
103 ¡0.5 1.031 ¡0.9 0.966 ¡0.5 1.015 ¡0.9 0.999
¡0.4 0.985 ¡0.8 1.009 ¡0.4 0.991 ¡0.8 1.015
104 ¡0.4 1.019 ¡1.4 0.993 ¡0.8 1.025 ¡1.1 0.997
¡0.3 0.961 ¡1.3 1.005 ¡0.7 0.996 ¡1 1.025
C is 191.02 MPa for profile shift X 1 D 0.3 and lies in between
point B and point D. However, the magnitude of s max was lower
in the 25 pressure angle compared to the 20 pressure angle.
For f D 20 , X 1 D¡0.4, and tooth-sum of 104 teeth, it has
been noted that the s max at point C is 150.21 MPa. In this case,
the length of T 1 C is smaller compared to T 1 B (10.60 mm <
13.32 mm). Point C is in between point A and point B and falls
in a two-pair mesh. In this case, the contact stress is lower
because the contact ratio is 2.01 (two pairs of teeth are lifting the
load). However, for the same tooth-sum the s max is high for a
TABLE 3—MAGNITUDE AND POINT OF s MAX FOR ALTERED TOOTH-SUM GEARING
Altered
s max at
Tooth-sum X 1 B 1 (Mpa)
For f D 20
s max at
B 2 (Mpa)
25 pressure angle compared to a 20 pressure angle. This is due
to fact that the pitch point C lies in between point B and point D
and falls in a single-pair mesh with a contact ratio of 1.68.
From Table 3 it is observed that the value of contact stress at
point B 1 and point B 2 increases up to a tooth-sum of 102 for a
20 pressure angle as the tooth-sum increases. Further, the
observed increased tooth-sum (103 and 104) decreased the magnitude
of the contact stress. This is due to the reduction in length
of T 1 C.Fora25 pressure angle it is seen that the value of contact
stress at point B 1 and point B 2 continuously increases from
s max at
s max at
C (Mpa) X 1 B 1 (Mpa)
For f D 25
s max at
B 2 (Mpa)
s max
at C (Mpa)
96 1.6 133.81 189.24 189.48 1.6 127.46 180.25 180.52 B
1.7 133.81 189.24 133.98 1.7 127.67 180.55 127.64 C
97 1.2 136.44 192.65 193.25 1.3 129.23 182.62 182.83 B
1.3 136.44 192.65 136.65 1.4 129.35 182.93 129.3 C
98 0.8 139.39 197.13 197.32 0.9 130.74 184.84 185.06 B
0.9 139.39 197.13 139.52 1 130.91 185.14 130.85 C
99 0.5 143.14 202.43 202.52 0.7 132.94 188.01 188.01 B
0.6 143.14 202.43 143.2 0.8 133.19 188.36 132.94 C
100 0.1 147.34 208.37 208.53 0.3 135 190.93 191.02 B
0.2 147.34 208.37 147.45 0.4 135.24 191.26 135.07 C
101 ¡0.2 152.81 216.1 216.31 0 137.69 194.63 194.89 B
¡0.1 152.81 216.1 152.96 0.1 137.83 194.12 137.81 C
102 ¡0.4 159.78 225.96 159.9 ¡0.3 140.65 198.91 199.11 B
¡0.3 159.78 225.96 226.36 ¡0.2 140.86 199.21 140.79 C
103 ¡0.5 138.33 169.42 138.4 ¡0.5 144.44 204.27 204.46 B
¡0.4 138.33 169.42 169.65 ¡0.4 144.66 204.58 144.57 C
104 ¡0.4 149.91 183.61 150.21 ¡0.8 148.81 210.46 210.68 B
¡0.3 149.91 183.61 183.97 ¡0.7 149 210.72 148.97 C
Point
of s max

Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
742 H. K. SACHIDANANDA ET AL.
Fig. 4—Gear tooth surface morphology: (a) 96 tooth-sum (point B), (b) 96 tooth-sum (point D), (c) 100 tooth-sum (point B), (d) 100 tooth-sum (point D),
(e) 104 tooth-sum (point B), and (f) 104 tooth-sum (point D).
96 teeth to 104 teeth due to a continuous decrease in the radius
of curvature from negative alteration to positive alteration in
tooth-sum.
The s max for negative alteration in tooth-sum is lower
compared to standard tooth-sum for both 20 and 25 pressure
angles. Similarly, for a tooth-sum of 103 the contact
stress induced is lower compared to a standard tooth-sum for
f D 20 even though the length of T 1 T 2 is smaller compared
to a standard tooth-sum. This is due to a negative profile
shift for both pinion and gear compared to a positive shift in
standard gearing.
