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Investigation of the mechanical characteristics of the Cu/low-k BEOL under wire bonding process loading Cu/low-k BEOL在线接过程载荷下的力学特性研究
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2022-01-01 DOI: 10.1093/jom/ufac044
Cadmus C A Yuan, H. M. Chang, K. Chiang
Wire bonding is a key integrated circuit (IC) interconnect technology, and it adheres metal wires to the IC pad and substrate by applying significant compression and energic loading. On the other hand, the Cu/low-k technology of the advanced IC industry is driven by the market demands of small size, and low resistance-capacitance delay applications. Because material properties of Cu/low-k back end of line (BEOL) exhibit significant differences from the conventional Al-based system, 3 new reliability failure modes are introduced after the wire bonding process, including the Al pad lift, Cu pad lift and the nanoscaled Cu diffusion barrier crack. To study the mechanical characteristics of the Cu/low-k BEOL under the wire bonding process loading, this research establishes a set of transient numerical models with mesh control and computation acceleration techniques. The mechanical characteristics of the wire bonding process and the differences between the conventional and Cu/low-k BEOLs are analyzed via the detailed analysis of the historical stress plots over the wire bonding process time. Moreover, the risks of wire bonding induced the failure modes against different Cu/low-k designs are studied by the proper mechanical indices, and optimized design trends are suggested.
线键合是一种关键的集成电路互连技术,它通过施加显著的压缩和能量负载将金属导线粘接在IC衬垫和衬底上。另一方面,先进集成电路产业的Cu/low-k技术是由小尺寸、低阻容延迟应用的市场需求驱动的。由于Cu/低k后端线(BEOL)的材料性能与传统Al基系统存在显著差异,因此引入了Al焊盘抬升、Cu焊盘抬升和纳米级Cu扩散势垒裂纹3种新型可靠性失效模式。为了研究Cu/low-k BEOL在线接过程载荷下的力学特性,本研究建立了一套采用网格控制和计算加速技术的瞬态数值模型。通过详细分析金属丝键合过程的历史应力图,分析了金属丝键合过程的力学特性以及传统与Cu/低k BEOLs之间的差异。此外,通过适当的力学指标,研究了不同铜/低钾设计下焊丝键合失效模式的风险,并提出了优化设计趋势。
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引用次数: 2
An experimental study on the torsional stiffness and limit torque of a jaw coupling with consideration of spacer's hardness and installation methods 考虑垫片硬度和安装方法的颚式联轴器抗扭刚度和极限转矩试验研究
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2022-01-01 DOI: 10.1093/jom/ufac018
Chih-Ming Chen, Huey-Ling Chang, Chun-Ying Lee
The jaw coupling with a flexible spacer is frequently used in the torque transmission between shafts with misalignment for machinery. Its torsional stiffness and limit torque closely determine the operational capacity and the dynamic characteristics of the system because the coupling is usually the most flexible link in the driving chain. In this study, the optimal design of a jaw coupling with an elastomeric spacer was investigated using the Taguchi method by considering four design factors: the tightening method of the clamping bolts, the tightening torque of the clamping bolts, the hardness of the thermoplastic polyether ester elastomer spacer and the installation angle between the two end blocks of the coupling. All specimens were tested by using an in-house torsion tester to record the torque-angular deformation responses. The results showed good reliability and repeatability, with a coefficient of variance within 5%. Spacer's hardness was found to be the most significant factor regarding the torsional stiffness, while the magnitude of the clamping torque had the most critical role in the limit torque. The estimation formulae for the torsional stiffness and limit torque of the jaw coupling were obtained by using the statistical regression of the measured data, respectively. Both formulae predicted the performance of the optimal designs within 5% of error compared to the confirmation tests.
