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Bending fatigue in spur gears, which transpires due to cyclic and variable tooth root stresses, is one of the main reasons for gear failure. Bending fatigue can bring about crack initiation, propagation and possible complete failure of the gear tooth. To investigate and possibly prevent such occurrence, single tooth bending fatigue tests are often used to obtain statistically significant bending fatigue data at a comparatively low price. In material fatigue, relatively minor change of nominal stress results can produce significant shift in fatigue lives. Hence, to accurately interpret and apply single tooth bending fatigue results on a running gear pair, it is of great importance to properly consider the effect of friction forces on gear load capacity. In this paper, numerical investigation of tooth flank friction effect on gear load capacity during single tooth bending fatigue test is conducted. Finite element analysis, whilst considering various friction coefficients and test fixture dimensions, is carried out to obtain nominal tooth root stresses. The aim of the research is to optimize the rigidity of the experimental fixture to minimize the influence of friction forces on nominal tooth root stress results. Confirmation of the aforestated goal is insinuated by the preliminary results of the numerical investigation.

A numerical model, based on the finite element and the strain-life methods, is proposed to estimate tooth bending fatigue life of case- carburized steel spur gear from number of cycles required to initiate surface fatigue crack at the tooth root fillet. The fatigue life estimates were found to correlate very well with the available experimental lives from pulsator testing. The model is used then to correlate fatigue life estimates for two load cases: the first one in which the gear tooth is loaded with pulsating load acting at the outer point of single pair tooth contact, and the second one in which quasi-static meshing of the gears is considered.

Spur gears are one of the most commonly employed machine elements for power transmission. During their operating life, they are subjected to variable and cyclic loading. Consequently, material fatigue may occur in the tooth root region, more commonly referred to as bending fatigue. Steel gears are typically subjected to heat treatment processes such as carburizing to reduce wear. Additionally, the gears may be shot peened to induce a beneficial, fatigue-resistant surface layer of compressive residual stresses. However, this may result in bending fatigue crack initiation below the surface, i.e., subsurface bending failure. This type of crack is hardly detectable during regular service intervals. Hence, it may often go unnoticed, grow, and propagate rapidly through the brittle carburized layer, resulting in tooth breakage and gear failure. This doctoral thesis establishes a computational model for predicting the bending fatigue crack location (surface vs. subsurface) and the required number of cycles for surface-hardened spur gears. Due to the relative complexity of the gear’s geometry and loading conditions, the finite element method is employed to obtain load-induced stresses and strains. The multilayer method is employed to account for inhomogeneous material, while the strain life approach (ε – N) is used to predict the bending fatigue life. The research is divided into multiple stages. During the initial stages, bending fatigue with surface/subsurface crack initiation is investigated on relatively simple geometry, such as surface-hardened gear steel specimens. Then, the model is gradually upgraded to account for more complex loading conditions, residual stress distributions, and inhomogeneous material until the final model applicable to the running gear pair is acquired. According to the obtained numerical results and confirmed by the experimental investigations from the available literature, subsurface bending fatigue crack initiation tends to occur only in carburized and additionally shot-peened gears. The critical region for subsurface failure is located in the proximity of sharp loss of compressive residual stresses and still relatively high load-induced stresses. The probability of subsurface crack initiation can be reduced by modifying the gear’s geometry (choosing a smaller normal module) or increasing the beneficial compressive residual stresses by prolonging the carburization time. Zupčanici su jedni od najčešće korištenih strojnih elemenata u prijenosnicima snage i gibanja. Vođeni strogim proračunskim kriterijima prema relevantnim standardima kao što je ISO 6336, čelični zupčanici s ravnim zubima u pravilu zadovoljavaju minimalni očekivani radni vijek. Međutim, postojeći standardi ne uzimaju u obzir zajednički utjecaj dodatnih postupaka površinskog otvrdnjavanja, kao što su cementiranje i sačmarenje, na pojavu zamora materijala u korijenu zuba. U takvim slučajevima, javlja se potreba za računskim modelom koji može procijeniti ne samo broj ciklusa do pojave zamorne pukotine, već i mjesto nastanka spomenute pukotine (površinski naspram potpovršinski nastanak). Mjesto nastanka zamorne pukotine od posebne je važnosti zbog njene otežane detekcije tijekom redovnih servisnih intervala. U okviru rada razvijen je računski model temeljen na metodi slojeva (eng: multilayer method) te metodi konačnih elemenata (eng: finite element method – FEM) koji predviđa mjesto te broj ciklusa do nastanka zamorne pukotine u korijenu zuba zupčanika. Zbog relativne kompleksnosti modela, istraživanje je započeto na uzorcima izrađenim od materijala tipično korištenim za izradu čeličnih zupčanika. Predloženi model postepeno je unaprijeđen kako bi se simulirala stvarna geometrija te opterećenje zupčanog para.

