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A comparison of gear tooth bending fatigue lives from single tooth bending and rotating gear tests

Ein Vergleich der Ermüdungserscheinungen von Zahnradzähnen aus Einzelzahnbiege- und Drehgetriebetests

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Abstract

Gear tooth bending fatigue failures are instantaneously catastrophic to gear drive power transmission systems. For this reason, gear designers must understand the limits of their design with respect to the desired application and service time. Fatigue testing on gear specimens has been preferred metric on which to base future designs. Single Tooth Bending test (STB) or a Rotating Gear (RG) test methodologies have been used for this purpose. STB type tests generally form the large majority of gear fatigue testing due to cost and availability but does not fully simulate the actual operating conditions of rotating gears in service. As RG evaluations are costly and time-consuming, it is desirable to quantify how a stress-life (SN) relationship regressed through STB testing compares to that produced in RG testing. In this study, both STB and RG test methodologies are employed to test the same specimen design. Matrices of fatigue tests are executed and statistical regression techniques are used to estimate bending fatigue lives as a function of stress for both sets of data. The resultant SN curves are compared to determine any differences in allowable stress. Techniques are then employed using single set data (STBF or RG individually) to demonstrate the calculation of correlation coefficients, which can approximate the total difference determined between the two data sets.

Zusammenfassung

Ermüdungsfehler der Zahnzahnbiegung sind augenblicklich katastrophal für Getriebeantriebssysteme. Ermüdungsprüfungen an Verzahnungsproben wurden für zukünftige Konstruktionen bevorzugt. STB-Baumusterprüfungen bilden in der Regel aufgrund der Kosten und der Verfügbarkeit die überwiegende Mehrheit der Getriebeermüdungsprüfungen, simulieren aber nicht vollständig die tatsächlichen Betriebsbedingungen rotierender Zahnräder im Betrieb. In dieser Studie werden sowohl STB- als auch RG-Testmethoden verwendet, um dasselbe Probendesign zu testen. Die resultierenden SN-Kurven werden verglichen, um eventuelle Unterschiede in der zulässigen Spannung zu bestimmen. Techniken werden dann unter Verwendung einzelner gesetzter Daten (STBF oder RG einzeln) verwendet, um die Berechnung der Korrelationskoeffizienten zu demonstrieren, die die Gesamtdifferenz näherungsweise bestimmen können, die zwischen den zwei Datensätzen bestimmt wird.

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Abbreviations

B 50 :

50% failure rate

f :

fatigue test frequency

f s :

number of surface initiated failures

f s s :

number of subsurface initiated failures

F :

STBF test applied force

K d :

dynamic factor

K I :

initiation location factor

K S :

statistical factor

K R S :

total RG to STB factor

K F :

loading factor

K R :

stress factor

N :

number of cycle in a test

N f :

number of cycles to failure

\(N_{if}^{s}\) :

number of cycles to failure for a surface initiated specimen

\(N_{if}^{ss}\) :

number of cycle to failure for a subsurface initiated specimen

p :

failure percentile

q R G :

failure percentile of teeth on a RG specimen

r f :

ratio of surface initiated to total number of failures

R :

fatigue test stress ratio

α 1 :

regressed intercept constant

α 2 :

regressed slope constant

β 1 :

regressed variance constant

γ :

regressed fatigue strength constant

σa :

stress amplitude

σm :

stress mean

σult :

ultimate tensile stress

\(\sigma _{\mathrm{fat}-RG}\) :

fatigue strength from RG test

\(\sigma _{\mathrm{fat}-\mathrm{STB}}\) :

fatigue strength from STBF test

\(\overline{\sigma }_{g}^{f=0}\) :

measured gage stress at 0 Hz

\(\overline{\sigma }_{g}^{f=40}\) :

measured gage stress at 40 Hz

\(\overline{\sigma }_{\max }\) :

normalized maximum gear tooth root bending stress

\(\overline{\sigma }_{RG}^{\left(p\right)}\left(N_{f}\right)\) :

RG SN curve at specified failure percentile

\(\overline{\sigma }_{\mathrm{STB}}^{\left(p\right)}\left(N_{f}\right)\) :

STB SN curve at specified failure percentile

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  1. Gear and Power Transmission Research Laboratory, Department of Mechanical and Aerospace Engineering, The Ohio State University, 43210, Columbus, OH, USA

    Isaac Hong, Zach Teaford & Ahmet Kahraman

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  1. Isaac Hong
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Correspondence to Isaac Hong.

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I. Hong, Z. Teaford and A. Kahraman declare that they have no competing interests.

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Hong, I., Teaford, Z. & Kahraman, A. A comparison of gear tooth bending fatigue lives from single tooth bending and rotating gear tests. Forsch Ingenieurwes 86, 259–271 (2022). https://doi.org/10.1007/s10010-021-00510-w

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