中文摘要：

随着微纳米测量系统中测头微探球尺寸的不断减小和测量不确定度要求的不断提高，测力所引起的力变形误差对测量系统不确定度有着不可忽略的影响。根据Hertz理论，构建了微探球与工件接触时的接触模型、微探球与试样力变形模型，给出了最大允许测力估计方法和力变形计算方法。以现有的3种微纳米三坐标测量机微探球为参考，分别估计了允许最大测力及引起的力变形。结果表明，对于纳米量级测量不确定要求，接触式测量中微探球的受力变形误差是不可忽略的。

英文摘要：

As the size of microball used for micro-nano measurement system decreased continuous- ly and the uncertainty of measurement in nanometer measurement should be improves constantly,the influence of deformation caused by measurement force on the uncertainty of the measurement system was becoming an issue gradually that could not be ignored. Herein,the contact model between the microball and the workpiece, and the force deformation model of microball and workpieee were built based on Hertz theory,and then the estimation method of maximum allowable measurement force and the force deformation were given. Microballs made of three kinds of material,which were used for micro-nano CMM were selected as reference,the maximum allowable measurement force and the deformation were estimated. The results show that the errors of force deformation should not to be ignored and needs to be paid more attention in contact nano-measurement.