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4.3 Rotational inertia of detecting roller As shown in Fig. 8, if the rotational inertia of detecting roller is large, the detecting roller occurs relative sliding with the strip in the acceleration or Fig. 7 Force transfer curve of detecting roller Fig. 8 Force drawing of shape detecting roller deceleration process, which leads to scratching the strip surface [19]. Thus, the detecting roller is usually machined as the structure of hollow cylindrical to reduce the rotational inertia. The unit radial pressure p of detecting roller generated by the strip tension T can be equivalent to the total radial force N [7]. By the force balance equation, Eq. (10) is concluded as sin2TN
(10) If the friction coefficient μ is known, the torque M1 of the detecting roller by friction force f can be expressed as RTfRM sin2 1 (11) When the cold mill is working under the maximum acceleration or deceleration, after t, the rolling speed changes from v1 to v2, then the angular acceleration an is Rtvvtan1212 (12) where ω1 and ω2 are angular velocities of detecting roller at different time, respectively. From Eqs. (10)−(12), the rotational inertia J can be obtained as ))(( π21)(21 2222b22rRrRLrRmJ (13) where Lb is length of the detecting roller. Then, the inertia moment M2 of detecting roller is M2=Jan (14) When M2>M1, the detecting roller will occur relative sliding with the strip. Therefore, M2<M1 should be ensured in the absence of motor-driven situation. 4.4 Collecting ring of detecting roller The role of collecting ring is achieving static output of original shape signals of high-speed rotation sensor, and its structure significantly affects stability and accuracy of the shape signals. As shown in Fig. 9, a highly integrated collecting ring was developed and mainly composed of the encoder, the signal line, the sub-heads, the brushes, the connectors, the spacing ring, the slip ring, the brush holder, the hollow shaft and other components. 5 Embeded DSP shape signal processing board As shown in Fig. 10, the DSP shape signal processing board is mainly composed of the lock-in amplifier, the AD converter, the magnetic isolation, the photoelectric isolation, the DSP chip and so on. It can realize rapid processing and remote transmission of shape signals. Multiple isolation measures were used to prevent industrial interference signals of magnetic field, temperature, humidity, vibration and other external factors. Moreover, USB, CAN bus, Ethernet, RS232 and other standard interfaces are equipped to facilitate quick information communication and system expansion. It changes traditional signal processing modes (ISA, PCI and PXI), and achieves miniaturization, integration and networking of the shape signal processing. Within the embeded DSP shape signal processing board, the rotational speed and the rotation direction are determined by signals of the optical encoder. When the zero signal of encoder arrives, the DSP chip identifies the maximum value (positive) of each channel and the minimum (negative) at one period, and the average value of both absolute values is treated as an effective signal of one period. Then, the effective signals are real time transmitted to the signal processing software for comprehensive compensation and shape pattern recognition. Finally, the close-loop shape control is realized by the shape control system and the regulated means of mill. Figure 11 shows the shape signal processing control cabinet and its internal-embeded DSP circuit board. Fig. 11 DSP control cabinet and its circuit board 6 Principle of shape control Shape control mainly includes the tilting backup roller, the positive and negative bending working roller, the positive bending middle roller, the shifting middle roller and the subsection cooling. As shown in Fig. 12, where the titling is expressed as the tilting backup roller, the WR (working roll)-bending is expressed as the bending working roller, the IR (intermediate roll)- bending is expressed as the bending middle roller and the IR-shifting is expressed as the shifting middle roller. In these rollers, the shape detecting roller and the DSP shape signal processing board are the core components of shape detecting system, which determine precisions of the shape detecting and the shape control to a great extent. So, the shape detecting system is the basis and prerequisite of achieving the close-loop shape control of cold rolling strip. In the rolling process, radial forces are imposed on surface of the detecting roll by the strip, and passed to the sensors through the elastic blocks, then the sensors produce the original shape real-time signals (voltage signals) at the same time. After the DSP shape signal processing board receives the original shape signals via modem, AD conversion and other signal processing occur in turn. Then, the real-time digital signals are transferred to the shape signal processing software system, and the shape signals are comprehensively compensated and broken into different shape patterns. Ultimately, the close loop shape control is realized. Besides, the shape signals are real-time displayed, printed and stored in external devices. 7 Industrial applications The shape detecting system was successfully used in Angang 1 250 mm HC 6-high reversible cold rolling mill, which verified the stability, accuracy and relevance of the system. Main steel types of cold rolling mill are carbon steel, excellent carbon steel and low alloying steel. On behalf of steel were Q195−Q235, 08Al, 16Mn, thickness range 0.2−0.55 mm of finished strip, width range 800−1 130 mm, coil diameter range 610−2 000 mm, range of wrapping angle 4°−23°, the maximum rolling speed 1 200 m/min, coiling tension range 7−140 kN. The diameter of detecting roller was 350 mm, Length 1 350 mm, effective working width 1 196 mm, effective wear thickness 6 mm, surface hardness >58 HRC. Other parameters are listed in Table 1..