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Identification of dynamic stiffness matrix of bearing joint region

Feng HU, Bo WU, Youmin HU, Tielin SHI

《机械工程前沿（英文）》 2009年第4卷第3期页码 289-299 doi: 10.1007/s11465-009-0064-3

摘要： The paper proposes an identification method of the dynamic stiffness matrix of a bearing joint region on the basis of theoretical analysis and experiments. The author deduces an identification model of the dynamic stiffness matrix from the synthetic substructure method. The dynamic stiffness matrix of the bearing joint region can be identified by measuring the matrix of frequency response function (FRFs) of the substructure (axle) and whole structure (assembly of the axle, bearing, and bearing housing) in different positions. Considering difficulty in measuring angular displacement, applying moment, and directly measuring relevant FRFs of rotational degree of freedom, the author employs an accurately calibrated finite element model of the unconstrained structure for indirect estimation. With experiments and simulation analysis, FRFs related with translational degree of freedom, which is estimated through the finite element model, agrees with experimental results, and there is very high reliability in the identified dynamic stiffness matrix of the bearing joint region.

关键词： frequency response function (FRFs) dynamic stiffness finite element synthetic substructure method joint region

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A dynamic stiffness-based framework for harmonic input estimation and response reconstruction considering

Yixian LI; Limin SUN; Wang ZHU; Wei ZHANG

《结构与土木工程前沿（英文）》 2022年第16卷第4期页码 448-460 doi: 10.1007/s11709-022-0805-5

摘要： In structural health monitoring (SHM), the measurement is point-wise but structures are continuous. Thus, input estimation has become a hot research subject with which the full-field structural response can be calculated with a finite element model (FEM). This paper proposes a framework based on the dynamic stiffness theory, to estimate harmonic input, reconstruct responses, and to localize damages from seriously deficient measurements. To begin, Fourier transform converts the dynamic equilibrium equation to an equivalent static one in the frequency domain, which is under-determined since the dimension of measurement vector is far less than the FEM-node number. The principal component analysis has been adopted to “compress” the under-determined equation, and formed an over-determined equation to estimate the unknown input. Then, inverse Fourier transform converts the estimated input in the frequency domain to the time domain. Applying this to the FEM can reconstruct the target responses. If a structure is damaged, the estimated nodal force can localize the damage. To improve the damage-detection accuracy, a multi-measurement-based indicator has been proposed. Numerical simulations have validated that the proposed framework can capably estimate input and reconstruct multi-types of full-field responses, and the damage indicator can localize minor damages even with the existence of noise.

关键词： dynamic stiffness principal component analysis response reconstruction damage localization under-determined equation

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Variable stiffness and damping magnetorheological isolator

Yang ZHOU, Xingyu WANG, Xianzhou ZHANG, Weihua LI

《机械工程前沿（英文）》 2009年第4卷第3期页码 310-315 doi: 10.1007/s11465-009-0039-4

摘要： This paper presents the development and characterization of a magnetorheological (MR) fluid-based variable stiffness and damping isolator. The prototype of the MR fluid isolator is fabricated, and its dynamic behavior is measured under various applied magnetic fields. The parameters of the model under various magnetic fields are identified, and the dynamic performance of the isolator is evaluated in simulation. Experimental results indicate that both the stiffness and damping capability of the developed MR isolator can be controlled by an external magnetic field.

关键词： magnetorheological (MR) fluid stiffness damping mathematical model dynamic performance parameter identification

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Nonlinear analysis of cable structures using the dynamic relaxation method

Mohammad REZAIEE-PAJAND, Mohammad MOHAMMADI-KHATAMI

《结构与土木工程前沿（英文）》 2021年第15卷第1期页码 253-274 doi: 10.1007/s11709-020-0639-y

摘要： The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers. Because they have highly nonlinear behavior, it is difficult to find solutions to these problems. Thus far, different assumptions and methods have been proposed to solve such structures. The dynamic relaxation method (DRM) is an explicit procedure for analyzing these types of structures. To utilize this scheme, investigators have suggested various stiffness matrices for a cable element. In this study, the efficiency and suitability of six well-known proposed matrices are assessed using the DRM. To achieve this goal, 16 numerical examples and two criteria, namely, the number of iterations and the analysis time, are employed. Based on a comprehensive comparison, the methods are ranked according to the two criteria. The numerical findings clearly reveal the best techniques. Moreover, a variety of benchmark problems are suggested by the authors for future studies of cable structures.

