MODEL AND HARVEST CHARACTERISTIC RESEARCH OF PIEZOELECTRIC ENERGY HARVESTER USED IN COAL MINE
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摘要: 采煤机的无线监测节点存在供电难问题, 采用压电俘能器将振动能转化为电能可为其供电, 研究俘能特性具有重要科学意义. 采用实验与数据拟合方法建立恢复力模型, 磁化电流法建立磁力模型, 拉格朗日函数建立动力学模型, RecurDyn提取滚筒、摇臂的截割方向加速度, 龙格库塔法求解动力学模型, 分析在不同磁距的俘能特性, 并开展实验研究. 结果表明: 受到前滚筒、后滚筒、前摇臂和后摇臂的截割方向加速度, 在俘能特性较好的磁距时, 电压依次减小且均随煤层硬度的增大而增大, 截割f4煤层时, 磁距分别为12 mm, 16 mm, 12 mm和12 mm的俘能特性较好, 电压有效值分别为5.107 V, 4.224 V, 0.998 V和0.882 V, 截割f6煤层时, 磁距均为16 mm的俘能特性较好, 电压有效值分别为7.298 V, 6.747 V, 1.592 V和1.397 V, 加入磁力可以加大电压. 实验研究发现, 受到截割f4和f6煤层的前滚筒截割方向加速度, 在俘能特性较好的磁距时, 电压随煤层硬度的增大而增大, 磁距分别为12 mm和16 mm的俘能特性较好, 电压有效值分别为3.340 V和4.959 V, 加入磁力可以加大电压, 验证了理论分析结果具有正确性. 研究为提高电压提供理论基础, 为无线监测节点自供电提供思路.Abstract: About the problem of difficult electricity supply for wireless monitoring node of exploiting coal machine,a piezoelectric energy harvester is used to convert the vibration energy into electricity,the research of energy harvest characteristic has scientific significance.Using experimental and data fitting method to establish restoring force model,using magnetization current method to establish magnetic force model,using the Lagrange function to establish dynamic model,using RecurDyn to extract the exploiting direction acceleration of roller and swing arm,the dynamic model is solved by using Runge Kutta method,analyzing energy harvest characteristic at different magnetic distances,conducting experimental research.The results show that it is subjected to exploiting direction acceleration of front roller,after roller,front swing arm and after swing arm,at the magnetic distance with great energy harvest characteristic,the voltage gradually decreases,the voltage increases entirely when the hardness of the coal seam increases,when exploiting f4 coal seam,the energy harvest characteristic are great at magnetic distances of 12 mm,16 mm,12 mm and 12 mm, the effective voltage values are 5.107 V,4.224 V,0.998 V and 0.882 V,when exploiting the f6 coal seam, the energy harvest characteristic are entirely great at magnetic distance of 16 mm,the effective voltage values are 7.298 V,6.747 V,1.592 V and1.397 V,the voltage increases when adding magnetic force.Through experimental research, it was found that it is subjected to exploiting direction acceleration of front roller when exploiting f4,f6 seam,the voltage increases when the hardness of coal seam increases at a magnetic distance with great energy harvest characteristic,the energy harvest characteristic are great at magnetic distances of 12 mm and 16 mm,the effective voltage values are 3.340 V and 4.959 V,the voltage increases when adding magnetic force,verifing the correctness of theoretical result.The research provides a theoretical basis for improving the voltage,providing idea for self electricity supply of wireless monitoring node.
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引 言
由于煤矿环境恶劣、危险系数大, 为了避免发生人员伤亡事故, 将工作人员从井下撤离出来, 让采煤机自主运行, 此时需要在采煤机上安装大量无线监测节点对运行状态进行实时监测, 并将监测信息反馈给工作人员, 保证采煤机正常运行. 由于化学电池不能长时间为无线监测节点供电, 供电成为瓶颈问题. 压电俘能器可以将振动能转化为电能, 研究俘能特性非常重要.
