Analysis on the Performance of the SLIP Runner with Nonlinear Spring Leg

The spring-loaded inverted pendulum(SLIP) has been widely studied in both animals and robots.Generally,the majority of the relevant theoretical studies deal with elastic leg,the linear leg length-force relationship of which is obviously conflict with the biological observations.A planar spring-mass model with a nonlinear spring leg is presented to explore the intrinsic mechanism of legged locomotion with elastic component.The leg model is formulated via decoupling the stiffness coefficient and exponent of the leg compression in order that the unified stiffness can be scaled as convex,concave as well as linear profile.The apex return map of the SLIP runner is established to investigate dynamical behavior of the fixed point.The basin of attraction and Floquet Multiplier are introduced to evaluate the self-stability and initial state sensitivity of the SLIP model with different stiffness profiles.The numerical results show that larger stiffness exponent can increase top speed of stable running and also can enlarge the size of attraction domain of the fixed point.In addition,the parameter variation is conducted to detect the effect of parameter dependency,and demonstrates that on the fixed energy level and stiffness profile,the faster running speed with larger convergence rate of the stable fixed point under small local perturbation can be achieved via decreasing the angle of attack and increasing the stiffness coefficient.The perturbation recovery test is implemented to judge the ability of the model resisting large external disturbance.The result shows that the convex stiffness performs best in enhancing the robustness of SLIP runner negotiating irregular terrain.This research sheds light on the running performance of the SLIP runner with nonlinear leg spring from a theoretical perspective,and also guides the design and control of the bio-inspired legged robot.

Macro Model Study for Nonlinear Spring of Tense Torsion Bar in Gap-Closing Type Electrostatic Micromirror

Nonlinear spring characteristics of the tense torsion bar in the gap-closing type electrostatic micromirror are examined. The macro model is introduced for the experimental study. The tension applied in the torsion bar is well controlled using the electromagnetic attraction. This controllability is suited for clearing the nonlinear nature. The tension is confirmed to have the effect to widen the controllable angle range of the mirror suppressing the pull-in. The pull-in angle is observed to increases to about 74% of the mechanical limit angle at the tension of 0,96 N. This is significantly larger than 44% of the case with the linear spring. The larger resonant frequency is maintained. The hardening of the spring can keep the balance with the electrostatic force over the limit of the linear spring. The observed features are explained reasonably with the combination of twisting and bending displacements of the torsion bar.

On Generating Expected Kinetostatic Nonlinear Stiffness Characteristics by the Kinematic Limb-Singularity of a Crank-Slider Linkage with Springs

Being di erent from avoidance of singularity of closed-loop linkages, this paper employs the kinematic singularity to construct compliant mechanisms with expected nonlinear sti ness characteristics to enrich the methods of compliant mechanisms synthesis. The theory for generating kinetostatic nonlinear sti ness characteristic by the kinematic limb-singularity of a crank-slider linkage is developed. Based on the principle of virtual work, the kinetostatic model of the crank-linkage with springs is established. The influences of spring sti ness on the toque-position angle relation are analyzed. It indicates that corresponding spring sti ness may generate one of four types of nonlinear sti ness characteristics including the bi-stable, local negative-sti ness, zero-sti ness or positive-sti ness when the mechanism works around the kinematic limb-singularity position. Thus the compliant mechanism with an expected sti ness characteristic can be constructed by employing the pseudo rigid-body model of the mechanism whose joints or links are replaced by corresponding flexures. Finally, a tri-symmetrical constant-torque compliant mechanism is fabricated,where the curve of torque-position angle is obtained by an experimental testing. The measurement indicates that the compliant mechanism can generate a nearly constant-torque zone.

Static Electric-Spring and Nonlinear Oscillations

The author designed a family of nonlinear static electric-springs. The nonlinear oscillations of a massively charged particle under the influence of one such spring are studied. The equation of motion of the spring-mass system is highly nonlinear. Utilizing Mathematica [1] the equation of motion is solved numerically. The kinematics of the particle namely, its position, velocity and acceleration as a function of time, are displayed in three separate phase diagrams. Energy of the oscillator is analyzed. The nonlinear motion of the charged particle is set into an actual three-dimensional setting and animated for a comprehensive understanding.

Nonlinear Oscillations of a Magneto Static Spring-Mass

The Duffing equation describes the oscillations of a damped nonlinear oscillator [1]. Its non-linearity is confined to a one coordinate-dependent cubic term. Its applications describing a mechanical system is limited e.g. oscillations of a theoretical weightless-spring. We propose generalizing the mathematical features of the Duffing equation by including in addition to the cubic term unlimited number of odd powers of coordinate-dependent terms. The proposed generalization describes a true mass-less magneto static-spring capable of performing highly non-linear oscillations. The equation describing the motion is a super non-linear ODE. Utilizing Mathematica [2] we solve the equation numerically displaying its time series. We investigate the impact of the proposed generalization on a handful of kinematic quantities. For a comprehensive understanding utilizing Mathematica animation we bring to life the non-linear oscillations.