关键词： nonlinear analysis cable structure stiffness matrix dynamic relaxation method

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Development and testing of a wireless smart toolholder with multi-sensor fusion

《机械工程前沿（英文）》 2023年第18卷第4期 doi: 10.1007/s11465-023-0774-y

摘要： The smart toolholder is the core component in the development of intelligent and precise manufacturing. It enables in situ monitoring of cutting data and machining accuracy evolution and has become a focal point in academic research and industrial applications. However, current table and rotational dynamometers for milling force, vibration, and temperature testing suffer from cumbersome installation and provide only a single acquisition signal, which limits their use in laboratory settings. In this study, we propose a wireless smart toolholder with multi-sensor fusion for simultaneous sensing of milling force, vibration, and temperature signals. We select force, vibration, and temperature sensors suitable for smart toolholder fusion to adapt to the cutting environment. Thereafter, structural design, circular runout, dynamic balancing, static stiffness, and dynamic inherent frequency tests are conducted to assess its dynamic and static performance. Finally, the smart toolholder is tested for accuracy and repeatability in terms of force, vibration, and temperature. Experimental results demonstrate that the smart toolholder accurately captures machining data with a relative deviation of less than 1.5% compared with existing force gauges and provides high repeatability of milling temperature and vibration signals. Therefore, it is a smart solution for machining condition monitoring.

关键词： wireless smart toolholder multi-sensor fusion circular runout dynamic balancing static stiffness dynamic inherent frequency

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Mesh relationship modeling and dynamic characteristic analysis of external spur gears with gear wear

《机械工程前沿（英文）》 2022年第17卷第1期页码 9-9 doi: 10.1007/s11465-021-0665-z

摘要： Gear wear is one of the most common gear failures, which changes the mesh relationship of normal gear. A new mesh relationship caused by gear wear affects meshing excitations, such as mesh stiffness and transmission error, and further increases vibration and noise level. This paper aims to establish the model of mesh relationship and reveal the vibration characteristics of external spur gears with gear wear. A geometric model for a new mesh relationship with gear wear is proposed, which is utilized to evaluate the influence of gear wear on mesh stiffness and unloaded static transmission error (USTE). Based on the mesh stiffness and USTE considering gear wear, a gear dynamic model is established, and the vibration characteristics of gear wear are numerically studied. Comparison with the experimental results verifies the proposed dynamic model based on the new mesh relationship. The numerical and experimental results indicate that gear wear does not change the structure of the spectrum, but it alters the amplitude of the meshing frequencies and their sidebands. Several condition indicators, such as root-mean-square, kurtosis, and first-order meshing frequency amplitude, can be regarded as important bases for judging gear wear state.

关键词： gear wear mesh relationship mesh stiffness transmission error vibration characteristics

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液体静压支承动态性能新表达式探索与实验验证

孟心斋,杨建玺,孟昭焱

《中国工程科学》 2003年第5卷第3期页码 62-66

摘要：

液体静压支承具有很多优良性能：高运动精度，低摩擦功耗，小轴心偏移，大承载能力，强抗振性能与长使用寿命等，但这些优良的静态性能必须在上佳的动态性能保证下才能充分显示出来，因此，液体静压支承静态性能保证机床运动与加工精度，而动态性能则保证设备的安全与工作条件。文章根据力平衡与流量连续条件建立支承系统传递函数，导出支承系统动态性能新表达式即稳定性判别、抗瞬态干扰能力、固有频率与在稳态周期干扰力作用下产生的动刚度与最大振幅。通过试验台实验证实，液体静压支承动态性能新表达式计算结果可靠而且物理概念清晰，公式简单，故可用于实际。

关键词：动态性能传递函数动刚度谐振频率液体静压支承

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Mechanical design and analysis of a novel variable stiffness actuator with symmetrical pivot adjustment

《机械工程前沿（英文）》 2021年第16卷第4期页码 711-725 doi: 10.1007/s11465-021-0647-1

摘要： The safety of human–robot interaction is an essential requirement for designing collaborative robotics. Thus, this paper aims to design a novel variable stiffness actuator (VSA) that can provide safer physical human–robot interaction for collaborative robotics. VSA follows the idea of modular design, mainly including a variable stiffness module and a drive module. The variable stiffness module transmits the motion from the drive module in a roundabout manner, making the modularization of VSA possible. As the key component of the variable stiffness module, a stiffness adjustment mechanism with a symmetrical structure is applied to change the positions of a pair of pivots in two levers linearly and simultaneously, which can eliminate the additional bending moment caused by the asymmetric structure. The design of the double-deck grooves in the lever allows the pivot to move freely in the groove, avoiding the geometric constraint between the parts. Consequently, the VSA stiffness can change from zero to infinity as the pivot moves from one end of the groove to the other. To facilitate building a manipulator in the future, an expandable electrical system with a distributed structure is also proposed. Stiffness calibration and control experiments are performed to evaluate the physical performance of the designed VSA. Experiment results show that the VSA stiffness is close to the theoretical design stiffness. Furthermore, the VSA with a proportional–derivative feedback plus feedforward controller exhibits a fast response for stiffness regulation and a good performance for position tracking.