张伟等[1]发现增大压电俘能器的正弦激励强度可以增大功率输出. 张颖等[2]研究提高计算俘能器磁力精度的方法. 钱有华等[3]研究压电俘能器的阻尼比、势阱深浅程度和负载电阻对俘能效果的影响. 曹东兴等[4]研究俘能器的俘能特性, 加入磁力可以降低共振频率, 提高电压输出. 吴娟娟等[5]研究压电俘能器在不同中心频率的高斯白噪声激励下的输出电压. 刘琦等[6-7]设计一种能使驱动力放大的双固支梁压电俘能结构, 发现在弱高斯白噪声激励下可以发生突跳运动. 马天兵等[8]研究不同形状压电悬臂梁在正弦激励下的输出功率. 张忠华等[9]分析俘能器在不同强度正弦激励下的输出电压峰值. 满大伟等[10-12]研究发现俘能器在合适的起振位置可以产生大幅值运动, 并研究磁距、磁铁质量、负载电阻对输出响应的影响. 李颍等[13]发现通过改变激励幅值可以使三稳态压电能量采集器实现阱间运动, 提高功率输出. 张强等[14-16]采用压电俘能装置为刨煤机的刨刀受力检测系统、采煤机扭矩检测系统和刮板输送机张力检测系统提供电量, 通过实验发现在采煤机、刨煤机和刮板输送机工作时能够产生电量. Xie等[17]发现具有非对称势阱的压电能量采集器在高斯白噪声激励下的输出电压比传统的压电能量采集器的输出电压大. Chen等[18]发现双耦合梁的压电能量收集器加入弹簧可以降低势垒, 在较低的激励下能够实现大幅值运动, 选择合适的弹簧刚度可以提高功率输出. 赵丽娟等[19-21]采用EDEM建立煤层模型, 采用EDEM与RecurDyn耦合提取采煤机的振动加速度. Xia等[22]发现增加压电能量采集器的端部质量可以降低共振频率, 有利于提高能量收集效果. 张宇等[23]发现悬臂梁在不同频率的简谐激励下存在跳跃现象. 张广义等[24]发现梯形压电梁比矩形压电梁的输出功率大. Lu等[25]发现加入多层压电材料可以加大能量采集器的输出电压. 高扬等[26]采用振动能量采集装置为矿用无线监测系统供电, 发现在谐振频率处的发电量最大, 发电量与激励幅度呈正相关. 刘建政等[27]采用压电−电磁−摩擦能量采集器实现矿用无线监测系统自供电. 解胜东[28]采用压电叠堆俘能器为煤机检测系统提供电量, 发现压电片的厚度与发电量呈正相关.
综上所述, 目前研究压电俘能器受到采煤机采掘激励下的俘能特性非常少. 因此, 本文采用实验与数据拟合方法建立恢复力模型, 磁化电流法建立磁力模型, 拉格朗日函数建立动力学模型, RecurDyn提取滚筒、摇臂的截割方向加速度, 龙格库塔法求解动力学模型, 分析在不同磁距的俘能特性, 并开展实验研究.
1. 压电俘能器结构
压电俘能器结构, 如图1所示. 在悬臂梁上固定压电薄膜, 悬臂梁固定在基座上, 磁铁A, B分别固定在悬臂梁末端与基座上. 目前压电梁大多采用直线结构, 文献[29-30]发现曲线结构压电梁与直线结构压电梁受到同等作用力, 采用曲线结构可以提高电压与功率输出, 因此, 本文压电梁采用曲线结构. 压电俘能器分别受到滚筒、摇臂的截割方向加速度影响, 由于有煤落在滚筒上, 导致俘能器无法安装在滚筒上, 现分别安装在摇臂上端、摇臂质心位置, 如图2的1, 2, 3, 4位置.
悬臂梁与压电薄膜的线形段长度、拱形段半径分别为2 cm和1 cm, 悬臂梁与压电薄膜的宽度为0.8 cm, 悬臂梁与压电薄膜的厚度分别为0.02 cm与0.011 cm, 悬臂梁与压电薄膜的密度分别为8300 kg/m3和1780 kg/m3, 悬臂梁与压电薄膜的弹性模量分别为1.28 × 1011 Pa和3.0 × 109 Pa, 磁铁A, B的长、宽、厚分别为0.5 cm, 1 cm和1 cm, 磁化强度、真空磁导率和密度分别为5.5 × 105 A/m, 4π × 10−7 H/m和7500 kg/m3.
