基于停留时间的深锥浓密机耙架扭矩计算模型

基于停留时间的深锥浓密机耙架扭矩计算模型 Calculation model of rake torque of deep cone thickener based on residence time 1 2 first-author 1 2 1 2 3 corresp 王少勇，博士，高级工程师，从事膏体充填理论与技术研究；E-mail：wangshaoyong@ustb.edu.cn 王少勇，博士，高级工程师，从事膏体充填理论与技术研究；E-mail：wangshaoyong@ustb.edu.cn wangshaoyong@ustb.edu.cn 1 2 1 2 1 2 北京科技大学 金属矿山高效开采与安全教育部重点实验室，北京，100083 北京科技大学 金属矿山高效开采与安全教育部重点实验室，北京，100083 Key Laboratory of Ministry of Education for High-efficient Mining and Safety of Metal Mines, University of Science and Technology Beijing, Beijing 100083, China Key Laboratory of Ministry of Education for High-efficient Mining and Safety of Metal Mines, University of Science and Technology Beijing, Beijing 100083, China 北京科技大学 土木与资源工程学院，北京，100083 北京科技大学 土木与资源工程学院，北京，100083 School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China 金诚信矿业管理股份有限公司，北京，100070 金诚信矿业管理股份有限公司，北京，100070 JCHX Mining Management Co. Ltd., Beijing 100070, China JCHX Mining Management Co. Ltd., Beijing 100070, China 伍锦花 在膏体充填过程中，间歇式充填作业会使料浆在深锥浓密机(DCT)中的停留时间延长。为研究料浆停留时间对DCT耙架扭矩的影响，首先，进行不同停留时间下的深锥相似模拟实验，得到底流料浆屈服应力与耙架扭矩的变化规律；其次，将DCT耙架分解为水平横梁、导水杆、耙臂及刮泥耙这4个构件进行受力分析，联立屈服应力与停留时间的函数关系，建立不同停留时间的DCT耙架扭矩计算模型。最后，对扭矩计算值与实测值的相对误差进行分析，结合对DCT锥部泥层的观测，探索停留时间对耙架扭矩的影响及压耙机理。研究结果表明：模型中耙架扭矩随停留时间的变化规律与实际结果一致，可划分为缓慢增长和快速增长2个阶段；粗颗粒尾砂(CPT)在“重-压-剪”三力作用下，随着停留时间延长而不断向DCT底部运移、密实，逐渐在锥部形成“高CPT占比、高浓度、高摩擦、难屈服”的“三高一难”致密层，料浆反作用于耙臂和刮泥耙导致耙架扭矩增大，最终导致DCT压耙。 In the process of paste backfill, the intermittent filling operation increases the residence time of slurry in deep cone thickener(DCT). In order to explore the influence of slurry residence time on DCT rake torque, firstly, deep cone similar simulation experiments were carried out to obtain the variation law of underflow slurry yield stress and rake torque with the residence time. Then, the DCT rake was decomposed into four components: beam, pickets, rake arm and rake scraper for stress analysis. The functional relationship between yield stress and residence time was combined to establish the rake torque calculation model of DCT with different residence time. The calculated torque of the model was compared with the measured torque. Finally, combined with the error analysis of measured torque and calculated torque and the observation of the mud layer in the DCT cone, the influence of residence time on the rake torque and the mechanism of rake blockage were explored. The results show that variation law of rake torque with residence time is consistent with actual practice, which can be divided into two stages, i.e., slow growth and rapid growth stages. Under the action of "heavy-pressure-shear" forces, coarse particle tailings(CPT) continuously migrate and compact to the bottom of DCT with residence time, and gradually form a "three high and one difficult"(high CPT content, high concentration, high friction and difficult yield) dense layer in the cone. The slurry reacts on the rake arm and scraper, resulting in the increase of rake torque and rake blockage. 深锥浓密机 停留时间 耙架扭矩 计算模型 压耙 粗颗粒尾砂 deep cone thickener(DCT) residence time rake torque calculation model rake blockage coarse particle tailing(CPT) 膏体充填采矿为地下采空区处理和尾矿处置提供了安全、绿色、高效的技术保障 [ 1 1 - 2 2 1-2 ] 。膏体充填技术将成为深部资源安全绿色开采的核心方案 [ 3 3 - 4 4 3-4 ] 。深锥浓缩机(DCT)是尾矿脱水浓密制备的主要设备，耙架通过搅拌剪切作用，将低浓度全尾砂料浆浓密脱水成高浓度料浆，用于膏体充填 [ 5 5 ] 。 DCT耙架扭矩主要来源于耙架在转动时克服浆料的屈服应力和对矿浆进行剪切过程中产生的剪切应力 [ 6 6 ] 。在实际运行中，常常出现耙架扭矩过大出现过载停机的现象即压耙事故 [ 7 7 ] ，目前已知的压耙原因主要包括尾砂性质不稳定 [ 8 8 ] 、给料速度过大 [ 9 9 ] 、全尾砂粒径较大 [ 10 10 ] 、设备操作不当 [ 11 11 ] 等。吴爱祥等 [ 12 12 ] 基于不同区域内耙架构件的受力分析，建立了复杂结构耙架的扭矩力学模型；王洪江等 [ 13 13 ] 通过建立DCT泥床料浆初始剪切力与不同泥层高度料浆浓度的函数关系，提出了耙架扭矩预测模型；杨莹等 [ 14 14 ] 提出了基于泥层高度的耙架扭矩力学模型，并从微观角度解释了泥层高度对耙架扭矩的影响机理；TAN等 [ 15 15 ] 推导出了将耙架扭矩作为固体质量分数的函数，并克服了屈服应力测量精度不高的缺点；RUDMAN等 [ 16 16 ] 发现料浆的屈服应力是决定耙架扭矩的主要因素；BÜRGER等 [ 17 17 ] 提出了一个模型，用于模拟存在旋转耙结构的圆形装置中的澄清和浓密过程；赵睿等 [ 18 18 ] 通过对耙臂的受力分析，建立了DCT耙臂扭矩与给料浓度、耙臂转速的计算模型，发现模型计算数据与实测数据的相对误差在±1%之内；RUAN等 [ 19 19 ] 基于泥床密度、摩擦因数、耙转速和DCT锥角影响的DCT耙架功率理论模型，研究了尾砂性质对耙架扭矩的影响。 在实际生产中，为满足地下采矿和充填计划的要求，DCT底流排放并不是连续的，而是间歇式充填作业 [ 20 20 ] ，尾砂料浆在DCT中的停留时间增加，压耙事故发生的可能性增大。基于泥层高度 [ 14 14 ] 和料浆浓度的 [ 13 13 ] 耙架力学模型已经建立，而不同停留时间对耙架扭矩的影响以及压耙机理还不清晰。同时，在传统耙架扭矩计算模型的构建中，没有考虑刮泥耙克服料浆转动所产生的扭矩 [ 12 12 ] 。 