CN115263985A - Constant-value quasi-zero stiffness vibration isolation structure and method based on negative stiffness mechanism of three pairs of inclined rods - Google Patents
Constant-value quasi-zero stiffness vibration isolation structure and method based on negative stiffness mechanism of three pairs of inclined rods Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及振动控制领域,特别是涉及一种基于三对斜杆负刚度机制的恒值准零刚度隔振结构及方法。The invention relates to the field of vibration control, in particular to a constant-value quasi-zero stiffness vibration isolation structure and method based on the negative stiffness mechanism of three pairs of oblique bars.
背景技术Background technique
文献[1]中研究的一种单对斜杆准零刚度模型,附带三次非线性刚度因素,在大幅激励下,传递率向右弯曲,降低隔振频带;并且此文献给出的参数设计方法复杂(含数个不等式),不便于设计和应用。上述文献中的技术方案无法获得静平衡点附近是直线的零刚度特性,无法降低线性振子的共振频率,且存在非线性因素影响;在大幅激励条件下,隔振频带会因非线性向右弯曲而降低。A quasi-zero stiffness model of a single pair of oblique rods studied in literature [1], with a cubic nonlinear stiffness factor, under large excitations, the transmissibility bends to the right, reducing the vibration isolation frequency band; and the parameter design method given in this literature Complex (including several inequalities), not easy to design and apply. The technical solutions in the above documents cannot obtain the zero-stiffness characteristic of a straight line near the static equilibrium point, cannot reduce the resonance frequency of the linear oscillator, and are affected by nonlinear factors; under large-scale excitation conditions, the vibration isolation frequency band will bend to the right due to nonlinearity And lower.
文献[2]基于单对斜杆负刚度机制构造的隔振器,提出了一种恒值准零刚度的调试方法。本申请以不同的结构、不同的调试方法的形式,提出了另外一种恒值准零刚度结构,具有与文献[2]在结构和调试方法上完全不同。文献[2]的水平弹簧需要较大的刚度,而本专利申请的水平弹簧需要较小的刚度,在结构上更加适用于更小的尺寸空间,虽然都是恒值准零刚度结构,但在使用效果上有一些明显区别。Literature [2] proposed a constant value quasi-zero stiffness debugging method based on the vibration isolator constructed by the negative stiffness mechanism of a single pair of oblique bars. In the form of different structures and different debugging methods, this application proposes another constant value quasi-zero stiffness structure, which is completely different from the literature [2] in terms of structure and debugging methods. The horizontal spring in document [2] needs a larger stiffness, but the horizontal spring in this patent application needs a smaller stiffness, which is more suitable for a smaller size space in structure. Although they are all constant value quasi-zero stiffness structures, they are in There are some noticeable differences in usage.
参考文献:references:
[1]Thanh Danh Le,Kyoung Kwan Ahn,A vibration isolation system in lowfrequency excitation region using negative stiffness structure for vehicleseat,Journal of Sound and Vibration,2011,330,6311-6335.[1] Thanh Danh Le, Kyoung Kwan Ahn, A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicleseat, Journal of Sound and Vibration, 2011, 330, 6311-6335.
[2]赵峰,曹树谦,侯远航,李博,宋茜,一种单对斜杆负刚度机制构成零刚度隔振结构及方法[P],CN202111347500.9,2022-03-01。[2] Zhao Feng, Cao Shuqian, Hou Yuanhang, Li Bo, Song Qian, A zero-stiffness vibration isolation structure and method formed by a single pair of inclined bars with negative stiffness mechanism [P], CN202111347500.9, 2022-03-01.
发明内容Contents of the invention
本发明的目的是为了克服现有技术中的不足,提供一种基于三对斜杆负刚度机制的恒值准零刚度隔振结构及方法。The purpose of the present invention is to overcome the deficiencies in the prior art, and provide a constant value quasi-zero stiffness vibration isolation structure and method based on the negative stiffness mechanism of three pairs of oblique bars.
