RESEARCH ON GAS FLOW CHARACTERISTICS OF BERNOULLI GRIPPER BASED ON MACHINE LEARNING
-
摘要: 电子元器件的非接触输运是实现其全自动化生产的瓶颈之一. 伯努利夹持器作为一种非接触式气动夹持装置被广泛应用于工业中物体的抓取、定位和运输, 而适用于mm级别半导体器件清洁无损运输的微型伯努利夹持器还鲜有研究. 文章采用SSTk-ω并结合层流/湍流转捩γ模型, 探讨了夹持间隙、喷嘴直径、夹持器尺寸以及供气压力对吸持力和气体消耗率的影响, 并分析了其内部的气体流动特性变化; 以数值模拟获得的数百个数据作为数据集, 利用机器学习方法建立6个夹持器性能预测模型, 并结合相应的智能算法对机器学习模型的超参数进行调优, 进行特征相关性分析, 并比较了各机器学习模型的预测效果. 结果表明, 吸持力受多因素综合影响: 其随供气压力、夹持器尺寸的增大而增大, 随夹持间隙及喷嘴直径的增大先增大后减小; 气体消耗率随供气压力、夹持间隙以及喷嘴直径的增大而增大. 最佳的机器学习模型对吸持力和气体消耗率的预测准确率评价指标R2 (越接近1越准确)分别在0.95和0.97左右, 预测了不同夹持器尺寸下的最大吸持力及所对应的夹持器参数, 与数值结果进行比较其误差小于5%, 具有良好的预测能力. 此外发现, 为保证夹持器低G-F因子工作(产生单位吸持力所需的气体消耗率g/s·N)其供气压力和夹持间隙应分别控制在3 ~ 5 bar和0.045 ~ 0.08 mm之间, 模型可用于多参数影响下的伯努利夹持器吸持力和气体消耗率的预测. 结果可为微型伯努利夹持器设计及结构参数优化提供参考.Abstract: The non-contact transport of electronic components is one of the bottlenecks in achieving its fully automated production. Bernoulli gripper, a non-contact pneumatic gripper device, is widely used for gripping, positioning, and transporting objects in industry. However, the miniature Bernoulli gripper, which is used for clean and non-destructive transport of millimeter-scale semiconductor devices, has rarely been studied. In this study, combining the SSTk-ωand laminar/turbulent turningγmodels, the effects of the gripping gap, nozzle diameter, gripper size, and gas supply pressure on the suction force and gas consumption rate are first explored and the variation of the gas flow characteristics inside them is analysed. Then, based on hundreds of data obtained from numerical simulations as a dataset, six gripper performance prediction models were established using machine learning methods, and the hyper-parameters of the machine learning models were optimised by combining them with the corresponding intelligent algorithms. Finally, feature correlation analysis and comparison of the prediction effect of each machine learning model were conducted. The results show that the holding force is influenced by multiple factors: it grows with the gas supply pressure and the gripper size, while it initially rises and then declines with the gripping gap and the nozzle diameter; The gas consumption rate grows with the gas supply pressure, the gripping gap and the nozzle diameter. The optimal machine learning model has good prediction ability for holding force and gas consumption rate with accuracy evaluation metricsR2 around 0.95 and 0.97 (the closer to 1 the more accurate), respectively. The model prediction results for maximum holding force and corresponding gripper parameters at different gripper sizes have less than 5% error compared to the numerical simulation results. In addition, it was found that the gas supply pressure and the clamping gap should be controlled at 3 ~ 5 bar and 0.045 ~ 0.08 mm, respectively, for lowG-Ffactor operation of the gripper (gas consumption rate required to generate a unit of holding power g/s·N), and the model is used for prediction on holding force and gas consumption rate of the Bernoulli gripper under the influence of multiple parameters. The results of this paper can provide a reference for the design of miniature Bernoulli grippers and the optimisation of structural parameters.
-
引 言
国家《第十四个五年规划和2035年远景目标纲要》中提出要加强在人工智能及集成电路等前沿领域的前瞻性布局[1]. 集成电路等半导体器件在生产制造过程中涉及众多的工序与检测环节, 各工序及检测环节之间相互切换时要求器件频繁移动[2]. 机械夹持器[3]和真空吸盘[4]等传统的接触式输运方式容易造成器件碎裂及表面损伤, 同时也暴露出静电和金属污染等诸多缺陷, 微型半导体器件的清洁与无损运输是实现其全自动化生产的瓶颈之一.
伯努利夹持器作为一种无接触式气动夹持装置被广泛应用于工业中物体的抓取、定位和运输[5-9], 其原理即众所周知的伯努利效应-一条流线上流体的流速高压强低, 流体高速掠过物体表面时形成负压, 在大气压的作用下使物体悬浮, 理论研究可以追溯到1956年Welanetz[10]的学术报告, 工作原理示意如图1(a). 因其极具实用价值, 学者们一直致力于夹持器的优化设计, 以提高夹持器的性能. Wang等[11]、Liu等[9, 12]和Failli等[13]通过对多个伯努利夹持器进行分布式布局来增加对硅片和皮革的吸持性能, 具有结构简单的优点, 但其需要更大的安装空间; 在夹持器结构优化上主要考虑以下两类影响因素[14]. 一类考虑夹持器间隙流结构因素, Dini等[15]通过设置多个径向文丘里流道来增强气流产生的负压吸附能力, Shi等[16]分析了夹持器外径对吸持力的影响, 并对外径进行了优化, Yu等[17]设计夹持器与工件之间的微小倾斜锥体结构形成发散流, 进而提高负压和吸持力, 这些方法虽在一定程度上改善了负压场, 但存在结构复杂及加工精度要求高等缺点; 另一类考虑气流的供应流等因素[9, 18-19], 其通过安装锥形结构改变气流喷射方向, 如图1(b)所示, 其引入科恩达效应使锥形结构下方区域形成负压, 以消除因供气气流对工件的冲击而产生的排斥力, 并提高气流进入间隙时的速度, 该类方法也存在结构复杂、装配精度要求高等缺点. 此外, 针对不引入锥形结构的垂直喷射夹持器, Li等[20]将供应的流动工质由空气改为水, 水作为不可压缩流体, 很容易达到很高的供给压力, 相同流量下, 实现了吸持能力在数量级上的提高, 也拓宽了伯努利夹持器的应用范围, 特别是在以下两个领域: 水下现场吸附(例如水下打捞救助、新型船体吸附式水下攀爬机器人)和厚重工件吸附(例如建筑材料)上. 为进一步将伯努利夹持器的应用范围拓展至微型半导体器件的搬运上, 考虑到结构的加工以及装配精度, 适用于mm尺寸半导体器件搬运的微型伯努力夹持器, 不引入锥形结构的气流垂直喷射式是更有前景的.
对于气流垂直喷射的夹持器流动特性, 起初一些研究者使用理想流体的动量方程来描述物体表面压力分布并计算吸持力[21-22], 因其忽略了夹持间隙内气体流动时十分重要的黏性效应, 根据理论公式会得出: 当夹持间隙$ {h_{\text{c}}} $变得非常小时, 吸持力$ {F_{\text{L}}} $变为无穷大; 当夹持器尺寸变得很大时, $ {F_{\text{L}}} $也变得无限大. 另一些研究学者虽考虑了空气的黏性, 但忽略了空气的可压缩性, 即气流马赫数超过可压缩阈值0.32时, 其理论模型失效[10,23-26]. Li等[8]和Shi等[16]在上述研究基础上考虑黏性、可压缩性等, 对伯努利夹持器的影响因素进行了理论与实验研究并优化了夹持器外径. 后续Shi等[27]基于实验研究了工件提升的瞬态过程, 发现工件在提升后开始发生竖直方向的振荡, 随后, 振荡幅度减小直至工件稳定, 并提出一个质量-弹簧-阻尼模型可以准确地描述与预测工件的运动过程.
随着计算机技术的发展, 数值模拟已成为预测气体在间隙内流动特性的有效工具[28-29]. Paivanas等[30-31]基于稳定、层流假设对垂直气流喷射的伯努利夹持器进行模拟, 模型无法捕捉到流动中的分离现象. Brun等[32]采用RANS方法求解NS方程对有锥形结构的斜向气流喷射的伯努利夹持器进行模拟, 结果发现喷嘴出口周围出现大尺度涡流以及流动分离区, 此外喷嘴出口到夹持器外缘出现了湍流-层流的过渡; Paivanas等[30]在垂直气流喷射夹持器上也发现了类似的趋势. 证实了模拟伯努利夹持器气体流动特性时使用湍流模型的必要性, 同时需考虑层流-湍流过渡.
