On the buckling of helical compression springs

A new set of dynamic, partial differential equations is developed for helical compression springs, and is solved for fixed ends and circular cross-section using the transfer matrix method to produce buckling design charts. The effect of the number of turns of the spring on its buckling behaviour is investigated, and comparisons are drawn to existing theories of instability.     

On the buckling of helical springs under combined compression and torsion

The linearized disturbance equations governing the buckling behaviour of circular-bar helical springs subjected to combined compression and twist are solved numerically using the transfer matrix method to produce buckling design charts. The effects of the number of turns of the spring and the angle of twist are investigated for clamped-clamped ends and the results are compared to existing theories of instability.     

Vibration from a shaft-bearing-plate system due to an axial excitation of helical gears

In this paper, a simplified model is studied to predict analytically the vibration from the helical gear system due to an axial excitation of helical gears. The simplified model describes gear, shaft, bearing, and housing. In order to obtain the axial force of helical gears, the mesh stiffness is calculated in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer matrices for the rod and bearing are used, using a spectral method with four pole parameters. The model is validated by finite element analysis. Using the model, parameter studies are carried out. As a result, the linearized dynamic shaft force due to the gear excitation in the frequency domain was proposed. Out-of-plan displacement from the forced vibrating circular plate and the renewed mode normalization constant of the circular plate were also proposed. In order to control the axial vibration of the helical gear system, the plate was more important than the shaft and the bearing. Finally, the effect of the dominant design parameters for the gear system can be investigated by this model.     

谐波力激励下螺旋形弹簧的拉扭耦合动力响应

建立一种普遍的解析理论，利用简正模态法研究确定性载荷作用下拉扭耦合螺旋形弹簧的动力响应。假定确定性载荷是谐波变化的，得到各种谐波激励下封闭形式的解，并对动力拉伸位移和扭转位移的数值结果进行讨论，与文献中已有方法的比较验证了文中所提方法的有效性和精确性。     

弹簧蓄能密封圈中蓄能弹簧的有限元计算及等效建模研究

弹簧蓄能密封圈是一种性能优良的密封装置,其中的蓄能弹簧可以为密封圈提供初始密封压力,起到辅助密封的作用。但目前对弹簧蓄能密封圈的研究多是在有限元软件中建立二维轴对称模型进行仿真实验,对蓄能弹簧的力学特性和建模计算方法的认识尚有不足。为实现不同结构的弹簧蓄能密封圈的参数化仿真设计,推导环形蓄能弹簧的空间曲线参数方程,建立双层螺旋蓄能弹簧的三维有限元模型,并仿真分析其力学特性。定义蓄能弹簧的内侧刚度和外侧刚度,研究弹簧不同结构参数对其刚度的影响。结果表明,弹簧的厚度和弹簧截面外径对刚度的影响较大,而弹簧中径和匝数对刚度影响可忽略不计。提出轴对称等效模型的建立原则,建立轴对称等效模型的经验公式,为弹簧蓄能密封圈的参数化仿真设计提供了参考。     

基于螺旋弹簧的柔性杆形状感知技术

为了实现柔性杆形状的动态感知,研究了螺旋弹簧变形的检测方法,实现了对螺旋弹簧三维变形的实时感知。根据采集到的螺旋弹簧表面离散点的应变数据,计算出簧丝的曲率和挠率,建立了递推方程,将螺旋弹簧变形形状重建出来。建立了一套实验系统,验证了所提出方法的正确性,应变信息由簧丝表面上的应变片采集,采集到的应变信息直接输入到计算机,并通过VC++程序处理,实时绘制出螺旋弹簧变形后的形状。研究结果表明,该研究提出了一种有效获取在不可见环境下的形状解决方案,具有一定的理论和实际意义。     

Linear free vibration analysis of cross-ply laminated cylindrical helical springs

A linear free vibration analysis of symmetric cross-ply laminated cylindrical helical springs is performed based on the first-order shear deformation theory. Considering the rotary inertia, the shear and axial deformation effects, governing equations of symmetric laminated helical springs made of a linear, homogeneous, and orthotropic material are presented in a straightforward manner based on the classical beam theory. The free vibration equations consisting of 12 scalar ordinary differential equations are solved by the transfer matrix method. The overall transfer matrix of the helix is computed up to any desired accuracy. The soundness of the present results are verified with the reported values which were obtained theoretically and experimentally. After presenting the non-dimensional graphical forms of the free vibrational characteristics of (0°/90°/90°/0°) laminated helical spring made of graphite-epoxy material (AS4/3501-6) with fixed–fixed ends, a non-dimensional parametric study is worked out to examine the effects of the number of active turns, the shear modulus in the 1–2 plane (G₁₂), the ratio of the cylinder diameter to the thickness (D/d), and Young's moduli ratio in 1 and 2 directions (E₁/E₂) on the first six natural frequencies of a uniaxial composite helical spring with clamped-free, clamped-simple, and clamped–clamped ends.     

