Study on an internal gear with asymmetric involute teeth

In the field of mechanical engineering, involute helical gears are widely used. Compared with the involute spur gear, helical gears have a high bearing strength, more smooth transmission, less impact and less noise. The internal gear pairs have the features of large transmission ratio, low vibration, low noise and low wear and hence are widely used in planetary gear transmission systems. In order to meet the requirements of high strength, high speed of the modern gear transmission systems, a new type of asymmetric involute internal helical gears is designed based on conventional involute gears. This paper discusses the gear shaper cutter modeling for machining this new gear, analyzes the formation principle of asymmetric tooth profile and establishes a three-dimensional modeling by SolidWorks. Through MATLAB simulation, pressure angle, tooth number, coefficient of displacement and contact ratio of conventional and asymmetric gear are compared and analyzed. Using ANSYS, two types of gears are compared on strength in order to demonstrate superiority of asymmetric tooth and further study about the asymmetric internal helical gears.

The internal gear is part of the planetary and epicyclic gear pairs in the transmission system of the helicopter. Gear tooth wear is one of the most usual gear failures. This paper establishes an analytical model to evaluate the influence of tooth wear on the mesh relationship. A new mesh relationship can be derived for internal spur gears with tooth wear by the proposed analytical model. Consequently, using the new mesh relationship, the two most important meshing excitations, mesh stiffness and unloaded static transmission error (USTE), are quantitatively evaluated for the internal gear with tooth wear. The results indicate that tooth wear mainly affects the meshing ranges of single-tooth and double-teeth in mesh stiffness, rather than its amplitude. Additionally, the amplitudes of USTE increase with the increasing wear depth. Finally, this study can offer a foundation for the dynamic modeling and fault diagnosis of internal spur gears with wear faults.

Recently, internal gears become widely used and highly required according to its ability to transmit large torque to weight ratio, high bending strength, smooth transmission, low noise, and low vibration. Therefore, internal gears are strongly recommended in particular “planetary gear transmission systems”. In this paper, internal involute spur gears are designed based on conventional approach of involute gears. Matlab is used to attain the points of internal gear and to get the main parameters of internal tooth profile, these points have been read by AutoCad to have two dimensional tooth profile. Finite element analysis using Ansys is achieved to analyze and compared the strength of three types of internal gears, Symmetric (20° - 20°) that has been chose to be the standard case, Asymmetric (14.5° - 35°) and Corrected Asymmetric (14.5° - 35°). Tetrahedral type patch conforming method with element size1mm have been chose for fine meshing. The internal gear is fixed supported from the outer ring then, 6500 N.m torque is applied at the rotating axis of the pinion. The bending stresses are calculated based on Von-Mises theory using (FEA). Finally, this study is presented to demonstrate the superiority of internal asymmetric tooth and improve and optimize this significant type of gears.

The present study is part of a series aimed at enhancing the reliability of JIS B 1759, ”Estimation of tooth bending strength of cylindrical plastic gears.” This study examined the stress correction factor converting the nominal tooth bending stress into the local one. The current version has a problem with underestimating the load capacity of internal gears, but considering the contact ratio under load has alleviated the problem. Nevertheless, some issues remain, which led the present paper to determine an alternative stress correction factor through finite element analyses of internal virtual spur gears. Before discussing the alternative factor, examining the fillet profile of injection-molded internal spur gears led to proposing a single circular arc as the standard fillet. Based on that, FEAs of internal virtual spur gears with a single circular fillet determined the modified stress correction factor, which can relieve JIS B 1759 of the underestimations. The modified factor enables the standard to estimate load capacity regardless of external or internal gears, which improves the reliability of the standard.

To further develop the performance testing and practical application of internal meshing gear with curve configuration, the grinding manufacturing method is proposed in this paper. Based on basic principle of internal meshing gear with curve configuration, Newton’s iterative method is used to derive the contact line condition equation during the process of form grinding. Then, the spatial coordinate transformation relationship of the pinion is established, and normal profile of the grinding wheel is derived. An improved transversal algorithm is proposed to analyze the tooth profile error after form grinding simulation, and the results verify the correctness of the designed grinding wheel. A meshing model with single tooth is established. The effects of different parameters on the grinding temperature field under dry and wet grinding conditions are simulated respectively, which will be helpful to the optimization and control of temperature in grinding process. The research results lay the essential theoretical foundation and engineering analysis for practical form grinding applications of the new internal gears. Further study on experimental analysis of grinding manufacturing process of the new tooth surfaces will be carried out.

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

Dudley's Handbook of Practical Gear Design and Manufacture

Bu makalede iç ve dış dişlilerdeki girişimi belirleyen analitik yaklaşımlar araştırılmaktadır. Dış helisel dişliler için fonksiyonel ve imalat tipi girişimler dikkate alınmaktadır. İç düz dişliler için evolvent ve takılma girişimleri ele alınmıştır. Girişim limitleri için literatürde bulunan denklemler incelenmiştir. Ayrıca iç düz dişliler için evolvent girişimi profil kaydırma ile önlemek için bir denklem önerilmiştir. Tasarım parametrelerinin etkisini araştırmak için hem kremayer tipi hem de pinyon tipi dişli imalatı için bilgisayar programları geliştirilmiştir. Geliştirilen programlara dayalı olarak sayısal örnekler verilmiştir. Bu çalışma dişli tasarım sürecinin ilk aşamalarında girişim olup olmadığını belirlemek için kullanılabilir.