近年来, AI在高技术领域的应用——“技术智能”(AI for technology)的典型特征和科学问题, 并成功对CPU芯片进行了全自动设计, 其不仅可加速创新流程并减少人工投入, 同时也被寄望具备更强的创造能力, 最终超过人类的水平. 同时, 机器学习方法和智能算法在解决工程问题和科学研究中的复杂问题时呈现出了优越性[33], 未来随着数字孪生的发展, 大量可用数据的出现以及算法和计算能力的进步, 机器学习在时间和成本方面将更具有优势[34], 这也为伯努利夹持器气体流动特性的预测提供了一种新思路. 针对力学相关领域小样本问题作用明显并且对高维和非线性问题的适应性较好的机器学习模型已被应用于压气机叶型气动特性、机翼翼型气动系数、航空航天领域高$ Re $数绕流湍流建模及管道输运时气-固流动及管道磨损等流动特性预测[35-38]. 杜周等[35]采用卷积神经网络准确预测了压气机内流场气动参数, 压力系数误差率小于0.2%, 总压损失系数误差率低于1.2%. Wang等[38]通过气-固流动数据, 采用极限学习机模型对气-固流动特性及管道磨损率进行预测, 显示出很好的一致性. 肖盛鹏等[39]建立了不同机器学习模型对弯管固-液两相流动特性进行预测并比较了它们的预测效果. 贺登辉等[40]基于随机森林模型对离心泵气-液两相流动中的压升特性实现了准确预测. 上述研究多集中于尺度较大的气体流动问题, 针对于mm级狭小缝隙内的惯性及黏性共同支配的流动特性问题, 相关机器学习模型还鲜有应用.
此外, 与对夹持较大型物体(约几十cm)的斜向喷气伯努利夹持器、涡流夹持器的广泛研究相比[9,32,41-42], 对于mm级的微型夹持器的这类狭小缝隙内的气体流动过程, “惯性加速效应”与“黏性摩擦减速效应”的平衡主导着其流动特性, 同时也要考虑流动中的层流/湍流转捩效应, 并且相比于夹持较大型工件的夹持器也存在着加工难度大的问题, 适用于电子元器件搬运的微型伯努利夹持器气体流动特性研究还未见报道. 因此, 为满足mm级电子元器件非接触搬运所提出的迫切需求, 需对其流动特性进行预测及评估.
本文采用数值方法计算了微型伯努利夹持器在不同夹持间隙、喷嘴直径、夹持器外缘尺寸以及供气压力下的吸持力和气体消耗率, 全面分析了各参数对其的影响机理, 在数值模拟数据的基础上, 建立6种机器学习模型并结合智能优化算法进行超参数调优, 研究了不同机器学习模型对夹持器吸持力和气体消耗率的预测能力, 利用最优的模型预测了不同夹持器尺寸下的最大吸持力及对应的夹持器参数, 获取了为保证夹持器低G-F因子(产生单位吸附力所需的气体消耗)工作时供气压力和夹持间隙的控制区间范围, 以期为适用于电子元器件搬运的微型伯努利夹持器设计及优化提供参考, 并进一步推进伯努利夹持器在微型工件搬运领域的拓展应用.
1. 数值模型的设计与验证
1.1 湍流模型及湍流间歇输运方程
Menter 和Huang提出的k-ω SST湍流模型, 其作为一种出色的全能型RANS模型, 也是目前广泛使用的涡黏假设模型中性能评价最优的一个, 适用于逆压力梯度流动、翼面及跨声速激波等流动的精确和可靠模拟[43]. 为考虑层流/湍流转捩对流场细节和整体性能的影响, 采用Menter等[44-46]提出的基于局部相关性过渡建模方法处理转捩机制, 用局部信息来激活间歇方程中的产生项, 再利用涡度雷诺数建立相关关系与间歇方程的联系. $ \gamma $湍流间歇输运方程如下
$$ \frac{{\partial (\rho \gamma )}}{{\partial t}} + \frac{{\partial (\rho {{{U}}_j}\gamma )}}{{\partial {x_j}}} = {P_\gamma } - {E_\gamma } + \frac{\partial }{{\partial {x_j}}}\left[ {\left(\mu + \frac{{{\mu _{\text{t}}}}}{{{\sigma _\gamma }}}\right)\frac{{\partial \gamma }}{{\partial {x_j}}}} \right] $$ (1) 式中$ {P_\gamma } $和$ {E_\gamma } $分别为转捩源项及耗散项/再层流化源项; $ \rho $为密度; $ {{U}}_j $为速度; $ \mu $为动力黏度; $ {\mu _{\text{t}}} $为湍流动力黏度; $ {\sigma _\gamma } $为模型常数取1. 间歇因子$ \gamma $触发层流边界向湍流边界层的转变, 自由流时$ \gamma = 1 $, 层流边界层中, $ \gamma $趋向于0.
耦合$ \gamma $间歇因子后的SST模型中湍动能$ k $输运方程如式(2), 比耗散率$ \omega $输运方程不变
$$ \begin{split} &\frac{{\partial (\rho k)}}{{\partial t}} + \frac{{\partial (\rho {{{U}}_j}k)}}{{\partial {x_j}}} = {\tilde P_k} + P_k^{\lim } - {\tilde D_k} +\\ &\qquad \frac{\partial }{{\partial {x_j}}}\left[\left(\mu + {\sigma _k}{\mu _{\text{t}}}\right)\frac{{\partial k}}{{\partial {x_j}}}\right] \end{split}$$ (2) $$ {\tilde P_k} = \gamma {P_k} $$ (3) $$ {\tilde D_k} = \max (\gamma ,0.1) \cdot {D_k} $$ (4) $$ {\mu _{\text{t}}} = \frac{{{a_1}k}}{{\max ({a_1}\omega ,\varOmega {F_2})}} $$ (5) $$ {P_\gamma } = {L_{\text{z}}}\rho S\gamma (1 - \gamma ){F_{{\text{onset}}}} $$ (6) $$ {E_\gamma } = {c_{a2}}\rho \varOmega \gamma {F_{{\text{turb}}}}({c_{e2}}\gamma - 1) $$ (7) $$ {S_{ij}} = \frac{1}{2}\left( {\frac{{\partial {{{U}}_i}}}{{\partial {x_j}}} + \frac{{\partial {{{U}}_j}}}{{\partial {x_i}}}} \right),\quad {S^2} = 2{S_{ij}}{S_{ij}} $$ (8) $$ {\varOmega _{ij}} = \frac{1}{2}\left( {\frac{{\partial {{{U}}_i}}}{{\partial {x_j}}} - \frac{{\partial {{{U}}_j}}}{{\partial {x_i}}}} \right),\quad {\varOmega ^2} = 2{\varOmega_{ij}}{\varOmega_{ij}} $$ (9) 式中$ S $为应变率; $ {L_{\text{z}}} $表示控制过渡区长度的经验系数(取默认值$ {L_{\text{z}}} = 100 $); 下标$i$和$j$分别代表笛卡尔坐标系下$x$和$y$方向; $ {a_1} $为模型结构参数取0.31, $ {\sigma _k} $为模型常数, $ {F_2} $为边界层混合函数[46]; $ \varOmega $为绝对涡率; $ {c_{a2}} = 0.06 $, $ {c_{e2}} = 50 $, $ \varOmega \gamma = 1 $; $ {P_k} $和$ {D_k} $分别为负责产生和耗散湍流的一次项[45, 47]; $ P_k^{\lim } $为$ k $方程中引入的额外项, 保证在任意低湍流水平下, 过渡点均可产生适当的$ k $
$$ {P_k} = {\mu _{\text{t}}}S\varOmega $$ (10) $$ {D_k} = {\beta ^*}\rho \omega k $$ (11) $$\left.\begin{aligned} & P_k^{\lim } = 5{C_k}\max (\gamma - 0.2,0)(1 - \gamma )\cdot\\ &\qquad F_{{\text{on}}}^{\lim }\max ({C_{{\text{SEP}}}}\mu - {\mu _{\text{t}}}\varOmega ) \\ & {C_k} = 1.0,{C_{{\text{SEP}}}} = 1.0 \end{aligned}\right\} $$ (12) $$ F_{{\text{on}}}^{\lim } = \min \left(\max \left(\frac{{R{e_V}}}{{2.2Re_{\theta c}^{\lim }}} - 1,0\right),3\right),Re_{\theta c}^{\lim } = 1100 $$ (13) 转捩的起始由以下函数控制
$$ {F_{{\text{onset1}}}} = \frac{{R{e_\nu }}}{{2.2R{e_{\theta c}}}} $$ (14) $$ {F_{{\text{onset2}}}} = \min ({F_{{\text{onset1}}}},2.0) $$ (15) $$ {F_{{\text{onset3}}}} = \max \left(1 - {\left(\frac{{{R_T}}}{{3.5}}\right)^3},0\right) $$ (16) $$ {F_{{\text{onset}}}} = \max ({F_{{\text{onset2}}}} - {F_{{\text{onset3}}}},0) $$ (17) $$ {F_{{\text{turb}}}} = {{\mathrm{e}}^{ - {{\left(\tfrac{{{R_T}}}{2}\right)}^4}}} $$ (18) $$ {R_T} = \frac{{\rho k}}{{\mu \omega }} $$ (19) $$ R{e_\nu } = \frac{{\rho {d_{\text{w}}}^2S}}{\mu } $$ (20) $$ R{e_{\theta c}}(T{u_L},{\lambda _{\theta L}}) = {C_{{\text{TU1}}}} + {C_{{\text{TU2}}}}{{\mathrm{e}}^{\left( { - {C_{{\text{TU3}}}}T{u_L}{F_{{\text{PG}}}}({\lambda _{\theta L}})} \right)}} $$ (21) 式中$ {d_{\text{w}}} $为壁面距离; $ R{e_{\theta c}} $为过渡动量厚度雷诺数, 是用来触发转捩模型的关联量; $ T{u_L} $和$ {\lambda _{\theta L}} $为局部定的变量, 分别近似自由流湍流强度和压力梯度参数, ${\text{d}}{\boldsymbol{V}}/{\text{d}}y$为边界层速度梯度
$$ T{u_L} = \min \left(100\frac{{\sqrt {2k/3} }}{{\omega {d_{\text{w}}}}},100\right) $$ (22) $$ {\lambda _{\theta L}} = - 0.111\;1\frac{{{\mathrm{d}}{{V}}}}{{{\mathrm{d}}y}}\frac{{\rho {d_{\text{w}}}^2}}{\mu } + 0.187\;5 $$ (23) $ {F_{{\text{PG}}}} $函数考虑了压力梯度对过渡的影响, 其定义为
$$ {F_{{\text{PG}}}}({\lambda _{\theta L}}) = {\text{min}}(1 + {C_{{\text{PG1}}}}{\lambda _{\theta L}},C_{{\text{PG1}}}^{{\text{lim}}}),{\lambda _{\theta L}} \geqslant 0 $$ (24) $$\begin{split} & {F_{{\text{PG}}}}({\lambda _{\theta L}}) = {\text{min}}(1 + {C_{{\text{PG2}}}}{\lambda _{\theta L}} + \\ &\qquad {C_{{\text{PG3}}}}{\text{min}}\left( {{\lambda _{\theta L}} + 1.0,0} \right),C_{{\text{PG2}}}^{{\text{lim}}}),{\lambda _{\theta L}} < 0 \end{split} $$ (25) 其中$ {C_{{\text{TU1}}}} $, $ {C_{{\text{TU2}}}} $, $ {C_{{\text{TU3}}}} $, $ {C_{{\text{PG1}}}} $, $ {C_{{\text{PG2}}}} $, $ {C_{{\text{PG3}}}} $, $ C_{{\text{PG1}}}^{{\text{lim}}} $和$ C_{{\text{PG2}}}^{{\text{lim}}} $为经验系数[48], 取值分别为100, 1000, 1, 1, −0.5, 0, 1.5和3.0.
