Surface design and tooth contact analysis of an innovative modified spur gear with crowned teeth

Author(s):  
J-L Li ◽  
S-T Chiou

An innovative modified spur gear with crowned teeth and its generating mechanism are proposed in this study. The main purpose of tooth surface modification is to change line contact to point contact at the middle of gear tooth surfaces in order to avoid edge contact resulting from possible unavoidable axial misalignment. Moreover, the surface of one gear tooth can be generated with just one cutting process, thereby facilitating easy manufacturing. Based on gearing theory, the model for surface design is developed. A tooth contact analysis (TCA) model for the modified gear pair is also built to investigate meshing characteristics, so that transmission errors (TEs) under assembly errors can also be studied. Examples are included to verify the correctness of the models developed and to demonstrate gear characteristics.

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
M. Kolivand ◽  
A. Kahraman

Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.


Author(s):  
Li-Chi Chao ◽  
Chung-Biau Tsay

The spherical gear is a new type of gear proposed by Mitome et al. [1]. Different from that of the conventional spur or helical gear sets, the spherical gear set can allow variable shaft angles and large axial misalignments without gear interference during the gear drive meshing [1, 2]. Geometrically, the spherical gear has two types of gear tooth profiles, the concave tooth and convex tooth. In practical transmission applications, the contact situation of a spherical gear set is very complex. To obtain a more realistic simulation result, the loaded tooth contact analysis (LTCA) has been performed by employing the finite element method (FEM). According to the derived mathematical model of spherical gear tooth surfaces, an automatic meshes generation program for three-dimensional spherical gears has been developed. Beside, tooth contact analysis (TCA) of spherical gears has been performed to simulate the contact points of the spherical gear set. Furthermore, the contact stress contours of spherical gear tooth surfaces and bending stress of tooth roots have been investigated by giving the design parameters, material properties, loadings and boundary conditions of spherical gears.


2013 ◽  
Vol 392 ◽  
pp. 151-155
Author(s):  
Zheng Li ◽  
Yang Chen

The gear meshing is a very complicated process due to the nonlinear behaviors during the teeth contact. It is necessary to build a reliable model to simulate gear meshing process which can consider geometry and boundary conditions nonlinear behavior in gear tooth contact analysis. This paper propose a 3D finite element model to simulate the meshing process of a pair of spur gears, and then carry out the gear tooth contact analysis with the consideration of nonlinear behaviors. The results and relevant discussions will indicate and explain some significant phenomena of the gear tooth contact characteristics in gear meshing process.


Author(s):  
C H Wink ◽  
A L Serpa

In this paper tooth contact deviations from the plane of action and their effects on gear transmission error are investigated. Tooth contact deviations come from intentional modification of involute tooth surfaces such as tip and root profile relief; manufacturing errors such as adjacent pitch error, profile errors, misalignment and lead errors; and tooth elastic deflections under load, for example, bending and local contact deflections. Those deviations are usually neglected on gear tooth contact models. A procedure to calculate the static transmission error of spur and helical gears under loading is proposed. In the proposed procedure, contact analysis is carried out on the whole tooth surface, eliminating the usual assumption that tooth contact occurs only on the plane of action. Lead and profile modifications, manufacturing errors and tooth elastic deflections are considered in the calculation procedure. The method of influence coefficients is employed to calculate the tooth elastic deflections. Load distribution on gear meshing is determined using an iterative-incremental method. Results of some numerical examples of spur and helical gears are analysed and discussed. The results indicate that the tooth contact deviations from the plane of action can lead to imprecision on the gear transmission error calculation if they are not take into account. Therefore, the proposed procedure provides a more accurate calculation methodology of gear transmission error, since a global contact analysis is done.


Author(s):  
Caichao Zhu ◽  
Haixia Wang ◽  
Mingyong Liu ◽  
Xuesong Du ◽  
Chaosheng Song

Beveloid gears are widely applied in fields like ships, automobiles and industrial precision transmissions. In this paper, the formulas of the beveloid gear tooth surface used in marine transmissions were derived and a mesh model for the intersected beveloid gear pair was setup. Then loaded tooth contact analysis was performed using the finite element method considering the coupling of the assembly errors and the elastic deformation of tooth surface. Through the analysis, the influences of assembly errors on contact patterns, mesh force and tooth surface deformations were investigated. In a further step, the tooth profile modifications were performed to alleviate the edge contact and a subsequent major improvement of the mesh condition was obtained. Finally, loaded tooth contact experiments for marine gearboxes with small shaft angle were conducted. The tested results showed good correlation with the computed results. This work may provide some value for the practical design aiming at improved contact characteristics of the beveloid gears with intersected axes.