本发明的目的是通过以下技术方案实现的:The purpose of the present invention is achieved through the following technical solutions:
一种基于三对斜杆负刚度机制的恒值准零刚度隔振结构,包括固定板、支架、横向导杆、斜杆、斜杆铰链支座、支座连接块、竖向导杆、垂直弹簧、空心管、载重盘和横向弹簧;所述固定板的两侧相对称的安装有支架,固定板的中部安装有竖向导杆,所述竖向导杆的上部安装有支座连接块,所述支座连接块上安装有与竖向导杆连接的竖向导杆直线轴承;所述支座连接块底部与固定板之间的竖向导杆上安装有垂直弹簧;A constant value quasi-zero stiffness vibration isolation structure based on the negative stiffness mechanism of three pairs of oblique rods, including fixed plates, brackets, transverse guide rods, oblique rods, oblique rod hinge supports, support connecting blocks, vertical guide rods, and vertical springs , a hollow tube, a load plate and a transverse spring; the two sides of the fixed plate are symmetrically equipped with brackets, the middle part of the fixed plate is equipped with a vertical guide rod, and the upper part of the vertical guide rod is equipped with a support connecting block. A vertical guide rod linear bearing connected to the vertical guide rod is installed on the support connecting block; a vertical spring is installed on the vertical guide rod between the bottom of the support connecting block and the fixed plate;
所述支座连接块的左右两端连接有斜杆铰链支座,所述斜杆铰链支座为U型结构;每个所述支架上等间距的通过固定件安装有三个直线轴承,每个直线轴承装有横向导杆,每个横向导杆朝向竖向导杆的一端设置有U型槽,U型槽旁边的横向导杆上设有弹簧卡板,弹簧卡板与固定件之间的每个横向导杆上均安装有横向弹簧;The left and right ends of the connecting block of the support are connected with a slanting bar hinge support, and the slanting bar hinge support is a U-shaped structure; each of the supports is equidistantly installed with three linear bearings through the fixing parts, each The linear bearing is equipped with horizontal guide rods, and each horizontal guide rod is provided with a U-shaped groove at one end facing the vertical guide rod, and a spring clip is provided on the horizontal guide rod next to the U-shaped groove, and each gap between the spring clip and the fixing piece A transverse spring is installed on each transverse guide rod;
所述竖向导杆两侧分别相对称的设置有三个斜杆,所述斜杆的一端与U型槽通过轴杆铰接,另一端与斜杆铰链支座铰接;Three oblique rods are symmetrically arranged on both sides of the vertical guide rod, one end of the oblique rod is hinged with the U-shaped groove through the shaft rod, and the other end is hinged with the hinged support of the oblique rod;
所述支座连接块的两侧分别设有连接孔,所述连接孔上设置有空心管,所述空心管顶端设置有载重盘并通过螺栓穿过所述空心管与连接孔连接固定所述载重盘。The two sides of the connecting block of the support are respectively provided with connecting holes, the connecting holes are provided with a hollow tube, and the top of the hollow tube is provided with a load plate, and the bolts pass through the hollow tube to connect with the connecting holes and fix the load plate.
进一步的,所述支架中部设有一条用于横向导杆通过的粗竖向通孔,粗竖向通孔两侧设置有两条平行的细竖向通孔,所述固定件采用与紧固螺栓及与直线轴承固接的连接板,连接板的中部设有用于横向导杆通过的通孔,连接板的两侧设有螺栓孔,所述连接板通过紧固螺栓穿过所述螺栓孔和细竖向通孔与螺母连接固定在支架上。Further, a thick vertical through hole is provided in the middle of the bracket for the passage of the transverse guide rod, and two parallel thin vertical through holes are arranged on both sides of the thick vertical through hole, and the fixing member is fastened with The bolts and the connecting plate fixedly connected with the linear bearing, the middle part of the connecting plate is provided with a through hole for the passage of the transverse guide rod, and the two sides of the connecting plate are provided with bolt holes, and the connecting plate passes through the bolt holes through fastening bolts It is connected with the thin vertical through hole and the nut to be fixed on the bracket.
进一步的,所述支架上等间距的设置有三个圆形通孔,所述固定件采用卡簧,直线轴承与支架通过卡簧固定。Further, three circular through holes are arranged at equal intervals on the bracket, and the fixing member adopts a snap spring, and the linear bearing and the bracket are fixed by the snap spring.
