中文摘要：

提出了离子束加工可达性问题的理论描述和定义，分析了驻留函数解的存在条件，进而分析了采用不同直径的离子束去除不同频率面形误差时额外去除量的大小，最后进行了仿真验证。分析结果表明，对于高斯型的束函数，驻留函数解总是存在的。但是面形误差频率越高，驻留函数解越太，去除面形误差时去除的额外材料越多。额外的材料去除量随着离子束径和空间误差波长之比（d／λ）的增加而指数增加。当d／λ=0．5时，额外材料去除量为15％，还是可以接受的；当d／λ=1时，额外材料去除量迅速上升到73％，该值即很难被接受。理论分析和仿真结果表明，为了优化加工过程，d／λ应该〈0．5。

英文摘要：

The conception and theoretical definition of machining reachability problem is proposed, and the existence condition of the solution of Dwell Time（DT） function is analyzed. Furthermore, we ana lyze and simulate the magnitude of the Extra Material Removal （EMR） in different process condition using different ion beam diameter to remove different spatial frequency surface errors. The analysis resuits show that the solution of DT function exists for the ion beam removal functions of G-aussian shape. However, for the higher spatial frequency surface error, the larger the solution of DT function is; the larger the magnitude of the EMR is. The magnitude of EMR is an exponential function of the ratio of ion beam diameter to the spatial surface error wavelength （i. e. d/λ）. And when d/λ= 0. 5, the EMR is 15%, which is acceptable in ion beam figuring process. When d/λ=1, it rapidly increases to 73 %, which is unacceptable. Theoretical analysis and simulation results indicate that d/λ should be less than 0.5 in Order to obtain acceptable process in 1BF.