Huang Pu, Xie Jin, Haitjema Han, Lu Kuo, Shi Shengyu
School of Mechanical and Automobile Engineering, South China University of Technology, Guangzhou 510640, PR China.
Manufacturing Metrology Section, Manufacturing, Processes and Systems (MaPS), Department of Mechanical Engineering, KU Leuven, 3001 Leuven, Belgium.
ISA Trans. 2024 Nov;154:465-475. doi: 10.1016/j.isatra.2024.08.011. Epub 2024 Aug 11.
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.
可靠且精确的直线度轮廓测量对于制造超精密部件至关重要，并且能够进一步提高其精度。傅里叶三探针（F3P）直线度测量通过消除滑台误差运动的有害影响，能够在机床上对工件轮廓进行精确评估。然而，探针间距的不确定性会显著降低测量精度；而且，这一现象背后的影响机制尚未得到详细研究。在此背景下，本文深入研究了F3P测量中探针间距不确定性的传播。首先，分析了探针间距偏差的影响。其次，通过计算工件轮廓拉普拉斯变换的偏导数，我们代数推导了探针间距不确定性的传播规律，特别是在谐波域。随后，进行蒙特卡罗模拟以验证所推导的传播规律。为了减少不确定性传播，提出了一种混合方法：（I）在变化的探针间距下进行F3P测量，以产生几组傅里叶系数；（II）根据谐波不确定性分别选择最优谐波估计值。最后，进行模拟和实验测量以进行验证。
