Unified Numerical Representation Method for Unimodal and Bimodal Waveform Signals of a Roll-type Flatness Meter

The roll-type flatness meter is a critical detection device in the cold rolling process of strip production. It demands extremely high precision while being highly sensitive to strip tension and wrap angle. Research shows that as the strip tension or wrap angle increases, the pressure distribution of the strip changes gradually in the roll circumferential direction, resulting in the output of unimodal and bimodal waveform signals. Owing to the impulsive nature of the unimodal waveform, earlier methods typically extract and use the peak value as the numerical representation of the pressure exerted by strip. However, when both types of waveforms appear in different detection channels simultaneously and the same representation method is applied, significant detection errors can arise. To identify a unified numerical representation method applicable to all output waveforms, this study introduces the concept of the sensor perception zone of roll-type flatness meters. Based on the idea of the influence function, a fast and effective integration-based value method is proposed, which fully considers the mapping relationship between the roll surface pressure in the perception zone and the output waveform signal. This approach eliminates the effects of varying operational conditions and signal outputs, enabling the direct calculation of effective values meeting the same gradient, which serves as the data source for determining the strip flatness distribution in real-time detection. Furthermore, to account for the differences in sensor perception zones while applying the integration method, an integration-based calibration method is proposed. Finally, finite element simulations were conducted to obtain output data under varying wrap angle and varying tension conditions. The correctness of the method is verified according to the calculated Pearson correlation coefficients.