Effect Of Rim Thickness Research Articles

Fatigue failure analysis of spur gear under moving load

This paper is prepared to analyze the crack propagation by developing a pointed moving load condition. The moving load from lower point tooth contact (LPTC) to high point tooth contact (HPTC) is applied on the gear flank, where the maximum load is acted on the pitch-point of the tooth flank. Different models of gear, taking a three teeth sector model (TTSM), are developed for different backup ratio (BR) of 0.3, 0.5, 0.8, 1.5 & 3.3 and initiating the initial crack (IC) length of 0.1 mm, 0.25 mm & 0.5 mm at orientation of critical planes for shear model oriented at 180° at the root region of the tooth. The finite element analysis (FEA) software - ANSYS is used to study the problem statement. The arbitrary crack method is used to initiate the crack presence in gear flank. The Paris law method is applied in separating morphing and adaptive remeshing technology (SMART) crack growth setup in static structural module of ANSYS, which helps in evaluation of number of cycles with crack extension length. The number of life cycles, crack extension length and crack propagation path are analyzed and their graphs are plotted to analyze the situation. From current study, the effect of rim thickness on the life cycle is studied when the point load is applied movable from LPTC to HPTC. It is observed that by having thin rims, the number of cycles of gear increases, but its failure is catastrophic that it can fracture other parts, mounted with gear. Although, higher backup ratios or larger rims have lower number of life cycles, but it will never lead to the catastrophic failure of the gear.

Effect of design parameters on stresses occurring at the tooth root in a spur gear pressed on a shaft

Gears are commonly used in transmission systems to adjust velocity and torque. An integral gear or an interference fit could be used in a gearbox. Integral gears are mostly preferred as driving gear for a compact design to reduce the weight of the system. Interference fit makes the replacement of damaged gear possible and re-use of the shaft compared to the integral shaft. However, internal pressure occurs between mating surfaces of the components mated. This internal pressure affects the stress distribution at the root and bottom land of the gear. In this case, gear parameters should be re-considered to assure gear life while reducing the size of the gear. In this study, interference fitted gear-shaft assembly was examined numerically. The effects of rim thickness, profile shifting, module and fit tolerance on bending stress occurring at the root of the gear were investigated to optimize gear design parameters. Finite element models were in good agreement with analytical solutions. Results showed that the rim thickness of the gear is the main parameter in terms of tangential stress occurring at the bottom land of the gear. Positive profile shifting reduces the tangential stress while the pitch diameter of the gear remains constant. Also, lower tolerance class could be selected to moderate stress for small rim thickness.

Effects of rim thickness and drive side pressure angle on gear tooth root stress and fatigue crack propagation life

Gears are the most significant machine elements in power transmission systems. They are used in almost every area of the industry, such as small watches to wind turbines. During the power transmission, gears are subjected to high loads, even unstable conditions, high impact force can be seen. Due to these unexpected conditions, cracks can be seen on the gear surfaces. Moreover, these cracks can propagate, and tooth or body failures can be seen. The fatigue propagation life is related to the gear tooth root stress. If the root stresses decrease, the fatigue life of the gears will increase. In this study, standard and non-standard (asymmetric) gear geometries are formed for four different rim thicknesses and four different pressure angles to examine fatigue crack propagation life. Moreover, the effects of the rim thickness and drive side pressure angle on the root stress are investigated. The static stress analyses are carried out to determine the starting points of the cracks, and the maximum point of the stress is defined as the starting point of the cracks. Fatigue crack propagation analyzes are performed for gears whose crack starting points are determined. The static stress analyses are conducted in ANSYS Workbench; similarly, the fatigue propagation analysis is performed in ANSYS smart crack growth. In this way, the directions of the cracks are determined for different rim thicknesses and drive side pressure angles. Besides, the number of cycles and da/dN graphs is obtained for all cases depending on crack propagation. As a result of the study, maximum stress values were decreased by 66%. The fatigue propagation life was increased approximately fifteen times by using the maximum drive side pressure angle and optimum rim thickness.

