Solid Gears Research Articles

Effect of Rim and Web Thickness on Tooth Root Stress of Spur Gear

This study investigated the impact of spur gear rim and web thickness on root stress. A finite-element analysis model (FEM) was utilized and validated through a gear-bending test. Four gears with different rim and web specifications, including a solid gear, were designed and tested using strain gages to measure their root stress. The 3D FEM was validated by comparing the measured root stresses with that analyzed by the developed FEM. Using this model, a parametric study was conducted by varying the web position, pressure angle, and module to investigate the effect of the backup ratio on the root stress ratio of the gear. A stress-ratio map was generated based on the results. This stress-ratio map was compared with the rim thickness factor (YB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Y}_{B}$$\\end{document}) for external spur gears specified in ISO 6336-3. The comparison reveals that the rim thickness factor specified in ISO 6336 is overly conservative compared to values obtained in this study. Our results suggest that the thickness of both the rim and web should be considered to reduce the weight of spur gears. These findings can be applied to the design of lightweight spur gears.

Characterization of damping in 3D metal printed gear body using parameter optimization

With the rapid development of the global economy and the widespread use of high-speed machinery, vibration and noise pollution is becoming increasingly serious. The increased energy costs, environmental pollution, and carbon emissions have prioritized sustainable development for industry. As an important link of mechanical transmission, the gear transmission vibration and noise adversely affect the physical and mental health of operators and interfere with the normal use of machinery. This paper proposes a new metal 3D printing-made vibration-damping lightweight gear model. The solid gear web is replaced with a lightening hole structure that is expected to ensure rigidity and torsional compliance while controlling the damping effects of the gear web structure. Gears were manufactured from an additive manufacturing material using a metal 3D printing technique. This work advanced an experimental analysis of the dissipation properties of metal printed gear exploiting vibration tests. A gear frequency-sweeping excitation test bench was designed and developed to simulate in-plane excitation to produce a circumferential torsional mode of the specimen. Circumference damping estimates are guided by executing vibration exciter excitation on the setup. The half-power bandwidth and modal fitting methods were arranged and compared, relying on the measured frequency response function (FRF) single-degree-of-freedom (SDOF) approximation.

МЕТОД ОБЪЕКТНОГО МОДЕЛИРОВАНИЯ ПРИ РАЗРАБОТКЕ ПАТЕНТОСПОСОБНЫХ КОНСТРУКЦИЙ УЗЛОВ ТЯГОВОГО ПРИВОДА

Work objective is to develop a patentable design of locomotive traction drive mechanisms using the example of a suspension unit. Research methods: object modeling method, analytical methods for calculating dynamics of rolling stock. Research results and novelty: the design of the railway electric motor suspension unit, which will reduce costs in the course of maintenance and repair of a locomotive with a solid gear by increasing the reliability of the suspension unit parts, eliminating their wear, has been developed; a compensation coupling device has been devised. We will synthesize the object model of a technical system based on the identification of its typical structure by classifying technical systems. Conclusion: the application of the object modeling method together with the object model allows avoiding errors in the development of new designs of technical objects based on existing comparables and eliminates defects of the selected prototype. The use of the object modeling method makes it possible to synthesize patentable designs of the locomotive underframe mechanisms.

Finite Element Analysis of a Spur Gear Considering Mass Relief Strategies

This paper deals with analyzing the structural influence of mass reliefs in spur gears. For this purpose, a system composed of pinion and a gear was designed, such that for gear several geometries were designed with different reliefs shapes and soul thicknesses. From the proposed geometries, finite element analysis (FEA) was performed, and the tooth stresses of each model were compared with the solid gear. From the results, it was observed that the tooth stresses are reduced in some cases. Besides, from the aforementioned cases, it is possible to observe that the maximum stresses may take place in its core instead of the teeth (rim area). On the other hand, based on other cases, the core thickness plays an important role as a criterion that defines the local stress.

Cad for Gears Part 1 Helical and Double Helical Gears.(Dept.M)

The aim of this paper is to construct a software containing a complete design procedure and detailed drawing for spur, helical and double helical gears. This software can be executed on all the IBM personal computers XT/AT or compatibles. The main elements of the design In this program are : input data, type end shape of gear tooth system (IS. US, BS and DIN), module, minimum number of teeth to avoid interference, tooth profile modification, centre distance, contact ratio, face width, helix angle, material, equations for bending strength (Lewis, modified Lewis and Buckingham) and surface durability, and load carrying capacity for bending strength and surface durability using ISO, AGMA and BS equations with constant or variable tooth load. Many equations and practical formulae are selected for making the gear construction integer gear, solid gear, gear with web, gear with web and holes, gear with arms, gear with Two walls and composite gear). With running the software. full specifications, geometry, kinematics, loads, stresses and detailed drawing of the gears are obtained according to the input data. Different examples are selected to show the variety of the Output data and the strength of the software. Also these runs show the sava in time and accuracy of the results.

