Nenad G. Nenadic, Joseph A. Wodenscheck, and Michael G. Thurston

Rochester Institute of Technology, Rochester, New York

David G. Lewicki

Glenn Research Center, Cleveland, Ohio

Seeding Cracks Using a Fatigue Tester for

Accelerated Gear Tooth Breaking

NASA/TM—2011-216983

February 2011
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Nenad G. Nenadic, Joseph A. Wodenscheck, and Michael G. Thurston

Rochester Institute of Technology, Rochester, New York

David G. Lewicki

Glenn Research Center, Cleveland, Ohio

Seeding Cracks Using a Fatigue Tester for

Accelerated Gear Tooth Breaking

NASA/TM—2011-216983

February 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

IMAC XXIX A Conference and Exposition on Structural Dynamics

sponsored by the Society for Experimental Mechanics (SEM)

Jacksonville, Florida, January 31 to February 3, 2011
Acknowledgments

This work was made possible by Army Research Laboratory under Award No. W911NF-07-2-0080. We gratefully 

acknowledge the help of our colleagues from Rochester Institute of Technology Dr. Michael Haselkorn, David Fister,

Michael Leaty, and Dominic Maiola for their assistance in destructive crack assessment; Mark Walluk and

Michael Bradley for design of the crack initiation fi xture; and Art Dee LabVIEW

for implementation of the crack detection. 

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2011-216983 1 

Seeding Cracks Using a Fatigue Tester for 

Accelerated Gear Tooth Breaking 

Nenad G. Nenadic, Joseph A. Wodenscheck, and Michael G. Thurston 

Rochester Institute of Technology 

Rochester, New York 14623 

David G. Lewicki 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

This report describes fatigue-induced seeded cracks in spur gears and compares them to cracks 

created using a more traditional seeding method, notching. Finite element analysis (FEA) compares the 

effective compliance of a cracked tooth to the effective compliance of a notched tooth where the crack 

and the notch are of the same depth. In this analysis, cracks are propagated to the desired depth using 

FRANC2D and effective compliances are computed in ANSYS. A compliance-based feature for detecting 

cracks on the fatigue tester is described. The initiated cracks are examined using both nondestructive and 

destructive methods. The destructive examination reveals variability in the shape of crack surfaces. 

Background of the Study 

Of the four dominant modes of gear tooth failure (breakage, wear, pitting, and scoring), breakage is 

the most catastrophic and occurs precipitously, with no advanced warning. The present study is concerned 

with the breakage failure mode exclusively. 

The work described here is a subset of a larger empirical study conducted on high-quality spur gears 

to evaluate performance of vibration-based features for detecting cracks and assessing crack depths. The 

features, also referred to as condition indicators (CIs), are summarized by References 1 to 3. 

In this larger study, the gears are first spun in a dynamometer-based fixture to obtain feature 

baselines. The cracks are then initiated using a fatigue tester to simulate overload conditions. Finally, the 

fatigue induced-cracks are propagated on the dynamometer-based fixture under different operating 

conditions, i.e., different levels of angular speed and torque, while the actual crack length on each gear 

face is measured using crack-propagation sensors. The main objective is to create well-documented, 

statistically significant data for monitoring cracks from inception to failure. 

The complete service life of a gear has two phases: crack initiation and crack propagation (Ref. 4). A 

crack initiation phase is typically much longer than the subsequent crack propagation phase. In crack 

propagation studies, the crack initiation phase is often accelerated by introducing a notch in a gear tooth. 

The present article describes an alternative approach to accelerate crack initiation where higher-thannormal loads are applied on a gear tooth using a fatigue tester. 

Finite Element Analysis (FEA) of a Cracked and a Notched Tooth 

Before proceeding with accelerated crack initiation on a fatigue tester, it was of interest to compare the 

geometry of cracked and notched gear teeth. A gear with a notch was compared to a gear with a crack of the 

same length as the notch using FEA. The gear geometry was generated using a toolkit implemented in 

MATLAB for spur gear drawing and analysis, as shown in Figure 1. The first version of the software was 

created by Reference 5 and implemented by the Army Research Laboratory and NASA in Fortran. The 

present version is implemented by RIT, with added capabilities that include mesh generation and import and 
NASA/TM—2011-216983 2 

Figure 1.—Spur gear geometry generation. 