本发明还提供一种基于上述三对斜杆负刚度机制的恒值准零刚度隔振结构进行调试的方法,包括:The present invention also provides a method for debugging a constant value quasi-zero stiffness vibration isolation structure based on the negative stiffness mechanism of the above three pairs of oblique bars, including:
S1.依据准零刚度特性的参数条件,确定初始状态下下对横向弹簧的预压缩量δ2、斜杆两端铰接点之间的距离在水平方向上投影长度a、垂直弹簧的长度,使初始状态下δ2=a,初始状态指三对斜杆的交叉点与自由长度的垂直弹簧的顶端接触的状态;S1. According to the parameter condition of the quasi-zero stiffness characteristic, determine the precompression δ 2 of the transverse spring in the initial state, the projected length a of the distance between the hinge points at both ends of the oblique rod in the horizontal direction, and the length of the vertical spring, so that In the initial state, δ 2 =a, the initial state refers to the state where the intersection of three pairs of oblique rods is in contact with the top of the free-length vertical spring;
S2.设定恒值准零刚度隔振结构中从上到下的三对横向弹簧的刚度分别为k1、k3和k1,垂直弹簧的刚度k2,通过确定横向弹簧的刚度k1和k3,确定垂直弹簧的刚度k2,构建无量纲参数和使参数α和α1满足 S2. Set the stiffnesses of the three pairs of transverse springs from top to bottom in the constant-value quasi-zero stiffness vibration isolation structure as k 1 , k 3 and k 1 respectively, and the stiffness of the vertical springs k 2 , by determining the stiffness of the transverse springs k 1 and k 3 , determine the stiffness k 2 of the vertical spring, and construct the dimensionless parameter and Make parameters α and α 1 satisfy
S3.确定好上述参数后,绘制力位移曲线f-x,f为应用力即施加到载重盘上的力,x为从初始位置处开始的位移,此时力位移曲线为一条倾斜的直线,具有恒定刚度特性,计算刚度值K,根据载重盘上隔振质量m之间的关系,计算起始隔振频率若起始隔振频率不满足设计要求,则重复步骤S1至S3。S3. After determining the above parameters, draw the force-displacement curve fx. Stiffness characteristics, calculate the stiffness value K, and calculate the initial vibration isolation frequency according to the relationship between the vibration isolation mass m on the load plate If the initial vibration isolation frequency does not meet the design requirements, repeat steps S1 to S3.
与现有技术相比,本发明的技术方案所带来的有益效果是:Compared with the prior art, the beneficial effects brought by the technical solution of the present invention are:
1.本发明提出了三对斜杆和水平弹簧负刚度机制构造的恒值准零刚度隔振器,这种结构在恒值准零刚度研究方面,属首次被提出。1. The present invention proposes a constant-value quasi-zero-stiffness vibration isolator constructed with three pairs of oblique rods and a horizontal spring negative-stiffness mechanism. This structure is proposed for the first time in the research of constant-value quasi-zero stiffness.
2.本发明提出了三对斜杆负刚度机制构造的准零刚度隔振结构,并进行了参数设计,获得了力、刚度表达式与先有技术完全不同;在静态平衡点位置,令刚度等于零和刚度二阶导数等于零,获得两个零刚度参数条件,根据参数条件进行恒值准零刚度按需调节是一种全新的调试方法,调试简单,精度绝佳。参数设计(理论技术分析)时,所谓静态平衡点位置,即三对斜杆成中心对称的状态(或中间对斜杆水平的状态)。三对水平弹簧具有相同的自由长度。2. The present invention proposes a quasi-zero-stiffness vibration isolation structure constructed by three pairs of oblique rods with negative stiffness mechanism, and performs parameter design to obtain force and stiffness expressions that are completely different from those of the prior art; at the position of the static equilibrium point, let the stiffness Equal to zero and the second order derivative of stiffness equal to zero, obtain two zero stiffness parameter conditions, and adjust the constant quasi-zero stiffness on demand according to the parameter conditions is a new debugging method, which is simple to debug and has excellent accuracy. In parameter design (theoretical and technical analysis), the position of the so-called static equilibrium point is the state where the three pairs of diagonal bars are symmetrical to the center (or the state where the middle pair of diagonal bars is horizontal). Three pairs of horizontal springs have the same free length.
