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摘要:
大行程柔性微定位平台在运动过程中不可避免地产生伴生转动现象，并对其定位精度造成消极影响。为降低伴生转动对平台定位精度的影响，提出一种基于柔性杆的三移一转（3-PPPR）型大行程柔性微定位平台，基于线弹性梁理论模型并考虑柔性杆轴向形变，对两移一转（PPR）柔性运动副伴生转角进行了理论建模，并基于此完成了对所提平台在单轴、双轴及三轴驱动时产生伴生转角的理论分析；再采用有限元分析对理论模型进行验证。最后探究了柔性杆尺寸参数与平台伴生转角之间的灵敏度关系，为所提平台性能提升奠定了基础，并据此提出了改善所提平台运动性能的优化方案。结果表明：3种驱动条件下平台伴生转角理论值与仿真值最大相对误差为2.46%。
Abstract:Parasitic rotation is inevitable during the movement of large stroke compliant micro-positioning platforms, causing a negative impact on their positioning precision. To reduce this effect, a 3-PPPR compliant micro-positioning platform with large stroke is proposed based on compliant beams. Then, based on linear elastic beam theory, the theoretical parasitic rotational angle of the PPR compliant kinematic joint is modeled considering the axial deformations of the beams. The parasitic rotational angles of the platform are also analyzed theoretically in uniaxial, biaxial and triaxial cases. Furthermore, the theoretical models are verified by finite element analysis. Finally, the sensitivity between the dimension parameters of the compliant beams and the parasitic rotational angle of the platform is analyzed, laying a foundation for the improvement of the platform. On this basis, the optimization schemes are proposed to improve the motion performance of the platform. results show that the maximum relative errors of the theoretical and simulated values of the parasitic rotational angle is 2.46% in three driven cases.
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图 6 外四杆结构受力形变示意图
Figure 6. Deformation of external beams subjected to horizontal force
图 8 内四杆结构受力形变示意图
Figure 8. Deformation of internal beams subjected to horizontal force
图 15 不同驱动条件下平台的仿真分析
Figure 15. Simulation analysis of platform under different driving conditions
图 17 平台伴生转角与柔性杆尺寸参数之间的关系
Figure 17. Relationship between beam parameters and parasitic rotation of platform
表 1 平台材料及尺寸参数
Table 1. Material and dimension parameters of platform
参数 数值 参数 数值 l/mm 40 弹性模量E/GPa 71.7 t/mm 1 剪切模量G/GPa 26.9 d/mm 24 泊松比ν 0.33 s/mm 6 屈服强度σ/MPa 503 L/mm 47 密度ρ/(kg·m−3) 2 810 D/mm 25 
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表 2 平台伴生转角理论、仿真值及其相对误差
Table 2. Theoretical values, simulation values and relative errors of parasitic rotational angles
运动状态 伴生转角 理论值/rad 仿真值/rad 相对误差/% 单支链 ${\theta _{{\text{limb}}}}$ 8.96×10−4 8.77×10−4 2.12 x单轴 $\theta _y^x$ 4.48×10−4 4.39×10−4 2.01 $\theta _z^x$ 4.48×10−4 4.40×10−4 1.79 x、y
双轴$\theta _x^{xy}$ 4.48×10−4 4.37×10−4 2.46 $\theta _y^{xy}$ 4.48×10−4 4.42×10−4 1.34 $\theta _z^{xy}$ 0 1.2×10−7 x、y、z
三轴$\theta _x^{xyz}$ 0 4.0×10−7 $\theta _y^{xyz}$ 0 8.8×10−7 $\theta _z^{xyz}$ 0 4.0×10−7
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