Figure 2.—A notched tooth generation within the MATLAB-based toolkit. (a) Entire tooth 

geometry using MATLAB. (b) Zoom into crack using MATLAB. (c) Notch exported into ANSYS. 

export capabilities. The toolkit is capable of generating the gear tooth geometry, creating a finite element 

mesh using linear triangular elements, and exporting the meshed geometry to two commercially available 

finite element programs, FRANC2D and ANSYS. The mesh generator employs the distmesh algorithm and 

implementation (Ref. 6). The implementation is tailored to generate finer mesh near the application of force 

and high stress areas. Figure 2 shows the meshed geometry of a notched tooth, with nonuniform mesh 

density, generated entirely within the toolkit. The generation of the cracked tooth is a bit more involved. The 

uncracked tooth geometry is generated in the MATLAB toolkit. The geometry is then exported to 

FRANC2D, a program for simulation of crack growth (Ref. 7) where the initial crack was formed and 

propagated to the desired length. The cracked geometry is then read and exported to ANSYS via the 

MATLAB toolkit. 

(a) (b) (c)
NASA/TM—2011-216983 3 

Figure 3 shows ANSYS static analysis of a gear with a notch, and a gear with a crack. The view is 

zoomed into the area of notch/crack. To minimize the difference in the crack length and the notch length, we 

generated the cracked geometry first, and then generated the notch later by aligning the tip of the notch to 

the tip of the crack. 

In the first analysis, a static force of 1000 lb was applied at the gear pitch radius, normal to the 

surface, and the magnitude of the displacement was measured at the tip of the outer radius, as depicted in 

Figure 4(a). The simulation was repeated for two crack/notch lengths: ≈ 1/8 of the total gear thickness and 

≈ 1/4 of the total gear thickness. Two notch sizes were studied. One for a notch radius of R = 0.001 in., 

and the other for a notch radius of R = 0.002 in. The effect of mesh density on the result for the cracked 

tooth was also considered. Although we computed displacements, the results can be expressed also as 

effective compliances, since the force is held constant. 

The FEA results are summarized in Table 1 and Figure 4(b). For the crack/notch length of 1/8 of the 

gear thickness all the displacements are virtually indistinguishable, they are within less than 0.2 percent of 

the mean. For a crack/notch length equal to 1/4 of gear thickness, the notched gear exhibits larger 

displacements. 

Figure 3.—Exaggerated deformations and contours of equivalent stress (psi). (a) Notch. (b) Crack. 

Figure 4.—Static analysis. (a) Annotated contours of equivalent stress. (b) Plot summary of 

displacements versus crack length. 

(a) (b)

|u| = 0.00133

(a) (b) F = 1000 lb
NASA/TM—2011-216983 4 

TABLE 1.—FEM DISPLACEMENTS (in.) OF CRACKED AND NOTCHED GEAR TEETH 

Normalized 

crack length 

Crack Notch 

Regular mesh Refined mesh R = 0.001 in. R = 0.002 in. 

0.125 1.33420E-03 1.33530E-03 1.33620E-03 1.33660E-03 

0.25 1.87280E-03 1.87740E-03 1.97050E-03 2.00100E-03 

TABLE 2.—FUNDAMENTAL FREQUENCY (Hz) OF NOTCHED 

AND CRACKED GEAR TEETH

Normalized 

crack length 

Crack Notch 

Regular mesh Refined mesh R = 0.001 in. R = 0.002 in. 

0.125 3.02100E+03 3.02100E+03 3.00200E+03 2.98900E+03 

0.25 2.56700E+03 2.56300E+03 2.54500E+03 2.52400E+03 

Figure 5.—Modal analysis. (a) Fundamental mode shape. (b) Summary of fundamental frequencies. 

An alternative metric for comparison of cracked and notched teeth is the fundamental natural 

frequency of a gear tooth. Figure 5(a) shows the fundamental mode shape of the gear section of interest 

associated with the fundamental natural frequency. The fixed boundary conditions are indicated. 

Table 2 and Figure 5(b) summarize the FEA results of the modal analysis. Table 2 shows the actual 

frequencies, while Figure 5(b) shows the frequency shifts from the baseline case, where the baseline is a 

healthy gear. The frequency decreases as the crack/notch grows. The notches give rise to the larger shifts, 

but the difference between the notched and cracked teeth is small. 

