# Machining deformation prediction of large straight bevel gear

Comprehensively analyze the research data related to gear machining deformation. In order to realize the prediction of machining deformation of super large spur bevel gear, it is necessary to study a series of theoretical and technical problems, such as the prediction of cutting accuracy of a single split body, the prediction of machining accuracy of base and the prediction of assembly accuracy of gear pair. Among them, the most important is to study the machining deformation mechanism of single split spur bevel gear.

### 1.Research and theoretical modeling of stiffness evolution law during wheel blank processing

Aiming at the equivalent stiffness calculation method of bending strain energy of complex variable cross-section beam, the splitting large straight bevel gear blank is equivalent to the equal cross-section beam with the same length. According to the mechanics of materials, the bending strain energy of splitting large straight bevel gear blank and equal cross-section beam is calculated respectively, and the equation for calculating the equivalent stiffness of splitting large straight bevel gear blank is established. The theoretical model of stiffness calculation is programmed and calculated with MATLAB software, and the average bending stiffness of large spur bevel gear blank under different working conditions in the machining process can be obtained. Then draw the stiffness change diagram of large straight bevel gear blank under different process routes, and analyze the comparative relationship between the stiffness change and material removal rate of large straight bevel gear blank under different process routes, so as to analyze the stiffness evolution law of large straight bevel gear blank under different process routes.

### 2.Establishment of mapping relationship model of wheel blank stiffness change residual stress evolution deformation

The formula of the position change of the neutral axis of the section and the relationship between the deformation curvature of the wheel blank before and after machining are deduced. On this basis, the relationship between the change value of additional stress and the change of curvature of large spur bevel gear blank is deduced, and then the mathematical model of additional stress in the residual material of large spur bevel gear blank during gear cutting can be established. By iteratively adding the additional stress calculated by the large spur bevel gear blank and the corresponding initial stress before machining, the internal stress redistributed in each layer of the remaining material after the machining of the large spur bevel gear blank can be obtained. According to the redistributed internal stress of large spur bevel gear blank, the calculation model of additional torque change of internal stress to corresponding neutral shaft is established. Then, according to the torque area method, the calculation formula of bending deformation is deduced, and the previously calculated time-varying stiffness of large spur bevel gear blank is substituted into the formula to obtain the mapping relationship model based on stiffness change internal stress evolution blank deformation.

### 3.Finite element simulation of machining deformation of split straight bevel gear

Obtain the initial stress law of the material of large spur bevel gear blank, fit the initial stress in MATLAB software, and establish the function between the initial stress field and the thickness of large spur bevel gear blank. The subroutine sigini is written in FORTRAN language to express the functional relationship of the initial stress field. The subroutine is called in ABAQUS software to establish the finite element model of the large spur bevel gear blank containing the initial stress. In the finite element software, the elements of the model machining area and non machining area are separated, and the life and death element technology is used to simulate the machining process of dividing the large spur bevel gear blank. After the simulation, the corresponding stress and displacement nephogram of the large spur bevel gear blank is output, and the simulation results are analyzed. By changing the parameters of dividing the large spur bevel gear blank, the finite element simulation of dividing the large spur bevel gear blank with different sizes is carried out, and the law of each simulation result is explored.

### 4.Experimental verification of machining deformation of split straight bevel gear

According to the machining process characteristics of super large split spur bevel gear, the machining method of split spur bevel gear is planned. The tooth surface points generated by MATLAB program are imported into UG to establish the three-dimensional model of split gear. The rough and finish machining of large spur bevel gear blank are simulated by using the cam module of UG, and the rough and finish machining NC programs are generated through the post-processing function of this software. The NC cutter model is imported into the NC cutter simulation software icut, and the appropriate code is generated in the subsequent NC cutter simulation. The numerical control program is introduced into the actual machine tool for gear cutting, and the actual deformation of large spur bevel gear blank is measured. The test results are compared with the results of finite element simulation and theoretical model.

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