Root Fillet Research Articles

Failure analysis on connection components of turbo-disk and main-shaft used in a locomotive turbocharger

Three bolts, three pins connecting turbo-disk and main-shaft and the navel of turbo-disk fractured during servicing, which were used in a locomotive turbocharger. Examination and analysis results show that one of location pins was not riveted into the pin hole on the plate of the main-shaft due to dislocation. The pin encountered greater hammering force and resistance to moving downward when being riveted into the hole, so corresponding impact tensile load was exerted on opposite bolt and the navel. The cracks initiated at the last engaged thread root of the bolt and the root fillet of navel and propagated in fatigue mode under the action of alternative loads. The bolt and the navel fractured first. Other components fractured in succession. Defective operation of riveting is responsible for the fracture of connection components.

Failure analysis of a locomotive turbocharger main-shaft

A failure investigation has been conducted on a locomotive turbocharger main-shaft. The fracture position is located at a sharp edged groove between two journals with different cross-sectional area. Fractography investigation indicates that the rotating bending fatigue is the dominant failure mechanism of the main-shaft. Detailed metallurgical analysis indicates the root fillet region of the groove had subjected to abnormal high-temperature resulting from the intense friction between the bearing-sleeve and the assisted pushing bearing, which makes the fatigue strength of the root fillet region of the groove decrease. Over-small root fillet radius of the groove by which stress concentration is created facilitates the fatigue cracks to initiate in the root fillet region.

Failure analysis of coal pulveriser gear box

The premature failure of coal pulveriser gear box has been studied in this investigation. Complete breakage as well as cracking in a number of gear teeth were noticed in which the cracking initiated from the middle of the root-fillet of the teeth and propagated beneath the root region. Studies were conducted using microstructural studies, hardness measurements, fracture surface studies, etc. The failure was found to be initiated by bending fatigue from the root fillet region of teeth which mainly constituted coarse ferrite–carbide aggregate resulting in a relatively low hardness level. The life of gear box could be improved by local hardening of the fillet root to provide a fine martensitic structure with hardness in the range of 55RC.

Generating standard 20° involute pinions with increased fillet strength by using 25° rack cutters with non-standard module

According to all prevailing standards for gear design, a strict guideline is that the individual gears of a gear pair must be of the same module and pressure angle in order to mesh properly and the compatibility of the remaining geometrical parameters is determined under this assumption. However, in this article, the fundamental meshing principles of a generating rack and pinion are reinterpreted, and a more insightful form of the compatibility equations for involute gears is presented. In this context, stronger tooth forms with thicker root fillets can be produced using 25° rack cutters and still be able to mesh with standard 20° involute gears indiscriminately. The increased strength of pinions of the proposed design versus their standard counterparts is verified with finite element analysis.

Influence of carburizing and nitriding on failure of gears – A case study

Designing of mechanical parts covers many basic aspects of mechanical engineering. Coupling a proper choice of material and surface treatment, the static and the dynamic designing follow well consolidated criteria, often suggested by experience or prescribed by standards. In gear design many efforts are planned to extend life against wear and contact fatigue, hence the main role is played by a proper selection of surface hardening methods. Complex phenomena of failure are involved for such components during their working life, therefore a deeper comprehension of the damaging mechanisms is necessary to prevent them. To this aim a particular case of failure analysis of a pinion gear is considered. It was built in 18NiCrMo5 UNI 7846 case-carburized, quench hardened and tempered steel. By very few working cycles, the transmission gear prematurely failed. Several ruptures on teeth were noticeable to the unaided eye which covered either a small area of the tooth flank (near the root fillet) or a large zone of the flank itself. In any case, the failure involved only upper part of the pinion teeth. A detailed investigation was needed to clarify the reasons of such a premature rupture. The root of failure was determined to be external overloading and the initial stage of the damage was close related to complex surface contact fatigue mechanism. Following on this investigation the effect of carburising was studied in relation to the mechanism of failure and an alternative nitriding treatment was considered to solve this problem.

