David G. Lewicki

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Effect of Speed (Centrifugal Load) on

Gear Crack Propagation Direction

NASA/TM—2001-211117

August 2001

ARL–TR–1314

U.S. ARMY

RESEARCH LABORATORY
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U.S. ARMY

RESEARCH LABORATORY

David G. Lewicki

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Effect of Speed (Centrifugal Load) on

Gear Crack Propagation Direction

NASA/TM—2001-211117 ARL–TR–1314
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

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Available electronically at http://gltrs.grc.nasa.gov/GLTRS
EFFECT OF SPEED (CENTRIFUGAL LOAD) ON 

GEAR CRACK PROPAGATION DIRECTION 

Keywords: Crack Propagation , Fracture Mechanics, Centrifugal Force, Finite Element Method

ABSTRACT 

The effect of rotational speed (centrifugal force) on gear crack 

propagation direction was explored. Gears were analyzed using 

finite element analysis and linear elastic fracture mechanics. The 

analysis was validated with crack propagation experiments 

performed in a spur gear fatigue rig. The effects of speed, rim 

thickness, and initial crack location on gear crack propagation 

direction were investigated. Crack paths from the finite element 

method correlated well with those deduced from gear experiments. 

For the test gear with a backup ratio (rim thickness divided by tooth 

height) of mb=0.5, cracks initiating in the tooth fillet propagated to 

rim fractures when run at a speed of 10,000 rpm and became tooth 

fractures for speeds slower than 10,000 rpm for both the 

experiments and analysis. From additional analysis, speed had 

little effect on crack propagation direction except when initial crack 

locations were near the tooth/rim fracture transition point for a 

given backup ratio. When at that point, higher speeds tended to 

promote rim fracture while lower speeds (or neglecting centrifugal 

force) produced tooth fractures. 

INTRODUCTION 

Effective gear designs balance strength, durability, reliability, 

size, weight, and cost. However, unexpected gear failures may 

occur even with adequate gear tooth design [1]. In order to design 

an extremely safe system, the designer must ask and address the 

question “what happens when a failure occurs”. With regard to 

gear tooth bending fatigue, tooth or rim fractures may occur. For 

aircraft, a crack which propagates through a rim would be 

catastrophic, leading to disengagement of a rotor or propeller, loss 

of an aircraft, and possible fatalities [2]. This failure mode should 

be avoided. A crack which propagates through a tooth itself may or 

may not be catastrophic, depending on the design and operating 

conditions. Also, early warning of this failure mode may be 

possible due to advances in modern diagnostic systems. 

Fracture mechanics has developed into a useful discipline for 

predicting strength and life of cracked structures. Linear elastic 

fracture mechanics applied to gear teeth has become increasingly 

popular. The stress intensity factors are the key parameters to 

estimate the characteristics of a crack. Analytical methods (such as 

weight function techniques) as well as numerical methods have 

been used to estimate gear tooth stress intensity factors [3-4]. 

Based on stress intensity factors, fatigue crack growth and gear life 

predictions have been investigated [5-6]. In addition, gear crack 

trajectory predictions have been addressed in a few studies [7-10]. 

In high speed components, centrifugal force can significantly 

contribute to the applied loading of the structure. This effect on 

crack propagation has been investigated for turbine blades [11] but 

has not been looked at with respect to gears. 

The objective of the current study is to determine the effect of 

centrifugal force on gear crack propagation. The goal is to prevent 

catastrophic rim fracture failure modes when considering gear tooth 

bending fatigue. Analysis was performed using the finite element 

method with principles of linear elastic fracture mechanics. Crack 

propagation paths were predicted for a variety of gear tooth and rim 

configurations. Experiments were performed in a gear fatigue 

apparatus to validate crack predictions. The effects of speed 

(centrifugal force), rim thickness, and initial crack location were 

considered. Crack trajectories are presented for the variety of cases 

studied indicating gear tooth or gear rim fracture modes. 

ANALYSIS 

Basic gear tooth geometry data was input to a tooth coordinate 

generation computer program. The tooth coordinate generator 

program used the method of [12] to determine the tooth coordinates. 

