2218 平歯車とかみ合う内歯コニカルギヤの設計法(OS1-10 コニカルギヤ)

In order to resolve the issues of low efficiency and poor precision in the traditional finishing process of hardened internal gears, a method is proposed for calculating the profile curves of a drum-shaped grinding tool suitable for mass finishing of hardened internal gears. Additionally, the impact of drum-shaped grinding tool installation errors on the tooth surface deviation of internal gears is analyzed. Firstly, the processing principle for the generation grinding of internal gears by the drum-shaped grinding tool is introduced. Based on differential geometry, meshing theory, and two-degree-of-freedom enveloping method, a mathematical model is developed for the generation grinding of internal gears. Profile curves of the drum-shaped grinding tool are obtained by solving the meshing equation between the drum-shaped grinding tool and the internal gear. Then, the tooth surface equation for the internal gear is derived in the presence of drum-shaped grinding tool installation errors. By discretizing the error tooth surface of the internal gear, the average normal deviation of the tooth surface is calculated. In the end, the distribution of normal deviation on the tooth surface of the internal gear with different drum-shaped grinding tool installation errors is acquired, and the influence of four kinds of installation errors on the tooth surface of the internal gear is analyzed. The sensitive direction is identified for drum-shaped grinding tool installation errors on the tooth surface of the internal gear. Consequently, this research provides a calculation method for the drum-shaped grinding tool fit for high-precision and high-efficiency finishing of mass-produced hardened internal gear and offers a reference for correcting deviation in the tooth surface of internal gear with installation errors of the drum-shaped grinding tool.

Conical gear is an involute gear having a cone angle. When the conical gears are meshed on the intersecting axis or nonintersecting- nonparallel axis, the contact between tooth surfaces is a point contact. So the tooth surface strength is generally small. It is the Concave conical gear that was developed in order to overcome this weak point. Its tooth surface is a curved surface having the reverse crowning on the tooth surface of the conical gear. Conventionally, this tooth surface has been generated by the conical shaped wheel. By this method, however, it is not necessarily easy to make an ideal tooth surface. Therefore, we devised a new rack for generating the concave conical gear. This is the rack in which the tooth thickness of normal rack is corrected in the direction of the tooth trace. We obtained the theoretical tooth surface generated by the new rack. And, we made the gear having the theoretical tooth surface by the five axis machining center. In this research, first we developed a coordinate calculation method of the theoretical tooth surface, and next a 3D model, and finally an optimal tool path by using CAM. And we measured the curved line of the tooth surface in the plane of principal radii of curvature of the test gear and confirmed that this line agrees well with the ideal curved line. From the above results, the validity of this design and production system is confirmed.

Study on an internal gear with asymmetric involute teeth

On gear time-varying meshing stiffness calculation considering indexing feeds and processing characteristics of gear shaping processing

Conical involute gears used for marine transmissions are mostly helical conical involute gears. Besides these gears are not intersecting axis gears but also nonintersecting-nonparallel axis gears. The contact between tooth surfaces of a pair of gears is the point contact. Hence the tooth surface durability is generally small. In order to overcome this weak point, one of the authors invented a new type of conical gear, which is called conical Concave conical gear has higher tooth durability than the conventional conical involute gear. In this research, a new method to generate the helical Concave conical gear is presented. First the principle of generating method is introduced. Theoretical tooth surface is analyzed. Secondly test gears are ground. Tooth surfaces of the test gears are measured and compared with theoretical ones. Two tooth surfaces are in good agreement.

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.

Dudley's Handbook of Practical Gear Design and Manufacture

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.

Conical involute gears (beveloids) are used in transmissions with intersecting or skew axes and for backlash-free transmissions with parallel axes. Conical gears are spur or helical gears with variable addendum modification (tooth thickness) across the face width. They can mesh with all gears made with the same tool. The geometry of such gears is generally known, but applications in power transmissions are more or less exceptional. ZF applications so far include marine transmissions with inclined output shafts and low backlash robot transmissions. The latest development has been realized for the AWD version of a six-speed automatic transmission. Here, the torque must be transmitted from a center differential to a front-axle bevel gear. By means of conical spur gears, it has been possible to realize an inclined drive shaft which offers considerable advantages in terms of installation space. This lecture deals with the development of conical gears for vehicle transmissions: basic geometry, design, production and testing.

In many situations, the polymer gears are the perfect replacement for traditional metal gears. Compared to metal gears, the polymer gears will generate more heat at the gear tooth contact surface and more wear loss. Hence, this study aims to decrease the wear loss and increase the load-carrying capacity of the polymer gears. To achieve this, the reinforcement materials were added to the base polymer gear material. In this study, Nylon-66 was chosen as the polymer matrix material and an isolated glass fibre and steel grid were used as the reinforcement materials. Three different types of polymer spur gears such as Polyamide Gear (Nylon-66), Reinforced Polyamide Gear (Nylon-66+Glass Fibre), and Hybrid Glass Fiber Steel Grid Gear (Nylon-66+Glass Fibre+Steel Grid) named PG, RPG and HGFSGG were fabricated using injection moulding machine and each type of gears were compared for wear loss and specific wear rate under the similar testing conditions. The wear test was performed in the Forschungsstelle fur Zahnrader und Getriebebau (FZG) test rig at 1500 rpm with an applied load of 20 N for 12.5 h continuously. From the test results, it was identified that HGFSGG polymer spur gears have exhibited a lower surface temperature and better wear properties compared to the other two types of spur gears. From the Scanning Electron Microscope (SEM) analysis, it was noticed that the PG spur gear exhibited deep and uniform wear at the gear tooth surface. In contrast, RPG spur gear exhibited glass fibre distortion and abrasive-type wear. The SEM micrograph of the HGFSGG spur gear reveals the presence of very few surface flaws in the gear tooth surface.

A control method of finishing dimensions of a helical concave conical gear, called center-ball measurement, is newly developed. The tooth surface of the concave conical gear is different from that of the conical involute gear, which is concave compared to the tooth surface of the conical involute gear. So the over-ball measurement of the conical involute gear can not be used at it is, but can be applied to a special measuring conditions. This center-ball measurement is based on the over-ball measurement of the helical conical gear. But in this method, the measuring ball, which is composed of two hemispheres, must be used. So the over-ball diameter can not be measured, but a center-ball diameter, which is the distance between two ball centers, can be measured instead. In this research, first the measuring condition is established. Second the center-ball diameter is obtained analytically. Finally, the center-ball diameter is verified through experiments. The experiments prove that this method has opened a door to the control of finishing dimensions in hobbing and grinding of the helical concave conical gear.

Optimal tooth profile design of a gear shaper cutter when meshing with internal straight splines

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.

Involute gears are a vital component used in industry due to their ability to provide flexible and accurate rotary motion. Gear shaping is one of the most prominent gear cutting processes as it can be used to effectively manufacture spur and helical external as well as internal gears. Thus, the accurate prediction of the cutting forces developed during the cutting process is of great importance because it can greatly affect the wear and the cutting tool’s life. In this work, a simulation model was developed based on a commercial CAD software, able to simulate the kinematics involved in the process and provide accurate results regarding the undeformed chip geometry as well as the cutting forces. In order to verify the accuracy of the model, the produced gear flanks are compared with the theoretical ones and the calculated cutting forces are compared with the respective measured forces obtained from the literature.