中文摘要：

齿廓误差是齿轮重要的单项误差之一,随着坐标测量机在齿轮测量中的广泛应用,直角坐标测量法在齿轮误差测量中的应用也越来越广。以齿廓误差为研究对象,针对直角坐标系下的齿廓误差测量及评定方法进行了系统研究。从齿轮工件坐标系的建立、齿廓测量路径的规划到齿廓误差的评定的完整过程进行了系统介绍,详细分析了几何法齿廓误差评定方法、公式法齿廓误差评定方法以及滑动法齿廓误差评定方法的实现原理,并比较了三种评定方法的算法精度与效率。实验结果表明,在算法精度方面,三种齿廓误差评定方法算法计算精度都达1×10~（-14）量级;测量效率方面,50万齿廓测量点误差评定条件下,几何法齿廓误差评定方法算法效率最低,公式法齿廓误差评定方法效率最高,效率比达94倍。因此在实际应用中建议采用公式法齿廓误差评定方法。

英文摘要：

The tooth profile error is one important individual errors of gear,with wide use of the coordinate measuring machine in gear measurement,the Cartesian coordinate measuring method is becoming more and more widely applied in gear error measurement field. The tooth profile error evaluation method is taken as research subject,the tooth profile error measurement and evaluation methods in the Cartesian coordinate system are systematic researched. The whole process of tooth profile error measurement is introduced,which includes the establishment of gear workpiece coordinate system,tooth profile measurement path planning,and tooth profile error evaluation. The tooth profile error evaluation methods are detailed analyzed and compared,including geometric tooth profile error evaluation method,formula tooth profile error evaluation method and sliding tooth profile error evaluation method,then their algorithm accuracies and efficiencies are compared. The experimental results show that three profile error evaluation algorithms are up to 1 × 10~（-14） level in aspect of accuracy. In aspect of measurement efficiency,the geometric profile error evaluation method is the lowest,formula profile error evaluation method is the highest,and efficiency rate is up to 94 times on the condition of 500 000 measurement points. So the formula profile error evaluation method is recommended in the practical application.