WO2022022243A1 - 一种双稳态能量收集器离心距离优化匹配方法 - Google Patents

一种双稳态能量收集器离心距离优化匹配方法 Download PDF

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WO2022022243A1
WO2022022243A1 PCT/CN2021/104855 CN2021104855W WO2022022243A1 WO 2022022243 A1 WO2022022243 A1 WO 2022022243A1 CN 2021104855 W CN2021104855 W CN 2021104855W WO 2022022243 A1 WO2022022243 A1 WO 2022022243A1
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centrifugal
magnet
cantilever beam
equation
energy
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张云顺
石小青
赵香帅
王勇
郑仁成
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Jiangsu University
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Jiangsu University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
    • H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
    • H02N2/18—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing electrical output from mechanical input, e.g. generators
    • H02N2/186—Vibration harvesters

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  • the invention relates to the technical field of bistable energy collectors, in particular to a method for optimizing the centrifugal distance of a bistable energy collector.
  • centrifugal distance is set by the estimation method or the empirical method to further simulate and study its efficiency.
  • the performance and efficiency of the energy harvester are very sensitive to the centrifugal distance, even in the order of magnitude of 0.0001 m.
  • the present invention provides the following scheme:
  • a method for optimizing the centrifugal distance of a bistable energy harvester comprises the following steps:
  • Step 1 establish the kinetic model of the bistable energy harvester with centrifugal effect
  • Step 2 carry out a working simulation of the bistable energy harvester
  • Step 3 During the vibration of the cantilever beam, the magnetic force received by the magnet is F M , and the tangential component force is F H ;
  • F N is the pressure received by the magnet at the end of the cantilever beam, and
  • Step 4 The dynamic equation of the bistable energy harvesting system based on the magnet oscillating in the high-energy potential energy well is expressed as where m is the mass of the magnet at the end of the cantilever beam; c is the damping; k is the initial stiffness of the cantilever beam; L is the length of the cantilever beam; r is the distance from the center of rotation to the root of the cantilever beam; The distance between the centers of rotation; a is the linear coefficient of the magnet force; b is the nonlinear coefficient of the magnet force;
  • Step 6 The frequency equation of the lower jump point is The better the fitting effect of the ⁇ curve and the frequency curve ⁇ is, the higher the energy of the corresponding monostable high-energy orbit after the drift, and the wider the frequency band.
  • the equation is a complex domain equation, ⁇ is the frequency value corresponding to the position where the trajectory of the lower jump point and the frequency curve intersect, and ⁇ only takes positive real roots.
  • a further improvement lies in: the frequency corresponding to the position where the locus of the jump point and ⁇ intersects when the centrifugal distance H effect is optimal is:
  • the effective collection frequency band is the widest.
  • the invention further improves the energy collection efficiency of the bistable energy collector and widens the effective collection frequency band by adjusting the installation centrifugal distance of the magnet at the end of the cantilever beam.
  • the calculation equation of the optimal centrifugal distance is deduced, which can greatly shorten the installation and debugging time of magnets at different centrifugal distances when the centrifugal effect is used to improve the bistable energy harvester.
  • the rotation frequency corresponding to the most efficient energy harvesting efficiency under the optimal centrifugal distance H is deduced. In this way, bistable energy harvesters with different parameters can be designed to adapt to rotating machines (vehicles) that often work at a fixed rotational frequency (vehicle speed), and further improve the performance and efficiency of bistable energy harvesters.
  • Fig. 1 is the kinetic model diagram of the bistable energy harvester of centrifugal effect of the present invention
  • Fig. 2 is the force analysis diagram of the cantilever beam end magnet of the present invention
  • FIG. 3 is a matching diagram of the ⁇ curve and the frequency curve under different centrifugal distances of the present invention.
  • the dynamic model of the centrifugal effect bistable energy harvester includes a frame 1, a magnet 2, a cantilever beam 3, a piezoelectric sheet 4 and a rotation center 5, and the frame 1 is installed on the rotating environment (disc) , the magnet 2 includes a fixed magnet and a tip magnet; the fixed magnet is fixed on the frame 1 through lifting ears or using strong glue, the tip magnet is fixed on the end of the cantilever beam 3 with strong glue, and the piezoelectric sheet 4 is pasted on both sides of the cantilever beam 3,
  • the cantilever beam 3 is fixed on the rotating disk through the lifting lugs and ensures that the straight line where the cantilever beam 3 is located passes the rotation center 5 , which is the rotation center 5 of the disk and the rotation center 5 of the rotating shaft.
  • This embodiment provides a method for optimizing the centrifugal distance of a bistable energy harvester, and the matching method includes the following steps:
  • Step 1 Establish the kinetic model of the bistable energy harvester with centrifugal effect.
  • Step 2 Carry out a working simulation of the bistable energy harvester.
  • Step 3 During the vibration of the cantilever beam, as shown in Figure 2, the magnetic force received by the magnet is F M , and the tangential component force is F H ; F N is the pressure on the magnet at the end of the cantilever beam, and F C is the magnet at the end of the cantilever beam.
  • F H F M sin ⁇
  • ⁇ is the volume of the magnet
  • ⁇ is the magnetic permeability in vacuum
  • Mf (M fx , M fy )
  • M fx is the magnetization amplitude of the magnet installed on the rack in the horizontal direction
  • M fy is the magnetization amplitude of the magnet installed on the rack in the vertical direction
  • M cx is the magnetization of the tip magnet in the horizontal direction
  • M cy is the magnetization amplitude of the tip magnet in the vertical direction
  • x r is the real-time displacement of the tip magnet
  • d is the distance between the magnet installed on the rack and the tip magnet.
  • Step 4 The dynamic equation of the bistable energy harvesting system based on the magnet oscillating in the high-energy potential energy well is expressed as where m is the mass of the magnet at the end of the cantilever beam; c is the damping; k is the initial stiffness of the cantilever beam; L is the length of the cantilever beam; r is the distance from the center of rotation to the root of the cantilever beam; The distance between the centers of rotation; a is the linear coefficient of the magnetic force; b is the nonlinear coefficient of the magnetic force, is the acceleration of the vertical vibration of the tip magnet, is the vertical vibration velocity of the tip magnet, x r is the vertical vibration displacement of the tip magnet, ⁇ is the rotational angular velocity, G is the equivalent gravity of the tip magnet, and ⁇ t+ ⁇ 0 is the real-time phase angle during the rotation of the tip magnet.
  • Step 6 The frequency equation of the lower jump point is The better the fitting effect between the ⁇ curve and the frequency curve ⁇ , the higher the energy of the monostable high-energy orbit after the corresponding drift and the wider the frequency band.
  • Figure 3 shows the matching diagram of the ⁇ curve and the frequency curve under different centrifugal distances.
  • the frequency corresponding to the position where the trajectory of the jump point intersects with ⁇ is is the bending stiffness of the cantilever beam
  • E is the elastic modulus of the cantilever beam material
  • I is the moment of inertia of the cantilever beam section, at this time
  • the effective collection frequency band is the widest.

