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随着制造业信息化的发展,建立齿轮的数学模型显得尤为重要,它是分析齿轮啮合性能的基础。对于直齿锥齿轮产品,由于理论球面渐开线设计制造困难,其实际齿形为大端切平面内的平面渐开线齿形。为了达到锥齿轮产品建模、设计、制造的一致性,应用当量齿数法,通过坐标变换给出了直齿锥齿轮大、小端背锥切平面上的渐开线参数方程,可简化建模过程。同时利用该方程建立了直齿锥齿轮的数学模型,并对建模精度进行了分析,建模精度满足设计、制造要求。
With the development of manufacturing informatization, it is very important to establish the mathematical model of gear, which is the basis of analyzing the gear meshing performance. For spur bevel gear products, due to the design and manufacture of the theoretical spherical involute difficult, the actual tooth profile is flat involute tooth profile in the large end tangent plane. In order to achieve the consistency of the bevel gear product modeling, design and manufacturing, the equivalent involute method is used to obtain the involute parameter equation of the large and small back tapering conical plane of the bevel gear by coordinate transformation, which can simplify the modeling process. At the same time, the mathematical model of straight bevel gear was established by using this equation, and the modeling precision was analyzed. The modeling accuracy satisfied the design and manufacture requirements.