1.2 边界条件与参数设置
如图2所示, 进出口条件设置压力入口与压力出口边界条件, 主流湍流强度设置为5%, 其余壁面设置为无滑移壁面. 网格类型为poly-hexcore, 边界层网格为10层, 第一层网格高度为1.0 × 10−6 m, 使得y + 值在1附近, 为提高壁面湍流分辨率, 网格增长率设定为1.1. 气体动力黏度关联式采用Sutherland定律. 在数值格式上, 控制方程采用有限体积法求解, 空间离散采用二阶迎风格式, 压力和速度的解耦采用coupled速算法, 压力、动量收敛因子为0.4, 保证数值稳定性和更快的收敛速度.
1.3 模型及网格独立性验证
为验证本文数值模型的准确性, 采用文献[8]中的实验进行数值验证, 图3为standard k-ω、RNG k-ε和SST k-ω 3种湍流模型对伯努利夹持器工件表面压力分布的预测效果, 可以发现SST k-ω模型能够更好地吻合实验结果. 此外, Mykhailyshyn等[47]也采用SST k-ω并结合层流/湍流转捩$ \gamma $模型, 对圆形伯努利夹持器的气体流动特性进行数值模拟, 分析了喷嘴几何参数对径向间隙压力分布性质及其吸持力的影响. 流动间隙网格尺寸特征尺度控制以夹持间隙$ {h_{\text{c}}} $尺寸的1, 3/4, 1/2和1/4分别设置对应为粗、中、较细和细4种网格进行模拟, 网格增长率均为1.2, 体网格数量约为2.0 × 104, 6.0 × 104, 1.1 × 105和3.2 × 105, 网格质量要求不低于0.2, 较细与细网格结果基本重合, 如图4所示, 偏差小于1%, 选用较细网格进行后续计算.
![]()
图 4 计算结果随网格数量的变化曲线Figure 4. The variation curve of the calculation results with the number of grids2. 数值模拟结果分析
夹持器的内部气体流动特性受夹持间隙、喷嘴直径、夹持器尺寸以及供气压力影响. 夹持器的吸持力由工件表面的压力分布积分获得, $ {F_{\text{L}}} $定义为
$$ {F_{\text{L}}} = \iint {{p_{\text{g}}}(x,y){\text{d}}x{\text{d}}y} $$ (26) 式中表压力${p_{\text{g}}}$ < 0时为负压提供升力, ${p_{\text{g}}} $ > 0时为正压产生斥力, 吸持力为升力与排斥力的差值, 图5给出了工件表面压力分布的示意图.
![]()
图 5 工件表面压力分布示意图Figure 5. Schematic diagram of pressure distribution on the surface of the workpiece2.1 夹持间隙hc
夹持器长宽为4 mm × 2 mm, 喷嘴直径为0.5 mm, 供气压力为3 bar (1 bar = 1.0 × 105 Pa), 夹持间隙分别为0.025, 0.05, 0.1, 0.15, 0.2和0.25 mm. 图6显示了工件表面压力分布随夹持间隙的变化; 图7显示了夹持间隙对吸持力和气体消耗率的影响, 吸持力随夹持间隙的增大先增大后减小, 存在一个$ {h_{{\text{cmax}}}} $使得吸持力最大, 气体消耗率随夹持间隙的增大而增大. 结合图6和图7分析, 当夹持间隙$ {h_{\text{c}}} < {h_{{\text{cmax}}}} $时, 随着夹持间隙减小, 气流从喷嘴流向间隙的阻力增加, 喷嘴正下方的工件表面正压力峰值分布范围增加, 气流进入间隙后虽然速度会增加但黏滞摩擦效应对气流的减速作用显著, 负压峰值以及负压区域减小, 进而吸持力减小. 当夹持间隙$ {h_{\text{c}}} > {h_{{\text{cmax}}}} $时, 随着夹持间隙的增大, 气流进入间隙的阻力减小, 喷嘴正下方的工件表面正压力峰值减小, 气流加速的惯性效应减弱, 产生的负压峰值和负压区域减小, 惯性效应减弱产生的负压变化强于阻力减小产生的正压变化, 吸持力减小. 此外, 假设工件的质量为${{m}}$, 当工件位于${{A}}$点或${{B}}$点时, 吸持力等于其重力${{mg}}$, ${{A}}$点为稳定悬浮位置, 而${{B}}$点是悬浮临界位置, ${{A}}$与${{B}}$之间为悬浮区域. 工件只能在${{A}}$点实现稳定悬浮, 当工件略微偏离${{A}}$点时, 吸持力能自动调整, 保证工件返回到${{A}}$点. 然而, 在${{B}}$点的悬浮是不稳定的, 若工件偏离${{B}}$点的左侧, 吸持力超过其重量并将其吸向${{A}}$点. 如果工件偏离${{B}}$点的右侧, 吸持力将小于其重量而工件掉落.
![]()
图 6 不同夹持间隙下的工件表面压力分布曲线Figure 6. Pressure distribution curve on workpiece surface with different gripping gap![]()
图 7 吸持力、气体消耗率随夹持间隙的变化曲线Figure 7. Curve of holding force and gas consumption rate with gripping gap2.2 夹持器喷嘴直径d
夹持器长宽为4 mm × 2 mm, 夹持间隙为0.1 mm, 供气压力为3 bar, 喷嘴直径分别为0.4, 0.5, 0.6, 0.7, 0.8, 0.9和1.0 mm, 工件表面压力分布见图8. 图9为吸持力与气体消耗率随喷嘴直径的变化曲线. 随着喷嘴直径的增加, 气流流量增加, 气流进入间隙的阻力增加, 工件表面正压区域增大, 负压区域向外夹持器边缘移动, 气体流动范围缩小导致负压区域先增加后减小, 短轴(宽)上负压区域以及负压峰值呈减小状态. 吸持力是工件表面正压与负压分布共同作用的结果, 故随着喷嘴直径的增大, 呈现先增加后减小的趋势. 夹持器在设计过程中喷嘴直径应与其他参数综合考虑进行确定.
![]()
图 8 不同喷嘴直径下的工件表面压力分布曲线Figure 8. Pressure distribution curve on workpiece surface with different nozzle diameter![]()
图 9 吸持力、气体消耗率随喷嘴直径的变化曲线Figure 9. Curve of holding force and gas consumption rate with nozzle diameter2.3 夹持器长宽a × b
夹持间隙为0.1 mm, 供气压力为3 bar, 喷嘴直径为0.5 mm, 不同夹持器尺寸下的工件表面压力分布曲线如图10所示. 图11为吸持力与气体消耗率随夹持器尺寸的变化曲线. 工件表面正压区域不变, 随着夹持器尺寸增加, 气体流动范围增加, 气流得以更充分地发展加速, 惯性效应产生的负压区域增加, 在短轴(宽)上负压区域的增大更加显著, 故吸持力随夹持器尺寸增加而增大. 气体消耗率几乎不随夹持器尺寸变化.