Crack propagation behavior in planet gears

Aim of this work is to investigate crack propagation paths in planet gears for aerospace applications in order to find how gears parameters may affect the crack path and, consequently, may provide information about gears design to avoid catastrophic failures. The research activity has been carried on by means of extended finite element models (XFEM).In particular, the effect of rim thickness (expressed as backup ratio) and crack initiation point on crack paths has been considered. Obtained results have been compared with those available for standard gears, to highlight the different behavior in crack propagation.

Fracture mechanics of planetary gear set by using extended finite element method-linear elastic fracture mechanics approach

Contour integral method is the conventional approach in order to characterise main crack parameters in fracture studies. This method is used in verity fields in fractures mechanics because of its capability in linear and non-linear fracture mechanics. Whereas, requirements such as mesh singularity in crack tip and refined layers of elements in surrounding contours, which increase computing time and make it prolix for large components. The main aim of this paper is to develop an extended finite element method-linear elastic fracture mechanics (XFEM-LEFM) model to impart XFEM advantages in survey of fracture mechanics of planetary gear sets. At first main crack parameters of root crack of the planet gear have been obtained and compared with conventional method, and after that crack growth path is predicted, and finally effect of rim thickness is investigated and compared with other researches to illustrate the efficiency of the developed model. For this purpose, Python script code is generated to automatically calculate the stress intensity factors of root crack and after that simulate the crack growth path until final fracture.

Effect of Rim Thickness on Load Sharing in the Rotating Elements

The aim of the study is to obtain an optimal arm section for the structures like pulleys, gears, flywheels etc. considering variation of rim thickness with pulley radius. Presently, the design of arm pulley with thin rim is being carried out with an assumption that the bending moment (BM) is shared by half the number of arms, whereas in case of arm gear or V-Belt pulley the assumption is made that BM is shared by total number of arms. In the present paper, Finite Element Method (FEM) is used to determine the BM shared by the arms for its different angular positions. The distribution of bending stress in the arms is also obtained. Finally, design modifications have been suggested considering radius to rim thickness ratio (r/t). Hence it is concluded that when, 15 ≥ r/t > 10.5 – BM is shared by N/2 number of arms, 10.5 ≥ r/t > 7.5 – BM is shared by 4N/7 number of arms, 7.5 ≥ r/t > 5 – BM is shared by 2N/3 number of arms, 5 ≥ r/t > 3 – BM is shared by 4N/5 number of arms, 3 ≥ r/t –BM is shared by N number of arms.

Dynamic Characteristic Research on Thin Rim Structure for Herringbone Planetary Gear Train

A torsional and translational vibration dynamics model for serial herringbone planetary gear train, which considers the effects of the time-varying errors and meshing stiffness as well as elastic coupling between two stage trains at the same time, was established by using lumped mass method. Time domain dynamic load excitation which derived from dynamics equation is taken as the input of steady-state response solution. The steady-state response of gear structure was solved with mode superposition method combined with external judgment program. The effects of rim thickness for thin wall herringbone planetary gear and single-stage internal gear were also analyzed. Through the comparison, the displacement and stress results of key locations on structure have reached the satisfying and disirable values when the rim thickness of planetary gear is greater than 4.0 mn and rim thickness of internal gear greater than 6.5 mn.

A study on the bending stress of the hollow sun gear in a planetary gear train

Generally, planetary gear type traveling reduction gear is composed of multiple planetary gear stages and has a hollow sun gear in the last stage planetary gear. In designing reduction gear, it is important to evaluate accurately the bending stress at the tooth root of the sun gear as the sun gear is the weakest component in the reduction gear system. Although bending stress can be calculated easily using gear standard codes such as the American Gear Manufacturers Association (AGMA) and International Organization for Standardization (ISO) 6336 for almost all gears, meticulous calculation is needed for the hollow sun gear because of its low backup ratio (rim thickness divided by tooth height) and comparatively large root fillet radius. In this study, a finite element analysis (FEA) is carried out to investigate the effect of rim thickness and root fillet radius on bending stress at the tooth root of the hollow sun gear. In standard codes, bending stress at the tooth root is calculated linearly with a constant slope for the backup ratio below 1.2. However, the effect of the rim thickness on bending stress is more complex in the planetary gear system. Bending stresses calculated by FEA with various backup ratios and root filler radii are compared with the bending stresses calculated by the standard codes.

