D. B. Owen: Handbook of Statistical Tables. London: Pergamon Press; Reading, Massachusetts: Addison‐Wesley, 1962. Pp. xii+580. 70s.

Handbook of Statistical Tables.

On the useful life of tribo-pairs experiencing variable loading and sliding speed

In this study, a crack initiation life prediction methodology for the tooth bending fatigue of hypoid gears is proposed. This methodology employs a previously developed finite-element based hypoid gear root stress model (Hotait et al. 2011, “An Investigation of Root Stresses of Hypoid Gears with Misalignments,” ASME J. Mech. Des., 133, p. 071006) of face-milled and face-hobbed hypoid gears to establish the multiaxial stress time histories within the root fillet regions. These stress time histories are combined with a multiaxial crack initiation fatigue criterion to predict life distributions along roots of the pinion and the gear. The predictions of the multiaxial fatigue model are compared to those from a conventional uniaxial fatigue model to establish the necessity for a multiaxial approach. The model is exercised with an example face-milled hypoid gear set from an automotive application to demonstrate the impact of various misalignments well as the key cutting tool parameters on the resultant tooth bending lives.

Estimation of Bending Fatigue Life of Hypoid Gears Using a Multiaxial Fatigue Criterion

The gears in a gear box fitted in an armoured tracked vehicle for the purpose of power transmission and positioning of rotating heavy mass to the desired angle with high accuracy are subjected to fluctuating loads that are random in nature. One of the important modes of failure in cyclic loading conditions including random loads is fatigue failure. It is thus important from the design point of view to estimate the life of the gears under these conditions. The fatigue life of components subjected to sinusoidal loading can be estimated by using cumulative damage theories. Their extension to random load fatigue, though straightforward, may not be very accurate owing to inherent scatter exhibited by the fatigue phenomenon. It is therefore necessary experimentally to determine the fatigue life of randomly loaded components and establish the validity of the theoretical model. An electrohydraulic test rig has been designed and fabricated that is capable of generating different types of load pattern by ad...

Bending fatigue testing of gear teeth under random loading

This paper presents a design method for prediciting the fatigue life of T-joint assemblies loaded by random loads, based on a statistical analysis of tests. This sduty was on the correclation between the types of loading observed in practive and test results obtained for fatigue life determination. The work follows three steps: analysis tof the statistical distributions of random loads that illustrate extremen value from Markov matrix representations; statistical analysis of lifetimes obtained when the specimens are sbumitted to random loads defined earlier; design of a set of endurance curves [stress-number of cycles to failure (S-N) curves], called ‘random’ S-N curves. These SN curves. These S-N curves are shifted compared with that obtained under sinusoidal loading. Random S-N curve positions in the S-N plane are obtimized depending on the lifetime able to take into account the damege due to the small cycles that are often present in actual loading. The use of random S-N curves for fatigue life...

Design of welded structures working under random loading

Bending Fatigue Strength of Gear Teeth under Random Loading

This report presents the test results about bending fatigue strength of gear tooth under two kinds of repeated 16 steps program loads which are gradually increasing or decreasing. Load frequencies are gamma distributed. Materials of test gears are normalized S38C and carburized SCM21. Each of test gears has module 4mm, pressure angle 20 degrees, number of teeth 27 and width 8mm. Miner's cumulative damage theorem is statistically tested and the following facts have become clear : (1) Factor of loading sequence and load frequency distribution are not significant. (2) Factor of material is significant. (3) Fatigue life has a trend that the longer the program load cycle period is, the longer is the fatigue life in comparison with the values calculated from Miner's theorem. (4) Frequency of stress which is higher than fatigue limit strength has little correlation to C. (5) The scatter of Miner's constant C is mainly due to the scatter of fatigue life, and C itself is rather deterministic.

Bending Fatique Strength of Gear Teeth under Random Loading : Part 2, Program test under gamma distributed 16 steps Loading

Power transmission gears are usually used under fluctuating loads. But in the case of strength design of such gears we cannot get sufficient fatigue data and therefore the effectiveness of Miner's rule on fatigue strength is uncertain. This report deals with a new gear tooth pulsator for program and random fatigue tests and with the results of a test which was carried out under a programmed 16 steps loading. The frequencies of loads are distributed uniformly and the variation of mean load is like a saw tooth wave with positive and negative slopes. Normalized S38C and carburized SCM21 gears were tested. Every test gear had 27 teeth, 4mm module and 8mm width. Under the above condition the effects of loading sequence, changing rate and mean level of program load, gear material and heat treatment were investigated. And, though Hardrath has shown a program loading sequence effect for 7075-T6 aluminium alloy, the author's experiment indicates that its effect is not significant at the 5% level for both S38C and SCM21 gears. By arranging the cumulative damage statistically, it is concluded that Miner's theorem is not valid in the strict sense and further investigation is necessary to conclude whether Miner's rule is applicable to the fatigue design of gears.

Bending Fatique Strength of Gear Teeth under Random Loading : Part 1, About the Gear Tooth Pulsator and the Results of Fatique Tests under Uniformly Distributed 16 Steps Program Loading

Kunikazu Hayashi

Papers

Bending Fatigue Strength of Gear Teeth under Random Loading

Bending Fatique Strength of Gear Teeth under Random Loading : Part 2, Program test under gamma distributed 16 steps Loading

Bending Fatique Strength of Gear Teeth under Random Loading : Part 1, About the Gear Tooth Pulsator and the Results of Fatique Tests under Uniformly Distributed 16 Steps Program Loading

On the Static Stiffness of Contiguous Surface of Machine Tools : Stiffness for Bending Milling Arbor