五轴线性刀路的局部能量光顺及奇异避免方法

陈良骥; 武文义; 李慧莹; 唐津梦; 魏子森

doi:10.13433/j.cnki.1003-8728.20230027

五轴线性刀路的局部能量光顺及奇异避免方法

doi: 10.13433/j.cnki.1003-8728.20230027

1.
天津工业大学机械工程学院, 天津 300387
2.
桂林理工大学机械与控制工程学院, 广西桂林 541006

基金项目:

广西自然科学基金项目 2021GXNSFAA220019

详细信息

作者简介:
陈良骥，教授，博士，1192500951@qq.com

中图分类号: TP391
计量
- 文章访问数: 8
- HTML全文浏览量: 3
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2022-04-20
- 刊出日期: 2024-07-25

Local Energy Smoothing and Singularity Avoidance Method of Five-axis Linear Toolpath

1.
School of Mechanical Engineering, Tiangong University, Tianjin 300387, China
2.
College of Mechanical and Control Engineering, Guilin University of Technology, Guilin 541006, Guangxi, China

摘要

摘要: 针对现行五轴加工中存在的路径拐角处平动轴减速过度, 奇异区域旋转轴角度变化剧烈的问题, 以AC双转台五轴机床为研究对象, 提出一种满足机床运动学约束的路径优化方法。该方法首先以刀心点光顺前后最大许用偏移量作为约束, 利用转角向量和双弦弓高进行建模, 寻求微小线段拐角处局部能量最优解。并对奇异范围内部和边缘的刀轴矢量点二次规划, 使得矢量末端刚好绕过单位球面上的奇异区域, 极大地保留原有加工特性。通过结合三角函数加减速控制算法, 对优化效果进行评估。仿真结果表明: 该路径优化方法在拟合偏差与弓高误差均没有超过许用值的同时, 平均进给速度提升了10.64%, 而且能有效避免加工中奇异现象的发生。可见本文所提出的方法在提高五轴加工效率和加工质量等方面具有较高的理论意义和实际应用价值。
- 五轴加工 /
- 局部能量光顺 /
- 奇异区域 /
- 运动控制
Abstract: Aiming at the problems existing in the current five-axis machining that the translation axis at the corner of the toolpath decelerates excessively and the angle of the rotation axis changes drastically in the singular area. This paper takes the AC dual-table five-axis machine tool as the research object and proposes a path optimization method that satisfies the kinematics constraints of the machine tool. Firstly, the method takes the maximum allowable offset before and after the smoothing of the tool center point as a constraint, and uses the corner vector and the double-chord bow height for modeling to seek the local energy optimal solution at the corner of the micro-line segment. Then the cutter axis vector points inside and at the edges of the singular range are planned again so that the end of the vector just bypasses the singular region on the unit sphere; thus the original machining characteristics are greatly preserved. Finally, the optimization effect is evaluated by the trigonometric function acceleration and deceleration control algorithm. The simulation results show that the path optimization method improves the average feed rate by 10.64% while the fitting deviation and bow height error do not exceed the allowable values, and can effectively avoid the occurrence of singularities in machining. Consequently, the proposed method has high theoretical significance and practical application value in improving the efficiency and quality of five-axis machining.
- five-axis machining /
- local energy smoothing /
- singular regions /
- motion control

HTML全文

图 1 相邻插补点间的弓高误差

Figure 1. Bow height error between adjacent interpolation points

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图 2 相邻插补点间的双弦弓高

Figure 2. Double-chord bow height between adjacent interpolation points

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图 3 局部能量光顺

Figure 3. Local energy smoothing

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图 4 AC双转台五轴机床正逆运动学变换

Figure 4. Forward and inverse kinematics transformation of AC dual-table five-axis machine tool

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图 5 Δc、γ₂、φ的曲面映射

Figure 5. The surface mappings of Δc、γ₂、φ

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图 6 单位球面刀轴矢量优化示意图

Figure 6. Unit spherical cutter axis vector optimization diagram

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图 7 实验所用自由曲面

Figure 7. The free surface used in the experiment

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图 8 三角函数加减速控制算法

Figure 8. Trigonometric function acceleration and deceleration control algorithm

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图 9 光顺前后进给速度分布

Figure 9. Feed rate distribution before and after smoothing

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图 10 光顺后拟合偏差分布

Figure 10. Fitting deviation distribution after smoothing

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图 11 C轴角速度变化情况

Figure 11. C-axis angular velocity changes

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图 12 C轴角加速度变化情况

Figure 12. Change of angular acceleration of C-axis

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图 13 未经过优化的刀轴轨迹

Figure 13. Unoptimized tool axis trajectory

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图 14 优化后的刀轴轨迹

Figure 14. Optimized tool axis trajectory

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表 1 机床约束条件

Table 1. Constraint conditions of machine tool

参数	数值
最大进给速度v_m	25 m/min
最大加速度a_m	3 000 mm/s²
许用弓高误差δ_max	4×10^-7 m
最大拟合偏差ε_max	8×10^-7 m
数控系统采样插补周期ΔT	0.02 s
A、C轴最大角速度	0.73 rad/s
A、C轴最大角加速度	30 rad/s²
权重系数λ	0.6

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表 2 光顺前后拐点处的进给速度

Table 2. Feed rates at turning points before and after smoothing

拐点位置	光顺前进给速度/(m·min^-1)	光顺后进给速度/(m·min^-1)
D₁	9.382	20.987
D₂	8.979	20.085
D₃	8.624	19.291
D₄	8.410	18.811
D₅	9.411	21.051
D₆	9.682	21.659

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