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摘要:
为提升滚动直线导轨副耐磨性,结合导轨副摩擦磨损试验及理论分析,将最大碰撞力,最大接触应力,摩擦阻力作为导轨副耐磨性能的表征和优化目标。根据设计要求,确定滑块反力约束函数和结构参数约束范围。通过分析模型的参数灵敏度,选取初始接触角,滑块滚道曲率比,滚珠直径和导轨高度增量作为设计变量;优化使用CCRD联合Kriging响应面构建代理模型;通过NSGA-Ⅱ算法,使结构在最大接触应力仅增加4.33%的情况下,摩擦阻力降低2.09%,最大碰撞力降低15.00%。设计变量中滚珠直径由5.56 mm降低至5.1744 mm,初始接触角由45°降低至38.878°,两者变动最大。基于Spearman相关性分析,可知滚珠直径与滑块反力相关系数值为0.23,初始接触角与滑块反力系数值达到−0.82,两者在优化中相互平衡达到最优解。
Abstract:In order to improve the wear resistance of rolling linear guide, combined with the wear test and theoretical analysis, the maximum impact force, maximum contact stress and friction resistance are taken as optimization goals. The constraint function of slider reaction force and the range of structural parameters were determined by desgin requirement. By analyzing the parameter sensitivity, initial contact angle, curve ratio of the slider raceway, ball diameter and the increment of the rail height were selected as variables; The optimization used CCRD and Kriging response surface to construct the agent model. Though the NSGA-Ⅱ algorithm, the friction resistance and maximum impact force of the structure were reduced by 2.09% and 15.00% respectively, while the maximum contact stress increased by only 4.33%. The ball diameter decreased from 5.56 to 5.1744 mm, and the initial contact angle decreased from 45 to 38.878°. Though Spearman correlation analysis, it is known that the coefficient value between the ball diameter and the slider reaction force is 0.23, and the coefficient value between the initial contact angle and slider reaction force are −0.82. These two variables balance each other to achieve the optimal solution in optimization.
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Key words:
- rolling linear guide /
- wear resistance /
- optimization design /
- Kriging /
- NSGA-Ⅱ algorithm
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表 1 有限元模型结果
Table 1. FEM Model results
参数 试验数据 求解结果 修正结果 误差 Fry2/N 8400 15344.8 8439.61 0.5% 表 2 参数灵敏度表
Table 2. Parameter sensitivity table
参数 Fm Ff σmax Fry2 Da 0.93 0.14 −0.19 0.23 α −0.01 −0.27 −0.18 −0.81 G1 0 −0.05 −0.04 −0.05 f −0.26 −0.91 0.92 −0.43 Xa 0.28 −0.03 −0.03 −0.02 表 3 相关系数矩阵表
Table 3. Correlation coefficient matrix
项目 Fry2 Fm Ff σmax Fry2 1 0.32 0.70 −0.23 Fm 1 0.33 −0.40 Ff 1 −0.75 σmax 1 表 4 优化结果
Table 4. Optimization results
项目/单位 原结果 优化结果 σmax/MPa 2215.2 2283.6 Ff /N 7.9009 7.3739 Fm/N 244.36 207.33 Da/mm 5.56 5.1744 α/(°) 45 38.878 f 0.52 0.52076 Xa/mm 0 0.24664 Fry2/N 8439.64 8478.2 表 5 最终结果
Table 5. Final result
项目 σmax /MPa Ff /N Fm/N Fry2 /N 计算结果 2311.1 7.7351 207.71 8787.9 变动率/% 4.33 −2.09 −15.00 4.13 准确率/% 98.81 95.33 99.82 96.48 表 6 结构参数相关系数表
Table 6. Correlation coefficient of structural parameters
结构参数 目标函数与约束函数 Fry2 Fm Ff σmax Da 0.23 0.93 0.14 −0.19 α −0.82 −0.01 −0.27 −0.19 -
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