Mathematical Model Based On The Folded Section Method For Double Arc Gear Bending Stress

The drive of the double-circular-arc gear is one of important means of mechanical transmission drives, and the analysis of the double-circular-arc gear bending strength is the basis of the application of the double-circular-arc gear drive as well as the research of its load-bearing capacity, vibration, mating features and tooth profile modification. So it is very significant to set up a more precise gear basic practical mathematical model of bending stress on the base of the precise mathematical model, and solve accurately the bending stress on any point of load-on the double-circular-arc gear.Firstly, this dissertation presents the selection of double-circular-arc gear tooth profile, tooth surface mathematical model and the choice of the double-circular-arc gear basic parameter and the calculation of noodle cutter method in detail. It also elucidates the superiority of mathematical model of the double circular arc gear tooth profile at any corner: the accurate and factual description of double circular-arc gear tooth profile curve at any corner can not only avoid the cumbersome matrix and complexity calculation but also solve the problem that the error is larger with non-zero helix angles.Secondly, this dissertation has a detail study on the stress analysis of broken-line section method and the calculation formula about the traditional double-arc gear bending stress. Based on the broken-line section method and the mathematical model of the double-arc gear on any point a new mathematical model of bending stress is conducted, and most of the geometric parameters have been derived and computed. With the powerful parametric modeling capabilities of Pro / E software, a series of double circular arc gear models about different helix angle,modulus and number of teeth are conducted. Meanwhile, in this dissertation, the author applies finite element analysis calculation function of the software Pro / Mechanics to perform finite element analysis calculations about three-dimensional model of dual-circular-arc gear, more calculations and graphics are performed by the features of C language and the Excel spreadsheet. After a series of studies, parameters C of the mathematical model on a double circular gear bending stress profile is summarized, and a new mathematical model about the dual circular-arc gear bending stress is built eventually.Lastly, after comparing and analyzing the theoretical value and the finite element simulation of the mathematical model of the bending stress, the author comes to the conclusion that the two methods actually do not have much difference, thus the mathematical model in this dissertation possesses the accuracy and feasibility. And this result has a new frame of reference to the design and parameter selection optimization of double circular gear, which also offers a new mathematical model about the double circular gear bending stress numerical analysis.