The output was tooth coordinate and rim coordinate data which 

defined a single-tooth sector of a gear. This output was used by a 

commercially available pre- and post-processing finite element 

analysis software package [13]. This package created the finite 

element mesh of the complete gear. The mesh was then imported to 

the FRANC (FRacture ANalysis Code) computer program. 

FRANC is a general purpose finite element code for the static 

analysis of cracked structures [14]. The program is designed for 

two-dimensional problems, uses principles of linear elastic fracture 

mechanics, and is capable of analyzing plane strain, plane stress, or 

axi-symmetric problems. Eight-node quadrilateral or six-node 

triangular elements can be used. Point forces can be applied at 

nodes to simulate gear tooth loading. Also, body forces due to 

angular rotation can be used to account for centrifugal force speed 

effects. The deflections, stresses, and stress intensity factors from 

the point forces and body forces can then be added together using 

superposition. 

Among the variety of capabilities, a unique feature of the 

program is the ability to model a crack in a structure. The program 

uses a method called "delete and fill" to accomplish this. To 

illustrate, consider a finite element mesh of an uncracked structure. 

The user would first define an initial crack by identifying the node 

of the crack mouth and coordinates of the crack tip (Fig. 1a). 

FRANC would then delete the elements in the vicinity of the crack 

tip, insert a rosette of quarter-point, six-node triangular elements 

around the crack tip to model the inverse square-root stress 

singularity, then fill the remaining area between the rosette and 

original mesh with conventional six-node triangular elements (Fig. 

1b). The user would then run the finite element equation solver to 

determine nodal displacements, forces, stresses, and strains. Mode 

I and mode II stress intensity factors, KI and KII, respectively, can 

be calculated using a variety of methods. (Mode I loading refers to 

loads applied normal to the crack plane which tend to open the 

crack. Mode II refers to in-plane shear loading. In addition, the 

crack propagation angle is a function of KII / KI.) The stress 

intensity factors quantify the state of stress in the region near the 

crack tip. In the program, the stress intensity factors can also be 

used to predict the crack propagation trajectory angles, again using 

a variety of methods. 

A further unique feature of FRANC is the automatic crack 

propagation capability. After an initial crack is inserted in a mesh, 

the program simulates crack propagation as a number of straight 

line segments. For each segment (or step), the program solves the 

David G. Lewicki

U.S. Army Research Laboratory

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

NASA/TM—2001-211117 1
finite element equations, calculates the stress intensity factors, and 

calculates the crack propagation angle. The program then places 

the new crack tip at the calculated angle and at a user-defined crack 

increment length. The model is then re-meshed using the "delete 

and fill" method described above. The procedure is repeated a 

number of times as specified by the user. Fig. 1c shows the 

predicted crack propagation path of a gear tooth. In this example, 

the predicted crack trajectory was after 29 steps, i.e., the crack 

trajectory was approximated by 29 line segments. 

A typical finite element gear model used in the current study 

is shown in Fig. 2. The mesh shown is for an uncracked gear. The 

gear design is the baseline used in the current study. The design 

parameters are: 28 teeth, 3.175-mm module, 44.45-mm pitch radius, 

20° pressure angle, and a 6.35-mm face width. The model had 2255 

plane stress, 8-node, quadrilateral elements and 7122 nodes. For 

improved accuracy, the mesh was refined in the upper portion of 

the model (this is the region where cracks will be inserted). The 

tooth load was placed at the highest point of single tooth contact 

(HPSTC), normal to the surface. Although the tooth load changes 

in magnitude and direction in actual gear operations, a static 

analysis with the load at the HPSTC has given accurate results with 

respect to crack propagation analysis [9]. Four hub nodes at the 

gear inner diameter were fixed to ground to constrain the model. 

The material used was steel. In addition, slots were incorporated in 

the model to vary the rim thickness. The model shown has a 

backup ratio, mb=1.0. The backup ratio is defined as the rim 

thickness, b, divided by the tooth height, h (Fig. 3). As stated 

before, crack propagation angles are determined from the 

calculated stress intensity factors. In the current study, the stress 

intensity factors were determined from the finite element method 

nodal displacements and forces using the J-integral method [15]. In 

addition, the crack propagation angles were determined from the 

stress intensity factors using the maximum tangential stress theory 

[16]. 

