Conical Involute Gear Research Articles

Two-Sided Contact Mesh Stiffness and Transmission Error for a Type of Backlash-Compensated Conical Involute Gear Pair

Both the drive- and back-side contact mesh stiffnesses (two-sided contact mesh stiffness) for a new type of conical involute gear (NTCIG) is developed analytically. Instead of the conventional spring preload anti-backlash method, an active control strategy to eliminate the time-varying backlash is presented by adjusting the axial displacement of the driven gear. The dynamic transmission error (DTE) of the gear pair is calculated under different load excitations to analyze the differences between the drive- and back-side meshes under a time-varying backlash with anti-backlash conditions based on the NTCIG model with an eccentricity error. Considering the additional rotational angle caused by the anti-backlash and the differences from the two-sided contact, the theory of no-load transmission error for the NTCIG is modified by agreeing considerably well with the low component of the DTE. Moreover, the DTE curve under varying load excitations showed that the dynamics of the NTCIG improved considerably after backlash compensation. The drive- and back-side tooth meshes were analyzed according to the DTE of NTCIG with backlash control under various external excitations at different speeds and variable initial phases, frequencies, and amplitudes of the sinusoidal load.

Analytical design method for beveloid gears with a small shaft angle and offset

In addition to more sophisticated flank modifications, there is a discernible trend toward special gearing that is reflected in the increased use of beveloid gears. Beveloid gears (conical involute gears) are increasingly used in automotive and marine gearboxes, as well as in industrial gearboxes (e.g., for twin-screw extruders). Due to the rising demand, it is crucial to apply a purposeful method for designing the main gearing data. A key benefit of beveloid gears is the largely arbitrary arrangement of the gear axes within space. However, there is a need for a generally applicable design method for deriving suitable main gearing data for the available mounting space and the desired axis position. Most analysis and optimization tools for gearings particularly require these main gearing data as known input. To address this issue, this paper introduces a design method for determining the main gearing data based on strength-related aspects and mounting space. The geometric characteristics of beveloid gears are taken into account in order to subsequently optimize the designed gearings. An analytical design method for beveloid gears in arbitrary axis arrangements is presented: This yields a centered contact pattern with a predefined gear backlash without iterations. In addition to the direct determination of the gearing data, the freely definable ratios of the gearing parameters are new. The applicability of this method is then demonstrated by selected examples. Compared to existing design strategies, the exact mathematical mesh condition is taken into account here, which enables subsequent analytical modification.

Method for the pre-dimensioning of beveloid gears

Conical involute gears – also referred to as beveloid gears – are based on cylindrical involute gears, as both gear geometries are based on a basic rack. They differ from cylindrical gears in that the beveloid gears’ addendum modification along the face width is not constant, but linearly variable. This allows beveloid gears to transfer mechanical power with parallel, intersecting or even skewed axes up to shaft angles of approximately 20°, whereas bevel or hypoid gears are applied with larger shaft angles. Compared with both cylindrical and bevel gears, there is less knowledge available concerning the design of beveloid gears. Existing tools for contact analysis are based on predetermined main gearing data. Therefore a method to pre-dimension main beveloid gearing data based on application requirements was developed. Initially, equivalent cylindrical gears are dimensioned and then transformed into beveloid gears with the required mounting positions. The method involves pre-optimizing of beveloid gears with several targets. Firstly, to comply with selected boundaries of the addendum modification coefficient, as well as to minimize ease-off between the tooth flanks achieved by a centric contact pattern and ensure adequate tip clearance by reducing tip circles. The method was implemented in a software environment for tooth contact analysis and applied to a wide range of data sets. The evaluation demonstrated the efficient design of the main data of beveloid gears including pre-optimization to achieve the objectives mentioned previously. In further optimizations, the microgeometry of beveloid gears must be adapted regarding the gap that occurs between the flanks.

The Calculation of Meshing Efficiency of a New Type of Conical Involute Gear

A new type of conical involute gear, proposed in this paper, can be applied in precise gear transmission for adjusting the backlash because of the special characteristics of its teeth. The meshing states of parallel external gear transmission based on the proposed gears are analysed and presented. The expressions of the length of contact and relative sliding velocity at any meshing position are derived. Then, the calculation formula of meshing efficiency is given by utilizing the piecewise equivalent method. Next, the variation of the length of contact line, unit load, meshing efficiency in a meshing period with different gear parameters and different operations are illustrated by employing numerical examples, and the influences of gear parameters and operations on meshing efficiency of the proposed gears are discussed based on the computing results. In the end, the applicability of the calculation is introduced.