3.通过本发明的恒值准零刚度调试方法,可获得静平衡点附近是直线的零刚度特性,并且可获得更宽范围的恒值准零刚度特性,可以降低线性振子的共振频率,且不附带任何非线性因素;相比传统弱三次非线性特性的准零刚度隔振器,在大幅激励条件下,隔振频带不会因非线性向右弯曲而降低。3. Through the constant value quasi-zero stiffness debugging method of the present invention, the zero stiffness characteristic of a straight line near the static equilibrium point can be obtained, and a wider range of constant value quasi-zero stiffness characteristics can be obtained, which can reduce the resonance frequency of the linear vibrator, and No nonlinear factors are attached; compared with the traditional quasi-zero stiffness vibration isolator with weak cubic nonlinear characteristics, the vibration isolation frequency band will not be reduced due to nonlinear bending to the right under large excitation conditions.
4.本发明解决了传统准零刚度隔振器具有三次非线性的问题,可用于大激励幅值、变载重工况的低频隔振问题。本发明为恒值准零刚度隔振结构,在具体应用效果上,具有无穷多个静态平衡位置。4. The invention solves the problem of the third-order nonlinearity of the traditional quasi-zero stiffness vibration isolator, and can be used for low-frequency vibration isolation problems of large excitation amplitude and variable load conditions. The invention is a constant-value quasi-zero stiffness vibration isolation structure, and has infinitely many static equilibrium positions in terms of specific application effects.
5.本发明能应用于低频隔振的工程应用,解决传统线性刚度隔振系统在低频隔振时需要小的动态刚度但产生大的静态变形这一矛盾问题。5. The invention can be applied to the engineering application of low-frequency vibration isolation, and solves the contradictory problem that the traditional linear stiffness vibration isolation system needs small dynamic stiffness but produces large static deformation during low-frequency vibration isolation.
附图说明Description of drawings
图1是本发明恒值准零刚度隔振结构的结构示意图。Fig. 1 is a schematic structural view of a quasi-zero-stiffness constant-value vibration isolation structure of the present invention.
图2a和图2b分别是支架的其中一个实施例的主视图和左视图。Figures 2a and 2b are a front view and a left side view of one embodiment of the bracket, respectively.
图3a和图3b分别是支架的另一个实施例的主视图和左视图。Fig. 3a and Fig. 3b are the front view and the left side view of another embodiment of the bracket respectively.
图4是斜杆的主视图。Fig. 4 is a front view of the oblique rod.
图5a和图5b分别是斜杆铰链支座的主视图和俯视图。Fig. 5a and Fig. 5b are the front view and the top view of the tilt bar hinge support respectively.
图6a和图6b分别是横向导杆的主视图和俯视图。Figures 6a and 6b are a front view and a top view, respectively, of the transverse guide rod.
图7a和图7b分别是支座连接块的主视图和俯视图。Fig. 7a and Fig. 7b are the front view and the top view of the connecting block of the support respectively.
图8a和图8b分别是本发明恒值准零刚度隔振结构简化后的力学示意图。Fig. 8a and Fig. 8b are simplified mechanical schematic diagrams of the constant-value quasi-zero stiffness vibration isolation structure of the present invention, respectively.
图9a和图9b分别是刚度位移曲线和力位移曲线示意图。Figure 9a and Figure 9b are schematic diagrams of stiffness-displacement curves and force-displacement curves, respectively.
附图标记:1-固定板,2-支架,3-横向导杆直线轴承,4-横向导杆,5-弹簧卡板,6-径向轴承,7-斜杆,8-斜杆铰链支座,9-支座连接块,10-竖向导杆,11-垂直弹簧,12-空心管,13-载重盘,14-竖向导杆直线轴承,15-横向弹簧,16-粗竖向通孔,17-细竖向通孔。Reference signs: 1-fixed plate, 2-bracket, 3-transverse guide rod linear bearing, 4-transverse guide rod, 5-spring clamp, 6-radial bearing, 7-slanting rod, 8-slanting rod hinge support Seat, 9-support connecting block, 10-vertical guide rod, 11-vertical spring, 12-hollow tube, 13-loading plate, 14-vertical guide rod linear bearing, 15-transverse spring, 16-thick vertical through hole , 17-thin vertical through hole.