带柔性垫片的颚式联轴器是机械偏心轴间扭矩传递中常用的一种联轴器。联轴器通常是传动链中最灵活的环节,其抗扭刚度和极限转矩密切决定着系统的运行能力和动态特性。通过考虑夹紧螺栓的紧固方式、夹紧螺栓的紧固力矩、热塑性聚醚酯弹性体垫片的硬度以及联轴器两端块的安装角度等4个设计因素,采用田口法对带弹性体垫片的颚式联轴器进行了优化设计。所有试件均采用内部扭振仪进行测试,记录扭矩-角变形响应。结果具有良好的信度和重复性,方差系数在5%以内。研究发现,隔片硬度对隔片扭转刚度的影响最为显著,夹紧力矩的大小对隔片扭转刚度的影响最为关键。通过对实测数据的统计回归,分别得到了爪形联轴器扭转刚度和极限扭矩的估计公式。与确认试验相比,两个公式预测的最佳设计性能误差在5%以内。
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引用次数: 0
Analytical solution of cloaking in creeping flow inside composite porous media with simultaneous heat transfer 复合多孔介质内蠕变流动同时换热的隐蔽性解析解
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2022-01-01 DOI: 10.1093/jom/ufac029
W. Yeung, Fu-Sui Hung, V. Mai, Ruey-Jen Yang
This paper presents a theoretical analysis of steady-state creeping flow in a composite porous domain with coupling heat transfer. The problem arises in thermal cloaking studies in which it is desirable to hide an obstacle from the surrounding hydrodynamic and thermal fields, by suitably covering the obstacle with a cloak having specific material properties. The particular system under investigation consists of a porous composite region, with a thermal-hydro field driven by imposed temperature and pressure difference in the surrounding. Both two dimensional circular and three-dimensional axisymmetric spherical annuli are considered. Under the validity of Darcy law for a porous medium, an exact solution satisfying the continuity, momentum and energy equations at any Péclet number is derived. The analytical results have been numerically verified using the commercial code COMSOL.
本文对耦合传热的复合多孔区域内稳态蠕变流动进行了理论分析。在热隐身研究中出现了这个问题,在热隐身研究中,人们希望通过适当地用具有特定材料特性的斗篷覆盖障碍物来隐藏障碍物,使其不受周围流体动力和热场的影响。所研究的特殊系统由多孔复合区域组成,其周围的温度和压力差驱动着热-水力场。考虑了二维圆形环空和三维轴对称球形环空。在达西定律对多孔介质的有效性下,导出了在任意psamclet数下满足连续性、动量和能量方程的精确解。利用商业代码COMSOL对分析结果进行了数值验证。
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引用次数: 0
Bandgaps for flexural waves in infinite beams and plates with a periodic array of resonators 具有周期性谐振器阵列的无限束和板中弯曲波的带隙
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2022-01-01 DOI: 10.1093/jom/ufac033
Jing-Heng Chen, I-Chein Chao, Tungyang Chen
The subject of seismic metamaterials, inspired from novel ideas in optics and acoustics, has attracted great attention in the last decade for potential applications in earthquake engineering. Simple structure systems, like beams and plates, with periodically attached mechanical resonators provide a simple physical model to interpret the existence of certain frequency bandgap in dispersion relations and to simulate the mechanism of flexural energy attenuation. In this work, we consider simple structure systems of beams and plates with periodically attached resonators. The resonator is composed of a spring, a damper and a mass attached along the beam direction. We utilize the Timoshenko beam model and the Mindlin plate theory to incorporate the shear effect. The plane wave expansion method together with the Bloch theorem is used to expand the governing field into an eigenvalue problem of an infinite complex system, allowing us to characterize the band structures of the dispersion relations. Local resonance and Bragg bandgaps are identified and examined. The effect of thickness ratios, the damping ratio and the shear modulus are exemplified to demonstrate how these factors will affect the formation of bandgaps. This formulation demonstrates a feasibility that a periodic array of mechanical resonators together with suitable material and geometric parameters of beams and plates can be designed to tune with the dispersion behavior in the control of flexure waves. This study may open up new potential in the control of wave propagation in complex continuum systems through the interaction of adequately designed resonators.