Odgovarajućom nosivošću zupčanih parova osigurava se da ne dođe do nastanka oštećenja koja mogu utjecati na normalan rad unutar predviđenog životnog vijeka. S obzirom da se opterećenje s pogonskog na gonjeni zupčanik prenosi na način da mijenja svoj pravac djelovanja, položaj i intenzitet, mijenja se i naprezanje u korijenu zuba zupčanika koje može izazvati lom zuba uslijed zamora materijala. U radu je primjenom metode konačnih elemenata pomoću programskog paketa Abaqus određen ciklus naprezanja u korijenu zuba. Pretpostavljeno je da su oba zupčanika izrađena od istog materijala te da je materijal homogen, izotropan i linearno elastičan. Analizirani su cilindrični zupčanici s ravnim simetričnim i asimetričnim zubima te je provedena usporedba njihovih ciklusa naprezanja. Kako bi sama računalna simulacija što realnije odgovarala stvarnim uvjetima rada zupčanog para, u obzir su uzeti i faktori poput centrifugalnog opterećenja i/ili trenja te je analiziran i njihov utjecaj. Određeno je mjesto maksimalnog naprezanja u korijenu zuba, tj. kritični presjek te je uspoređeno s mjestom maksimalnog naprezanja prema normi HRN EN ISO 6336-3. By choosing the appropriate load capacity of gear pairs it is ensured that no damage occurs which could affect normal operation within the expected service life. Since the load from the operating to the driven gear is transferred in a way that it changes it's direction, position and intensity, the tooth root stress also changes, which can cause breakage of the teeth due to bending fatigue. In thesis, the tooth root stress cycle was determined using finite element method and Abaqus software package. It s assumed that both gears are made of the same material which is considered to be homogenous, isotropic and linearly elastic. Cylindrical gears with symmetric and assymetric involute teeth were analyzed and their stress cycles were compared. In order to conduct the simulation as accurately as possible, factors such as centrifugal load and/or friction were taken into account and their influence on the tooth root stress cycle was analyzed. The place of maximum principal stress in tooth root, i.e. the critical cross section, was determined and compared with the place of maximum stress according to the standard HRN EN ISO 6336-3.

Zamor materijala uslijed cikličkog opterećenja jedan je od glavnih uzroka loma zuba zupčanika. Na mjestima gdje dolazi do koncentracije naprezanja, kao što je korijen zuba zupčanika, mogu nastati pukotine, a njihovim daljnjim širenjem može doći i do konačnog loma zuba što može imati katastrofalne posljedice na stroj. Jedna od metoda kojom se ispituje nosivost korijena zuba zupčanika je metoda cikličkog savijanja jednog zuba. Takvo testiranje omogućuje prikupljanje podataka o ponašanju zupčanika u području zamora velikim brojem ciklusa na brz i financijski učinkovit način u kontroliranim laboratorijskim uvjetima. U uvodu rada dan je kratak pregled glavnih uzroka oštećenja zupčanika općenito, zajedno s vrstama najčešćih oštećenja zupčanika. U nastavku rada opisano je nekoliko metoda ispitivanja cikličkim savijanjem jednog ili više zuba istovremeno. Metoda opterećivanja zupčanika u tri točke i metoda ispitivanja u SAE postolju detaljnije će se obraditi. Fokus rada je na utjecaju sile trenja na rezultate ispitivanja navedenih metoda. Primarno će se razmotriti utjecaj sile trenja na naprezanje u korijenu zuba. Analiza spomenutih metoda biti će provedena pomoću metode konačnih elemenata, korištenjem programskog paketa Abaqus 6.13-1. Na samom kraju rada prikazat će se dobivenih rezultati i iz njih izvedeni zaključci. Fatigue caused by cyclic loading is one of the main reasons for gear tooth failure. In areas with high stress concentration, such as gear tooth root, cracks can develop and further spreading of those cracks can result in the final fracture of gear tooth, which can have catastrophic consequences on the machine. One of the methods used for testing load capacity of gear tooth root is the single-tooth fatigue test. This type of test allows collecting fatigue data in high-cycle field of loading in a fast and economically efficient manner under controlled laboratory conditions. The introduction of this paper gives a brief overview of the main causes of gear tooth failures in general, along with the most common types of gear tooth failures. Furthermore, several methods for testing gear teeth via cyclic bending test are described. The three-point load application and the SAE method of testing will be examined in more details. Focus of this paper lies in the effect of friction on the results of single-tooth bending fatigue tests performed by abovementioned methods. It will be primary to consider the effect of friction on the gear tooth root stress. The analysis of these methods will be carried out using the finite element method, with the help of Abaqus 6.13-1 software package. At the very end of the paper, the results obtained from previous analyses will be presented along with the conclusions drawn from them.

U ovom radu korištenjem metode konačnih elemenata i principa lokalne deformacije (ε-N metoda) te programskih paketa Abaqus i FE-Safe izvršena je simulacija nastanka pukotine u korijenu zuba cilindričnih čeličnih zupčanika s ravnim zubima. Budući da je potrebno sa što većom točnošću aproksimirati stvarne uvjete eksperimenta, faktori kao što su centrifugalna sila, trenje, hrapavost površine i zaostala naprezanja uslijed obrade površine su također uzeti u obzir. Kako bi se ubrzao proces loma zuba zupčanika a samim time i vrijeme do nastanka pukotine, u korijenu zuba napravljen je zarez EDM (Electrical Discharge Machining) postupkom. Dobiveni rezultati, odnosno broj ciklusa do nastanka pukotine u korijenu zuba uspoređeni su s eksperimentalnim rezultatima iz kojih su preuzeti podaci o zupčanicima, kao i s drugim numeričkim analizama iz dostupne literature. In this thesis, finite element method and local stress-strain fatigue method (ε-N) are used in combination with software programs Abaqus and FE-Safe to carry out a crack initiation simulation in the area of cylindrical spur gear tooth root. In order to increase the accuracy of the simulaction, real life conditions have to be taken into account such as centrifugal force, friction, material surface finish and residual stress as a result of heat treatment processes. In the interest of saving time, a small notch was created in the tooth root via EDM method, resulting in a significant decrease in gear work life, subsequently reducing the time needed for the crack initiation. Results obtained by numerical analyses, i.e. number of cycles needed for crack initiation are then compared to the experimental and numerical results provided in the avaliable literature from where geometrical and material parameters of the gear pair were obtained.