Cad for Gears Part 2 Bevel Gears.(Dept.M)

The aim of this paper is to construct a software containing a complete design procedure and detailed drawing for bevel gears (straight, skew, zerol and spiral). This software can be executed on all the IBM personal computers XT/AT or compatibles. The main elements of the design in this program are: input data, type of bevel gear, type and shape of gear tooth system (ISO, US, BS, DIN and Gleason), module, virtual number of teeth, minimum number of teeth to avoid Interference, tooth profile modification, shaft angle, contact ratio, face width, spiral angle, force analysis, sliding velocity and efficiency, material, equations for bending strength (Modified Lewis, Buckingham, AGMA and Gleason) and surface durability, also load carrying capacity for bending strength and surface durability using ISO, AGMA, Gleason and 8S equations with constant or variable tooth load. Many equations and practical formulae are selected for making the gear construction (integar gear, solid gear, gear with web, gear with web and holes, gear with arms and composite gear). With running the software, full specifications, geometry, kinematics. loads, stresses and detailed drawing of the gears are obtained according to the input data. Different examples are selected 10 show the variety of the output data and the strength of the software. Also these runs show the save in time and accuracy of the results.

Principal stress lines based design method of lightweight and low vibration amplitude gear web

<abstract> <p>A lightweight and low vibration amplitude web design method was investigated to reduce gear weight and noise. It was based upon the relationship between length and orthogonality that the principal stress lines were designed at the gear web. By constructing a vibration control model with gear design parameters, the optimal distance was calculated. By offsetting the principal stress lines at the optimal distance, the lightweight gear web with the low vibration amplitude was then generated. A vibration experimental platform was built to verify the novel gear vibration performances, and it was compared with other gears with the same web's porosity to verify loading performance. The experimental results indicated that compared with the solid gear, the novel gear is 20.50% lighter and with a 29.46% vibration amplitude reduction.</p> </abstract>

Effects of lightweight gear blank on noise, vibration and harshness for electric drive system in electric vehicles

In this paper, effects of lightweight gear blank on static and dynamic behavior for electric drive system in electric vehicles are studied. First, a hybrid finite element-analytical method is proposed in this paper to establish gear load contact analysis model considering the structure of lightweight gear blank, which can balance the computing speed and numerical accuracy. Second, this paper establishes a rigid-flexible coupled dynamic model of electric drive system considering shaft elasticity, bearing stiffness, and housing flexibility. Finally, aiming at the noise, vibration, and harshness problem of an electric drive system equipped on electric vehicles, effects of gear web and gear rim thickness on noise, vibration, and harshness excitation source such as static transmission error and dynamic meshing force as well as dynamic response at bearings and housing are analyzed. The results show that changing gear web and gear rim thickness can significantly reduce dynamic meshing force and dynamic response. Compared with solid gear, dynamic meshing force is reduced by 68.50%, and dynamic response is reduced by 66.70% after optimization, thereby significantly improving the noise, vibration, and harshness performance of gear transmission system in electric vehicles.

Quality of Service and Reliability Analysis of Wireless Networks

Dependability is the fundamental worry in remote systems. Subsequently, assessing unwavering quality has turned out to be fundamental in frameworks. Many subsisting remote system steering conventions propose the accessibility of solid hubs. This, in any case, isn't a bona fide hypothesis given the elements of remote systems. Withal, because of continuous changes in topology, connect disappointments and hub disappointments are conceivable. Therefore, a credible technique is expected to assess the unwavering quality of remote systems in the event of such vulnerabilities. The unwavering quality of a remote system is constant by specific factors, for example, delay, throughput, dormancy, and overhead. For exploratory investigation, the system execution include that will be used in the test set up will be the throughput of the system. Throughput can be consigned as the volume or measure of information or activity that can saturate a system at a given time. Throughput can be habituated to evaluate arrange productivity and dependability. Very solid creations, gear, and foundation are required for a high gauge of unwavering quality.

HOW TO STEER THE TRANSMISSION RATIO OF PLANETARY CONTINUOUSLY ADJUSTABLE GEAR TRAIN

The known attempts to create a continuously-adjustable gear train with solid gears have led to development of some so-called adaptive gears. The most structurally simple version of continuously- adjustable gear train is a two-wheel planetary gear. It is an obvious fact that an active regulation of gear ratio for the gear should be based on the presence of con- trolled elements (parameters) and a mechanism for their control. In respect of the mentioned gear one of the controlled elements that is a compound central toothed gear has such controlled parameter as a nominal pitch diameter. In this case it can rotate or remain motionless. Other controlled element which is a planetary carrier has its own radius as a controlled parameter and makes a rotary motion with a great speed of a leading element. The purpose of the control mechanism is to ensure radial displacement of central toothed gear and planet gear sectors in the working gear. The paper describes the mechanism modifications and considers two variants for transfer of control action from its source to an object to be controlled. The transfer is ensured by mechanical gears (two variants) and hydraulics.