2. 压电俘能器数学模型与采煤机截割煤层仿真模型
2.1 压电俘能器数学模型
2.1.1 恢复力模型
采用文献[18]实验方法测量恢复力, 如图3所示, 将线性端固定在基座上, 采用YLK-10测力计多次推动曲线端, 对不同位移的恢复力取平均值, 恢复力随位移变化, 如图4所示, 对恢复力进行拟合, 得到的模型为
$$ {F_r} = 41\;963.4{r^3}\left( t \right) + 18.29r\left( t \right) $$ (1) 2.1.2 磁力模型
采用磁化电流法建立磁力模型, 悬臂梁转动φ, 磁铁A同样转动φ. 磁铁A, B的位置图, 如图5所示.
在磁铁B的中心建立坐标系, 磁铁A上下表面的中心点分别为${{O}}_{1}$和${{O}}_{2}$. ∠AOC = φ, BC = d, AC = e. sinφ = e/(L + lA/2), lA和L分别为磁铁A的长度和悬臂梁的水平长度.
磁铁A受到磁铁B的磁力Fm为
$$\begin{split} &{F_m}{{ = }}{\mu _0}{M_A}{S_A}\left\{ {H_x}_2\left[ {{O_{\text{2}}}\left( {d - \frac{{{h_A}}}{2} \sin \varphi ,e - \frac{{{h_A}}}{2} \cos \varphi ,0} \right)} \right] - \right.\\ &\qquad \left.{H_x}_1\left[ {{O_1}\left( {d + \frac{{{h_A}}}{2} \sin \varphi ,e + \frac{{{h_A}}}{2} \cos \varphi ,0} \right)} \right] \right\} \\[-12pt]\end{split} $$ (2) 式中, $ {\mu }_{0} $为真空磁导率, $ {M}_{A} $, $ {S}_{A} $, e, hA为磁铁A的磁化强度、面积、位移、高度, Hx2(O2), Hx1(O1)为磁铁B在O2, O1点的磁场强度, d为磁铁A, B的水平距离.
磁铁B在O处的磁场强度Hx(O)为
$$\begin{split} &{H_x}(O) = \frac{{{M_B}}}{{4\text{π} }}\left[ {{\tan }^{ - 1}}\left(\frac{{{y_p}{z_p}}}{{x\sqrt {y_p^2 + z_p^2 + {x^2}} }}\right) + \right.\\ &\quad {{\tan }^{ - 1}}\left(\frac{{{y_q}{z_q}}}{{x\sqrt {y_q^2 + z_q^2 + {x^2}} }}\right) - {{\tan }^{ - 1}}\left(\frac{{{y_q}{z_p}}}{{x\sqrt {y_q^2 + z_p^2 + {x^2}} }}\right) -\\ &\quad \left.{{\tan }^{ - 1}}\left(\frac{{{y_p}{z_q}}}{{x\sqrt {y_p^2 + z_q^2 + {x^2}} }}\right) \right] \\[-16pt] \end{split} $$ (3) $$ {{y}}_{p} = y + \frac{{h}_{B}}{2}\text{, }{{y}}_{q} = y-\frac{{h}_{B}}{2},{{z}}_{p} = \frac{{w}_{B}}{2},{{z}}_{q} = -\frac{{w}_{B}}{2} $$ (4) 式中, MB, hB和wB为磁铁B的磁化强度、高度和宽度, x和y为O处的坐标值.
2.1.3 动力学模型
动力学模型为
$$ L = T - U + W $$ (5) 式中, L, T, U和W为总能量、动能、弹性势能与磁场势能之和、电能.
动能为
$$\begin{split} &T = \frac{1}{2}({\rho _P}{A_P} + {\rho _S}{A_S}){\int_0^L {\left( {\dot w\left( {x,t} \right) + \dot z\left( t \right)} \right)} ^{\text{2}}}{\rm{d}}x +\\ &\qquad \frac{1}{2}m{\left( {\dot w\left( {L,t} \right) + \dot z(t)} \right)^2}{\text{ + }}\frac{{\text{1}}}{{\text{2}}}I{\left[ {\frac{{{\partial ^2}\left( {w\left( {L,t} \right) + z\left( t \right)} \right)}}{{\partial t\partial x}}} \right]^2}\end{split} $$ (6) 式中, ρS和ρP为悬臂梁和压电薄膜的密度, AS和AP为悬臂梁和压电薄膜的侧面积, $ \dot{w} $(x,t)为悬臂梁的x点在t时刻相对于基座的速度, $ \dot{z} $(t)和z(t)为基座的速度和位移, $ \dot{w} $(L,t), w(L,t), I和m为磁铁A相对基座的速度、位移、转动惯量和质量, t为时间, x为距悬臂梁基点的水平距离.
