•Multi-objective optimization of gear pair parameters was conducted.•Main goal was reducing the transmission volume and power losses.•Five optimization variables were used; z1, b, m, x1, and ...x2.•Solutions have shown that the trade-off between volume and efficiency is obligatory.•Combination of the lower gear module, the lower face width, and the higher profile shift coefficients yield good results.
Besides satisfying the essential strength requirements, gearbox design should ensure additional desirable properties in order to be competitive. For example, a gearbox should be efficient, durable, quiet, compact, and light. Nowadays, as a consequence of rising environmental concerns, high efficiency is a rather desirable feature. In this article, a genetic algorithm was used for conducting a multi-objective optimization of gear pair parameters with a goal of reducing the transmission volume and power losses. Gearing efficiency primarily depends on the normal load, sliding velocities, and the friction coefficient. Gearing efficiency was calculated analytically, using the approximate load distribution formulae and efficiency formulation developed by Schlenk. The resulting formula was included in the genetic algorithm as an objective. To verify it, results were compared to the ones obtained by other authors. Optimization variables consisted of the gear module, the face width, the pinion and wheel profile shift coefficients and the number of teeth of the pinion. Solutions have shown that the trade-off between volume and efficiency is obligatory and a combination of the lower gear module, the lower face width, the higher profile shift coefficients and the higher number of teeth of the pinion yield good results regarding both objectives.
•A model is proposed for bending fatigue life prediction of surface hardened spur gears.•Finite element, elastic–plastic correction, and strain-life methods are used.•The multilayer method is ...employed to model the surface hardened layer.•Surface from subsurface bending fatigue failure is distinguished.•The proposed model is validated against experimental results.
A computational model for predicting both the location and the required number of cycles for bending fatigue failure in surface hardened spur gears is proposed. Linear elastic stresses and strains in a single tooth bending fatigue test are corrected for elastic–plastic material behavior. The tooth root region of spur gear is divided into layers. Fatigue properties are assigned to each layer via the hardness method. Based on the multiaxial fatigue criteria, fatigue failure location and corresponding fatigue lives are estimated. Predicted fatigue lives, failure locations, and transition from surface to subsurface fatigue failure show good agreement with the experimental results.
•A model for bending fatigue crack initiation of steel spur gears was proposed.•The multilayer method was employed to consider inhomogeneous material.•Non-proportional loading and stresses were ...considered by the critical plane method.•Predicted fatigue lives agree with the experimentally obtained ones.•Critical location for subsurface fatigue failure agrees with experimental results.
In this paper, a numerical model is proposed to predict the location and the number of cycles for bending fatigue failure of surface-hardened gears. The predictions are validated against experimental results. Linear-elastic stresses and strains obtained by a finite element simulation are imported into the fatigue model. Bending fatigue lives at the observed tooth root region are estimated based on the multilayer method, hardness method, and strain-life approach. The critical plane approach is employed due to non-proportional loading. Good agreement between actual and predicted bending fatigue lives was observed, as well as between the estimated and actual subsurface failure location.
Effect of friction in a single-tooth fatigue test Vuckovic, Krešimir; Galic, Ivica; Božic, Željko ...
International journal of fatigue,
September 2018, 2018-09-00, 20180901, Letnik:
114
Journal Article
Recenzirano
The primary objective of the single tooth fatigue test is to generate gear-tooth bending fatigue data at a comparatively low price. Assuming a negligible influence on fatigue data, the effect of ...friction is not evaluated. The aim of this study is to evaluate the effect of tooth friction on tooth bending fatigue life and on the location of the crack initiation site in a single-tooth fatigue test of case carburized steel spur gear. By using Neuber’s rule, tooth root stresses predicted by means of two-dimensional elastic finite element analysis are translated into estimates of elastic-plastic stress and strain behaviour. The fatigue life and location of crack initiation site are predicted on the basis of the strain-life approach with consideration of mean stress, surface finish and residual stress effects. Two load models are considered. In the first load model, which represents the operating principle commonly used in practice, the test tooth is loaded through the actuating arm. In the second one, which is proposed in this study, the test tooth supports the reaction through the fixed anvil. In both load models, the test tooth is contacted at the highest point of single tooth contact, while the other one is contacted at a lower position along the tooth profile. The computational model is validated against experimental crack initiation lives from literature. The study revealed that friction has a more significant impact on tooth bending fatigue life and location of the crack initiation for the first load model as opposed to the second one.