Determination of effective involute parameter limit in generation simulation of gears manufactured by rack-type cutters

This paper studies the computerized tooth profile generation of involute gears cut with rack-type cutters. Based on the theory of gearing the mathematical models of generating cutter with asymmetric involute teeth and generated involute gears are given. Beveloid (conical involute) gears are considered for a generalized type of involute gearing for connecting parallel shafts. Effective limits of involute design parameters that determine the actual tip circle radii of the generated gears are investigated. An approach based on contact path of mating gears is proposed to eliminate further operations for standard value of tip circle radius. Computer simulation programs are developed to obtain graphs of generating tools and generated teeth surfaces.

Study on modular modeling and performance evaluation of a conical gear for marine transmission system

Conical involute gears, which are also known as beveloid gears, are the involute gears with cone-shape gear body rather than cylindrical gear body. Generally, conical gears are used in anti-backlash transmission systems and marine transmission systems. In marine transmission system, in order to obtain optimal propulsive force, 7–14 degree inclination angle was needed. In this paper, a 7 degree cone angle conical gear used in 375 kW class marine power transmission system was selected as research objective. And in order to establish the design theory of conical gear, a design system named conical gear modular modeling system was developed. The prototype conical gear was developed by the above design system to be used to simulate in a certain condition. The simulated and optimized prototype conical gear was manufactured which is as a specimen to complete a series of performance tests which contains gear tooth profile test and contact rate test. As the results, the developed conical gear can well meet the performance requirements of the 375 kW class marine power transmission system.

コニカルギヤの歯面損傷に及ぼす歯面修整の影響

The conical involute gears have been applied to automotive parts such as 4WD transfer. The conical gear pair has characteristic large ease-off and this is equivalent to meshing of cylindrical gears which has large crowning for lead direction. Consequently, the trochoidal interference is thought to be caused because of tooth stiffness reduction. In this study, to clarify the influence of the tooth flank modification on the tooth surface damage, tooth surface endurance test with several tooth flank modification forms is experimented. As a result, the gear pair with crowning for tooth profile direction and reverse crowning for lead direction can extend the pitting fatigue life because of the edge load reduction of tip or root.

코니칼 인볼류트 기어의 Total 설계에 관한 연구

ABSTRACT Currently, there are many power transmission devices, including gears, friction wheels, chains, and belts.Becausethe power transmission ofgears is most certainin these devices, gears are widely used in different power transmission fields and environments. In accordance with the gear shape, gears can be classified as cylindrical gears and conical gears. A cylindrical gear, which provides a means of power transmission under parallel axis and skewed axis conditions, contains a spur gear, a helical gear and a worm gear. A conical gear, which can be used on a skewed axis as well as parallel and crossed axes, includes a bevel gear(e.g., straight bevel, spiral bevel, hypoid gear) anda conical involute gear(or a beveloid gear). In this paper, a conical involute gear which utilizes the fabrication method of other involute gears such as spur and helical gears using a CNC hobbing machine isdiscussed. Key Words : Conical Involute Gear(코니칼 인볼류우트 기어 ), Parallel Axis(평행축), Crossed Axis(교차축), Skewed Axis(엇 갈린축), Beveloid Gear(베벨로이드 기어)

헬리컬 코니칼 인볼류트기어의 3D 모델링과 치면 응력해석에 관한 연구

Generally, marine transmissions contain straight shafts and helical gears, meaning that enginerooms require more space. In order to guarantee a levelengine space for conical involute gears or beveloid gears, both of which are important machine parts, a conical gear was used to replace the traditional cylinder gear. Owing to weak points such as the point contact phenomenon of the teeth, a limitation of the width of each tooth in terms of the addendum, the variational modification coefficient,and the difficulty of processing, research about conical involute gears remains at a standstill. Along with the increasing number of applications of conical involute gears, research on conical gear design technology is necessary. In this paper, in an effort to enhance conical gear design technology, research on the 3D modeling and stress analyses of helical conical involute gears were done.

Mesh efficiency analysis of conical involute gears

The conical involute gears have been applied to automotive parts such as FR-4WD transfer. To apply for automobile, high capacity, higher quietness and efficiency are required. However the tooth contact of conical gear pair is point contact, so the large ease off happens even though each tooth surface has no manufacture error. Also the tooth depth and thickness of conical involute gears change along the lead direction. These characteristics have to be considered for the tooth mesh analysis. We have already published the transmission error analysis and tooth surface durability analysis considering these peculiar characteristics. In this paper, we develop the mesh efficiency analysis and show the improvement method of mesh efficiency by tooth surface modification. From this investigation, it is found that the mesh efficiency of conical involute gears is better than same size cylindrical gears due to the peculiar ease off distribution.