磁铁A绕通过O点的Z轴做旋转运动, 磁铁A转动惯量[31]为
$$ I = \frac{m}{{12}}\left( {{{ {{l^2_A}} }} + {{ {{h^2_A}} }}} \right){\text{ + }}m{\left( {L + \frac{{{l_A}}}{2}} \right)^2} $$ (7) 弹性势能与磁场势能之和为
$$\begin{split} &U = \frac{1}{2}({A_P}C_{11}^E + {A_S}{Y_S}){\int_0^L {\left( { - z\frac{{{\partial ^2}w(x,t)}}{{\partial {x^2}}}} \right)} ^2}{\rm{d}}x -\\ &\qquad \frac{1}{2}{A_P}{e_{31}}z\frac{{v\left( t \right)}}{{{h_p}}}\int_0^L {\frac{{{\partial ^2}w\left( {x,t} \right)}}{{\partial {x^2}}}} {\rm{d}}x + \int {{F_m}{\rm{d}}r(t)} \end{split}$$ (8) 式中, $ {C}_{11}^{E} $, e31, v(t)和hP为压电薄膜的弹性模量、压电应力常数、电压和厚度. YS和hS为悬臂梁的弹性模量和厚度, z为悬臂梁中性层到压电薄膜上表面的距离, z = hP + hS/2. w(x, t)为悬臂梁的x点在t时刻相对于基座的位移, r(t)为位移.
电能为
$$ W = \frac{1}{2}{e_{31}}{A_P}\frac{{v\left( t \right)}}{{{h_P}}}\int_0^L {\left( {z\frac{{{\partial ^2}w\left( {x,t} \right)}}{{\partial {x^2}}}} \right)} {\rm{d}}x + \frac{{\varepsilon _{33}^S{b_P}{L_P}}}{{2{h_P}}}{v^2}(t) $$ (9) 式中, bP, Lp和$ {\varepsilon }_{33}^{S} $为压电薄膜的宽度、水平长度和介电常数.
压电俘能器主要以一阶振动模态为主, 故仅考虑一阶振动模态. 对w(x,t)进行离散, 采用一端夹紧、一端自由的悬臂梁容许函数近似振型函数$ \phi \left(x\right) $
$$ w\left( {x,t} \right) = \varphi (x)r\left( t \right){\text{ = }}\left[ {1 - \cos \left( {\frac{{\text{π} x}}{{2L}}} \right)} \right]r\left( t \right) $$ (10) 拉格朗日方程为
$$ \frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial L}}{{\partial \dot r\left( t \right)}}} \right) - \frac{{\partial L}}{{\partial r\left( t \right)}} = - C\dot r\left( t \right) = - 2M\zeta w\dot r\left( t \right) $$ (11) $$ \frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial L}}{{\partial \dot v(t)}}} \right) - \frac{{\partial L}}{{\partial v\left( t \right)}} = \int {\frac{{v(t)}}{R}} {\rm{d}}t $$ (12) 式中, R为电阻, C为等效阻尼[32], w为谐振频率, ζ为阻尼比, M为等效质量.
将式(10)分别代入式(6)、式(8)和式(9), 将分别算出的结果代入式(5), 将代入式(5)算出的结果分别代入式(11)和式(12), 得出动力学模型为
$$ M\ddot r\left( t \right) + C\dot r\left( t \right) + Kr(t) + {F_m} - \vartheta v\left( t \right) = - {H_S}\ddot z\left( t \right) $$ (13) $$ \vartheta \dot r\left( t \right) + {C_p}\dot v\left( t \right) + v\left( t \right)/R{\text{ = 0}} $$ (14) 式中, K为等效刚度, $ {H}_{S} $为基础激励系数, $ \vartheta $为机电耦合系数, $ {C}_{P} $为电容, $ \ddot{z} $(t)为加速度.