本文作者通过对DCT耙架构件进行力学分析，借助屈服应力与停留时间的回归关系，建立不同停留时间的耙架扭矩计算模型，得到耙架扭矩随停留时间的变化规律；将耙架扭矩模型计算值与实测值进行对比，结合DCT锥部料浆的观测结果分析误差出现的原因，进一步研究停留时间对DCT锥部料浆CPT分布、料浆浓度及耙架扭矩的影响机理，以期为减少DCT的压耙事故提供理论支撑。 1 实验与结果 1 1.1 　实验材料 2 实验所用全尾砂的基本物理性质见 表1 表1 。使用激光粒度仪对尾砂粒径分布展开分析。全尾砂粒径分布(PSD)分布曲线如 图1 图1 所示。从 图1 图1 可见：尾砂体中值粒径( d 50 ，即颗粒质量分数为50%时对应的粒径，其余依此类推)为94.65 μm，有效粒径( d 10 )为4.92 μm，连续粒径( d 30 )为28.02 μm，限制粒径( d 60 )为100.65 μm，通过计算可得到全尾砂的不均匀系数和曲率系数分别为20.46和1.59。此外，全尾砂中粒径小于20 μm的颗粒质量分数达到37.14%，粒径小于75 μm的颗粒质量分数仅为59.77%，可见全尾砂中粗颗粒质量分数较大，属于粗颗粒全尾砂 [ 21 21 ] 。选用Magnafloc 5250阴离子型聚丙烯酰胺絮凝剂，其相对分子质量为18×10 6 。 密度/ (t·m -3 ) 松散堆积密度/(t·m -3 ) 密实堆积密度/(t·m -3 ) 松散孔隙率/% 密实孔隙率/% 2.730 1.367 1.908 51.52 32.34 1.2 　实验方法 2 采用深锥相似模型进行半连续动态浓密实验，实验系统如 图2 图2 所示。 将尾砂烘干后配置成15%(质量分数，下同)的全尾砂料浆，搅拌均匀由泵送系统以1 000 mL/min的流量送入自制DCT内；同时按单耗20 g/t，将提前配置质量分数为0.1‰的絮凝剂溶液经蠕动泵以75 mL/min的流速送入DCT给料井，浓密机耙架转速为1.2 r/min。持续进料4 h，泥层高度达到25 cm，此时沉降柱内物料质量分数升高至凝胶点 [ 10 10 ] 。此后停止进料，但保持耙架继续转动，停留时间即为停止进料后开始计时的时间。每隔1 h从底流取样，测试底流屈服应力，并读取该时段内扭矩传感器监测到的最大扭矩。 1.3 　实验结果 2 1.3.1　不同停留时间的底流料浆屈服应力变化规律 3 底流料浆屈服应力随停留时间的变化规律如 图3 图3 (a)所示。 (a) 屈服应力；(b) 耙架扭矩 随着物料在DCT内停留时间的延长，底流浆体的屈服应力总体保持增大趋势。对停留时间与底流屈服应力的变化曲线进行回归分析，发现动态浓密底流料浆屈服应力随停留时间的变化趋势遵循ExpDec1函数(相关系数 R ²为0.987)： <math display="block" id="M1"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">14.9</mn><mo>×</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo stretchy="false">(</mo><mi>t</mi><mo>/</mo><mn mathvariant="normal">4.38</mn><mo stretchy="false">)</mo></mrow></msup><mo>+</mo><mn mathvariant="normal">123.2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682218&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682208&type= 35.13666534 4.06400013 式中： <math id="M2"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682662&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682660&type= 2.62466669 3.72533321 为动态浓密底流屈服应力，Pa； t 为停留时间，h。 1.3.2　不同停留时间的耙架扭矩变化规律 3 动态浓密耙架扭矩随物料停留时间增加的变化规律如 图3 图3 (b)所示。 不同停留时间耙架扭矩的变化规律与底流屈服应力的变化趋势保持一致，再次验证了可使用料浆屈服应力来表征耙架扭矩。动态浓密耙架扭矩随停留时间的变化遵循ExpDec1函数(相关系数 R ²为0.999)： <math display="block" id="M3"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">M</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">12.9</mn><mo>×</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo stretchy="false">(</mo><mi>t</mi><mo>/</mo><mn mathvariant="normal">5.73</mn><mo stretchy="false">)</mo></mrow></msup><mo>+</mo><mn mathvariant="normal">23.6</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682213&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682212&type= 34.88266373 4.06400013 式中： <math id="M4"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">M</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682224&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682215&type= 4.23333359 3.72533321 为动态浓密实验中的最大耙架扭矩，N·m。 2 不同停留时间深锥浓密机耙架扭矩计算模型 1 2.1 　深锥浓密机耙架结构与尺寸 2 深锥浓密机耙架结构由中心传动轴、水平横梁、导水杆、耙臂及刮泥耙组成，动态浓密系统的耙架结构与尺寸如 图4 图4 所示。水平衡梁十字相交于中心轴上部，在传动轴与横梁之间安装导水杆，导水杆底部固定于耙臂上，耙臂与中心轴的角度为45°，刮泥耙安装于耙臂上。 数据单位：cm。 (a) 水平横梁与导水杆；(b) 耙臂与刮泥耙 2.2 　深锥浓密机耙架扭矩计算模型 2 在动态浓密过程中，耙架各构件均绕中心传动轴转动，水平横梁绕中心轴自转，导水杆、耙臂、刮泥耙绕中心轴公转。构件旋转对料浆产生剪切作用，料浆自身发生屈服，且屈服发生在耙架构件旋转所产生的剪切面附近。因此，各构件旋转所产生的扭矩可用剪切应力及剪切面积表示 [ 22 22 ] ： <math display="block" id="M5"><mi>T</mi><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mo>∫</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>A</mi></mrow></mfenced><mo>⋅</mo><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682228&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682227&type= 24.89200020 7.61999989 式中： <math id="M6"><msub><mrow><mi>T</mi></mrow><mrow/></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682238&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682230&type= 3.04800010 3.72533321 为构件扭矩，N·m； <math id="M7"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682255&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682254&type= 2.79399991 3.72533321 为剪切应力，Pa； A 为剪切面积，m 2 ； r 为力臂，m。 在构建耙架扭矩计算模型前，需要进行如下假设： 1) 构件在剪切面需克服浆体的屈服应力才能产生转动，剪切应力的最大值出现在浆体屈服流动的时候，因此，计算过程中可用屈服应力 <math id="M8"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682253&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682239&type= 2.62466669 3.72533321 代替剪切应力 <math id="M9"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682255&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682254&type= 2.79399991 3.72533321 ，且屈服应力均匀分布在剪切面上； 2) DCT内耙架所处泥层为均匀泥层，耙架各构件转动所克服的料浆屈服应力均一致，在计算过程中可采用底流屈服应力计算扭矩。 