关键词： variable stiffness actuator variable stiffness module drive module symmetrical structure double-deck grooves expandable electrical system

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Novel modular quasi-zero stiffness vibration isolator with high linearity and integrated fluid damping

《机械工程前沿（英文）》 2024年第19卷第1期 doi: 10.1007/s11465-023-0778-7

摘要： Passive vibration isolation systems have been widely applied due to their low power consumption and high reliability. Nevertheless, the design of vibration isolators is usually limited by the narrow space of installation, and the requirement of heavy loads needs the high supporting stiffness that leads to the narrow isolation frequency band. To improve the vibration isolation performance of passive isolation systems for dynamic loaded equipment, a novel modular quasi-zero stiffness vibration isolator (MQZS-VI) with high linearity and integrated fluid damping is proposed. The MQZS-VI can achieve high-performance vibration isolation under a constraint mounted space, which is realized by highly integrating a novel combined magnetic negative stiffness mechanism into a damping structure: The stator magnets are integrated into the cylinder block, and the moving magnets providing negative-stiffness force also function as the piston supplying damping force simultaneously. An analytical model of the novel MQZS-VI is established and verified first. The effects of geometric parameters on the characteristics of negative stiffness and damping are then elucidated in detail based on the analytical model, and the design procedure is proposed to provide guidelines for the performance optimization of the MQZS-VI. Finally, static and dynamic experiments are conducted on the prototype. The experimental results demonstrate the proposed analytical model can be effectively utilized in the optimal design of the MQZS-VI, and the optimized MQZS-VI broadened greatly the isolation frequency band and suppressed the resonance peak simultaneously, which presented a substantial potential for application in vibration isolation for dynamic loaded equipment.

关键词： vibration isolation quasi-zero stiffness damping magnetic spring integrated design

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Comparison of indices for stiffness performance evaluation

Giuseppe CARBONE, Marco CECCARELLI,

《机械工程前沿（英文）》 2010年第5卷第3期页码 270-278 doi: 10.1007/s11465-010-0023-z

摘要： This paper addresses the problem of a numerical evaluation of the stiffness performance for multibody robotic systems. An overview is presented with basic formulation concerning indices that are proposed in literature. New indices are also outlined. Stiffness indices are computed and compared for a case study. Results are used for comparing the effectiveness of the stiffness indices. The main goal is to propose a performance index describing synthetically the elastostatic response of a multibody robotic system and also for design purposes.

关键词： robotics stiffness performance indices

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Mechanical performance analysis and stiffness test of a new type of suspension bridge

《结构与土木工程前沿（英文）》 2021年第15卷第5期页码 1160-1180 doi: 10.1007/s11709-021-0760-6

摘要： A new type of suspension bridge is proposed based on the gravity stiffness principle. Compared with a conventional suspension bridge, the proposed bridge adds rigid webs and cross braces. The rigid webs connect the main cable and main girder to form a truss that can improve the bending stiffness of the bridge. The cross braces connect the main cables to form a closed space truss structure that can improve the torsional stiffness of the bridge. The rigid webs and cross braces are installed after the construction of a conventional suspension bridge is completed to resist different loads with different structural forms. A new type of railway suspension bridge with a span of 340 m and a highway suspension bridge with a span of 1020 m were designed and analysed using the finite element method. The stress, deflection of the girders, unbalanced forces of the main towers, and natural frequencies were compared with those of conventional suspension bridges. A stiffness test was carried out on the new type of suspension bridge with a small span, and the results were compared with those for a conventional bridge. The results showed that the new suspension bridge had a better performance than the conventional suspension bridge.

