纵—扭复合振动模式超声变幅杆研究

本文对窄端带有均匀截面直棒的指数型纵-扭复合振动模式超声变幅杆进行了理论及实验研究,推出了该复合模式变幅杆纵向振动及扭转振动的共振频率方程。为了克服同一变幅杆纵向与扭转振动很难实现同频共振的问题,提出了一种通过改变指数型变幅杆的截面变化规律而实现改变纵向及扭转振动传播速度的方法。通过合理选择指数变幅杆的截面半径减缩系数(即参数β),实现了纵-扭复合变幅杆纵向振动与扭转振动的同频共振。实测结果表明,共振频率的理论值与测试值基本一致,变幅杆纵向及扭转振动共振频率的测试值也比较符合。该变幅杆具有比较高的位移放大系数。可望应用于超声加工、超声疲劳实验及超声焊接等功率超声技术中。     

余弦形负载超声变幅杆输入阻抗特性的研究

研究余弦形负载超声变幅杆输入阻抗特性。求解了加负载时四种超声变幅杆的输入阻抗,得到加负载时输入阻抗和M"obius变换参数的统一算式。当变幅杆的输入抗分量为零时,计算了余弦形负载变幅杆的纵向振动共振频率方程和放大系数。由输入阻抗的表达式讨论了此类变幅杆的工作稳定性条件和相对阻抗相等点,对余弦形变幅杆的实际应用有一定的参考意义。     

大尺寸余弦形超声变幅杆的设计

通过瑞利的近似理论假设,对大尺寸的余弦形变幅杆的纵向振动的共振频率进行了修正,得到了修正频率表达式。利用有限元软件ANSYS对一组大尺寸的余弦变幅杆进行模态分析。并发现当R1/L〉0.5时,振动时伴随有弯曲振动或扭转振动,振动较为复杂,此时瑞利理论不再适用。但需要指出的是,与一维理论相比,修正后的值适用范围更大,因此对大尺寸的余弦形超声变幅杆的工程计算具有一定的指导意义。     

超声变幅杆与杯型工具一体化设计

基于细长杆纵振理论和薄圆盘振动理论,针对超声变幅杆与杯型工具开展一体化设计研究。通过分析各段的振动模态,将超声变幅杆和杯型工具的振动分为"纵-弯-纵"三个部分,分别建立三段位移和应力函数及边界条件,推导得出超声变幅杆和杯型工具的总体频率方程。根据得到的总体频率方程,设计出典型的超声变幅杆和杯型工具。对所设计的超声变幅杆和杯型工具的振动性能进行有限元分析和试验测试,分析和试验结果表明,超声变幅杆和杯型工具谐振频率的设计结果和有限元分析及测试结果的误差均在10%以内,验证了所建立的超声变幅杆和杯型工具的频率方程的正确性,并分析了各段长度和半径对超声变幅杆和杯型工具谐振频率的影响规律,为其谐振频率的修正提供了依据。     

抛物线型超声变幅杆的探讨

提出了一种新型的变幅杆-抛物线型变幅杆。根据变截面杆纵向振动的波动方程,推导出抛物线型变幅杆的频率方程、节点位置方程、放大系数、形状因数等参数,并用有限元软件ANSYS分析了几个半波长抛物线型变幅杆,得出共振频率。结果表明:抛物线型变幅杆在保持圆锥变幅杆形状因数较大的优点上,放大系数有所提高;有限元分析结果与理论值符合的较好。     

余弦型和类余弦型超声变幅杆的研究

本文导出余弦型纵振变幅杆和扭振类余弦型变幅杆的频率方程及参数的计算式和曲线，对简单型杆及由其与圆柱型段和双曲正割型段组成的复合杆件进行谐振频率和放大系数测试，实验结果与理论值基本吻合。     

