中图分类号：TH161 DOI：10.3969/j.issn.1004-132X.2025.04.004

Instantaneous Milling Force Modeling and Coefficient Calibration Method of Variable Helical Circular-arc End Mills with Unequal Rake Angle

QI Shutao LI Jiaqi ZHENG Shucai XU Jinting SUN Yuwen* School of Mechanical Engineering，Dalian University of Technology，Dalian，Liaoning，

Abstract：Variable helical end mills with unequal rake angle maight effectively suppress milling chatters，which significantly improved the machined surface quality and simultaneously reduced the risk of tool breakages，however，due to the unequal geometric parameters of each cuttng edge，the existing models had dificulty to accurately predict the cuting forces，hence，a new instantaneous milling force modeling and coefficient calibration method were proposed. Firstly，the geometry and position relational expression of the cuting edges for variable helical circular-arc end mills were given， then considering the tool runout and variation of geometrical parameters of cutting edges，an instantaneous uncut chip thickness calculation and element cuting force prediction model was established; Subsequently，a nonlinear optimization method to simultaneously calibrate the cutting force coefficients and tool runout parameters was proposed，and an efcient algorithm for solving the model parameter initial values was also given based on linear least squares and oblique cutting theory. The experimental results show that the amplitude and waveform of predicted cutting forces are consistent with the measured ones with errors of less than 15% ，verifying the effectiveness of the proposed model.

Key words： unequal rake angle; variable helix end mill; flank milling； milling force;cutting force coefficient identification

0 引言

变螺旋铣刀因其优异的抑振性能而在航空航天等领域结构件的加工中得到广泛应用[1]。然而，因变螺旋铣刀各齿螺旋角不同，导致各刀刃强度也不相同，从而显著增加了崩刃风险。对各刀齿采用不等前角设计可有效解决上述问题2，但与常规铣刀相比，不等前角变螺旋铣刀各刀齿的前角和螺旋角均不相同，理论上各齿切削力系数也存在较大差异，因此，为了实现对该类刀具切削力的准确预测，需针对上述问题开展相关的建模分析。

当前，对切削力的建模主要包括经验模型[3]、有限元仿真模型[4]、基于切削机理的解析模型[5]、机械力学模型[6-7]等，其中机械力学模型由于可实现对瞬时切削力的准确预测而在铣削加工中广泛应用。以机械力学模型为基础，目前针对变螺旋铣刀切削力系数的标定主要有两种处理方式。一是对于等法向前角的刀具，通常忽略螺旋角差异引起的影响，假定各齿切削力系数是一致的。如NIU等8假定各齿切削力系数相同，以此建模并通过非线性优化实现切削力系数与跳动参数的并行标定，实验结果也证实了其假设的可行性。目前该假设在等前角变螺旋铣刀的动力学建模中广泛应用[9-10]。二是基于正交斜变换计算各个刀齿的切削力系数，该方法的关键在于获取与工件-刀具相关的材料剪切屈服强度、剪切角、摩擦角等参数。如CHEN等[11]基于斜角切削理论，引入材料J-C本构来计算上述参数，该方法无需开展加工实验，但需提前明确材料的本构参数，同时由于模型存在较多假设，辨识精度较难保证。……