Effects of pressure angle and tip relief on the life of speed increasing gearbox: a case study
Effects of pressure angle and tip relief on the life of speed increasing gearbox: a case study
Sankar Shanmugasundaram 0
Manivarma Kumaresan 2
Nataraj Muthusamy 1
0 Department of Mechanical Engineering, Nehru College of Engineering and Research Centre , Thrissur , India
1 Department of Mechanical Engineering, Government College of Technology , Coimbatore , India
2 Department of Mechanical Engineering, Sri Krishna College of Engineering and Technology , Coimbatore , India
This paper examines failure of helical gear in speed increasing gearbox used in the wind turbine generator (WTG). In addition, an attempt has been made to get suitable gear micro-geometry such as pressure angle and tip relief to minimize the gear failure in the wind turbines. As the gear trains in the wind turbine gearbox is prearranged with higher speed ratio and the gearboxes experience shock load due to atmospheric turbulence, gust wind speed, non-synchronization of pitching, frequent grid drops and failure of braking, the gear failure occurs either in the intermediate or high speed stage pinion. KISS soft gear calculation software was used to determine the gear specifications and analysis is carried out in ANSYS software version.11.0 for the existing and the proposed gear to evaluate the performance of bending stress tooth deflection and stiffness. The main objective of this research study is to propose suitable gear micro-geometry that is tip relief and pressure angle blend for increasing tooth strength of the helical gear used in the wind turbine for trouble free operation.
Failure analysis; Helical gear; Wind turbine gearbox; Profile modification; Bending stress; Tooth deflection; KISS soft; ANSYS
The function of gear drive is to transmit high power
with compact design as to run with free of noise and
vibration with least manufacturing and maintenance cost.
Sankar and Nataraj have introduced circular root fillet
instead of trochoidal root fillet in spur gear to increase
the tooth strength (Sankar and Nataraj 2011). Many
works have been done to improve the gear tooth strength
out of which most of them attempted with positive profile
shifting (Fredette and Brown 1997; Ciavarella and Demelio
1999). Sankar and Nataraj have launched a novel method
called composite profile along with tip relief in helical gear
to prevent gear failure in the wind turbine generator
gearbox (Sankar and Nataraj 2010). Andrzej and Jerzy have
done a comparative study to evaluate root strength using
ISO and AGMA standards and the results are verified
using the finite element technique with model
development and simulations (Andrzej and Jerzy 2006). Simon
formulated a design method to find out the optimal tooth
tip relief and crowning for spur and helical gears (Simon
1989). Sankar et al. (2011) have formulated mathematical
model to analyze the failure of shear pin in the wind turbne
generator using finite element technique. Hebbal et al.
(2009) have formulated a finite element model with a
segment of three teeth for analysis and stress relieving features
of various sizes on helical gear teeth at various locations.
Senthilvelan and Gnanamoorthy (2004) have evaluated
the gear performance with the help of finite element
analysis using a power absorption type gear test rig.
Mao established the gear micro geometry
modifications mathematically for power train gear transmission
using python script interfaced with finite element
models (Mao 2006).
Jiande Wang and Ian Howard (2008) demonstrated
the influence of high-contact-ratio spur gears in mesh
with tooth profile modification by using modern
numerical methods via comprehensive analysis. Tae et al. (2001)
discussed tooth modification for minimizing the vibration
exiting force and noise in helical gears. Beghini et al.
(2004) proposed a method to reduce the transmission
error of spur gear at the normal torque through profile
modification parameters. Satoshi et al. (1988) studied the
effect of standard pressure angle on the bending strength
of helical gears by using the approximate equation to a
Figure 1 Sectional view of the wind turbine generator gearbox.
considerable extent. Satoshi et al. (1986) analyzed the
tooth deflection and bending moment at the root fillet in
helical gear for various pressure angles by finite difference
method. Shan Chang et al. (2005) used tip relief and root
relief to reduce the high contact stresses occur at the root
corners in the entering and exiting regions. Alexander
et al. (2003) presented a novel method for bending stress
Figure 2 Failed pinions.
Figure 3 Gear profile with tip relief.
Figure 4 Gear pressure angle.
balance using one-hundred-year-old Lewis equation
suggesting an approach to the tooth parameter’s tolerance
and tooth profile definition.
