Contact and Bending Stress Analysis of Composite Gear
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摘要: 为了研究复合材料齿轮啮合过程的力学特性, 提出了一种三维五向编织复合材料齿轮参数化设计方法, 在考虑编织角、纤维束截面形状的基础上, 采用有限元方法分析了复合材料单胞在细观尺度下的力学特性, 并与试验测试结果进行了对比验证; 在此基础上, 基于均质化思想建立了复合材料与齿轮力学性能间的联系, 进而构建了复合材料齿轮啮合有限元模型, 并进行啮合过程仿真分析, 获得了齿面接触应力、齿根弯曲应力、接触与弯曲疲劳危险点, 以及加载条件与接触应力、弯曲应力的匹配关系, 分析结果符合赫兹接触规律, 为碳纤维三维编织复合材料及齿轮性能分析提供了理论支撑。Abstract: In order to study mechanical characteristics of composite gear meshing, a parametric design method of three-dimensional five directional braided composite gear is proposed. Based on the consideration of braiding angle and fiber bundle cross-section shape, the mechanical properties of composite cell at meso-scale are analyzed by using the finite element method, and compared with the experimental results. On the above mentioned basis and in terms of the homogenization, the relationship between the mechanical properties of composite and the gear is established, and then the finite element model for composite gear meshing is constructed. The meshing process is simulated and analyzed, and the contact stress of tooth surface and bending stress of root, the fatigue risk points of contact and bending, and the matching relationship between the loading conditions and the contact stress, bending stress are obtained. The analysis results is according with the Hertz contact law, which provides theoretical support for the performance analysis of carbon fiber three-dimensional braided composites and gears.
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Key words:
- composite gear /
- finite element model /
- contact stress /
- bending stress
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表 1 组分材料属性
组分材料属性 T300 PEEK Ef1/GPa 220 - Ef2/GPa 13.8 - Em/GPa - 3.55 Gf12/GPa 9 - Gf23/GPa 4.8 - Gm/GPa - 1.27 v12 0.2 - vm - 0.4 Vf 0.5 0.5 ρ/(g·cm-3) 1.76 1.32 
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表 2 45°编织角三维五向复合材料弹性常数预测结果
弹性常数 试验值 预测值 E1/GPa 53.00 53.94 E2/GPa - 9.68 E3/GPa - 9.68 G12/GPa - 11.89 G13/GPa - 11.89 G23/GPa - 7.18 v12 - 0.50 v13 - 0.50 v23 - 0.57
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表 3 算例齿轮基本参数
参数 主动轮 从动轮 齿数z 20 20 模数m/mm 5 5 标准压力角α/(°) 20 20 分度圆直径d/mm 100 100 齿顶圆直径da/mm 110 110 齿根圆直径df/mm 87.5 87.5 齿宽b/mm 20 20
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