The s max for negative alteration in tooth-sum is lower compared
to a standard tooth-sum. This is due to the longer length of
T 1 T 2 . However, the magnitudes of contact stresses were higher
for positive alteration in tooth-sum compared to a standard
tooth-sum. From Table 3 it is seen that negative alteration in
tooth-sum performed better compared to a standard tooth-sum
from a contact stress point of view and the stresses are much

Design of Spur Gears Using Profile Modification 743
Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
lower in a 25 pressure angle compared to a 20 pressure angle.
This analysis holds for changing of s max from point C to point D
similar to point B and point C. The behavior of altered toothsum
gearing performs in the same way as discussed above for
changing of points from point C to point D.
Morphological Investigation
Generally, to ensure long-term transmission reliability in
automotive vehicles the gear designer must consider requirements
such as high static strength, bending fatigue, and rolling
contact fatigue (William and Richard (30)). In particular, rolling
contact fatigue cracks are one of the most important problems
for gears (Aslantas and Tasgetiren (16); Vera and Ivana (29)).
Under rolling contact, various surface damage (pitting, spalling,
and cracking) occurs and cracks develop in the gear tooth surface,
thus leading to loss of serviceability of the gear (Anders
and Soren (13); Singh, et al. (28)). Both macro- and microcracks
lead to surface damage, and subsurface cracks generate heavy
surface damage like pitting. In most material failures, tensile
stresses appear to be the common mode and the material surface
is stretched or pulled apart, thus leading to microscopic surface
cracking and macroscopic-scale pitting or spalling (Dimitrov,
et al. (17); Michele and Giuseppe (23)).
In a meshing gear pair LPSTC to the HPSTC only one pair of
gear tooth in contact and the normal force is higher for this
region. Below the LPSTC and above the HPSTC there is more
than one pair in contact (Marco, et al. (22)). Hence, in the present
investigation point B (LPSTC) and point D (HPSTC) on the
pinion are the critical points of contact that are considered in
gears for rolling type of failure. In this context, 96, 100, and 104
tooth-sum gears were selected for experimentation and are subjected
to fatigue loading. The surfaces at point B (LPSTC) and
point D (HPSTC) on the tested pinion tooth surface were
selected and specimens were prepared for morphological investigations.
SEM micrographs of these surfaces are shown in Fig. 3.
In the experimental results, it is observed that pitting failures
occur roughly between the initial point of a single-tooth contact
(point B) and pitch point C and from pitch point C to the final
point of the single-tooth contact (point D) because these are the
points of highest load when the contact ratio is greater than 1.2
and less than 2.
Figures 3a and 3b show SEM micrographs of the pinion tooth
surface at points B and D for a tooth-sum of 96. The sum of the
profile shift coefficient is 2.27 mm and in this case both gear and
pinion wer generated with equal amounts of profile shift and the
maximum contact stress at point B 1 is 189.48 MPa. This is the initial
point of the single-tooth contact. Microcracks are observed
at point B (Fig. 3a, higher magnification) and multiple macrocracks
are observed at point D (Fig. 3a, higher magnification). It
is found that the crack intensity and number of cracks are greater
at point D compared to point B. This is due to s max at D. From
these micrographs it can be seen that the surface deterioration at
the region of point D is greater compared to that at point B. In
driving and driven members the sliding direction and rolling are
opposite each other (as observed in all SEM micrographs) and
cracks grow opposite to the direction of sliding.
Figures 3c and 3d show SEM micrographs of 100 tooth-sum
pinion teeth surfaces at points B and D. From Figs. 3c and 3d it
is seen that the surface damage is more severe at point B (Fig. 3c,
lower magnification) compared to point D (Fig. 3d, higher magnification).
However, plastic deformation is observed on the surface
in both points of contacts. This is due to the kinematic
characteristics of the gear teeth contact and teeth lubricating
conditions (Joze and Gorazd (21)). It can be stated that the more
aggressive the contact conditions and a thin lubricating specific
film thickness lead to plastic deformation and a feather edge
forms due to plastic flow of material (Fig. 3c; Errichelo (18)).