In general, tooth profile modification methods are
used to reduce the meshing vibration and noise of gear
train. Kinds of such methods are (i) Tooth profile
modification towards involute curve (ii) Lead crowning and
End relief towards face width and so on. Many research
papers have been published towards reducing noise and
vibration of spur gears by make use of tooth profile
modification towards involute curve but an attempt has
not been made to propose simultaneous optimum profile
modification towards involute curve for various pressure
angle of helical gears employed in the wind turbine
generator gearbox, to the best knowledge of the investigator.
Therefore, it is imperative to investigate the problem of
failure of helical gear in the wind turbine.
The particular model wind turbine generator is built
with gearbox comprising of one planetary stage and two
Table 1 Design specifications of the existing pinion
Tip relief (mm)
Table 2 Design specifications of the modified gear pair
helical stages. The first helical stage called slow speed
line has 94 teeth/24 teeth gear combination and the
second helical stage called high speed line has 106 teeth/35
teeth gear combination to get the final rated speed of an
electric generator. This speed increasing gearbox raises
abnormal noise, have scuffing wear and pitting wear,
during peak generation of the wind turbine in high wind
season, which ultimately leads to either tooth damage or
failure of pinion itself. Besides, if any pinion in the
intermediate stage undergone failure, while the wind turbine
generator is running, it’s horrible to swap the pinion
alone at tower top (nacelle) at the wind turbine site due
to complication in the gearbox design. At this point of
time, the only available solution is de-erection of the
nacelle for swapping the gearbox. Moreover, for
deerection of nacelle a huge capacity crane (400 or 800
Ton capacity) is required at wind turbine site for
swapping the gearbox. The sectional view of the wind turbine
generator gearbox is depicted in Figure 1.
In the past 2-3 years, the wind turbine site come
across numerous failures of 24 teeth pinion which is
coming in 94 teeth/24 teeth gear combination. Figure 2
shows two different cases of 24 teeth intermediate
pinion failure happen at the wind turbine site recently. The
gear pair is made of 8 mm module having 20° pressure
angle with tiny say 0.002 mm tip relief. The technical
team inspected the damaged pinion (Figure 2) and
presumed that the failures may be due to either overload by
wind force or misalignment of shaft between the gearbox
and the generator. Gear manufacturer and researchers
are exploring the possibilities either on development of
advanced materials such as 3Ni-4.5Mo alloy and
3Ni2Cu alloy (Popgoshey and Valori 2009) new methods of
Number of teeth (z)
Face width (b)
Reference diameter (d)
Base diameter (db)
Tooth quality (Q-DIN3961)
Center distance (a)
Tip diameter (da)
Addendum modification co-efficient (x)
Root diameter (df)
Total contact ratio
Tip relief ( Ca)
Effective chordal tooth thickness
Table 3 Tooth details from KISS soft gear calculation
No of teeth (z) Pr angle (α) Add (ha) Ded (hf) Centre distance(a)
24 15 12.278 5.288 485.00
Figure 5 Pro-E models of the modified 24 teeth pinion.
heat treatment for gears such as Low Pressure
Carburizing (LPC) with high pressure gas quench and Press
Quenching of Gears (Nicholas Bugliarello et al. 2010) or
on the design of stronger tooth profiles (Sankar et al.
2011) and on the new gear manufacturing process. This
research study is intended to know the root cause of
failure of pinion and to minimize to minimize the
pinion failures in gearboxes used in the wind turbines
through design modification such as pressure angle and
the tip relief.
Geometry of the tip relief
Tip relief is discretionary modification of the tooth
profile near the tip of the tooth to eliminate tip interference.
It is considered desirable for the involute to be a few
thousandths minus at the tip and never plus. Tip relief is
given to gears during gear grinding operation through
dressing or truing of grinding wheel with the help of
special diamond disc in case of multi rib grinding wheel
Figure 6 Tooth forces in helical gear.
Table 4 Force components of the load
Table 5 Material properties
Force components (N)
and single point diamond dresser with special template
for single rib grinding wheel. The conventional amount
of tip relief is given in the existing standards like British
Standard (BS 1970) and (ISO/DIS 1983), where the
maximum amount of tip and flank modifications are defined
as shown in Figure 3, including parameters such as
maximum amount of tip relief (Ca max) = 0.02 times of
module and maximum length of tip relief (ΔLa max) = 0.6
times of module to prevent the possibility of excess
relief. In Figure 3, where
In this study the standard tip relief limitations have been
chosen as reference values to normalize the amount of
profile modification. There are two different tip relief
methods exist for profile modification which are (i) Linear
and (ii) Parabolic variations. The modified profile form
used in this research involves the original involute and the
relief was achieved by rotating the original curve through
relief angle ‘αr’ about the relief starting point ‘S’ as shown
in Figure 3. Pressure angle is the angle between the tooth
profile and a perpendicular to the pitch circle usually at
the point where the pitch circle meets the tooth profile as
shown in Figure 4. The pressure angle affects the force
that tends to separate mating gears.