基于非线性弹簧的圆锥滚子轴承建模与分析

为解决风机主轴承滚动体数目多、尺寸大,进行有限元分析计算量大、收敛困难的难题,提出一种基于非线性弹簧的圆锥滚子轴承有限元等效模型,滚动体沿轴线方向分片,各分片与滚道接触以及球基面与挡边接触的“载荷-变形”关系采用弹簧单元等效模拟,等效弹簧的刚度通过赫兹接触理论确定。以某兆瓦级风机主轴承为例分析了该模型滚动体载荷分布及套圈整体变形,并与实体滚动体接触分析计算结果进行了对比。结果表明:基于非线性弹簧的等效模型能准确反映轴承内部载荷分布及整体变形情况,大大缩减计算量,为风机圆锥滚子主轴承的设计与分析提供了理论依据和指导。

基于ANSYS的三维非线性有限元螺旋弹簧接触仿真分析

螺旋弹簧作为车辆悬架中重要弹性元件之一,直接影响到车辆运行品质。为研究螺旋弹簧的几何参数对弹簧刚度的影响,利用ANSYS的APDL语言参数化建立的有限元模型进行计算,从是否考虑支撑圈与工作圈接触问题的结果,与弹簧刚度理论公式分析计算对比分析,验证三维非线性接触有限元螺旋弹簧模型的合理性,进一步分析锥形角度对弹簧刚度等的影响。改变参数快速建立0°、5°、10°的三种不同锥形角度螺旋弹簧模型,计算得到各种模型的荷载位移曲线,进而分析弹簧刚度、Mises应力、接触应力等影响规律。本文建议锥形螺旋弹簧设置锥度在5°以内,既可提高极限荷载,又可降低接触应力,减少材料疲劳破坏,提高使用寿命,为锥形螺旋弹簧的设计提供参考依据。

约束Green函数与非线性地基梁模态分析

在生物和医学领域,微机电系统(MEMS)中的微梁结构在植入人体的使用时,由于体内的细胞环境类似于水凝胶,在这种环境下工作,设备和仪器的精度和稳定性很大程度上受到细胞弹性的影响.为了分析此类地基梁的动力学问题,本文建立了非线性基础上的梁振动模型,研究了任意位置弹簧和非线性弹簧基础上的梁模态.通过Laplace变换和线性叠加原理,得到了一种约束Green函数,利用数值计算验证方案的有效性,并研究了各种重要物理参数的影响,发现弹簧位置向跨中移动时,模态对称性被打破,弹簧刚度增加,模态阶数改变.

垂直弹射系统中缓冲及反后坐效应的建模方法

针对垂直弹射过程中,由缓冲以及弹射后坐引发的对发射性能与阵地产生的负面影响问题,从缓冲吸能角度,提出按缓冲器的塑性应变能-压缩量关系曲线拟合并求导解算缓冲力-压缩量关系模型的方法,有效规避了缓冲力波动所造成的拟合漂移问题,并据此构造了模拟缓冲器的线弹性-塑性弹簧模型;依据弹射试验数据,反演了反后坐效应的动态数据,据此构造了模拟反后坐效应的非线性粘弹性-塑性弹簧模型;通过力元、状态变量及牛顿迭代法的有机结合,在动力学模型中实现了上述二模型的高效解算。仿真结果表明:两模型计算稳定高效且缓冲特性与有限元仿真结果高度吻合、反后坐效应和试验数据符合良好,这验证了数据处理方法的有效性和建模方法的可信性,为后续含缓冲和反后坐效应的弹射动力学仿真提供了一种稳定而又可信的建模思路。

非均匀锈蚀钢筋与混凝土的黏结滑移行为

在近海和海洋环境下,钢筋极易产生锈蚀。锈蚀对于钢筋混凝土间的黏结性能与钢筋混凝土结构的耐久性有着十分不利的影响,是目前工程中十分关心的问题。采用改进后的ABAQUS的Spring2非线性弹簧模型对非均匀锈蚀钢筋与混凝土之间的黏接滑移行为进行模拟,以改善零厚度弹簧引起的钢筋结点处混凝土的应力集中现象。基于收集到的不同箍筋间距的32个试件的试验结果,拟合给出了考虑箍筋间距影响的箍筋锈蚀下的黏结强度影响系数。结合非均匀锈蚀钢筋分布模型,基于ABAQUS软件进行钢筋混凝土试件拉拔过程的精细化数值模拟。结果表明:改进后的非线性弹簧模型在计算精度与效率上优于零厚度弹簧模型。箍筋修正系数与箍筋间距近似呈线性关系;考虑箍筋间距影响的黏结滑移模型在拉拔试验的模拟上与有关试验有较好的一致性。韦布尔分布对于钢筋非均匀锈蚀的拟合比起耿贝尔分布更为合理,非均匀锈蚀试件钢筋应力分布有一定程度的波动,应力数值有所减小。箍筋锈蚀会对箍筋的约束作用产生较为严重的影响。