Failure analysis of an idler gear of diesel engine gearbox

A failure investigation has been conducted on an idler gear of diesel-engine gearbox used in a truck, which is made from 20CrMnTi steel. The gear was plasma-carburized. The inner circle is splined. The crack origin zone is situated at the root fillet location of the weld region of the splined inner circle. The macro-fracture surfaces show brittle cracking characteristics and the micro-fracture exhibits intergranular cracking features. The delayed brittle fracture is the dominant failure mechanism of the idle gear. The detailed metallurgical examinations on the carburized layer and the core zone were conducted. The failure causes were assessed.

Increasing the Strength of Standard Involute Gear Teeth with Novel Circular Root Fillet Design

In this study the idea of spur gear teeth with circular instead of the standard trochoidal root fillet is introduced and investigated numerically using BEM. The strength of these new teeth is studied in comparison with the standard design by discretizing the tooth boundary using isoparametric Boundary Elements. In order to facilitate the analysis the teeth are treated as non-dimensional assuming unitary loading normal to the profile at their Highest Point of Single Tooth Contact (HPSTC), so that non-dimensional stress vs. Contact ratio diagrams are plotted. The analysis demonstrates that the novel teeth exhibit higher bending strength (up to 70%) in certain cases without affecting the pitting resistance since the geometry of the load carrying involute is not changed. The circular fillet design is particularly suitable in gear with a small number of teeth (pinions) and these novels gears can replace their existing counterparts in any mechanism without any alterations. Finally the geometry of the generating tool (i.e. rack) is determined in order to be able to cut these teeth using a generating method (i.e. hobbing).

Tooth profile design for the manufacture of helical gear sets with small numbers of teeth

Based on gear theory and generating mechanism, this investigation presents a complete mathematical model of a helical gear set with small number of teeth. The unavoidable tooth-profile undercutting of the gears with small number of teeth is examined by using the developed mathematical model and the conventional method of tooth-profile shifting. Furthermore, an alternative method for lessening the tooth-profile undercutting is also presented by considering a modification of the basic fillet geometry using a modified rack cutter. A third method, combining the aforementioned two methods for the design of helical gears with small number of teeth is also proposed to yield a gear set without tooth undercutting. The mating gear with profile shifting is generated using the pinion as a shaper. The tip fillet and root fillet are modified and a clearance between the pinion and the mating gear is also included in the design. Analysis results indicate that the change of distance between the centers of gear set depends only on gear shifting. Moreover, computer graphs are demonstrated the profile-shifted and the proposed modified gear tooth profiles.

Effect of gear tooth fillet radius on the performance of injection molded Nylon 6/6 gears

In metal gears the gear manufacturing process and cutting tool dimensions decide the gear tooth geometry and affect the gear performance. In polymer base gears, injection molding process permits development of gears with any tooth geometry economically. In this paper, the effect of gear tooth fillet radius on the performance of injection molded Nylon 6/6 gear made with different tooth fillet radius 0.25 and 0.75 mm is reported. Finite element analysis carried out indicates high fillet root stresses and gear tooth deflection in gears with low fillet radius. Gear performance was evaluated using a power absorption type gear test rig. Repeated gear tooth loading during service causes a rise in the gear temperature which is due to hysteresis effects and friction. The temperature rise depends on the fillet radius. At low applied loads, gears with less fillet radius fail by crack initiation at the root region due to increased stress concentration whereas gears with large fillet radius fail by micro cracking at the pitch region.

Failure analysis of diesel engine flywheel ring-gears

This paper presents a failure analysis on three diesel engine flywheel ring-gears used in trucks. The ring-gears fractured when starting engines at low temperature (−25 °C). The fracture occurred from the root fillet region on the side of the load contact surface in all cases. Fractographic studies indicate that the fracture surfaces of three failed ring-gears have similar features, which exhibit cleavage fractures reflective of low toughness of the material. The detailed metallurgical analysis was conducted on the fractured gear teeth and compared with the ring-gear unfailed in service. The failed ring-gears present general metallurgical characteristics that network of grain boundary ferrite even Widmannstätten structure ferrite appeared in the induction hardened region and a continuous network of grain boundary ferrite appeared in the core and tooth groove regions. The appearance of the network ferrite makes the strength of the gear teeth decrease particularly in tooth groove region. The thinner induction hardened layer in the tooth groove region is also responsible for the decrease in strength of the ring-gears. It has been found that there are some forging cracks in the root fillet region. Additionally, the smaller root fillet radius makes the stress concentration in the fillet regions. The metallurgical defects with machining defect result in premature embrittlement fracture of the ring-gears. The unsuitable normalizing technology or forging technology should be responsible for the formation of continuous network of grain boundary ferrite.