Analysis of mixed model in gear transmission based on ADAMS

The traditional method of mechanical gear driving simulation includes gear pair method and solid to solid contact method. The former has higher solving efficiency but lower results accuracy; the latter usually obtains higher precision of results while the calculation process is complex, also it is not easy to converge. Currently, most of the researches are focused on the description of geometric models and the definition of boundary conditions. However, none of them can solve the problems fundamentally. To improve the simulation efficiency while ensure the results with high accuracy, a mixed model method which uses gear tooth profiles to take the place of the solid gear to simulate gear movement is presented under these circumstances. In the process of modeling, build the solid models of the mechanism in the SolidWorks firstly; Then collect the point coordinates of outline curves of the gear using SolidWorks API and create fit curves in Adams based on the point coordinates; Next, adjust the position of those fitting curves according to the position of the contact area; Finally, define the loading conditions, boundary conditions and simulation parameters. The method provides gear shape information by tooth profile curves; simulates the mesh process through tooth profile curve to curve contact and offer mass as well as inertia data via solid gear models. This simulation process combines the two models to complete the gear driving analysis. In order to verify the validity of the method presented, both theoretical derivation and numerical simulation on a runaway escapement are conducted. The results show that the computational efficiency of the mixed model method is 1.4 times over the traditional method which contains solid to solid contact. Meanwhile, the simulation results are more closely to theoretical calculations. Consequently, mixed model method has a high application value regarding to the study of the dynamics of gear mechanism.

Effects of Rim and Web Thicknesses on Root Stresses of Thin-Rimmed Helical Gear

This paper presents a study on root stresses of thin-rimmed helical gears with web arrangement of various rim and web thickness. Thin-rimmed helical gears used in this study were meshed with solid helical gear. Root stresses were measured from the beginning of engagement to the end of engagement by using the strain gauge method. The changes of root stresses from the beginning of engagement to the end of engagement were examined and the meshing position where the maximum root stress occurred (worst loading position) was determined. Effects of rim and web thickness on the root stress, the maximum root stress and the position of maximum root stress were clarified.

Preform and forging process designs based on geometrical features using 2D and 3D FEM simulations

The requirements of compact and integrated industrial products make it more difficult to produce these complicated parts. The aim of this paper attempts to propose methods of finish forging die and preform designs to produce a product consisting of a solid spur gear and cylindrical cup features. One- and two-step forming processes were proposed and evaluated using computer-aided engineering simulations. For one-step extrusion or upsetting processes, diameters and heights of billet were calculated using the product volume and the corresponding cup or gear features, respectively. For two-step forming process, Tee-shaped preform designs were proposed based on the product volume and the feature volume ratio of cup to gear; corner and fillet arcs were adopted to modify the profile of Tee and control the material flow in the finisher die. The forming processes of preform and finisher were analyzed using the two- and three-dimensional finite-element method models to predict the detail characteristics of sectional material flow and the completely three-dimensional deformation results, respectively. Experimental tests were also carried out to validate the proposed simulation models and design methods. The forming loads, the stress and strain distributions of forged part, and the occurrences of defects were studied and a suitable preform and corresponding die designs were obtained. The proposed preform designs were verified via the numerical analyses for the feasibility study. Finally, a sound gear product had been made successfully using the proposed suitable design of preform.

CAD-based simulation of the hobbing process for the manufacturing of spur and helical gears

Targeting an accurate and realistic simulation of the gear hobbing process, we present an effective and factual approximation based on three-dimensional computer-aided design. Hobbing kinematics is directly applied in one gear gap. Each generating position formulates a spatial surface path which bounds its penetrating volume into the workpiece. The three-dimensional surface paths generated from the combination of the relative rotations and displacements of hob and work gear are used to split the subjected volume, creating concurrently the chip and the remaining work gear solid geometries. The developed software program HOB3D simulates accurately the manufacturing of spur and helical gears, exploiting the modeling and graphics capabilities of a commercial CAD software package. The resulting three-dimensional solid geometrical data, chips and gears provide the whole geometrical information needed for further research, such as prediction of the cutting forces, tool stresses and wear development as well as the optimization of the gear hobbing process.