Optimization of dimensions of a device for circular magnetization of cylindrical components. III. Investigation of circular field component generated by a one-layer toroidal coil

The effect of dimensions of a toroidal coil and the number of turns in the coil on the circular magnetic field component within the region limited by the inside axial sections of the turns has been studied. The configuration of this field has been determined. Optimal dimensions of the coil have been calculated. In order to obtain a higher amplitude of the circular field, one should use coils with smaller numbers of turns. In the inner region of a one-layer toroidal coil close to the turns, the peaks of the circular field diminish with the number of turns, but the number of points where the field intensity is maximal becomes larger, i.e., the field becomes more uniform. Methods of further increase in the circular component of the magnetic field have been suggested.     

基于ANSYS的汽车悬架螺旋弹簧限元分析

为了准确的测定汽车悬架螺旋弹簧的应力分布情况,采用有限元分析软件ANSYS,对某型号汽车悬架螺旋弹簧进行了CAE分析.分析结果显示,汽车悬架螺旋弹簧内侧剪切应力均大于外侧剪切应力;随着汽车悬架螺旋弹簧所承受载荷的变化,剪切应力最大值出现的位置会发生变化;而且在不同载荷作用下,剪切应力最大值均出现在汽车悬架螺旋弹簧底端开...     

振动状态下螺旋弹簧运动状态模型

螺旋弹簧受到冲击载荷时,特别是多股螺旋弹簧,由于有质量、惯性,再加上自身的谐振,钢丝材料的弹性变形、多股螺旋弹簧中钢丝与钢丝之间的相对滑移而产生的摩擦阻力等诸多因素,簧圈的运动将变得非常复杂。基于此,建立一套用于检测振动状态下螺旋弹簧任意簧圈的运动状态模型,用于揭示振动状态下螺旋弹簧任意簧圈的位移、速度、加速度随时间的变化规律,特别是用于检测冲击载荷下多股螺旋弹簧的内部变形规律。试验结果表明:螺旋弹簧运动状态分析模型结合非接触多通道检测装置,可以成功地揭示振动状态下螺旋弹簧任意簧圈的运动状态随时间的变化规律,为螺旋弹簧的动态设计理论的建立提供了试验依据。     

Optimization of dimensions of a device for circular magnetization of cylindrical components. IV. Investigation of circular magnetizing field generated by a multilayered toroidal coil

The effect of dimensions of a toroidal coil, the number of turns and layers in its winding on the circular field component generated in its inside volume defined by the inside axial sections of the turns has been investigated. The configuration of the field in this region has been calculated, and the principles of the design of magnetizing coils have been formulated. In order to obtain a higher circular field intensity in the region close to the turns, it is advisable to use multilayered windings. A fairly uniform circular field is generated in a local region if the winding is divided into equal sectors containing zones with turns of wire and gaps between them. In order to obtain a circular field component of a relatively high intensity and a constant sign over a wide sector of the inside volume, one should build a coil of several sections uniformly distributed over the frame perimeter.     

基于不同载荷的圆柱螺旋弹簧刚度特性分析

运用SolidWorks软件本身的建模功能构建弹簧的三维模型,并对圆柱螺旋弹簧进行有限元分析,通过不同的加载方法（位移加载和直接力加载）,获得不同加载方法下螺旋弹簧的刚度。研究表明：Solid-Works分析软件能够获得足够精度的计算结果,并且位移加载更符合理论计算的结果,为圆柱螺旋弹簧的精确设计和计算提供了可靠的方法和依据。     

多股簧冲击载荷特性试验研究

以多股簧应用于复进簧时的工况为例,按照质量-弹簧-阻尼模型,建立了多股簧和各个簧圈的冲击响应动力学模型;对多股簧进行了冲击载荷试验,分析了弹簧内部运动规律,并识别出弹簧的等效刚度、等效阻尼等模态参数。试验结果表明：受冲击载荷时,多股簧的结构呈非线性特性,更能体现其减振的优势;弹簧内部运动规律也为非线性,各簧圈的运动速度沿轴向不再是线性分布。     