Overall, the analysis shows that a crack and notch of the same length agree very well. Although by a 

small amount, notched gears exhibit more change in effective compliance and frequency shifts than their 

cracked counterparts. Thus, it is expected that a vibration feature is slightly more sensitive to the notched 

tooth than to the cracked tooth. 

(a) (b)
NASA/TM—2011-216983 5 

Crack Initiation Fixture and Crack Initiation Process 

The cracks were initiated on a commercially available fatigue tester. A special fixture, shown in 

Figure 6, was designed, developed, and built for this purpose. The fixture captures a single gear between 

two steel plates and uses an anvil to assert a load on to a single tooth. The gray anvil holder, shown in 

Figure 6(a), is inserted into the machine’s lower ram and secured using a pin. The anvil is held within the 

anvil holder and captured with two set screws. The anvil width is greater than the gear tooth width and the 

anvil material is made of tool steel for strength. The anvil gear tooth interface is 5 with respect to 

horizontal, similar to the ASME J1619 single tooth fatigue test fixture (Ref. 8). To provide the contact 

area near the high point of single tooth contact (HPSTC), the centerline of the gear tooth under test is 

located at 15.4 with respect to the ground; see Figure 6(c). The gear is located between the 1 in. thick 

steel plates with a 1.181 in. diameter shaft locating the center of the gear. Keys were used to position the 

gear teeth with respect to polar angle. The primary device to react the input torque to the gear, however, 

was three internal gear teeth, shown in brown below, and three fasteners to provide clamping friction. 

Interfacing with several points within the fixture to transfer the input torque to the machine prevented 

damage to gear teeth not under test. The two side plates were fastened together and then bolted to a 

bottom subplate. This subplate was threaded and welded to a connecting rod, shown in red that threaded 

into the load cell on the fatigue tester. 

The fatigue tester operated in load control mode with a cyclic compressive load between 100 and 

3100 lb applied at a rate of 10 Hz. The crack initiation region (tooth root) was always held in tension 

during the test. 

A compliance-based feature was developed for early detection of cracks, since the displacementbased feature did not have sufficient resolution. The crack detection is based on observation of N

estimations of the feature. We compute the described feature in N points. The first N-M points are used to 

establish the baseline distribution of the feature, and the last M points are used for determining if the 

crack occurred. The crack detection is then based on the likelihood ratio as follows 

 

    

 

N

k N M k o

k

c H

c H

1

1

Pr

Pr

(1) 

where Ho is the null hypothesis that states that there is no crack, i.e., the feature is distributed according 

to the distribution of a healthy gear 

  o k c c H : c ~ N  , (2) 

c and c are sample mean and standard deviation of the feature, excluding the last M points. 





   

N M

k

c k c

N M 1

1 (3)

  



     

N M

k

c k c c

N M 1

2

1

1 (4) 

The alternative hypothesis states that the crack has occurred, that is, the feature ck does not belong to 

the baseline distribution, but to a normal distribution centered around threshold 

  k c H1 : c ~ N , (5) 
NASA/TM—2011-216983 6 

Figure 6.—The fixture for crack initiation. (a) Computer aided design image. (b) Photograph of the built fixture. 

(c) Anvil angle detail. 

Figure 7.—Crack detection process. (a) Characteristic signals. (b) Angled view of a cracked tooth. 

(c) 90 view of a cracked tooth. 

Figure 7 depicts the process of crack detection. The compliance feature and the threshold are shown, 

as well as the distribution of the compliance feature. The threshold is set initially at a conservative, 

empirically determined, relatively high value. As more data becomes available, the threshold is adjusted 

to become a certain Mahalanobis distance from the distribution mean. The distance equals to 2.5 c for 

the example shown in Figure 7(a).

(a) (b) (c)

0 20 40

3.5

4

4.5

5

Gear = 23, Tooth = 2

Compliance 

c [

in/lb]

Last Run t (min)

feature c

threshold 

0 10 20

3.5

4

4.5

5

t

@bin [min]

0 20 40

-100

-50

0

50

100

Log Likelihood Ratio

(a)

(b)

(c)
NASA/TM—2011-216983 7 

Figure 8.—Nondestructive method for crack verification. (a) Imaging system. (b) Custom gear fixture. (c) Imaged tooth. 

