Research On Meshing Theory Of Conjugate-Curve Gear Transmission

Gear drive plays an important role in the manufacturing equipments and national defence industry. The demands on gear transmission with high performance for major mechanism are gradually increased. The performance and technology of gears have been developed effectively in China. However, there is still a gap between current domestic and international levels. Not only the aerial, spacecraft and new energy fields, but also the weapon, high-speed rail and ship aspects all raise higher requirements for properties characterized by long lifetime, high load capacity, high reliability, low weight and low noise, etc. The innovation and development of gear drive with high performance have become a key scientific and technical issue in relative industrial fields and is also the scientific research frontier of mechanical engineering field.Tooth surfaces are the direct surfaces of action for motion and power transmission and they are also the important innovation points for gear development. Considering the diversity of curve contact, the new theory and technology of gear transmission are investigated in this article based on curve meshing element. It lays the theoretical foundation for explaining the meshing principles of existing gear drive and proposing the new types of gearing. This research will play an important part in improving the whole gear performance and it has a significant theoretical meaning and a broad application prospect. The prime content of the paper may summarize as follows:① Conjugate curves are put forward based on the definition of continuous and tangency contact between curves. The contact conditions of conjugate curves are given. Meshing principle of conjugate-curve gears is proposed and mathematical descriptions of contact are carried out. Based on differential geometry, the normal vector to contact point in arbitrary direction of contact angle is discussed. The meshing relationship along given contact position between conjugate curves is derived and the equation of conjugated curve is also deduced. The application examples of planar and spatial curves are obtained.② The meshing rule and property of conjugate curves are revealed through the discussions of geometric and contact characteristics. The modeling method of osculating plane is put forward. The calculations of curvature and torsion of conjugate curves based on arc length parameter are provided. Enveloping conditions of the family of curves with single parameter are demonstrated and the characteristic point is analyzed. The varietal law of meshing equation under different contact positions is discussed. Meshing unique and identity of conjugate curves are reflected, respectively. General motion property of conjugate curves is also described.③ The tubular tooth surfaces which have the characteristics of conjugate curves are generated according to the principle of conjugate curves. The equidistance-enveloping approach is provided to generate the tooth surfaces. It means that a spherical body with given radius performs the continuous enveloping motion along the designated equidistant curves of conjugate curves. The equations of equidistant curves and tubular tooth surfaces are derived, respectively. Different contact patterns of tooth surfaces are generated based on the various equidistance and direction. The new types of conjugate-curve gear transmission are proposed on the basis of meshing theory of conjugate curves.④ The geometric and contact characteristics of tubular meshing tooth surfaces are analyzed. The general conditions of tooth surfaces for keeping the fixed gear ratio and continuous transmission are proposed. Pressure angle of tubular meshing tooth surfaces is defined in terms of a space curve trihedron model. The characteristic line and ridge line are described, respectively. According to gear geometry, the non-undercutting conditions of tooth surfaces are discussed and the calculation methods of induced normal curvature and torsion are provided. The meshing and curvature interferences of tubular tooth surfaces are analyzed. A new approach to the calculation of sliding ratio of conjugate-curve gear pair based on conjugate curves is put forward. The conjugate successive property of tubular tooth surfaces is demonstrated. The nature and meshing rule of tooth surfaces are revealed.⑤ General principle and characteristics of conventional circular arc gear drive are introduced. The meshing principle of circular arc gears based on conjugate curves is put forward. The meshing theory of traditional circular arc gearing is newly explained and meshing essence of tooth surfaces is also revealed through the analysis of generation principle, geometric and motion characteristics, meshing property, etc. The relationship between two kinds of theories is demonstrated and the important application of conjugate curves theory can be realized.