Influence of friction coefficient asymmetry on vibration and stability of rolling mills during hot rolling
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摘要: 建立了摩擦系數非對稱性的軋制過程模型，并與某熱軋機傳動系統的垂直?水平?扭轉結構模型相結合，建立了結構?過程相耦合的動力學模型。利用穩定性準則確定了摩擦系數非對稱作用下軋機系統的穩定域，分析了摩擦系數的非對稱性對軋機系統振動特性和穩定性的影響規律。通過仿真分析表明，摩擦系數的非對稱性對系統的穩定性有顯著的影響，隨著非對稱程度的不同，系統會出現穩定域、水平失穩域和水平扭轉失穩域，不同程度的非對稱性會造成不同的振動形態。通過對某熱軋廠現場測試，得到了軋機系統的振動信號，驗證了仿真分析的正確性，同時指出軋制集裝箱板和普板（Q235）時的變形抗力不同引起穩定域的差異，從而使得在摩擦系數的非對稱程度一樣時，軋制集裝箱板時落在了水平失穩域，系統出現了明顯的水平振動；軋制普板（Q235）時落在了穩定域，系統沒有明顯的振動。Abstract: The modern rolling industry has improved product quality, and the technical requirements of high accuracy and high dynamic performance have made the issue of rolling mill vibration more prominent. Rolling mill system instability seriously affects the quality of the product, reduces the accuracy of the product, and even causes serious damage to the rolling mill equipment. During hot rolling process, friction is of great importance to vibration and stability of the rolling mill. There is a difference in the friction coefficient between the upper rolling interface and lower rolling interface. Considering the asymmetric friction coefficient, a chatter model was established by combing the rolling process model and the vertical?horizontal?torsional structure model of a hot rolling mill to study the relationship between friction coefficient asymmetry and stability of the rolling mill system. According to the mathematical model, the friction coefficient stability domain of a rolling mill system is determined by the application of stability criterion. And it shows that the influence of the asymmetric friction coefficient on the stability domain is significant. Due to the different degrees of asymmetry, the system is divided into stable domain, horizontal instability domain, and horizontal?torsional instability domain. As the asymmetry in terms of the friction coefficient becomes considerable, it would occur various vibration modes. Through a field test of a hot rolling mill, the vibration signal of the rolling mill system was obtained, which verified the correctness and validity of the simulation analysis results. The degree of asymmetry in the friction coefficient is the same when rolling the container plate and the Q235 plate, but the deformation resistance of the system is different. The system falls into the horizontal instability domain when the container plate is rolled, displaying clearly horizontal vibration. However, the system falls into the stable domain when the Q235 plate is rolled, and the system shows no obvious vibration.
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Key words:
- hot rolling /
- friction coefficient /
- asymmetric /
- vibration /
- stability domain
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圖 1 工作輥垂直?水平?扭轉振動時軋件變形區示意圖
Figure 1. Schematic of deformation zone of vertical?horizontal?torsional vibration
圖 3 上下表面不同摩擦系數下的穩定域
Figure 3. Stability domain at different friction coefficients between upper and lower surfaces
圖 4 現場測試圖. （a）試驗臺架；（b）水平振動測試點位置
Figure 4. Picture of field test: (a) rolling mill for test; (b) horizontal vibration test point
圖 5 F3軋制普板時上工作輥水平振動圖. （a）時域；（b）頻域
Figure 5. Graph of upper work roll horizontal vibration during rolling of a Q235 plate: (a) time domain; (b) frequency domain
圖 6 F3軋制集裝箱板時上工作輥水平振動圖. （a）時域；（b）頻域
Figure 6. Graph of upper work roll horizontal vibration during rolling container plate: (a) time domain; (b) frequency domain
圖 7 F3軋制板材時工作輥振動響應. （a）普板；（b）集裝箱板
Figure 7. Dynamic response of work roll during rolling plate: (a) Q235 plate; (b) container plate
圖 9 軋制板材時上下表面不同摩擦系數下的穩定域. （a）集裝箱板；（b）普板
Figure 9. Stability domain at different friction coefficients of upper and lower surfaces during rolling plate: (a) container plate; (b) Q235 plate
表 1 F3機架軋機結構參數
Table 1. Structural parameters of F3 rolling mill
J1 /（kg·m2） J2 /（kg·m2） J3 /（kg·m2） J4 /（kg·m2） J5 /（kg·m2） J6 /（kg·m2） 2.12×104 5.31×103 3.81×102 1.3×102 1.3×102 1.70×103 J7 /（kg·m2） m1 /kg m2 /kg k1/（N·m?1·rad） k2/（N·m?1·rad） k3/（N·m?1·rad） 1.73×103 1.17×104 1.17×104 2×109 1×108 3.83×108 k4/（N·m?1·rad） k5/（N·m?1·rad） k6/（N·m?1·rad） kh1 /（N?1·m） kh2 /（N?1·m） kv1 /（N?1·m） 2×108 1.1×108 1.1×108 7.3×108 7.3×108 1.6×1010 kv2 /（N?1·m） R1 /m R2 /m r2 /m r3 /m r4 /m 1.6×1010 0.345 0.345 0.195 0.544 0.245 
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表 2 F3機架軋制工藝參數
Table 2. Process parameters of F3 rolling mill
入口厚度/m 出口厚度/m 入口張力/MPa 出口張力/MPa 變形抗力/MPa 11.187×10?3 4.605×10?3 14.939 14.939 188.7
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表 3 A、B、C、D點穩定性失穩形式
Table 3. Eigenvalue and instability type of point A, point B, point C, and point D
數據點 $\,{\mu _1}$ $\,{\mu _2}$ ${\lambda _{1,2}}/{10^3}$ ${\lambda _{3,4}}/{10^3}$ 失穩形式 A 0.3 0.17 0.0001±0.2376i ?0.002+0.0855i 37.8 Hz水平失穩 B 0.17 0.17 ?0.0002±0.2418i ?0.005+0.0755i 穩定 C 0.09 0.17 0.0003± 0.2457i ?0.002±0.0642i 39.1 Hz水平失穩 D 0.06 0.17 0.0009± 0.2472i 0.0012+0.0613i 39.3 Hz水平失穩 9.76 Hz扭轉失穩
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表 4 E、B、F、G點穩定性失穩形式
Table 4. Eigenvalue and instability type of point E, point B, point F, and point G
數據點 $\,{\mu _1}$ $\,{\mu _2}$ ${\lambda _{1,2}}/{10^3}$ ${\lambda _{3,4}}/{10^3}$ 失穩形式 E 0.27 0.07 0.0017±0.2456i ?0.005+0.0932i 39.1 Hz水平失穩 B 0.17 0.17 ?0.0002±0.2418i ?0.005+0.0755i 穩定 F 0.12 0.22 0.0004± 0.2428i ?0.002±0.0605i 38.6 Hz水平失穩 G 0.07 0.27 0.0019± 0.2457i 0.0034+0.0572i 39.1 Hz水平失穩 9.10 Hz扭轉失穩
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表 5 H點穩定性失穩形式
Table 5. Eigenvalue and instability type at point H
${\mu _1}$ ${\mu _2}$ ${\lambda _{1,2}}$ ${\lambda _{3,4}}$ 失穩形式 0.14 0.20 0.0198±242.168i ?3.244±69.42i 38.54 Hz水平失穩
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