Prediction Model for Tooth Profile Concave Error ofMulti-source Coupled Shaving Gear
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摘要: 为提高剃齿齿形中凹误差的预测能力，以轴向剃齿方法为例，提出多源耦合剃齿齿形中凹误差预测模型。该模型在考虑安装误差的同时，对剃齿重合度和机床运动等因素进行了耦合。为分析安装误差对剃齿加工的影响，首先，建立含有轴交角误差、中心距误差和高速轴同步误差的剃齿分析模型；然后，基于剃削原理将影响剃齿加工的多源因素耦合成啮合点单次切削面积，在遗传算法改进BP神经网络（GA-BP）的基础上建立了剃齿齿形中凹误差预测模型，并揭示了啮合点单次切削面积对齿形中凹误差的影响规律,实现了多因素耦合的齿形中凹误差的定量预测及其机理的研究。实验结果表明：在考虑安装误差的情况下，剃齿啮合点的单次切削面积过大是导致剃齿齿形中凹误差的主要成因。Abstract: In order to improve the prediction ability of shaving tooth profile concave error, a multi-source coupled error prediction model was proposed by taking the axial gear shaving method as the example. In the present model, some factors such as shaving tooth contact ratio and machine tool movement are coupled while considering the installation error. Firstly, a gear shaving analysis model with axial angle error, center distance error and high speed axis synchronization error is established. Then, based on the principle of shaving, multi-source factors affecting the shaving processing are coupled into a single cutting area of the meshing point, and a prediction model for the concave error of the shaving tooth profile is built on the basis of the genetic algorithm BP neural network (GA-BP). The paper reveals the influence of the single cutting area of the meshing point on the concave error of the tooth profile, and realizes the quantitative prediction and mechanism research of the multi-source factor coupling of the concave error of the shaving tooth profile. The experimental results show that, considering the installation error, the single cutting area of the tooth shaving mesh point is too large, which is the main cause of the concave error of the shaving tooth profile.
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表 1 剃齿刀参数
参数 剃齿刀编号 1 2 3 4 齿数 53 52 53 52 模数 4.2333 4.2333 4.2333 4.2333 压力角/（°） 20 20 20 20 螺旋角/（°） 15 15 10 10 变位系数 −0.3793 −0.3744 −0.3649 −0.3603 重合度 1.8294 1.7712 1.7133 1.6548 
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表 2 仿真预测值与实测值的误差
数据 序号 1 2 3 4 5 6 7 8 9 10 Umax/μm2 2.157 2.349 2.235 2.219 1.216 1.516 1.624 1.245 0.804 0.756 Umin/μm2 0.745 0.846 0.694 0.679 0.397 0.541 0.467 0.347 0.216 0.214 $ {\theta _{\max }} $/（°） 27.11 28.57 27.76 27.78 25.45 26.24 26.78 25.54 24.78 24.54 E/mm 0.0303 0.0249 0.0297 0.0315 0.0213 0.0231 0.0239 0.0227 0.0181 0.0160 E实测值 0.0321 0.0267 0.0319 0.0330 0.0229 0.0249 0.0261 0.0246 0.0194 0.0176 误差/% 5.56 6.48 6.78 4.53 6.95 7.15 8.34 7.76 6.46 9.35 $ \theta $/（°） 27.57 29.08 28.99 28.47 25.37 26.66 27.48 26.42 25.23 24.92 $ \theta $实测值/（°） 26.96 27.99 27.95 27.20 25.76 26.53 26.71 26.38 25.45 25.28 误差/% 2.26 3.89 3.72 4.67 1.51 0.49 2.88 0.15 0.86 1.42
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表 3 不同切削参数的最大单次切削面积
序号 重合度 $ {V}_{轴} $/（mm·s−1） $ {V}_{径} $/（μm·s−1） n/（r·s−1） $\Delta \varSigma $/（º） $ \Delta a $/mm $ \Delta {\omega _1} $/（r·min−1） Umax/μm2 1 1.8294 1 5.8 6 0.1 0.01 0.01 2.157 2 1.7712 1 5.8 6 0.1 0.01 0.01 2.349 3 1.7133 1 5.8 6 0.1 0.01 0.01 2.235 4 1.6548 1 5.8 6 0.1 0.01 0.01 2.219 5 1.8294 1 5.8 6 0.1 0.01 0.01 1.216 6 1.8294 1 5.8 8 0.1 0.01 0.01 1.516 7 1.8294 0.50 5.8 6 0.1 0.01 0.01 1.624 8 1.8294 0.85 5.8 6 0.1 0.01 0.01 1.245 9 1.8294 1 3.3 6 0.1 0.01 0.01 0.804 10 1.8294 1 5.8 6 0.3 0.01 0.01 1.956 11 1.8294 1 5.8 6 0.1 0.03 0.01 1.534 12 1.8294 1 5.8 6 0.1 0.01 0.03 1.227
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