目的 针对多种表面粗糙度影响因素的耦合作用使轮廓形成机理不清，导致表面粗糙度数学模型存在表面质量智能管控工业应用预测精度不足的技术难题，建立端面铣削工件表面粗糙度数学模型。方法 首先，基于加工运动学机理和刀具几何学分析端面铣削工件表面轮廓形成机理，建立考虑刀具跳动的工件表面轮廓模型以及轮廓高度偏差关于铣削力的补偿函数，并通过卷积神经网络(Convolution Neural Network，CNN)进行解析。其次，建立端面铣削表面粗糙度数学模型。最后，进行可转位面铣刀端面铣削ZG32MnMo的实验验证，分别采集轮廓数据与铣削力信号，建立以铣削力为输入、轮廓高度偏差数据为输出的铣削数据集，训练卷积神经网络解析轮廓高度补偿值并验证理论模型的准确性，对比分析考虑刀具跳动的表面粗糙度数学模型与CNN优化考虑刀具跳动的表面粗糙度数学模型的精度。结果 CNN优化考虑刀具跳动的表面粗糙度数学模型对加工重叠区与非重叠区内沿刀具进给方向的轮廓算术平均偏差Ra的预测误差分别为18.71%和14.14%，与考虑刀具跳动的表面粗糙度数学模型相比，精度分别提高了10.61%和32.83%，CNN优化考虑刀具跳动的表面粗糙度数学模型对轮廓单元的平均宽度Rsm和支承长度率Rmr(c)的预测结果与实验值吻合。结论 考虑刀具跳动以及动态铣削力耦合作用边界条件的表面粗糙度数学模型能够有效预测端面铣削表面粗糙度，可为在质量管控工程中的应用提供理论指导与技术支撑。

Surface roughness has a significant impact on the wear resistance, corrosion resistance, and reliability of components. Accurate prediction of surface roughness can effectively control the manufacturing process and optimize processing parameters. However, the coupling effects of various influencing factors on surface roughness obscure the formation mechanism of profiles, leading to technical challenges in the insufficient predictive accuracy of mathematical models for surface roughness intelligent control in industrial applications. This study established a mathematical model for surface roughness in face milling to address this issue. Firstly, the surface profile forming mechanism of face milling workpiece was analyzed and the surface profile model along the tool feed direction was established based on tool geometry and machining kinematics, taking into consideration the tool runout boundary conditions. The mapping between dynamic factors (tool wear, tool vibration, elastic recovery) and surface roughness was established through the milling force. The compensation function of profile height deviation about milling force was established and resolved by a convolutional neural network (CNN) which contained 5 convolutional layers and 3 fully connected layers. Next, the mathematical model for surface roughness in face milling was developed, with Ra serving as a characterization parameter for surface roughness. Finally, the face milling ZG32MnMo experiment was carried out to collect the profile data and milling force signals respectively, which used indexable face milling cutters. The milling data set was established with cutting force as input and profile height deviation data as output. The CNN was trained and the profile height compensation values was analyzed. CNN training results showed RMSE of 0.81 μm and 0.84 μm for the training and test sets, respectively. Through CNN, compensation values for profile height were analyzed to enhance the prediction accuracy of the mathematical model for surface roughness. The surface roughness mathematical model accuracy was validated. Surface roughness mathematical model considering tool runout and surface roughness mathematical model considering tool runout optimized by CNN were compared in terms of accuracy. The results showed that the surface roughness mathematical model considering tool runout optimized by CNN and the surface roughness mathematical model considering tool runout predicted Rsm and Rmr(c) close to the experimental values in the overlapping and non-overlapping along the feed direction, and the surface roughness mathematical model considering tool runout optimized by CNN exhibited higher predictive accuracy for Rmr(c) compared with the surface roughness mathematical model considering tool runout. The surface roughness mathematical model considering tool runout optimized by CNN predicted errors for Ra in the overlapping and non-overlapping along the tool feed direction to be 18.71% and 14.14%, respectively, while the surface roughness mathematical model considering tool runout predicted errors of 29.32% and 46.97% in the same regions. The surface roughness mathematical model considering tool runout optimized by CNN improved the accuracy by 10.61% and 32.83%, respectively, compared with the surface roughness mathematical model considering tool runout. The surface roughness mathematical model established by considering the boundary conditions of tool runout and dynamic milling force coupling can effectively characterize the surface roughness of face milling and provide reference for its application in quality control engineering.