具体实施方式Detailed ways
以下结合附图和具体实施例对本发明作进一步详细说明。应当理解,此处所描述的具体实施例仅用以解释本发明,并不用于限定本发明。The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.
如图1所示,本实施例提供一种基于三对斜杆负刚度机制的恒值准零刚度隔振结构,包括固定板1、支架2、横向导杆4、斜杆7、斜杆铰链支座8、支座连接块9、竖向导杆10、垂直弹簧11、空心管12、载重盘13和横向弹簧15;As shown in Figure 1, this embodiment provides a constant value quasi-zero stiffness vibration isolation structure based on the negative stiffness mechanism of three pairs of oblique bars, including a fixed
固定板1的两侧相对称的安装有支架2,支架2底部与固定板1通过标准件螺栓固定连接。固定板1的中部安装有竖向导杆10,竖向导杆10的上部安装有支座连接块9,支座连接块9上安装有与竖向导杆10连接的竖向导杆直线轴承14;支座连接块9底部与固定板1之间的竖向导杆10上安装有垂直弹簧11;
支座连接块9的左右两端连接有斜杆铰链支座8,斜杆铰链支座9为U型结构;每个支架2上等间距的通过固定件安装有三个直线轴承,每个直线轴承装有横向导杆4,每个横向导杆4朝向竖向导杆10的一端设置有U型槽,U型槽旁边的横向导杆上设有弹簧卡板5,弹簧卡板5与固定件之间的每个横向导杆4上均安装有横向弹簧15;The left and right ends of the
竖向导杆10两侧分别相对称的设置有三个斜杆7,斜杆7结构见图4,每个斜杆7的两端分别与斜杆铰链支座8和横向导杆4上的U型槽通过径向轴承6及销轴铰接。具体的,斜杆7(图4)端部有圆孔,这个圆孔与径向轴承的外圈配合(径向轴承比较小,外径为5mm,内径为2mm,厚大概mm左右,销售平台大多称为微型轴承),将放有径向轴承的斜杆7的一端插入横向导杆4(图6b的右端),之后用销轴插入图6a右端的小孔,同时也穿过径向轴承的内孔。此时斜杆7和横向导杆4通过径向轴承铰接在了一起。Two sides of the
支座连接块9的两侧分别设有连接孔,连接孔上设置有空心管12,空心管12顶端设置有载重盘13并通过螺栓穿过空心管12与连接孔连接固定载重盘13。Both sides of the
具体的,见图2a和图2b,本实施例中支架2上等间距的设置有三个圆形通孔,固定件采用卡簧,以标准件的直线轴承3上具有卡簧槽的特点,横向导杆直线轴承3与支架2通过标准件卡簧连接,以约束横向导杆直线轴承3的横向位移。Specifically, as shown in Fig. 2a and Fig. 2b, in this embodiment, three circular through holes are arranged at equal intervals on the
具体实施过程中,支架2还可采用见图3a和图3b所示的结构,该实施例中,支架中部设有一条用于横向导杆4通过的粗竖向通孔16,粗竖向通孔16两侧设置有两条平行的细竖向通孔17,固定件采用紧固螺栓及连接板,连接板的中部安装有用于连接横向导杆的直线轴承,连接板的两侧设有螺栓孔,连接板通过紧固螺栓穿过螺栓孔和细竖向通孔17与螺母连接固定在支架2上。In the specific implementation process, the
见图5a和5b,本实施例中斜杆铰链支座8为U型结构,由一底板和两侧板构成,底板上设有用于与支座连接块9连接的螺栓孔,两个侧板上相对称的设有三个轴孔,用于与斜杆铰接。See Figures 5a and 5b. In this embodiment, the
见图6a和6b,横向导杆的一端设有U型槽,U型槽两侧侧板上对称的开有用于斜杆铰接的轴孔,U型槽一旁的横向导杆上设有用于安装弹簧卡板5的凹槽。As shown in Figures 6a and 6b, one end of the transverse guide rod is provided with a U-shaped groove, and the side plates on both sides of the U-shaped groove are symmetrically opened with shaft holes for the hinged connection of the oblique rod. The groove of
见图7a和7b,支座连接块的两端设有用于铰链支座8连接的螺栓孔,中部设有轴承孔,两侧设有用于固定载重盘的连接孔。As shown in Figures 7a and 7b, the two ends of the support connecting block are provided with bolt holes for connecting the
本实施例中,斜杆铰链支座8与支座连接块9通过螺柱连接,支座连接块9、空心管12、载重盘13、竖向导杆直线轴承14通过标准件长螺栓紧固在一起,载重盘13受到的隔振质量力可传导到三对斜杆7。横向导杆4通过横向导杆直线轴承3约束后可在水平方向做低摩擦移动。横向弹簧15通过弹簧卡板5和横向导杆直线轴承3进行轴向约束,横向弹簧的弹性力可通过斜杆7传递给载重盘13以获得垂向力支撑力,特别是获得垂直方向的负刚度特性。垂直弹簧11通过竖向导杆10约束,并且通过竖向导杆直线轴承14和固定板1限定垂向位移,使载重盘13获得载重能力。In this embodiment, the inclined