扭转振动超声变幅杆计算及其等效电路

在平面波近似条件下,对几种常用的扭转振动半坡变幅杆(截面极惯性矩变化规律为圆锥、指数及悬链线型)进行了系统的理论分析。导出了变幅杆的等效电路,得出了变幅杆的输入机械阻抗、共振频率方程及振幅放大倍数的数学表达式。文中理论分析及所得结果可作为设计或计算扭转变幅杆的理论基础和依据。     

三维振动里兹法在变幅杆谐振特性分析中的应用研究

针对变幅杆振动分析的一维振动求解理论和齿轮超声加工研究现状,提出基于三维弹性动力学方程,利用能量变分原理,采用里兹法求解特征值的方法,统一了圆锥、圆截面指数形和悬链形变幅杆的扭转、纵向、弯曲振动的固有频率和振型求解方法;计算了不同直径比、长径比变幅杆的四位有效数字无量纲固有圆频率。设计加工了大、中、小截面指数形变幅杆,并利用锤击激励法做了模态实验。对其一维欧拉-伯努利、三维振动里兹数值法、有限单元法、实验模态法进行对比分析,结果表明：三维振动里兹数值法求解结果比一维振动求解理论准确,可以作为其他数值求解方法的验证标准;为其他非均匀截面变幅杆的振动特性分析提供了一种新的求解方法。     

微超声振动细胞切割系统中变幅杆的分析与设计

针对细胞微超声振动切割系统对超声变幅杆的要求,将等截面圆柱形阶梯变幅杆的一端替换成圆锥形变幅杆构成一种复合圆锥阶梯形变幅杆。由任意变截面杆纵向振动的波动方程出发,推导了复合圆锥阶梯形变幅杆的基本理论参量,设计了超声变幅杆的基本结构,给出其制造尺寸。并应用有限元法对变幅杆进行了模态分析,得到了共振频率和位移节点等重要参数。     

大尺寸矩形截面幂函数复合变幅杆的研究

利用传输矩阵法,计算得到了幂函数复合变幅杆一维纵振动的频率方程,并在此基础上运用表观弹性法分析了大尺寸矩形截面幂函数复合变幅杆,得到了考虑横向耦合振动后的谐振频率方程,最后利用有限元软件ANSYS对三组变幅杆进行了模态分析。结果表明：变幅杆谐振频率的计算值与模拟值符合得很好,与一维理论相比,考虑横向耦合振动的二维理论具有更高的精确度。     

轴系横向裂纹模型对其扭转剪应力的影响

本文对轴系横向直线裂纹和半椭圆裂纹两种模型的裂纹最深点处的应力强度因子 进行了推导,以研究不同模型对轴系扭转剪应力计算的影响。计算表明：采用这两种模型计算扭转剪应力时其相对差值会很大,最大可达60％左右。但在特定范围内差值很小。本文定义了该两种模型扭转剪应力的临界相对差值 ,确定了不同裂纹深度比 （ ）所对应的临界椭圆参数 ;拟合了不同裂纹深度比 （ ）下临界椭圆参数 的计算公式,为科学选取模型提供了理论依据。     

发动机前端附件驱动系统-曲轴扭振系统耦合建模与曲轴扭振分析

为了综合研究曲轴扭振与发动机前端附件驱动的系统(FEAD)的旋转振动,建立了发动机FEAD-曲轴扭振系统的耦合模型.两系统之间的连接是通过曲轴前端的扭转减振器.扭转减振器的惯量环可为驱动FEAD的皮带轮,或独立.利用建立的模型,计算系统的固有特性,研究曲轴前端安装不同形式的扭转减振器时,FEAD对曲轴扭振的影响和FEA...     

Torsional rod wave scattering from tapering between regions of different cross-sections

Previously (Engan 1998) we have studied the scattering of torsional waves in circular rods with a free surface where the rod diameter is subject to abrupt diameter changes. Here, we discuss the scattering of torsional waves from tapered regions and, in particular, transmission of the fundamental torsional mode. The calculations are based on a mode expansion technique in which propagating as well as cut-off modes are taken into account. The tapered region is approximated by numerous steps separated by uniform rod parts arranged so that they closely render the taper shape. Transfer matrices for all steps and uniform parts are combined to yield the desired transmission coefficient through the taper region. Numerical results of the frequency variation of fundamental mode transmission are presented, depending on geometrical parameters, such as taper length and the diameters of the two uniform adjacent rod parts. The dependence of the transmission on taper shape is demonstrated by calculating the response of various shapes.     

