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首页> 外文会议>ASME international mechanical engineering congress and exposition >DEPENDENCE OF MEASURING INSTRUMENT ECCENTRICITY AND TILT ERROR ON THE FOUR MATHEMATICAL METHODS OF CIRCULARITY FORM ERRORS
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DEPENDENCE OF MEASURING INSTRUMENT ECCENTRICITY AND TILT ERROR ON THE FOUR MATHEMATICAL METHODS OF CIRCULARITY FORM ERRORS

机译：圆形误差的四种数学方法的测量仪器偏心量和倾斜度的依赖

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In precision machining of cylindrical parts, the measurement and evaluation of circularity is an indispensable component to quantify form tolerance. Of all the methods of measuring these form errors, the most precise is the one with accurate spindle/turntable type measuring instrument. On the instrument, the component is rotated on a highly accurate spindle which provides an imaginary circular datum. The workpiece axis is aligned with the axis of the spindle by means of a centering and tilt adjustment leveling table. Based on reference circles, this paper focuses on the four modeling methods of roundness, namely. (1) Least Squares Circle (LSC), (2) Maximum Inscribed Circle (MIC), (3) Minimum Circumscribed Circle (MCC) and (4) Minimum Zone or Minimum Radial Separation (MRS) Circles. These methods have been explained in author's previous article in the context of their implications on design applications, advantages and disadvantages. In this article, the authors have investigated the dependence of these mathematical methods based circularity form error on instrument's centering error (also known as eccentricity) and tilt error. Some intriguing results were observed for the highly nonlinear relationship of machine's centering/tilt error with circularity results outside its useful linear region (50 - 600 uin for this specific machine used in this investigation). Further, the linear and nonlinear relationship was mapped within the effective boundaries of eccentricity settings to investigate the best and worst methods of circularity measurements that are susceptible to instrument errors. Very high and low machine eccentricity settings in its nonlinear regions were not accurately compensated by the machine in circularity results processing. In this study, a master part with different circular and cylindrical features was studied with varying levels of preset instrument eccentricity and tilt errors. Off the four methods, MRS reported the least circularity results. The other three methods didn't provide any predictable trend. Circularity results were observed to differ up to 35% within these four methods. However, in this preliminary investigation, this maximum difference doesn't appear to follow any predictable trend with varying machine eccentricities. This article also reinforces the significance of these parameters, and the way they should be understood and be incorporated into undergraduate and graduate engineering curriculum, and be taught as an improved toolkit to the aspiring engineers.
机译：在圆柱零件的精密加工中，圆度的测量和评估是量化形状公差必不可少的组件。在测量这些形状误差的所有方法中，最精确的是一种具有精确的主轴/转盘式测量仪器的方法。在仪器上，零件在高度精确的主轴上旋转，该主轴提供了一个假想的圆形基准。工件轴通过定心和倾斜度调节平台与主轴轴对齐。本文基于参考圆，重点介绍了圆度的四种建模方法。 （1）最小二乘圆（LSC），（2）最大内切圆（MIC），（3）最小外接圆（MCC）和（4）最小区域或最小径向分隔（MRS）圆。这些方法已在作者的前一篇文章中进行了解释，涉及了它们对设计应用程序的影响，优缺点。在本文中，作者研究了这些基于圆度形式误差的数学方法对仪器对中误差（也称为偏心率）和倾斜误差的依赖性。对于机器的定心/倾斜误差与圆度结果在其有用的线性区域之外（对于本研究中使用的该特定机器为50-600 uin）的高度非线性关系，观察到一些有趣的结果。此外，将线性和非线性关系映射到偏心设置的有效范围内，以研究易受仪器误差影响的最佳和最差的圆形度测量方法。在圆度结果处理中，机器无法准确地补偿其非线性区域中的极高和极低的机器偏心率设置。在这项研究中，研究了具有不同圆形和圆柱形特征的主零件，并具有不同级别的预设仪器偏心率和倾斜误差。在这四种方法中，MRS报告的圆度结果最少。其他三种方法没有提供任何可预测的趋势。在这四种方法中，观察到圆度结果的差异最大为35％。但是，在此初步调查中，在机器偏心率变化的情况下，这种最大差异似乎并没有遵循任何可预测的趋势。本文还强调了这些参数的重要性，以及应理解这些参数并将其纳入本科和研究生工程课程中的方法，并作为有抱负的工程师的改进工具包进行了讲授。

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