A deformable body dynamic analysis of planetary gears with thin rims

Planetary gear sets are used commonly by automotive and aerospace industries. Typical applications include jet propulsion systems, rotorcraft transmissions, passenger vehicle automatic transmissions and transfer cases and off-highway vehicle gearboxes. Their high-power-density design combined with their kinematic flexibility in achieving different speed ratios make planetary gears sets often preferable to counter-shaft gear reduction systems. As planetary gear sets possess unique kinematic and geometric properties, they require specialized design knowledge [1]. One type of the key parameters, the rim thickness of the gears, must be defined carefully by the designer in order to meet certain design objectives regarding power density, planet load sharing, noise and durability. From the power density point of view, the rim of the each gear forming the planetary gear set must be as thin as possible in order to minimize mass. Besides reducing mass, added gear flexibility through reduced rim thickness was shown to reduce the influence of a number of internal gear and carrier errors, and piloting inaccuracies [2]. In addition, it was also reported that a flexible internal gear helps improve the load sharing amongst the planets when a number of manufacturing and assembly related gear and carrier errors are present [3–6]. Many of these effects of flexible gear rims were quantified under quasi-static conditions in the absence of any dynamic effects. The effect of rim thickness on gear stresses attracted significant attention in the past. A number of theoretical studies [7–14] modelled mostly a segment of spur gear with a thin rim. In these studies, the gear segment was typically constrained using certain boundary conditions at the cut ends and a point load along the line of action was applied to a single tooth in order to simulate the forces imposed on a sun or an internal gear by the mating planet. This segment of the gear was modelled by using the conventional finite element (FE) method with the same boundary conditions applied in order to simulate the actual support conditions. These models do not

Effects of Rim Thickness on Spur Gear Bending Stress

Thin rim gears find application in high-power, lightweight aircraft transmissions. Bending stresses in thin rim spur gear tooth fillets and root areas differ from the stresses in solid gears due to rim deformations. Rim thickness is a significant design parameter for these gears. To study this parameter, a finite element analysis was conducted on a segment of a thin rim gear. The rim thickness was varied and the location and magnitude of the maximum bending stresses reported. Design limits are discussed and compared with the results of other researchers.

Effects of rim thickness and standard pressure angle on residual stress of case-hardened internal spur gear.

This paper presents a study on the residual stresses of case-hardened internal spur gears with various rim thicknesses and standard pressure angles. A heat conduction analysis of the temperature and an elastic-plastic analysis of the stress in a cooling process for the case-hardened internal spur gear are carried out by finite element method (FEM). The effects of the case depth, the rim thickness and the standard pressure angle on the residual stress are examined. The optimum case depth for the residual stress is also clarified.

Bending Stress Analysis of Idle Gear with Thin Rim : Effect of Rim Thickness on Stresses

Stress distributions in planet gears with a thin rim are analyzed by the photoelastic method and the following results are obtained: Although the position of the maximum stress occurring on a fillet varies with both the tooth load and the radial clearance between rim and gear shaft, it may be sufficient to consider the maximum tensile and compressive fillet stresses in the planet gear concerning the bending strength. In the case of a thin rim, if the radial clearance increases by more than a certain value, the stress amplitude on a fillet may increase rapidly and the value of the clearance may decrease when the rim thickness decreases.