An Approach to the Determination of Spur Gear Tooth Root Fillet

The purpose of this paper is to present an approach for the determination of geometry of spur gear tooth root fillet. An equation is developed to determine the point of tangency of involute profile and root fillet on the base circle for a spur gear without undercutting and the point of intersection of root fillet and involute profile above the base circle for an undercut gear. Generation using a hob or rack type cutter with protuberance (increase in tooth thickness at the tip of the hob tooth) is also discussed.

布基材フェノール樹脂積層材料を用いた動力伝達用歯車の疲労強度の算定法(O.S.09-3 プラスチック歯車(3))

In this research, a laminate material (a phenolic resin reinforced by plain woven cotton cloth) was used for the gear material. The gear was produced by hobbing. In this paper, we addressed the bending strength of gear teeth in the basic design process. First, Vibration characteristics between metal gear and metal gear and cotton fiber-reinforced plastic gear and metal gear when the gears meshed are compared. Second, bending fractures in teeth, were examined by a line load applied to the tooth root fillet and tooth breakage in this area during bending was investigated. Third, to investigate the repetition fatigue strength of teeth, a fatigue test was performed. Forth, tension, uniaxial compression, 3-point and 4-point bending, and shearing tests were performed for the gear materials used in order to investigate the destruction strength of the gear shape and the primary factors in the destruction form.

A New Photoelastic Investigation of the Dynamic Bending Stress of Spur Gears

In this paper, the maximum tensile bending stress (MTBS) and the critical point in the root fillet of spur gear tooth during transmission are determined by a digital photoelastic system involving real time imaging. The behavioral characteristics of the bending stresses of the gear tooth are analyzed at different rotation speeds, transmitted torques, and contact points. Then, the dynamic effects, the various critical points and the maximum tensile bending stresses are compared experimentally and theoretically, and discussed. Finally, the best approaches for determining the maximum bending stress and its position in the root fillet of spur gear tooth are recommended.

Metallurgical analysis of failed gear

Bronze is used for the fabrication of special purpose gears in mechanical transmission systems. Recently, fracture of gear teeth occurred when a gear was in use. The fractured gear teeth were subjected to detailed analysis using standard metallurgical techniques. The results revealed that corrosive wear at the root fillet caused pitting, intense localised plastic strain and folds, leading to crack formation. Advancement of the crack took place under the successive stress repetitions to which the gear was subjected, causing the tooth to fail by fatigue.

Centrifugal Lubrication of Spur Gears. 2nd Report, Influence of Cooling Hole on Tooth Fillet Stress.

We have recently proposed a new centrifugal lubrication method in which oil is injected through a hole drilled on the tooth crest of a spur gear. To adapt the method for wide face width spur gears, we set up a cooling hole parallel to the tooth trace on the center line of the tooth profile. The results of numerical analyses have been demonstrated that the recommended setting position of the hole is that where the hole inscribes to the root circle on the center line of the tooth profile; the addendum modification coefficient and rim thickness of the gear should be not less than zero and be not less than five times the module respectively. In such a spur gear, an increase in maximum tensile root fillet stress on the active flank side due to the hole of one module in diameter is less than 10% of the stress of the gear with no hole.

