Study on precise control of coal caving mechanisms based on the kinematics of support structures
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摘要: 放煤机构的精准控制是实现智能化、无人化放顶煤开采的重要基础，放煤机构与后部刮板输送机的空间关系及支架姿态对空间关系的影响规律是构建放顶煤支架控制模型的关键。以ZF17000/27.5/42D型低位放顶煤支架为研究对象，阐述了支架顶板和底板不同俯仰姿态下放煤机构与后部刮板输送机的空间关系；基于液压支架放煤机构开口度控制逻辑，搭建了支架姿态感知系统，提出了液压支架放煤机构末端运动学分析方法；建立了基于D−H矩阵的低位放顶煤液压支架放煤机构末端运动学模型，并据此构建了液压支架放煤机构开口度计算模型，平均计算误差仅为1.71%，满足现场应用精度要求；提出了基于姿态反馈的支架放煤机构闭环控制方法，并将基于放煤机构开口度计算模型开发的放煤决策模型应用于现场。应用效果表明：自动放煤时各支架平均放煤时间的均方差仅为0.13 min，较人工放煤方式整体放煤效率提高20%～43.9%；顶煤采出率达89%，后部刮板输送机负载更加均衡，过载率仅为0.73%。Abstract: Precise control of the coal caving mechanism is a crucial foundation for realizing intelligent and unmanned top coal caving mining. The spatial relationship between the coal caving mechanism and the rear scraper conveyor, as well as the top coal influence of the hydraulic support's posture on this spatial relationship, is key to constructing a control model for the caving support. Using the ZF17000/27.5/42D low-position top coal caving support as the research object, this study explained the spatial relationship between the coal caving mechanism and the rear scraper conveyor under different pitch angles of the support's roof and base. Based on the control logic for the opening degree of the hydraulic support's coal caving mechanism, a support posture sensing system was established, and a method for kinematic analysis of the hydraulic support's coal caving mechanism was proposed. A kinematic model for the end of the low-position hydraulic support's coal caving mechanism based on the D-H matrix was developed, and a calculation model for the opening degree of the hydraulic support's coal caving mechanism was constructed. The average calculation error was only 1.71%, meeting the accuracy requirements for field applications. A closed-loop control method for the coal caving mechanism based on posture feedback was proposed, and the coal caving decision model developed from the opening degree calculation model was applied in the field. Application results showed that during automatic coal caving, the mean square deviation of the average caving time for each support was only 0.13 minutes, with an overall caving efficiency improvement of 20%-43.9% compared to manual caving. The top coal recovery rate reached 89%, and the load on the rear scraper conveyor was more balanced, with an overload rate of only 0.73%.
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图 2 底座、顶梁不同状态时液压支架姿态特征
Figure 2. Posture characteristics of hydraulic support under different states of base and top beam
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图 3 体坐标系与世界坐标系的空间关系
Figure 3. Spatial relationship between body coordinate system and world coordinate system
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图 4 标准D−H坐标系及其变换参数
Figure 4. Standard D-H coordinate system and its transformation parameters