2.2.1　水平横梁扭矩计算模型 3 水平横梁与中心传动轴连接，在剪切过程中，水平横梁绕轴自转，运动轨迹为一圆柱体，如 图5 图5 所示。水平横梁转动产生的剪切面即为剪切圆柱体的上下端面和侧面；横梁的最大扭矩 <math id="M10"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682296&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682293&type= 3.72533321 3.72533321 即可认为是由剪切圆柱上下端面扭矩 <math id="M11"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682262&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682260&type= 3.38666677 3.72533321 、 <math id="M12"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682265&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682264&type= 3.38666677 3.72533321 以及侧面扭矩 <math id="M13"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682245&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682244&type= 3.38666677 3.72533321 叠加产生。 剪切圆柱体上下端面的扭矩为 <math display="block" id="M14"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>r</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>r</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><mi>r</mi><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi mathvariant="normal">d</mi><mi>x</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682275&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682273&type= 62.99200058 9.05933285 剪切圆柱体侧面扭矩为 <math display="block" id="M15"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><mi mathvariant="normal">d</mi><mi>x</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682278&type= 62.14533615 9.05933285 水平横梁的最大扭矩可表示为 <math display="block" id="M16"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><mo>×</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi mathvariant="normal">d</mi><mi>r</mi></mrow><mo>+</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msup><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><mi mathvariant="normal">d</mi><mi>x</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682284&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682282&type= 74.67600250 7.95866632 <math display="block" id="M17"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mfrac><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">3</mn></mrow></mfrac><mi mathvariant="normal">π</mi><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msubsup><mo>+</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>=</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682289&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682286&type= 46.90533447 7.28133297 式中： <math id="M18"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682296&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682293&type= 3.72533321 3.72533321 为水平横梁的最大扭矩，N·m； <math id="M19"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682292&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682297&type= 4.23333359 3.72533321 为水平横梁的尺寸参数； <math id="M20"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682298&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682309&type= 3.64066648 3.72533321 为剪切圆柱体的半径，m； <math id="M21"><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682300&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682299&type= 4.06400013 3.72533321 为剪切圆柱体的高度，m； <math id="M22"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682662&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682660&type= 2.62466669 3.72533321 为料浆屈服应力，Pa。 2.2.2　导水杆扭矩计算模型 3 导水杆浸没在浆体中，在中心传动轴的带动下克服料浆屈服应力转动，形成导水通道，因网状结构破坏而被释放出来的絮团内部水沿着导水通道排出。导水杆的转动轨迹为一圆环体，产生的剪切面为上下圆环端面、内外圆柱体侧面，如 图6 图6 所示。导水杆的最大扭矩 <math id="M23"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682363&type= 3.47133350 3.72533321 即可认为是由上下端面扭矩 <math id="M24"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682324&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682307&type= 3.38666677 3.72533321 、 <math id="M25"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682328&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682326&type= 3.38666677 3.72533321 和内外圆柱面扭矩 <math id="M26"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682316&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682330&type= 3.38666677 3.72533321 、 <math id="M27"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682333&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682332&type= 3.38666677 3.72533321 叠加产生。