Scuffing (scoring) is a form of gear tooth surface damage that
occurs due to the absence or breakdown of a lubricant film
between the contacting surfaces of the mating gears (Vera and
Ivana (29); Sheng and Ahmet (27)). Figures 3e and 3f show the
micrographs of 104 tooth-sum pinion teeth surfaces at points B
and D. It can be seen from Table 3 that the contact stress is at
point B and remains the same at point D because of the two-pair
mesh. Though the maximum contact stress value in this case is
lower than in the above two cases, the contact ratio in this case is
2.07, which is higher. This leads to a shorter path of contact and
the product of contact stress and sliding velocity is the highest
for this case of gearing compared to all other cases. Therefore,
the lubricant between meshing surfaces is subjected to squeezing
and breakdown of the lubricant film. This indicates a severe scoring
effect. The extreme pressure and high sliding velocity caused
ploughing of the material. In addition, dry sliding wear at the
point of contact generates high friction and material removal
from the surface acts as three-body wear and creates ploughing
of the material, as shown in Figs. 3e and 3f. However, the cases
of gearing with positive values of tooth number alterations are
marginally scored compared to standard gearing. Surface examinations
carried out by considering SEM microphotographs
revealed better surface integrity for the cases of negative number
of tooth alterations.
CONCLUSIONS
The analyses of maximum contact stress in altered tooth-sum
gearing for a tooth-sum of 100 when altered by §4% have been
studied. The magnitude of s max and morphological studies have
been done for point B and point D. From the computational,
experimental, and morphological analysis, the following conclusions
are drawn:
Better performance is obtained for negative alteration in
tooth-sum gears compared to standard gearing. This is
because the contact stress induced for negative alteration in
tooth-sums of 96, 97, 98, and 99 is lower compared to the
standard tooth-sum of 100. For positive alteration in toothsum
the contact stress at points B 1 and B 2 is higher; in turn,
standard gears perform better under these conditions for a
25 pressure angle. Similarly, the analysis holds for a 20
pressure angle.
It is proved that by a profile modification technique it is
possible to trace the point of switchover of s max . In addition,
it has design flexibility in gear design with respect to
the range of contact ratio.

744 H. K. SACHIDANANDA ET AL.
Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015
In a gear pair, altering the tooth number requires the use of
a profile shift; moreover, these gears operate on an altered
pressure angle. Thus, contact stress in these gears is influenced
by changes due to altering the tooth numbers.
Altering tooth-sum gearing using a profile shift has been
used in design of gears with higher flexibility. This helps in
designing gears with moderate material by utilizing its surface
strength to a maximum extent. The analysis of maximum
contact stresses in altered tooth-sum gearing helps in
understanding the importance of a profile shift in design of
gears for applications like rolling mills, etc. Altered toothsum
gearing helps gear designers in exercising greater flexibility
while designing gears.
The SEM observations of the tooth surface show the importance
of s max on surface damage. In addition, the morphology
of the tooth specimen shows that microcracks are
generated due to cyclic loading and will lead to pitting failure
in the rolling direction.
REFERENCES
(1) Nabih, F. J., Cavoret, V., and Philippe, V. (2013), “Gear Tooth Pitting
Modelling and Detection Based on Transmission Error Measurements,”
European Journal of Computational Mechanics, 22(2–4), pp 106–119.
(2) Ruben, D. C., Luis, J. A., Miguel, A., Diaz, A., and Jose, A. (2010),
“Analysis of Stress Due to Contact between Spur Gears,” International
Conference of Advances in Computational Intelligence, Man–Machine
Systems and Cybernetics, Dec 14–16, Venezuela, pp 216–220.
(3) Stachowiak, G. W. and Batchelor, A. W. (2005), Engineering Tribology,
4th ed., Elsevier.
(4) Miryam, B., Sanchez, J. P. I., and Miguel, P. (2013), “Contact Stress Calculation
of High Transverse Contact Ratio Spur and Helical Gear
Teeth,” Mechanism and Machine Theory, 64, pp 93–110.
(5) Valentin, O. (2008), “Tooth Wear Modeling and Prognostication Parameters
of Engagement of Spur Gear Power Transmissions,” Mechanism
and Machine Theory, 43(12), pp 1639–1664.
(6) Hayrettin, D. (2009), “PA66 Spur Gear Durability with Tooth Width
Modification,” Materials and Design, 30, pp 1060–1067.
(7) Fatih, K. and Stephen, E. O. (2008), “Influence of Tip Relief Modification
on the Wear of Spur Gears with Asymmetric Teeth,” Tribology
Transactions, 51(5), pp 581–588.
(8) Ali, R. H. (2009), “Contact Stress Analysis of Spur Gear Teeth Pair,”
World Academy of Science, Engineering and Technology, 3(10), pp 587–
592.
(9) Sfakiotakis, V. G., Vaitsis, J. P., and Anifantis, N. K. (2001), “Numerical
Simulation of Conjugate Spur Gear Action,” Computers and Simulation,
79(12), pp 1153–1160.
