<p>Envelope-free error evaluation model simplifies the complex arithmetic of standard machining error recommended by the ISO, and it is preferable in application. However, a theoretical analysis on the difference between standard machining errors and envelope-free ones is still missing, which may weaken the feasibility of envelope-free errors in tool path optimization for 5-axis flank milling, especially when cutter runouts or circle-segment cutters are considered. In this paper, a simple error evaluation model which measures the cutter-workpiece distance in plane spanned by the normal vector of the design surface and the tool axis is adopted. This tool-axis-based error is analyzed quantitatively with a comparison to the envelope-based error to demonstrate the difference between the two kinds of errors is a high-order small quantity under certain condition which is described with a simple formula. On base of tool-axis-based errors, the linear relation between error variations and differential displacements of the tool axis trajectory surface is established, and an improved minimax tool path optimization model regarding both the global and local machining errors is accordingly provided. In addition, the established model can serve as a general framework to cope with flank milling with runouts or circle segment cutters. Finally, numerical simulation and experimental cutting are given to verify our proposition and methods.</p>