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Gear root load-carrying capacity is primarily influenced by fillet geometry. Many different fillet geometries and optimization approaches have been tried to increase gears' load-carrying capacity. One such approach was proposed by Akpolat and Yilmaz et al. Authors proposed using an asymmetric root profile to minimize root stresses in spur gears. Such a method is reported to improve the load- carrying capacity by up to 12%. Root stress was determined in using static FE analysis by applying load to the highest point of single tooth contact. In this research, the effect of asymmetric fillet geometry on root fatigue life was investigated. Moreover, the effect of the adjacent tooth was also explored.

In this paper the authors conducted a numerical investigation of residual stress distribution on two butt-welded plates. Subsequently, they incorporated the obtained residual stresses into a welded model that included a hypothetical semielliptic crack. The stress intensity factors (SIFs) were calculated using the eXtended Finite Element Method (X-FEM). The obtained SIFs results match very well with the analytical results of the API 579-1 standard with the biggest difference being 6.73%. Similar differences can be noticed in the comparison between X-FEM and the results obtained by the conventional Finite Element Method (FEM), where the biggest difference between these two results is 6.75%.

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.

In recent years, growing demand for light-weight, efficient and quiet transmissions, fueled by the introduction of electric vehicles is observed. This calls for simultaneous gear optimization regarding efficiency, mass, and NVH (noise vibration harshness). Herewith gear macro-geometry was optimized for efficiency and mass using pressure and helix angles, gear width, modulus, tooth count, addendum, dedendum and root radius coefficients as variables. Optimization was carried out using NSGA-II. The optimization algorithm results have shown that a clear trade- off between weight and efficiency exists, as previously reported by other authors. Since the third axis of solution space, the transmission error, was not implemented yet the algorithm will tend to minimize addendum coefficient values so as to minimize sliding. In-turn, this will worsen the NVH (noise vibration harshness) behavior of the gear pair. Consequently, minimum transverse and axial contact ratio value constraints were implemented to ensure that the algorithm returns a solution with decent NVH behavior. On the other hand, such constraints will prevent the algorithm from finding the actual global optimum of the original objective function. This was implemented to prepare the algorithm for the future introduction of the third objective, which is the transmission error. With the current setup of constraints, the resulting gearing will always fall in the category of high contact ratio gearing.

Uporaba polimernih zupčanika u stalnom je porastu, ponajprije zbog povoljnih mehaničkih svojstava, potencijala za masovnu proizvodnju te prihvatljive cijene. Navedena svojstva ih čine povoljnim rješenjem i za mehanizme gdje je potrebno prenijeti isključivo gibanje, ali i za kućanske uređaje. S druge strane, smjernice za pravilno oblikovanje polimernih zupčanika nisu dostupne te se u praksi kvaliteta konstrukcijskog rješenja unaprjeđuje iterativnim postupkom. Iz tog razloga, provedeno je istraživanje kojim bi se omogućila primjena optimizacijskih algoritama u postupku osnivanja parova polimernih zupčanika. U prvom koraku, zbog nedostatka konsenzusa u literaturi, određen je potrebni broj varijabli te je prilagođen dostupni model za izračun gubitaka snage. U nastavku je eksperimentalno dobiven model za predikciju faktora trenja, omogućavajući provedbu više-ciljnog optimizacijskog postupka. Eksperimentalna validacija rezultata potvrđuje da je u svim slučajevima povoljno odabrati veći broj zubi te pomake profila između 0, 5 i 0, 55 za pogonski te između 0, 65 i 0, 7 za gonjeni zupčanik. Kombinacija manjeg modula i veće širine uzrokuje manji volumen i veće gubitke i obrnuto.

Elektropoliranje pri povišenim vrijednostima gusto e struje uzrokuje formiranje jamica na površini obratka. Prednost elektropoliranja o ituje se u jednostavnoj primjeni na dijelovima kompleksne geometrije kao što su zup anici. Cilj je bio ukazati na mogu nost prilagodbe teksture površine cementiranog elika 16MnCr5. Dobiveni profili površina uspore eni su s podacima iz literature te rezultati ukazuju da je dobivena tekstura površine povoljna i ima pozitivan utjecaj na smanjenje trenja i trošenja. Elektropoliranjem eli nih uzoraka, parametar profila površine Rku poprima visoke vrijednosti (Rku > 10), dok parametar Rsk poprima izrazito negativne vrijednosti (Rsk < -2). Dodatno, mogu e je ostvariti geometriju jamica na površini opisanu omjerom dubine i širine jamice ( ) u rasponu od 0.15 do 0.3. Spomenuta metoda predstavljala bi alternativu ustaljenim postupcima laserskog i kemijskog graviranja koji se naj eš e koriste pri promjeni teksture površine

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.

Surface hardened spur gears are one of the most commonly used machine elements regarding the power transmission. During gear service life, variable and cyclic nature of the stresses at the tooth root may lead to material fatigue, commonly known as bending fatigue. The bending fatigue may cause crack initiation and consequently propagation at the tooth root fillet, eventually resulting in a tooth breakage. In this paper, the authors presented a computational model for predicting the number of cycles required for crack initiation. Two cases of driven gears are considered. Elastic finite element analysis is used to generate the numerical models which accounts for the nominal tooth root stress change during the gear meshing. Additional effects due to friction and centrifugal force are also considered. Fatigue models are generated using the strain-life approach and finite element analysis results. Mean and residual stresses, along with the local plastic deformation effects, are also considered. The bending fatigue life results are in good agreement with the experimental data from the available literature for the first case and conservative for the second.

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.

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.

U ovom radu analizirati će se ciklus naprezanja korijena zuba opterećenog zadanim momentom. Odrediti će se mjesto maksimalnog naprezanja u korijenu zuba, te usporediti sa mjestom očekivanog maksimalnog naprezanja po ISO 6336. Budući da se zupčanici rotiraju brzinom vrtnje od 10 000 min-1, uzeti će se u obzir i utjecaj centrifugalne sile na promatrani korijen zuba te usporediti sa ciklusom naprezanja bez uračunate centrifugalne sile. Debljina tankog vijenca mijenjati će se tijekom analiza kako bi se promotrio utjecaj koji ima na ciklus naprezanja tokom prolaska zuba kroz zahvat. Također će se promatrati utjecaj veličine sektorskog otvora zupčanika od početnog sektorskog otvora koji obuhvaća sedam zubi do krajnje vrijednosti od jednog zuba. Nakon provedene analize i usporedbe svih spomenutih ciklusa, dobivene vrijednosti usporediti će se s proračunom preko norme ISO 6336. In this paper, gear stress analysis will be carried out to determine a place of maximum root bending stress of a cylindricall gear tooth. Location of the maximum bending stress will then be compared with the place of expected maximum bending stress according to ISO 6336 standard. Since both gears are rotating with a speed of 10 000 rpm, centrifugal force will also be taken into account and compared to results where no centrifugal force was involved. Thickness of a thin rim will also vary to determine the effect it has on a stress cycle, as will the size of a sector opening, starting with the initial value of seven-tooth span to one-tooth span. After analyzing and comparing all of cycles mentioned above, results will be compared with those obtained through ISO 6336 standard.