Effects of Rim Thickness and Number of Teet on Bending Strength of Internal Gear

An internal gear which meshed with three planet gears in the same bearing condition, the angles between those planet gears being same and 120° respectively, and which was supported through a thin cylinder, was chosen as the subject of study. The bending moment, the bending stress and the radial displacement in the rim of the internal gear were obtained theoretically, and by using these results the form of an internal gear model was determined. Furthermore, the stresses in the internal gear models were analyzed by the photoelastic method, and the effects of rim thickness and number of teeth of the internal gear on the magnitude and the position of the maximum stress produced in the internal gear were clarified.

Effects of Rim Thickness on Root Stress and Bending Fatigue Strength of Internal Gear Tooth

This paper presents a study on the effects of rim thickness on root stress and bending fatigue strength of internal gear tooth. A root stress analysis by the 2-dimensional finite element method (FEM), a static loading test and a bending fatigue test for internal gears of different rim thicknesses were carried out. The root stresses increase with a decrease in rim thickness on both the tensile and compressive sides. The bending fatigue-limit-load of the thin-rimmed internal gears decreases with a decrease in rim thickness for lw<3m and remains almost constant for lw≥3m. The validity of the calculating formula of tooth bending strength of internal gear proposed by ISO was examined on the basis of the results of the static loading and the bending fatigue tests.

Root Stresses and Bending Fatigue Breakage of Planet Gear

A root stress analysis by means of the two-dimensional finite element method (FEM) and a bending fatigue test for planet and idle gears were carried out. The effects of rim thickness and internal pressure due to a press-fitted bush on the root stresses and the position of the fatigue crack initiation were investigated. In thin-rimed planet and idle gears considerably large stresses occur near the bottom of every unloaded tooth as well as two loaded teeth. The root stresses increase at the tensile side and decrease at the compressive side with a decreasing rim thickness. The fatigue crack of a planet or an idle gear with a press-fitted bush may occur near the tooth bottom due to the effect of residual tensile stress produced by press-fitting.

Effects of Rim Thickness on Root Stress and Bending Fatigue Strength of Internal Gear Tooth

本論文では,種々のリム厚さの内歯平歯車に対して,有限要素法による歯元応力解析,静的負荷試験による歯元応力測定および曲げ疲労試験を行い,歯元応力,曲げ疲労強度に及ぼすリム厚さの影響について明らかにしている。またISO(案)曲げ強度計算式による歯元応力,曲げ疲労限度荷重と静的負荷試験結果,曲げ疲労試験結果との比較検討を行って,ISO(案)曲げ強度計算式の妥当性についても明らかにしている。

Effects of Rim Thickness and Number of Teeth on Bending Strength of Internal Gear

本研究では、3個の遊星歯車が中心角120°ごとに同じ状態でかみあう内歯平歯車で、かつ内歯車と一体の円筒環を通して支持されている内歯車を対象とした。そして、内歯車円環部の曲げモーメント、曲げ応力、半径方向変位を理論的に求め、これらの結果を考慮して内歯車実験モデルを作成し、光弾性法による内歯車の応力解析を行い、内歯車に生ずる最大応力の大きさやその発生位置と内歯車円環部の厚さや歯数との関係を明らかにした。

Study on Welded Structure Gears : 1st Report, Effect of Rim Thickness on Root Stresses and Bending Fatigue Strength

Weldability and bending fatigue strength of rim materials for welded structure gears were examined and the recommendable materials were indicated. Effects of rim and web thickness on root fillet stresses were investigated experimentally. The root fillet stress shows the highest value at the middle of the face width and it increases as the rim and web thickness decrease. Welded gears with different rim thickness were tested using a pulsator of hydraulic type. It was found that the bending fatigue strength of gear teeth decreases with a decreasing rim thickness and that the rim part may break when rim thickness is smaller than one module. The minimum allowable rim thickness for welded gears is also suggested, from the viewpoint of bending fatigue strength, on the basis of experimental results.

Study on Welded Structure Gears : 1st Report, Effect of Rim Thickness on Root Stress and Bending Fatigue Strength

Study on Welded Structure Gears : 1st Report, Effect of Rim Thickness on Root Stress and Bending Fatigue Strength