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  • General Electrical Machinery Utilizing Piezoelectricity, Electrostriction Or Magnetostriction (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)

Abstract

一种双稳态能量收集器离心距离优化匹配方法，通过考虑离心效应对于双稳态能量收集装置收集效率的影响，探究不同离心距离下的双稳态能量收集装置收集效率，求解出最优离心距离，进一步优化双稳态能量收集器的有效收集频带带宽和能量收集效率。利用调节悬臂梁末端磁铁的安装离心距离来进一步提高双稳态能量收集器的能量收集效率和拓宽有效收集频带。推导出了最优离心距离的计算方程式，可以大幅度缩短利用离心效应提高双稳态能量收集器效能时使磁铁处于不同离心距离下的安装和调试时间。

Description

一种双稳态能量收集器离心距离优化匹配方法
本申请要求于2020年07月31日提交中国专利局、申请号为202010759431.1、发明名称为“一种双稳态能量收集器离心距离优化匹配方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本发明涉及双稳态能量收集器技术领域，特别是涉及一种双稳态能量收集器离心距离优化匹配方法。
背景技术
在过去的十年中，能量收集的研究越来越丰富，特别是利用压电陶瓷来收集振动能量。能量收集器被广泛认为可以为汽车或其他风力发电装置等中小型传感器提供能量。但是，该能量收集器的问题在于，当激励频率偏离共振频率时，能量收集器无法在更宽的频率上保持这种性能。为了解决这一问题，许多研究人员正在研究如何扩展能量采集器的有效频率范围。其中，非线性能量收集器的研究非常广泛，例如共振机制对能量收集器的性能和效率的影响，此外，双稳态能量收集系统，三稳态能量收集系统和多稳态能量收集系统的研究也非常丰富。但是，离心效应对于双稳态能量收集器的性能和效率的影响的研究不够成熟，多数时候是采用估值法或经验法对离心距离进行设定，以进一步仿真研究其效能；由于双稳态能量收集器的性能和效率对于离心距离非常敏感，甚至在0.0001m数量级范围，当能量收集器的系统参数发生改变，研究者在进行仿真或实验时无法迅速找到最优的离心距离范围。
发明内容
基于此，有必要提供一种双稳态能量收集器离心距离优化匹配方法，以通过考虑离心效应对于双稳态能量收集装置收集效率的影响，探究不同离心距离下的双稳态能量收集装置收集效率，求解出最优离心距离，进一步优化双稳态能量收集器的有效收集频带带宽和能量收集效率。
为实现上述目的，本发明提供了如下方案：
一种双稳态能量收集器离心距离优化匹配方法，所述匹配方法包括以下步骤：
步骤一：建立离心效应的双稳态能量采集器的动力学模型；
步骤二：对双稳态能量采集器进行工作模拟；
步骤三：悬臂梁在振动过程中，磁铁受到的磁力为F M，切向分力为F H；F N为悬臂梁末端磁铁受到的压力，F C为悬臂梁末端磁铁受到的离心力，则
Figure PCTCN2021104855-appb-000001
Figure PCTCN2021104855-appb-000002
其中：ν是磁铁的体积；μ是真空中的磁导率；Mf＝(Mf x,M fy),Mc＝(M cx,M cy)是安装在机架上的永磁体的磁化强度振幅和磁端质量；
步骤四：基于磁体在高能势能阱中振荡的双稳态能量采集系统的动力学方程表示为
Figure PCTCN2021104855-appb-000003
Figure PCTCN2021104855-appb-000004
Figure PCTCN2021104855-appb-000005
其中m为悬臂梁末端磁铁质量；c为阻尼；k为初始时悬臂梁刚度；L为悬臂梁长度；r为旋转中心距离悬臂梁根部的距离；H≈L+r为悬臂梁末端磁铁质心与旋转中心间的距离；a为磁铁力的线性系数；b为磁铁力的非线性系数；
步骤五：运用谐波振动法求解动力学方程，设x＝B+Xcosωt，则
