Multi-objective Optimization for Tensioner Arm using Improved Combination Weighting Radar Chart Method
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摘要: 以自动张紧器为研究对象,结合发动机前端附件轮系(Engine front end accessory drive, EFEAD)系统的非线性有限元分析,采用折衷规划法定义张紧臂各摆角工况下结构的静态、稳态刚度和动态振动频率最大化的综合目标函数,并提出了一种改进的组合赋权雷达图法来确定各工况的最优权重系数,进行张紧臂结构的多目标优化设计。同时对比经验法、平均分配法和层次分析法定义权重系数的优化结果,验证了改进的组合赋权雷达图法的优越性。最后对张紧臂进行优化设计,分析结果表明:优化后张紧臂在质量减少的情况下,刚度性能和强度性能明显提高,各阶模态频率均可达到要求。Abstract: Based on the study of auto-tensioner and Combining the nonlinear finite element analysis of the EFEAD (Engine front end accessory drive) system, a comprehensive objective function was defined by the compromise programming approach, which maximized the static, steady-state stiffness and dynamic vibration frequency. An improved combination weighting radar chart method was applied to obtain the optimal weights of various loading conditions in order to conduct multi-objective optimization design of a tensioner arm. Moreover, the contrastive study was carried out to compare the results on the radar chart methods that determine the weight ratio with empirical design, equipartition law and analytic hierarchy process. The comparison results indicate that the radar chart method is superior to other reference methods. Finally, the tensioner arm was optimized, and the analytic results show that as the mass of the optimized structure is reduced, the stiffness and strength performances are enhanced and that the natural frequency of the model of each order meets the requirement.
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表 1 张紧器静态各工况参数
工况位置(静态) 张紧臂位置 摆角/(°) 轮毂载荷Ft/N 张紧臂应力/MPa 张紧器变形/mm 皮带应力/MPa 相对工作时长 1 最大工作摆角 246 910 123.14 0.77 1.77 0.20 2 过渡摆角1 240 916 123.07 0.75 2.21 0.20 3 过渡摆角2 238 922 121.30 0.73 2.53 0.20 4 最佳工作摆角 232 928 118.45 0.69 2.85 0.30 5 最小工作摆角 230 930 119.37 0.66 3.22 0.10 表 2 张紧臂稳态不同转速工况参数
工况位置(稳态) 输入转速/(r·min-1) 轮毂载荷Ft/N 张紧臂应力/MPa 张紧器变形/mm 皮带应力/MPa 带轮滑移率/% 皮带横向振动/mm 工作时长/h 6 1 000~1 500 928.13 121.40 0.72 2.51 5.9 2.15 10 7 1 500~2 000 779.94 101.00 0.56 1.94 4.6 1.94 15 8 2 000~3 000 550.66 70.52 0.40 1.25 3.2 1.53 20 9 3 000~4 000 462.07 59.11 0.34 0.99 3.5 0.93 120 10 4 000~5 000 442.35 57.40 0.30 0.78 3.8 0.76 150 11 5 000~6 000 437.28 56.72 0.25 0.86 3.3 0.69 150 12 >6 000 458.96 58.05 0.33 0.90 2.8 0.61 80 表 3 静态工况指标各种赋权方法所确定的权重对比
方法 摇臂应力 摇臂变形 工作时长 带应力 AHP法 0.200 0.200 0.522 0.078 专家打分法 0.270 0.250 0.330 0.150 优序图法 0.250 0.250 0.437 0.063 熵权法 0.294 0.251 0.213 0.242 变异系数法 0.272 0.248 0.232 0.248 综合权值 0.274 0.232 0.341 0.153 表 4 稳态工况指标各种赋权方法所确定的权重对比
方法 摇臂应力 摇臂变形 工作时长 带轮滑移率 横向振动 皮带应力 AHP法 0.178 0.178 0.445 0.062 0.053 0.083 专家打分法 0.225 0.192 0.333 0.070 0.072 0.108 优序图法 0.222 0.222 0.306 0.055 0.056 0.139 熵权法 0.228 0.135 0.160 0.125 0.163 0.189 变异系数法 0.203 0.153 0.152 0.148 0.157 0.187 综合权值 0.215 0.179 0.306 0.089 0.097 0.114 表 5 静态各工况权重系数
静态工况 1 2 3 4 5 权重 0.184 0.196 0.204 0.249 0.167 表 6 稳态各工况权重系数
稳态工况 6 7 8 9 10 11 12 权重 0.237 0.168 0.099 0.135 0.147 0.121 0.093 表 7 优化后张紧臂与参考模型工况最大应力对比
MPa 工况 1 2 3 4 参考模型 123.14 123.07 121.30 121.40 优化模型 80.70 76.56 74.50 76.22 表 8 优化后张紧臂与参考模型工况最大位移对比mm
工况 1 2 3 4 参考模型 0.77 0.75 0.73 0.72 优化模型 0.61 0.58 0.54 0.57 表 9 优化后张紧臂与参考模型前4阶模态频率对比
Hz 工况 第1阶 第2阶 第3阶 第4阶 参考模型 531.08 1 880.0 2 990.0 3 567.7 优化模型 664.08 2 141.4 3 217.3 3 673.8 -
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