![]()
图 10 不同夹持器尺寸下的工件表面压力分布曲线Figure 10. Pressure distribution curve on workpiece surface with different gripper size![]()
图 11 吸持力、气体消耗率随夹持器尺寸的变化曲线Figure 11. Curve of holding force and gas consumption rate with gripper size2.4 夹持器供气压力P
夹持器长宽为4 mm × 2 mm, 夹持间隙为0.1 mm, 喷嘴直径为0.5 mm, 供气压力分别为2, 3, 4和5 bar, 工件表面压力分布见图12. 图13为吸持力与气体消耗率随供气压力的变化曲线, 吸持力与气体消耗率随供气压力增加而增大. 供气压力增加, 更高动能的来流冲击工件表面, 表面正压峰值及区域增加, 更高速的气流进入间隙后, 气流加速的惯性效应产生负压区域增大, 长轴(长)上更加显著, 短轴(宽)上供气压力位3, 4与5 bar变化不大. 惯性效应产生的负压变化强于气流冲击以及黏性产生的压升变化, 故吸持力增大.
![]()
图 12 不同供气压力下的工件表面压力分布曲线Figure 12. Pressure distribution curve on workpiece surface with different supply pressure![]()
图 13 吸持力、气体消耗率随供气压力的变化曲线Figure 13. Curve of holding force and gas consumption rate with supply pressure3. 机器学习数据集及模型
3.1 数据集生成
微型伯努利夹持器内气体流动特性较为复杂, 受到不同参数的综合影响. 在多参数条件下其吸持力与气体消耗率的预测难度较大, 基于数值方法将耗费大量的计算时间与资源. 因此, 采用机器学习方法, 通过对已有数据的学习实现较为精准的预测. 对应前文的参数变量, 经数值方法计算后, 得到432组数据作为数据集, 数据集被随机划分为训练集、验证集与测试集, 比例为8:1:1. 为去除量纲影响、确保模型公平性以及减少数据分布对优化算法的收敛速度和稳定性存在的影响, 采用Z-Score标准化数据[49].
3.2 机器学习模型
基于3.1节的数据集, 模型训练的数据符合小样本数据特点. 针对小样本特点及多因素影响下的夹持器流动特性的高维与非线性的适应性, 同时考虑到基于不同算法原理构建的机器学习模型对同一数据集会有不同的预测性能. 因此本文采用了支持向量回归(support vector regression, SVR)、随机森林(random forest, RF)、极限学习机(extreme learning machine, ELM)、人工神经网络(artificial neural network, ANN)和LSBoost与广义加性模型(generali-zed additive models, GAM) 6个机器学习模型, 并对它们的预测性能进行评估比较. 各模型原理及其超参数简要介绍如下.
3.2.1 支持向量回归(SVR)
SVR的目标是找到一个函数$ f(x) $, 尽可能地拟合训练样本, 通过设置不敏感损失函数阈值$ \varepsilon $和松弛变量$ \xi $, 忽略预测误差小于阈值$ \varepsilon $的样本点, $w$为权重向量系数. 其模型数学定义如下[50]
$$ \mathop {\min }\limits_{w,b} \frac{1}{2}\parallel w{\parallel ^2} + C\sum\limits_{i = 1}^N {({\xi _i} + {{\hat \xi }_i}} ) $$ (27) $$\left. \begin{aligned} &{\mathrm{s.t.}}\quad - {y_i} + w\phi ({x_i}) + b \leqslant \varepsilon + {\xi _i} \\ &\qquad\;\; {y_i} - w\phi ({x_i}) - b \leqslant \varepsilon + {{\hat \xi }_i} \\ &\qquad\;\; {\xi _i},{{\hat \xi }_i} \geqslant 0,i = 1,2,\cdots,N \end{aligned}\right\} $$ (28) 引入Largrange函数转化为对偶形式求解得到回归函数$f(x)$
$$ f(x) = \sum\limits_{i = 1}^q {({\alpha _i} - \alpha _i^*)K({x_i},x)} + {b^*} $$ (29) 式中$ ({\alpha _i} - \alpha _i^*) $为支持向量系数, $ K({x_i},x) $为核函数, 取前文的夹持器气体流动特性影响因素即夹持间隙等5个变量数据作为输入$x$, 吸持力数据作为$y$, $ {{\boldsymbol{x}}_i} \in {{\bf{R}}^5} $, ${{\boldsymbol{x}}_i}$为第$i$个训练样本的输入列向量, ${{\boldsymbol{x}}_i} = [x_i^1,x_i^2, \cdots ,x_i^5]$, $ {y_i} \in {{\bf{R}}^{}} $为对应的输出值. SVR的总体结构与神经网络较为近似, 原理与输入与输出示意如图14所示. 受篇幅限制, 因均为回归预测, 其他模型的输入与输出类型与其相同, 后续简洁给出.
SVR模型的预测效果主要受到正则化参数$ C $、阈值$ \varepsilon $以及核函数参数$ g $的影响.
3.2.2 随机森林(RF)
RF以决策树作为基学习器并在决策树的训练过程中引入随机选择的子集与属性, 通过对每棵决策树的预测结果取平均或加权平均得到最终的预测结果[51]. 模型数学定义如下
$$ {\hat y_i} = \frac{1}{{{N_{{\text{tree}}}}}}\sum\limits_{j = 1}^{{N_{{\text{tree}}}}} {{T_j}({{\boldsymbol{x}}_i})} $$ (30) 其中$ {T_j} $代表每颗决策树的结果, $ {N_{{\text{tree}}}} $为决策树个数, $ {{\boldsymbol{x}}_i} $为夹持器的气体流动特性影响因素数据列向量. RF模型的预测效果主要受到决策树数量、最小叶子节点样本数及最大分离特征数等影响.
3.2.3 极限学习机(ELM)
ELM模型训练阶段采用随机的输入层权值和偏差, 对于输出层权重则通过广义逆矩阵理论计算得到[52]. 设置隐含层节点, 在所有节点上的权值和偏置均得到后, 即完成训练用于后续预测. 模型输出用矩阵表示[53]
$$\qquad\quad \hat {\boldsymbol{y}} = {\boldsymbol{h}}({\boldsymbol{x}}) \times {\boldsymbol{\beta}} = {\boldsymbol{H}} \times {\boldsymbol{\beta}} = {\boldsymbol{L}} $$ (31) $$\qquad\quad {\boldsymbol{\beta}} = {{\boldsymbol{H}}^*} \times {\boldsymbol{L}} $$ (32) 其中$ {\boldsymbol{x}} $为网络输入即夹持器气体流动特性影响因素数据矩阵, $ {\boldsymbol{h}}({\boldsymbol{x}}) $为特征映射矩阵, ${\boldsymbol{ \beta}} $为输出权值, $ {\boldsymbol{L}} $为期望输出, $ {{\boldsymbol{H}}^*} $为$ {\boldsymbol{H}} $的Moore-Penrose广义逆矩阵. ELM模型的预测效果主要由隐含节点数h_n和激活函数等决定.
3.2.4 人工神经网络(ANN)
ANN通过反向传播迭代更新神经网络神经元权重${\boldsymbol{W}}$, 输入向量由输入层输入网络, 通过非线性激活函数$f$得到本层输出, 传递至下一层神经元, 并重复此过程直至传输至输出层得到预测结果. ${\boldsymbol{x}}$为夹持器气体流动特性影响因素数据矩阵, 模型输出使用矩阵形式表达为[54]
$$ \hat {\boldsymbol{y}} = f({{\boldsymbol{W}}^{\text{T}}}{\boldsymbol{x}} + {\boldsymbol{b}}) $$ (33) ANN模型的预测效果受到网络结构—各层神经元个数(h1_n, h2_n, h3_n)、激活函数和学习率等较多超参数影响.
3.2.5 LSBoost
LSBoost以决策树为弱学习器模型, 构建线性模型的集合来工作, 以迭代的方式逐步改进模型的预测能力, 最小化均方误差来优化模型进而确定每个弱学习器的权重和最终集成模型的形式[55]. 模型数学定义如下
$$ \hat {\boldsymbol{y}} = \sum\limits_{i = 1}^N {{\beta _i}} {h_i}({\boldsymbol{x}}) $$ (34) 其中$ {\beta _i} $为每个弱学习器的权重, $ {h_i}({\boldsymbol{x}}) $为每个弱学习器的输出, ${\boldsymbol{x}}$为夹持器气体流动特性影响因素数据矩阵. LSBoost模型的预测效果主要受到集成学习周期数, 学习率以及最小叶子节点样本数等较多超参数影响.