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•A model was proposed for bending fatigue life prediction of carburized spur gears.•Finite element, elastic–plastic correction, and strain-life methods were used.•The effect of the ...adjacent tooth on bending fatigue lives was investigated.•Bending fatigue lives were reduced when adjacent tooth effect was considered.•A modifying analytical factor was proposed to account for the adjacent tooth effect.
In this paper, a computational model for bending fatigue failure prediction of case hardened spur gears is proposed. The model consists of finite element gear and fatigue failure models, and it accounts for the actual stress–strain state at the tooth root by accounting for local elastic–plastic correction. By employing the proposed model, the effect of the adjacent tooth on bending fatigue lives is investigated. It is observed that bending fatigue lives can vary by approximately 22% when accounting for the adjacent tooth effect. Therefore, this effect should be considered when estimating bending fatigue lives of spur gears.
•Fatigue analysis of valve bodies DN100 and DN50.•Crack initiation on a valve body according to Basquin-Coffin-Manson equation.•Stress intensity factor estimation with eXtended Finite Element Method ...(XFEM).•Cycles for crack growth across the valve body thickness.•The engineering and the true stress–strain diagrams and cycle fatigue behaviour of GP240GH steel.
Global industry depends of the different type of valves, such as globe valves which are used for precise flow regulation. Since most of the power plants rely on performance of globe valves, it is necessary that valves function without interruption. In this paper, the main part of the globe valve, valve body, is investigated. Simulation of crack initiation and its growth in a wall of valve body is carried out. Required number of cycles for crack initiation is estimated according to Basquin-Coffin-Manson equation. Afterwards, stress intensity factor is estimated through eXtended Finite Element Method (XFEM) and required number of cycles for crack growth across the valve body thickness is calculated according to Paris’ law. The aforementioned method is validated on the results from the available literature by employing relatively simple shapes such as steel pipe with integrated flaw. Subsequently, the method is used on a relatively complex geometry, as is the valve body. The obtained results indicate lack of brittle fracture in a valve body. In other words, the results imply occurrence of Leakage Before Brake (LBB). This is utterly important for power plant industries, since it ensures the proper reaction of the user and possibly avoids possible catastrophic consequences for personnel and the equipment located in the proximity of the valve.
The purpose of this study concerning the pitting damage on worm wheels is dual. The first aim is to formulate an empirical correlation between the pitted area and the number of load cycles based on ...the determination of damaged areas from digital images. Second, it aims at revealing damage dynamics by using the very same set of digital images processed and presented in a novel way. Test results for 6 teeth are used to formulate a new correlation between the pitted area and the number of load cycles, which is then compared to the referent one. Results show that the differences between the pitted areas measured in this study and in the referent one surely exist, which has an impact on the empirical formulation and thus the prediction of the worm wheel life. Also, an interesting finding is how the damaged areas overlap on the teeth, with more than 50% occurring only on one tooth or two. This could be explained through the contact complexity of a real worm pair.