A torsional transducer through in-plane shearing of paired planar piezoelectric elements

A torsional microtransducer for high-power applications was developed using standard bulk lead zirconium titantate (PZT) placed upon a small rectangular prism made from phosphor bronze, with a tapered conical end serving as a horn and a machined interior to improve the actuator's response. Torsion was obtained from a prototype at the design frequency of 192 kHz as well as over a wide range of frequencies from 136 kHz to 1.02 MHz. Torsional vibration velocities of 335 mm/s at 192 kHz were measured at 27.3 V(RMS) on the 1.5-mm diameter output tip, amounting to 25,600 degree/s vibration velocity along the outer circumference of the tip. At 1.02 MHz, a torsional vibration velocity of 1750 mm/s (134,000 degree/s) at 17.8 V(RMS) was obtained through use of the thickness mode of the PZT elements. Using the design described in this study, high-power torsional transducers with diameters of 5 mm and below are now possible.     

Study on reinforced lightweight coconut shell concrete beam behavior under torsion

This research investigates and evaluates the results of coconut shell concrete beams subjected to torsion and compared with conventional concrete beams. Eight beams, four with coconut shell concrete and four with conventional concrete were fabricated and tested. Study includes the general cracking characteristics, pre cracking behavior and analysis, post cracking behavior and analysis, minimum torsional reinforcement, torsional reinforcement, ductility, crack width and stiffness. It was observed that the torsional behavior of coconut shell concrete is comparable to that of conventional concrete. Compare to ACI prediction, equation suggested by Macgregor is more conservative in calculating cracking torsional resistance. But for the calculation of ultimate torque strength ACI prediction is more conservative compared to the equation suggested by Macgregor. Indian standard is also conservative in this regard, but it was under estimated compared to ACI and Macgregor equations. Minimum torsional reinforcement in beams is necessary to ensure that the beam do not fail at cracking. Compared to conventional concrete specimens, coconut shell concrete specimens have more ductility. Crack width at initial cracking torque for both conventional and coconut shell concrete with corresponding reinforcement ratios is almost similar.     

双发动机工作时倾转旋翼机传动系统扭转振动的计算

为了获得双发动机工作时倾转旋翼机传动系统扭转振动的特性,进行了倾转旋翼机传动系统扭转振动的计算和分析。在简化传动系统结构的基础上,将倾转旋翼机传动系统划分为若干个轴段和圆盘的子系统,根据动量矩定理和振型叠加原理,分别列出扭转运动方程,再利用边界关系,合成子系统的扭转运动方程,得到传动系统的扭转运动方程,通过求解传动系统的扭转运动方程,并根据振型叠加原理,得到双发动机工作时倾转旋翼机传动系统扭转振动的角位移,在此基础上,给出算例,分析了传动系统的扭转频响函数。     

Frequency equation and mode shape formulae for composite Timoshenko beams

Exact expressions for the frequency equation and mode shapes of composite Timoshenko beams with cantilever end conditions are derived in explicit analytical form by using symbolic computation. The effect of material coupling between the bending and torsional modes of deformation together with the effects of shear deformation and rotatory inertia is taken into account when formulating the theory (and thus it applies to a composite Timoshenko beam). The governing differential equations for the composite Timoshenko beam in free vibration are solved analytically for bending displacements, bending rotation and torsional rotations. The application of boundary conditions for displacement and forces for cantilever end condition of the beam yields the frequency equation in determinantal form. The determinant is expanded algebraically, and simplified in an explicit form by extensive use of symbolic computation. The expressions for the mode shapes are also derived in explicit form using symbolic computation. The method is demonstrated by an illustrative example of a composite Timoshenko beam for which some published results are available.