EXPERIMENTS 

Crack propagation experiments were performed in the NASA 

Glenn Spur Gear Fatigue Rig (Fig. 4). The test stand operated on a 

torque-regenerative principle in which torque was circulated in a 

loop of test gears and slave gears. Oil pressure was supplied to load 

vanes in one slave gear which displaced the gear with respect to its 

shaft. This produced a torque on the test gears, slave gears, and 

connecting shafts proportional to the amount of applied oil pressure. 

An 18.6-kW, variable-speed motor provided speed to the drive 

shaft using a belt and pulley. Note that in a torque-regenerative 

system, the required input drive power needs only to overcome the 

losses in the system. 

Separate lubrication systems were provided for the tests gears 

and the main gearbox. The test gears were lubricated using a single 

oil jet at the in-to-mesh location. The main gearbox lubrication 

system provided oil to the loading vanes using a high-pressure 

pump. Also, the main gearbox lubrication system provided oil to 

Fig. 3. Definition of terms backup ratio, mb=b/h.

b 

h 

Fig. 2. Typical finite element model of an uncracked gear; 

28 teeth, 3.175-mm module, 44.45-mm pitch radius, 20° 

pressure angle, mb=1.0.

Tooth load at HPSTC

Slots

Fixed

inner-hub

B.C.s

Fig. 2. Typical finite element model of an uncracked gear; 

28 teeth, 3.175-mm module, 44.45-mm pitch radius, 20° 

pressure angle, mb=1.0.

Tooth load at HPSTC

Slots

Fixed

inner-hub

B.C.s

Test gears

Slave gears

Load

pressure

Loading

vane

Drive shaft

Fig. 4. NASA Glenn spur gear fatigue rig.

Test gears

Slave gears

Load

pressure

Loading

vane

Drive shaft

Fig. 4. NASA Glenn spur gear fatigue rig.

Crack mouth

Crack tip Quarterpoint

rosette

Simulated

crack

trajectory

(a) (b)

(c)

Fig. 1. Crack modeling scheme using finite element method. 

(a) user-defined initial crack, (b) final mesh of initial crack, 

(c) predicted crack propagation path.

Initial

crack

region

Crack mouth

Crack tip Quarterpoint

rosette

Simulated

crack

trajectory

(a) (b)

(c)

Fig. 1. Crack modeling scheme using finite element method. 

(a) user-defined initial crack, (b) final mesh of initial crack, 

(c) predicted crack propagation path.

Initial

crack

region

NASA/TM—2001-211117 2
the slave gears and support bearings. The test gear and main 

gearbox lubrication systems were separated by labyrinth seals on 

the gear shafts pressurized with nitrogen gas. Even though two 

separate systems existed, a common oil was used for both since 

some leakage occurred between the two. The lubricant used was a 

synthetic paraffin oil. In addition, the test gear lubricant was 

filtered through a 5-micron fiberglass filter. 

The spur gear fatigue rig was primarily developed for surface 

pitting fatigue life investigations. For surface pitting fatigue tests, 

the test gears are run offset to increase the tooth contact stress and 

promote surface fatigue. For the current crack propagation studies, 

however, the desired failure mode was tooth bending fatigue. 

Therefore, the gears were run with full tooth width contact, not 

offset. 

The test gear geometry data are given in Table I. The gears 

were external spur gears. The teeth had involute profiles with 

linear tip relief starting at the HPSTC and ending at the tooth tip. 

The maximum amount of tip relief was 0.013 mm at the tooth tip. 

The test gear material was consumable-electrode vacuum-melted 

AISI 9310 steel. The gears were case-carburized and ground. The 

teeth were hardened to a case hardness of Rc 61 and a core hardness 

of Rc 38. The effective case depth (depth at a hardness of Rc 50) 

was 0.81 mm. Previous studies on these test gears showed that 

speed effects on crack propagation direction would be most 

prevalent for a backup ratio of mb=0.5 [7]. Thus, slots were 

machined in the gears to give a backup ratio of mb=0.5 (Fig. 5a). 

