Study On Minimum Teeth Without Undercutting Of Involute Gears

This paper is based on the traditional undercutting principle of standard spur involute gear, which focused on the point that people had missed over the past60years, in what the related data or literatures of mechanical design and mechanisms and machine theory, the minimum teeth without undercutting of involute gear, which has been confused for the reason that the rack has been regarded as standard rack cutter mistakenly. Theoretical research and computer simulation and analysis for undercut phenomena were given. The minimum teeth without undercutting of standard spur involute gear are deduced with rack cutter, and based on this conclusion, the same work are done also for involute gears under stub tooth system and with off-standard pressure angles as for the standard spur involute gear, then the correct minimum teeth for different types of involute gears under three kinds of systems without undercutting are obtained. After that, based on the principle of gear generating and according to the simulations and analysis, what are got by using the Visual Basic software, the Two-Dimensional model of relation between parameters such as teeth number and the undercutting phenomenon corresponding to them has been bilut, then the influence of teeth number on undercutting value is simulated, and what we got has demonstrated the theoretical derivation is accurate. Further more, by making use of the curvature of conjugate tooth face, the relational model between the rack cutter’s addendum and the part of it’s tooth root fillet has been maken, based on the characteristics of non-linear mapping of neural networks, the relation curves of teeth number on undercutting value and modulus on that are simulated respectively with MATLAB, according to the simulation results, we can make a clear visible of the response process.Through the researches and analysis of parts what spoken of earlier in this paper, not only we have pointed out the mistake, solved the long-standing problems in the traditional undercutting theory, but also the correct minimum teeth without undercutting of kinds of involute gears are presented, all of this will make contributions and provide theory basis and accurate data for the design, manufacturing and applications of gear transmission in the years ahead.