processing． If the spindle angular swings in the plane，the workpiece will definitely generate tapers． With the assumed conditions，the calculation of the workpiece's taper is( 59. 804－58. 048) /100 = 0. 01756．When the swing frequency is lower than the spindle rotation frequency，the different swinging frequencies cause the tapers changing． The relationship is shown in Table 1．

  From Table 1，it can be seen that there is no linear correlation between the tapers and the swinging frequency． But when the swinging frequency is half of the rotation frequency ( n = 0. 5) ，the workpiece taper suddenly drops to the minimum value． It indicates that when n = 0. 5，spindle swinging has a minimal impact on the workpiece taper． Therefore， in the actual design and production，if the spindle swinging cannot be avoided，we should try to make swinging frequency close to half the value of rotation frequency to minimize taper error．

Table 1 Taper of the workpiece at different源'自^吹冰],论`文'网]www.chuibin.com

low swing frequencies3.2 Taper analysis at high swing frequency

  When the spindle swing frequency is greater than the spindle rotation frequency， referring to the conclusions，at different swing frequencies，the ideal diameter and the workpiece diameter are always equal． Therefore， with the assumed conditions，no matter how n changes; the workpiece will not generate taper． But its surface will generate larger waviness，roughness and the fluctuation of the cross-sectional contours will enlarge with the length of processing，so in this case the influence of the spindle swinging mainly reflects on the significant change of the surface quality．

4 Conclusions

  The spindle rotation error of machine tool significantly matters to the precision machinery design and manufacture． This paper analyzes the taper error caused by spindle swinging at different swinging frequencies and fills the blank theoretically in this field．

When the machine tool spindle occurs angular swingings，the workpiece taper changes along with the spindle swinging frequency． Specifically， when spindle swing frequency is high，the workpiece does not generate the taper，but it has great influence on surface quality; when the spindle swinging frequency is low，the workpiece generates the taper，and when the swinging frequency is half of the rotation

frequency，the taper approaches its minimum． In the practical design and production， the specific association should be fully taken into account． If the machining precision cannot meet the requirements，the equipment should be check in time and eliminate the factors that cause the spindle system angular swinging．

Ｒeferences

［1］ Zhang X J． Elementary technology of exchangeability measurement ［M］． Beijing: Tsinghua University Press，2013 ( in Chinese)

［2］ Wang X K． Technology of mechanical manufacture ［M］． Beijing: Machinery Industry Press，2013 ( in Chinese)

［3］ Yan S T，Chen H X． Mathematical analysis of the machining spindle movement ［J］．Mechanical Design and Manufacturing，1999( 2) : 40-42 ( in Chinese)

［4］ Yu X W． Mechanical manufacturing engineering［M］．Harbin: Harbin Institute of Technology Press，2011 ( in Chinese)

［5］ Wen X L，Lin S etc．Ultra precision machining technology and equipme［M］． Beijing:

Chemical Industry Press，2006 ( in Chinese)

［6］ Compilation group of“Mechanical Design Manual”． Mechanical design manual．2［M］．Beijing: Machinery Industry Press，1978 ( in Chinese)

摘要：本文重点探讨在普通车床主轴，定量分析加工精密主轴摆动几何方法，推导了不同摆动频率的加工误差的数学表达式，运用MATLAB模拟工件的横截面在不同的摆动频率，锥度，分析总结了变化规律。