由于导水杆固定于水平横梁和耙臂上，其转动过程中产生的上下圆环剪切面已在水平横梁扭矩计算模型中进行计算，此处不再考虑。 剪切内圆柱面的扭矩为 <math display="block" id="M28"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mi mathvariant="normal">d</mi><mi>x</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682354&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682322&type= 62.14533615 9.05933285 剪切外圆柱面的扭矩为 <math display="block" id="M29"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mi mathvariant="normal">d</mi><mi>x</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682359&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682355&type= 62.14533615 9.05933285 导水杆的最大扭矩可表示为 <math display="block" id="M30"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mi mathvariant="normal">d</mi><mi>x</mi></mrow><mo>+</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mi mathvariant="normal">d</mi><mi>x</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682341&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682361&type= 62.31467056 7.95866632 <math display="block" id="M31"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo stretchy="false">)</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>=</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682362&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682342&type= 40.80933380 4.82600021 式中： <math id="M32"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682363&type= 3.47133350 3.72533321 为导水杆的最大扭矩，N·m； <math id="M33"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682371&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682368&type= 3.97933316 3.72533321 为导水杆的尺寸参数； <math id="M34"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682349&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682347&type= 3.64066648 3.72533321 为剪切内圆柱面的半径，m； <math id="M35"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682352&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682350&type= 3.64066648 3.72533321 为剪切外圆柱面的半径，m； <math id="M36"><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682381&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682378&type= 4.06400013 3.72533321 为导水杆高度，m； <math id="M37"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682662&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682660&type= 2.62466669 3.72533321 为料浆屈服应力，Pa。 耙架由6根导水杆组成，因此，耙架导水杆的总扭矩为 <math display="block" id="M38"><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi>i</mi></mrow></msub></mrow><mo>=</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi>i</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682405&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682402&type= 27.34733391 8.72066593 式中： <math id="M39"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682388&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682386&type= 4.14866638 3.72533321 和 <math id="M40"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682391&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682390&type= 4.65666676 3.72533321 分别为第 i 根导水杆的最大扭矩和尺寸参数。 2.2.3　耙臂扭矩计算模型 3 耙臂在浓密机锥部绕轴转动，转动轨迹为一空心圆锥体，产生的剪切面为圆柱侧面、内外圆锥面，如 图7 图7 所示。耙臂的最大扭矩 <math id="M41"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682477&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682474&type= 3.89466691 3.72533321 即可认为是由内外圆锥面扭矩 <math id="M42"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">8</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682430&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682414&type= 3.38666677 3.72533321 和 <math id="M43"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682433&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682416&type= 3.38666677 3.72533321 以及圆柱侧面扭矩 <math id="M44"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682420&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682436&type= 4.48733330 3.72533321 叠加产生。 