Figure PCTCN2021104855-appb-000006
步骤六：下跳点频率方程为
Figure PCTCN2021104855-appb-000007
γ曲线与频率曲线ω的拟合效果越好，则对应漂移后的单稳态高能轨道能量越高，频带越宽。
进一步改进在于：当γ曲线与频率曲线ω相切时的离心距离H的求解：令γ＝ω，化简有：
Figure PCTCN2021104855-appb-000008
方程为复数域方程，ω为下跳点轨迹与频率曲线相交处位置对应的频率值，且ω只取正实根。
进一步改进在于：所述离心距离H的求解方程中令W＝ω 2，且W仅取正值，方程化简为
Figure PCTCN2021104855-appb-000009
上述方程看作关于W的一元二次方程，由一元二次方程求根公式：
Figure PCTCN2021104855-appb-000010
Figure PCTCN2021104855-appb-000011
γ曲线与频率曲线ω相切，即对应方程仅有一个实根，Δ＝16m 2(a-k) 2+(16m 2-24m 2H/L)·3mbG 2/c 2＝0，即：H＝(2/3+2(a-k) 2c 2/9mbG 2)L，此时的离心距离H的离心效应最优，有效收集频带最宽。
进一步改进在于：所述离心距离H效应最优时下跳点轨迹与ω相交处位置对应的频率值为
Figure PCTCN2021104855-appb-000012
为悬臂梁的抗弯刚度，E为悬臂梁材料的弹性模量，I为悬臂梁截面惯性矩，此时
Figure PCTCN2021104855-appb-000013
即：
Figure PCTCN2021104855-appb-000014
时系统的能量收集效率最优，有效收集频带最宽。
与现有技术相比，本发明的有益效果是：
本发明利用调节悬臂梁末端磁铁的安装离心距离来进一步提高双稳态能量收集器的能量收集效率和拓宽有效收集频带。推导出了最优离心距离的计算方程式，可以大幅度缩短利用离心效应提高双稳态能量收集器时使磁铁处于不同离心距离下的安装和调试时间。推导出了最优离心距离H下，最高效能量收集效率对应的旋转频率。以此可以设计出不同参数的双稳态能量收集器，以适应经常工作于某一固定旋转频率(车速)下的旋转机械(车辆)，进一步提高双稳态能量收集器的性能和效率。
说明书附图
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。
图1是本发明的离心效应的双稳态能量采集器的动力学模型图；
图2是本发明的悬臂梁末端磁铁受力分析图；
图3是本发明的不同离心距离下的γ曲线与频率曲线匹配图。
符号说明
1-框架、2-磁铁、3-悬臂梁、4-压电片、5-旋转中心。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进 行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
为使本发明的上述目的、特征和优点能够更加明显易懂，下面结合附图和具体实施方式对本发明作进一步详细的说明。
如图1所示，离心效应的双稳态能量采集器的动力学模型包括框架1、磁铁2、悬臂梁3、压电片4和旋转中心5，框架1安装于旋转环境(圆盘)上，磁铁2包括固定磁铁和尖端磁铁；固定磁铁通过吊耳或是使用强力胶水固定在框架1上，尖端磁铁使用强力胶水固定在悬臂梁3末端，压电片4粘贴在悬臂梁3两侧，悬臂梁3通过吊耳固定在旋转圆盘上且保证悬臂梁3所在直线过旋转中心5，旋转中心5是圆盘的旋转中心5也是旋转轴的旋转中心5。
本实施例提供了一种双稳态能量收集器离心距离优化匹配方法，所述匹配方法包括以下步骤：
步骤一：建立离心效应的双稳态能量采集器的动力学模型。
步骤二：对双稳态能量采集器进行工作模拟。
步骤三：悬臂梁在振动过程中，如图2所示，磁铁受到的磁力为F M，切向分力为F H；F N为悬臂梁末端磁铁受到的压力，F C为悬臂梁末端磁铁受到的离心力，则F H＝F M sinθ,
Figure PCTCN2021104855-appb-000015