3.2.6 广义加性模型(GAM)
GAM利用非线性光滑函数对特征变量的作用进行建模, 并且通过非线性函数加和得到最终的预测结果[56]. 模型数学定义如下
$$ {\hat {\boldsymbol{y}}_i} = {\beta _0} + {f_1}\left( {{x_{i1}}} \right) + {f_2}\left( {{x_{i2}}} \right) + \cdots+{f_{{p}}}\left( {{x_{{{ip}}}}} \right) $$ (35) 其中$ {\beta _0} $是常数项, $ {f_1}{\text{, }}{f_2}{\text{, }}\cdots{\text{, }}{f_{\text{p}}} $是非线性的光滑函数, $ {{\boldsymbol{x}}_i} $为夹持器的气体流动特性影响因素数据列向量. GAM模型的预测效果主要受单变量形函数(预测树)数量与双变量形函数(交互树)数量影响.
3.2.7 模型评价指标
为量化机器学习模型的预测效果, 采用决定系数($ {{{R}}^2} $: 范围0 ~ 1)、平均绝对误差($ {{MAE}} $)以及均方根误差($ {{RMSE}} $)作为评价指标, $ {y_i} $为数据真实值, $ {\hat y_i} $为模型预测值, $ \bar y $为数据真实值的平均值, $ n $为数据量.
$$ {{{R}}^2} = 1 - {\sum\limits_{i = 1}^n {({y_i} - {{\hat y}_i})} ^2}\Biggr/{\sum\limits_{i = 1}^n {({y_i} - \bar y)} ^2} $$ (36) $$ {{MAE}} = 1 - \sum\limits_{i = 1}^n {\left| {{y_i} - {{\hat y}_i}} \right|} $$ (37) $$ {{RMSE}} = \sqrt {\frac{1}{n}{{\sum\limits_{i = 1}^n {({y_i} - {{\hat y}_i})^2} }}} $$ (38) 式中$ {{{R}}^2} $是衡量机器学习模型拟合优度的统计量, 它表示模型对观测值的拟合程度, 代表了模型中因变量可由自变量解释的百分比; $ {{MAE}} $描述了真实值与预测值的偏离程度; $ {{RMSE}} $描述了误差的平均大小, 并且对异常值敏感. $ {{{R}}^2} $值越接近1, $ {{MAE}} $与$ {{RMSE}} $值越小, 机器学习模型预测准确率越高.
3.3 智能算法优化机器学习模型超参数
群智能(swarm intelligence, SI)算法[57-58]与贝叶斯(Bayesian)算法被应用于机器学习模型的超参数优化中, 各机器学习模型超参数优化对应的算法如图15所示, 采用SI中的粒子群算法(PSO)[59]、北方苍鹰优化算法(NGO)[60]和鹈鹕优化算法(POA)[61]分别优化SVR、GAM和ELM模型的超参数, 初始种群数35, 迭代次数30. 采用贝叶斯优化[62]ANN、RF和LSBoost模型的超参数, Bayesian迭代30次.
![]()
图 15 各机器学习模型超参数优化对应的算法Figure 15. Algorithms corresponding to hyperparameter optimisation for various machine learning models4. 机器学习模型预测效果及讨论
4.1 特征相关性分析
为了对输入特征和输出特征进行相关性分析, 分别计算了Pearson相关系数、Spearman相关系数以及Kendall相关系数, 见式(39), 结果见图16和图17.
![]()
图 16 各特征参数与吸持力的相关性Figure 16. Correlation of each feature parameter with holding force![]()
图 17 各特征参数与气体消耗率的相关性Figure 17. Correlation of each feature parameter with gas consumption rate$$ {\text{Pearson}}(x,y) = \frac{{\displaystyle\sum\limits_{i = 1}^q {({x_i} - \bar x)({y_i} - \bar y)} }}{{{{\left[ {\displaystyle\sum\limits_{i = 1}^q {{{({x_i} - \bar x)}^2}\sum\limits_{i = 1}^q {{{({y_i} - \bar y)}^2}} } } \right]}^{1/2}}}} $$ (39) $$ {\text{Spearman(}}x,y{{) = 1 - }}\frac{{6\displaystyle\sum\limits_{i = 1}^q {{d_i}^2} }}{{q({q^2} - 1)}} $$ (40) $$\left.\begin{aligned} & {\text{Kendall(}}x,y{\text{) = }}\frac{{2\left(\displaystyle\sum\limits_{i = 1}^{q - 1} {\sum\limits_{j = j + 1}^q \xi } \right)}}{{q(q - 1)}}, \\ &\quad {\mathrm{if}}\;({x_i} - {x_j})({y_i} - {y_j}) > 0,\quad \xi = 1 \\ &\quad {\mathrm{if}}\;({x_i} - {x_j})({y_i} - {y_j}) = 0,\quad \xi = 0 \\ &\quad {\mathrm{if}}\;({x_i} - {x_j})({y_i} - {y_j}) < 0,\quad \xi = - 1\end{aligned}\right\}$$ (41) 式中$ q $为总观测样本数, $ {d_i} $为第$ i $个数据对的位次值之差.
如图16和图17所示, 3个相关系数的取值范围在−1 ~ 1之间, 绝对值越接近1, 相关性越强[63]. 输出特征吸持力与夹持器尺寸及夹持间隙呈正相关, 与喷嘴直径呈负相关, 与供气压力呈弱负相关. 输出特征气体消耗率与供气压力、喷嘴直径及夹持间隙呈正相关, 其中与夹持间隙正相关性程度最高, 与夹持器尺寸几乎无关. 各特征的相关性与第2节分析的规律大致吻合.
4.2 各机器学习模型对吸持力的预测效果
预测吸持力的各机器学习模型超参数设置和预测效果如表1所示, 以$ {{{R}}^2} $为主要评价指标依次进行排序得: ANN和LSBoost的准确率超过0.9, ANN的准确率最高为
0.9512 , 同时对应模型的$ {{MAE}} $和$ {{RMSE}} $也较低, ANN的$ {{MAE = 0}}{{.032\;458}} $和$ {{RMSE = }}0.045\;212 $最低, 各模型在测试集上的预测效果见图18, 图中$ y\_{{{\mathrm{value}}}} $为测试集上模型对吸持力的预测输出值, $ y\_{{{\mathrm{true}}}} $为吸持力真实值. 预测效果最差的为ELM, 其$ {{{R}}^2} $仅为0.64593 .表 1 预测吸持力的各模型超参数及预测效果Table 1. Hyper parameters and prediction effects of various models for holding forceModel Hyper parameters Prediction effects on the test set R2 MAE RMSE ANN h1_n:211, h2_n:292, h3_n:7, batch_size:24, activation function: sigmoid,
learning_rate:0.0062 0.9512 0.032458 0.045212 LSBoost num_learning cycles:70, learning_ rate: 0.33934 , min_samples_leaf:10.90729 0.053685 0.062316 SVR kernel: ‘polynomial’, C: 14.2472 , ε:1.14108 , g:1.6915 0.87492 0.055125 0.072381 GAM num_predictor trees:42, num_ interaction trees:9 0.83897 0.066984 0.082128 RF n_estimators:988, min_samples_leaf:1, max_features:3 0.76604 0.083493 0.098993 ELM h_n:190, activation function: sin, bach_size:18 0.64593 0.10909 0.12178 4.3 各机器学习模型对气体消耗率的预测效果
预测气体消耗率的各机器学习模型超参数设置和预测效果如表2所示, ANN、GAM和LSBoost准确率均超过0.95, 其中ANN的准确率最高为 0.9784, $ {{MAE}} $和$ {{RMSE}} $最低分别为
0.0099042 和0.022188 . 此外各模型在测试集上的预测效果见图19. 预测效果最差的为ELM, 其$ {{{R}}^2} $仅为0.73217 .表 2 预测气体消耗率的各模型超参数及预测效果Table 2. Hyper parameters and prediction effects of various models for gas consumption rateModel Hyper parameters Prediction effects on the test set R2 MAE RMSE ANN h1_n:65, h2_n:220, h3_n:45, batch_size:44, activation function: tanh,
learning_rate:0.0046 0.9784 0.0099042 0.022188 GAM num_predictor trees:159, num_ interaction trees:10 0.96432 0.014035 0.031213 LSBoost num_learning cycles:81, learning_ rate: 0.15185 , min_samples_leaf:10.96163 0.017045 0.03237 RF n_estimators:299, min_samples_leaf:1, max_features:5 0.94153 0.024918 0.039956 SVR kernel: ‘RBF’, C: 453.8064 , ε:0.002, g:50.93716 0.028926 0.041423 ELM h_n:152, activation function: sin,
bach_size:100.73217 0.068103 0.085518 ![]()
图 19 各模型对气体消耗率的预测效果Figure 19. Prediction effect of various models on gas consumption rate4.4 数据量对机器学习模型预测效果影响及讨论
分别用数据量为200, 300和432的数据集对各模型进行训练评估, 以${{{R}}^2}$为主要评价指标, 如图20所示, 可以发现: 在吸持力与气体消耗率的预测上, 各数据量下的ANN模型都优于其他模型, 数据量由300增至432后其预测准确率基本不变. 各机器学习模型的预测准确率${{{R}}^2}$随着数据量的增加都有所增大, 除LSBoost随着数据量的增加其${{{R}}^2}$较为均匀地增加外, 其余模型的${{{R}}^2}$均趋向稳定. 但LSBoost模型随着数据量的增加, 其最终对吸持力和气体消耗率的预测均取得了较为令人满意的结果.
