轴系空间运动测试及误差运动分析

发布时间：2018-06-12 03:54

本文选题：四点正交差分法 + 误差运动测试　；参考：《大连理工大学》2015年硕士论文

【摘要】：轴系中的回转轴,其理想运动是单自由度的回转运动,而真实运动状态则是复杂的空间六自由度运动,实际运动偏离理想运动的部分即为误差运动。本文以刚体运动学为基础,描述了回转轴的空间运动,揭示了轴系的误差运动测试与回转轴空间六自由度位姿的内在联系,并对误差运动的大小进行了评价和衡量。为准确分析轴系回转精度、研制空间误差运动测试装置提供了理论依据,具有一定的实用价值和应用前景。首先,将回转轴的运动等效为刚体的空间六自由度运动,采用齐次坐标变换的方法描述了回转轴的空间位姿,得到了轴上的观测点在静坐标系下的位移与刚体六个自由度的运动分量之间的关系,提出了轴系空间误差运动的概念,并分析了误差运动测量结果与回转轴的空间位姿之间的关系。其次,分析了回转轴径向运动的频率分量和周期特性,提出了四点正交差分法来实现轴系的径向误差运动测试,通过MATLAB算例对该方法进行验证。在此基础上,设计了轴系空间误差运动的试验方案,在两个平行截面上采用四点法,同时在轴端面进行轴向测量,通过计算可得到空间五个自由度的误差运动分量。对回转误差测试试验台进行改造,并对由试验台安装误差导致的系统误差进行了简要分析。空间误差运动试验共进行了三组,按空间方向误差和位置误差对轴系的空间误差运动进行数值评价,倾角运动的球面最小包络圆直径为0.107281μm,对应绕X轴和Y轴的最大倾角分别是0°0'13.57″和0°0'9.30",径向运动轨迹的平面最小包络圆直径为26.7563μm,轴向运动的曲线峰谷差值为9.324μm,符合一般精度轴承装配起来的简单轴系的回转精度情况。最后,用动态测量不确定度对径向误差运动的单圈重复性进行了分析,按最大极差评价为8.6675μm,按最大标准差评价为2.8896μm,说明了径向误差运动具有一定的单圈重复性。对径向传感器测量数据的多圈周期性进行了分析,在另外两组连续40圈回转的测试中,测量数据波动周期约为5圈,基本符合计算结果。
[Abstract]:The ideal motion of the rotation axis in the shaft system is a single degree of freedom rotational motion, while the real motion state is a complex spatial six degree of freedom motion. The actual motion deviating from the ideal motion is the error motion. Based on the rigid body kinematics, this paper describes the spatial motion of the rotation axis, reveals the inherent relationship between the measurement of the error motion of the shaft system and the position of six degrees of freedom in the rotation axis space, and evaluates and measures the magnitude of the error motion. It provides a theoretical basis for the accurate analysis of the rotation accuracy of shafting and the development of a measuring device for spatial error motion. It has certain practical value and application prospect. Firstly, the motion of rotation axis is equivalent to that of rigid body with six degrees of freedom, and the pose of rotation axis is described by the method of homogeneous coordinate transformation. The relation between the displacement of the observation point on the axis and the motion component of six degrees of freedom of the rigid body in the static coordinate system is obtained, and the concept of the spatial error motion of the shaft system is put forward. The relationship between the error motion measurement results and the spatial position and attitude of the rotation axis is analyzed. Secondly, the frequency components and periodic characteristics of radial motion of rotary shaft are analyzed, and a four-point orthogonal difference method is proposed to test the radial error motion of shaft system, and the method is verified by MATLAB example. On this basis, the experimental scheme of the spatial error motion of the shafting is designed. The four-point method is adopted on two parallel sections, and the axial measurement is carried out at the same time. The error motion components of five degrees of freedom in space can be obtained by calculation. The system error caused by the installation error of the test bed is analyzed briefly. Three groups of spatial error motion tests were carried out, and the spatial error motion of shafting was evaluated numerically according to spatial direction error and position error. The minimum envelope circle diameter of obliquity motion is 0.107281 渭 m, the maximum inclination angle about X axis and Y axis is 0 掳0N 13.57 "and 0 掳0N 9.30", respectively. The plane minimum envelope circle diameter of radial motion track is 26.7563 渭 m, and the curve peak and valley difference of axial motion is 9.324 渭 m. The rotation accuracy of a simple shaft system assembled with general precision bearings. Finally, the single loop repeatability of radial error motion is analyzed by dynamic measurement uncertainty. The maximum range is 8.6675 渭 m and the maximum standard deviation is 2.8896 渭 m, which shows that the radial error motion has a certain single loop repeatability. The periodicity of the measurement data of radial sensor is analyzed. The fluctuation period of the measured data is about 5 cycles in the other two groups of continuous 40 turns, which basically accords with the calculated results.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TH113.2;TH133.2

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