Research On Gear Contact Strength Analysis Of Automobile Gearbox By Fractal Theory

Gear transmission system is an important institution in automobile gearbox. In order to improve its transmissible performance, micro-segment gear is used here to replace the existing involute gear. Known from the construction of micro-segment gear, the gears contact in the form of "convex- concave" and have the same radius of curvature in contact point, so the question of analyzing on the micro-segment gear's contact strength can't be solved by Hertz elastic contact theory The finite element method (FEM) can be used to solve the question, but its process is too complicated. Solving the question of analyzing on the micro-segment gear's contact strength, calculating its contact stress and proving the high carrying capacity of the gear, is the original intention of the research.The common contact stress theory——Hertz elastic contact theory and FEM contact theory are reviewed at the beginning of the paper, and then their shortcomings are pointed out: FEM contact theory has the shortcomings of tedious solution process and volatile result by many factors. And Hertz elastic theory can not calculate the contact stress of the same surfaces by inner contact. What's more, these two theory only consider the contact body'macroscopical factors (such as the size of contactors and material) to calculate the contact stress.To make up for the deficiencies of the two above ways, M-B fractal contact model is introduced here for the analysis of contact strength. This model analyze contact stress of the contact bodies from the microcosmic factors (such as the surface morphology ), and its analysis result has the advantages of preciseness and dimension independency. But M-B fractal contact model can not considers the contact body's macroscopical factors (such as the size of contactors and the contact style) , and can not be used for the analysis of contact strength between the rough surfaces (namely, not flat plane).To solve these above problems, on the basis of combining the M-B fractal contact model and traditional Hertz contact model, and after introducing the surface contact coefficient, the fractal contact model of two rough surfaces is set up. The establishment of the model solves the question that M-B fractal contact model can not analyze on the contact strength of rough surfaces, which also supplies a theoretical basis for setting up the fractal contact model of gear combined surfaces. After refering to the surface contact coefficient, the inner contact coefficient with the same surface is constructed. And combining with the research result of the M-B fractal contact model and the fractal model of two rough surfaces, the fractal contact model of rough surfaces with the same radius of curvature by inner contact is set up. The establishment of the model solves the question that Hertz model can not solve the contact strength analysis of the same surfaces by inner contact and calculate the micro-segemnt gear's contact stress. What's more, the establishment of the model also expands the application scope of using the fractal theory to analyze on the contact strength.Based on the fractal contact model of the two rough surfaces and the fractal model of rough surfaces with the same radius of curvature by inner contact, contact stress calculation based on the fractal theory ('CSCBOF'for short) is founded. This method can calculate the contact stress of the involute gear gear and micro-segment gear and can synthetically consider the gears'microcosmic factors (such as the surface morphology of the gear) and macroscopical factors (such as the size of the gear and the contact style), so the calculting results are more reliable and the analyzing results are more comprehensive. The application of using CSCBOF method to caculate the gear's contact stress is an effective supplement for the existing theory of calculating the gears'contact stress, and also supplies a new theoretical basis for contact stress calculation and optimized design of the gears.At the end of the paper, through the experimentation of contact stress measurement for involutes gear by the photoelastic method , the calculating result of the gears'contact stress by the fractal theory is tested. The result shows that CSCBOF method is scientific and feasible.