三对斜杆负刚度机制构造的恒值准零刚度隔振结构,初始状态下的力学示意图,见图8a和图8b。k2是垂直弹簧刚度,fh是横向弹簧(或水平拉簧)产生的内向弹性力,fh_u为刚度为k1的上对横向弹簧在初始状态预压缩量δ条件下产生的弹性力,fh_m为刚度为k3的中对横向弹簧在初始状态预压缩量δ1条件下产生的弹性力,fh_l为刚度为k1的下对横向弹簧在初始状态预压缩量δ2条件下产生的弹性力,h是初始状态到静平衡位置的垂向距离,初始状态为三对斜杆的交点与自由状态下垂直弹簧的上端接触的状态,x是从初始位置开始的位移,y是从静平衡位置开始的位移。a是初始状态下斜杆两端铰接点之间的距离在水平方向的投影长度;上、下对横向弹簧刚度与垂直弹簧刚度的比值α;中对横向弹簧刚度与垂直弹簧刚度的比值α1;δ指上对横向弹簧在初始状态下的预压缩长度;δ1指中对横向弹簧在初始状态下的预压缩长度;δ2指下对横向弹簧在初始状态下的预压缩长度。上对斜弹簧的水平位置到下对斜弹簧的水平位置的垂向距离为2d,2d的中间位置为静态平衡位置。The mechanical schematic diagram of the constant value quasi-zero stiffness vibration isolation structure constructed by the negative stiffness mechanism of three pairs of oblique bars in the initial state is shown in Fig. 8a and Fig. 8b. k 2 is the stiffness of the vertical spring, f h is the inward elastic force produced by the transverse spring (or horizontal extension spring), f h_u is the elastic force produced by the upper pair of transverse springs with stiffness k 1 under the condition of precompression δ in the initial state, f h_m is the elastic force produced by the middle pair of transverse springs with stiffness k 3 under the condition of initial state precompression δ 1 , and f h_l is the elastic force produced by the lower pair of transverse springs with stiffness k 1 under the condition of initial state precompression δ 2 The elastic force of , h is the vertical distance from the initial state to the static equilibrium position, the initial state is the state where the intersection of the three pairs of oblique rods is in contact with the upper end of the vertical spring in the free state, x is the displacement from the initial position, y is the distance from Displacement from static equilibrium position. a is the projected length in the horizontal direction of the distance between the hinge points at both ends of the oblique bar in the initial state; the ratio α of the transverse spring stiffness to the vertical spring stiffness of the upper and lower pairs; the ratio α of the transverse spring stiffness to the vertical spring stiffness of the middle pair 1 ; δ refers to the precompressed length of the upper pair of transverse springs in the initial state; δ 1 refers to the precompressed length of the middle pair of transverse springs in the initial state; δ 2 refers to the precompressed length of the lower pair of transverse springs in the initial state. The vertical distance from the horizontal position of the upper oblique spring to the horizontal position of the lower oblique spring is 2d, and the middle position of 2d is the static equilibrium position.