The aim of this study is to check the possibility of replacing the pinion gear made of structural steel with the one made of sintered material. The pinion is part of the gear pair mounted in front of ...the gearbox of the skidder Ecotrac 55V to increase the speed and lower torque. In larger series, powder metallurgy (PM) gears are used as a cost-effective alternative for wrought metal gears in a number of industries including the one producing forest products. The present paper discusses the computational and experimental approach for determining the service life of sintered PM gears in regard to tooth bending fatigue. The proposed computational model is based on the stress-life approach, where the stress field in a gear tooth root is determined numerically using finite element method. The needed material data have been taken from the authors' previous work. Due to the scattering nature of fatigue, the statistic approach has also been considered by presentation of computational results. The experimental procedure was done on a custom made back-to-back gear testing rig. The comparison between computational and experimental results has shown that the proposed computational approach is an appropriate calculation method for estimating the service life of sintered gears regarding tooth root strength. Namely, it has been shown that, in case of proper heat treatment of tested gears, tooth breakage occurred in the interval with 95% probability of failure, which has been determined using the proposed computational model. Keywords: skidder, service life, sintered powder metallurgy gears, tooth bending fatigue, stresslife approach, back-to-back test rig
Globe valve is a type of industrial valve used to obstruct or regulate flow of the fluid in pipelines via linear motion of the plug. The main component of the valve, the valve body, is the carrier of ...the internal and often variable pressure. The body itself is usually made by sand casting which may result in impurities and metallurgic or shrinkage defects. The above-mentioned, coupled with the relatively geometrically complex shape of the valve bodies, makes the accurate determination of the crack formation and growth often challenging. Additionally, formation of the cracks in a pressure vessel such as globe valves usually leads to one of the two outcomes. If the crack reaches its critical size under specified loading conditions, a catastrophic failure may occur. On the other hand, the preferred option of stable crack growth can lead to the effect known as leak-before-break. Therefore, it is necessary to accurately determine stress intensity factors (SIF) for cracks in such geometry. This determination is usually made by classical finite element method, and it is very hard to do on complex shape. In addition, it is possible to determine SIF using eXtended Finite Element Method (X-FEM) which is proved on simple geometry. In this paper, the verification of the X-FEM has been conducted by comparison of results obtained by this method and by the classical method on valve body. Presented computational model suggest the possibility of accurately determining fracture mechanics parameters for cracks in geometrically complex components such as those of valve bodies.
U ovome radu analiziraju se kvalitativna svojstva peleta izrađenih iz vrsta drva turopoljskog kraja – sadržaj pepela, ogrjevna vrijednost, gustoća peleta i tlačna čvrstoća. Prikupljeni su uzorci ...hrasta lužnjaka (
Quercus robur
L.), običnoga graba (
Carpinus betulus
L.), poljskog jasena (
Fraxinus angustifolia
Vahl.), crne johe (
Alnus glutinosa
L.) i crne topole (
Populus nigra
L.). Prikupljeni i okorani uzorci usitnjeni su na mlinu s noževima na granulaciju 2,00 mm. Na uzorcima je ispitan sadržaj vode, pepela i ogrjevna vrijednost. Sadržaj pepela određen je zasebno za koru i drvo. Sadržaj pepela u kori pokazuje visok udio kod hrasta lužnjaka koji iznosi 13,64 % i graba sa 11,91 %, dok je kod ostalih vrsta udio pepela u kori između 7 i 10 %. Sadržaj pepela okoranog drva pokazuje vrijednosti 0,63 % za hrast, 0,50 % za jasen, 0,46 % za grab. Vrijednosti sadržaja pepela kod johe i topole bile su oko 0,4 %. Rezultati ukazuju na potrebu okoravanja u proizvodnji peleta s ciljem postizanja kvalitete peleta klase A1 i A2. Određivanjem ogrjevne vrijednosti najbolji rezultati utvrđeni su kod uzorka drva crne topole koja iznosi 19,63 MJ/g, a najmanja vrijednost izmjerena je kod uzorka graba 18,94 MJ/g. Nadalje, navedeni uzorci pomiješani su te su fomirane 3 grupe mješavina. Udio tvrdih vrsta listača hrasta, graba i jasena u svakoj pojedinoj mješavini bio je 60 % dok su u preostalom udjelu od 40 % jednoliko sudjelovale joha (20 %) i topola (20 %). Formirane mješavine materijala JTJ (jasen 60 : topola 20 : joha 20), HTJ (hrast 60 : topola 20 : joha 20) i GTJ (grab 60 : topola 20 : joha 20) prešane su u pelete uz pomoć hidrauličke laboratorijske preše pri 2 veličine sile (3,0 i 6,0 kN) i 2 temperature (150 i 200 °C). Po isprešanju, peleti su ostavljeni 15 dana da se dimenzijski stabiliziraju te su im određene dimenzije i gustoća. Peleti su potom ispitani na tlačnu čvrstoću u radijalnom smjeru pomoću kidalice. Peleti iz svih mješavina, prešani silom 6,0 kN kod temperature 200 °C pokazali su visoku gustoću koja je bila u rasponu 1 207 – 1 234 kg/m3. Peleti osnovne mješavine jasena dali su kod sile 3,0 kN i temperature 200 °C vrlo visoku gustoću od ≈ 1200 kg/m3, dok su općenito najmanju gustoću imali peleti osnovne mješavine graba kod svih režima prešanja. Rezultati tlačne čvrstoće u radijalnom smjeru pokazuju najbolje rezultate kod peleta prešanih pri 6,0 kN i 200 °C i to 13,59 MPa kod osnovne mješavine jasena, 11,1 MPa mješavine hrasta i 9,06 MPa mješavine graba.
