滚子轴承是现代制造领域中必不可少的一部分，它为机械设备提供了转动和降低

滚子轴承是现代制造领域中必不可少的一部分，它为机械设备提供了转动和降低摩擦等作用，使制造业得到了飞速的发展。同时，各种优化滚子轴承的方法相继而出，其中基于对数曲线修形法制造的对数曲线滚子轴承，能够很好的减少“应力集中现象”的产生，从而有效的提高滚子轴承的使用寿命，间接提高机械设备的精度和使用期限。因此，研究能够提高评定对数曲线轮廓度误差的方法，对滚子轴承寿命和机械设备的性能有重要意义。<br>本文在查找并分析了中外诸多有关平面曲线误差评定的文献后，再结合最小条件评定原则、对数曲线的几何特性及线轮廓度误差评定的要求，确定了最小二乘算法和基于最小区域的几何遍历匹配算法、几何遍历匹配算法，这三种对数曲线误差评定算法。<br>最小二乘算法评定对数曲线轮廓度误差，先建立对数曲线数学模型，在根据最小二乘算法的原理，确定拟合最小二乘对数曲线，计算测量点到拟合对数曲线法向距离值，得到对数曲线轮廓度误差。由实例数据算出的对数曲线轮廓度误差值，结合数学模型反应的图像特征，确定算法的可行性。在最小二乘算法的基础上，根据最小区域评定原则，得到了基于最小区域的几何遍历匹配算法、几何遍历匹配算法。通过实例验证和图像分析，证明了算法的有效性和精度。<br>论文中所述的三种算法是根据误差评定要求结合对数曲线的几何特性提出的，因此，算法的原理很简单，同时，在评定的过程中，没有涉及复杂的数学公式，所以运用本文所述的算法评定时，计算也比较快速、方便，<br>论文中通过对平面内任意位置的对数曲线几何特性分析，结合最小二乘、最小区域原理，实现对对数曲线误差有效的评定。

滚子轴承是现代制造领域中必不可少的一部分，它为机械设备提供了转动和降低摩擦等作用，使制造业得到了飞速的发展。 同时，各种优化滚子轴承的方法相继而出，其中基于对数曲线修形法制造的对数曲线滚子轴承，能够很好的减少“应力集中现象”的产生，从而有效的提高滚子轴承的使用寿命，间接提高机械设备的精度和使用期限。 因此，研究能够提高评定对数曲线轮廓度误差的方法，对滚子轴承寿命和机械设备的性能有重要意义。<br>本文在查找并分析了中外诸多有关平面曲线误差评定的文献后，再结合最小条件评定原则、对数曲线的几何特性及线轮廓度误差评定的要求，确定了最小二乘算法和基于最小区域的几何遍历匹配算法、几何遍历匹配算法，这三种对数曲线误差评定算法。<br>最小二乘算法评定对数曲线轮廓度误差，先建立对数曲线数学模型，在根据最小二乘算法的原理，确定拟合最小二乘对数曲线，计算测量点到拟合对数曲线法向距离值，得到对数曲线轮廓度误差。 由实例数据算出的对数曲线轮廓度误差值，结合数学模型反应的图像特征，确定算法的可行性。 在最小二乘算法的基础上，根据最小区域评定原则，得到了基于最小区域的几何遍历匹配算法、几何遍历匹配算法。 通过实例验证和图像分析，证明了算法的有效性和精度。<br>论文中所述的三种算法是根据误差评定要求结合对数曲线的几何特性提出的，因此，算法的原理很简单，同时，在评定的过程中，没有涉及复杂的数学公式，所以运用本文所述的算法评定时，计算也比较快速、方便，<br>论文中通过对平面内任意位置的对数曲线几何特性分析，结合最小二乘、最小区域原理，实现对对数曲线误差有效的评定。

Roller bearing is an indispensable part of modern manufacturing field. It provides the function of turning and reducing friction for mechanical equipment, which makes the manufacturing industry develop rapidly. At the same time, various methods to optimize the roller bearing have been developed one after another. Among them, the logarithmic curve roller bearing based on the logarithmic curve modification method can well reduce the "stress concentration phenomenon", thus effectively improving the service life of the roller bearing and indirectly improving the accuracy and service life of the mechanical equipment. Therefore, it is of great significance for the life of roller bearing and the performance of mechanical equipment to study the method that can improve the evaluation of log curve profile error.<br>In this paper, after searching and analyzing a lot of documents about the error evaluation of plane curve at home and abroad, combined with the minimum condition evaluation principle, the geometric characteristics of logarithmic curve and the requirements of the error evaluation of line profile, the least square algorithm, the geometric ergodic matching algorithm based on the minimum region and the geometric ergodic matching algorithm are determined. These three algorithms are used to evaluate the error of logarithmic curve.<br>The least square algorithm evaluates the profile error of logarithmic curve. Firstly, the mathematical model of logarithmic curve is established. According to the principle of least square algorithm, the least square logarithmic curve is fitted, and the normal distance between the measurement point and the fitted logarithmic curve is calculated to get the profile error of logarithmic curve. Based on the logarithm curve profile error calculated from the example data and the image characteristics reflected by the mathematical model, the feasibility of the algorithm is determined. On the basis of the least square algorithm, according to the principle of minimum area evaluation, the geometric traversal matching algorithm and the geometric traversal matching algorithm based on the minimum area are obtained. The effectiveness and accuracy of the algorithm are proved by example verification and image analysis.<br>The three algorithms mentioned in this paper are put forward according to the requirements of error evaluation combined with the geometric characteristics of logarithmic curve. Therefore, the principle of the algorithm is very simple. At the same time, there is no complicated mathematical formula involved in the evaluation process. Therefore, when using the algorithm described in this paper to evaluate, the calculation is relatively fast and convenient,<br>In this paper, through the analysis of the geometric characteristics of the logarithmic curve at any position in the plane, combined with the principle of least square and minimum area, the effective evaluation of the logarithmic curve error is realized.<br>