| Involute cylindrical helical gear is characterized by steady transmission, low meshing shock and low vibration noise capacity. It has been widely used in the mechanical transmission industry which requires high speed heavy haul and high performance. But there is a gap in the high precision gear design and manufacture with the international advanced level at present, this paper is based on the national science and technology support project plan, using the theoretical method of active design of spiral bevel gears as reference. This paper researches on the active design research of involute cylindrical helical gear which has high precision based on the transmission error.In this paper, a meshing and contact mathematic models of helical gears with hob installation and assembling errors are established, which are based on the spatial mesh theory of involute cylindrical helical gears. The simulating analysis of helical gears based on TCA(Tooth Contact Analysis) technique skill is achieved by MATLAB software. This paper analyzed the effect of different machining error which has influence on the processing precision of gears and installation error on the gear transmission error curve and contact trace. Using the compensation technology, the active design of the engagement quality of parallel helical gears is realized according to the theory of machining error compensation and assembly error. The main contents of this paper.1) Based on the theoretical basis of the hob processing and the formation method of helical gears, the proper equation of meshing tooth surface and the unit normal vector are derived. According to the theory of differential geometry and space meshing, a tooth contact model of helical gear with the hob installation error is established by using vector rotation and coordinate transformation method. According to the conjugate contact condition of gear meshing principle, the TCA equations and the meshing expression of the meshing tooth surface at the contact point are derived. The program of gear tooth contact analysis simulation was written by using MATLAB software. The simulation results show that the transmission error is less sensitive to installing axis angle error, while the sensitivity is raised with the increase of the installing axis angle error.. And the sensitivity of tooth surface machining error caused by the radial pulsation of hob is larger, while the sensitivity is reduced with the increase of the radial pulsation of hob.2) According to the profile mesh fundamental theorem and the solvent properties of the parallel axis of involute helical gear pair, it is concluded that the center distance error has little effect on the transmission error of the gear pair. Using the TCA(Tooth Contact Analysis) technology, the error simulation analysis based on gear contact mathematical model has been conducted, considering the installation error. The analysis shows that the gear position of the contact trace will be influenced by both the parallel error of axis plane and the vertical plane, it also shows that with the increase of the parallel degree error of the axis plane, the extent of increasing and the sensitivity is reduced, and the extent of increasing and the sensitivity increases with the increase of the parallelism error in the vertical plane.3) Using the compensation technology, the change of the tooth surface shape of the machined gear is realized by changing the installation error of the hob. The compensation effect of the contact trace caused by installation error of the gear pair has been analyzed by the different sources of errors. Conclusions can be made through the observation of the contact trace: the controllability of contact characteristics of tooth surfaces can be achieved effectively by changing the angle of the hob installation axis error. |
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