受光学和声学新思想的启发,地震超材料在过去十年中因其在地震工程中的潜在应用而引起了人们的极大关注。具有周期性附加机械谐振器的梁、板等简单结构系统提供了一个简单的物理模型来解释色散关系中存在一定的频率带隙,并模拟弯曲能量衰减的机理。在这项工作中,我们考虑具有周期性附加谐振器的梁和板的简单结构系统。谐振器由弹簧、阻尼器和沿光束方向附着的质量组成。我们采用Timoshenko梁模型和Mindlin板理论来考虑剪切效应。利用平面波展开法和布洛赫定理将控制场展开为一个无限复杂系统的特征值问题,从而表征色散关系的能带结构。局部共振和布拉格带隙被识别和检查。举例说明了厚度比、阻尼比和剪切模量对带隙形成的影响。该公式证明了在控制挠性波的过程中,通过设计合适的材料和梁、板的几何参数来调节色散特性的周期性机械谐振器阵列的可行性。该研究为通过设计合理的谐振器相互作用来控制复杂连续体系统中的波传播开辟了新的潜力。
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引用次数: 2
Stroh formalism for various types of materials and deformations 强大的形式主义,各种类型的材料和变形
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2022-01-01 DOI: 10.1093/jom/ufac031
C. Hwu, W. Becker
The Stroh formalism is a complex variable formulation developed originally for solving the problems of two-dimensional linear anisotropic elasticity. By separation of the third variable for the linear variation of displacements along the thickness direction, it was proved to be applicable for the problems with coupled stretching-bending deformation. By the Radon transform which maps a three-dimensional solid to a two-dimensional plane, it can be applied to the three-dimensional deformation. By the elastic-viscoelastic correspondence principle, it is also valid for the viscoelastic materials in the Laplace domain. By expansion of the matrix dimension, it can be generalized to the coupled-field materials such as piezoelectric, piezomagnetic and magneto-electro-elastic materials. By introducing a small perturbation on the material constants, it can also be applied to the degenerate materials such as isotropic materials. Thus, in this paper, the Stroh formalism for several different types of materials (anisotropic elastic, piezoelectric, piezomagnetic, magneto-electro-elastic, viscoelastic) and deformations (two-dimensional, coupled stretching-bending, three-dimensional) are organized together and presented in the same mathematical form.
Stroh形式是一种复杂的变量公式,最初是为了解决二维线性各向异性弹性问题而发展起来的。通过分离位移沿厚度方向线性变化的第三变量,证明了该方法适用于拉伸-弯曲耦合变形问题。Radon变换将三维实体映射到二维平面,可以应用于三维变形。根据弹粘弹性对应原理,在拉普拉斯域中对粘弹性材料也是有效的。通过扩展矩阵维数,可以推广到压电、压磁、磁电弹性等耦合场材料。通过在材料常数上引入一个小的扰动,它也可以应用于各向同性材料等简并材料。因此,本文将几种不同类型的材料(各向异性弹性、压电、压磁、磁-电弹性、粘弹性)和变形(二维、耦合拉伸-弯曲、三维)的Stroh形式组织在一起,并以相同的数学形式表示。
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引用次数: 1
Discovery and study of abrasion behavior in granular shear flow 颗粒剪切流中磨损行为的发现与研究
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2022-01-01 DOI: 10.1093/jom/ufac032
S. Hsiau, K. Hutter, Li-Shin Lu, Andreas Teufel, S. Chou, L. Sheng
Experiments were performed in an Couette ring shear cell with particles from the food industry of nearly spherical geometry and nominal diameters between 2.0 and 6.7 mm and with quartz grains with 2.1 to 3.3 mm diameter to examine whether rapid shear flow would give rise to an appreciable change in the granular properties. In particular, it was suspected that surface roughness would change during shearing and lead to changes in the values of the internal and wall friction angles. Measuring these angles corroborated the supposition that abrasion of the particles reduced their frictional resistance, both via the internal and wall friction angles. This demonstrates that roughness changes may occur in granular flows and should in those situations not be ignored in the theoretical descriptions.