剪切内、外圆锥面的扭矩为 <math display="block" id="M45"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">8</mn></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>r</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><mi>r</mi><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi mathvariant="normal">d</mi><mi>x</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682425&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682444&type= 75.26866913 9.05933285 剪切圆柱侧面的扭矩为 <math display="block" id="M46"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>R</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><mi>R</mi><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><msubsup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></mrow></msubsup><mrow><mi mathvariant="normal">d</mi><mi>x</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682460&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682427&type= 72.64399719 9.05933285 耙臂的最大扭矩可表示为 <math display="block" id="M47"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">8</mn></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">2</mn><mo stretchy="false">(</mo><mn mathvariant="normal">4</mn><mi mathvariant="normal">π</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi mathvariant="normal">d</mi><mi>x</mi></mrow><mo>+</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682451&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682462&type= 68.91867065 7.95866632 <math display="block" id="M48"><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><msubsup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></mrow></msubsup><mrow><mi mathvariant="normal">d</mi><mi>x</mi></mrow><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682454&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682467&type= 32.59666443 7.95866632 <math display="block" id="M49"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">4</mn><mi mathvariant="normal">π</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>θ</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">(</mo><mfrac><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mn mathvariant="normal">3</mn></mrow></mfrac><msubsup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msubsup><mo>+</mo><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msubsup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682473&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682471&type= 57.91199875 7.28133297 式中： <math id="M50"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682477&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682474&type= 3.89466691 3.72533321 为耙臂的最大扭矩，N·m； <math id="M51"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682490&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682478&type= 4.40266657 3.72533321 为耙臂的尺寸参数； <math id="M52"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682493&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682483&type= 3.47133350 3.72533321 为耙臂的长度，m； <math id="M53"><msub><mrow><mi>H</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682486&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682496&type= 4.06400013 3.72533321 为剪切圆柱的高度，m； <math id="M54"><mi>θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682504&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682487&type= 1.86266661 2.62466669 为耙架锥角，(°)； <math id="M55"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682662&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682660&type= 2.62466669 3.72533321 为料浆屈服应力，Pa。 2.2.4　刮泥耙扭矩计算模型 3 将刮泥耙安装在耙臂上，运动轨迹为一碟状几何体，产生的剪切面为4个圆台侧面，如 图8 图8 所示。刮泥耙的最大扭矩 <math id="M56"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682610&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682605&type= 3.47133350 3.72533321 即可认为是由刮泥耙4条边旋转形成的4个圆台侧面扭矩 <math id="M57"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682511&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682522&type= 4.48733330 3.72533321 ~ <math id="M58"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">14</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682528&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682513&type= 4.48733330 3.72533321 叠加产生。 