![]()
图 20 数据量对各模型的预测效果影响Figure 20. The influence of data size on the prediction effect of various models4.5 夹持器参数预测与优化
采用前文中对吸持力预测准确率最优的ANN模型对不同夹持器尺寸下的最大吸持力进行预测并获取对应的各参数变量, 随后与数值方法计算的结果进行比较, 结果见表3. 随着夹持器尺寸增加, 最大吸持力下对应的夹持间隙以及喷嘴直径均增加. 预测的吸持力${F_{{\text{L-p}}}}$与数值方法计算的吸持力${F_{{\text{L-s}}}}$误差小于5%, 机器学习模型的预测效果十分接近实际数值计算结果. 定义G-F因子为产生单位吸持力${F_{\text{L}}}$所需的气体消耗率G, 其在一定程度上反应了夹持器工作过程的能耗. 预测了在夹持器尺寸为4 mm × 2 mm, 喷孔直径为0.47 mm时, 其工作过程中随夹持间隙、供气压力的改变所对应的G-F因子分布见图21. 由图可知, 为保证夹持器低G-F因子工作, 供气压力应控制在3 ~ 5 bar, 夹持间隙应控制在0.045 ~ 0.08 mm.
表 3 机器学习模型预测吸持力的最大值和对应的夹持器参数Table 3. Maximum values of holding force and corresponding gripper parameters predicted by machine learning modelGripper size
a × b/mm×mmClamping gap
hc/mmNozzle diameter
d/mmSupply pressure
P/barHolding force FL-p/N Holding force FL-s/N Relative error/% 4 × 2 0.084 0.47 4.9 0.1661 0.1617 2.72 5 × 3 0.092 0.59 5.0 0.4278 0.4130 3.58 5. 结论
本文通过数值方法探讨了夹持间隙、喷嘴直径、夹持器尺寸以及供气压力对微型伯努利夹持器内部的气体流动特性的影响, 并提出了一种基于机器学习与群智能/贝叶斯方法相结合的伯努力夹持器气体流动特性智能预测方法, 计算所用时间与常规模拟计算相比可忽略不计, 大大节省了实验和计算成本, 为夹持器性能预测、定制及优化设计创造了重要条件, 主要结论如下.
(1)微型伯努利夹持器的吸持力随着供气压力与夹持器尺寸的增大而增大, 随着夹持间隙与喷嘴直径的增大先增大后减小, 吸持力受多因素综合影响. 气体消耗率随供气压力、夹持间隙以及喷嘴直径的增大而增大. 气体压力分布特性上, 随着间隙增大, 负压峰值及区域呈先增大后减小趋势; 随着喷嘴直径增大, 负压区域先增加后减小, 负压峰值呈减小趋势; 随着供气压力增大, 其负压峰值及区域增大. 微型伯努力夹持器气体流动特性结果也可为诸如气浮轴承、航天器微低重力气浮模拟平台以及空天飞行器推进系统中的冲击冷却结构等狭小缝隙内的气体流动特性分析提供一定参考.
(2)基于数值方法产生的数据集, 建立的6个机器学习模型并运用智能优化算法进行超参数调优, 分别对夹持器的吸持力和气体消耗率进行预测. 其中ANN、GAM和LSBoost对气体消耗率的预测效果良好且接近, 决定系数$ {{{R}}^2} $在0.96左右, 在吸持力的预测上, ANN模型预测效果最好, 决定系数$ {{{R}}^2} $在0.95左右.
(3)采用提出的夹持器气体流动特性智能预测方法对不同夹持器尺寸下的最大吸持力进行预测, 与数值方法结果进行对比验证误差小于5%, 预测了夹持器工作时, 随着夹持间隙和供气压力变化的G-F因子分布, 为保证低G-F因子, 供气压力应控制在3 ~ 5 bar, 夹持间隙应控制在0.045 ~ 0.08 mm. 本文所提出的智能预测方法也可为空天飞行器的升阻、冷却特性在线感知与控制方法研究提供新思路.
在气体消耗率的预测上有3个机器学习模型准确率在0.96左右, 而在吸持力的预测准确率上仅神经网络模型预测较为优异, 后续拟考虑将效果较好且相近的模型进行组合形成新的机器学习模型提升预测效果. 此外由于不同的群智能算法具有不同的搜索策略和参数调整方式, 对于不同问题的适用性也不尽相同, 后续也将尝试更多的群智能优化算法对模型超参数进行寻优并比较; 另一方面将采用精密微尺度3D打印技术加工微型伯努利夹持器, 通过试验并结合数值模拟分析更复杂的现象, 如夹持器吸附工件的瞬态过程中的动力学质心变化与夹持超薄工件产生变形时的双向流固耦合等问题, 同时也能获得更丰富的数据集以训练出适应度更高的机器学习模型.
-
![]()
图 4 计算结果随网格数量的变化曲线
Figure 4. The variation curve of the calculation results with the number of grids
![]()
图 5 工件表面压力分布示意图
Figure 5. Schematic diagram of pressure distribution on the surface of the workpiece
![]()
图 6 不同夹持间隙下的工件表面压力分布曲线
Figure 6. Pressure distribution curve on workpiece surface with different gripping gap
![]()
图 7 吸持力、气体消耗率随夹持间隙的变化曲线
Figure 7. Curve of holding force and gas consumption rate with gripping gap
![]()
图 8 不同喷嘴直径下的工件表面压力分布曲线
Figure 8. Pressure distribution curve on workpiece surface with different nozzle diameter
![]()
图 9 吸持力、气体消耗率随喷嘴直径的变化曲线
Figure 9. Curve of holding force and gas consumption rate with nozzle diameter
![]()
图 10 不同夹持器尺寸下的工件表面压力分布曲线
Figure 10. Pressure distribution curve on workpiece surface with different gripper size
![]()
图 11 吸持力、气体消耗率随夹持器尺寸的变化曲线
Figure 11. Curve of holding force and gas consumption rate with gripper size
![]()
图 12 不同供气压力下的工件表面压力分布曲线
Figure 12. Pressure distribution curve on workpiece surface with different supply pressure
![]()
图 13 吸持力、气体消耗率随供气压力的变化曲线
Figure 13. Curve of holding force and gas consumption rate with supply pressure
![]()
图 15 各机器学习模型超参数优化对应的算法
Figure 15. Algorithms corresponding to hyperparameter optimisation for various machine learning models
![]()
图 16 各特征参数与吸持力的相关性
Figure 16. Correlation of each feature parameter with holding force
![]()
图 17 各特征参数与气体消耗率的相关性
Figure 17. Correlation of each feature parameter with gas consumption rate
![]()
图 19 各模型对气体消耗率的预测效果
Figure 19. Prediction effect of various models on gas consumption rate
![]()
图 20 数据量对各模型的预测效果影响
Figure 20. The influence of data size on the prediction effect of various models
表 1 预测吸持力的各模型超参数及预测效果
Table 1 Hyper parameters and prediction effects of various models for holding force
Model Hyper parameters Prediction effects on the test set R2 MAE RMSE ANN h1_n:211, h2_n:292, h3_n:7, batch_size:24, activation function: sigmoid,
learning_rate:0.0062 0.9512 0.032458 0.045212 LSBoost num_learning cycles:70, learning_ rate: 0.33934 , min_samples_leaf:10.90729 0.053685 0.062316 SVR kernel: ‘polynomial’, C: 14.2472 , ε:1.14108 , g:1.6915 0.87492 0.055125 0.072381 GAM num_predictor trees:42, num_ interaction trees:9 0.83897 0.066984 0.082128 RF n_estimators:988, min_samples_leaf:1, max_features:3 0.76604 0.083493 0.098993 ELM h_n:190, activation function: sin, bach_size:18 0.64593 0.10909 0.12178 
下载: 导出CSV
表 2 预测气体消耗率的各模型超参数及预测效果
Table 2 Hyper parameters and prediction effects of various models for gas consumption rate
Model Hyper parameters Prediction effects on the test set R2 MAE RMSE ANN h1_n:65, h2_n:220, h3_n:45, batch_size:44, activation function: tanh,
learning_rate:0.0046 0.9784 0.0099042 0.022188 GAM num_predictor trees:159, num_ interaction trees:10 0.96432 0.014035 0.031213 LSBoost num_learning cycles:81, learning_ rate: 0.15185 , min_samples_leaf:10.96163 0.017045 0.03237 RF n_estimators:299, min_samples_leaf:1, max_features:5 0.94153 0.024918 0.039956 SVR kernel: ‘RBF’, C: 453.8064 , ε:0.002, g:50.93716 0.028926 0.041423 ELM h_n:152, activation function: sin,
bach_size:100.73217 0.068103 0.085518
下载: 导出CSV
表 3 机器学习模型预测吸持力的最大值和对应的夹持器参数
Table 3 Maximum values of holding force and corresponding gripper parameters predicted by machine learning model
Gripper size
a × b/mm×mmClamping gap
hc/mmNozzle diameter
d/mmSupply pressure
P/barHolding force FL-p/N Holding force FL-s/N Relative error/% 4 × 2 0.084 0.47 4.9 0.1661 0.1617 2.72 5 × 3 0.092 0.59 5.0 0.4278 0.4130 3.58
下载: 导出CSV
-
[1] 《国家及各地区国民经济和社会发展第十四个五年规划和2035年远景目标纲要》. 中国信息界, 2022, (5): 110 (Outline of the fourteenth five-year plan and vision 2035 for national economic and social development of the state and regions. China Information Community, 2022, (5): 110 (in Chinese) Outline of the fourteenth five-year plan and vision 2035 for national economic and social development of the state and regions. China Information Community, 2022, (5): 110 (in Chinese)
[2] Zhang L. Silicon process and manufacturing technology evolution: An overview of advancements in chip making. IEEE Consumer Electronics Magazine, 2014, 3(3): 44-48 doi: 10.1109/MCE.2014.2317896
[3] Xu Q. Precision position/force interaction control of a piezoelectric multimorph microgripper for microassembly. IEEE Transactions on Automation Science and Engineering, 2013, 10(3): 503-514 doi: 10.1109/TASE.2013.2239288
[4] Mantriota G. Theoretical model of the grasp with vacuum gripper. Mechanism and Machine Theory, 2007, 42(1): 2-17 doi: 10.1016/j.mechmachtheory.2006.03.003
[5] Erzincanli F, Sharp JM. Development of a non-contact end effector for robotic handling of non-rigid materials. Robotica, 1997, 15(3): 331-335 doi: 10.1017/S0263574797000374
[6] Armengol J, Calbó J, Pujol T, et al. Bernoulli correction to viscous losses: Radial flow between two parallel discs. American Journal of Physics, 2008, 76(8): 730-737 doi: 10.1119/1.2897290