首先获得应用力f的表达式,为了分析更广泛的结构参数特征,对应用力f及其表达式进行无量刚化,见公式(1),可得无量纲化的应用力表达式,求表达式对的一阶导数,可得无量纲刚度见公式(2);公式(3)为参数表达式;在静平衡位置,对无量纲刚度求二阶导数并令刚度等于零,可获得零刚度特性的参数条件,见公式(4)。以静平衡位置为零点位移,静态平衡点为图8a中2d的中间位置(中间杆处于水平的状态),静平衡点附近的准零刚度特性如图8b所示,具有恒值准零刚度的特性(通过双对斜杆负刚度机制可以把垂直弹簧的动态刚度降低成恒值准零刚度的状态,且同时保持较高的静态刚度以承受载荷),特别是恒值准零刚度可以根据需要进行调节。First, the expression of the applied force f is obtained. In order to analyze the characteristics of a wider range of structural parameters, the applied force f and its expression are infinitely stiffened, see formula (1), and the dimensionless applied force can be obtained expression, seek expression right The first derivative of , the dimensionless stiffness can be obtained See formula (2); formula (3) is a parametric expression; at the static equilibrium position, for dimensionless stiffness Finding the second order derivative and setting the stiffness equal to zero can obtain the parameter condition of the zero stiffness characteristic, see formula (4). Taking the static equilibrium position as the zero point displacement, the static equilibrium point is the middle position of 2d in Figure 8a (the middle rod is in a horizontal state), the quasi-zero stiffness characteristics near the static equilibrium point are shown in Figure 8b, and the quasi-zero stiffness with constant value Characteristics (the dynamic stiffness of the vertical spring can be reduced to a state of constant quasi-zero stiffness through the negative stiffness mechanism of double pairs of oblique rods, and at the same time maintain a high static stiffness to bear the load), especially the constant quasi-zero stiffness can be customized according to the needs Make adjustments.
斜杆和横向弹簧,产生垂向负刚度,称为双对斜杆负刚度机制,与垂直弹簧的正刚度并联,在静平衡点附近(静态平衡点为上下对斜杆处于上下对称的位置),按公式(5)的调试方法,垂向可获得恒值准零刚度特性。Diagonal rods and transverse springs produce vertical negative stiffness, which is called the negative stiffness mechanism of double pairs of oblique rods, which are connected in parallel with the positive stiffness of vertical springs, near the static equilibrium point (the static equilibrium point is that the upper and lower pairs of oblique rods are in a symmetrical position up and down) , according to the debugging method of formula (5), the constant value quasi-zero stiffness characteristic can be obtained in the vertical direction.
其中,P1到P9为中间变量。无量纲应用力,无量x纲位移,α、α1无量纲刚度,斜杆倾斜角度,γ无量纲初始位置,初始状态下无量纲压缩量。Among them, P 1 to P 9 are intermediate variables. Dimensionless applied force, Dimensionless x - dimensional displacement, α, α1 dimensionless stiffness, Angle of inclined bar, γ dimensionless initial position, The dimensionless compression amount in the initial state.
恒值准零刚度(图8b所示)的调试方法,使选择的横向弹簧刚度与垂直弹簧刚度的比值α满足并且横向弹簧的预压缩长度δ等于斜杆的下对斜杆在初始状态下的两铰接点之间的水平长度a。若满足上述两个条件,恒值准零刚度特性可以获得。The debugging method of constant quasi-zero stiffness (shown in Figure 8b) makes the ratio α of the selected transverse spring stiffness to vertical spring stiffness satisfy And the pre-compression length δ of the transverse spring is equal to the horizontal length a between the two hinge points of the lower pair of diagonal rods in the initial state. If the above two conditions are satisfied, the constant quasi-zero stiffness property can be obtained.