(10) Johnson, K. L. (1985), Contact Mechanics, Cambridge University Press.
(11) BS ISO 6336-2. (1996), “Calculation of Load Capacity of Spur and Helical
Gears, Part 2: Calculation of Surface Durability (Pitting).”
(12) Shuting, L. (2007), “Finite Element Analyses for Contact Strength and
Bending Strength of a Pair of Spur Gears with Machining Errors, Assembly
Errors and Tooth Modifications,” Mechanisms and Machine Theory,
42(1), pp 1–27.
(13) Anders, F. and Soren, A. (2001), “A Simplified Model for Wear Prediction
in Helical Gears,” Wear, 249(3–4), pp 285–292.
(14) Amarnath, M. and Sujatha, C. (2014), “Surface Contact Fatigue Failure
Assessment in Spur Gears Using Lubricant Film Thickness and Vibration
Signal Analysis,” Tribology Transactions, 58(2), pp 327–336.
(15) Li, S. and Kahraman, A. (2010), “Prediction of Spur Gear Mechanical
Power Losses Using a Transient Elastohydrodynamic Lubrication Model,”
Tribology Transactions, 53(4), pp 554–563.
(16) Aslantas, K. and Tasgetiren, S.(2004), “A Study of Spur Gear Pitting
Formation and Life Prediction,” Wear, 256(11), pp 1167–1175.
(17) Dimitrov, L., Michalopoulos, D., and Apostolopoulus, T. D. N. (2009),
“Investigation of Contact Fatigue of High Strength Steel Gears Subjected
to Surface Treatment,” Journal of Materials Engineering and Performance,
18(7), pp 939–946.
(18) Errichello, R. L. (2012), “Morphology of Micropitting,” Gear Technology,
4, pp 74–81.
(19) Fernandes, P. J. L. and Mcduling, C. (1997), “Surface Contact Fatigue in
Gears,” Engineering Failure Analysis, 4(2), pp 99–107.
(20) Gitin, M. M. (2011), Handbook of Gear Design, 2nd ed., Tata McGraw
Hill Education Private Limited: New Delhi.
(21) Joze, H. and Gorazd, H. (2008), Constructive Measures to Increase the
Load-Carrying Capacity of Gears: The Characteristics of S-Gears, Faculty
of Technical Sciences, University of Ljubljana, Novi Sad, Serbia.
(22) Marco, A. M., Fabio, K., Urbano, R., and Carlos, H. S. (2012), “The
Influence of Contact Stress Distribution and Specific Film Thickness on
the Wear of Spur Gears during Pitting Tests,” Journal of Braz. Society of
Mechanical Science and Engineering, 34(2), pp 135–144.
(23) Michele, C. and Giuseppe, D. (1999), “Numerical Methods for the Optimization
of Specific Sliding, Stress Concentration and Fatigue Life of
Gears,” International Journal of Fatigue, 21(5), pp 465–474.
(24) Moldovan, Gh., Velicu, D., and Velicu, R. (2007), “On the Maximal
Contact Stress for Cylindrical Gears,” 12th IFToMM World Congress,
Besancon, France, June 18–27.
(25) Sachidananda, H. K., Joseph, G., and Prakash, H. R. (2012), “Analysis of
Contact Stresses in Altered Tooth-Sum Spur Gearing,” Journal of
Applied Mechanical Engineering, 1(1), pp 1–5.
(26) Sachidananda, H. K., Joseph, G., and Prakash, H. R. (2012),
“Experimental Investigation of Fatigue Behavior of Spur Gear in Altered
Tooth-Sum Gearing,” Frontiers of Mechanical Engineering, 7(3), pp 268–
278.
(27) Sheng, L. and Ahmet, K. (2011), “A Fatigue Model for Contacts under
Mixed Elastohydrodynamic Lubrication Condition,” International Journal
of Fatigue, 33(3), pp 427–436.
(28) Singh, A., Houser, D. R., and Vijayakar, S. (1996), “Early Detection of
Gear Pitting,” ASME Power Transmission and Gearing Conference, 88,
pp 673–678.
(29) Vera, N. S. and Ivana, C. (2003). “The Analysis of Contact Stress on
Meshed Teeth’s Flanks along the Path of Contact for a Tooth Pair,”
Mechanics, Automatic Control and Robotics, 3(15), pp 1055–1066.
(30) William, J. and Richard, S. (2005), “Rolling Contact Fatigue of Surface
Densified FLN2-4405,” International Journal of Powder Metallurgy,
41(3), pp 49–61.
View publication stats