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-  2017 

采用NSGA-Ⅱ算法的面齿轮副小轮 拓扑修形多目标优化
NSGA-Ⅱ Based Multi??Objective Optimization on Topologically Modified Pinions for Face Gear Pairs

DOI: 10.7652/xjtuxb201707015

Keywords: 面齿轮,拓扑修形,多目标优化,NSGA-Ⅱ,传动误差,接触印痕
face gear
,topological modification,multi??objective optimization,NSGA?并?,transmission error,contact path

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Abstract:

为合理确定面齿轮副小轮的修形参数,设计了均由2段抛物线与1段直线组成的直齿小轮齿廓和齿向修形曲线,将由三次B样条拟合得到的修形曲面与理论齿面相叠加来构造拓扑修形齿面。采用带精英策略的快速非支配排序遗传算法(NSGA-Ⅱ),结合面齿轮副的几何接触分析(TCA)和承载接触分析(LTCA)技术,提出了以修形曲线参数为优化变量,使抛物线几何传动误差曲线两端对称、接触印痕限制在齿宽中部、承载传动误差波动幅值最小的小轮拓扑修形多目标优化设计方法,并编制了相应的Matlab程序。算例表明:优化修形参数后得到了对称的抛物线几何传动误差和位于大轮齿宽中部的接触印痕,并大幅度减小了承载传动误差波动,从而可有效降低安装误差敏感性和齿轮副的振动、噪声。
To reasonably determine the technical parameters in profile modification of face gear pairs, a tooth profile and an axial modification curve both composed of two sections of parabola and a straight line on a spur pinion are created. A topologically modified tooth surface can be represented as a superposition of theoretical tooth surface and the deviation surface obtained by cubic B??splines fitting on the tooth surface grid. Based on the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) of the face gear pairs, taking the parabolic transmission error curve being symmetrical in geometry, the contact path being limited in the central tooth width, and the minimum wave amplitude of loaded transmission errors as the three optimization objectives, a multi??objective optimization model is established, and the corresponding programs are developed by software Matlab. The fast elitist non??dominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ) is selected as the multi??objective optimization algorithm. An optimization example shows that the present method obtains symmetric parabola geometry transmission error and the contact path in the middle of gear tooth width, which greatly reduces the wave amplitude of loaded transmission errors, hence effectively reduces installation error sensitivity, vibration and noise

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