Optimization of Vibration Measuring Points of Gearbox using Virtual Simulation and Locally Linear Embedding Algorithm
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摘要: 为克服某型行星变速箱故障试验测点选择依赖经验导致有效信息遗失或信息冗余的弊端，论文提出了一种融合虚拟仿真技术与局部线性嵌入算法的振动测点优化方法。在ADAMS软件中建立行星变速箱齿轮-箱体刚柔耦合动力学模型，对不同齿轮状态下箱体表面振动信号进行了仿真；在箱体表面初选传感器测点的基础上，仿真分析了各测点振动信号的各项特征参数；采用局部线性嵌入算法对测点特征参数所构成的高维特征矩阵进行降维，获得了不同齿轮状态下的测点敏感度排序，最后采用加权计算方法得到了振动测点重要度综合排序。结果表明，变速箱各行星排正上方箱体表面和左侧轴承正上方竖直方向测点对太阳轮断齿、行星轮断齿和正常工况区分均具有较高敏感度，可重点采集分析这些测点振动信号来反映齿轮状态，为后续实测试验打下了基础。Abstract: In order to overcome the drawbacks of the effective information loss or redundancy caused by subjectively selecting sensor measuring points in planetary gearbox fault detection. In this paper, an optimization method of vibration measuring points based on virtual simulation technology and locally linear embedding algorithm was studied. The planetary gearbox rigid-flexible coupling dynamics model was firstly established in ADAMS software, and the vibration signals under different gear states were simulated. Then, considering the actual situation of the gearbox and the operability of the measuring points, these points were preselected and characteristic parameters of signals were calculated. Finally, the high-dimensional feature matrix formed by the characteristic parameters is reduced by locally linear embedding, and the sensitivity of measuring points in different states is obtained to determine the optimal measuring points. The results show that four measuring points have high sensitivity under the sun gear broken teeth, planetary gear broken teeth and normal conditions, which can effectively collect vibration signals to reflect the gear state and lay good foundation for actual test.
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表 1 传感器测点说明
测点序号 安装位置 测试方向 1 箱体右侧联轴器上 变速箱轴向 2 箱体右侧定轴轮系上方 竖直于变速箱轴向 3 箱体上方正对K1行星排 竖直于变速箱轴向 4 箱体上方正对K2行星排 竖直于变速箱轴向 5 箱体上方正对K3行星排 竖直于变速箱轴向 6 箱体左侧联轴器上 竖直于变速箱轴向 7 箱体左侧端盖上 变速箱轴向 8 箱体底部正对K1行星排 竖直于变速箱轴向 9 箱体底部正对K2行星排 竖直于变速箱轴向 10 箱体底部正对K3行星排 竖直于变速箱轴向 
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表 2 Z30太阳轮断齿时各测点特征向量
测点
序号峰峰值/
(m·s-2)均方根值/
(m·s-2)幅值平均值/
(m·s-2)峭度
指标波形
指标峰值
指标脉冲
指标裕度
指标样本熵 1 598.26 66.15 76.21 7.48 1.37 9.03 10.99 15.20 1.90 2 785.42 112.40 108.98 6.35 1.32 12.96 16.82 16.01 1.56 3 764.90 104.22 101.20 8.90 1.48 10.22 18.00 22.19 1.43 4 656.01 118.07 95.42 9.27 1.54 11.98 17.43 20.51 1.40 5 904.23 130.28 134.59 9.82 1.67 15.57 21.75 27.32 1.38 6 754.07 103.56 96.12 8.63 1.45 13.72 16.82 17.43 1.75 7 567.53 78.13 71.30 6.59 1.21 9.86 11.44 14.39 1.89 8 581.11 56.08 50.15 5.06 1.14 10.53 14.42 15.72 1.76 9 592.13 59.57 52.75 5.91 1.09 10.32 15.03 14.48 1.71 10 617.05 63.08 55.20 5.68 1.16 10.19 16.58 15.21 1.68
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表 3 Z30太阳轮断齿时各测点低维坐标值
测点序号 x y z 矢量2-范数 1 0.093 7 -0.280 6 -0.738 7 0.795 8 2 0.829 0 -0.659 1 -0.967 6 1.434 6 3 -0.468 1 -0.500 6 -2.014 7 2.128 1 4 0.956 4 2.056 7 -0.202 5 2.277 2 5 -2.282 7 0.262 1 0.754 2 2.418 3 6 0.011 7 1.285 0 0.888 0 1.562 1 7 0.166 8 -0.286 0 -0.633 6 0.714 8 8 0.394 0 -1.074 0 0.770 4 1.379 2 9 0.602 3 -0.818 4 0.967 8 1.403 3 10 0.796 9 -0.853 2 1.076 8 1.588 2
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表 4 各测点低维矢量2-范数排序
变速箱状态 测点排序(由大至小) 正常状态 3、5、4、6、2、10、8、1、9、7 Z30太阳轮断齿状态 5、4、3、10、6、2、9、8、1、7 Z15行星轮断齿状态 5、4、6、3、10、8、2、9、1、7
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表 5 测点重要度最终排序
测点号 1 2 3 4 5 6 7 8 9 10 重要度
排序值8.7 6 2.7 2.3 1.3 4 10 7 8 5 重要度由小到大排序 5、4、3、6、10、2、8、9、1、7
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