<p>Process damping plays a decisive role in the stability prediction of difficult-to-machine materials at low rotational speeds, thereby becoming a key focus in both academia and industrial manufacturing. Existing modeling methods for process damping in the milling of thin-walled components only achieve corrections for the cutting vibration effects in the feed direction or feed normal direction, failing to account for the influence of multi-factors of cutting velocity changes on process damping. Consequently, the applicability of these models requires further expansion. To address this, this article simultaneously considers the variations in actual cutting velocity due to three-directional vibrations of the tool-workpiece system, namely in the feed direction, feed normal direction, and tool axial direction. It characterizes the impact of velocity direction changes on dynamic cutting forces, establishes a multi-factor velocity-direction-variation damping model for thin-walled components, and performs chatter stability analysis accordingly. This extends the applicability of the stability prediction model for thin-walled components to complex scenarios involving dual-flexibility systems (both tool and workpiece), multi-directional vibrations (feed, feed normal, and tool axial directions), and coupled effects such as radial and axial cutting forces. Experimental validation through milling chatter tests on titanium alloy thin-walled components demonstrates that the predicted stability lobe diagrams for both peripheral and bottom edge milling process show good agreement with measured chatter results, confirming the effectiveness of the proposed method.</p>