Figure PCTCN2021104855-appb-000016
Figure PCTCN2021104855-appb-000017
其中：ν是磁铁的体积；μ是真空中的磁导率；Mf＝(M fx,M fy),Mc＝(M cx,M cy)分别是安装在 机架上的永磁体和尖端磁铁的磁化强度幅值，M fx为水平方向安装在机架上磁铁的磁化强度幅值，M fy为竖直方向安装在机架上磁铁的磁化强度幅值，M cx为水平方向尖端磁铁的磁化强度幅值，M cy为竖直方向尖端磁铁的磁化强度幅值，x r为尖端磁铁的实时位移，d为安装在机架上的磁铁与尖端磁铁间的距离。
步骤四：基于磁体在高能势能阱中振荡的双稳态能量采集系统的动力学方程表示为
Figure PCTCN2021104855-appb-000018
Figure PCTCN2021104855-appb-000019
Figure PCTCN2021104855-appb-000020
其中m为悬臂梁末端磁铁质量；c为阻尼；k为初始时悬臂梁刚度；L为悬臂梁长度；r为旋转中心距离悬臂梁根部的距离；H≈L+r为悬臂梁末端磁铁质心与旋转中心间的距离；a为磁铁力的线性系数；b为磁铁力的非线性系数，
Figure PCTCN2021104855-appb-000021
为尖端磁铁垂直方向振动的加速度，
Figure PCTCN2021104855-appb-000022
为尖端磁铁垂直方向振动的速度，x r为尖端磁铁垂直方向振动的位移，ω为旋转角速度，G为尖端磁铁等效重力，ωt+μ 0为尖端磁铁旋转过程中的实时相位角。
步骤五：运用谐波振动法求解动力学方程，设x＝B+Xcosωt，则
Figure PCTCN2021104855-appb-000023
x为尖端磁铁实时位移，B为尖端磁铁的平衡位移，X为尖端磁铁振动的位移幅值，ωt为尖端磁铁振动的相位角，H为安装离心距离，g为重力加速度。
步骤六：下跳点频率方程为
Figure PCTCN2021104855-appb-000024
γ曲线与频率曲线ω 的拟合效果越好，则对应漂移后的单稳态高能轨道能量越高，频带越宽，图3为不同离心距离下的γ曲线与频率曲线匹配图。
当γ曲线与频率曲线ω相切时的离心距离H的求解：令γ＝ω，化简有：
Figure PCTCN2021104855-appb-000025
方程为复数域方程，ω为下跳点轨迹与频率曲线相交处位置对应的频率值，且ω只取正实根。
所述离心距离H的求解方程中令W＝ω 2，且W仅取正值，方程化简为
Figure PCTCN2021104855-appb-000026
上述方程看作关于W的一元二次方程，由一元二次方程求根公式：
Figure PCTCN2021104855-appb-000027
Figure PCTCN2021104855-appb-000028
W 1,2为W的第一个根和W的第二个根，ω 1,2表示ω的第一个根ω 1和ω的第二个根ω 2，ω 1表示下跳点的频率数值，ω 2表示下跳后的峰值频率的数值，γ曲线与频率曲线ω相切，即对应方程仅有一个实根，Δ＝16m 2(a-k) 2+(16m 2-24m 2H/L)·3mbG 2/c 2＝0，即：H＝(2/3+2(a-k) 2c 2/9mbG 2)L，此时的离心距离H的离心效应最优，有效收集频带最宽。
所述离心距离H效应最优时下跳点轨迹与ω相交处位置对应的频率值为
Figure PCTCN2021104855-appb-000029
为悬臂梁的抗弯刚度，E为悬臂梁材料的弹性模量，I为悬臂梁截面惯性矩，此时
Figure PCTCN2021104855-appb-000030
即：
Figure PCTCN2021104855-appb-000031
时系统的能量收集效率最优，有效收集频带最宽。
本说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同相似部分互相参见即可。
本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处。综上所述，本说明书内容不应理解为对本发明的限制。