Centrifugal load and its effects on bending strength and contact strength of a high speed thin-walled spur gear with offset web

Abstract This paper discusses effects of centrifugal load on bending strength and contact strength of a thin-walled spur gear used at high speed. A three-dimensional (3D), finite element method (FEM) is presented in this paper for analyzing centrifugal deformations and centrifugal stresses of the thin-walled gear at high speed and the responsive FEM software are developed through many years’ efforts. It is verified that the developed FEM software can calculate correct centrifugal deformations and centrifugal stresses of the thin-walled gear by a cantilever model. Then centrifugal deformations and centrifugal stresses of a thin-walled spur gear with offset web are analyzed with the FEM software at speed range 5000–40,000 rpm. It is found that effects of centrifugal load on deformations and stresses of the thin-walled gear can be neglected when gear speed is below 10,000 rpm. But it is necessary to consider the effects of centrifugal stresses on strength design of the thin-walled gear when the gear speed exceeds 10,000 rpm. Effects of the centrifugal load-deformed thin-walled spur gear on tooth contact pattern, surface contact stress, root bending stress and tooth load-sharing ratio of the gear are also investigated through performing loaded tooth contact analyses of the gear when it is engaged with a solid mating gear under a torque. It is found that centrifugal deformation of the gear at high speed has greater effects on tooth contact pattern, tooth surface contact stress, root bending stress and tooth load-sharing ratio of the pair of gears. Finally it is pointed out that strength calculation methods of a thin-walled gear are quite different from a solid gear. Methods for exact bending strength and contact strength calculations of a thin-walled gear at high speed are presented in this paper.

The applicability of process design system for forward extrusion of spur gears

In this study, the applicability of the automated process design system developed for cold forward extrusion of solid or hollow spur gears was confirmed through experiments. Extrusion die set was designed by employing the developed system. An elastic analysis of dies considering a shrink fit was carried out to determine level of hoop and effective stresses depending on its ratios. Depending on material types and lubricants, hollow and solid gears were extruded in the present investigation. From experiments, it was found out that filling status of the hollow gear was improved in comparison with that of the solid gear irrespective of forming conditions and the predicted forming load obtained from the developed design system matched well with the experimental load requirements. From the current study, it was expected that the developed system can efficiently be used for the process and die design of gear extrusion at room temperature.

Error Analysis on Finite Element Modeling of Involute Spur Gears

Finite element analysis can incorporate two-dimensional (2D) modeling if the geometry, load, and boundary conditions meet the requirements. For many applications, a wide range of problems are solved in 2D, due to the efficiency and costs of computation. However, care has to be taken to avoid modeling errors from significantly influencing the result. When the application area is nonlinear, such as when modeling contact problems or fracture analysis, etc, the 2D assumption must be used cautiously. In this paper, a large number of 2D and three-dimensional (3D) gear models were investigated using finite element analysis. The models included contact analysis between teeth in mesh, a gear body (disk), and teeth with and without a crack at the tooth root. The model results were compared using parameters such as the torsional (mesh) stiffness, tooth stresses and the stress intensity factors that are obtained under assumptions of plane stress, plane strain, and 3D analysis. The models considered variations of face width of the gear from 5 mm to 300 mm. This research shows that caution must be used especially where 2D assumptions are used in the modeling of solid gears.

Determination of a Major Design Parameter for Forward Extrusion of Spur Gears

In this study, a major design parameter was identified for cold forward extrusion of solid or hollow spur gears by investigating the effect of gear geometries and forming variables on formation of gear teeth by finite element simulations. A limiting extrusion ratio was determined for reducing the likeliness of underfilling in the die cavity. An equivalent radius of the cross-sectional geometry of a gear was also determined to predict the forming load requirement from an axi-symmetric approximation. Based on this approximation, a modified empirical equation was determined for simple determination of forming loads required.

浸炭焼入れ薄肉対称ウェブ構造平歯車の残留応力と曲げ疲労強度に及ぼす浸炭部の影響(O.S.02-1 歯車の強度(1))

This paper presents a study on effects of case-carburized parts on residual stress and bending fatigue strength of case-carburized thin-rimmed spur gears with symmetric web arrangement. A heat conduction analysis and an elastic-plastic stress analysis during the case-carburizing process were carried out for various case-carburizing conditions by the three dimensional finite-element method (3D-FEM), considering changes of the thermal expansion coefficient and the yield stress with the temperature, and then residual stresses were obtained. Bending fatigue tests were carried out for different case-carburized thin-rimmed spur gears with symmetric web arrangement. Effects of case-carburized parts on the residual stress and the bending fatigue strength were examined. These results were also compared with those of solid gears.

유한요소해석에 의한 플라스틱 스퍼기어의 내구성 향상방안 연구

Stress patterns are created in the plastic spur gear tooth body by introducing a hole or a steel pin to improve stress distribution. Static analysis using finite element method is carried out to show the effect. The result shows that maximum stress as well as tooth tip displacement is dependent on the size and location of a hole or a steel pin. When a hole located on the tooth center line, the maximum static stress level and the tooth tip deflection is always higher than that of a solid gear. But, a considerable reduction in the maximum stress and tooth tip displacement is achieved by insertion of steel pin.