Lines of Contact
(before surface is crowned)
Path of Contact
(after surface is crowned)
Points of Contact
(after surface is crowned)
Lines of Contact (Helical Gear) ANSI/AGMA 1012-G05
A high pressure angle means that higher ratio of teeth
are not in contact. However, this allows (i) the teeth to
have higher load carrying capacity (ii) allows less
number of teeth without undercutting (iii) tooth flank
becomes more curved and hence relative sliding velocity is
reduced (iv) the tooth pressure and axial pressure is
increased. (v) Increase of pressure angle results in a
stronger teeth, because the tooth acting as a beam is wider at
the root (Sankar and Nataraj 2010). This analysis is
carried out for three different pressure angles say 15°, 20°
and 22.5° for various tip relief length and amount.
Table 1 gives the design specifications of the existing 24
teeth helical pinion and Table 2 gives the design
specifications of the modified 24 teeth helical pinion. These design
specifications have been arrived from KISS soft software
according to DIN 3990 method ‘B’ standards. According
to KISS soft gear calculation software, the addendum and
dedendum values can be interchanged for the mating gear
pair having correction factor. As the addendum of the
pinion may be more than one module and the dedendum has
been reduced to less than one module.
The tip relief is introduced in the pinion profile for the
corresponding change in pressure angle as given in
Table 2. The models with appropriate tip relief with
respective pressure angles generated through Pro-E
wildfire version 3.0 software are presented in Figure 5.
Figure 7 Line of contact in helical gear.
Figure 8 FEA meshed model of a single tooth.
Table 6 Lewis maximum bending stress values
Maximum bending stress (N/mm2)
Force analysis for helical gears can be made in similar
manner as in the case of spur gears (Sankar and Nataraj
2011). Because of the helix angle, an additional force
component is produced. This appears as an axial force
with the resulting axial thrust on the bearings. The
pictorial view of helical gear tooth forces is shown in Figure 6.
In helical gears tooth force FN acts normal to the tooth
surface at an angle equal to the pressure angle. This tooth
force is resolved into three components which act at right
angles to one another. The interrelations of these
components are established from Figure 6. The three
dimensional force patterns are obtained with their magnitudes
which are shown below (Equation 1 to 5):
Tangential forceðFtÞ ¼ 2000T=d
Axial forceðFaÞ ¼ Ft
PowerðPÞ ¼ T
α Pressure angle
β Helix angle
N Speed in rpm
d Pitch circle diameter in mm
T Driving torque in Nm
While the helical gear pair is transmitting the load, the
leading end of the tooth comes in contact first and the
trailing end last. Thus the tooth picks up load gradually
and the contact progresses gradually along the whole
range of the tooth width that is in helical gear pair,
sharing of load will take place based on the contact ratio,
covering the tooth face and flank.
In actual practice, trochoidal root filet is formed in gears
during manufacturing process depending on the tip radius
of the hob. It was proved that the bending stress decreases
gradually in gears as the number of teeth increases and
the total contact ratio increases (Spitas et al. 2005).
According to Gitin Maitra, if a gear is undercut for one
reason or another, it may become sometimes necessary to
know the magnitude of the undercutting radius (Gitin
Maitra 1998). Under such circumferences, he proposed a
formula (Equation 6) to find out the minimum number of
teeth to avoid undercutting which is as follows:
Figure 9 ANSYS resultsc.
Referring to the above equation, the minimum number
of teeth to avoid undercut problem for 15° pressure
angle pinion is 30. Similarly, it is 17 and 14 for 20°
pressure angle pinion and 22.5° pressure angle pinion
respectively. Further, the above expression is valid for
standard gear tooth with the addendum of the rack
being equal to the module ‘Mn′. However, the undercut–
free minimum number of teeth is given by Equation 7.