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图 5 放顶煤液压支架D−H坐标系模型
Figure 5. D-H coordinate system model of top coal caving hydraulic support
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图 8 不同姿态下支架放煤机构运动轨迹及开口度特征
Figure 8. Motion trajectory and opening degree characteristics of coal caving mechanism under different postures of support
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图 9 放顶煤液压支架数值仿真模型
Figure 9. Numerical simulation model of top coal caving hydraulic support
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图 10 基于放煤机构开口度控制的自动放煤流程
Figure 10. Automatic coal caving flow based on the coal caving mechanism's opening degree
表 1 放顶煤液压支架D−H坐标系变换参数
Table 1 Transformation parameters of D-H coordinate system for top coal caving hydraulic support
关节i αi gi di θi 1 0 0 0 θ1 2 0 g2 0 θ2 3 0 g3 0 θ3 4 0 g4 0 θ4 5 0 g5 0 θ5 6 0 g6 0 θ6 
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表 2 液压支架D−H参数
Table 2 D-H parameters of hydraulic support
序号 D−H参数 结构参数 数值 含义 1 g2 lOB 1 712.5 mm 前连杆下铰接点B距固定
坐标系原点O的距离2 g3 lBD 1 884.7 mm 前连杆上下2个铰接点间的距离 3 g4 lDF 1 564.8 mm 前连杆上铰接点D与掩护梁上
铰接点F的距离4 g5 lFI 2 473.7 mm 掩护梁上下2个铰接点间的距离 5 g6 lIJ 1 707.0 mm 尾梁上铰接点到尾梁末端的距离 6 θ1 β1 实测数据 底座与水平面的夹角 7 θ2 ∠AOB 57° OB线与底座的夹角，固定值 8 θ3 180°−∠OBD 计算数据 OB线与前连杆夹角的补角 9 θ4 180°−∠BDF 计算数据 DF线与前连杆夹角的补角 10 θ5 180°−∠DFI 168° DF线与掩护梁夹角的补角 11 θ6 180°−∠HIJ 计算数据 掩护梁与尾梁之间的夹角
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表 3 部分支架构件参数
Table 3 Parameters of some support structural components
序号 结构参数 数值 含义 1 β2 实测数据 前连杆与水平面的夹角 2 ∠DFI 12° DF线与掩护梁的夹角 3 $ {l}_{{D}^{0}D} $ 493.9 mm 前连杆上铰接点到HE线的距离 4 lDE 500.1 mm 前后连杆上铰接点间的距离 5 lBC 1 033.4 mm 前后连杆下铰接点间的距离 6 ∠BCCʹ 25° C点到AB的垂线与BC的夹角 7 lCE 1 519.6 mm 后连杆上下铰接点间的距离 8 ∠IʹIP 70° 尾梁行程传感器上安装杆至
尾梁关节处形成的夹角9 ∠NIJʹ 13° 尾梁行程传感器下安装杆至
尾梁关节处形成的夹角10 lPI 336.7 mm 尾梁行程传感器上铰接点至
尾梁上铰接点的距离11 lIN 892.7 mm 尾梁行程传感器下铰接点至
尾梁上铰接点的距离12 lPN 714 mm+ lw 尾梁行程传感器2个铰接点间
的距离（实测数据）
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表 4 放煤机构开口度测试结果
Table 4 Test results of opening degree of coal caving mechanism
序号 底座倾
角/（°）前连杆
倾角/（°）尾梁行
程/mm计算值/
mm测量值/
mm差值/
mm误差/
%1 0 45 220 459.27 465.13 5.86 1.26 2 0 46 220 479.68 487.93 8.25 1.69 3 0 47 220 499.42 508.19 8.77 1.73 4 0 48 220 536.59 533.48 −3.11 −0.58 5 0 49 220 565.27 557.02 −8.25 −1.48 6 0 50 220 590.60 583.02 −7.58 −1.30 7 1 47 220 544.24 555.68 11.44 2.06 8 2 47 220 591.79 605.76 13.97 2.31 9 3 47 220 642.19 655.05 12.86 1.96 10 4 47 220 695.54 707.06 11.52 1.63 11 5 47 220 751.99 761.27 9.28 1.22 12 −1 47 220 457.26 465.27 8.01 1.72 13 −2 47 220 417.69 422.16 4.47 1.06 14 −3 47 220 380.65 380.80 0.15 0.04 15 −4 47 220 346.10 341.08 −5.02 −1.47 16 −5 47 220 314.01 303.01 −7.00 −2.31 17 0 47 350 58.11 61.80 3.69 5.97 18 0 47 280 282.41 289.30 6.89 2.38 19 0 47 230 488.30 494.47 6.17 1.25 20 0 47 170 726.81 732.40 5.59 0.76 21 0 47 110 990.70 995.86 5.16 0.52 22 0 47 50 1300.71 1307.65 6.94 0.53
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