Table I. Test gear geometry 

(gear tolerance per AGMA class 12) 

Number of teeth 28 

Module, mm 3.175 

Whole depth, mm 7.620 

Addendum, mm 3.175 

Base circle radius, mm 41.77 

Chordal tooth thickness, mm 4.851 

Pressure angle, deg 20 

Pitch diameter, mm 88.90 

Outside diameter, mm 95.25 

Root fillet, mm 1.016 to 1.524 

Tip relief (at tooth tip), mm 0.013 

Tooth profile surface finish, μm rms 0.41 

Tooth and rim width, mm 6.35 

Hub width, mm 19.05 

It was believed that tooth bending fatigue cracks would be 

difficult to initiate based on the load capacity of the test rig. Due to 

this limitation, notches were fabricated in the fillet region (loaded 

side) on one tooth of each of the test gears to promote crack 

initiation. Notch specifications were as follows: 0.25 to 0.50-mm 

notch length, 40.5-mm notch mouth radius (location of greatest 

tensile stress of an uncracked gear), notch angle normal to fillet 

surface, notch machined along entire tooth face width. Fig. 5b 

shows a magnified view of a typical notched tooth. The notches 

were fabricated using electrodischarge machining (EDM) with a 

0.10-mm diameter wire electrode. A total of four test gears had 

notches installed. Table II gives the measured notch characteristics. 

Fig. 6 gives the nomenclature for the notch parameters of Table II. 

The objective of the tests was to determine the effect of speed 

on gear crack propagation direction. Four tests were performed. 

Test 1 was run at 2500 rpm, test 2 at 4920 rpm, test 3 at 7500 rpm, 

and test 4 at 10,000 rpm (Table II). Note that test 2 was originally 

specified for 5000 rpm, but was reduced to 4920 rpm due to facility 

resonance conditions. At the start of each test, the gears were run 

for a short break-in period of 20 to 123 N⋅m torque. After break-in, 

the gears were run at a steady load condition of 123 N⋅m. If fracture 

did not occur after a reasonable period of time, the load was 

incrementally increased and the gear were run until fracture 

occurred. The actual run loads ranged from 123 to 152 N⋅m. Test 

gear oil inlet temperature was set at 46° C. After occurrence of a 

failure (tooth or rim breakage), the gears were removed from the rig, 

cleaned, and photographed. 

RESULTS AND DISCUSSION 

Rotating Disk Model

Before analyzing gears, the FRANC finite element solution 

using the body force loading option was compared to a closed-form 

theoretical solution of a rotating disk. This was done to validate the 

solution using the body force load option of the program. A thin 

disk of uniform thickness rotating with a constant angular velocity 

ω was considered. The finite element model of the disk is shown in 

Fig. 7a. The inner and outer radii of the disk were a=14.73 mm and 

b=48.26 mm, respectively. The disk thickness was 25.40 mm. 

These dimensions roughly matched those of the test gears used in 

the study. However, no slots were used such as with the test gears. 

Material properties for steel were used (Young's modulus: 

E=207 GPa, Poisson's ratio: ν=0.3, mass density: ρ=7700 kg/m3

). 

The model had 768 8-node, plane stress, quadrilateral elements and 

2432 nodes. Only body force due to the angular velocity was used 

Fig. 5. Test gear, mB=0.5. (a) full view, (b) magnified

view of notch in tooth fillet.

(a) (b)

Fig. 5. Test gear, mB=0.5. (a) full view, (b) magnified

view of notch in tooth fillet.

(a) (b)

Table II. Measured notch characteristics. 

Test 

(test gear)

Notch 

mouth, R0

(mm)

Notch 

length, l

(mm)

Notch 

angle, γ

(deg)

Test 

speed 

(rpm)

1 40.50 0.36 93.8 2500 

2 40.60 0.32 108.7 4920 

3 40.42 0.50 96.3 7500 

4 40.50 0.26 118.5 10,000 

R0

l 

γ

Tooth 

fillet 

Notch 

Fig. 6. Measured notch characteristics nomenclature . 