Where, hca is the addendum of the rack cutter without
tip filet rounding. It is obvious from KISS soft gear
calculation (Table 3) that the addendum and dedendum of
the in-use 20° pressure angle pinions is 12.279 mm and
5.481 mm respectively. Similarly, the addendum and
dedendum of its mating gear are 9.20 mm and 8.56 mm
respectively. So, if addendum of the cutter is 5.481 mm
without tip fillet rounding then based on Equation 7, the
minimum number of teeth to avoid undercut–free
operation on 20° pressure angle pinion is 12. So, it is very
clear that the undercut risk is carefully considered in this
20° pressure angle design and hence the pinion number
of teeth is chosen as 24. In the same way, the addendum
and dedendum of the 15° pressure angle pinions is 12.278
mm and 5.288 mm respectively. Also, it is 9.006 and 8.56
mm for its mating gear. So, if addendum of the cutter is
5.288 mm without tip fillet rounding then based on
Equation 7, the minimum number of teeth to avoid
undercut–free operation for 15° pressure angle pinions is 20.
But, in these study only 24 teeth was considered for the
entire model. So it is very clear from the study that the 15°
pressure angle pinion does not have an undercut problem.
Besides, according to shigley, the minimum number of
teeth to avoid interference for 20° pressure angle full depth
profile is 17. Similarly, it is greater than 23 for 15° pressure
angle pinion (Shigley 2008). So, the modified design would
not face any interference problem too.
The force exerted by the helical pinion on its mating
gear acts normal to the contacting surface if the friction
is neglected. However, a normal force in case of helical
gear has three components that is apart from the
tangential force (Ft) and radial force (Fr) that are present in
spur gear, a third component parallel to the axis of the
shaft called axial force (Fa) or thrust force exists. These
components of force are computed for a power value of
1252 kW at pinion speed of 509.2 rpm. These values are
given in Table 4.
As far as the transmission power is concerned, the
tangential force (Ft) is really the useful component,
because the radial force (Fr) and axial force (Fa) serves no
useful purpose. Hence, only the tangential force was
applied in the entire model say 15°, 20° and 22.5° for
evaluating the performance in FEA using ANSYS.
Finite element analysis
In this study finite element model with a single tooth is
considered for analysis. Gear material strength is major
consideration for the operational loading and environment.
Generally cast iron is used in normal loading and higher
wear resisting conditions. In modern practice, the heat
Table 7 FEA results
and contact ratio
Ca = 0.002
Ca = 0.16
Ca = 0.002
Ca = 0.08
Ca = 0.16
Ca = 0.002
Ca = 0.08
Ca = 0.16
Figure 10 Deflection comparison graph.
treated alloy steels are used to overcome the wear
resistance. In this work, carburized and case hardened alloy steel
(17CrNiMo6) is considered and ANSYS version 11.0
software is used for analysis. According to ANSI/AGMA
1012G05 standard as in Figure 7, the strength analysis is carried
out for the traditional and the modified 24 teeth pinion.
The gear tooth is meshed in 3 dimensional (3-D)
SOLID 20 nodes 186 elements with fine mesh (size 3).
SOLID186 has a quadratic displacement behavior and is
well suited to model irregular meshes. The material
properties chosen for analysis are presented in Table 5. In order
to facilitate the finite element analysis the gear tooth is
considered as cantilever beam and tooth force is applied
diagonally along the line of contact as shown in Figures 7
and 8. Besides, same number of elements was selected and
the loading was followed for the entire three models
during the Finite Element Analysis for the better results.
Further, the maximum tooth bending stress (σ) for the
particular pinion speed is calculated (Table 6) using
the Lewis formula (Equation 8) and are compared with
the ANSYS result (Shigley 2008).
K y ¼ 5:56 ffiVffiffi; V = π × d × N/60,000 (m/s) and
Y=Lewis form factor
Maximum Deflection (mm) for 0.08 mm Tip Relief
Maximum Deflection ( mm) for 0.16 mm Tip Relief
Maximum Bending Stress (N / mm²)
Maximum Bending Stress (N / mm²)
Maximum Bending Stress (N / mm²)
Figure 11 Bending stress comparison graph.
Discussion and evaluation
In this paper a comparative study was carried out
between three different pressure angles to select an
appropriate profile to avoid frequent failure of pinion used in
the gearbox of wind turbine generator. The analysis was
carried out after introducing tip relief amount of 0.002
mm, 0.08 mm and 0.16 mm to the pinions in ANSYS.
The induced bending stress and deflection (Figure 9) in
24 teeth pinion provided with known tip relief for
different pressure angle and the calculated stiffness for the
corresponding tangential force are presented in Table 7.