Claims (4)

  1. 一种双稳态能量收集器离心距离优化匹配方法，其特征在于：所述匹配方法包括以下步骤：
    步骤一：建立离心效应的双稳态能量采集器的动力学模型；
    步骤二：对双稳态能量采集器进行工作模拟；
    步骤三：悬臂梁在振动过程中，磁铁受到的磁力为F M，切向分力为F H；F N为悬臂梁末端磁铁受到的压力，F C为悬臂梁末端磁铁受到的离心力，则
    Figure PCTCN2021104855-appb-100001
    Figure PCTCN2021104855-appb-100002
    Figure PCTCN2021104855-appb-100003
    其中：ν是磁铁的体积；μ是真空中的磁导率；Mf＝(M fx,M fy),Mc＝(M cx,M cy)是安装在机架上的永磁体的磁化强度振幅和磁端质量；
    步骤四：基于磁体在高能势能阱中振荡的双稳态能量采集系统的动力学方程表示为
    Figure PCTCN2021104855-appb-100004
    Figure PCTCN2021104855-appb-100005
    Figure PCTCN2021104855-appb-100006
    其中m为悬臂梁末端磁铁质量；c为阻尼；k为初始时悬臂梁刚度；L为悬臂梁长度；r为旋转中心距离悬臂梁根部的距离；H≈L+r为悬臂梁末端磁铁质心与旋转中心间的距离；a为磁铁力的线性系数；b为磁铁力的非线性系数；
    步骤五：运用谐波振动法求解动力学方程，设x＝B+Xcosωt，则
    Figure PCTCN2021104855-appb-100007
    步骤六：下跳点频率方程为
    Figure PCTCN2021104855-appb-100008
    γ曲线与频率曲线ω的拟合效果越好，则对应漂移后的单稳态高能轨道能量越高，频带越宽。
  2. 如权利要求1所述的一种双稳态能量收集器离心距离优化匹配方法，其特征在于：当γ曲线与频率曲线ω相切时的离心距离H的求解：令γ＝ω，化简有：
    Figure PCTCN2021104855-appb-100009
    方程为复数域方程，ω为下跳点轨迹与频率曲线相交处位置对应的频率值，且ω只取正实根。
  3. 如权利要求2所述的一种双稳态能量收集器离心距离优化匹配方法，其特征在于：所述离心距离H的求解方程中令W＝ω 2，且W仅取正值，方程化简为
    Figure PCTCN2021104855-appb-100010
    上述方程看作关于W的一元二次方程，由一元二次方程求根公式：
    Figure PCTCN2021104855-appb-100011
    Figure PCTCN2021104855-appb-100012
    γ曲线与频率曲线ω相切，即对应方程仅有一个实根，Δ＝16m 2(a-k) 2+(16m 2-24m 2H/L)·3mbG 2/c 2＝0，即：H＝(2/3+2(a-k) 2c 2/9mbG 2)L，此时的离心距离H的离心效应最优，有效收集频带最宽。
  4. 如权利要求3所述的一种双稳态能量收集器离心距离优化匹配方 法，其特征在于：所述离心距离H效应最优时下跳点轨迹与ω相交处位置对应的频率值为
    Figure PCTCN2021104855-appb-100013
    Figure PCTCN2021104855-appb-100014
    为悬臂梁的抗弯刚度，E为悬臂梁材料的弹性模量，I为悬臂梁截面惯性矩，此时
    Figure PCTCN2021104855-appb-100015
    即：
    Figure PCTCN2021104855-appb-100016
    时系统的能量收集效率最优，有效收集频带最宽。
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