Author(s):  
Masaki Watanabe ◽  
Minoru Maki ◽  
Sumio Hirokawa ◽  
Yasuhiro Kishimoto

This study reports the method of forging of spiral bevel gear. Two ideas for crowning of tooth surface to obtain point contact for forging gears are proposed. By one idea, tooth surface of pinion meshes with the gear tooth surface by conjugate point contact. And the trace of contact points on the gear tooth surface is perpendicular to the lengthwise direction of gear tooth, namely becomes the “square contact” so called in gear technology. The trace can be set arbitrarily on the gear tooth, by setting the pitch point arbitrarily. By another idea, the trace of contact points lies along the tooth trace of the gear tooth. Both ideas proposed in this report, the numerical dataset of teeth surface of pinion and gear are given by the contact lines with the cutter cone. The dataset of teeth surface of pinion and gear are calculated to cut a pair of electrodes of spiral bevel gear. Tooth contacts of proposed gearing are confirmed by the 3D drawing of tooth surfaces. The tooth contact of the master pinion and gear were made and tested by tooth contact testing apparatus. The contact marks coincide well with the theoretical contact pattern estimated by 3D/CAD expression. The good results of running test of the performance of the master gear has been given. The authors completed the forging of spiral bevel gear pairs by two methods proposed in this report.


1988 ◽  
Vol 110 (3) ◽  
pp. 337-342 ◽  
Author(s):  
F. L. Litvin ◽  
J. Zhang ◽  
R. F. Handschuh

A topology of crowned spur pinion tooth surface that reduces the level of transmission errors due to misalignment is proposed. The geometry of the deviated pinion tooth surface and regular gear tooth surface, along with tooth contact analysis is discussed. Generation of the deviated pinion tooth surface by a plane whose motion is controlled by a five-degree-of-freedom system is proposed. Numerical results are included and indicate that transmission errors remain low as the gears are misaligned.


2013 ◽  
Vol 341-342 ◽  
pp. 572-576 ◽  
Author(s):  
Jin Fu Du ◽  
Zong De Fang ◽  
Min Xu ◽  
Xing Long Zhao ◽  
Yu Min Feng

The geometry of the tooth surface is important for tooth contact analysis, load tooth contact analysis and the ease-off of gear pairs. This paper presents a mathematical model for the determination of the tooth geometry of Klingelnberg face-hobbed hypoid gears. The formulation for the generation of gear and pinion tooth surfaces and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated and tooth surfaces and 3D tooth geometries of gear and pinion are obtained. This method may also applied to other face-hobbing gears.


2011 ◽  
Vol 86 ◽  
pp. 411-414
Author(s):  
Yun Bo Shen ◽  
Jie Gao ◽  
Wen Qiang Ding

Bending stress is a principal factor that defines the fatigue life of face gear. A new tooth surface structure with circular arc of fillet surface for the face gear has been developed. A method of processing or cutting of fillet surfaces of helical face gear by application of a shaper with tooth rounded top has also been represented. The bending stress of the tooth of face gear with new surface structure has been performed by computer simulation. Two versions of finite element model of tooth surfaces of face gear are generated by application of numerical technology. One version is based on the cutting shaper with tooth top shaper corner and another version is with addendum rounded top. Tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) for the two versions of face gear drives with helical spur gear are also considered. The results of simulation show that the bending stress of tooth surface of the face gear with fillet surface generated by the rounded top of the shaper is 12% lower than the first version’s.


1988 ◽  
Vol 110 (3) ◽  
pp. 343-347 ◽  
Author(s):  
F. L. Litvin ◽  
J. Zhang ◽  
R. F. Handschuh

A method for generation of crowned pinion tooth surfaces using a surface of revolution is developed. The crowned pinion meshes with a regular involute gear and has a prescribed parabolic type of transmission errors when the gears operate in the aligned mode. When the gears are misaligned the transmission error remains parabolic with the maximum level still remaining very small (less than 0.34 arc second for the numerical examples). Tooth Contact Analysis (TCA) is used to simulate the conditions of meshing, determine the transmission error, and the bearing contact.


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