Prediction of assembly eccentricity and optimization of installation phase for short precision bolted connection structures
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摘要:
为了有效提高短精密螺栓连接结构的装配精度，分析了两级盘组合后形心、质心偏心影响因素，阐述了两级盘配合过程中的平动转动行为和定心原理，建立了两级转子形心偏差预测模型、初始不平衡量预测模型。提出了以短精密螺栓连接的转子盘安装相位为变量，形心偏心和初始不平衡量最小为优化为目标的工艺优化模型，通过实物实验进行了验证。结果表明：形心偏差模长最大相对误差为13.28%，组合不平衡量的计算结果精度最大提高了37.3%，工艺优化结果与实验结果相符，对于短精密螺栓连接结构装配工艺优化具有重要的参考意义。
Abstract:In order to effectively improve the assembly accuracy of the short precision bolted connection structures, the influencing factors of the centroid and centroid eccentricity after combination of the two-stage disks were analyzed, the translational rotation behavior and centering principle during the matching process of the two-stage disks were expounded, and a two-stage rotor was established. Centroid deviation prediction model and initial imbalance prediction model were established. A process optimization model was proposed, the installation phase of the rotor disk connected by short precision bolts was taken as the variable, and the centroid eccentricity and the mini-mum initial unbalance amount were taken as the optimization objective, which were verified by the physical test. The results showed that the maximum relative error of the module length of the centroid deviation was 13.28%, the maximum accuracy of the calculation result of the combined unbalance increased by 37.3%, and the process optimization results were consistent with the test results, which had important reference significance for the optimization of the assembly process of short precision bolted connection structures.
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Key words:
- short precision bolt /
- concentricity /
- unbalance /
- installation phase /
- process optimization
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图 5 质心与旋转轴线不重合示意图
Figure 5. Schematic diagram of misalignment of center of mass and axis of rotation
表 1 精密螺栓孔的偏心偏差
Table 1. Eccentricity deviation of precision bolt holes
螺栓孔编号 偏心距/mm 偏心角/（°） 1 0.020 202 2 0.024 166 3 0.016 68 4 0.018 131 5 0.020 102 6 0.022 105 
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表 2 偏心计算结果
Table 2. Eccentricity calculation results
X分量/mm Y分量/mm 偏心距/mm 偏心角/（°） 0.00811 −0.00978 0.01271 −50.3512
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表 3 零件B的形心坐标
Table 3. Part B centroid coordinates
mm 工况 X分量 Y分量 仿真前 −1.701×10−5 −0.516×10−5 仿真后 0.00774 −0.00956
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表 4 偏心距、偏心角结果对比
Table 4. Comparison of eccentric distance and eccentric angle results
参数 绝对误差 相对误差/% 偏心距/mm 0.000 41 3.33 偏心角/（°） 0.6528
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表 5 转子零件测量数据拟合结果
Table 5. Fitting results of measured data of rotor parts
mm 位置 拟合中心 半径 X分量 Y分量 一级转
实验件1号孔 139.9886 0 3.1797 7号孔 −70.01658 −121.22245 3.1798 13号孔 −70.00579 121.25805 3.1794 二级转
实验件1号孔 139.98860 0 3.1797 7号孔 −70.01755 −121.24723 3.1801 13号孔 −70.00201 121.23842 3.1802 轴颈柱面 0.00055 −0.03252 129.49418
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表 6 轴颈中心计算结果
Table 6. Calculation result of journal center
方案 预测中心坐标/mm 模长/mm 相位/（°） X分量 Y分量 1-1 −0.00158 −0.01772 0.01779 264.90 1-7 0.00775 0.03607 0.03689 77.87 1-13 −0.04349 0.01725 0.04679 158.36
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表 7 转子零件初始不平衡量
Table 7. Initial unbalance of rotor parts
位置 不平衡
质量/mg半径/
mm相位/
（°）静不平衡量/
（g·mm）一级转子实验件 490 104 157 50.96 二级转子实验件 1 902 104 76 197.808
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表 8 不同安装相位下第二级转子不平衡量
Table 8. Second-stage rotor unbalance under different installation phases
方案 质心位置/mm 静不平衡量/（g·mm） 相位/（°） 1-1 0.13567 197.808 76 1-7 0.13908 202.779 183.64 1-13 0.11100 161.838 308.21
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表 9 不同安装相位组合不平衡量预测结果
Table 9. Combined unbalance prediction results under different installation phases
方案 组合不平衡量/（g·mm） 相位/（°） 1-1 211.85 89.8 1-7 249.38 178.38 1-13 119.72 296.38
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表 10 可行解列表
Table 10. List of feasible solution
可行解方案 偏心误差/mm 组合不平衡量/（g·mm） 1-1 0.01779 211.85
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表 11 轴颈中心测量结果
Table 11. Measurement results of journal center
方案 拟合中心坐标/mm 模长/mm 相位/（°） X分量 Y分量 1-1 −0.00351 −0.01922 0.01954 259.65 1-7 0.01254 0.04066 0.04254 73.62 1-13 −0.04190 0.02848 0.05066 145.80
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表 12 计算结果与实验结果比较
Table 12. Comparing of calculated results with experimental results
方案 模长相对误差/% 相位绝对误差/（°） 1-1 8.96 5.25 1-7 13.28 4.25 1-13 7.64 12.56
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表 13 不平衡量测量数据
Table 13. Unbalance measurement data
方案 不平衡
质量/mg半径/mm 组合不平
衡量/（g·mm）相位/（°） 1-1 2036 104 211.744 90 1-7 2389 248.456 172 1-13 858 89.232 286
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表 14 计算结果误差
Table 14. Calculation result error
方案 不考虑装配偏差 考虑装配偏差 不平衡量
相对误差/%相位绝对
误差/（°）不平衡量
相对误差/%相位绝对
误差/（°）1-7 3.6 16.30 0.4 6.38 1-13 69.5 23.40 34.2 10.38
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表 15 优化结果对比
Table 15. Optimization results comparison
项目 方案1-1预测值 方案1-1实测值 误差 偏心量 模长 0.01779 mm 0.01954 mm 8.96% 相位/（°） 264.9 259.65 5.25 组合不平
衡量数值 211.85 g·mm 211.744 g·mm 0.4% 相位/（°） 89.8 90 0.2
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