Abstract
Sensitivity analysis is used to quantify the contribution of the uncertainty of input variables to the uncertainty of systematic output responses. For tolerance design in manufacturing and assembly, sensitivity analysis is applied to help designers allocate tolerances optimally. However, different sensitivity indices derived from different sensitivity analysis methods will always lead to conflicting results. It is necessary to find a sensitivity index suitable for tolerance allocation to transmission mechanisms so that the sensitivity results can truly reflect the effects of tolerances on kinematic and dynamic performances. In this paper, a variety of sensitivity indices are investigated and compared based on hybrid simulation. Firstly, the hybrid simulation model of the crank-slider mechanism is established. Secondly, samples of the kinematic and dynamic responses of the mechanism with joint clearances and link length errors are obtained, and the surrogate model established using polynomial chaos expansion (PCE). Then, different sensitivity indices are calculated based on the PCE model and are further used to evaluate the effect of joint clearances and link length errors on the output response. Combined with the tolerance-cost function, the corresponding tolerance allocation schemes are obtained based on different sensitivity analysis results. Finally, the kinematic and dynamic responses of the mechanism adopting different tolerance allocation schemes are simulated, and the sensitivity index corresponding to the optimal response is determined as the most appropriate index.
概要
目的
在制造和装配的公差设计阶段,应用灵敏度分析方法可以帮助设计人员优化分配公差。然而,不同的灵敏度分析方法得出的灵敏度指标往往导致结果相互矛盾。因此,需要通过对比找到一种适合传动机构公差分配的灵敏度指标,使灵敏度结果能够真实反映传动机构公差对运动学和动力学性能的影响。
创新点
1. 建立了一种传动机构的混合仿真模型,既降低了试验成本,也保证了实验精度;2. 提出了一种基于传动机构混合仿真模型的灵敏度指标对比方法。
方法
1. 建立曲柄滑块机构的混合仿真模型;2. 获得含有铰间隙误差和连杆长度误差机构的运动学和动力学响应样本,并使用多项式混沌展开(PCE)法建立其结构参数与动力学响应的代理模型;3. 基于PCE模型计算不同的灵敏度指标,并进一步评估铰间隙和连杆长度误差对输出响应的影响;4. 结合公差-成本函数,根据不同的灵敏度分析结果得到相应的公差分配方案;5. 对采用不同公差分配方案机构的运动学和动力学响应进行模拟,确定最优响应对应的灵敏度指标为最合适的指标。
结论
1. 基于曲柄滑块实验平台的实验数据建立了混合仿真模型,并在降低实验成本和自由控制输入变量的情况下,保证了仿真数据的准确性和可靠性。2. 基于混合仿真模型的实验数据,建立了基于PCE法的代理模型进行灵敏度计算,从而显著简化了计算。3. 根据灵敏度计算结果和成本-公差函数分配公差,得到了每个灵敏度指标对应的公差方案;通过对各公差方案下机构的运动学和动力学性能进行对比,提出了一种具有工程价值的灵敏度评价新方法。4. 与本文其他灵敏度指标相比, Sobol指标可以通过公差分配更好地优化传动机构的运动学和动力学性能。
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Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 52075480 and 52105279), the High-Level Talent Special Support Plan of Zhejiang Province (No. 2020R52004), and the Ningbo Natural Science Foundation (No. 2021J163), China.
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Zhen-yu LIU designed the research. Han-chao XU and Guo-dong SA processed the experimental and simulation data. Guo-dong SA was in charge of the whole project. Yu-feng LYU assisted with the sampling and laboratory analyses. Jian-rong TAN gave theoretical guidance on the whole work.
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Zhen-yu LIU, Han-chao XU, Guo-dong SA, Yu-feng LYU, and Jian-rong TAN declare that they have no conflict of interest.
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Liu, Zy., Xu, Hc., Sa, Gd. et al. A comparison of sensitivity indices for tolerance design of a transmission mechanism. J. Zhejiang Univ. Sci. A 23, 527–542 (2022). https://doi.org/10.1631/jzus.A2100461
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DOI: https://doi.org/10.1631/jzus.A2100461
Key words
- Transmission mechanism
- Sensitivity analysis
- Tolerance allocation
- Hybrid simulation
- Polynomial chaos expansion (PCE)