剪切内圆台侧面的扭矩为 <math display="block" id="M59"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub><mo>=</mo><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>r</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><mi>r</mi><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">[</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682550&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682517&type= 54.52533722 7.95866632 <math display="block" id="M60"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">3</mn></mrow></mfrac><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682543&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682552&type= 49.10666656 7.28133297 <math display="block" id="M61"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>r</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><mi>r</mi><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">[</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682565&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682546&type= 57.57332993 9.05933285 <math display="block" id="M62"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">3</mn></mrow></mfrac><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682569&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682567&type= 49.10666656 7.28133297 剪切外圆台侧面的扭矩为 <math display="block" id="M63"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>r</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><mi>r</mi><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">[</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682559&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682556&type= 57.57332993 9.05933285 <math display="block" id="M64"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">3</mn></mrow></mfrac><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682578&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682576&type= 49.10666656 7.28133297 <math display="block" id="M65"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">14</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><mi>r</mi><mo>⋅</mo><mi mathvariant="normal">d</mi><mi>x</mi></mrow></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><mi>r</mi><mo>=</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">[</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682582&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682594&type= 57.57332993 9.05933285 <math display="block" id="M66"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">3</mn></mrow></mfrac><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682586&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682597&type= 49.10666656 7.28133297 刮泥耙的最大扭矩可表示为 <math display="block" id="M67"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">14</mn></mrow></msub><mo>=</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682603&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682601&type= 44.61933517 3.72533321 式中： <math id="M68"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682610&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682605&type= 3.47133350 3.72533321 为刮泥耙的最大扭矩，N·m； <math id="M69"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682626&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682611&type= 3.97933316 3.72533321 为刮泥耙的尺寸参数； <math id="M70"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682618&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682630&type= 3.47133350 3.72533321 为刮泥耙长边旋转形成的圆台母线长度，m； <math id="M71"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682637&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682635&type= 3.47133350 3.72533321 为刮泥耙短边旋转形成的圆台母线长度，m； <math id="M72"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682656&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682640&type= 3.64066648 3.72533321 ~ <math id="M73"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682659&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682642&type= 3.64066648 3.72533321 为刮泥耙4个顶点旋转形成的圆的半径，m； <math id="M74"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682662&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682660&type= 2.62466669 3.72533321 为料浆屈服应力，Pa。 