$$ M = \left( {{\rho _P}{A_P} + {\rho _S}{A_S}} \right)\int_0^L {{\varphi ^2}\left( x \right){\rm{d}}x + m} {\varphi ^2}\left( L \right) + I{\dot \varphi ^2}\left( L \right) $$ (15) $$ K = ({Y_S}{A_S} + C_{11}^E{A_P})\int_0^L {{z^2}{{\left( {\ddot \varphi (x)} \right)}^2}{\rm{d}}x} $$ (16) $$ {H_S} = \left( {{\rho _P}{A_P} + {\rho _S}{A_S}} \right)\int_0^L {\varphi \left( x \right){\rm{d}}x + m} \varphi \left( L \right) $$ (17) $$ \vartheta = \frac{{z{e_{31}}{A_P}}}{{{h_P}}}\int_0^L {\ddot \varphi \left( x \right){\rm{d}}x} $$ (18) $$ {C_P} = \frac{{{b_P}{L_P}\varepsilon _{33}^S}}{{{h_P}}} $$ (19) 让振动台以加速度为20 m/s2, 频率为13 Hz的激励振动, 振动一段时间后, 停止振动, 采用激光测振仪测量压电俘能器速度, 采用coco80采集速度信号. 速度原始信号和滤波信号, 如图6和图7, 速度信号衰减线与包络线, 如图8所示.
对速度衰减信号的振幅进行指数函数拟合[33], 为下式, 其中ζw = 0.934 7.
$$ \dot r(t) = A{{\rm{e}}^{ - \zeta_{w}{t}}}{\text{ = 445}}{\text{.158}}{{\rm{e}}^{ - {\text{0}}{\text{.934 7}}t}} $$ (20) 式(13)的Kr(t)项为恢复力, 表示出恢复力随位移变化为线性关系, 而压电俘能器结构为曲线型, 恢复力随位移变化为非线性关系, Kr(t)项采用式(1)代替
$$ {r}_{1}\left(t\right) = r\left(t\right)\text{, }{r}_{\text{2}}\left(t\right) = \dot{r}\left(t\right)\text{, }{r}_{\text{3}}\left(t\right) = v\left(t\right) $$ (21) 在Matlab中, 采用龙格库塔法对式(13)和式(14)求解, 得出电压
$$ {\dot r_1}\left( t \right) = {r_2}\left( t \right) $$ (22) $$ {\dot r_2}\left( t \right) = \frac{{ - {H_s}\ddot z\left( t \right) + \vartheta {r_3}\left( t \right) - {F_m} - {F_r} - C{r_2}\left( t \right)}}{M} $$ (23) $$ {\dot r_3}\left( t \right) = - \frac{1}{{{c_p}}}\left( {\frac{{{r_3}\left( t \right)}}{R} + \vartheta {r_2}\left( t \right)} \right) $$ (24) 其中, r1(t)为位移, r2(t)为速度, r3(t)为电压.
2.2 采煤机截割煤层仿真模型
2.2.1 煤层模型
在EDEM建立硬度为f4和f6的煤粒, 半径均为50 mm, f4煤的剪切模量和泊松比为9.56 × 108 Pa和0.15, f6煤的剪切模量和泊松比为1.72 × 109 Pa和0.22, f6煤的硬度相对于f4煤的硬度大, 将煤层几何模型导入EDEM, 煤粒在煤层几何模型中生成, 并采用黏结键黏结煤粒. 黏结键参数计算公式为
$$ {S_n} = \frac{{2G\left( {1 + \mu } \right)}}{{2.2r}} = 2\left( {1 + \mu } \right){S_t} $$ (25) $$ {\sigma _y} = 10 f $$ (26) 式中, $ {S}_{n} $, $ {S}_{t} $和$ {\sigma }_{y} $分别为法向刚度、切向刚度和极限法向应力, G, μ, r和f为煤粒的剪切模量、泊松比、半径和普氏系数.
根据式(25)和式(26), f4煤层的$ {S}_{n} $, $ {S}_{t} $和$ {\sigma }_{y} $为1.99891 × 1010 N/m3, 8.6909 × 109 N/m3和4.0 × 107 Pa, 极限切向应力1.6 × 107 Pa; f6煤层的$ {S}_{n} $, $ {S}_{t} $和$ {\sigma }_{y} $为3.81527 × 1010 N/m3, 1.5636 × 1010 N/m3和6.0 × 107 Pa, 极限切向应力2.4 × 107 Pa. 煤粒模型、煤层几何模型和煤层模型, 分别如图9 ~ 图11所示.
