考虑移动边界约束作用的薄壁件铣削动特性研究

王小娟; 宋清华; 刘战强; 王兵

doi:10.13433/j.cnki.1003-8728.20240078

考虑移动边界约束作用的薄壁件铣削动特性研究

doi: 10.13433/j.cnki.1003-8728.20240078

山东大学机械工程学院, 济南 250061

基金项目:

国家自然科学基金项目 52275445

山东省重点研发计划项目 202228125

详细信息

作者简介:
王小娟, 博士研究生, wxjuan@mail.sdu.edu.cn

通讯作者:
宋清华, 教授, 博士生导师, ssinghua@sdu.edu.cn

中图分类号: TH164
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- 被引次数: 0
出版历程
- 收稿日期: 2023-11-02
- 刊出日期: 2024-07-25

Research of Dynamic Characteristics in Milling of Thin-walled Parts Under Moving Boundary Constraint

School of Mechanical Engineering, Shandong University, Ji'nan 250061, China

摘要

摘要: 针对薄壁件铣削过程工件约束边界复杂及动特性难预测等问题, 创新性的提出了接触移动边界约束的概念, 深入研究了接触移动边界约束对系统动特性的影响规律。首先, 建立了考虑刀-工接触移动边界约束作用的薄板切削过程动力学模型, 提取刀-工接触区域, 分析了接触刚度力和阻尼力与接触参数的复杂影响关系。其次, 预测了任意接触移动边界约束作用的薄板动态响应, 形成了更为全面地任意边界约束选择方案, 包括接触移动边界条件和经典边界条件。基于薄板理论建立系统运动学方程, 综合考虑包括移动边界约束产生的能量项、常规任意边界约束产生的能量项以及薄板变形产生的能量项的组合。最后, 通过不同案例以及有限元法, 与现有文献中的数值、解析和实验等方法获得的结果作了大量对比, 证明了本文提出方法的准确性。结果表明, 接触移动约束效应对系统动态特性的影响不可忽视。
- 薄壁铣削 /
- 刀-工接触 /
- 移动约束边界 /
- 动态响应
Abstract: In view of the complexity of the workpiece constraint boundary and the difficulty of predicting the dynamic characteristics in the milling of thin-walled parts, the moving contact boundary constraint (MCC) was proposed, and the influence of MCC on the dynamic characteristics of the system was studied in detail. Firstly, a dynamic model for thin plate cutting was established considering the constraint of tool-worker contact moving boundary, and the tool-worker contact region was extracted, and the complex relationship between the contact stiffness and damping force and the contact parameters was analyzed. Secondly, the dynamic response of the thin plate under arbitrary MCC is predicted, and a more comprehensive selection scheme for arbitrary boundary constraints is formed, including contact moving boundary conditions and classical boundary conditions. The kinematic equation of the system is established based on the thin plate theory, and the combination of the energy term generated by MCC, conventional arbitrary boundary constraint and thin plate deformation is considered comprehensively. Finally, a large number of results via numerical, analytical and experimental methods in existing literature are compared with that under different cases and via finite element method to prove the accuracy of the present method. The results show that the effect of the contact movement constraint on the dynamic characteristics of the system cannot be ignored.
- thin-walled milling /
- tool-workpiece contact /
- moving constraint boundaries /
- dynamic response

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图 1 刀-工接触移动边界约束铣削系统模型

Figure 1. Model of milling system with tool-workpiece contact moving boundary constraint

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图 2 平衡状态下接触参数、切削深度的计算结果

Figure 2. Calculation results of contact parameters and cutting depth in equilibrium state

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图 3 不同接触边界移动速度对薄板响应影响(边界条件: SFSF)

Figure 3. Effects of different contact response of thin plate boundary moving speed on(boundary condition: SFSF)

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图 4 不同长厚比薄板在不同移动速度下的响应

Figure 4. Responses of thin plates with different length to thickness ratios at different moving speeds

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图 5 薄板在不同接触刚度下的动力响应

Figure 5. Dynamic response of thin plate under different contact stiffness

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图 6 悬臂板在不同移动边界约束位置的前4阶模态(边界条件: FCFF)

Figure 6. First four modes of thin plate under different moving boundary constraints positions(boundary condition: FCFF)

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图 7 简支-自由板在不同移动边界约束位置的前4阶模态(边界条件: SFSF)