本实施例为实现一种恒值准零刚度力学特性的结构和调试方法,属于准零刚度隔振的研究范围,应用于十几赫兹以下的低频隔振工程问题,如海浪对船舶造成的低频激励及响应、车辆对人体造成的低频激励、航天器调整造成的低频激励及响应,本发明应用于低频隔振的工程应用,解决传统线性刚度隔振系统在低频隔振时需要小的动态刚度但产生大的静态变形这一矛盾问题。This embodiment is to realize a structure and debugging method of constant quasi-zero stiffness mechanical properties, which belongs to the research scope of quasi-zero stiffness vibration isolation, and is applied to low-frequency vibration isolation engineering problems below a dozen hertz, such as the low-frequency vibration caused by waves to ships. Excitation and response, low-frequency excitation caused by vehicles to the human body, low-frequency excitation and response caused by spacecraft adjustment, the invention is applied to the engineering application of low-frequency vibration isolation, and solves the problem that the traditional linear stiffness vibration isolation system needs small dynamic stiffness in low-frequency vibration isolation But there is a paradoxical problem of large static deformation.
具体调试方法如下:The specific debugging method is as follows:
第一步,按本申请在结构上的描述,制作一种三对斜杆负刚度机制构造恒值准零刚度隔振结构;In the first step, according to the structural description of this application, a vibration isolation structure with constant value and quasi-zero stiffness of three pairs of oblique rods with negative stiffness mechanism is produced;
第二步,依据公式(5),确定初始状态下横向弹簧的预压缩量δ、斜杆在水平方向上投影长度a、垂直弹簧的长度,使初始状态下δ=a;In the second step, according to the formula (5), determine the pre-compression amount δ of the transverse spring in the initial state, the projected length a of the oblique rod in the horizontal direction, and the length of the vertical spring, so that δ=a in the initial state;
第三步,依据公式(5),确定横向弹簧的刚度k1和k3,确定垂直弹簧的刚度k2,构建无量纲参数和使参数α和α1满足 The third step, according to formula (5), determine the stiffness k 1 and k 3 of the transverse spring, determine the stiffness k 2 of the vertical spring, and construct the dimensionless parameter and Make parameters α and α 1 satisfy
第四步,确定好上述参数后,绘制力位移曲线f-x,见图9b,其中图9a为相应的恒值刚度曲线,力位移曲线为一条倾斜向上的直线,具有恒定刚度特性,计算刚度值K,根据隔振质量m之间的关系,计算起始隔振频率若起始隔振频率不满足设计要求,则重复第二到第四步。The fourth step, after determining the above parameters, draw the force-displacement curve fx, as shown in Figure 9b, where Figure 9a is the corresponding constant value stiffness curve, the force-displacement curve is a straight line with a constant stiffness characteristic, and calculate the stiffness value K , according to the relationship between the vibration isolation mass m, calculate the initial vibration isolation frequency If the initial vibration isolation frequency does not meet the design requirements, repeat steps 2 to 4.
本发明最终实验了恒值准零刚度特性的隔振器,解决了传统准零刚度隔振器具有三次非线性的问题,可用于大激励幅值、变载重工况的低频隔振问题。传统的三次非线性刚度隔振器,只有一个静态平衡位置,而本发明为恒值准零刚度隔振器,具有无穷多个静态平衡位置。The present invention finally tests a vibration isolator with constant quasi-zero stiffness characteristics, which solves the problem of cubic nonlinearity of traditional quasi-zero stiffness vibration isolators, and can be used for low-frequency vibration isolation problems with large excitation amplitude and variable load conditions. A traditional cubic nonlinear stiffness vibration isolator has only one static equilibrium position, while the present invention is a constant-value quasi-zero stiffness vibration isolator with infinitely many static equilibrium positions.
本发明并不限于上文描述的实施方式。以上对具体实施方式的描述旨在描述和说明本发明的技术方案,上述的具体实施方式仅仅是示意性的,并不是限制性的。在不脱离本发明宗旨和权利要求所保护的范围情况下,本领域的普通技术人员在本发明的启示下还可做出很多形式的具体变换,这些均属于本发明的保护范围之内。The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solution of the present invention, and the above specific embodiments are only illustrative and not restrictive. Without departing from the gist of the present invention and the scope of protection of the claims, those skilled in the art can also make many specific changes under the inspiration of the present invention, and these all belong to the protection scope of the present invention.
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