Uncertainty propagation from probe spacing to Fourier 3-probe straightness measurement

IF 6.3 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
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Abstract

Reliable and precise straightness profile measurements are crucial for manufacturing ultra-precision components and are capable of further enhancing their accuracy. The Fourier three-probe (F3P) straightness measurement allows for precise assessment of the workpiece profile on the machine by eliminating the harmful influence of the error motion of the sliding table. However, the probe spacing uncertainty deteriorates the measurement accuracy remarkably; and, the affecting mechanism behind this phenomenon has not yet been studied in detail. In this context, this paper thoroughly investigated the propagation of the probe spacing uncertainty in the F3P measurement. First, the influence of the probe spacing deviation is analyzed. Next, by calculating the partial differential of Laplace transform of the workpiece profile, we algebraically deduce the probe spacing uncertainty propagation law, especially in the harmonic domain. Subsequently, Monte Carlo simulations are carried out to confirm the derived propagation law. To reduce uncertainty propagation, a hybrid approach is presented: (I) F3P measurements are carried out under changing probe spacings to produce several sets of Fourier coefficients; (II) optimal harmonic estimates are selected individually according to the harmonic uncertainty. Finally, simulations and experimental measurements are performed for verification.
从探针间距到傅立叶三探针直线度测量的不确定性传播。
可靠而精确的直线度轮廓测量对于制造超精密部件至关重要,并能进一步提高其精度。傅立叶三探针(F3P)直线度测量可消除滑动工作台误差运动的有害影响,从而精确评估机床上的工件轮廓。然而,测头间距的不确定性会显著降低测量精度;而且,这种现象背后的影响机制尚未得到详细研究。在此背景下,本文对 F3P 测量中探头间距不确定度的传播进行了深入研究。首先,分析了探头间距偏差的影响。接着,通过计算工件轮廓的拉普拉斯变换偏微分,我们用代数方法推导出了测头间距不确定度的传播规律,尤其是在谐波域。随后,我们进行了蒙特卡罗模拟,以确认推导出的传播规律。为了减少不确定性的传播,提出了一种混合方法:(I)在改变探头间距的情况下进行 F3P 测量,以产生多组傅立叶系数;(II)根据谐波不确定性单独选择最佳谐波估计值。最后,进行模拟和实验测量进行验证。
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来源期刊
ISA transactions
ISA transactions 工程技术-工程:综合
CiteScore
11.70
自引率
12.30%
发文量
824
审稿时长
4.4 months
期刊介绍: ISA Transactions serves as a platform for showcasing advancements in measurement and automation, catering to both industrial practitioners and applied researchers. It covers a wide array of topics within measurement, including sensors, signal processing, data analysis, and fault detection, supported by techniques such as artificial intelligence and communication systems. Automation topics encompass control strategies, modelling, system reliability, and maintenance, alongside optimization and human-machine interaction. The journal targets research and development professionals in control systems, process instrumentation, and automation from academia and industry.
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