Internal gear transmission, boasting advantages such as compact structure, high transmission efficiency, and strong load-carrying capacity, is widely applied in high-end equipment fields, including aerospace, precision machine tools, and new energy vehicle transmission systems. As a key means to enhance the stability and loadcarrying capacity of internal gear transmission, the large contact ratio design involves a coupling relationship between its contact characteristics (e.g., contact stress, contact area morphology, and load distribution rules) and fatigue failure mechanisms. This relationship directly determines the reliability and service life of transmission systems, thus becoming a current research focus and challenge in the field of gear transmission. This study takes a certain type of high-precision internal gear pair with a large contact ratio as the research object. Combined with finite element simulation, it analyzes the impacts of different design parameters on the contact area status, tooth surface contact stress distribution, and tooth surface load. Fatigue life prediction of the gears is conducted through theoretical analysis and numerical simulation. The research results provide key technical support for the structural optimization design and strength check of gears, and also offer important references for improving the reliability and extending the service life of high-end equipment transmission systems, thus possessing high theoretical value and promising engineering application prospects.

This paper presents a method for determining the mathematical model of an elbow mechanism with a convex tooth and a concave tooth. Based on this method, the mathematical model presents the meshing principles of a conical cutter meshed with a tooth that is either convex or concave. Using the developed mathematical models and the tooth contact analysis, kinematic errors are investigated according to the obtained geometric modelling of the designed gear meshing when assembly errors are present. The influence of misalignment on kinematic errors has been investigated. The goal of the current study is to investigate von-Mises stress for three teeth contact pairs. A structural load is assumed to act on a gear of the proposed mechanism. The von-Mises of the proposed gear is determined. The conical cutter used in the design and manufacture of the convex and concave gear is shown. For example, the proposed mechanism with a transmission ratio of 3:2 was determined with the aid of the proposed mathematical model. Using rapid prototyping and manufacturing technology, an elbow mechanism with a convex gear, a concave gear and a frame was designed. The RP primitives provide an actual full-size physical model that can be analysed and used for further development. Results from these mathematical models are applicable to the design of an elbow mechanism.

The effect on dynamics of using a new transmission design for eccentric speed reducers

Tooth root bending stress and surface contact stress are two major determinants of the load carrying capacity of gear drives. Generally, a high contact ratio has the potential to enhance the gear strength. In this paper, the basic procedures and methods for constructing a high-contact-ratio (HCR) internal spur gear pair with the arc path of the contact are presented. The effects of design and modification parameters such as deflection angle, modification angle, and addendum coefficient on gear drive are analyzed in detail based on 2D finite-element models (FEMs). A comparison of experimental and finite-element analyses (FEA) of the bending stress, contact stress, and contact ratio between HCR and involute internal spur gear drives was conducted to demonstrate the advantages of the HCR gear drive in terms of load capacity. The results show that appropriately increasing the deflection angle and addendum coefficient is beneficial for reducing bending and contact stresses. It was also observed that the bending and contact stresses of a HCR pinion are lower than those of an involute one. Moreover, the contact ratio increases with input torque.

A three-dimensional probe is mounted on a specialized gear measuring machine whose measurement target is limited on the working flanks. The newly developed measuring machine has a coordinate measuring mechanism, aiming to be a highly versatile and relatively inexpensive measuring machine. According to our previous research, in addition to the working tooth surface, shape data of the root, bottom and tip profiles can be acquired with a single measurement operation. However, the target object for which this developed method has been applied was only the external cylindrical gear. In this paper, we applied and expanded the development method to the internal cylindrical gear and the evaluation of the axial displacement in the same cross-sectional scanning of the internal helical gear are performed.

The planocentric gearboxes are characterized by the coaxial input and output shafts and large transmission ratios, which can be achieved based on a ring gear with internal gearing in combination with usually two planet gears with external gearing, where the difference in the numbers of teeth between the gear ring and the planet gears is small, preferably amounting one. The proposed solution is based on the S-shaped tooth flank geometry. Since the required gear train characteristics impose strict limitations (e.g. near zero backlash) on the assembled product, it is necessary to simulate its tolerance behaviour. So, a professional or proprietary developed CA tools are necessary to deal with such analyses, e.g. KissSoft. Properties of a such gear train can be successfully modified in this way. A sophisticated testing rig was developed to verify actual gear train characteristics, and to test its short-term and long-term behaviour. Backlash, stiffness, kinematic error, and dynamic behaviour of produced gear trains are measured in this way.

<div class="htmlview paragraph">This paper presents a method of specifying the essential information for detailing the geometry of an external involute profiled spur or helical gear tooth. Internal gears are not included for reasons stated in the paper. It assumes that the reader is familiar with basic gear design terms and concepts.</div>