The tool run-out significantly affects prediction of milling force, which is crucial for monitoring the micro-end-milling processes. For accurately predicting milling force, a novel tool run-out model is presented, which is based on spatial tool position to reflect a more realistic clamping situation. In the established model, the direction vector $\stackrel{⃑}{s}$ of the tool axis replacing the location angle ψ and tilt angle τ is firstly proposed to describe the tool position in space to simplify the calculation. The mechanistic cutting force model, which is relevant to instantaneous uncut chip thickness (IUCT), is adopted to predict milling force. An accurate IUCT at different axial positions is calculated by incorporating the proposed run out model on spatial tool position. The predicted cutting forces show a close agreement with the experimental cutting force. The proposed run-out model can be employed to identify the tool state as well as predict cutting force, thereof monitor the machining process.

刀具跳动显着影响铣削力的预测，这对于监测微端铣削过程至关重要。为了准确预测铣削力，提出了一种新颖的刀具跳动模型，该模型基于空间刀具位置来反映更真实的夹紧情况。在建立的模型中，方向向量$\stackrel{⃑}{秒}$首先提出用刀具轴的位置角ψ和倾斜角τ来描述刀具在空间中的位置，以简化计算。采用与瞬时未切削切屑厚度（IUCT）相关的机械切削力模型来预测铣削力。通过在空间工具位置上结合建议的跳动模型，计算不同轴向位置的准确 IUCT。预测的切削力与实验切削力非常吻合。提出的跳动模型可用于识别刀具状态以及预测切削力，从而监控加工过程。