螺旋弹簧悬架车辆振动的波动理论建模及频响分析

针对车辆建模不能完全反映高频振动的情况,应用古典振动理论及冲击波动理论,对螺旋弹簧悬架车辆的振动进行模拟并对响应进行分析。提出用冲击波动力学分析车辆振动的理论依据,推导螺旋弹簧应力波波阻的表达式,由此建立车辆的波阻力及变形力振动模型。通过冲击波影响螺旋弹簧的长度及其对应的质量,建立了螺旋弹簧惯性力及变形力车辆振动模型,综合多种因素,建立螺旋弹簧悬架车辆振动的波动理论模型,探讨了模型的求解方法,并对各种模型从理论和解法两个方面进行对比。仿真验证冲击波动理论模型与古典振动理论模型在低频段的一致性及弥补后者不能表达高频振动的缺陷。提出了在波动理论下螺旋弹簧多参数的应用方法及悬架高频响应的模拟方法。     

STEADY STATE RESPONSE ANALYSIS ON HELICAL SPRING IMPACTED BY SHORT WAVE

The wave transmission character of helical spring is applied to establish 2-DOF model of impacted vehicle on the wave impact theory. Considering the concrete structure of helical spring, corresponding responses under different impact frequency of the vehicle are imitated. The reason why the vehicle floor overresponds in some special frequency fields is explored based on analyzing the responses. When the impactions are in low frequency, the change of the spring has not been considered, but this does not affect the results. Because the transmission characters of velocity and acceleration are unanimous in helical spring, the responses characters of velocity and acceleration are also unanimous, the only difference is the magnitude, which can make use of acceleration responses to analyse velocity responses.     

液压支架侧护板装置圆柱螺旋压缩弹簧计算

目前液压支架都有较完善的侧护板装置,侧护板主要通过圆柱螺旋压缩弹簧与侧推千斤顶控制其伸缩。根据液压支架侧护装置的工作特点,综合圆柱螺旋压缩弹簧的设计理论,介绍了液压支柱侧护装置中圆柱螺旋压缩弹簧的计算方法,并给出了其计算实例。     

随机振动下隔振器中圆锥螺旋弹簧的疲劳分析

文中针对某电子设备上隔振器中圆锥螺旋弹簧在耐久试验中发生多次断裂的问题展开了研究。由于圆锥螺旋弹簧的非线性,无法进行模态分析和随机振动分析,因而依据加速度等效的原则将随机振动分析等效成静力分析,用有限元分析软件ANSYS Workbench得出圆锥螺旋弹簧的应力值。利用PSD频域分析法和"高斯三区间法"进行疲劳计算,经过几次迭代计算得出最优的弹簧材料参数和直径尺寸。按照仿真分析和疲劳计算结果设计的隔振器目前已顺利通过了耐久试验。     

双圆弧圆柱齿轮传动系统的振动分析

建立了双圆弧圆柱齿轮传动系统的周向—径向—轴向—扭摆耦合的动力学模型,通过实例分析计算了其振动响应,并和实测结果进行了对比。结果表明：二者的变化规律是基本吻合的。为开展双圆弧圆柱齿轮传动的动态设计提供了依据。     

拉刀刃形的优化

提出一种新的键槽拉刀,即凸圆弧齿键槽拉刀,并将其与现行技术中的直齿键槽拉刀和斜齿键槽拉刀进行对比。经分析认为,凸圆弧齿键槽拉刀比其它键槽拉刀更具有优越性。     

Design and Modeling on Stranded Wires Helical Springs

A stranded wires helical spring is formed of a multilayer and coaxial strand of several wires twisted together with the same direction of spiral. Compared with the conventional single wire spring, the stranded wires helical spring has the notable predominance in strength, damping and vibration reduction, which is usually used in aircraft engines, automatic weapons, etc. However, due to its complicated structure, the precise computation of its strength and rigidity need be a correct mathematical model, which then will be imported to finite element analysis software for solutions. Equations on solving geometric parameters, such as external diameters of strands and screw pitches of wires, are put forward in the paper. It also proposes a novel methodology on solving geometric parameters and establishing entity models of the stranded wires helical spring, which provides foundation of computing mechanical parameters by FEA. Then mathematical models on the centre line of the strand and the surface curve of each wire, after closing two ends in a spring, are proposed. Finally, geometric parameters are solved in a case study, and a 3D entity model of a spring with 3 layers and 16 wires is established, which has validated the accuracy of the proposed methodology and the 3D entity mathematical model. The method provides a new way to design stranded wire helical spring.