Figure 7. First four modes of thin plate under different moving boundary constraints positions obtained(boundary conditions: SFSF)

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图 8 FEM获得的悬臂板在不同移动边界约束位置的前4阶模态(边界条件: FCFF)

Figure 8. First four modes of thin plate under different moving boundary constraints positions obtained by FEM (boundary conditions: FCFF)

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图 9 FEM悬臂板在不同移动边界约束位置的前4阶模态(边界条件: SFSF)

Figure 9. First four modes of thin plate under different moving boundary constraint positions obtained by FEM (boundary conditions: SFSF)

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表 1 不同边界约束的弹簧系数组合

Table 1. Combination of spring coefficients with different boundary constraints

约束方式		边界1	边界2	边界3	边界4
M_v	k_ct k_cr	k_ct k_cr	k_ct k_cr	k_ct k_cr	k_ct k_cr
F	k_t k_r	0 0	0 0	0 0	0 0
S	k_t k_r	∞ 0	∞ 0	∞ 0	∞ 0
C	k_t k_r	∞ ∞	∞ ∞	∞ ∞	∞ ∞
G	k_t k_r	0 ∞	0 ∞	0 ∞	0 ∞

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表 2 梁-板的几何及物理参数

Table 2. Geometric and physical parameters of beam-plate

参数	数值	参数	数值
长度L/m	0.103 60	密度ρ/(kg·m^-3)	10 686.9
宽度W/m	0.006 35	弹性模量E/GPa	206.8
厚度h/m	0.006 35	泊松比υ	0.29

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表 3 不同移动速度下的动态放大系数的对比

Table 3. Comparison of dynamic amplitude factor with different moving velocity

v_F(m·s^-1)	本文方法	文献[23]	文献[30]	文献[11]	文献[31]
15.6	1.063	1.063	1.063	1.045	1.025
31.2	1.124	1.127	1.151	1.350	1.121
62.4	1.273	1.275	1.281	1.273	1.258
93.6	1.580	1.586	1.586	1.572	1.572
124.8	1.705	1.708	1.704	1.704	1.701
156.0	1.721	1.729	1.716	1.716	1.719
250.0	1.530	1.530	1.542	1.542	1.548

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表 4 不同接触刚度的局部约束边界条件

Table 4. Boundary conditions of local constraints for different contact stiffness

案例	a	b	c	d
接触刚度K_C/(N·m^-1)	10³	10⁵	10⁷	10⁹
局部约束边界(y=W)	x=0-L, x=0-L/2, x=L/2-L

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表 5 方形板的几何及物理参数

Table 5. Geometric and physical parameters of square plate

长度L/m	宽度W/m	厚度h/m	密度ρ/(kg·m^-3)	弹性模量E/GPa	泊松比υ
1	1	0.065 5	7 850	200	0.3

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表 6 薄板前10阶固有频率

Table 6. First ten natural frequencies of thin plate Hz

	本文方法				有限元法				不考虑刀工接触约束
阶数	x₁	x₂	x₃	x₄	x₁	x₂	x₃	x₄	不考虑刀工接触约束
1	253.48	436.57	337.70	254.05	250.48	433.57	337.70	254.05	147.87
2	482.47	498.76	601.10	502.67	478.47	495.76	601.10	502.67	427.04
3	779.13	1 038.96	1 006.73	1 001.28	773.13	1 036.96	1 006.73	1 001.28	597.94
4	1 223.58	1 566.24	1 453.80	1 395.21	1 220.58	1 563.24	1 453.80	1 395.21	1 000.45
5	1 390.86	1 742.55	1 806.74	1 720.70	1 386.86	1 742.55	1 806.74	1 720.70	1 352.74
6	1 696.17	1 829.70	1 884.31	1 840.73	1 692.17	1 829.70	1 881.31	1 840.73	1 631.89
7	2 022.87	2 396.55	2 385.69	2 358.17	2 019.87	2 396.55	2 381.29	2 358.17	1 808.63
8	2 177.60	2 917.42	2 919.46	2 933.91	2 173.60	2 917.42	2 916.46	2 933.91	2 267.03
10	2 695.69	3 241.95	3 221.78	3 209.80	2 691.69	3 241.95	3 221.78	3 209.80	2 410.25

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