Research on the characteristics of cold-rolled deformation zone of thin strip and the applicability of contact pressure model
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摘要: 薄带冷轧过程中轧辊会产生不同程度的弹性压扁现象，而各变形区理论对该现象认识的不同导致其计算精度和适用范围存在显著差异。为此采用有限元手段分析了薄带冷轧过程中变形区特征的变化规律，并对比探究了Stone全滑移、Johnson全弹性和组合型三种接触压力模型的推导特点、成立的先决条件和适用区间。结果表明：变形区轮廓随轧辊弹性压扁程度的加剧依次经历了圆弧形、圆弧压扁增大形、非圆弧形和近直线形，中性区的出现及其所占变形区比例的不断增加是导致实际压下率快减和变形区形状系数快增的主要原因。通过对比变形区接触压力曲线的模拟值与理论值可发现，Stone模型、Johnson模型和组合型模型分别适用于道次压下率大于10%、小于1%和1%～10%的轧制工况。Abstract: In the process of cold rolling of thin strip, the roll will produce different degrees of elastic flattening, and the different understandings of this phenomenon in each deformation in each deformation zone theory lead to significant difference in its calculation accuracy and application range. Therefore, the finite element method is used to analyze the variation law of the characteristics of the deformation zone in the process of cold rolling of thin strip, and the derivation characteristics, prerequisites and applicable intervals of the three contact pressure models of Stone total slip, Johnson full elasticity and combined type are compared and explored. The results show that with the increasing of the elastic flattening degree of the roll, the contour of the deformation zone undergoes arc shape, arc flattening enlargement, non-arc shape and nearly linear shape, and the occurrence of neutral zone and the increasing proportion of the deformation zone are the main reasons for the rapid decrease of the actual depression rate and the rapid increase of the shape coefficient of the deformation zone. By comparing the simulated and theoretical values of the contact pressure curve in the deformation zone, it can be found out that the Stone model, Johnson model and combined model are suitable for rolling conditions where the pass reduction ratio is greater than 10%, less than 1% and 1%～10%, respectively.
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图 1 变形区微元体的受力示意
Figure 1. Schematic diagram of applied force in the deformation zone microelement
图 2 Stone模型变形区受力及接触压力分布示意
Figure 2. Schematic diagram of force and contact pressure distribution in the deformation under Stone model
图 3 Johnson模型变形区受力及接触压力分布示意
Figure 3. Schematic diagram of force and contact pressure distribution in the deformation zone under Johnson model
图 4 组合型模型变形区受力及接触压力分布示意
Figure 4. Schematic diagram of the force and contact pressure distribution in the deformation zone under the combined model
图 6 不同厚度薄带的变形区接触轮廓随压下率的变化
(a) 0.3 mm；(b) 0.2 mm；(c) 0.1 mm；(d) 0.075 mm；(e) 0.05 mm；(f) 0.03 mm
Figure 6. The contact profile of the deformation zone under different thicknesses thin strips with reduction ratio
图 7 变形区接触特征随薄带厚度的变化规律
(a) 预设压下率40%；(b) 预设压下率100%
Figure 7. The variation of the contact characteristics in deformation zone with thin strip thickness
图 8 不同厚度薄带的变形区接触压力
(a) 0.3 mm； (b) 0.2 mm；(c) 0.1 mm；(d) 0.075 mm；(e) 0.05 mm；(f) 0.03 mm
Figure 8. The contact pressure of the deformation zone under different thicknesses thin strips
图 9 接触弧长的模拟值与Hitchcock和Johnson理论值对比
(a) Hitchcock理论值；(b) Johnson理论值
Figure 9. Comparison of the contact arc length from FE simulation and Hitchcock & Johnson models
图 10 入口塑性区临界点的模拟值与组合模型理论值对比
(a) xB ；(b) xC
Figure 10. Comparison of critical point of the plastic zone at the inlet from FE simulation and combined model
图 11 接触压力模拟值与三种模型理论值对比
(a) 0.2 mm；(b) 0.1 mm；(c) 0.075 mm
Figure 11. Comparison of contact pressures from FE and three models
图 12 实际压下率划分的三种模型的适用范围
Figure 12. Mapping of the three models by the actual reduction ratio
表 1 薄带轧制工艺参数
Table 1. Thin strip rolling process parameters
薄带初始厚度h0 /mm 预设压下率y/% 0.3、0.2、0.1、0.075、0.05、0.03、0.02 20、40、60、80、100 
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表 2 单位宽度轧制力模拟值与Johnson模型和组合模型理论值
Table 2. Rolling force per unit width from FE simulation and Johnson model & combined model
厚度/mm 预设压下率/% 模拟值/N 组合型理论值/N 组合型相对误差/% Stone理论值/N Stone相对误差/% 0.075 20 470.7 478.2 1.587 425.0 −9.717 40 995.0 1017.7 2.284 1082.6 8.808 60 1540.1 1554.0 0.905 2195.7 42.572 80 2105.7 2106.4 0.036 3649.7 73.326 100 2688.2 2674.3 −0.515 5629.7 109.424 0.1 20 632.5 645.0 1.975 552.2 −12.693 40 1313.7 1318.1 0.335 1284.0 −2.261 60 2036.2 2009.2 −1.326 2197.0 7.900 80 2790.9 2724.1 −2.394 4405.7 57.858 100 3572.0 3460.0 −3.136 5889.7 64.884 0.2 20 1077.3 1091.4 1.304 1068.5 −0.819 40 2231.0 2112.3 −5.318 2191.1 −1.787 60 3594.7 3273.2 −8.945 3690.6 2.666 80 5186.6 4561.5 −12.053 5203.1 0.318 100 6924.8 6011.9 −13.182 7627.7 10.151
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