The Meshing Characteristic Research Of Logarithmic Spiral Bevel Gear

Spiral bevel gear is a common room meshing gear. Relative to traditional bevel gear,the spiral bevel gear has a larger overlap coefficient, higher loading capacity and been usedwidely in such high-speed heavy-duty mechinery as space flight, naval ships and automobile.For the traditional spiral bevel gear, the gear transmission fails to reach the most reasonablemeshing because the involute, arc line and epicycloid adopted by it as dentiform line areincapable of ensuring the equal helix angle of all points at the lines. Although this is can beimproved by regulating the machine tools, such problems as the high requirements for theequipments and increased cost are caused accordingly.Logarithmic spiral, adopted by the topic group as the dentiform line with an equal helixangle everywhere has solved all kinds of problems caused by the unequal helix angle of thecommon spiral bevel gear and not only realizes the most reasonable meshing theoretically,obtains higher reliability and more stable transmission and improve the transmissionefficiency but also the regular curved surface formed by the involute and logarithmic spiral ismore convenient. Considering the advantages above, it is necessary to study the logarithmicspiral bevel gear.The gear meshing theory occupies an important position in the gear system, is theimportant content of the gear technology, whether the transmission form or new processingtechnology, all need to master the gear meshing theory. On the basis of the previous study ofthe spiral bevel gear meshing characteristics, this project will study the meshingcharacteristics of the logarithm spiral bevel gear, combined with the gear meshing theory anddifferential geometry principle, to further improve the system of spiral bevel gear meshing,more comprehensively reflect the meshing essence of the logarithm spiral bevel gear, toenable them to have better application in engineering practice, also lay the foundation fortransmission simulation, stress analysis and other research work in the future, to facilitate theimprovement of engineering and technical personnel better.The main content of the subject is as follows:1. Establish the equation of sliding ratio, quantitative analysis of wear on the toothsurface. The sliding coefficient of tooth surface is: the limit of the two conjugate toothrelative sliding arc length ratio. In other conditions being equal, the absolute value of thesliding coefficient is bigger, then the wear on the tooth surface is bigger. There for it is animportant symbol to measure the wear of the tooth surface. This paper uses the methods and ideas for solving which mentioned in the paper of’Calculation Method of Sliding Ratio for Spot Contact Tooth Surfaces and Application to Crossed Helical Involute Gears’ of Zhao yaping teacher. Through the Sliding Ratio to reflect the points of the gear tooth surface in gear meshing process.2. Calculation the undercutting boundary limits of function, The so-called undercutting boundaries of function, is the boundary between the conjugate surface which has been undercutting and did not happen undercutting. It has an important significance for improving the life of the transmission system and to avoid interference. The undercutting boundary points and the undercutting limit curve modeling and calculation, can provide a theoretical basis for the interference in the process of meshing gear pair, and can also ensure that the conjugate surface does not occur undercutting in the manufacturing process. So the undercutting boundaries function has a great significance for the protection of the gear transmission quality and processing quality.3. On the base of undercutting boundary limits to solve the meshing boundary line function, A pair of conjugate curved surface can maintain good transmission performance, only to meet the meshing condition is not enough, also need to discuss the meshing boundary. The tooth surface is divided into two parts, which are to participate in the meshing area and do not to participate in the meshing area. It will improve the size of the tooth surface and reduce the nonmeshing area according to the calculation results of meshing boundary function, then make the gears miniaturization and light type.4. To deduced the discriminant of tooth surface with secondary contact, to judge the contact situation of the contact point in the meshing region. It can clear all meshing points which is the first contact, which is secondary contacts through the discriminant. The derivation of the discriminant can be formed by the meshing equation changed into the trigonometric functions, using the range of trigonometric functions to judge the number of contacts of each contact point.