实验在Couette环形剪切池中进行,实验中来自食品工业的颗粒接近球形,公称直径在2.0到6.7毫米之间,石英颗粒直径在2.1到3.3毫米之间,以检验快速剪切流是否会引起颗粒特性的明显变化。特别是,怀疑在剪切过程中表面粗糙度会发生变化,从而导致内摩擦角和壁面摩擦角的值发生变化。测量这些角度证实了这样的假设,即颗粒的磨损通过内部和壁面摩擦角降低了它们的摩擦阻力。这表明粗糙度变化可能发生在颗粒流中,在这些情况下不应在理论描述中被忽视。
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引用次数: 2
On the response of eccentric non-structures subjected to horizontal oscillation 偏心非结构在水平振动作用下的响应
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2022-01-01 DOI: 10.1093/jom/ufac040
Liang-Shen Su, Chi-Hao Lin, Kuo-Ching Chen
In contrast to building structures, little attention has been paid to the seismic performance of non-structures in buildings, especially of eccentric non-structures. This paper attempts to explore the rocking and overturning of eccentric blocks, which could be the equipment or non-structural components in buildings, subjected to horizontal vibration. In the present study, a non-structure is regarded as a rigid block with tunable mass eccentricity, and the contact friction is assumed to be large enough to prevent the rigid block from sliding. A free shaking test is first carried out to determine the value of the coefficient of restitution. Force oscillations are then investigated to determine the critical time and acceleration when the eccentric blocks fall down under the swept-frequency oscillation. Finally, an actual acceleration from the seismic records is executed on each of the eccentric blocks to measure and to explore the corresponding toppling probability. It is found that the toppling of blocks is not necessarily linked to the magnitude of the peak ground acceleration.
相对于建筑结构,非结构抗震性能的研究较少,特别是偏心非结构抗震性能的研究较少。偏心块可能是建筑物中的设备或非结构部件,在水平振动作用下,本文试图探讨偏心块的摇晃和倾覆。在本研究中,将非结构视为具有可调质量偏心率的刚体,并假定接触摩擦大到足以防止刚体滑动。首先进行了自由振动试验,确定了恢复系数的取值。然后研究了偏心块在扫频振荡下下落时的临界时间和加速度。最后,根据地震记录对每个偏心块体进行实际加速度测量,并探讨相应的倾倒概率。研究发现,砌块的倾倒与地面加速度峰值的大小没有必然的联系。
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引用次数: 0
A passive planar model with rolling contact and its application for bounding and pronking on a quadruped robot 一种具有滚动接触的被动平面模型及其在四足机器人上的应用
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2022-01-01 DOI: 10.1093/jom/ufac046
Chun-Kai Huang, Chia-Jui Hu, I-Chia Chang, Pei-Chun Lin
The development and investigation of a quadruped robot's dynamic bounding and pronking gaits using a sagittal planar model that captures the robot's natural dynamics are presented. The proposed reduced-order model, termed the Two-rolling-leg (TRL) model, is a 3-DOF planar rigid-body model consisting of two half-circular compliant legs with pure rolling contact. Throughout the non-dimensional steps-to-fall and fixed-point analysis, the model with feasible intrinsic parameters can passively perform the periodic dynamic behavior of bounding and pronking, revealing a relationship between the body parameters and the preferred dynamic behaviors. Dynamic bounding and pronking on a quadruped robot were initiated by developing a model-based control strategy based on the searched periodic dynamic behaviors of the TRL model. The experimental results showed that the robot can initiate its dynamic bounding and pronking behaviors at various forward speeds merely by causing the motor to track a preset trajectory derived from the fixed-point motion of the TRL model using position control. The higher success rate of the robot in stable bounding than in pronking is in line with the results from the analysis of the model. This paper confirms that the dynamic multi-gait locomotion of a quadrupedal robot can be initiated by utilizing a reduced-order model for control guidance and that the body configuration plays an important role in determining the characteristics of the dynamic behaviors.