混凝土中灌浆套筒的本构模型研究

提出了通过改变灌浆套筒位置处钢筋弹性模量模拟套筒连接混凝土构件的有限元建模方法,套筒和钢筋本构模型采用双折线本构模型,通过汇总60个灌浆套筒钢筋拉拔试验结果并对数据进行拟合,给出了套筒本构曲线与钢筋本构曲线之间的关系式。使用推导出的关系式计算套筒本构曲线,通过ABAQUS有限元软件,利用非线性弹簧模拟钢筋粘结滑移、粘性接触模拟钢筋粘结滑移和界面裂缝,对3个灌浆套筒连接预制构件进行滞回分析。通过对比滞回曲线、钢筋应变、钢筋滑移量和界面裂缝,发现模拟结果与试验值吻合程度较高。

非线性超谐共振时效系统弹簧设计方法的研究

为解决难以获取满足非线性超谐共振时效系统所需要的非线性参数,以系统的核心元件—非线性弹簧为研究对象,提出了适用于此系统的不等节距圆柱螺旋弹簧结构参数设计的方法,从而实现系统所要达到的超谐共振。首先,依据工件振动时效所需的弹簧力学特性曲线,计算得到符合该系统用不等节距圆柱螺旋弹簧的结构参数。其次,通过弹簧压缩试验证明了该弹簧设计方法的可行性。最后,以圆柱工件为试验对象,搭建非线性超谐振动台进行试验研究。结果表明:运用此方法设计的不等节距螺旋弹簧作用下的非线性超谐振动试验台能够产生超谐振动,且可产生高于200Hz的高次超谐频率,对推广非线性超谐式共振时效方法在消减高刚工件的残余应力方面具有重要的意义。

基于被动区土弹簧刚度降低过程的基坑围护结构计算增量法及软化p-y曲线

基坑围护结构的计算常采用基于杆系有限元的增量法,被动区土弹簧刚度在基坑开挖作用下发生动态降低导致土抗力软化,目前缺少在非线性地基模型基础上对该问题的研究。通过引入两个刚度变化系数来综合量化被动区土弹簧参数随基坑开挖的动态变化过程,建立了基于该过程的基坑围护结构计算增量法。针对非线性地基模型,提出了细化增量法进行数值计算。采用线弹性、理想弹塑性以及双曲线3种基本土弹簧模型计算得到被动区软化p-y曲线,对比显示,基于双曲线基本模型得到的等效水平抗力系数变化曲线更符合实际规律。工程实例计算显示,基于基本土弹簧为双曲线的计算结果与不同开挖阶段墙的位移监测数据对应更好。参数分析显示,与被动区土体极限抗力pu相关的刚度变化系数对计算结果影响较大,采用此方法应着重关注被动区pu的计算方法及开挖卸荷对pu的影响。

基于NFSR的分组密码算法SPRING

本文详细介绍分组密码算法SPRING的设计.根据分组长度和密钥长度的不同,SPRING具体包括三个算法版本SPRING-128-128、SPRING-128-256、SPRING-256-256,其中SPRING-n-m表示分组长度为n且密钥长度为m.SPRING是SP结构的分组密码,主要面向硬件实现设计,采用基于非线性反馈移位寄存器(NFSR)的32-比特S-盒和基于非线性反馈移位寄存器的密钥扩展算法.由于没有S-盒的存储,SPRING算法的硬件实现面积比较小.根据不同的应用需求,例如面积小或加/解密速率高,可以采用不同的实现方式.基于轮的实现,硬件面积最小,在TSMC 16 nm工艺库下,SPRING-128-128算法的硬件实现面积约1046μm^2;全轮展开实现,加/解密速率最大,SPRING-128-128算法的加密速率可以达到17482 Mbps,此时硬件实现面积约8079μm^2.SPRING的含义为SP结构分组密码和环状串联非线性反馈移位寄存器(A ring-like cascade connection of NFSRs).