2.2.2 采煤机动力学模型
(1)仿真模型的建立. 将采煤机和刮板输送机中部槽几何模型导入到RecurDyn, 仿真模型, 如图12.
(2)约束的建立. 为提取滚筒载荷, 在滚筒与摇臂、摇臂与机身、摇臂与油缸、活塞与机身的连接处建立旋转副, 在油缸与活塞、平滑靴与刮板输送机中部槽的连接处建立移动副, 在导向滑靴与机身、平滑靴与机身、大地与刮板输送机中部槽的连接处建立固定副; 为提取截割方向加速度, 在滚筒与摇臂、摇臂与机身、摇臂与油缸、活塞与机身、导向滑靴与机身、平滑靴与机身的连接处建立弹性与阻尼元件, 在油缸与活塞的连接处建立弹簧元件, 在平滑靴与刮板输送机中部槽连接处建立移动副, 在大地与刮板输送机中部槽的连接处建立固定副.
(3)驱动的建立. 为提取滚筒载荷和截割方向加速度, 在平滑靴与刮板输送机中部槽的移动副处建立移动速度驱动, 大小为4 m/min, 方向沿X轴负方向; 为提取滚筒载荷, 在滚筒与摇臂的旋转副处建立转速驱动, 大小为3π rad/s, 方向为逆时针.
采用提取滚筒载荷的动力学模型与煤层模型做采煤机截割煤层的仿真, 可以提取滚筒载荷, 截割煤层图, 如图13所示. 将滚筒载荷导进提取截割方向加速度的动力学模型, 可以提取截割方向加速度.
3. 采煤机截割方向加速度的提取
由图14和图15可知, 截割f4煤层的前滚筒的X向、Y向和Z向载荷有效值分别为3.694 × 105 N, 3.309 × 105 N和3.521 × 105 N, 后滚筒的X向、Y向、Z向载荷有效值分别为1.826 × 105 N, 2.905 × 105 N和3.404 × 105 N. 截割f6煤层的前滚筒的X向、Y向和Z向载荷有效值分别5.344 × 105 N, 4.832 × 105 N和6.501 × 105 N, 后滚筒的X向、Y向、Z向载荷有效值分别2.881 × 105 N, 3.960 × 105 N和5.324 × 105 N.
截割f4和f6煤层的采煤机各部位截割方向加速度, 分别如图16和图17所示.
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图 16 截割f4煤层的各部位截割方向加速度Figure 16. the exploiting direction acceleration of each part when exploiting f4 coal seam![]()
图 17 截割f6煤层的各部位截割方向加速度Figure 17. the exploiting direction acceleration of each part when exploiting f6 coal seam由图16和图17可知, 振动从滚筒传到摇臂会减小, 前滚筒3向载荷相对于后滚筒大, 且前、后滚筒的3向载荷随煤层硬度的增大而增大, 使前滚筒、后滚筒、前摇臂、后摇臂的截割方向加速度在依次减小且均随煤层硬度的增大而增大. 截割f4煤层的前滚筒、后滚筒、前摇臂和后摇臂的截割方向加速度的有效值分别为21.257 m/s2, 19.580 m/s2, 9.004 m/s2和8.455 m/s2, 截割f6煤层的前滚筒、后滚筒、前摇臂、后摇臂的截割方向加速度的有效值分别为30.724 m/s2, 28.538 m/s2, 13.095 m/s2和12.370 m/s2.
4. 压电俘能器的俘能特性分析
压电俘能器受到采煤机各部位截割方向加速度发生振动, 压电薄膜产生变形并输出电压. 将截割方向加速度导入到动力学模型中, 采用龙格库塔法求解, 得出电压随时间变化趋势.
4.1 在截割f4煤层的俘能特性分析
当受到前滚筒的截割方向加速度, 在不同磁距的电压如图18所示.
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图 18 受到前滚筒截割方向加速度的电压Figure 18. The voltage with exploiting direction acceleration of front roller由图18可知, 在无磁力时, 电压有效值为2.662 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为5.107 V, 4.049 V和3.845 V, 加入磁力可以加大电压, 磁距为12 mm, 俘能特性较好, 电压较大.
当受到前摇臂的截割方向加速度, 在不同磁距的电压如图19所示.
