Prime number-based multistep measurement for separation of roundness errors – T Hsieh and M Lin

Abstract
Roundness measurement is critical in manufacturing, as it ensures that products conform to precise design
specifications. However, traditional multistep measurements for roundness error separation are time-consuming and
limited in their ability to separate specific Fourier components. In this study, we propose a novel combined multistep
measurement method with prime numbers that overcomes these limitations. We demonstrate this method through
three experimental cases, achieving high levels of Fourier components in error separation with a limited number of
measurements. Our method combines two (p and q) or three (p, q, and r) steps of prime numbers to achieve high
levels of Fourier components for error separation, compared to traditional multistep measurements that require more
steps. In the first experimental case, we use a 2-step and 5-step measurement to achieve traditional multistep
measurement in ten steps. In the second case, we use 3-step and 5-step measurements, and in the third, we combine
the 2-step, 3-step, and 5-step measurements. We achieve roundness deviations (RONt) of 12.7, 7.8, and 9.9 nm,
respectively, and maximum En-values of 0.8, 0.8, and 0.7, respectively. Our proposed combined multistep measurement
method using prime numbers has practical applications in manufacturing, as it reduces the time and resources required
for roundness error separation while achieving a higher level of Fourier components. Our results demonstrate the
effectiveness of our method and its potential to revolutionize roundness measurement in industry.