Crack Verification Using Nondestructive Methods 

The nondestructive crack verification is based on the images taken using a commercially available 

high-resolution, optical video measuring system and custom fixture shown in Figure 8. The custom 

fixture was designed and built to place the test tooth in approximately 500 lb tension. Before the gear is 

placed in the fixture, the tooth under inspection is covered with a layer of fluorescent iron powder. The 

tooth is then placed in a strong magnetic field and observed under ultraviolet (UV) light. At a crack, the 

magnetic lines are disturbed. The magnetic-particle-based inspection method is a standard technique for 

crack detection and it is described in fracture mechanics textbooks, e.g., (Ref. 9). Glowing particles 

indicate fracture site. 

Figure 8 illustrates the nondestructive measurement process. Prior to imaging the tooth had been 

subjected to approximately 29 thousand cycles of load in the 100 to 3100 lb range. The final resulting 

threshold for the compliance feature was 4.40 μin./lb. The tooth was imaged 37.5× magnification. 

This nondestructive method was not completely successful in detecting gear tooth cracks. The gear 

face area was the only region where cracks could be observed. The gear flank surface was considerable 

rougher. Even after polishing, no cracks were detected on the gear flanks. 

Crack Characterization Using Destructive Methods 

The nondestructive inspection method was useful for confirmation of the crack initiation, but did not 

allow crack characterization, that is, determination of the actual crack depths. Two methods are described 

for measuring crack depth and characterization of the fracture surface: slicing and polishing (Method 1) 

and abruptly breaking teeth off after the initiation (Method 2). Figure 9 illustrates both methods. Cracks 

were initiated on several different teeth then inspected using both methods. The teeth in the top of 

Figure 9 were inspected using Method 1 and the three teeth in lower left corner were subjected to the 

ramped load on the fatigue tester until they fractured based on Method 2. 

Method 1 employed a wire EDM to first section a number of previously tested teeth from the gear. 

The sectioned teeth were then sliced perpendicularly to the initial cut. The slices were polished, etched 

with an alcohol/nitric acid solution, and imaged with a standard metallographic microscope. Figure 10 

shows the gear slices as well as images of polished sections of a tooth demonstrating crack length 

differences throughout the tooth thickness. The depth of gear tooth crack propagation was 1 to 1.5 mm in 

this example. 

(a) (b) (c)
NASA/TM—2011-216983 8 

Figure 9.—Destructive inspection of gear tooth cracks. 

Figure 10.—Destructive inspection using Method 1. 

Surface 2

Surface 4

Surface 6

Surface 8

Surface 2 Surface 4 Surface 6
NASA/TM—2011-216983 9 

Method 2 was relatively straight forward. After crack initiation, the test tooth was imaged with the 

fluorescent iron powder, returned to the fatigue fixture, and the static load increased until fracture 

resulted. The fracture surfaces were then imaged with a stereo microscope at 24 and 66× magnification. 

Figure 11 shows crack surfaces of four different teeth (all teeth imaged from the bottom). There is a clear, 

discernable boundary that separates the smooth surface of crack initiation from the rough surface of the 

abrupt breakage (see the annotation in Figure 11(b)). For the various gear tests, the crack depths in the 

middle of the tooth were consistent with imaging obtained using Method 1 and shown in Figure 10. 

However for some tests, the crack depths were virtually zero near the gear faces. It was clear that the 

crack profiles for these cases were significantly different than surfaces produced by notching, which have 

a uniform depth across the thickness of the gear. We have observed that generally as cracks propagate, the 

crack depth becomes more uniform across the gear thickness. Thus, for deeper cracks it is reasonable that 

the crack surface approaches an expected notch surface. This finding also suggests that the compliance 

change used for crack initiation detection as previously described will be different for notched teeth as 

compared to cracked teeth when the crack/notch depth is small. Method 2 was considerably more 

effective, far less labor intensive, and provided an immediate view of the entire crack surface as compared 

to Method 1. Method 1, in addition to being more laborious and requiring interpolation to visualize entire 

crack surface, suffered from a fundamental drawback. The wire EDM process affected crack propagation 

to an unknown and difficult to quantify degree. The advantage of Method 2 was that it was able to show 

details of the crack shape in the direction of the propagation, as shown in Figure 10. 