耙架由6个刮泥耙组成，因此，刮泥耙的总扭矩即为 <math display="block" id="M75"><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>S</mi><mi>i</mi></mrow></msub><mo>=</mo></mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mi>i</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi>y</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682665&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682648&type= 25.90800095 8.72066593 式中： <math id="M76"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">S</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682669&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682667&type= 4.14866638 3.72533321 和 <math id="M77"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682672&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682671&type= 4.65666676 3.72533321 分别为第 i 个刮泥耙的最大扭矩和尺寸参数。 2.2.5　耙架扭矩计算模型 3 根据上述分析，耙架在转动过程中产生的扭矩可由下式表示： <math display="block" id="M78"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">M</mi></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi>i</mi></mrow></msub></mrow><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">S</mi><mi>i</mi></mrow></msub></mrow><mo>=</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682676&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682674&type= 46.82066727 8.72066593 <math display="block" id="M79"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>P</mi><mi>i</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi>y</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mo>+</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mi>i</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi>y</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682689&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682678&type= 55.28733826 8.72066593 <math display="block" id="M80"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">M</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>P</mi><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mo>+</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>S</mi><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682692&type= 56.21866989 8.72066593 式中： <math id="M81"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">M</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682706&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682704&type= 4.23333359 3.72533321 为耙架的最大扭矩，N·m。 将 式(1) 式(1) 代入 式(20) 式(20) 即可建立不同停留时间下的深锥浓密机耙架扭矩计算模型： <math display="block" id="M82"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">M</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi>i</mi></mrow></msub></mrow><mo>+</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6</mn></mrow></munderover></mstyle><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi><mi>i</mi></mrow></msub></mrow><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn mathvariant="normal">14.9</mn><mo>×</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo stretchy="false">(</mo><mi>t</mi><mo>/</mo><mn mathvariant="normal">4.38</mn><mo stretchy="false">)</mo></mrow></msup><mo>+</mo><mn mathvariant="normal">123.2</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682715&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682713&type= 78.57066345 8.72066593 将动态浓密耙架装置各构件的尺寸参数( 图5 图5 )代入该模型，有 <math display="block" id="M83"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">M</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">4.065</mn><mo>×</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo stretchy="false">(</mo><mi>t</mi><mo>/</mo><mn mathvariant="normal">4.38</mn><mo stretchy="false">)</mo></mrow></msup><mo>+</mo><mn mathvariant="normal">33.613</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682709&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43682717&type= 40.47066879 4.06400013 2.3 　耙架扭矩计算模型与实测值相互验证 2 基于不同停留时间的耙架扭矩计算模型计算得到不同停留时间下的耙架扭矩，如 图9 图9 所示。 由 图9 图9 可知，耙架扭矩的预测值与实测值的变化规律( 图4 图4 )保持一致，以停留时间7 h为拐点同样可以划分为2个阶段：1) 缓慢增长阶段(0≤ t< 7 h)。