Figure 10 shows the comparison plot between deflection
and pressure angles while the pinion is subjected to load.
It is obvious from Table 7 that the pinion having 20°
pressure angle with 0.002 mm tip relief experience
236.606 N/mm2 bending stress and 0.017381 mm
deflection. Similarly, pinion having 15° pressure angle with
0.002 mm tip relief have undergone approximately the
same deflection (0.017056 mm) but least bending stress
(145.588 N/mm2) among the other models; whereas the
deflection is minimum (0.000122 mm) in pinion having
22.5° pressure angle with 0.16 mm tip relief but the
duced bending stress (479.471 N/mm ) is above the
Lewis maximum bending stress (432.180 N/mm2). It is
also understood from Table 7 that only the pinion having
15° pressure angle with 0.002 mm tip relief and 20°
pressure angle with 0.002 mm tip relief are experiencing lesser
bending stress (145.588 N/mm2 and 236.606 N/mm2) than
the Lewis maximum bending stress (432.180 N/mm2).
Further, it is obvious from force analysis topic that the
factors influencing for gear failure such as undercut and
interference problems are very well considered in this
design calculation. So, it is evident from the study that
the frequent pinion failure is not because of wrong
selection of minimum number of teeth.
Further, it is observed from the plot (Figure 10) that
the tooth deflection is in down trend for pinion with
0.16 mm tip relief with increase in pressure angle.
However, it is different in nature for the 0.002 mm and 0.08
mm tip relief. Looking in to the induced bending stress
comparison graph (Figure 11); the helical pinion having
22.5° pressure with 0.16 mm tip relief is around 479.471
N/mm2 which is higher than the Lewis maximum
bending stress (432.180 N/mm2). Further, among the entire
model, pinion having 22.5° pressure angle with 0.08 mm tip
relief undergone maximum bending stress (551.801 N/
mm ). The above analysis and investigation have been done
without changing the operational environment (power,
speed ratio and other critical design specifications).
Based on the results obtained in this study, the following
conclusions can be drawn,
1. It is obvious from Table 7 that only the pinions
having 15° pressure angle with 0.002 mm tip relief
and 20° pressure angle with 0.002 mm tip relief are
experiencing lesser bending stress than Lewis
maximum bending stress. Among the two models,
low pressure angle helical pinion (15° pressure angle
with 0.002 mm tip relief ) running at slow speed
(509.2 rpm) provide improved performance with
lesser bending stress (145.588 N/mm2) over more
traditional 20° pressure angle pinion (236.606 N/mm ).
This was verified through ANSYS analysis.
2. Even though the 20° pressure angle pinion have
many practical advantages such as it reduces the risk
of undercut, it has greater length of contact and
stronger at root, it is evident from Figure 2 that
because of more sharp and weaker at the tip when
compared to the modified pinion (15° pressure
angle) the traditional pinion (20° pressure angle)
undergone breakage of tooth only at the tip portion
in all the cases.
3. The study infers that the 15° pressure angle pinion
(contact ratio 3.117) is a superior choice for slow
speed stage of gearbox used in the wind turbine
generator. Here the author’s recommendation to
avoid frequent pinion failure is that instead of using
20° pressure angle gear pair in both slow speed and
high speed stage the traditional gear pair (20°
pressure angle) having contact ratio 2.948 can be
used only at high speed stage as the high-pressure
angle gears are most efficient when operated in
the high speed.
Z: Number of teeth; Mn: Normal module; α: Normal pressure angle; β: Helix
angle; d: Pitch circle diameter; db: Base circle diameter; a: Centre distance;
da: Tip circle diameter; x: Addendum modification co-efficient; dr: Root circle
diameter; ha: Addendum; hf: Deddendum; Ca: Permissible tip relief amount;
ΔLa: Allowable tip relief length; Fa: Axial force; Fr: Radial force; Ft: Tangential
force; FEA: Finite element analysis; WTG: Wind turbine generator.
The authors declare that they have no competing interests.
SS conducted the research study at P.V Gear Designers, Coimbatore, India. VKM
completed the analysis part in FEA using ANSYS. The published results are
actually received during the ANSYS study. The article was then written by SS and
reviewed by MN. The authors have read and approved the final manuscript.
The authors wish to acknowledge the help provided by the staff members
of P.V. Gear Designers, Combatore, India, in providing the necessary technical
support for successful completion of this study.
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