NASA/TM—2001-211117 3
as applied loading. Four nodes of the inner radius were fixed to 

prevent rigid body motion but allow the disk to grow radially. The 

stresses and displacements from the finite element analysis are 

shown in Fig. 7b and 7c for an angular velocity of ω=1047.2 rad/s. 

These compared rather well to those calculated from the 

closed-form elasticity solution of [17]. 

Comparison of Predicted and Experimental Gear Crack Paths

The results of the crack propagation experiments performed 

in the gear fatigue rig are shown in Fig. 8. As stated before, four 

experiments were performed. Test 1 was run at 2500 rpm (Fig. 8a), 

test 2 at 4920 rpm (Fig. 8b), test 3 at 7500 rpm (Fig. 8c), and test 4 

at 10,000 rpm (Fig. 8d). Again, the measured notch dimensions of 

the four test gears are shown in Table II. From the experiments, all 

cracks originated from the notch tip. For tests from 2500 to 7500 

rpm, tooth fractures occurred. For the test at 10,000 rpm, rim 

fracture occurred. For the test at 2500 rpm, tooth fracture occurred 

at an applied torque of 152 N⋅m. For all other tests, fracture 

occurred at an applied torque of 123 N⋅m. 

The predicted crack paths from the finite element analysis are 

compared to the actual crack paths from the experiments in Fig. 8. 

Separate finite element models were analyzed for each test gear 

configuration. Again, the models incorporated slots to give a 

backup ratio of mb=0.5. Initial cracks were inserted in the models 

to correlate with the corresponding notch size, location, and 

orientation of the test gears from Table II. Tooth loads were placed 

at the HPSTC and the magnitudes corresponded to the applied 

torque at fracture of the given test. Also, body loads were applied 

corresponding to the gear speed of the given test. Crack 

propagation was numerically simulated using a crack increment 

size of 0.25 mm. This took 24 to 27 steps to reach the tooth or rim 

boundaries. For models at speeds of 2500 to 7500 rpm, tooth 

fracture occurred. For the model at 10,000 rpm, rim fracture 

occurred. This correlated very nicely with the experiments (Fig. 8). 

Further analysis was performed on the finite element models 

described above. Each of the models of the test gears in Fig. 8 were 

analyzed at gear speeds of 2500, 5000, 7000, and 10,000 rpm. For 

the models of Figs. 8a (test gear 1) and 8b (test gear 2), tooth 

fractures were predicted for all speeds. For the models of Figs. 8c 

(test gear 3) and 8d (test gear 4), rim fractures were predicted at a 

speed of 10,000 rpm and tooth fractures were predicted at all other 

speeds. For the model of test gear 3, the notch mouth radius was 

slightly lower than the other cases (Table II, test gear 3, 7500 rpm). 

For the model of test gear 4, the notch orientation angle was slightly 

larger than the other cases (Table II, test gear 4, 10,000 rpm). These 

later two conditions tended to start the initial crack more toward the 

tooth root, and thus, promoted rim fractures at the higher speeds. 

It should also be noted that the effect of speed on predicted 

crack path is dependent on the magnitude of the applied tooth load 

as well as the magnitude of the gear speed. This is due to the fact 

that the crack propagation angle is a function of KII / KI, and the 

stress intensity factors are determined from the superposition of the 

applied tooth load and body force. Crack propagation paths due to 

only the applied tooth load can lead to tooth or rim fracture, 

depending on the tooth design, backup ratio, and location of the 

initial crack. Crack propagation paths due to the speed-related 

body force lead to rim fracture due to the hoop stress component. 

Thus, the crack path due to the superposition of the tooth load and 

body load is dependent on the relative contributions due to each. 