随着停留时间的延长，扭矩计算值渐渐增大，但此阶段线性拟合斜率较小，变化率小；2) 快速增长阶段(7≤ t ≤13 h)。此阶段线性拟合斜率明显变大，耙架扭矩计算值随停留时间延长而明显增大，变化率大，见 图9 图9 。 耙架扭矩计算值与实测值之间仍存在一定的误差。在初始阶段(0≤ t< 3 h)，这两者的相对误差绝对值小于5.0%，误差较小；在误差增大阶段(3≤ t< 7 h)，误差不断增大；在误差稳定阶段(7≤ t ≤13 h)，此阶段相对误差绝对值稳定在10%左右。计算耙架扭矩的2个主要变量是耙架在行驶方向上的投影面积和料浆的屈服应力，在耙架尺寸不变的情况下，当剪切面积一定时，部分构件实际的剪切应力远大于模型的底流屈服应力，从而导致出现误差。 3 全尾砂深锥浓密压耙机理分析 1 3.1 　耙架扭矩模型计算值与实测值误差原因分析 2 在动态浓密实验中，停留时间为13 h时耙架最大扭矩达到147.1 N·m，非常接近扭矩传感器的最大量程，为避免扭矩过大损坏驱动电机和扭矩传感器，停止实验。此时，可以明显地观察到锥部泥层出现分层现象(见 图10 图10 )，锥部的机壁上附着一层质感粗糙、流动性较差的致密层，从锥壁向中心延伸并且完全覆盖了耙臂和刮泥耙，且在该区域可观察到大量的粗颗粒分布。而锥体中部仍保持可泵送的料浆状态，致密层无法使用蠕动泵排出，需使用外力将其从锥壁刮掉。 从致密层的泥层取样，测得料浆质量分数和屈服应力分别高达79.95%和639.3 Pa，远远高于底流口排出的料浆浓度和屈服应力。耙臂和刮泥耙在锥壁附近转动，需要克服高浓度、高屈服应力的致密层的阻力，导致耙臂和刮泥耙的扭矩过大，耙架扭矩计算值与实测值出现误差，也导致压耙事故的发生。 3.2 　全尾砂深锥浓密压耙机理分析 2 结合深锥相似模型锥部致密层的观测结果以及误差原因分析结果发现，DCT锥部泥层随料浆停留时间延长会形成一层致密层，致密层粗颗粒尾砂(CPT)占比、浓度及屈服应力远比底流料浆的高，导致设计人员对位于DCT锥部的耙架构件(耙臂和刮泥耙)转动所产生的扭矩估计不足，进而导致驱动电机的设计扭矩偏小，易发生压耙事故 [ 12 12 ] 。 下面借助基于停留时间的耙架扭矩计算模型进一步阐释DCT压耙机理：根据Stokes定律，CPT絮凝沉降速度较快，受环流力作用的影响较小，粗粒尾砂从给料井进入沉降区后快速下沉。在沉降过程中，CPT被絮状物包裹成一个整体，带动絮体向泥层运移，CPT加速了全尾砂料浆的沉降，当CPT占比超过50%时，加速效应明显 [ 23 23 ] 。CPT和絮体形成一个整体，迅速沉降聚集于耙臂和刮泥耙附近并形成一定的泥层高度。 与选矿连续作业不同，采矿往往是间歇式充填作业，暂停排料时，尾砂颗粒在DCT中停留时间增加，此时，耙架的旋转剪切起主导作用，耙动行为使压密区的絮体结构发生显著重组，絮团结构破坏，尺寸变小，液相水释放上行，而由细颗粒絮凝形成的稳定絮体以及沉降过程中被絮网拦截的CPT继续向底层运移，锥部附近的泥层CPT含量逐渐升高 [ 24 24 ] 。CPT比表面积越小，保水性越差，因此，聚集在耙臂和刮泥耙附近的CPT在剪切作用下，群间水大量排出，形成的孔隙结构被剪切破坏后的絮团和细颗粒填充，使锥部附近的泥层更加致密，在耙臂和刮泥耙附近形成高浓度、难屈服的致密层。随着停留时间的延长，致密层浓度不断提高，致密层更加致密，甚至会演变为非流态化的散体区。在实际生产中，在锥体机壁附近也确实发现有难以清除的致密层 [ 7 7 , 12 12 , 19 19 ] 。 因此，全尾砂颗粒长时间停留导致压耙，主要归结于压密区颗粒群在“重力-压力-剪力”三力场作用下，颗粒群间水上行，CPT和细颗粒絮凝形成的稳定絮团向底部运移，DCT锥壁附近粗颗粒含量不断增加，并因CPT保水性差而逐渐变得密实，在锥壁附近形成了一圈致密层。致密层完全覆盖耙臂和刮泥耙，耙臂和刮泥耙在转动时要克服致密层物料内部作用力以及颗粒群与锥壁之间的摩擦阻力。颗粒尺寸直接影响料浆和锥壁之间的摩擦因数，粗颗粒的摩擦因数总是大于细颗粒的摩擦因数 [ 25 25 ] 。致密区缺乏适量群间水形成的润滑层，致密层随停留时间逐渐表现出的高浓度、难屈服特性以及CPT与锥壁之间的高摩擦性，导致锥部致密层产生过大的运转阻力，耙臂和刮泥耙需要克服的剪切阻力不断增大，DCT耙架扭矩随之增大。耙臂和刮泥耙的剪切作用使致密层的CPT含量和浓度不断提高，高摩擦和高浓度的致密层又反作用于耙臂和刮泥耙，导致耙架运转扭矩不断增大。在实际生产中，由于耙架的剪切作用，过度剪切脱水也会导致致密层形成，最终导致驱动电机超负荷运转，过载停机，发生压耙事故。 4 结论 1 1) 通过对耙架构件(水平横梁、导水杆、耙臂和刮泥耙)的力学分析，并联立底流屈服应力与停留时间的回归关系，建立了不同停留时间下的DCT耙架扭矩计算模型。底流屈服应力和耙架扭矩随不同停留时间的变化规律可分为缓慢增长和快速增长2个阶段。 2) 停留时间增加能够显著提高DCT锥部料浆的屈服应力，从而使得DCT耙架扭矩增大。 3) 当停留时间 t < 2 h时，耙架扭矩模型计算值与实测值的相对误差小于5%，预测结果可靠；当2≤ t ≤7 h时，两者相对误差不断增大；当 t > 7 h时，两者相对误差稳定于10%左右。锥部的耙臂和刮泥耙附近存在一层浓度和屈服应力均较高的致密层，导致耙臂和刮泥耙的实际运转扭矩远大于模型预测值。 4) 全尾砂中CPT含量过高，尾砂快速沉积于锥部耙架附近，粗颗粒由于比表面积小、保水性差、摩擦因数大，在“重力-压力-剪力”三力作用下，随着停留时间延长不断变得密实，逐渐形成“高CPT含量、高浓度、高摩擦、难屈服”的“三高一难”致密层，并反作用于耙臂和刮泥耙，导致耙架扭矩增大，最终导致DCT压耙。 参考文献 CAO Shuai , XUE Gaili , SONG Weidong , et al . 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Pore connectivity and dewatering mechanism of tailings bed in raking deep-cone thickener process 吴爱祥 , 李红 , 程海勇 , 等 . 全尾砂膏体流变学研究现状与展望(上): 概念、 特性与模型 [J]. 工程科学学报 , 2020 , 42 ( 7 ): 803 - 813 . 全尾砂膏体流变学研究现状与展望(上): 概念、 特性与模型 WU Aixiang , LI Hong , CHENG Haiyong , et al . Status and prospects of researches on rheology of paste backfill using unclassifiedtailings(Part 1): concepts, characteristics and models [J]. Chinese Journal of Engineering , 2020 , 42 ( 7 ): 803 - 813 . Status and prospects of researches on rheology of paste backfill using unclassifiedtailings(Part 1): concepts, characteristics and models 10.11817/j.issn.1672-7207.2023.04.026 TF11.31 A 1672-7207（2023）04-1491-09 吴爱祥, 武鹏杰, 王少勇, 等. 基于停留时间的深锥浓密机耙架扭矩计算模型[J]. 中南大学学报(自然科学版), 2023, 54(4): 1491-1499. 吴爱祥, 武鹏杰, 王少勇, 等. 基于停留时间的深锥浓密机耙架扭矩计算模型[J]. 中南大学学报(自然科学版), 2023, 54(4): 1491-1499. WU Aixiang, WU Pengjie, WANG Shaoyong, et al. Calculation model of rake torque of deep cone thickener based on residence time[J]. Journal of Central South University(Science and Technology), 2023, 54(4): 1491-1499. WU Aixiang, WU Pengjie, WANG Shaoyong, et al. Calculation model of rake torque of deep cone thickener based on residence time[J]. Journal of Central South University(Science and Technology), 2023, 54(4): 1491-1499. 国家自然科学基金资助项目(52130404)；中国博士后科学基金资助项目(2021M691359) Project(52130404) supported by the National Natural Science Foundation of China; Project(2021M691359) supported by the China Postdoctoral Science Foundation 2022-05-15 2022-07-07 2023-04-26 2023-05-22 37692585 中南大学学报(自然科学版) 4 54