关键词： new type of suspension bridge stiffness test mechanical performance railway bridge space truss

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New nonlinear stiffness actuator with predefined torque‒deflection profile

《机械工程前沿（英文）》 2023年第18卷第1期 doi: 10.1007/s11465-022-0721-3

摘要： A nonlinear stiffness actuator (NSA) could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range, both of which are beneficial for physical interaction between a robot and the environment. Currently, most of NSAs are complex and hardly used for engineering. In this paper, oriented to engineering applications, a new simple NSA was proposed, mainly including leaf springs and especially designed cams, which could perform a predefined relationship between torque and deflection. The new NSA has a compact structure, and it is lightweight, both of which are also beneficial for its practical application. An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed. The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring. Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism, the sliding displacement between the cam and the leaf spring is very small, and consumption of sliding friction force is very low. Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles. Three kinds of prototype experiments, including verification experiment of the predefined torque‒deflection profile, torque tracking experiment, and position tracking experiment under different loads, were conducted. The results prove the accuracy of performing the predefined torque‒deflection profile, the tracking performance, and the interactive performance of the new NSA.

关键词： compliant actuator nonlinear stiffness actuator nonlinear spring predefined torque−deflection profile

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Gear fault diagnosis using gear meshing stiffness identified by gearbox housing vibration signals

《机械工程前沿（英文）》 2022年第17卷第4期 doi: 10.1007/s11465-022-0713-3

摘要： Gearbox fault diagnosis based on vibration sensing has drawn much attention for a long time. For highly integrated complicated mechanical systems, the intercoupling of structure transfer paths results in a great reduction or even change of signal characteristics during the process of original vibration transmission. Therefore, using gearbox housing vibration signal to identify gear meshing excitation signal is of great significance to eliminate the influence of structure transfer paths, but accompanied by huge scientific challenges. This paper establishes an analytical mathematical description of the whole transfer process from gear meshing excitation to housing vibration. The gear meshing stiffness (GMS) identification approach is proposed by using housing vibration signals for two stages of inversion based on the mathematical description. Specifically, the linear system equations of transfer path analysis are first inverted to identify the bearing dynamic forces. Then the dynamic differential equations are inverted to identify the GMS. Numerical simulation and experimental results demonstrate the proposed method can realize gear fault diagnosis better than the original housing vibration signal and has the potential to be generalized to other speeds and loads. Some interesting properties are discovered in the identified GMS spectra, and the results also validate the rationality of using meshing stiffness to describe the actual gear meshing process. The identified GMS has a clear physical meaning and is thus very useful for fault diagnosis of the complicated equipment.

关键词： gearbox fault diagnosis meshing stiffness identification transfer path signal processing

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Stiffness of a 3-degree of freedom translational parallel kinematic machine

null

《机械工程前沿（英文）》 2014年第9卷第3期页码 233-241 doi: 10.1007/s11465-014-0312-z

摘要：

In this paper, a typical 3-degree of freedom (3-DOF) translational parallel kinematic machine (PKM) is studied and analyzed whose tool platform has only translations along X-, Y- and Z-axes. It consists of three limbs, each of which have arm and forearm with prismatic-revolute-revolute-revolute (PRRR) joints. Inverse kinematics analysis is carried out to find the slider coordinates and joint angles for a given position of tool platform. Stiffness modeling is done based on the compliance matrices of arm and forearm of each limb. Using the stiffness modeling the variations of minimum and maximum translational stiffness in the workspace are analyzed. For various architectural parameters of the 3-DOF PKM the tendency of variations on the minimum and maximum stiffness over the entire workspace is studied; and also the deflections of the tool platform along X, Y, and Z directions with respect to various forces are presented.

关键词： 3-DOF translational PKM inverse kinematics stiffness modeling translational stiffness

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Mechanical design, modeling, and identification for a novel antagonistic variable stiffness dexterous

《机械工程前沿（英文）》 2022年第17卷第3期 doi: 10.1007/s11465-022-0691-5

摘要： This study traces the development of dexterous hand research and proposes a novel antagonistic variable stiffness dexterous finger mechanism to improve the safety of dexterous hand in unpredictable environments, such as unstructured or man-made operational errors through comprehensive consideration of cost, accuracy, manufacturing, and application. Based on the concept of mechanical passive compliance, which is widely implemented in robots for interactions, a finger is dedicated to improving mechanical robustness. The finger mechanism not only achieves passive compliance against physical impacts, but also implements the variable stiffness actuator principle in a compact finger without adding supererogatory actuators. It achieves finger stiffness adjustability according to the biologically inspired stiffness variation principle of discarding some mobilities to adjust stiffness. The mechanical design of the finger and its stiffness adjusting methods are elaborated. The stiffness characteristics of the finger joint and the actuation unit are analyzed. Experimental results of the finger joint stiffness identification and finger impact tests under different finger stiffness presets are provided to verify the validity of the model. Fingers have been experimentally proven to be robust against physical impacts. Moreover, the experimental part verifies that fingers have good power, grasping, and manipulation performance.

关键词： multifingered hand mechanism design robot safety variable stiffness actuator