基于工件振动和刀具结构的周铣表面形貌分析与预测

doi:10.12382/bgxb.2022.0289

摘要/Abstract

摘要：

在铣削加工过程中,受铣削振动等因素的影响,已加工表面的不同位置会存在结构上的差异,严重影响已加工表面的加工质量。研究加工表面形貌的铣削成形方法对预测表面粗糙度和选取合理的加工参数具有重要意义。通过将“工件-夹具”接触模型合理地等效为线性“弹簧-阻尼”系统,利用能量法推导出工件在铣削过程中的振动微分方程。利用坐标转化法,提出有约束振动微分方程的模态分析与解耦方法,实现工件位置偏离的解算与预测。通过研究刀具接触点的判断方法,建立周铣过程中切削刃的运动轨迹方程,进一步结合工件的位置偏离提出工件表面形貌的表面形貌离散算法。利用铣削实验直接或间接地验证工件周铣形貌离散算法的有效性,结果表明:不考虑装夹振动的铣削表面粗糙度最大误差为7.56%,相比于不考虑装夹振动,考虑装夹振动的接触力和表面粗糙度的计算精度分别提高了3%和4.72%(逆铣)/3.00%(顺铣)。

关键词: 铣削加工, 工件位置偏移, 铣削振动, 表面形貌

Abstract:

In the milling process, vibrations can lead to variations in the structure of machined parts, significantly influencing the machining quality of the finished surface. Therefore, investigating the milling formation method of the machined surface morphology is of great significance for predicting surface roughness and selecting reasonable machining parameters. First, by equivalently transforming the contact mode between workpiece and fixture into a linear spring damping system, the vibration differential equation of the workpiece is derived for the milling process by using the energy method. By using the coordinate transformation method, the modal analysis solution method is proposed for the vibration differential equations with constraint conditions to obtain the workpiece position deviation. Secondly, a method for determining the tool contact point and establishing the motion trajectory equation for the cutting edge in peripheral milling is presented. This enables the development of a discrete algorithm for surface topography by incorporating the workpiece position deviation. Experimental validations are conducted to verify the proposed algorithm for peripheral milling topography simulation. The results show that the maximum surface roughness error is 7.56% without considering the fixturing layout vibration, whereas the maximum contact force error is no more than 12% with fixturing layout vibration. Compared with calculations without clamping vibration considered, the calculation accuracy of contact force and surface roughness considering clamping vibration are improved by 3% and 4.72% (up milling)/3.00% (down milling), respectively.

Key words: milling, workpiece position deviation, milling vibration, surface topography

刘扬, 秦国华, 吴竹溪, 娄维达, 赖晓春. 基于工件振动和刀具结构的周铣表面形貌分析与预测[J]. 兵工学报, 2023, 44(7): 2132-2146.

LIU Yang, QIN Guohua, WU Zhuxi, LOU Weida, LAI Xiaochun. Analysis and Prediction of Surface Topographyin Peripheral Milling Based on Workpiece Vibration and Milling-Tool Structure[J]. Acta Armamentarii, 2023, 44(7): 2132-2146.

图/表 18

图1 工件振动模型

Fig.1 Workpiece vibration model

图2 周铣切削刃运动示意图

Fig.2 Diagram of peripheral milling cutting edge movement

图3 坐标平面Oxy内的表面成形示意图

Fig.3 Diagram of surface formation in the coordinate plane Oxy

图4 周铣实验

Fig.4 Peripheral milling experiment

表1 周铣加工参数

Table 1 Peripheral milling parameters

刀具与工艺	参数	数值
	齿数z	2
刀具	半径R/mm	5
	螺旋角β/ (°)	45
	刃长L/mm	10
工艺	主轴转速ω/(r·min^-1)	500
	进给速度v_f/(mm·min^-1)	600

图5 不考虑振动的表面形貌

Fig.5 Surface morphology without considering vibration

图6 稳态加工中的实际加工表面(左为实际加工表面,中为黑白仿真表面,右为彩色仿真表面)

Fig.6 Actual machined surface in stable machining(the left represents the actual machining table, the middle represents the black and white simulated surface, and the right represents the colored simulated surface)

图7 粗糙度测量

Fig.7 Roughness measurement

表2 周铣形貌仿真实验验证结果

Table 2 Experimental verification of surface morphology

铣削方式	实测粗糙度/μm	仿真粗糙度/μm	相对误差/%
逆铣	2.428	2.294	5.52
顺铣	3.057	2.826	7.56

图8 3-2-1装夹方案

Fig.8 3-2-1 fixturing layout

表3 定位元件的位置与法向量

Table 3 Position and normal vector of locators

图9 不考虑阻尼的工件位置变化

Fig.9 Workpiece position error without damping

图10 考虑阻尼的工件位置变化

Fig.10 Workpiece position error with damping

图11 实验装置

Fig.11 Experimental device

图12 支撑反力

Fig.12 Supporting reaction force

图13 逆铣形貌

Fig.13 Morphology of up milling

图14 顺铣形貌

Fig.14 Morphology of down milling

图15 截面轮廓对比

Fig.15 Profile comparison

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