Optimisation of the column structure of a small drilling machine based on reverse engineering
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摘要: 立柱的结构性能是机床工作稳定的关键。为了满足在减轻立柱质量的同时提高其动静态特性,文章从机床结构模型获取出发,通过三维扫描采集机床零部件点云数据,然后利用逆向建模技术将其转换为实体模型,再使用有限元仿真求解立柱的关键性指标并完成优化。在模型获取方面,使用2D分析比较立柱实体外轮廓与点云数据偏差,测得整体平均偏差为−0.050 9 mm,满足试验需求。在结构优化方面,采用多目标拓扑优化快速确定立柱结构整体布局,进一步使用尺寸优化减少总变形增大对机床加工精度的影响,实现在总变形基本不变的情况下,立柱1阶固有频率有效提高16%,质量减轻5.3%。该方法将逆向工程和有限元仿真集成运用,为有限元分析提供了逆向获取的模型参数,增加了结构优化的工程可靠性,为产品改进和再设计提供新思路,加快了新产品开发效率,节约了设计和制造成本。Abstract: The structural performance of the column is the key to the stability of the machine tool. In order to improve the dynamic and static characteristics of the column while reducing its mass, we start from the acquisition of the machine structure model, collect the point cloud data of the machine parts through 3D scanning, and then convert it into a solid model by using the inverse modelling technology, and then use the finite element simulation to solve the key indexes of the column and complete the optimization. In terms of model acquisition, 2D analysis is used to compare the deviation between the solid profile of the column and the point cloud data, and the overall average deviation is measured to be −0.050 9 mm, which meets the test requirements. In terms of structural optimisation, multi-objective topology optimisation is used to quickly determine the overall layout of the column structure, and further dimensional optimisation is used to reduce the impact of increased total deformation on the machining accuracy of the machine. Under the condition that the total deformation is basically unchanged, the 1st-order intrinsic frequency of the column is effectively increased by 16%, and the mass is reduced by 5.3%. This method integrates the use of reverse engineering and finite element simulation, provides model parameters obtained in reverse for finite element analysis, increases the engineering reliability of structural optimisation, provides new ideas for product improvement and redesign, accelerates the efficiency of new product development, and saves design and manufacturing costs.
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表 1 材料属性
材料 弹性模量/MPa 泊松比 密度/(kg/m3) HT250 1.28×105 0.26 7 280 45#钢 2×105 0.3 7 850 表 2 立柱模态分析结果
阶数 频率/Hz 振形特征 1 148.97 在y轴方向上前后摆动 2 243.34 在x轴方向上前后摆动 3 782.5 在y轴方向上扭动 4 827.48 绕z轴方向上扭动 5 1457.6 在x轴方向上扭动 6 1736.1 在y轴方向上扭动 表 3 设计参数数值
参数名称 变量名 初值/mm 范围/mm 前板厚 X1 8 4~12 背板厚 X2 8 4~12 左侧板厚 X3 8 4~12 右侧板厚 X4 8 4~12 切割矩形长 X5 100 50~150 连接板厚 X6 12 6~18 连接板长 X7 40 20~40 表 4 CCD试验设计结果
序号 设计变量 频率/
Hz应力/
MPa变形/
µm质量/
