METHOD TO SOLVE ELASTIC CONJUGATE SURFACES IN MULTI-TEETH MESHING

A method to solve the elastic conjugate surfaces in multi-teeth meshing ispresented. In mechanical manufacturing and design, there exist a lot of problems relating toconjugate surfaces, such as three-dimensional engagement, steel rolling and workpiece machining,which cause great effects on the quality of machining and performances of transmission. This methoddescribes relation between conjugate motion and elastic deformation in the process of mesh-in andmesh-out, and can be used to determine the profile of gear tooth by a certain given load sharing.

PRINCIPLE AND TRANSMISSION TECHNOLOGY OF BERTRAND CONJUGATE SURFACES

Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of.conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.

Resolution of Digitized Conjugate Tooth-Face Surface Based on the Theory of Digitized Conjugate Surfaces

According to the principle of meshing engagement and the theory of the digitized conjugate surface, this paper applies the software Conjugater-1.0 that is developed by ourselves to compute, respectively, the digitized conjugate curved surfaces of the straight-tooth surface and drum-tooth surface, which will establish the theoretical and technical foundation for digitized engaging analysis, simulation, and digitized manufacturing technology of the diversified gears.

Theory of Digitized Conjugate Surface and Solution to Conjugate Surface

In order to meet the needs of designing and processing digitized surfaces, the method to spreading digitized surface has been proposed. The key technique is to solve the problem of digitized conjugate surface. In the paper, the digitized conjugate surface was theoretically investigated, and the solution of conjugate surface based on digitized surface was also studied. The digitized conjugate surface theory was then proposed, and applied to build the model of solving conjugate surface based on digitized surface. A corresponding algorithm was developed. This paper applies the software Conjugater-1.0 that is developed by ourselves to compute the digitized conjugate surfaces of the drum-tooth surface. This study provides theoretical and technical bases for analyzing engagement of digitized surface, simulation and numerical processing technique. Key words digitized conjugate surface - generating method - simulation CLC number O 186.1 - TH 122 Foundation item: Supported by the National Natural Science Foundation of China (50075031)Biography: Xiao Lai-yuan (1957-), male, Professor, Ph. D candidate, research direction: machanical design & theory, digital technology

NUMERICAL APPROACH TO DETERMINING INSTANTANEOUS CONTACT REGION FOR CONJUGATE SURFACES

According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to find the instantaneous contact boundary in local coordinate system, a modified Powell＇s hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvatm＇e and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.

Three-Dimensional Conjugate Tooth Surface Design and Contact Analysis of Harmonic Drive with Double-Circular-Arc Tooth Profle

A three-dimensional conjugate tooth surface design method for Harmonic Drive with a double-circular-arc tooth profle is proposed. The radial deformation function of the fexspline (FS), obtained through Finite Element (FE) analysis, is incorporated into the kinematics model. By analyzing the FS tooth enveloping process, the optimization of the overlapping conjugate tooth profle is achieved. By utilizing the hobbing process, the three-dimensional machinable tooth surface of FS can be acquired. Utilizing the coning deformation of the FS, simulations are conducted to analyze the multi-section assembly and meshing motion of the machinable tooth surface. The FE method is utilized to analyze and compare the loaded contact characteristics. Results demonstrate that the proposed design method can achieve an internal gear pair consisting of a circular spline with a spur gear tooth surface and the FS with a machinable tooth surface. With the rated torque, approximately 24% of the FS teeth are engaged in meshing, and more than 4/5 of the tooth surface in the axial direction carries the load. The contact patterns, maximum contact pressure, and transmission error of the machinable tooth surface are 227.2%, 40.67%, and 71.24% of those on the spur gear tooth surface, respectively. It clearly demonstrates exceptional transmission performance.