S112026 コニカルギヤのかみ合い効率解析([S112-02]伝動装置の基礎と応用(2))

S112026 コニカルギヤのかみ合い効率解析([S112-02]伝動装置の基礎と応用(2))

Tooth Surface Durability Analysis of Conical Involute Gears

Tooth Surface Durability Analysis of Conical Involute Gears

2208 コニカルギヤの歯面損傷に及ぼす歯面修整の影響(OS-02 歯車の強度/OS-16 一般講演)

2208 コニカルギヤの歯面損傷に及ぼす歯面修整の影響(OS-02 歯車の強度/OS-16 一般講演)

Influence of the manufacturing method on the running behavior of beveloid gears

Beveloid gears, also known as conical involute gears, gain more and more importance in industrial practice. They are based on cylindrical gears, but have a variable profile shift along their tooth width. For some time, beveloid gears have been applied to marine transmissions (Winkler 2002; Zhu et al. in Chin J Mech Eng 25:328–337, 2012), but in the last years they have been used increasingly in the automotive industry (Borner et al. in Gear Technol 6:28–35, 2005; Alxneit 2010). A crucial step of the manufacturing process is the grinding process that is necessary to achieve high load carrying capacity and low noise vibration harshness (NVH). During the grinding process the micro-geometry of the tooth flanks can be modified in order to increase the gear quality. For the generation grinding process of beveloids, two types of machine kinematics and two tool concepts are known. The different machine kinematics and tool concepts may lead to unintentional changes in micro-geometry of the flanks which has an impact on load carrying capacity and NVH qualities of the gear. Up to now, no research has been made to quantify the influence of the machine kinematics and the tool concept on load carrying capacity and NVH. Therefore, these influences are analyzed in this work by simulating the gear manufacturing with the help of the two known machine kinematics as well as the two known tool concepts and by meshing the simulated gears in an FE-based tooth contact analysis (TCA). The results of the TCA are parameters regarding the running behavior which are analyzed and compared for the four aforementioned manufacturing concepts.

Transmission Error Analysis of Conical Involute Gears

The conical involute gears have been applied to automotive parts such as FR-4WD transfer. To apply for automobile, high capacity and higher quietness are required. However the tooth contact of conical gear pair is point contact, so the large ease off happens even though each tooth surface has no manufacture error. Also the tooth depth and thickness of conical involute gears change along the lead direction. These characteristics have to be considered for the tooth mesh analysis. This paper proposes a simulation method for calculating the relative tooth surface form that is called ease-off. It also describes an improved method of estimating the tooth mesh compliance that takes into account the change of tooth shape. With these methods, we can accurately analyze the transmission error of a conical gear pair as well as a cylindrical gear pair.

183 コニカルギヤの歯面疲労強度に関する基礎研究(機素潤滑設計I,一般講演)

183 コニカルギヤの歯面疲労強度に関する基礎研究(機素潤滑設計I,一般講演)

S111055 コニカルギヤの歯面強度解析

S111055 コニカルギヤの歯面強度解析

182 調質コニカルギヤの歯面接触応力解析に関する研究(機素潤滑設計I,一般講演)

182 調質コニカルギヤの歯面接触応力解析に関する研究(機素潤滑設計I,一般講演)

Contact stress analysis of concave conical involute gear pairs with non-parallel axes

This study investigates the contact stress of concave conical involute gear pairs with non-parallel axes by means of finite element analysis. The complete mathematical models of the gear pair, including the working tooth surfaces and the fillets have been derived based on the theory of gearing and the generation mechanism. A mesh-generation program is also developed, which gives a dense mesh in the contact regions and a coarse mesh in the rest of the teeth. The commercial software, ABAQUS, capable of contact analysis of two 3-D deformable bodies is applied to evaluate the stress distribution on the tooth surfaces. Several numerical examples are presented to demonstrate the stress analysis of the gear pairs with various gear design parameters. The results show that the contact stress of non-parallel-axes concave conical involute gear pair can be reduced significantly by choosing grinding wheel with smaller radius. Therefore, concave involute gear pairs relieve the high contact stress problem of non-parallel-axes conventional conical involute gear pairs.

S111012 コニカルギヤのかみ合い伝達誤差解析法([S11101]伝動装置の基礎と応用(1))

The conical involute gears have been applied to automotive parts such as 4WD transfer. To apply for automobile, high capacity and higher quietness are required. However the tooth contact of conical gear pair is point contact, so the large ease off happens even though each tooth surface has no error. Also the tooth depth and thickness change along the lead direction. These characteristics have to be considered for the tooth mesh analysis. This paper proposes a simulation method for calculating the relative tooth surface form. It also describes an improved method of estimating the tooth mesh compliance that takes into account the change of tooth shape. With these methods, we can accurately analyze the transmission error of a conical gear pair as well as a cylindrical gear pair.