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L. Zhao et al.
to excessive surface contact stress and root fillet fractures due to excessive tooth
bending stress are two main fatigue failure modes for gears [1]. The accumulation
of defects and a high concentration of stresses in micro defects are also dangerous in
the event of shocks which occur during the operation of mechanisms. Micropitting
on the tooth surface of the gear can cause it to break [2]. Tooth breakage causes a
catastrophic failure, so gear bending stress analysis methods must be reliable and
understanding the key influence parameters on bending stress is very important to
improve bending strength. Pressure angle is one which plays an essential role in
determining the bending stress.
A pressure angle 20° was adopted for standard gears according to ISO 53:1998(E)
[3]. The standard pressure angle 20° is a compromise value and cannot meet all the
needs of the different applications because of the limited load capacity on root fillet.
So in many cases, non-standard pressure angles need to be designed in order to
improve the gear performance.
Recently, there have been many efforts made to explore the application of nonstandard pressure angle gears. Gupta [4] calculated and compared the maximum
bending and contact stress for the low dedendum spur gears with different pressure
angles using finite element method. Handschuh [5] investigated the effects of high
pressure angle gears compared with typical gear designs, the analysis of contact and
bending stress had been done on three gears- standard 3.18 module, 28 tooth and 20°
pressure angle, 2.12 module, 42 tooth and 25° pressure angle and 1.59 module, 56
tooth and 35° pressure angle. Sankar [6] studied the effects of pressure angle and tip
relief on the failure of a helical gear pairs. Dadhanlya [7] presented a study on the
effect of pressure angle on bending stress and deformation of asymmetric involute
spur gear using FEA. Oda [8] introduced a study on the effect of pressure angle,
helix angle and whole tooth depth on the bending strength.
However, a very critical parameter– root fillet radius is defined by tool (hob) tip
radius was not concerned in the research. Since the bending critical section occurs
in the gear root fillet, root fillet radius has a great influence on gear bending strength.
The root strength can be improved by using a circular fillet design or optimized
fillet design according to [9–11]. And the maximum tool tip radius will vary with
the pressure angle changing due to the geometrical relationship of basic rack [3].
So in this paper, the bending stress of a spur gear pair with identical dedendum and
different pressure angles (14.5°, 17.5°, 20°, 22.5° and 25°) and the variation of root
fillet radius are studied.
After reviewing the references, gear bending stress in spur gears can be evaluated
with four methods namely, standard methods like ISO standards [12] and AGMA
standards [13], 3D-TCA method, Finite Element Analysis (FEA) and experimental
methods. In this paper three methods of predicting bending stress—ISO standard,
3D-TCA method and Finite Element Analysis are applied to example gear geometry
and compared to make sure the results are valid.
L. Zhao et al.
to excessive surface contact stress and root fillet fractures due to excessive tooth
bending stress are two main fatigue failure modes for gears [1]. The accumulation
of defects and a high concentration of stresses in micro defects are also dangerous in
the event of shocks which occur during the operation of mechanisms. Micropitting
on the tooth surface of the gear can cause it to break [2]. Tooth breakage causes a
catastrophic failure, so gear bending stress analysis methods must be reliable and
understanding the key influence parameters on bending stress is very important to
improve bending strength. Pressure angle is one which plays an essential role in
determining the bending stress.
A pressure angle 20° was adopted for standard gears according to ISO 53:1998(E)
[3]. The standard pressure angle 20° is a compromise value and cannot meet all the
needs of the different applications because of the limited load capacity on root fillet.
So in many cases, non-standard pressure angles need to be designed in order to
improve the gear performance.
Recently, there have been many efforts made to explore the application of nonstandard pressure angle gears. Gupta [4] calculated and compared the maximum
bending and contact stress for the low dedendum spur gears with different pressure
angles using finite element method. Handschuh [5] investigated the effects of high
pressure angle gears compared with typical gear designs, the analysis of contact and
bending stress had been done on three gears- standard 3.18 module, 28 tooth and 20°
pressure angle, 2.12 module, 42 tooth and 25° pressure angle and 1.59 module, 56
tooth and 35° pressure angle. Sankar [6] studied the effects of pressure angle and tip
relief on the failure of a helical gear pairs. Dadhanlya [7] presented a study on the
effect of pressure angle on bending stress and deformation of asymmetric involute
spur gear using FEA. Oda [8] introduced a study on the effect of pressure angle,
helix angle and whole tooth depth on the bending strength.
However, a very critical parameter– root fillet radius is defined by tool (hob) tip
radius was not concerned in the research. Since the bending critical section occurs
in the gear root fillet, root fillet radius has a great influence on gear bending strength.
The root strength can be improved by using a circular fillet design or optimized
fillet design according to [9–11]. And the maximum tool tip radius will vary with
the pressure angle changing due to the geometrical relationship of basic rack [3].
So in this paper, the bending stress of a spur gear pair with identical dedendum and
different pressure angles (14.5°, 17.5°, 20°, 22.5° and 25°) and the variation of root
fillet radius are studied.
After reviewing the references, gear bending stress in spur gears can be evaluated
with four methods namely, standard methods like ISO standards [12] and AGMA
standards [13], 3D-TCA method, Finite Element Analysis (FEA) and experimental
methods. In this paper three methods of predicting bending stress—ISO standard,
3D-TCA method and Finite Element Analysis are applied to example gear geometry
and compared to make sure the results are valid.