Vibration Isolation of Extended Ultra-High Acceleration Macro–Micro Motion Platform Considering Floating Stator Stage

Abstract

It is a limitation for rapid development of microelectronics manufacturing industry to hardly overcome the acceleration limitation of macro–micro motion platform. The paper presents an extended ultra-high acceleration macro–micro motion platform to investigate breakthrough of acceleration limitation with driving modes “macro + micro + macro” (MMM). In the proposed platform, the number of the pair of VCMs was defined as n. Under ultra-high acceleration, floating stator stage is suggested to isolate the vibration and obtain superior performance of the platform. Its theoretical analyses including natural frequency analysis, transient response analysis and frequency response analysis are performed to verify vibration isolation of floating stator stage applied in the extended ultra-high acceleration macro–micro motion platform. The change trends and sensitivities of related objective functions incorporating vibration transmissibility, settling time and the maximum stroke of stator’s motion are explored with their related parameters, and their multi-objective optimization designs are carried out to achieve superior performances of different extended platforms. Moreover, one case is performed when n = 1. Its theoretical analyses, change trends and sensitivities are investigated. The superior performance of the platform is obtained to realize vibration isolation by multi-objective optimization. And its experiment of vibration isolation is also testified finally. The results provide a theoretical and technical basis on microelectronics manufacturing equipment upgrading and manufacturing rapid development.

Graphical Abstract

Appendices

Appendix A

Terms in Eq. (2):

$${\mathbf{M}}^{n} = \left[ {\begin{array}{*{20}c} {m_{{_{1} }}^{n} } & 0 \\ 0 & {m_{2} } \\ \end{array} } \right],{\mathbf{C}}^{n} = \left[ {\begin{array}{*{20}c} {2c_{{_{1} }}^{n} + 2c_{{_{0} }}^{n} } & { - \left( {2c_{{_{1} }}^{n} + 2c_{{_{0} }}^{n} } \right)} \\ { - \left( {2c_{{_{1} }}^{n} + 2c_{{_{0} }}^{n} } \right)} & {2c_{{_{1} }}^{n} + 2c_{{_{0} }}^{n} + c_{2} } \\ \end{array} } \right],{\mathbf{K}}^{n} = \left[ {\begin{array}{*{20}c} {2k_{{_{1} }}^{n} } & { - 2k_{{_{1} }}^{n} } \\ { - 2k_{{_{1} }}^{n} } & {2k_{{_{1} }}^{n} + k_{2} } \\ \end{array} } \right],{\mathbf{X}} = \left[ {\begin{array}{*{20}c} {x_{1} } \\ {x_{2} } \\ \end{array} } \right]\,{\text{and}}\,{\mathbf{F}}^{n} = \left[ {\begin{array}{*{20}c} {F_{{_{0} }}^{n} } \\ 0 \\ \end{array} } \right]$$

Appendix B

Input signal:

$$F^{n} \left( t \right) = \left\{ {\begin{array}{*{20}l} {\frac{{P^{n} }}{\xi }, \, 0 \le t \le \xi } \hfill \\ {0, \, t < 0\,or\,t > \xi } \hfill \\ \end{array} } \right.$$

Appendix C

Terms in Eq. (6):

$${\mathbf{A}}^{n} = \left[ {\begin{array}{*{20}c} 0 & 1 & 0 & 0 \\ { - \frac{{2k_{{_{1} }}^{n} }}{{m_{{_{1} }}^{n} }}} & { - \frac{{2c_{{_{1} }}^{n} }}{{m_{{_{1} }}^{n} }}} & {\frac{{2k_{{_{1} }}^{n} }}{{m_{{_{1} }}^{n} }}} & {\frac{{2c_{{_{1} }}^{n} }}{{m_{{_{1} }}^{n} }}} \\ 0 & 0 & 0 & 1 \\ {\frac{{2k_{{_{1} }}^{n} }}{{m_{2} }}} & {\frac{{2c_{{_{1} }}^{n} }}{{m_{2} }}} & { - \frac{{2k_{{_{1} }}^{n} + k_{2} }}{{m_{2} }}} & { - \frac{{2c_{{_{1} }}^{n} + c_{2} }}{{m_{2} }}} \\ \end{array} } \right],{\mathbf{B}} = \left[ {\begin{array}{*{20}c} 0 \\ { - \frac{1}{{m{}_{2}}}} \\ 0 \\ 0 \\ \end{array} } \right]\,{\text{and}}\,{\mathbf{C}} = \left[ {\begin{array}{*{20}c} 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right].$$

Appendix D

See Tables 3, 4, 5, 6 and 7.

Table 3 The optimal solution values when n = 1

Table 4 The optimal solution values when n = 2

Table 5 The optimal solution values when n = 3

Table 6 The optimal solution values when n = 4

Table 7 The optimal solution values when n = 5