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图 19 受到前摇臂截割方向加速度的电压Figure 19. The voltage with exploiting direction acceleration of front swing arm由图19可知, 在无磁力时, 电压有效值为0.513 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为0.998 V, 0.802 V和0.851 V, 加入磁力可以加大电压, 磁距为12 mm, 俘能特性较好, 电压较大.
当受到后滚筒的截割方向加速度, 在不同磁距的电压, 如图20所示.
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图 20 受到后滚筒截割方向加速度的电压Figure 20. The voltage with exploiting direction acceleration of after roller由图20可知, 在无磁力时, 电压有效值为2.655 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为3.078 V, 4.224 V和3.038 V, 加入磁力可以加大电压, 磁距为16 mm, 俘能特性较好, 电压较大.
当受到后摇臂的截割方向加速度, 在不同磁距的电压, 如图21所示.
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图 21 受到后摇臂截割方向加速度的电压Figure 21. The voltage with exploiting direction acceleration of after swing arm由图21可知, 在无磁力时, 电压有效值为0.477 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为0.882 V, 0.736 V和0.756 V, 加入磁力可以加大电压, 磁距为12 mm, 俘能特性较好, 电压较大.
截割方向加速度呈随机波动, 使电压呈随机波动. 截割f4煤层时, 前滚筒、后滚筒、前摇臂和后摇臂的截割方向加速度在依次减小, 使受到前滚筒、后滚筒、前摇臂和后摇臂的截割方向加速度, 在俘能特性较好的磁距时, 电压在依次减小.
4.2 在截割f6煤层的俘能特性分析
当受到前滚筒的截割方向加速度, 在不同磁距的电压, 如图22所示.
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图 22 受到前滚筒截割方向加速度的电压Figure 22. The voltage with exploiting direction acceleration of front roller由图22可知, 在无磁力时, 电压有效值为4.910 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为5.825 V, 7.298 V和5.571 V, 加入磁力可以加大电压, 磁距为16 mm, 俘能特性较好, 电压较大.
当受到前摇臂的截割方向加速度, 在不同磁距的电压, 如图23所示.
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图 23 受到前摇臂截割方向加速度的电压Figure 23. The voltage with exploiting direction acceleration of front swing arm由图23可知, 在无磁力时, 电压有效值为1.060 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为1.307 V, 1.592 V和1.048 V, 加入磁力可以加大电压, 磁距为16 mm, 俘能特性较好, 电压较大.
当受到后滚筒的截割方向加速度, 在不同磁距的电压, 如图24所示.
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图 24 受到后滚筒截割方向加速度的电压Figure 24. The voltage with exploiting direction acceleration of after roller由图24可知, 在无磁力时, 电压有效值为2.872 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为3.571 V, 6.747 V和3.798 V, 加入磁力可以加大电压, 磁距为16 mm, 俘能特性较好, 电压较大.
当受到后摇臂的截割方向加速度, 在不同磁距的电压, 如图25所示.
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图 25 受到后摇臂截割方向加速度的电压Figure 25. The voltage with exploiting direction acceleration of after swing arm由图25可知, 在无磁力时, 电压有效值为0.918 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为1.125 V, 1.397 V和0.928 V, 加入磁力可以加大电压, 磁距为16 mm, 俘能特性较好, 电压较大.
截割f6煤层时, 前滚筒、后滚筒、前摇臂和后摇臂的截割方向加速度在依次减小且均随煤层硬度的增大而增大, 使受到前滚筒、后滚筒、前摇臂和后摇臂的截割方向加速度, 在俘能特性较好的磁距时, 电压依次减小且均随煤层硬度的增大而增大.
5. 压电俘能器俘能特性实验验证
采用RecurDyn提取截割f4, f6煤层的前滚筒截割方向加速度的功率谱密度, 分别如图26和图27所示.
对俘能特性进行实验验证. 实验过程为: 将功率谱密度数据导进计算机中, 计算机控制振动控制器产生激励信号, 激励信号经过振动控制器、功率放大器传递到振动台, 振动台产生振动. 示波器与压电俘能器相连, 采集电压信号. 实验测试平台、压电俘能器, 分别如图28和图29所示.
当受到截割f4煤层的前滚筒截割方向加速度, 在不同磁距的电压, 如图30所示.
