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首页> 外文期刊>Applied Mathematical Modelling >A general mathematical model for two-parameter generating machining of involute cylindrical gears
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A general mathematical model for two-parameter generating machining of involute cylindrical gears

机译：渐开线圆柱齿轮两参数生成加工的通用数学模型

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摘要

Instead of the common analytical model for involute gears machining, a general mathematical model for two-parameter generating machining is developed in this study with adopting discrete enveloping to increase its robustness and generality for machined profile calculation and instant contact analysis. The geometric parameters and motion relationships are integrated according to the cross-axis gear meshing at first, and the enveloping theory for two-parameter generating process is analyzed briefly with involving middle gear rack. By transforming the multiple cutting edges relative to the gear blank according to the generating motions, a numerical algorithm is proposed to distinguish the external enveloping profile on the shaft section, then the derivation of instant contact points via the implied time sequences of profile points is introduced. Finally, the coordinate transformations for the spatial trajectory of instant contact points identifying and the engaged cutting edge segments distinguishing are investigated. At last, a non- involute profile skiving is performed to verify the generality and the robustness of proposed method, and several typically generating machining operations for cylindrical involute gear are simulated numerically to proof the accuracy of the proposed model by finding the deviations from the standard involute curves and the geometries of the instant contact points. (C) 2019 Elsevier Inc. All rights reserved.
机译：代替普通的渐开线齿轮加工分析模型，本研究开发了一种用于两参数生成加工的通用数学模型，采用离散包络提高了其鲁棒性和机械轮廓计算和即时接触分析的通用性。首先根据横轴齿轮的啮合情况对几何参数和运动关系进行整合，并以中间齿条为对象，简要分析了两参数生成过程的包络理论。通过根据产生的运动来改变相对于齿轮毛坯的多个切削刃，提出了一种数值算法来区分轴段上的外部包络轮廓，然后引入了隐含轮廓点时间序列的瞬时接触点推导。最后，研究了即时接触点识别和接合的切削刃段识别的空间轨迹的坐标变换。最后，进行非渐开线轮廓削皮，以验证所提出方法的通用性和鲁棒性，并数值模拟了圆柱渐开线齿轮的几种典型生成的加工操作，以通过发现与标准偏差来证明所提议模型的准确性。渐开线曲线和即时接触点的几何形状。 （C）2019 Elsevier Inc.保留所有权利。

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