利用矢状平面模型,研究了四足机器人的动态跳跃和前翻步态,并对其进行了仿真。所提出的降阶模型称为双滚动支腿(TRL)模型,是一个由两个半圆型柔性支腿组成的纯滚动接触的三自由度平面刚体模型。在无因次阶跃和不动点分析中,具有可行内在参数的模型可以被动地表现出弹跳和弹跳的周期性动力行为,揭示了物体参数与首选动力行为之间的关系。基于TRL模型的周期性动态行为,提出了一种基于模型的控制策略,实现了四足机器人的动态跳跃和跳跃。实验结果表明,通过位置控制,机器人只需使电机跟踪由TRL模型的定点运动导出的预设轨迹,就可以在不同的前进速度下启动其动态弹跳和弹跳行为。机器人在稳定跳跃时的成功率高于在原地跳跃时的成功率,这与模型分析的结果一致。本文证实了采用降阶模型进行控制引导可以启动四足机器人的动态多步态运动,并且确定了四足机器人的体形对其动态行为特征起着重要作用。
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引用次数: 1
Free vibration of a single-walled carbon nanotube based on the nonlocal Timoshenko beam model 基于非局部Timoshenko梁模型的单壁碳纳米管自由振动
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2021-10-13 DOI: 10.1093/jom/ufab028
Yu-Chi Su, TS Cho
Free vibration of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium is studied on the basis of the nonlocal Timoshenko beam model. Influences of the slenderness ratios, the boundary conditions, the atomic structures and the stiffness of the embedded medium on the natural frequencies and mode shapes of SWCNT are examined. The nonlocal effect is significant for the higher modes of SWCNT with a small slenderness ratio embedded in a soft elastic medium, and it softens the SWCNT except for the fundamental frequency of the clamped–free SWCNT.
基于非局部Timoshenko梁模型,研究了单壁碳纳米管在弹性介质中的自由振动。研究了长细比、边界条件、原子结构和嵌入介质刚度对swcnts固有频率和模态振型的影响。对于嵌入在软弹性介质中的小长细比高模态的单壁碳纳米管,非局部效应是显著的,除了无箝位的单壁碳纳米管的基频外,它还会软化单壁碳纳米管。
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引用次数: 6
On underwater sound radiation in a towing tank induced by continuous machine vibration in a steel circular cylinder 钢圆柱体连续振动对拖曳箱水声辐射的影响
IF 1.7 4区 工程技术 Q3 MECHANICS Pub Date : 2021-10-04 DOI: 10.1093/jom/ufab026
Wu C, Too G.
Abstract
An understanding of the characteristics and mechanisms of structural vibrations produced by underwater vehicles is required to reduce sound radiation in submarine environments. In this study, experiments were performed using a continuously running machine to produce low-frequency vibrations in a submerged, watertight, steel circular cylinder in the centre of a 176 × 8 × 4 m3 towing tank, and the underwater radiation sound field was measured. Finite element method simulations of the system were also performed and showed good agreement with the experimental results. The wall effects of the towing tank were simulated in detail by changing the alternative impedances of the wall. The reflection and acoustic impedance of the towing tank walls were found to significantly affect the underwater sound field in both the experiments and simulations. An analytical solution was used to verify the frequency range applied in the simulation analysis. The results of this study provide a measurement procedure and a simulation method, which can be used to evaluate the underwater radiation sound field from the vehicle machine running in the water at wall boundary environment.
摘要为了减少水下环境中的声辐射,需要了解水下航行器产生的结构振动的特征和机理。在本研究中,使用连续运转的机器在176 × 8 × 4 m3拖曳水箱中央的水下水密钢圆柱中产生低频振动,并测量水下辐射声场。对系统进行了有限元仿真,结果与实验结果吻合较好。通过改变拖曳舱壁面的交替阻抗,详细模拟了拖曳舱壁面效应。实验和仿真结果均表明,拖曳舱壁的反射和声阻抗对水声场有显著影响。用解析解验证了仿真分析中所采用的频率范围。本文的研究结果提供了一种测量方法和仿真方法,可用于评估在墙边界环境下水中运行的车辆机器的水下辐射声场。
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引用次数: 0
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