空气弹簧隔振器样机垂向刚度特性建模与实验

空气弹簧隔振器被广泛用于精密仪器和生产设备隔振,其刚度-重力平衡点位置关系,即刚度特性是分析其与其他新兴隔振技术相互作用的重要依据。依据理想气体状态方程建立了某型空气弹簧隔振器样机的垂向刚度特性模型。综合整机振动实验结果与密封橡胶膜的刚度特性测量结果,间接测量了实物样机中空气弹簧的刚度特性。基于实验数据修正了模型,采用幂多项式拟合了气室体积-重力平衡点位置改变量的非线性曲线。减少了模型的刚度计算误差,为后续技术改造奠定了基础。

基于Q-s曲线的大型LNG储罐桩板基础沉降计算方法

试桩Q-s曲线体现了现场桩基荷载和沉降的关系。文章以某LNG储罐桩板基础为背景,提出利用Q-s曲线求出桩端土层变形模量的方法,并考虑桩板共同作用的求解桩板基础沉降的方法。该方法将桩基模拟为非线性弹簧,弹簧刚度取自Q-s曲线,采用MIDAS进行建模求解,可得到设计需要的筏板和桩基的沉降等高线图以及轴力和弯矩图,用于指导设计。与仅考虑线性地弹簧系数的规范方法进行对比,该方法精度更高,与实际情况更加相符。该方法可针对不同位置的桩基输入不同的非线性弹簧,可用于解决复杂不均匀地层桩筏基础沉降计算的问题。

低频非线性浮筏隔振装置设计及特性研究

低频振动噪声影响水下装备声隐身性能。在原气囊隔振装置基础上,通过结构改进设计,使得侧向气囊能够为系统提供负刚度,通过与垂向气囊并联,设计了一种新型非线性浮筏隔振装置,提升了隔振装置的低频隔振能力。新型隔振装置由“侧向气囊-万向节-垂向气囊”非线性隔振器组和浮筏组成。分析了侧向气囊为系统提供负刚度原理,建立了非线性浮筏隔振装置六自由度动力学模型,设计了新型隔振装置样机并开展了相关性能试验。理论分析和试验结果表明,新型非线性浮筏隔振系统垂向一阶固有频率约为原系统的50%,垂向隔振性能提升了约6 dB,侧向隔振性能与原系统相当。此外,也研究了非线性浮筏隔振系统的摇摆稳定性。研究结果表明,在重载情况下,新系统能够具备较好的摇摆稳定性。

轻卡前板簧悬架刚度非线性行为研究

以轻卡少片簧前悬系统为研究对象,系统地探讨了板簧悬架安装几何参数及连接处衬套刚度对系统级悬架刚度非线性行为的影响。研究过程首先基于零部件级板簧测试及Adams仿真手段研究板簧自身结构刚度的线性行为,且证明了由Adams建立的虚拟板簧结构的可靠性。然后,基于系统级K&C测试及Adams仿真结果的对标分析,认识到悬架刚度的非线性行为,且证明Adams建立的悬架模型的准确性。最后,利用Adams前悬虚拟仿真的方法研究了悬架吊耳角度、吊耳长度、板簧安装中心距及衬套刚度对悬架刚度非线性行为的影响。此外,本文获得的板簧悬架刚度非线性行为的规律性认识可优化指导前期板簧悬架系统的开发工作。

轨道车辆用沙漏橡胶弹簧设计及其非线性等频特性分析

为了解决转向架空间有限与横向大变形间的结构性矛盾,提出了一种表征沙漏橡胶弹簧等频承载特性的计算方法,并以一款高铁列车转向架的沙漏橡胶弹簧为研究对象,采用1P4E网格法解决沙漏橡胶弹簧大变形仿真时因网格扭曲导致的收敛性难题;通过尺度敏感性分析计算出影响沙漏橡胶弹簧非线性刚度的四大结构尺寸;通过搭建等频承载模型,获得沙漏橡胶弹簧满足等频特性的承载区域,该沙漏橡胶弹簧满足等频承载要求的承载位移区为41~57.4 mm。

成都市域快轨减振措施效果分析

为评价市域快轨的减振效果,以成都市域快轨18号线某圆形盾构隧道为例,选取了线路条件基本相同的相近断面,对双层非线性减振扣件、减振垫浮置板、钢弹簧浮置板3种减振措施及对应普通道床断面进行现场测试,研究市域快轨减振措施的减振效果。通过对实测数据进行时域、频域和1/3倍频程分析,得到不同减振措施和普通断面的隧道壁最大Z振级(VL_(Zmax)),并对比得到不同减振措施的减振效果;通过对测点的隧道壁振动加速度级及地面振动进行1/3倍频程分析,得到振动的传播衰减情况。结果表明:3种减振措施都有减振效果,双层非线性减振扣件减振效果为7.3 dB,减振垫浮置板的减振效果为16.2 dB,钢弹簧浮置板的减振效果最好,达到了19.7 dB。