[7] Kamensky KM, Hellum AM, Mukherjee R. Power scaling of radial outflow: Bernoulli pads in equilibrium. Journal of Fluids Engineering, 2019, 141(10): 101201 doi: 10.1115/1.4043061
[8] Li X, Kagawa T. Theoretical and experimental study of factors affecting the suction force of a Bernoulli gripper. Journal of Engineering Mechanics, 2014, 140(9): 04014066 doi: 10.1061/(ASCE)EM.1943-7889.0000774
[9] Liu D, Teo CS, Liang W, et al. Soft-acting, noncontact gripping method for ultrathin wafers using distributed Bernoulli principle. IEEE Transactions on Automation Science and Engineering, 2018, 16(2): 668-677
[10] Welanetz LF. A suction device using air under pressure. 1956
[11] Wang S, Wang Y, Mei D, et al. Development of an annular-shaped Bernoulli gripper for contactless gripping of large-size silicon wafer//IEEE 16th International Conference on Nano/Micro Engineered and Molecular Systems (NEMS). IEEE, 2021: 1871-1876
[12] Liu D, Liang W, Zhu H, et al. Development of a distributed Bernoulli gripper for ultra-thin wafer handling//IEEE International Conference on Advanced Intelligent Mechatronics (AIM). IEEE, 2017: 265-270
[13] Failli F, Dini G. An innovative approach to the automated stacking and grasping of leather plies. CIRP Annals, 2004, 53(1): 31-34 doi: 10.1016/S0007-8506(07)60638-6
[14] Mykhailyshyn R, Savkiv V, Maruschak P, et al. A systematic review on pneumatic gripping devices for industrial robots. Transport, 2022, 37(3): 201-231
[15] Dini G, Fantoni G, Failli F. Grasping leather plies by Bernoulli grippers. CIRP Annals, 2009, 58(1): 21-24 doi: 10.1016/j.cirp.2009.03.076
[16] Shi K, Li X. Optimization of outer diameter of Bernoulli gripper. Experimental Thermal and Fluid Science, 2016, 77: 284-294 doi: 10.1016/j.expthermflusci.2016.03.024
[17] Yu X, Li X. Inertia-enhancement effect of divergent flow on the force characteristics of a Bernoulli gripper. Physics of Fluids, 2021, 33(5): 057108
[18] Giesen T, Bürk E, Fischmann C, et al. Advanced gripper development and tests for automated photovoltaic wafer handling. Assembly Automation, 2013, 33(4): 334-344 doi: 10.1108/AA-09-2012-075
[19] Sam R, Buniyamin N. A Bernoulli principle based flexible handling device for automation of food manufacturing processes//International Conference on Control, Automation and Information Sciences (ICCAIS). IEEE, 2012: 214-219
[20] Li X, Cao Q, Yu X. Experimental investigation and theoretical modeling on Bernoulli gripper using water for supply power enhancement. Physics of Fluids, 2024, 36(2): 027120
[21] Davis S, Gray JO, Caldwell DG. An end effector based on the Bernoulli principle for handling sliced fruit and vegetables. Robotics and Computer-Integrated Manufacturing, 2008, 24(2): 249-257 doi: 10.1016/j.rcim.2006.11.002
[22] Petterson A, Ohlsson T, Caldwell DG, et al. A Bernoulli principle gripper for handling of planar and 3D (food) products. Industrial Robot: An International Journal, 2010, 37(6): 518-526 doi: 10.1108/01439911011081669
[23] Takenaka T, Yamane R, Iwamizu T. Thrust of the disc valves. Bulletin of JSME, 1964, 7(27): 558-566 doi: 10.1299/jsme1958.7.558
[24] Jackson JD, Symmons GR. An investigation of laminar radial flow between two parallel discs. Applied Scientific Research, Section A, 1966, 15: 59-75
[25] Moller PS. A radial diffuser using incompressible flow between narrowly spaced disks. Journal of Basic Engineering, 1966, 88: 155-162
[26] Waltham C, Bendall S, Kotlicki A. Bernoulli levitation. American Journal of Physics, 2003, 71(2): 176-179 doi: 10.1119/1.1524162
[27] Shi K, Li X. Experimental and theoretical study of dynamic characteristics of Bernoulli gripper. Precision Engineering, 2018, 52: 323-331 doi: 10.1016/j.precisioneng.2018.01.006
[28] 刘昊阳, 杜强, 徐庆宗等. 冷气横流下复合角扩张孔的气膜冷却特性研究. 工程热物理学报, 2023, 44(10): 2685-2695 (Liu Haoyang, Du Qiang, Xu Qingzong, et al. Air film cooling characteristics of composite angular dilatation holes under cold air crossflow. Journal of Engineering Thermophysics, 2023, 44(10): 2685-2695 (in Chinese) Liu Haoyang, Du Qiang, Xu Qingzong, et al. Air film cooling characteristics of composite angular dilatation holes under cold air crossflow. Journal of Engineering Thermophysics, 2023, 44(10): 2685-2695 (in Chinese)
[29] 韦鼎元, 章思龙, 韦健飞等. 高马赫燃烧室离散孔燃料膜热防护和减阻特性研究. 航空学报, 2024, doi: 10.7527/S1000-6893.2023.29075 (Wei Dingyuan, Zhang Silong, Wei Jianfei, et al. Study on thermal protection and drag reduction characteristics of discrete hole fuel film for high Mach combustion chamber. Acta Aeronautica et Astronautica Sinica, 2024, doi: 10.7527/S1000-6893.2023.29075 (in Chinese) Wei Dingyuan, Zhang Silong, Wei Jianfei, et al. Study on thermal protection and drag reduction characteristics of discrete hole fuel film for high Mach combustion chamber. Acta Aeronautica et Astronautica Sinica, 2024, doi: 10.7527/S1000-6893.2023.29075 (in Chinese)
[30] Paivanas JA, Hassan JK. Air film system for handling semiconductor wafers. IBM Journal of Research and Development, 1979, 23(4): 361-375 doi: 10.1147/rd.234.0361
[31] Paivanas JA, Hassan JK. Attraction force characteristics engendered by bounded, radially diverging air flow. IBM Journal of Research and Development, 1981, 25(3): 176-186 doi: 10.1147/rd.252.0176
[32] Brun XF, Melkote SN. Modeling and prediction of the flow, pressure and holding force generated by a Bernoulli Handling Device. International Manufacturing Science and Engineering Conference, 2008, 4852(4): 351-358
[33] Pandya DA, Dennis BH, Russell RD. A computational fluid dynamics based artificial neural network model to predict solid particle erosion. Wear, 2017, 378: 198-210
[34] Wang W, Wang J, Tian J, et al. Application of digital twin in smart battery management systems. Chinese Journal of Mechanical Engineering, 2021, 34(1): 1-19 doi: 10.1186/s10033-020-00524-5
[35] 杜周, 徐全勇, 宋振寿等. 基于深度学习的压气机叶型气动特性预测. 航空动力学报, 2023, 38(9): 2251-2260 (Du Zhou, Xu Quanyong, Song Zhenshou, et al. Deep learning-based prediction of aerodynamic characteristics of compressor lobe shape. Journal of Aerospace Power, 2023, 38(9): 2251-2260 (in Chinese) Du Zhou, Xu Quanyong, Song Zhenshou, et al. Deep learning-based prediction of aerodynamic characteristics of compressor lobe shape. Journal of Aerospace Power, 2023, 38(9): 2251-2260 (in Chinese)
[36] 吕召阳,聂雪媛,赵奥博. 基于CNN机翼气动系数预测. 北京航空航天大学学报, 2023, 49(3): 674-680 (Lyu Zhaoyang, Nie Xueyuan, Zhao Aobo. Prediction of aerodynamic coefficients of wing based on CNN. Journal of Beijing University of Aeronautics and Astronautics, 2023, 49(3): 674-680 (in Chinese) Lyu Zhaoyang, Nie Xueyuan, Zhao Aobo. Prediction of aerodynamic coefficients of wing based on CNN. Journal of Beijing University of Aeronautics and Astronautics, 2023, 49(3): 674-680 (in Chinese)
[37] 张伟伟, 寇家庆, 刘溢浪. 智能赋能流体力学展望. 航空学报, 2021, 42(4): 26-71 (Zhang Weiwei, Ko Jiaqin, Liu Yilang. Prospects of intelligent empowered fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 26-71 (in Chinese) Zhang Weiwei, Ko Jiaqin, Liu Yilang. Prospects of intelligent empowered fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 26-71 (in Chinese)
