数控凸轮轴磨床运动误差分析与建模技术

范晋伟; 王鸿亮; 张兰清; 唐宇航

doi:10.11936/bjutxb2016040015

数控凸轮轴磨床运动误差分析与建模技术

doi: 10.11936/bjutxb2016040015

北京工业大学机械工程与应用电子技术学院, 北京 100124

基金项目: 国家科技重大专项资助项目(2013ZX04011013)；国家自然科学基金资助项目(51275014)

详细信息

作者简介:
作者简介: 范晋伟(1965—), 男, 教授, 博士生导师, 主要从事数控机床误差补偿技术方面的研究, E-mail:jwfan@bjut.edu.cn

中图分类号: TH161
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出版历程
- 收稿日期: 2016-04-06
- 网络出版日期: 2022-09-13
- 刊出日期: 2017-02-01

Motion Error Analysis and Modeling Technology of CNC Camshaft Grinder

College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China

摘要

摘要: 为了对某数控凸轮轴磨床的运动误差进行分析和建模,分析研究了各运动部件间运动形式和误差类型,运用相邻体坐标系间的运动变化来表达2相邻体之间的运动情况,建立了相邻体之间的理想运动方程和有误差情况下的实际运动方程. 将相邻体间的实际运动方程进一步推广到任意低序体阵列分析当中,为研究多分支数控凸轮轴磨床误差建模提供理论基础. 将复杂的多分支链数控凸轮轴磨床抽象为简单的多体系统,对各运动部件建立相应的体坐标系和运动参考坐标系,求出相邻体间对应的变换矩阵. 最后,将机床运动部件划分为“工件-床身”和“砂轮-床身”2条运动链,提出了有误差影响情况下实现精密加工约束条件方程为P_w=P_t,且对该方程进行了求解,为数控凸轮轴磨床误差补偿的研究提供了必要条件. 结果表明:误差补偿后的机床加工精度显著提高.
- 数控凸轮轴磨床 /
- 误差分析 /
- 多体系统 /
- 运动关系 /
- 误差建模
Abstract: Taking certain CNC camshaft grinder as the subject, its motion error analysis and modeling were studied. The movement forms and types of errors between the moving parts were analyzed, the movement between coordinate systems of the adjacent bodies was used to express the movement between the two adjacent bodies, and the ideal motion equation and actual motion equation in case of errors between the adjacent bodies were set up. Actual motion equation between adjacent bodies was made and further extended to analyze arbitrary low-order body arrays, which provides a theoretical basis for studying the multi-branch CNC camshaft grinding machine error modeling. Complex multi-branch chain CNC camshaft grinder simplified was made as a simple multibody system, and corresponding body coordinate systems and motion reference coordinate systems for moving parts were established to calculate the corresponding transformation matrix between adjacent bodies. Moving parts of the machine were divided into “workpieces-bed” and “wheel-bed” two kinematic chains. The precision constraint equation of the machine is P_w=P_t in case of using errors influence, and the constraint equation was solved. It provides necessary conditions for study of CNC camshaft grinder error compensation. Results show that the machine precision is significantly improved after error compensation.
- CNC camshaft grinder /
- error analysis /
- multibody system /
- motion relationship /
- error modeling
The authors have declared that no competing interests exist.

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图 1 数控凸轮轴磨床结构

Figure 1. Structure map of CNC camshaft grinder

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图 2 误差参数

Figure 2. Sketch map of error parameters

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图 3 数控凸轮轴磨床拓扑结构

Figure 3. Topology structure map of CNC camshaft grinder

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图 4 理想情况下相邻体相对运动

Figure 4. Relative movement between neighboring bodies in ideal conditions

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图 5 有误差情况下相邻体相对运动示意图

Figure 5. Relative movement between neighboring bodies in errors

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图 6 数控凸轮轴磨床拓扑结构

Figure 6. Topology structure map of CNC camshaft grinder

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表 1 数控凸轮轴磨床几何误差参数

Table 1. Geometric parameters of CNC camshaft grinder

误差性质	线位移误差	角位移误差
误差方向	沿x、沿y、沿z	绕x、绕y、绕z
沿x平移	δ_x(x)、δ_y(x)、δ_z(x)	ε_x(x)、ε_y(x) 、_z(x)
沿z平移	δ_x(z)、δ_y(z)、δ_z(z)	ε_x(z)、ε_y(z)、ε_z(z)
绕c转动	δ_x(c)、δ_y(c)、δ_z(c)	ε_x(c)、ε_y(c)、ε_z(c)
交叉	ε_xz、ε_xc、ε_zc

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表 2 数控凸轮轴磨床拓扑结构的低序体阵列

Table 2. Number array of low-order body for CNC camshaft grinder

L⁰(k)	2	3	4	5	6	7	8
L¹(k)	1	2	3	4	1	6	7
L²(k)	0	1	2	3	0	1	6
L³(k)	0	0	1	2	0	0	1
L⁴(k)	0	0	0	1	0	0	0
L⁵(k)	0	0	0	0	0	0	0

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参考文献(12)

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