kgX1 X2 X3 X5 X7 1 8 8 8 100 30 176.30 8.77 120.35 10.00 2 4 8 8 100 30 173.77 11.76 136.32 8.42 3 12 8 8 100 30 169.32 7.99 112.51 11.58 4 8 4 8 100 30 160.38 9.32 138.84 8.76 5 8 12 8 100 30 180.05 8.52 113.15 11.24 6 8 8 4 100 30 173.63 9.53 126.94 9.63 7 8 8 12 100 30 177.08 8.47 116.12 10.38 8 8 8 8 50 30 165.90 8.39 116.79 10.51 9 8 8 8 150 30 177.31 14.40 138.77 9.49 10 8 8 8 100 20 176.28 8.88 121.56 9.98 11 8 8 8 100 40 176.32 8.75 119.19 10.03 12 6.87 6.87 6.87 85.83 32.83 172.14 8.79 126.75 9.23 13 9.13 6.87 6.87 85.83 27.17 169.40 8.22 121.14 10.11 14 6.87 9.13 6.87 85.83 27.17 175.78 8.72 121.18 9.95 15 9.13 9.13 6.87 85.83 32.83 173.82 8.05 114.07 10.86 16 6.87 6.87 9.13 85.83 27.17 172.63 9.14 124.36 9.45 17 9.13 6.87 9.13 85.83 32.83 170.04 8.08 118.13 10.35 18 6.87 9.13 9.13 85.83 32.83 176.37 8.95 117.64 10.18 19 9.13 9.13 9.13 85.83 27.17 174.46 7.87 112.31 11.05 20 6.87 6.87 6.87 114.17 27.17 175.77 10.07 132.35 8.95 21 9.13 6.87 6.87 114.17 32.83 172.81 9.42 124.17 9.87 22 6.87 9.13 6.87 114.17 32.83 180.27 9.89 125.08 9.65 23 9.13 9.13 6.87 114.17 27.17 177.94 9.31 118.60 10.54 24 6.87 6.87 9.13 114.17 32.83 176.72 9.86 127.84 9.19 25 9.13 6.87 9.13 114.17 27.17 173.76 9.14 121.88 10.06 26 6.87 9.13 9.13 114.17 27.17 181.23 9.80 122.57 9.84 27 9.13 9.13 9.13 114.17 32.83 178.94 8.97 115.76 10.75 表 5 优化候选点
候选点1 候选点2 候选点3 X1 8.12 8.12 8.19 X2 8.05 8.05 7.91 X3 11.05 10.92 11.35 X5 75.63 72.12 69.94 X7 30.35 29.98 23.12 频率/Hz 172.86 172.06 171.12 应力/MPa 8.10 8.12 8.18 变形/µm 113.51 113.48 113.5 质量/kg 10.62 10.64 10.67 表 6 设计参数数值
参数名称 变量名 初值/mm 范围/mm 前板厚 Z1 8 4~12 背板厚 Z2 8 4~12 左侧板厚 Z3 8 4~12 右侧板厚 Z4 8 4~12 顶板厚 Z5 8 4~12 连接板厚 Z6 12 6~18 连接板长 Z7 40 20~40 表 7 CCD试验设计结果
序号 设计变量 频率/
Hz应力/
MPa变形/
µm质量/
kgZ1 Z2 Z5 1 8 8 8 148.83 7.55 114.29 11.23 2 4 8 8 138.29 8.21 132.96 9.73 3 12 8 8 149.13 7.33 107.31 12.74 4 8 4 8 141.70 9.41 127.17 9.73 5 8 12 8 147.04 7.05 108.08 12.74 6 8 8 4 150.89 7.49 114.25 11.14 7 8 8 12 146.93 7.48 114.26 11.32 8 4.75 4.75 4.75 141.52 8.92 137.47 8.70 9 11.25 4.75 4.75 145.21 8.07 118.02 11.16 10 4.75 11.25 4.75 141.01 7.64 122.24 11.16 11 11.25 11.25 4.75 150.39 6.91 102.81 13.62 12 4.75 4.75 11.25 137.09 9.15 137.53 8.87 13 11.25 4.75 11.25 142.12 8.79 118.06 11.30 14 4.75 11.25 11.25 137.94 7.90 122.26 11.30 15 11.25 11.25 11.25 148.23 6.96 102.74 13.73 表 8 优化候选点
变量名 候选点1 候选点2 候选点3 Z1 7.41 7.41 7.42 Z2 8.65 8.63 8.68 Z5 4.1 4.24 4.80 频率/Hz 151.06 150.96 150.63 应力/MPa 7.43 7.44 7.47 变形/µm 113.87 113.92 113.82 质量/kg 11.17 11.16 11.2 表 9 立柱结构优化分析结果
状态 频率/Hz 应力/MPa 变形/µm 质量/kg 原始 148.97 7.56 113.72 11.18 拓扑 177.39 9.02 120.32 9.97 差值/(%) +19.1 +19.3 +5.8 −10.8 尺寸 150.96 7.44 113.92 11.16 差值/(%) +1.3 −1.6 +0.2 −0.2 拓扑+尺寸 172.86 8.10 113.51 10.62 差值/(%) +16 +7.1 −0.2 −5.3 -
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