[38] Wang Z, Chen H, Wang M, et al. Solid particle erosion prediction in elbows based on machine learning and swarm intelligence algorithm. Journal of Petroleum Science and Engineering, 2022, 218: 111042 doi: 10.1016/j.petrol.2022.111042
[39] 肖盛鹏, 朱宏博, 周岱等. 基于机器学习的弯管固液两相流流动特性研究. 力学学报, 2024, 56(3): 613-625 (Xiao Shengpeng, Zhu Hongbo, Zhou Dai, et al. Study on the flow characteristics of solid-liquid two-phase flow in bent based on machine learning. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 613-625 (in Chinese) Xiao Shengpeng, Zhu Hongbo, Zhou Dai, et al. Study on the flow characteristics of solid-liquid two-phase flow in bent based on machine learning. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 613-625 (in Chinese)
[40] 贺登辉, 李芮林, 孙帅辉等. 基于机器学习的离心泵气液两相压升预测. 农业工程学报, 2022, 38(4): 33-41 (He Denghui, Li Ruilin, Sun Shuaihui, et al. Prediction of gas-liquid two-phase pressure increment of a centrifugal pump based on machine learning. Transactions of the Chinese Society of Agricultural Engineering, 2022, 38(4): 33-41 (in Chinese) doi: 10.11975/j.issn.1002-6819.2022.04.004 He Denghui, Li Ruilin, Sun Shuaihui, et al. Prediction of gas-liquid two-phase pressure increment of a centrifugal pump based on machine learning. Transactions of the Chinese Society of Agricultural Engineering, 2022, 38(4): 33-41 (in Chinese) doi: 10.11975/j.issn.1002-6819.2022.04.004
[41] Brun X, Melkote SN. Effect of substrate flexibility on the pressure distribution and lifting force generated by a Bernoulli gripper. Journal of Manufacturing Science and Engineering, 2012, 134(5): 051010
[42] Shi K, Li X. Efficiency Improvement of electrically activated rotation-flow suction unit based on drag torque and suction force modeling. IEEE/ASME Transactions on Mechatronics, 2019, 25(2): 882-893
[43] 曾宇, 汪洪波, 孙明波等. SST湍流模型改进研究综述. 航空学报, 2023, 44(9): 103-134 (Zeng Yu, Wang Hongbo, Sun Mingbo, et al. A review of SST turbulence model improvement studies. Acta Aeronautica et Astronautica Sinica, 2023, 44(9): 103-134 (in Chinese) Zeng Yu, Wang Hongbo, Sun Mingbo, et al. A review of SST turbulence model improvement studies. Acta Aeronautica et Astronautica Sinica, 2023, 44(9): 103-134 (in Chinese)
[44] Menter FR, Esch T, Kubacki S. Transition modelling based on local variables. Engineering turbulence modelling and experiments 5. Elsevier Science Ltd, 2002: 555-564
[45] Menter FR, Langtry RB, Likki SR, et al. A correlation-based transition model using local variables—part I: Model formulation. Journal of Turbomachinery, 2006, 128(3): 413-422 doi: 10.1115/1.2184352
[46] Menter FR, Langtry R, Völker S. Transition modelling for general purpose CFD codes. Flow, Turbulence and Combustion, 2006, 77: 277-303 doi: 10.1007/s10494-006-9047-1
[47] Mykhailyshyn R, Duchoň F, Virgala I, et al. Optimization of outer diameter bernoulli gripper with cylindrical nozzle. Machines, 2023, 11(6): 667 doi: 10.3390/machines11060667
[48] 雷娟棉, 曹家伟. 高超声速圆锥边界层转捩反转数值研究. 北京理工大学学报, 2022, 42(10): 991-1001 (Lei Juanmin, Cao Jiawei. Numerical study on transition reversal of hypersonic cone boundary layer. Transactions of Beijing Institute of Technology, 2022, 42(10): 991-1001 (in Chinese) Lei Juanmin, Cao Jiawei. Numerical study on transition reversal of hypersonic cone boundary layer. Transactions of Beijing Institute of Technology, 2022, 42(10): 991-1001 (in Chinese)
[49] 王志红, 董梦龙, 张远军等. 基于PSO-SVR的重型柴油车NO x排放预测. 内燃机学报, 2023, 41(6): 524-531 (Wang Zhihong, Dong Menglong, Zhang Yuanjun, et al. Prediction of NO x emissions of a heavy-duty diesel vehicle. Transactions of CSICE, 2023, 41(6): 524-531 (in Chinese) Wang Zhihong, Dong Menglong, Zhang Yuanjun, et al. Prediction of NOx emissions of a heavy-duty diesel vehicle. Transactions of CSICE, 2023, 41(6): 524-531 (in Chinese)
[50] Tang KE, Weng CY, Cheng YC, et al. Typical signal anomaly monitoring and support vector regression-based surface roughness prediction with acoustic emission signals in single-point diamond turning. Journal of Manufacturing Processes, 2024, 112: 126-135 doi: 10.1016/j.jmapro.2024.01.036
[51] Sun Z, Wang G, Li P, et al. An improved random forest based on the classification accuracy and correlation measurement of decision trees. Expert Systems with Applications, 2024, 237: 121549 doi: 10.1016/j.eswa.2023.121549
[52] Akcan E, Kuncan M, Kaplan K, et al. Diagnosing bearing fault location, size, and rotational speed with entropy variables using extreme learning machine. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2024, 46(1): 4 doi: 10.1007/s40430-023-04567-2
[53] Anandhakumar C, Murugan NSS, Kumaresan K. Extreme learning machine model with honey badger algorithm based state-of-charge estimation of lithium-ion battery. Expert Systems with Applications, 2024, 238: 121609 doi: 10.1016/j.eswa.2023.121609
[54] De R. Learning representations by back-propagation errors. Nature, 1986, 323: 533-536 doi: 10.1038/323533a0
[55] Moudiki T. LSBoost Gradient Boosted Penalized Nonlinear Least Squares. 2020
[56] Ponnet J, Segaert P, Van Aelst S, et al. Robust inference and modeling of mean and dispersion for generalized linear models. Journal of the American Statistical Association, 2024, 119(545): 678-689 doi: 10.1080/01621459.2022.2140054
[57] Phan HD, Ellis K, Barca JC, et al. A survey of dynamic parameter setting methods for nature-inspired swarm intelligence algorithms. Neural Computing and Applications, 2020, 32(2): 567-588 doi: 10.1007/s00521-019-04229-2
[58] Kicska G, Kiss A. Comparing swarm intelligence algorithms for dimension reduction in machine learning. Big Data and Cognitive Computing, 2021, 5(3): 36 doi: 10.3390/bdcc5030036
[59] Zhan ZH, Zhang J, Li Y, et al. Adaptive particle swarm optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2009, 39(6): 1362-1381 doi: 10.1109/TSMCB.2009.2015956
[60] Dehghani M, Hubálovský Š, Trojovský P. Northern goshawk optimization: a new swarm-based algorithm for solving optimization problems. IEEE Access, 2021, 9: 162059-162080 doi: 10.1109/ACCESS.2021.3133286
[61] Trojovský P, Dehghani M. Pelican optimization algorithm: A novel nature-inspired algorithm for engineering applications. Sensors, 2022, 22(3): 855 doi: 10.3390/s22030855
[62] Sultana N, Hossain SMZ, Abusaad M, et al. Prediction of biodiesel production from microalgal oil using Bayesian optimization algorithm-based machine learning approaches. Fuel, 2022, 309: 122184 doi: 10.1016/j.fuel.2021.122184
[63] Li J, Zhou L, Wu Q, et al. Double stochastic preference analysis on group decision making with interval additive preference relations. Computers & Industrial Engineering, 2024, 190: 110056
-
期刊类型引用(1)
1. 张利缘. 轻韧型产品夹持器的自动化设计. 中国机械. 2025(08): 42-45 . 
百度学术
其他类型引用(0)
计量
- 文章访问数: 194
- HTML全文浏览量: 105
- PDF下载量: 80
- 被引次数: 1
