Research On Basic Theory Of Internal Meshing Gear Transmission With Curve Element Constructed Tooth Profiles

As one of the important mechanical transmission forms,gear transmission plays an important rule in modern industry.The advanced equipment manufacturing fields such as automobile,aviation and aerospace,high-speed rail lay in a fast development time.And the demands for the high performance gears with the properties of high transmission efficiency,high precision,high load capacity,high transmission power,high reliability,low noise and light weight,are increasing.However,the low-end products occupy a big proportion in the total out-put value of the domestic gear industry.The high-end products,such as automobile transmission,the driver unit of high-speed rail,and the large gear transmission for energy industry,are obtained through importing form.And the gap between the domestic and foreign gear products in the aspects of transmission precision,transmission efficiency,the life-time and reliability is large.Therefore,the study on high performance gear transmission products is of great theoretical and practical values to meet the demands for important equipment.The power and motion transmission between gears rely on the engagement of the tooth surfaces.Geometric properties,lubrication status and surface integrity of tooth surfaces are the important factors for affecting the transmission performance.The point,line and surface are the common elements in nature.Base on gear geometry,the research team builds gear pairs with curve meshing element by using the diversities of the contact forms and the curve carriers.A new conjugate curve meshing theory is put forward and it is essential to solve the problems that restrict the performance improvement of gear transmission.The proposed theory has been widely applied in the parallel axes gear,intersecting axes gear and crossed axes gear transmission.It has gradually formed the technical basis including design theory,characteristic analysis and the manufacturing of tooth surface.Compared with the external gear transmission,the internal meshing gear transmission has the advantages of compact structure,larger gear ratio range,high carrying capacity,better dynamic characteristics and so on.It is an excellent transmission form.On the basis of the previous research,the studies in this paper concentrate on the basic theory of the internal meshing gear transmission with curve element constructed tooth pairs,and found the basic meshing principle,the generate method and the transmission characteristics analysis.It complements the conjugate curve meshing theory,and settles the theoretical foundation for the development of the better internal gear transmission.The main contents of this article are as follows:(1)Based on the conjugate-curve meshing principle,mathematical descriptions of the meshing principle for internal meshing gear drive with curve element constructed tooth pairs are carried out: The coordinate systems of internal meshing gears is established,and the matrix transformation relationships between the coordinate systems are derived;The relative motion conditions on the contact point are determined and the contact normal along the given contact direction is also analyzed;According to above conclusions,the meshing function is derived and the internal conjugate curve equations are also obtained.Numerical examples are illustrated to verify the proposed results.(2)The basic generate theory and method of tooth profiles of the internal meshing gear drive with curve element constructed tooth pairs are discussed.Three kinds of forming methods of tooth profiles are introduced,including the equidistance-enveloping method,the tooth profile spiral motion method and the basic tooth strip method;three methods are used to establish the tooth surface of the internal meshing gear drive with curve element constructed tooth pairs.The corresponding mathematical models are given.(3)Tooth profile design of the internal meshing gear drive with curve element constructed tooth pairs is studied.The geometric parameters of the gear and the selection principle of the tooth shape are discussed;And the tooth profile scheme of internal meshing gear drive with single point contact and two point contact are separately designed.Tooth profile equation and the 3D models of gears are also provided.(4)The finite element analysis of tooth profiles are carried out.The 3D gear models are simplified and the contact pairs of the meshing gear are provided.The load and boundary conditions are processed.The contact calculation is completed and the numerical results are analyzed for internal meshing gear drive with single point contact and two point contact.