Research On TheTooth Modification Methods Of The Straight Bevel Gear

The straight bevel gear is the important component part of the gearbox, where operating characteristic has the most important influence for entire transmission system. The focus of this thesis is on the gear modifications (including profile modification and axial modification). The transmission theory analysis of gear in mesh and numerical simulation methods are adopted to investigate.At present, it is generally believed that straight bevel gear is built with back cone involute for the investigation of the straight bevel gear in mesh. It is easy to built the model with the back cone involute, which is almost equal to the sphere involute. But there is an error in this method, the less the ratio of sphere radius R to gear modulus m , the larger the error, especially for the bevel gear used in the saloon car. According to this case, the sphere involute is deduced with the engaging principle of straight bevel gear. The swept model method and the universal 3D design method for gear are used to build precise parametric model with the advanced CAD package PRO/ENGINEER.Only modified their parameters, such as teeth, sphere radius, pressure angle and so on, it will be turned into other new gear model by regeneration. It improves the precision of the model and is easy to modify, so it improves the efficiency of the modelling largely.The MSC.MARC FEM software is used to simulate the contact problems of gears in mesh. The solid model is divided into some parts through PATRAN in order to conquer the problem, which the entire solid model came down from CAD software can not be meshed using hexahedron elements. The boundary conditions and the constrain method of gear in mesh are given. The tooth contact stresses, root stresses, static TE, combined torsional mesh stiffness, load sharing ratio and teeth"end contact"are studied through the simulation of gears in mesh and some conclusions are drawn, which lay the foundations for the gear modifications.The natural frequencies and corresponding vibration modes of teeth are analyzed by Finite Element Method (FEM). It can been seen that the achievement regarding gear teeth stiffness under quasi-static conditions is also available for the calculation of teeth dynamic deformations.The necessary of axial modifications has been shown through the teeth"end contact" phenomenon. After studying the deformation of gears in mesh, over the mesh cycle, the maximal modification quantum has been given. The straight bevel gear might be adopted two kinds of axial modifications, one is end-relieved, and the other is drum-shape. It has been found through the analysis the drum-shape is not sensitive to misalignment, but the end-relieved has more capability of bearing load. End-relieved teeth also have two kinds of forms: line modification and curve modification. Under the same elastic deformation condition, curve modification's loading areas is larger than the line modifictation's, the contact stress is smaller, the strength is higher, so the curve modification is the best choice.The transmission error of gears in mesh is considered to be one of the main causes of gear noise and vibration. Numerous papers have been published on gear transmission error measurement and many investigations have been devoted to gear vibration analysis. But they are based on the conventional methods. There still, however, remains to be developed a general Finite Element Model capable of predicting the effect of variations in rigid body gear tooth position, in which the critical stage is the prediction of the meshing characteristic of straight bevel gear with profile modifications (including tip-relief). Tooth profile modifications can affect the behavior of the gear meshing including the T.E., ratio of local deformation and load–sharing ratio, etc, providing an alternative method for gear design.After the analysis of the effect of the transmission error to the noise, the straight bevel gear only adopted three various forms of modifications, straight line, rotated profile, circular forms are put forward. The effects of the short and long tooth profile modifications with various types of curves have been presented with the transmission error illustrated using the Harris Map. The direct outcomes are:1) Even if the straight-line modification is the cheapest method, the tooth relief should not be adopted with the line modification. In the view of the transmission error and load sharing ratio, it affects the noise heavily.2)Among three various forms of modifications, including short and long profile modifications, the transmission error of the single zone retains its value, unaffected by the tip relief(ignoring the handover regions).The double zone retains its TE value unaffected by the tip relif within a small preserved region located in the middle of the double zone. This is for all the cases and the input loads. The double zone T.E. value can not exceed that of the single zone, or the maximum values of the double zone T.E. will fall into the trend of the single zone data, so that it is looks like the single zone has been extended when the load is increaded. For short tip relief, it can't decrease the noise of the gear significantly, so it must be adopted long profile modifications.3) For long profile modification, rotated modification can produce stable and smooth meshing over the mesh cycle for a range of loads. The rotated modification of three various forms of modifications might be the best for achieving the overall benefits and may be easier to apply.4) In the view of transmission error, three various forms of the tooth modifications, the best is rotated modification, the next is circular form, and the worst is linear modification.