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图 30 受到截割f4煤层的前滚筒截割方向加速度的电压Figure 30. The voltage with exploiting direction acceleration of front roller when exploiting f4 coal seam由图30可知, 在无磁力时, 电压有效值为2.219 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为3.340 V, 3.092 V和2.456 V, 相应的理论结果为: 在无磁力时, 电压有效值为2.662 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为5.107 V, 4.049 V和3.845 V, 将理论结果与实验结果对比发现, 磁距均为12 mm的俘能特性较好, 电压较大, 加入磁力可以加大电压, 理论结果与实验结果定性吻合, 验证了理论分析结果具有正确性.
当受到截割f6煤层的前滚筒截割方向加速度, 在不同磁距的电压, 如图31所示.
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图 31 受到截割f6煤层的前滚筒截割方向加速度的电压Figure 31. The voltage with exploiting direction acceleration of front roller when exploiting f6 coal seam由图31可知, 在无磁力时, 电压有效值为2.304 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为4.379 V, 4.959 V和2.856 V, 相应的理论结果为: 在无磁力时, 电压有效值为4.910 V, 磁距分别为12 mm, 16 mm和20 mm, 电压有效值分别为5.825 V, 7.298 V和5.571 V, 将理论结果与实验结果对比发现, 磁距均为16 mm的俘能特性较好, 电压较大, 加入磁力可以加大电压, 理论结果与实验结果定性吻合, 并通过实验结果发现, 当受到截割f4和f6煤层的前滚筒截割方向加速度, 在俘能特性较好的磁距时, 电压随煤层硬度的增大而增大, 通过理论结果分析发现同样有此现象, 验证了理论分析结果具有正确性.
6. 结论
(1)设计一种矿用压电俘能器, 采用实验与数据拟合的方法建立恢复力模型, 采用磁化电流法建立磁力模型, 采用拉格朗日函数建立动力学模型. 采用RecurDyn提取滚筒、摇臂的截割方向加速度.
(2)压电俘能器受到前滚筒、后滚筒、前摇臂和后摇臂的截割方向加速度, 在俘能特性较好的磁距时, 电压依次减小且均随煤层硬度的增大而增大. 截割f4煤层时, 磁距分别为12 mm, 16 mm, 12 mm和12 mm的俘能特性较好, 电压有效值分别为5.107 V, 4.224 V, 0.998 V和0.882 V, 截割f6煤层时, 磁距均为16 mm的俘能特性较好, 电压有效值分别为7.298 V, 6.747 V, 1.592 V和1.397 V.
(3)通过实验研究发现, 压电俘能器受到截割f4和f6煤层的前滚筒截割方向加速度, 在俘能特性较好的磁距时, 电压随煤层硬度的增大而增大, 磁距分别为12 mm和16 mm的俘能特性较好, 电压有效值分别为3.340 V和4.959 V, 加入磁力可以加大电压, 验证了理论分析结果具有正确性.
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图 16 截割f4煤层的各部位截割方向加速度
Figure 16. the exploiting direction acceleration of each part when exploiting f4 coal seam
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图 17 截割f6煤层的各部位截割方向加速度
Figure 17. the exploiting direction acceleration of each part when exploiting f6 coal seam
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图 18 受到前滚筒截割方向加速度的电压
Figure 18. The voltage with exploiting direction acceleration of front roller
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图 19 受到前摇臂截割方向加速度的电压
Figure 19. The voltage with exploiting direction acceleration of front swing arm
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图 20 受到后滚筒截割方向加速度的电压
Figure 20. The voltage with exploiting direction acceleration of after roller
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图 21 受到后摇臂截割方向加速度的电压
Figure 21. The voltage with exploiting direction acceleration of after swing arm
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图 22 受到前滚筒截割方向加速度的电压
Figure 22. The voltage with exploiting direction acceleration of front roller
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图 23 受到前摇臂截割方向加速度的电压
Figure 23. The voltage with exploiting direction acceleration of front swing arm
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图 24 受到后滚筒截割方向加速度的电压
Figure 24. The voltage with exploiting direction acceleration of after roller
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图 25 受到后摇臂截割方向加速度的电压
Figure 25. The voltage with exploiting direction acceleration of after swing arm
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图 30 受到截割f4煤层的前滚筒截割方向加速度的电压
Figure 30. The voltage with exploiting direction acceleration of front roller when exploiting f4 coal seam
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