Stress (MPa)

0

6

12

18

Radial position, r (mm)

10 20 30 40 50

Radial displacement (μm)

1.12

1.14

1.16

1.18

1.20

σθθ

σrr

Franc2d analysis

Elasticity solution

Fig. 7. Comparison of finite element analysis to closed-form 

elasticity solution for a rotating disk. (a) finite element 

model, (b) stresses, (c) displacements.

r

σrr

σθθ

θ a

b

(a)

(b)

(c)

Stress (MPa)

0

6

12

18

Radial position, r (mm)

10 20 30 40 50

Radial displacement (μm)

1.12

1.14

1.16

1.18

1.20

σθθ

σrr

Franc2d analysis

Elasticity solution

Fig. 7. Comparison of finite element analysis to closed-form 

elasticity solution for a rotating disk. (a) finite element 

model, (b) stresses, (c) displacements.

r

σrr

σθθ

θ a

b

(a)

r

σrr

σθθ

θ a

b

r

σrr

σθθ

θ a

b

(a)

(b)

(c)

Fig. 8. Comparison of predicted crack paths with experiments

(black lines: predictions, white lines: experiments). (a) 2500

rpm, (b) 4920 rpm, (c) 7500 rpm, (d) 10000 rpm. 

(a) (b) 

(c) (d) 

NASA/TM—2001-211117 4
As an example of this, the model of the test gear in Fig. 8c at 7500 

rpm and 123 N⋅m torque predicted tooth fracture while the same 

model at 7500 rpm and 61 N⋅m predicted rim fracture. 

Parametric Studies

Parametric studies were performed using the FRANC finite 

element crack propagation code. The effects of speed, backup ratio, 

and initial crack location on gear crack propagation direction were 

investigated. Backup ratios of mb=0.3, 0.5, 0.7, 1.0, and 1.3 were 

studied. Gear speeds of 0, 5000, 10,000, and 15,000 rpm were used. 

Initial crack locations from those slightly below the base circle on 

the tooth fillet to those on the tooth root centerline were 

investigated. For all cases, the applied tooth load was placed at the 

HPSTC and corresponded to an applied torque of 123 N⋅m. 

Fig. 9 shows the analysis for a backup ratio of mb=0.3. For an 

initial crack mouth location of R0=41.33 mm (slightly below the 

base circle), rim fracture occurred for a speed of 15,000 rpm and 

tooth fracture occurred for all other speeds (Fig. 9a). For initial 

cracks mouth locations lower than R0=41.33 mm, rim fractures 

occurred for all speeds (R0=40.81 mm shown in Fig. 9b). Fig. 10 

shows the analysis for a backup ratio of mb=0.5. Here, the 

transition point was at R0=40.35 mm. At R0=40.35 mm, tooth 

fractures occurred for 0 and 5000 rpm while rim fractures occurred 

at 10,000 and 15,000 rpm (Fig. 10b). For R0>40.35 mm, tooth 

fractures occurred for all speeds (Fig. 10a). For R0<40.35 mm, rim 

fractures occurred for all speeds (Fig. 10c). Fig. 11 shows the 

analysis for a backup ratio of mb=0.7. Here, the tooth/rim fracture 

transition point was at R0=41.33 mm. Fig. 12 shows the analysis 

for a backup ratio of mb=1.0 and Fig. 13 shows the analysis for a 

backup ratio of mb=1.3. For both of these cases, the tooth/rim 

fracture transition point was at the root centerline. 

As seen from these studies, speed had little effect on crack 

propagation direction except when the initial crack location was 

near the tooth/rim fracture transition point for the given backup 

ratio. When at that point, higher speeds tended to promote rim 

fracture while lower speeds (or neglecting centrifugal force) 

produced tooth fractures. 

CONCLUSIONS 

The effect of speed (centrifugal force) on gear crack 

propagation direction was explored. Gears were analyzed using 

finite element analysis and linear elastic fracture mechanics. The 

analysis was validated from crack propagation experiments 

performed in a spur gear fatigue rig. The effects of speed, backup 

ratio, and initial crack location on gear crack propagation direction 

were investigated. The following conclusions were derived: 

1) Stresses and deflections from the finite element method 

correlated well with a closed-form elasticity solution for a rotating 

disk example problem. Crack paths from the finite element method 

correlated well with those deduced from gear experiments. 

2) For the test gear with a backup ratio of mb=0.5, cracks 

initiating in the tooth fillet propagated to rim fractures when run at a 

speed of 10,000 rpm and tooth fractures for speeds slower than 

10,000 rpm for both the experiments and analysis. 

3) Speed had little effect on crack propagation direction 

except when initial crack locations were near the tooth/rim fracture 

transition point for a given backup ratio. When at that point, higher 

speeds tended to promote rim fracture while lower speeds (or 

neglecting centrifugal force) produced tooth fractures. 