Ako se tlačna čvrstoća peleta promatra zbirno prema mješavini, značajno bolje rezultate daju peleti izrađeni iz mješavine jasena, topole i johe u usporedbi s ostale dvije mješavine.
The paper deals with some quality characteristic of wood pellets from Turopolje area. The samples of pedunculate oak (
Quercus robur
L.), European hornbeam (
Carpinus betulus
L.), narrow-leaved ash (
Fraxinus angustifolia
Vahl.), European alder (
Alnus glutinosa
L.) and black poplar (
Populus nigra
L.) were collected. Collected and debarked samples were crushed by a mill with knives to 2.00 mm granulation. The content of water, ash and calorific value were examined on samples. The ash content was determined separately for the bark and the wood. The ash content in the barks shows a high rate in pedunculate oak which is 13.64 % and hornbeam with 11.91 %, while in other species the ash content in a bark is between 7 and 10 %. The ash content of a debarked wood shows the following values: 0.63 % for the oak, 0.50 % for the ash, 0.46 % for the hornbeam. Values of the ash content in the alder and the poplar were 0.4 %. Results indicate the need for debarking in pellet production in order to obtain the quality of class A1 and A2 pellet. By determining the calorific value the best results were determined in the black poplar sample which is 19.63 MJ/kg, and the lower value was measured in hornbeam sample 18.94 MJ/kg. Furthermore, the mentioned samples were mixed and 3 mixture groups were formed. The share of hard broad-leaved trees of oak, hornbeam and ash in each individual mixture was 60 %,while in the remaining 40 %,alder (20 %) and poplar (20 %) equally participated. Formed material mixtures APA (ash 60 : poplar 20 : alder 20), OPA (oak 60 : poplar 20 : alder 20) and HPA (hornbeam 60 : poplar 20 : alder 20) were pressed into pellets by hydraulic laboratory press in 2 forces
(3.0 and 6.0 kN) and 2 temperatures (150 and 200 °C). After pressing, pellets were left for 15 days to stabilise in dimension and their dimension and density were determined. Then, pellets were checked for pressure strength in a radial direction by a testing machine. Pellets from all the mixtures, pressed by a force of 6.0 kN at 200 °C showed a high density in the range from 1 207 – 1 234 kg/m3. Pellets of basic ash mixture at force of 3.0 kN and at 200 °C gave high density≈ 1200 kg/m3, while the smallest density was generally given by pellets of basic hornbeam mixture in all pressing regimes. The results of pressure strength in radial direction give best results in pellets pressed at 6.0 kN and 200 °C which is 13.59 MPa with the basic ash mixture, 11.1 MPa with the basic oak mixture and 9.06 MPa of basic hornbeam mixture.
If the pressure strength of a pellet is considered collectively according to the mixture, pellets made from the mixture of ash, poplar and alder give significantly better results in comparison to other two mixtures.
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