Vibration Behavior and Fatigue Strength of Mocked-Up Piping System

For the purpose of investigating vibration characteristics and fatigue strength of a socket-welded joint, a piping system was mocked-up by assembling a straight pipe of 350 mm nominal diameter and a long pipe of 20 mm nominal diameter consisting of straight pipes and elbows. The one end of the small-diameter piping is connected to the large-diameter pipe at its longitudinal midpoint by socket welding, and the rest is supported at several supporting points, the locations of which are changed as an experimental parameter. The materials of the small-diameter piping are carbon and stainless steels. The small-diameter piping was subjected to nearly resonant vibration with the frequency of about 11 Hz by a sinusoidal vibration load applied to the large-diameter pipe. The vibrating displacement amplitude measured on the actual piping was basically 0.05 mm in resonant condition; but the displacement was changed to obtain an S-N curve for the socket-welded joint in the fatigue life range of 104 to 107 cycles. In the mocked-up specimens, fatigue cracks were initiated from the toe of the socket-fillet welds at higher stress amplitude, but from the fillet root at lower stress amplitude. Comparative fatigue tests of straight shape socket-welded specimens fabricated with 20 mm nominal diameter pipe of the same material as used in the mocked-up specimen were carried out under four-point bending condition. The fatigue strength of the socket-welded joint in the mocked-up specimen was about 15 percent lower than that of the simple specimen fatigued by four-point bending load. The reason for this difference is probably due to the triaxial stress condition and three-dimensional restraint condition. The strain gage measurement showed that the shear stress was about 40 percent of the bending stress in the case of the mockedup specimen. In addition, vibration tests of the piping system showed good agreement between experimental and analytical results of vibration behavior.

Evaluation of Gear Tooth Stresses by Finite Element Method

Stresses developed in the root fillet of the spur gear tooth due to static load are evaluated by using the finite element method. The method is automated with a computer program with which the effects of module, contact ratio, fillet radius, pressure angle and teeth numbers of driving and driven gears are evaluated. The results are compared with previous studies. The formula which gives the closest results to this study is presented.

Leading-edge sweepback and shape effects on fin-induced fluctuating pressures

Measurements of the fluctuating wall pressure have been made on centerline upstream of blunt fins in a Mach 5 turbulent boundary layer. Leading-edge sweep considerably reduces the mean and rms pressure loading at the fin root, the extent of the region of unsteady separation shock motion (i.e., the intermittent region), and the separation length. The frequency of shock-induced pressure fluctuations in the intermittent region increases with leading-edge sweepback, while frequency spectra in the separated region are virtually unchanged. A strake at the root of an unswept fin has virtually no effect, whereas a swept blunted root fillet reduces the upstream influence and intermittent region lengths by 50%, and reduces the mean and rms pressure loading at the fin root by about 75% and 95%, respectively. Experiments using hemicylindrical, wedge-shaped, and flat leading edges show that separated-flow scales and root loading increase with increasing bluntness (i.e., wedge to hemicylinder to flat), while the intermittent-region length increases (in terms of fin thicknesses). The changes in flowfield unsteadiness are related to changes in separated-flow structure which alter the dynamics of the primary vortex and recirculation process.

Bending Strength Estimation of Thin-Rimmed Spur Gears.

This paper presents a study on bending strength estimation of thin-rimmed spur gears. A bending strength estimation method, using the fatigue limit diagram for gear material and cyclic stresses at root fillets of each tooth of thin-rimmed spur gears under the normal running condition calculated by the two-dimensional finite-element method (FEM), was proposed. The bending strength estimation using this estimation method and the bending fatigue test were carried out for a thin-rimmed spur gear with spokes, and the validity of the proposed bending strength estimation method was confirmed.

Discussion: Factored axial compressive resistance of schifflerized angles

'paper by Seshu Madhava Rao Adluri and Murty K.S. Madugula. 1991. Canadian Journal of Civil Engineering, 18: 926-932. where A = T(E/F,)~. These values of the normalized slenderness may be used with any appropriate column buckling curve, and give results comparable with those obtained by the authors. However, some questions are raised: 1. The ratio of the minimum moments of inertia for 90 and 60 angles is of the order 1.5: 1. How thick must the section be for the value to be 1.2: 1 as claimed by the authors (p. 926, column 2)? 2. A simple angle has negligible warping stiffness, regardless of the included angle. To what is the 100% increase in warping stiffness attributed, and is it significant? 3. No regard is paid to the various forms of bracing. Would K-bracing be of benefit? 4. To neglect the influence of the root fillet on the area is common practice, but its addition to the torsion constant can be as high as 870, thus its omission makes it difficult to justify the four-significant-figure values given for the buckling loads, and the five-figure precision of the constant in eq. [3]. Perhaps the authors could comment on their superdigitation. ' '