0-5k 

15k 10k 0k 15k 

Fig. 9. Effect of speed on crack propagation path, mB=0.3. (a)

R0=41.33 mm, (b) R0=40.81 mm. 

(a) (b) 

Fig. 10. Effect of speed on crack propagation path, mB=0.5. 

(a) R0=41.33 mm, (b) R0=40.35 mm, (c) R0=root centerline. 

(a) 

(b) 

0-15k 

0k 

5k 

15k 10k 0-15k 

(c) 

Fig. 11. Effect of speed on crack propagation path, mB=0.7. 

(a) R0=41.33 mm, (b) R0=40.03 mm, (c) R0=root centerline. 

(a) 

(b) 

0-15k 

0k 

5k 

15k 10k 

(c) 

0k 15k 

NASA/TM—2001-211117 5
REFERENCES 

1. Couchan, D.C., Barnes, G.K., and Cedoz, R.W., "Shot-Peened 

Gear Failures Due to Operation in a Misaligned Condition", 

AIAA Paper No. AIAA-93-2147 (1993). 

2. Albrecht, C., "Transmission Design Using Finite Element 

Method Analysis Techniques", Journal of American Helicopter 

Society, Vol. 33, No. 2 (1988), 3-14. 

3. Abersek, B., and Flasker, J., "Stress Intensity Factor for 

Cracked Gear Tooth", Theoretical and Applied Fracture 

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Optimization of Specific Sliding, Stress Concentration, and 

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A.R., and Handschuh, R.F., "Consideration of Moving Tooth 

Load in Gear Crack Propagation Predictions", Proceedings of 

the 8th International Power Transmission and Gearing 

Conference, Baltimore, MD, USA (2000). 

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D.G., "Simulating Fatigue Crack Growth in Spiral Bevel 

Gears", Engineering Fracture Mechanics, Vol. 68, No. 1 

(2001), 53-76. 

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Prediction of Turbine Blades by Computer Modeling", SBIR 

Phase II Final Report, Contract No. N688335-94-C-0193 

(1998). 

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Theory, Vol. 20, No. 4 (1985), 351-360. 

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(1991). 

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5k 

10k 15k 

0k 

15k 

Fig. 12. Effect of speed on crack propagation path, mB=1.0. 

(a) R0=40.01 mm, (b) R0=root centerline. 

(a) (b) 

0k 

10k 

15k 

0k 

15k 

Fig. 13. Effect of speed on crack propagation path, mB=1.3. 

(a) R0=39.99 mm, (b) R0=root centerline. 

(a) (b) 

0-5k 

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12

Effect of Speed (Centrifugal Load) on Gear Crack Propagation Direction

David G. Lewicki

Gears; Crack propagation; Fracture mechanics; Finite element method; Centrifugal force

Unclassified -Unlimited

Subject Category: 37 Distribution: Nonstandard

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Prepared for the International Conference on Motion and Power Transmissions sponsored by the Japan Society of

Mechanical Engineers, Fukuoka, Japan, November 15–17, 2001. Responsible person, David G. Lewicki, organization

code 5950, 216–433–3970.

The effect of rotational speed (centrifugal force) on gear crack propagation direction was explored. Gears were analyzed

using finite element analysis and linear elastic fracture mechanics. The analysis was validated with crack propagation

experiments performed in a spur gear fatigue rig. The effects of speed, rim thickness, and initial crack location on gear

crack propagation direction were investigated. Crack paths from the finite element method correlated well with those

deduced from gear experiments. For the test gear with a backup ratio (rim thickness divided by tooth height) of mb = 0.5,

cracks initiating in the tooth fillet propagated to rim fractures when run at a speed of 10,000 rpm and became tooth

fractures for speeds slower than 10,000 rpm for both the experiments and analysis. From additional analysis, speed had

little effect on crack propagation direction except when initial crack locations were near the tooth/rim fracture transition

point for a given backup ratio. When at that point, higher speeds tended to promote rim fracture while lower speeds (or

neglecting centrifugal force) produced tooth fractures.