Figure 11.—Destructive inspection using Method 2. Abrupt break off Init.

Boundary

Multiple initial cracks

(c) (d) (e)

(a) (b)
NASA/TM—2011-216983 10 

Summary 

This paper describes an accelerated crack initiation where a selected tooth is subjected to cyclic 

bending on a fatigue tester. This method of seeding cracks is related to the traditional method (notching) 

using FEA. FEA compares effective compliance and change in fundamental natural frequencies between 

a cracked gear tooth and a notched gear tooth, where the notch and the crack are of the same length and of 

uniform depth. Both metrics consistently show that their dependence on the length of the crack/notch is 

considerably higher than the dependence on the type of damage. The analysis suggests a plausible 

conclusion that a cracked and a notched tooth will exhibit very similar vibration features for a given 

length of crack/notch. 

The fixture for crack initiation and the associated process are described, including a compliancebased feature for crack detection. The induced cracks were verified using a nondestructive methods and 

characterized using the destructive methods. While the nondestructive methods indicate minimal damage 

to the tooth, closer (destructive) inspections show that the crack surface is somewhat irregular initially 

and that the maximum depth of crack propagation can be appreciable at the point of detection by the 

suggested feature. 

References 

1. Zakrajsek, J.J., and Lewicki, D.G., 1998, “Detecting Gear Tooth Fatigue Cracks in Advance of 

Complete Fracture,” Tribotest, 4(4), pp. 407–422. 

2. Lebold, M., Mcclintic, K., Campbell, R., Byington, C., and Maynard, K., 2000, “Review of Vibration 

Analysis Methods for Gearbox Diagnostics and Prognostics,” Proc. 54th Meeting of the Society for 

Machinery Failure Prevention Technology, Virginia Beach VA, pp. 623–634. 

3. Samuel, P.D., and Pines, D.J., 2005, “A Review of Vibration-Based Techniques for Helicopter 

Transmission Diagnostics,” Journal of Sound and Vibration, 282(1–2), pp. 475–508. 

4. Glodez, S., Sraml, M., and Kramberger, J., 2002, “A Computational Model for Determination of 

Service Life of Gears,” International Journal of Fatigue, 24(10), pp. 1013–1020. 

5. Hefeng, B., Savage, M., and Knorr, R.J., 1985, “Computer Modeling of Rack-Generated Spur Gears,” 

Mechanism and Machine Theory, 20(4), pp. 351–360. 

6. Persson, P.O., and Strang, G., 2004, “A Simple Mesh Generator in Matlab,” SIAM review, 46(2), 

pp. 329–345. 

7. Wawrzynek, P.A., 1991, “Discrete Modeling of Crack Propagation: Theoretical Aspects and 

Implementation Issues in Two and Three Dimensions,” Ph.D. Dissertation, Cornell University, 1991. 

8. Gasparini, G., Mariani, U., Gorla, C., Filippini, M., and Rosa, F., “Bending Fatigue Tests of 

Helicopter Case Carburized Gears: Influence of Material, Design and Manufacturing Parameters.” 

9. Broek, D., 1986, Elementary Engineering Fracture Mechanics, M. Nijhoff; Distributors for the U.S. 

and Canada, Kluwer Academic, Dordrecht; BostonHingham, Mass., U.S.A. 
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Seeding Cracks Using a Fatigue Tester for Accelerated Gear Tooth Breaking 

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Nenadic, Nenad, G.; Wodenscheck, Joseph, A.; Thurston, Michael, G.; Lewicki, David, G. 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

This report describes fatigue-induced seeded cracks in spur gears and compares them to cracks created using a more traditional seeding 

method, notching. Finite element analysis (FEA) compares the effective compliance of a cracked tooth to the effective compliance of a 

notched tooth where the crack and the notch are of the same depth. In this analysis, cracks are propagated to the desired depth using 

FRANC2D and effective compliances are computed in ANSYS. A compliance-based feature for detecting cracks on the fatigue tester is 

described. The initiated cracks are examined using both nondestructive and destructive methods. The destructive examination reveals 

variability in the shape of crack surfaces. 

15. SUBJECT TERMS

Cracks; Gear teeth; Crack propagation 

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